Subgroups — D₁₁₇₂₉ #37553271

Order 23458.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×C₃₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₁₇	—	37	1	no	maximal, Hall
3	C₃₁₇	D₃₇	1	1	yes	characteristic, complemented, Sylow
4	D₃₇	—	317	1	no	maximal, Hall
5	C₃₇	D₃₁₇	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	11729	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃₇×C₃₁₇	C₂
LCS	G ▷ C₃₇×C₃₁₇
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.