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The query <q>[[Satisfies property::Characteristic subgroup]] [[Dissatisfies property::Homomorph-containing subgroup]] [[Category:Particular subgroups]] OR [[Satisfies property.Stronger than::Characteristic subgroup]] [[Dissatisfies property.Weaker than::Homomorph-containing subgroup]] [[Category:Particular subgroups]]</q> was answered by the SMWSQLStore3 in 0.0174 seconds.


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 Group partSubgroup partQuotient part
Center of dihedral group:D16Dihedral group:D16Cyclic group:Z2Dihedral group:D8
Center of dihedral group:D8Dihedral group:D8Cyclic group:Z2Klein four-group
Center of direct product of D8 and Z2Direct product of D8 and Z2Klein four-groupKlein four-group
Center of semidihedral group:SD16Semidihedral group:SD16Cyclic group:Z2Dihedral group:D8
Center of unitriangular matrix group:UT(3,p)Unitriangular matrix group:UT(3,p)Group of prime orderElementary abelian group of prime-square order
Cyclic maximal subgroup of dihedral group:D16Dihedral group:D16Cyclic group:Z8Cyclic group:Z2
Cyclic maximal subgroup of dihedral group:D8Dihedral group:D8Cyclic group:Z4Cyclic group:Z2
Cyclic maximal subgroup of semidihedral group:SD16Semidihedral group:SD16Cyclic group:Z8Cyclic group:Z2
Derived subgroup of M16M16Cyclic group:Z2Direct product of Z4 and Z2
Derived subgroup of dihedral group:D16Dihedral group:D16Cyclic group:Z4Klein four-group
Derived subgroup of nontrivial semidirect product of Z4 and Z4Nontrivial semidirect product of Z4 and Z4Cyclic group:Z2Direct product of Z4 and Z2
First agemo subgroup of direct product of Z4 and Z2Direct product of Z4 and Z2Cyclic group:Z2Klein four-group
Klein four-subgroup of M16M16Klein four-groupCyclic group:Z4
Normal Klein four-subgroup of symmetric group:S4Symmetric group:S4Klein four-groupSymmetric group:S3
Q8 in SD16Semidihedral group:SD16Quaternion groupCyclic group:Z2
Q8 in central product of D8 and Z4Central product of D8 and Z4Quaternion groupCyclic group:Z2