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The query [[Category:Particular subgroups]] was answered by the SMWSQLStore3 in 0.0086 seconds.


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 Subgroup partGroup part
2-Sylow subgroup of general linear group:GL(2,3)Semidihedral group:SD16General linear group:GL(2,3)
2-Sylow subgroup of special linear group:SL(2,3)Quaternion groupSpecial linear group:SL(2,3)
2-Sylow subgroup of special linear group:SL(2,5)Quaternion groupSpecial linear group:SL(2,5)
2-core of general linear group:GL(2,3)Quaternion groupGeneral linear group:GL(2,3)
A3 in A4Cyclic group:Z3Alternating group:A4
A3 in A5Cyclic group:Z3Alternating group:A5
A3 in S3Cyclic group:Z3Symmetric group:S3
A3 in S4Cyclic group:Z3Symmetric group:S4
A3 in S5Cyclic group:Z3Symmetric group:S5
A4 in A5Alternating group:A4Alternating group:A5
A4 in S4Alternating group:A4Symmetric group:S4
A5 in A6Alternating group:A5Alternating group:A6
A5 in S5Alternating group:A5Symmetric group:S5
A6 in S6Alternating group:A6Symmetric group:S6
Center of M16Cyclic group:Z4M16
Center of binary octahedral groupCyclic group:Z2Binary octahedral group
Center of central product of D8 and Z4Cyclic group:Z4Central product of D8 and Z4
Center of dihedral group:D16Cyclic group:Z2Dihedral group:D16
Center of dihedral group:D8Cyclic group:Z2Dihedral group:D8
Center of direct product of D8 and Z2Klein four-groupDirect product of D8 and Z2
Center of general linear group:GL(2,3)Cyclic group:Z2General linear group:GL(2,3)
Center of nontrivial semidirect product of Z4 and Z4Klein four-groupNontrivial semidirect product of Z4 and Z4
Center of quaternion groupCyclic group:Z2Quaternion group
Center of semidihedral group:SD16Cyclic group:Z2Semidihedral group:SD16
Center of special linear group:SL(2,3)Cyclic group:Z2Special linear group:SL(2,3)
Center of special linear group:SL(2,5)Cyclic group:Z2Special linear group:SL(2,5)
Center of unitriangular matrix group:UT(3,p)Group of prime orderUnitriangular matrix group:UT(3,p)
Central subgroup generated by a non-square in nontrivial semidirect product of Z4 and Z4Cyclic group:Z2Nontrivial semidirect product of Z4 and Z4
Cyclic four-subgroups of symmetric group:S4Cyclic group:Z4Symmetric group:S4
Cyclic maximal subgroup of dihedral group:D16Cyclic group:Z8Dihedral group:D16
Cyclic maximal subgroup of dihedral group:D8Cyclic group:Z4Dihedral group:D8
Cyclic maximal subgroup of semidihedral group:SD16Cyclic group:Z8Semidihedral group:SD16
Cyclic maximal subgroups of quaternion groupCyclic group:Z4Quaternion group
D8 in A6Dihedral group:D8Alternating group:A6
D8 in D16Dihedral group:D8Dihedral group:D16
D8 in S4Dihedral group:D8Symmetric group:S4
D8 in SD16Dihedral group:D8Semidihedral group:SD16
Derived subgroup of M16Cyclic group:Z2M16
Derived subgroup of dihedral group:D16Cyclic group:Z4Dihedral group:D16
Derived subgroup of nontrivial semidirect product of Z4 and Z4Cyclic group:Z2Nontrivial semidirect product of Z4 and Z4
Diagonally embedded Z4 in direct product of Z8 and Z2Cyclic group:Z4Direct product of Z8 and Z2
Direct product of Z4 and Z2 in M16Direct product of Z4 and Z2M16
Elementary abelian subgroups of prime-square order in unitriangular matrix group:UT(3,p)Elementary abelian group of prime-square orderUnitriangular matrix group:UT(3,p)
First agemo subgroup of direct product of Z4 and Z2Cyclic group:Z2Direct product of Z4 and Z2
First omega subgroup of direct product of Z4 and Z2Klein four-groupDirect product of Z4 and Z2
Group of integers in group of rational numbersGroup of integersGroup of rational numbers
Klein four-subgroup of M16Klein four-groupM16
Klein four-subgroup of alternating group:A4Klein four-groupAlternating group:A4
Klein four-subgroup of alternating group:A5Klein four-groupAlternating group:A5
Klein four-subgroups of dihedral group:D16Klein four-groupDihedral group:D16