Subgroups — C₇×D₃₃⋊D₁₁ #23779054

Order 10164.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₇	D₃₃⋊D₁₁
commutator, cosocle, hypocenter	C₃×C₁₁²	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁²	C₂²
LCS	G ▷ C₃×C₁₁²
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₁×D₃₃	C₂	semidirect
2. C₃×C₇×C₁₁⋊D₁₁	C₂	semidirect
4. C₃×C₇×C₁₁²	C₂²	semidirect
5. C₇×C₁₁⋊D₁₁	D₃	semidirect
7. D₃₃⋊D₁₁	C₇	direct (N × H)
9. C₇×C₁₁²	C₂×D₃	semidirect
10. C₁₁×D₃₃	C₂×C₇	semidirect
11. C₃×C₁₁⋊D₁₁	C₂×C₇	semidirect
13. C₇×D₃₃	D₁₁	semidirect
17. C₃×C₁₁²	C₂²×C₇	semidirect
19. C₁₁⋊D₁₁	D₃×C₇	semidirect
22. C₃×C₇×C₁₁	C₂×D₁₁	semidirect
28. C₁₁²	C₂×D₃×C₇	semidirect
31. C₇×C₁₁	D₃×D₁₁	semidirect
32. D₃₃	C₇×D₁₁	semidirect
40. C₃×C₁₁	C₂×C₇×D₁₁	semidirect
46. C₃×C₇	D₁₁²	semidirect
51. C₁₁	D₃×C₇×D₁₁	semidirect
52. C₇	D₃₃⋊D₁₁	direct (N × H)
56. C₃	C₇×D₁₁²	semidirect

Subgroups — C7×D33⋊D11 #23779054

Conjugacy classes of subgroups

Complements

Subgroups — C₇×D₃₃⋊D₁₁ #23779054