Subgroups — C₃×D₇₇⋊D₁₁ #23779049

Order 10164.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₃	D₇₇⋊D₁₁
commutator, cosocle, hypocenter	C₇×C₁₁²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁²	C₂²
LCS	G ▷ C₇×C₁₁²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×D₇₇	C₂	semidirect
2. C₃×C₇×C₁₁⋊D₁₁	C₂	semidirect
3. D₇₇⋊D₁₁	C₃	direct (N × H)
4. C₃×C₇×C₁₁²	C₂²	semidirect
5. C₁₁×D₇₇	C₂×C₃	semidirect
6. C₇×C₁₁⋊D₁₁	C₂×C₃	semidirect
9. C₇×C₁₁²	C₂²×C₃	semidirect
10. C₃×C₁₁⋊D₁₁	D₇	semidirect
13. C₃×D₇₇	D₁₁	semidirect
17. C₃×C₁₁²	C₂×D₇	semidirect
19. C₁₁⋊D₁₁	C₃×D₇	semidirect
22. C₃×C₇×C₁₁	C₂×D₁₁	semidirect
23. D₇₇	C₃×D₁₁	semidirect
28. C₁₁²	C₂×C₃×D₇	semidirect
31. C₇×C₁₁	C₂×C₃×D₁₁	semidirect
40. C₃×C₁₁	D₇×D₁₁	semidirect
46. C₃×C₇	D₁₁²	semidirect
51. C₁₁	C₃×D₇×D₁₁	semidirect
52. C₇	C₃×D₁₁²	semidirect
56. C₃	D₇₇⋊D₁₁	direct (N × H)

Subgroups — C3×D77⋊D11 #23779049

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₇₇⋊D₁₁ #23779049