Subgroups — C₆₁×C₁₂₇⋊C₃ #37551242

Order 23241.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₂₇⋊C₃	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₆₁	—	127	1	no	maximal, Hall
4	C₁₂₇	C₃×C₆₁	1	1	yes	characteristic, complemented, Sylow
5	C₆₁	C₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₃	—	127	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₆₁	C₁₂₇⋊C₃
commutator, cosocle, hypocenter	C₁₂₇	C₃×C₆₁
Frattini	C₁	G
Fitting, socle	C₆₁×C₁₂₇	C₃
LCS	G ▷ C₁₂₇
UCS	C₁ ◁ C₆₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.