Subgroups — C₇²×D₃₁₇ #44526959

Order 31066.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₃₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₃₁₇	C₇	1	8	yes	maximal, direct product factor
3	C₇×C₃₁₇	C₂×C₇	1	8	yes	complemented
4	D₃₁₇	C₇²	1	1	yes	characteristic, direct product factor, Hall
5	C₃₁₇	C₂×C₇²	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₇²	—	317	1	no	maximal, Hall
7	C₇²	D₃₁₇	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₇	—	317	8	no	—
9	C₇	C₇×D₃₁₇	1	8	yes	direct product factor
10	C₂	—	317	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇²	D₃₁₇
commutator, cosocle, hypocenter	C₃₁₇	C₂×C₇²
Frattini	C₁	G
Fitting, socle	C₇²×C₃₁₇	C₂
LCS	G ▷ C₃₁₇
UCS	C₁ ◁ C₇²

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.