LAVERY, J.
The petitioners appeal from the judgments of the trial court dismissing their petitions for writs of habeas corpus.1 In this consolidated appeal, the petitioners claim that the trial court improperly granted the commissioner of correction’s (respondent) motion to quash their petitions because it failed to find a legally cognizable liberty interest on the face of the petitions. The petitioners also claim that the trial court improperly found that they did not allege sufficient facts to support a finding of cruel and unusual punishment. Finally, the petitioners claim that the department of correction (department) violated the Uniform Administrative Procedure Act by failing to promulgate properly the department’s Administrative Directive § 6.14.
The petitioners in this case are five inmates at various correctional facilities in Connecticut. At some point during their incarceration, the department designated each inmate as a security risk group member pursuant to the department’s Administrative Directive § 6.14.2 The petitioners claim that the department erroneously and unconstitutionally labeled them as members of various street gangs, which resulted in their being classified as security risk group members. They allege that such designation has violated their constitutional rights to due process under article first, §§ 8 and 10, of the Con[677]*677necticut constitution,3 and the fifth and fourteenth amendments to the United States constitution. They further claim that this designation has violated the constitutional right to be free from cruel and unusual punishment under the eighth and fourteenth amendments to the United States constitution.
Although this court has consolidated these appeals for the purposes of disposition, it is important to note that the allegations made in each of the petitions are not identical. The petitioners Joaquin Santiago, Eriberto DeLeon, Julio Arroyo and Everett Breedlove allege similar due process violations. These petitioners claim that they were denied due process because of the erroneous designation, and that they have suffered a loss of recreation, school and work privileges, as well as access to the prison law library. Santiago, DeLeon and Arroyo further allege that their rights to be free from cruel and unusual punishment have been violated “by the retention of erroneous information such that [they are] subjected to unduly harsh conditions of continuing confinement as long as the erroneous information remains on [their] records . . . .”
The petitioner Floyd Johnson alleges that as a direct result of the erroneous designation as a security risk group member he has lost good time credits toward the diminution of his length of confinement. He claims that the “erroneous designation . . . has made [him] ineligible for restoration of lost good time credits and thus, subjects [him] to a lengthier sentence in deprivation of his state and federal constitutional rights to be free from excessive confinement which constitutes [678]*678cruel and unusual punishment under the Eighth and Fourteenth Amendments to the U.S. Constitution.” As have the other petitioners, Johnson claims that as a result of the erroneous designation, he has suffered a loss of school, work and recreation privileges, as well as a loss of familial visits and access to the prison law library.
The trial court granted the respondent’s motion to quash all of the petitions on the ground that security classifications fall outside the subject matter jurisdiction of habeas corpus proceedings because such claims fail to attack the length of confinement. We affirm the trial court with respect to Santiago, DeLeon, Arroyo and Breedlove. We find, however, that Johnson has alleged sufficient facts to constitute a legally recognized habeas corpus claim. We therefore reverse the judgment of the trial court with respect to Johnson’s petition.
I
The proper vehicle for attacking the legal sufficiency of a petition for a writ of habeas corpus is a motion to quash. Practice Book § 532; see also Holcomb v. Commissioner of Correction, 39 Conn. App. 485, 490, 644 A.2d 1199 (1995). Practice Book § 532 provides that when the court considers a motion to quash a petition for a writ of habeas corpus, the allegations made in the petition are deemed admitted. Because a motion to quash is analogous to a motion to strike in a civil action, the court does not look to facts outside those alleged in the petition. Liljedahl Bros., Inc. v. Grigsby, 215 Conn. 345, 348-49, 576 A.2d 149 (1990); Pi v. Delta, 175 Conn. 527, 528, 400 A.2d 709 (1978); Holcomb v. Commissioner of Correction, supra, 490.
Basing our inquiry solely on the facts alleged in the petition, we must determine whether each petitioner has alleged sufficient facts to confer subject matter [679]*679jurisdiction on the habeas court. The scope of relief available through a petition for habeas corpus is limited. In order to invoke the trial court’s subject matter jurisdiction in a habeas action, a petitioner must allege that he is illegally confined or has been deprived of his liberty. Our Supreme Court found that “[t]he writ of habeas corpus, as it is employed in the twentieth century, however, does not focus solely upon a direct attack on the underlying judgment or upon release from confinement”; Lozada v. Warden, 223 Conn. 834, 841, 613 A.2d 818 (1992); but is available as aremedy for issues of fundamental fairness implicating constitutional rights. Id., 840; see also Arey v. Warden, 187 Conn. 324, 445 A.2d 916 (1982) (claims concerning conditions of confinement may be brought in habeas coipus proceeding). This court has similarly recognized that “the well established precepts of illegal detention and deprivation of constitutional rights remain the touchstones of [habeas coipus] jurisdiction.” Vincenzo v. Warden, 26 Conn. App. 132, 138 n.4, 599 A.2d 31 (1991). We must therefore determine whether the petitioners have alleged sufficient facts to constitute the deprivation of a legally recognized constitutional right.
II
The petitioners initially claim that the trial court improperly quashed their petitions by finding that they failed to allege sufficient facts to support a constitutional due process violation. On the basis of our examination of the allegations in each petition, we find that Santiago, DeLeon, Arroyo and Breedlove have not alleged sufficient facts to show that the department deprived them of their constitutional due process rights through its enforcement of Administrative Directive § 6.14. Johnson, however, has alleged sufficient facts in his petition to support a due process claim and to invoke the subject matter jurisdiction of the trial court in a habeas corpus proceeding.
[680]*680A
In order to prevail on a due process claim, the petitioners must show that they have been deprived of a legally recognized liberty interest, and that they have been deprived of liberty without due process of law. Johnson v. Meehan, 225 Conn.
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LAVERY, J.
The petitioners appeal from the judgments of the trial court dismissing their petitions for writs of habeas corpus.1 In this consolidated appeal, the petitioners claim that the trial court improperly granted the commissioner of correction’s (respondent) motion to quash their petitions because it failed to find a legally cognizable liberty interest on the face of the petitions. The petitioners also claim that the trial court improperly found that they did not allege sufficient facts to support a finding of cruel and unusual punishment. Finally, the petitioners claim that the department of correction (department) violated the Uniform Administrative Procedure Act by failing to promulgate properly the department’s Administrative Directive § 6.14.
The petitioners in this case are five inmates at various correctional facilities in Connecticut. At some point during their incarceration, the department designated each inmate as a security risk group member pursuant to the department’s Administrative Directive § 6.14.2 The petitioners claim that the department erroneously and unconstitutionally labeled them as members of various street gangs, which resulted in their being classified as security risk group members. They allege that such designation has violated their constitutional rights to due process under article first, §§ 8 and 10, of the Con[677]*677necticut constitution,3 and the fifth and fourteenth amendments to the United States constitution. They further claim that this designation has violated the constitutional right to be free from cruel and unusual punishment under the eighth and fourteenth amendments to the United States constitution.
Although this court has consolidated these appeals for the purposes of disposition, it is important to note that the allegations made in each of the petitions are not identical. The petitioners Joaquin Santiago, Eriberto DeLeon, Julio Arroyo and Everett Breedlove allege similar due process violations. These petitioners claim that they were denied due process because of the erroneous designation, and that they have suffered a loss of recreation, school and work privileges, as well as access to the prison law library. Santiago, DeLeon and Arroyo further allege that their rights to be free from cruel and unusual punishment have been violated “by the retention of erroneous information such that [they are] subjected to unduly harsh conditions of continuing confinement as long as the erroneous information remains on [their] records . . . .”
The petitioner Floyd Johnson alleges that as a direct result of the erroneous designation as a security risk group member he has lost good time credits toward the diminution of his length of confinement. He claims that the “erroneous designation . . . has made [him] ineligible for restoration of lost good time credits and thus, subjects [him] to a lengthier sentence in deprivation of his state and federal constitutional rights to be free from excessive confinement which constitutes [678]*678cruel and unusual punishment under the Eighth and Fourteenth Amendments to the U.S. Constitution.” As have the other petitioners, Johnson claims that as a result of the erroneous designation, he has suffered a loss of school, work and recreation privileges, as well as a loss of familial visits and access to the prison law library.
The trial court granted the respondent’s motion to quash all of the petitions on the ground that security classifications fall outside the subject matter jurisdiction of habeas corpus proceedings because such claims fail to attack the length of confinement. We affirm the trial court with respect to Santiago, DeLeon, Arroyo and Breedlove. We find, however, that Johnson has alleged sufficient facts to constitute a legally recognized habeas corpus claim. We therefore reverse the judgment of the trial court with respect to Johnson’s petition.
I
The proper vehicle for attacking the legal sufficiency of a petition for a writ of habeas corpus is a motion to quash. Practice Book § 532; see also Holcomb v. Commissioner of Correction, 39 Conn. App. 485, 490, 644 A.2d 1199 (1995). Practice Book § 532 provides that when the court considers a motion to quash a petition for a writ of habeas corpus, the allegations made in the petition are deemed admitted. Because a motion to quash is analogous to a motion to strike in a civil action, the court does not look to facts outside those alleged in the petition. Liljedahl Bros., Inc. v. Grigsby, 215 Conn. 345, 348-49, 576 A.2d 149 (1990); Pi v. Delta, 175 Conn. 527, 528, 400 A.2d 709 (1978); Holcomb v. Commissioner of Correction, supra, 490.
Basing our inquiry solely on the facts alleged in the petition, we must determine whether each petitioner has alleged sufficient facts to confer subject matter [679]*679jurisdiction on the habeas court. The scope of relief available through a petition for habeas corpus is limited. In order to invoke the trial court’s subject matter jurisdiction in a habeas action, a petitioner must allege that he is illegally confined or has been deprived of his liberty. Our Supreme Court found that “[t]he writ of habeas corpus, as it is employed in the twentieth century, however, does not focus solely upon a direct attack on the underlying judgment or upon release from confinement”; Lozada v. Warden, 223 Conn. 834, 841, 613 A.2d 818 (1992); but is available as aremedy for issues of fundamental fairness implicating constitutional rights. Id., 840; see also Arey v. Warden, 187 Conn. 324, 445 A.2d 916 (1982) (claims concerning conditions of confinement may be brought in habeas coipus proceeding). This court has similarly recognized that “the well established precepts of illegal detention and deprivation of constitutional rights remain the touchstones of [habeas coipus] jurisdiction.” Vincenzo v. Warden, 26 Conn. App. 132, 138 n.4, 599 A.2d 31 (1991). We must therefore determine whether the petitioners have alleged sufficient facts to constitute the deprivation of a legally recognized constitutional right.
II
The petitioners initially claim that the trial court improperly quashed their petitions by finding that they failed to allege sufficient facts to support a constitutional due process violation. On the basis of our examination of the allegations in each petition, we find that Santiago, DeLeon, Arroyo and Breedlove have not alleged sufficient facts to show that the department deprived them of their constitutional due process rights through its enforcement of Administrative Directive § 6.14. Johnson, however, has alleged sufficient facts in his petition to support a due process claim and to invoke the subject matter jurisdiction of the trial court in a habeas corpus proceeding.
[680]*680A
In order to prevail on a due process claim, the petitioners must show that they have been deprived of a legally recognized liberty interest, and that they have been deprived of liberty without due process of law. Johnson v. Meehan, 225 Conn. 528, 546, 626 A.2d 244 (1993). “While no State may ‘deprive any person of life, liberty, or property, without due process of law,’ it is well settled that only a limited range of interests fall within this provision. Liberty interests protected by the Fourteenth Amendment may arise from two sources—the Due Process Clause itself and the laws of the States.” Hewitt v. Helms, 459 U.S. 460, 466, 103 S. Ct. 864, 74 L. Ed. 2d 675 (1983).
Each petitioner alleges that he has suffered a loss of recreation, school and work privileges because of his designation as a security risk group member. Johnson and Breedlove allege that they have suffered a loss of contact visits with their families. Even if we assume those facts to be true, the allegations fail to implicate a protected liberty interest. A prisoner has no property or liberty interest in prison employment, increased recreation or educational courses. See Garza v. Miller, 688 F.2d 480, 485 (7th Cir. 1982), cert. denied, 459 U.S. 1150, 103 S. Ct. 796, 74 L. Ed. 2d 1000 (1983). Similarly, inmates have no protected liberty interest in access to visitors. Kentucky Dept. of Corrections v. Thompson, 490 U.S. 454, 460-61, 109 S. Ct. 1904, 104 L. Ed. 2d 506 (1989). The allegations are insufficient to support subject matter jurisdiction in a habeas corpus proceeding.
Each petitioner’s allegation that he has suffered a loss of any access to the prison law library similarly does not rise to a constitutional violation. We recognize that “the fundamental constitutional right of access to the courts requires prison authorities to assist inmates [681]*681in the preparation and filing of meaningful legal papers by providing prisoners with adequate law libraries or adequate assistance from persons trained in the law.” Bounds v. Smith, 430 U.S. 817, 828, 97 S. Ct. 1491, 52 L. Ed. 2d 72 (1977). Practices or regulations are invalid under Bounds only if the prisoner is denied access to both legal assistance and legal materials. See Casey v. Lewis, 43 F.3d 1261, 1267 (9th Cir. 1994), cert. granted, 514 U.S. 1126, 115 S. Ct. 1997, 131 L. Ed. 2d 999 (1995); Abdul-Akbar v. Watson, 4 F.3d 195, 203-204 (3d Cir. 1993); Morello v. James, 810 F.2d 344, 347 (2d Cir. 1987). The petitioners make no allegations that they have been denied access to legal materials or assistance in preparing legal memoranda. Therefore, the petitioners have failed to allege sufficient facts to constitute a constitutional violation under Bounds.
B
Because this court found insufficient facts alleging deprivation of a legally recognized liberty interest on the face of their petitions, Santiago, DeLeon, Arroyo and Breedlove next urge us to incorporate into their petitions all possible liberty interests implicated by the enforcement of Administrative Directive § 6.14. Specifically, these petitioners claim that they have been deprived of a liberty interest in retaining good time credit pursuant to General Statutes § 18-7a (c),4 even [682]*682though they make no such allegation in their petitions. It is well settled that essential allegations in a pleading may not be supplied by conjecture or remote implication. Cahill, v. Board of Education, 198 Conn. 229, 236, 502 A.2d 410 (1985); Preleski v. Farganiasz, 97 Conn. 345, 348, 116 A. 593 (1922). We decline to supplement their petitions by speculating as to any possible constitutional interests implicated by the department’s directive.
We find that Santiago, DeLeon, Arroyo and Breedlove have failed to allege sufficient facts showing a due process violation.
C
Johnson alleges in his petition that, as a direct result of his designation as a member of a security risk group, he has suffered a loss of good time credits that would have shortened the term of his confinement. We find that this allegation sufficiently implicates a liberty interest to support a constitutional due process claim.
While there is no fourteenth amendment right for an inmate to receive good time credits, when a state creates a right to good time credits, it is “required by the Due Process Clause to insure that the state-created right is not arbitrarily abrogated.” Wolff v. McDonnell, 418 U.S. 539, 557, 94 S. Ct. 2963, 41 L. Ed. 2d 935 (1974). Earned statutory good time credits cannot be forfeited without due process. Superintendent v. Hill, 472 U.S. 445, 453, 105 S. Ct. 2768, 86 L. Ed. 2d 356 (1985); Wolff v. McDonnell, supra, 557-58; McCarthy v. Warden, 213 Conn. 289, 298-99, 567 A.2d 1187 (1989), cert. denied, 496 U.S. 939, 110 S. Ct. 3220, 110 L. Ed. 2d 667 (1990). Because Johnson’s allegation can be construed to include a loss of earned statutory good time credits, we find that he has alleged facts sufficient to implicate [683]*683a recognized liberty interest.5 Therefore, the motion to quash directed to Johnson’s petition should not have been granted.
Ill
Santiago, DeLeon, Arroyo and Johnson also claim that their designation as security risk group members has rendered them subject to cruel and unusual punishment. They do not claim that their conditions of confinement would constitute cruel and unusual punishment if their designations as security risk group members are correct. Rather, they claim that an erroneous designation of a prisoner as a security risk group member results in enhanced penalties and constitutes cruel and unusual punishment.
Cruel and unusual punishment refers to punishment that involves the unnecessary and wanton infliction of pain or is grossly disproportionate to the severity of the crime. Arey v. Warden, supra, 187 Conn. 328. “In its prohibition of cruel and unusual punishments, the Eighth Amendment places restraints on prison officials, who may not, for example, use excessive physical force against prisoners. . . . The Amendment also imposes duties on these officials, who must provide humane conditions of confinement; prison officials must ensure that inmates receive adequate food, clothing, shelter, and medical care, and must take reasonable measures to guarantee the safety of the inmates . . . .’’(Citations omitted; internal quotation marks omitted.) Farmer v. Brennan, 511 U.S. 825, 832-33, 114 S. Ct. 1970, 128 L. Ed. 2d 811 (1994).
We agree with the habeas court that these petitioners have failed to allege sufficient facts demonstrating dep[684]*684rivation of the minimal civilized measure of life’s necessities or excessive force because of their designations as security risk group members. We conclude that these petitioners have not alleged sufficient facts to constitute an eighth amendment violation. The habeas court, therefore, properly granted the respondent’s motion to quash.6
The judgments in the Santiago, DeLeon, Arroyo and Breedlove cases are affirmed. The judgment in the Johnson case is reversed and the case is remanded for further proceedings.
In this opinion the other judges concurred.