Subgroups — D₁₅₈₁₁ #44539416

Order 31622.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉₇×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₆₃	—	97	1	no	maximal, Hall
3	D₉₇	—	163	1	no	maximal, Hall
4	C₁₆₃	D₉₇	1	1	yes	characteristic, complemented, Sylow
5	C₉₇	D₁₆₃	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	15811	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₉₇×C₁₆₃	C₂
LCS	G ▷ C₉₇×C₁₆₃
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.