Subgroups — #11924328

Order 1176.

43 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#3862	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₂²⋊D₇	—	3	1	no	maximal, Hall
3	#64418	—	4	1	no	maximal
4	C₂²×C₇²	D₃	1	1	yes	characteristic, complemented
5	C₂×C₇×D₇	—	3	1	no	—
6	C₇×Dic₇	—	3	1	no	—
7	#3862	—	4	1	no	Hall
8	C₂×C₇²	—	3	1	no	—
9	C₇×D₇	—	6	1	no	—
10	C₂²⋊ΓL(1,𝔽₈)	—	14	1	no	—
11	C₇×D₄	—	21	1	no	—
12	C₂²⋊D₇	—	3	1	no	—
13	C₇²	S₄	1	1	yes	characteristic, complemented, Sylow
14	C₂²×C₇	—	2	1	no	—
15	C₂²×C₇	—	3	1	no	—
16	C₂²×C₇	—	3	1	no	—
17	C₂²×C₇	—	21	1	no	—
18	C₂×D₇	—	3	1	no	—
19	C₄×C₇	—	21	1	no	—
20	Dic₇	—	3	1	no	—
21	S₄	—	49	1	no	maximal, Hall
22	ΓL(1,𝔽₈)	—	56	1	no	—
23	C₂×C₇	—	3	1	no	—
24	C₂×C₇	—	3	1	no	—
25	C₂×C₇	—	6	1	no	—
26	C₂×C₇	—	6	1	no	—
27	C₂×C₇	—	6	1	no	—
28	C₂×C₇	—	42	1	no	—
29	D₇	—	6	1	no	—
30	A₄	—	49	1	no	—
31	D₄	—	21	1	no	Sylow
32	C₇	—	2	1	no	—
33	C₇	—	3	1	no	—
34	C₇	—	3	1	no	—
35	D₃	—	196	1	no	—
36	C₂²	—	21	1	no	—
37	C₂²	#64418	1	1	yes	characteristic, complemented
38	C₄	—	21	1	no	—
39	C₃	—	196	1	no	Sylow
40	C₂	—	3	1	no	—
41	C₂	—	42	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₂²⋊#3862	C₂
Fitting, socle	C₂²×C₇²	D₃
LCS	G ▷ C₂²⋊#3862
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.