Subgroups — C₇×D₁₁×D₃₃ #23779053

Order 10164.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊(C₁₁⋊D₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₁₁×D₃₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₁₁×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×D₁₁²	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇×C₁₁⋊D₁₁	—	3	1	no	—
7	C₇×C₁₁×D₁₁	—	3	1	no	—
8	C₇×C₁₁×D₁₁	D₃	1	1	yes	characteristic, complemented
9	D₁₁×D₃₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₇×D₃₃	—	11	1	no	maximal
11	D₃×C₇×D₁₁	—	11	1	no	maximal
12	C₇×C₁₁²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃⋊(C₁₁⋊D₁₁)	C₂×C₇	1	1	yes	characteristic, complemented
14	C₁₁×D₃₃	C₂×C₇	1	1	yes	characteristic, complemented
15	C₃×C₁₁×D₁₁	C₂×C₇	1	1	yes	characteristic, complemented
16	D₁₁²	—	3	1	no	Hall
17	C₂×C₃×C₇×C₁₁	—	11	1	no	—
18	C₇×D₃₃	—	11	1	no	—
19	C₇×D₃₃	—	11	1	no	—
20	C₇×D₃₃	—	22	5	no	—
21	C₇×D₃₃	D₁₁	1	1	yes	characteristic, direct product factor
22	D₃×C₇×C₁₁	—	11	1	no	—
23	C₃×C₇×D₁₁	D₁₁	1	1	yes	characteristic, complemented
24	C₃×C₁₁²	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇×D₁₁	—	33	1	no	—
26	C₂×C₇×D₁₁	—	33	1	no	—
27	C₁₁⋊D₁₁	—	3	1	no	—
28	C₁₁×D₁₁	—	3	1	no	—
29	C₁₁×D₁₁	D₃×C₇	1	1	yes	characteristic, complemented
30	C₃×C₇×C₁₁	—	2	5	no	—
31	C₃×C₇×C₁₁	C₂×D₁₁	1	1	yes	characteristic, complemented
32	C₃×C₇×C₁₁	C₂×D₁₁	1	1	yes	characteristic, complemented
33	C₂×C₇×C₁₁	—	11	1	no	—
34	C₂×C₇×C₁₁	—	33	1	no	—
35	C₇×D₁₁	—	3	1	no	—
36	C₇×D₁₁	—	33	1	no	—
37	C₇×D₁₁	—	33	1	no	—
38	C₇×D₁₁	—	66	5	no	—
39	C₇×D₁₁	D₃₃	1	1	yes	characteristic, direct product factor
40	C₂×D₃₃	—	11	1	no	—
41	D₃×D₁₁	—	11	1	no	—
42	C₁₁²	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₃×C₇	—	121	1	no	Hall
44	C₇×C₁₁	—	2	5	no	—
45	C₇×C₁₁	D₃×D₁₁	1	1	yes	characteristic, complemented
46	C₇×C₁₁	C₂×D₃₃	1	1	yes	characteristic, complemented
47	C₂×C₃×C₁₁	—	11	1	no	—
48	D₃₃	—	11	1	no	—
49	D₃₃	—	11	1	no	—
50	D₃₃	—	22	5	no	—
51	D₃₃	C₇×D₁₁	1	1	yes	characteristic, direct product factor
52	C₃×D₁₁	C₇×D₁₁	1	1	yes	characteristic, complemented
53	D₃×C₁₁	—	11	1	no	—
54	C₂×D₁₁	—	33	1	no	—
55	C₂×D₁₁	—	33	1	no	—
56	C₂×C₃×C₇	—	11	1	no	—
57	D₃×C₇	—	11	1	no	—
58	D₃×C₇	—	121	1	no	—
59	C₃×C₁₁	—	2	5	no	—
60	C₃×C₁₁	C₂×C₇×D₁₁	1	1	yes	characteristic, complemented
61	C₃×C₁₁	C₂×C₇×D₁₁	1	1	yes	characteristic, complemented
62	C₂²×C₇	—	363	1	no	Hall
63	C₂×C₁₁	—	11	1	no	—
64	C₂×C₁₁	—	33	1	no	—
65	D₁₁	—	3	1	no	—
66	D₁₁	—	33	1	no	—
67	D₁₁	—	33	1	no	—
68	D₁₁	—	66	5	no	—
69	D₁₁	C₇×D₃₃	1	1	yes	characteristic, direct product factor
70	C₃×C₇	D₁₁²	1	1	yes	characteristic, complemented, Hall
71	C₂×C₇	—	11	1	no	—
72	C₂×C₇	—	33	1	no	—
73	C₂×C₇	—	363	1	no	—
74	C₂×D₃	—	121	1	no	Hall
75	C₁₁	—	2	5	no	—
76	C₁₁	D₃×C₇×D₁₁	1	1	yes	characteristic, complemented
77	C₁₁	C₂×C₇×D₃₃	1	1	yes	characteristic, complemented
78	C₇	D₁₁×D₃₃	1	1	yes	characteristic, direct product factor, Sylow
79	C₂×C₃	—	11	1	no	—
80	D₃	—	11	1	no	—
81	D₃	—	121	1	no	—
82	C₂²	—	363	1	no	Sylow
83	C₃	C₇×D₁₁²	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	11	1	no	—
85	C₂	—	33	1	no	—
86	C₂	—	363	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₁₁×D₃₃
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×C₃⋊(C₁₁⋊D₁₁)	C₂	semidirect
2. C₇×C₁₁×D₃₃	C₂	semidirect
3. C₃×C₇×C₁₁×D₁₁	C₂	semidirect
5. C₃×C₇×C₁₁²	C₂²	semidirect
8. C₇×C₁₁×D₁₁	D₃	semidirect
9. D₁₁×D₃₃	C₇	direct (N × H)
12. C₇×C₁₁²	C₂×D₃	semidirect
13. C₃⋊(C₁₁⋊D₁₁)	C₂×C₇	semidirect
14. C₁₁×D₃₃	C₂×C₇	semidirect
15. C₃×C₁₁×D₁₁	C₂×C₇	semidirect
21. C₇×D₃₃	D₁₁	direct (N × H)
23. C₃×C₇×D₁₁	D₁₁	semidirect
24. C₃×C₁₁²	C₂²×C₇	semidirect
29. C₁₁×D₁₁	D₃×C₇	semidirect
31. C₃×C₇×C₁₁	C₂×D₁₁	semidirect
32. C₃×C₇×C₁₁	C₂×D₁₁	semidirect
39. C₇×D₁₁	D₃₃	direct (N × H)
42. C₁₁²	C₂×D₃×C₇	semidirect
45. C₇×C₁₁	D₃×D₁₁	semidirect
46. C₇×C₁₁	C₂×D₃₃	semidirect
51. D₃₃	C₇×D₁₁	direct (N × H)
52. C₃×D₁₁	C₇×D₁₁	semidirect
60. C₃×C₁₁	C₂×C₇×D₁₁	semidirect
61. C₃×C₁₁	C₂×C₇×D₁₁	semidirect
69. D₁₁	C₇×D₃₃	direct (N × H)
70. C₃×C₇	D₁₁²	semidirect
76. C₁₁	D₃×C₇×D₁₁	semidirect
77. C₁₁	C₂×C₇×D₃₃	semidirect
78. C₇	D₁₁×D₃₃	direct (N × H)
83. C₃	C₇×D₁₁²	semidirect

Subgroups — C7×D11×D33 #23779053

Conjugacy classes of subgroups

Complements

Subgroups — C₇×D₁₁×D₃₃ #23779053