Subgroups — C₇×C₇⋊#90865 #37525563

Order 22932.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₇²×C₁₃	—	6	2	no	—
4	C₇⋊#90865	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₇×#90865	—	7	1	no	maximal
6	C₇×Dic₉₁	—	9	1	no	maximal, Hall
7	C₃×C₇²×C₁₃	—	2	2	no	—
8	C₇×C₇⋊#157	—	13	1	no	maximal, Hall
9	C₇×C₁₃×C₃⋊D₃	—	2	3	no	—
10	C₇×C₁₃×C₃⋊D₃	D₇	1	1	yes	characteristic
11	C₇×C₁₃×C₃⋊D₃	C₂×C₇	1	1	yes	characteristic
12	C₂×C₇²×C₁₃	—	9	1	no	—
13	C₇²×C₃⋊D₃	D₁₃	1	1	yes	characteristic
14	C₃²×C₇×C₁₃	—	2	3	no	—
15	C₃²×C₇×C₁₃	Dic₇	1	1	yes	characteristic, complemented
16	C₃²×C₇×C₁₃	C₄×C₇	1	1	yes	characteristic, complemented
17	C₇²×C₁₃	#157	1	1	yes	characteristic, complemented, Hall
18	D₃×C₇×C₁₃	—	6	2	no	—
19	D₃×C₇×C₁₃	—	6	2	no	—
20	D₃×C₇×C₁₃	—	6	12	no	—
21	#90865	—	7	1	no	Hall
22	C₃²×C₇²	Dic₁₃	1	1	yes	characteristic, complemented, Hall
23	Dic₉₁	—	9	1	no	—
24	C₇×Dic₁₃	—	63	1	no	—
25	D₃×C₇²	—	6	2	no	—
26	C₃×C₇×C₁₃	—	2	12	no	—
27	C₃×C₇×C₁₃	—	2	2	no	—
28	C₃×C₇×C₁₃	—	2	2	no	—
29	C₇⋊#157	—	13	1	no	—
30	C₇×#157	—	91	1	no	—
31	C₁₃×C₃⋊D₃	C₇×D₇	1	1	yes	characteristic
32	C₇×Dic₇	—	117	1	no	Hall
33	C₂×C₇×C₁₃	—	9	1	no	—
34	C₂×C₇×C₁₃	—	9	1	no	—
35	C₂×C₇×C₁₃	—	18	3	no	—
36	C₃×C₇²	—	2	2	no	—
37	C₇×C₃⋊D₃	—	2	3	no	—
38	C₇×C₃⋊D₃	C₇×D₁₃	1	1	yes	characteristic
39	C₇×C₃⋊D₃	D₉₁	1	1	yes	characteristic
40	C₃²×C₁₃	C₇×Dic₇	1	1	yes	characteristic, complemented, Hall
41	C₂×C₇²	—	9	1	no	—
42	C₇×C₁₃	—	2	3	no	—
43	C₇×C₁₃	C₇×#157	1	1	yes	characteristic, complemented
44	C₇×C₁₃	C₇⋊#157	1	1	yes	characteristic, complemented
45	D₃×C₁₃	—	6	2	no	—
46	C₃²×C₇	—	2	3	no	—
47	C₃²×C₇	C₇×Dic₁₃	1	1	yes	characteristic, complemented
48	C₃²×C₇	Dic₉₁	1	1	yes	characteristic, complemented
49	Dic₁₃	—	63	1	no	Hall
50	C₇²	#90865	1	1	yes	characteristic, complemented, Sylow
51	D₃×C₇	—	6	2	no	—
52	D₃×C₇	—	6	2	no	—
53	D₃×C₇	—	6	12	no	—
54	C₃×C₁₃	—	2	2	no	—
55	#157	—	91	1	no	Hall
56	C₄×C₇	—	819	1	no	—
57	Dic₇	—	117	1	no	—
58	C₂×C₁₃	—	9	1	no	—
59	C₃×C₇	—	2	12	no	—
60	C₃×C₇	—	2	2	no	—
61	C₃×C₇	—	2	2	no	—
62	C₃⋊D₃	C₇×D₉₁	1	1	yes	characteristic
63	C₂×C₇	—	9	1	no	—
64	C₂×C₇	—	9	1	no	—
65	C₂×C₇	—	18	3	no	—
66	C₁₃	C₇×C₇⋊#157	1	1	yes	characteristic, complemented, Sylow
67	C₃²	C₇×Dic₉₁	1	1	yes	characteristic, complemented, Sylow
68	C₇	—	2	3	no	—
69	C₇	C₇×#90865	1	1	yes	characteristic, complemented
70	C₇	C₇⋊#90865	1	1	yes	characteristic, direct product factor
71	D₃	—	6	2	no	—
72	C₄	—	819	1	no	Sylow
73	C₃	—	2	2	no	—
74	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₇	C₇⋊#90865
commutator, hypocenter	C₃²×C₇×C₁₃	C₄×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₃	C₄
prime radical	C₇²×C₁₃×C₃⋊D₃	C₂
cosocle	C₇×C₁₃×C₃⋊D₃	C₂×C₇
LCS	G ▷ C₃²×C₇×C₁₃
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
2. C₃²×C₇²×C₁₃	C₄	semidirect
4. C₇⋊#90865	C₇	direct (N × H)
15. C₃²×C₇×C₁₃	Dic₇	semidirect
16. C₃²×C₇×C₁₃	C₄×C₇	semidirect
17. C₇²×C₁₃	#157	semidirect
22. C₃²×C₇²	Dic₁₃	semidirect
40. C₃²×C₁₃	C₇×Dic₇	semidirect
43. C₇×C₁₃	C₇×#157	semidirect
44. C₇×C₁₃	C₇⋊#157	semidirect
47. C₃²×C₇	C₇×Dic₁₃	semidirect
48. C₃²×C₇	Dic₉₁	semidirect
50. C₇²	#90865	semidirect
66. C₁₃	C₇×C₇⋊#157	semidirect
67. C₃²	C₇×Dic₉₁	semidirect
69. C₇	C₇×#90865	semidirect
70. C₇	C₇⋊#90865	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇²×C₁₃×C₃⋊D₃	2
C₇⋊#90865	7
C₇×#90865	7
C₇×Dic₉₁	9
C₇×C₇⋊#157	13

Subgroups — C7×C7⋊#90865 #37525563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₇⋊#90865 #37525563