Subgroups — C₇⋊(C₇⋊#92150) #37557413

Order 23716.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₇²×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇⋊#92150	—	7	8	no	maximal
4	C₇×C₁₁⋊D₁₁	D₇	1	8	yes	—
5	C₇²×D₁₁	—	22	6	no	—
6	C₇×C₁₁²	Dic₇	1	8	yes	complemented
7	C₇²×C₁₁	—	2	6	no	—
8	#92150	—	49	1	no	Hall
9	C₁₁⋊D₁₁	C₇⋊D₇	1	1	yes	characteristic
10	C₇⋊Dic₇	—	121	1	no	maximal, Hall
11	C₇×D₁₁	—	22	48	no	—
12	C₁₁²	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₇²	—	121	1	no	—
14	C₇×C₁₁	—	2	48	no	—
15	C₇²	#92150	1	1	yes	characteristic, complemented, Sylow
16	Dic₇	—	847	8	no	—
17	D₁₁	—	22	6	no	—
18	C₂×C₇	—	121	8	no	—
19	C₁₁	—	2	6	no	—
20	C₇	C₇⋊#92150	1	8	yes	complemented
21	C₄	—	5929	1	no	Sylow
22	C₂	—	121	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₁₁²	C₄
prime radical, cosocle	C₇²×C₁₁⋊D₁₁	C₂
LCS	G ▷ C₇²×C₁₁²
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.