Subgroups — C₇⋊(C₇⋊#90866) #37525565

Order 22932.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₃⋊D₃₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇²×D₃₉	—	6	2	no	—
4	C₇⋊#90866	—	7	8	no	maximal
5	C₇⋊(C₇⋊#261)	—	9	1	no	maximal, Hall
6	C₃×C₇²×C₁₃	—	2	2	no	—
7	C₇⋊(C₇⋊#157)	—	13	1	no	maximal, Hall
8	C₇×C₃⋊D₃₉	D₇	1	8	yes	—
9	C₇²×D₁₃	—	9	1	no	—
10	C₇²×C₃⋊D₃	—	13	1	no	—
11	C₃²×C₇×C₁₃	Dic₇	1	8	yes	complemented
12	C₇²×C₁₃	#157	1	1	yes	characteristic, complemented, Hall
13	C₇×D₃₉	—	6	16	no	—
14	#90866	—	49	1	no	Hall
15	C₃²×C₇²	#261	1	1	yes	characteristic, complemented, Hall
16	C₇⋊#261	—	63	8	no	—
17	D₃×C₇²	—	78	2	no	—
18	C₃×C₇×C₁₃	—	2	16	no	—
19	C₇⋊#157	—	91	8	no	—
20	C₃⋊D₃₉	C₇⋊D₇	1	1	yes	characteristic
21	C₇⋊Dic₇	—	117	1	no	Hall
22	C₇×D₁₃	—	9	8	no	—
23	C₃×C₇²	—	2	2	no	—
24	C₇×C₃⋊D₃	—	13	8	no	—
25	C₃²×C₁₃	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇²	—	117	1	no	—
27	C₇×C₁₃	C₇⋊#157	1	8	yes	complemented
28	D₃₉	—	6	2	no	—
29	C₃²×C₇	C₇⋊#261	1	8	yes	complemented
30	#261	—	441	1	no	Hall
31	C₇²	#90866	1	1	yes	characteristic, complemented, Sylow
32	D₃×C₇	—	78	16	no	—
33	C₃×C₁₃	—	2	2	no	—
34	#157	—	637	1	no	Hall
35	Dic₇	—	819	8	no	—
36	D₁₃	—	9	1	no	—
37	C₃×C₇	—	2	16	no	—
38	C₃⋊D₃	—	13	1	no	—
39	C₂×C₇	—	117	8	no	—
40	C₁₃	C₇⋊(C₇⋊#157)	1	1	yes	characteristic, complemented, Sylow
41	C₃²	C₇⋊(C₇⋊#261)	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₇⋊#90866	1	8	yes	complemented
43	D₃	—	78	2	no	—
44	C₄	—	5733	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	117	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₇²×C₁₃	C₄
prime radical, cosocle	C₇²×C₃⋊D₃₉	C₂
LCS	G ▷ C₃²×C₇²×C₁₃
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃²×C₇²×C₁₃	C₄	semidirect
11. C₃²×C₇×C₁₃	Dic₇	semidirect
12. C₇²×C₁₃	#157	semidirect
15. C₃²×C₇²	#261	semidirect
25. C₃²×C₁₃	C₇⋊Dic₇	semidirect
27. C₇×C₁₃	C₇⋊#157	semidirect
29. C₃²×C₇	C₇⋊#261	semidirect
31. C₇²	#90866	semidirect
40. C₁₃	C₇⋊(C₇⋊#157)	semidirect
41. C₃²	C₇⋊(C₇⋊#261)	semidirect
42. C₇	C₇⋊#90866	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇²×C₃⋊D₃₉	2
C₇⋊#90866	7
C₇⋊(C₇⋊#261)	9
C₇⋊(C₇⋊#157)	13

Subgroups — C7⋊(C7⋊#90866) #37525565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊(C₇⋊#90866) #37525565