Subgroups — #23779059

Order 10164.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₂₃₁	C₂	1	2	yes	maximal, complemented
2	C₃×C₇×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₇₇⋊D₁₁	—	3	1	no	maximal, Hall
4	C₃×C₇×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₁×D₇₇	—	3	2	no	—
6	C₇×C₁₁⋊D₁₁	D₃	1	1	yes	characteristic, complemented
7	D₃₃⋊D₁₁	—	7	1	no	maximal, Hall
8	D₁₁×D₂₁	—	11	2	no	maximal
9	C₇×C₁₁²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₁₁×D₃₃	—	7	2	no	—
11	C₃×C₁₁⋊D₁₁	D₇	1	1	yes	characteristic, complemented
12	D₁₁²	—	21	1	no	Hall
13	D₂₃₁	D₁₁	1	2	yes	complemented
14	C₁₁×D₂₁	—	11	2	no	—
15	C₃×C₇×D₁₁	—	11	2	no	—
16	C₃×C₇×D₁₁	—	22	5	no	—
17	C₃×C₁₁²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
18	D₇×D₁₁	—	33	2	no	—
19	C₁₁⋊D₁₁	D₂₁	1	1	yes	characteristic, complemented
20	C₁₁×D₁₁	—	21	2	no	—
21	C₃×C₇×C₁₁	—	2	5	no	—
22	C₃×C₇×C₁₁	C₂×D₁₁	1	2	yes	complemented
23	D₇₇	—	3	2	no	—
24	C₇×D₁₁	—	11	2	no	—
25	C₇×D₁₁	—	22	5	no	—
26	C₁₁×D₇	—	33	2	no	—
27	D₃×D₁₁	—	77	2	no	—
28	C₁₁²	C₂×D₂₁	1	1	yes	characteristic, complemented, Sylow
29	C₂×D₂₁	—	121	1	no	Hall
30	C₇×C₁₁	—	2	5	no	—
31	C₇×C₁₁	D₃×D₁₁	1	2	yes	complemented
32	D₃₃	—	7	2	no	—
33	C₃×D₁₁	—	11	2	no	—
34	C₃×D₁₁	—	22	5	no	—
35	D₃×C₁₁	—	77	2	no	—
36	C₂×D₁₁	—	231	2	no	—
37	C₂×C₃×C₇	—	121	1	no	—
38	D₂₁	—	11	2	no	—
39	C₃×C₁₁	—	2	5	no	—
40	C₃×C₁₁	D₇×D₁₁	1	2	yes	complemented
41	C₂×D₇	—	363	1	no	Hall
42	C₂×C₁₁	—	231	2	no	—
43	D₁₁	—	11	2	no	—
44	D₁₁	—	21	2	no	—
45	D₁₁	—	22	5	no	—
46	C₃×C₇	D₁₁²	1	1	yes	characteristic, complemented, Hall
47	C₂×C₇	—	121	1	no	—
48	D₇	—	33	2	no	—
49	C₂×D₃	—	847	1	no	Hall
50	C₁₁	—	2	5	no	—
51	C₁₁	D₁₁×D₂₁	1	2	yes	complemented
52	C₇	D₃₃⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₃	—	121	1	no	—
54	D₃	—	77	2	no	—
55	C₂²	—	2541	1	no	Sylow
56	C₃	D₇₇⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	121	1	no	—
58	C₂	—	231	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₁²	C₂²
LCS	G ▷ C₃×C₇×C₁₁²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₂₃₁	C₂	semidirect
2. C₃×C₇×C₁₁⋊D₁₁	C₂	semidirect
4. C₃×C₇×C₁₁²	C₂²	semidirect
6. C₇×C₁₁⋊D₁₁	D₃	semidirect
9. C₇×C₁₁²	C₂×D₃	semidirect
11. C₃×C₁₁⋊D₁₁	D₇	semidirect
13. D₂₃₁	D₁₁	semidirect
17. C₃×C₁₁²	C₂×D₇	semidirect
19. C₁₁⋊D₁₁	D₂₁	semidirect
22. C₃×C₇×C₁₁	C₂×D₁₁	semidirect
28. C₁₁²	C₂×D₂₁	semidirect
31. C₇×C₁₁	D₃×D₁₁	semidirect
40. C₃×C₁₁	D₇×D₁₁	semidirect
46. C₃×C₇	D₁₁²	semidirect
51. C₁₁	D₁₁×D₂₁	semidirect
52. C₇	D₃₃⋊D₁₁	semidirect
56. C₃	D₇₇⋊D₁₁	semidirect