Subgroups — C₇⋊#17985008 #44530813

Order 31276.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₁₁₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₁₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#17985008	—	7	1	no	maximal, Hall
4	D₁₁₁₇	D₇	1	1	yes	characteristic
5	C₁₁₁₇	Dic₇	1	1	yes	characteristic, complemented, Sylow
6	Dic₇	—	1117	1	no	maximal, Hall
7	C₂×C₇	—	1117	1	no	—
8	C₇	#17985008	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	7819	1	no	Sylow
10	C₂	—	1117	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇×C₁₁₁₇	C₄
prime radical, cosocle	C₇×D₁₁₁₇	C₂
LCS	G ▷ C₇×C₁₁₁₇
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.