,"Group part","Subgroup part"
"A3 in S3","Symmetric group:S3","Cyclic group:Z3"
"A4 in S4","Symmetric group:S4","Alternating group:A4"
"Baer norm",,
Center,,
"Center of M16",M16,"Cyclic group:Z4"
"Center of central product of D8 and Z4","Central product of D8 and Z4","Cyclic group:Z4"
"Center of dihedral group:D16","Dihedral group:D16","Cyclic group:Z2"
"Center of dihedral group:D8","Dihedral group:D8","Cyclic group:Z2"
"Center of direct product of D8 and Z2","Direct product of D8 and Z2","Klein four-group"
"Center of nontrivial semidirect product of Z4 and Z4","Nontrivial semidirect product of Z4 and Z4","Klein four-group"
"Center of quaternion group","Quaternion group","Cyclic group:Z2"
"Center of semidihedral group:SD16","Semidihedral group:SD16","Cyclic group:Z2"
"Center of special linear group:SL(2,3)","Special linear group:SL(2,3)","Cyclic group:Z2"
"Center of special linear group:SL(2,5)","Special linear group:SL(2,5)","Cyclic group:Z2"
"Center of unitriangular matrix group:UT(3,p)","Unitriangular matrix group:UT(3,p)","Group of prime order"
"Central subgroup generated by a non-square in nontrivial semidirect product of Z4 and Z4","Nontrivial semidirect product of Z4 and Z4","Cyclic group:Z2"
"Cyclic maximal subgroup of dihedral group:D16","Dihedral group:D16","Cyclic group:Z8"
"Cyclic maximal subgroup of dihedral group:D8","Dihedral group:D8","Cyclic group:Z4"
"Cyclic maximal subgroup of semidihedral group:SD16","Semidihedral group:SD16","Cyclic group:Z8"
"Cyclic maximal subgroups of quaternion group","Quaternion group","Cyclic group:Z4"
"D8 in D16","Dihedral group:D16","Dihedral group:D8"
"D8 in SD16","Semidihedral group:SD16","Dihedral group:D8"
"Derived subgroup",,
"Derived subgroup of M16",M16,"Cyclic group:Z2"
"Derived subgroup of dihedral group:D16","Dihedral group:D16","Cyclic group:Z4"
"Derived subgroup of nontrivial semidirect product of Z4 and Z4","Nontrivial semidirect product of Z4 and Z4","Cyclic group:Z2"
"Diagonally embedded Z4 in direct product of Z8 and Z2","Direct product of Z8 and Z2","Cyclic group:Z4"
"Direct product of Z4 and Z2 in M16",M16,"Direct product of Z4 and Z2"
Epicenter,,
"First agemo subgroup of direct product of Z4 and Z2","Direct product of Z4 and Z2","Cyclic group:Z2"
"First omega subgroup of direct product of Z4 and Z2","Direct product of Z4 and Z2","Klein four-group"
"Group of integers in group of rational numbers","Group of rational numbers","Group of integers"
"Klein four-subgroup of M16",M16,"Klein four-group"
"Klein four-subgroup of alternating group:A4","Alternating group:A4","Klein four-group"
"Klein four-subgroups of dihedral group:D8","Dihedral group:D8","Klein four-group"
"Non-central Z4 in M16",M16,"Cyclic group:Z4"
"Non-characteristic order two subgroups of direct product of Z4 and Z2","Direct product of Z4 and Z2","Cyclic group:Z2"
"Normal Klein four-subgroup of symmetric group:S4","Symmetric group:S4","Klein four-group"
"Q8 in SD16","Semidihedral group:SD16","Quaternion group"
"Q8 in central product of D8 and Z4","Central product of D8 and Z4","Quaternion group"
"SL(2,3) in GL(2,3)","General linear group:GL(2,3)","Special linear group:SL(2,3)"
Socle,,
"Subgroup generated by a non-commutator square in nontrivial semidirect product of Z4 and Z4","Nontrivial semidirect product of Z4 and Z4","Cyclic group:Z2"
"Z2 in V4","Klein four-group","Cyclic group:Z2"
"Z4 in direct product of Z4 and Z2","Direct product of Z4 and Z2","Cyclic group:Z4"