Subgroups — #44538821

Order 31557.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×C₁₅₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₅₇⋊C₃	—	67	1	no	maximal, Hall
3	C₆₇⋊C₃	—	157	1	no	maximal, Hall
4	C₁₅₇	C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
5	C₆₇	C₁₅₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
6	C₃	—	10519	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₆₇×C₁₅₇	C₃
LCS	G ▷ C₆₇×C₁₅₇
UCS	C₁

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.