Subgroups — C₇×C₁₁×D₇×D₁₁ #37557402

Order 23716.

159 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₁×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₁₁²×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₁×D₇₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇²×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₁₁×D₁₁	—	7	1	no	maximal
6	C₁₁×D₇×D₁₁	C₇	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₇×C₁₁×D₇	—	11	1	no	maximal
8	C₇×D₇×D₁₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₇×C₁₁²	—	7	1	no	—
10	C₁₁×D₇₇	C₂×C₇	1	1	yes	characteristic, complemented
11	C₁₁²×D₇	C₂×C₇	1	1	yes	characteristic, complemented
12	C₇×C₁₁×D₁₁	—	2	3	no	—
13	C₇×C₁₁×D₁₁	—	7	1	no	—
14	C₇×C₁₁×D₁₁	D₇	1	1	yes	characteristic, direct product factor
15	C₇×C₁₁×D₁₁	C₂×C₇	1	1	yes	characteristic, complemented
16	C₂×C₇²×C₁₁	—	11	1	no	—
17	C₇×D₇₇	C₂×C₁₁	1	1	yes	characteristic, complemented
18	C₇×C₁₁×D₇	—	2	5	no	—
19	C₇×C₁₁×D₇	—	11	1	no	—
20	C₇×C₁₁×D₇	D₁₁	1	1	yes	characteristic, direct product factor
21	C₇×C₁₁×D₇	C₂×C₁₁	1	1	yes	characteristic, complemented
22	C₇²×D₁₁	C₂×C₁₁	1	1	yes	characteristic, complemented
23	C₇×C₁₁²	—	2	3	no	—
24	C₇×C₁₁²	C₂×D₇	1	1	yes	characteristic, complemented
25	C₇×C₁₁²	C₂²×C₇	1	1	yes	characteristic, complemented
26	C₇²×C₁₁	—	2	5	no	—
27	C₇²×C₁₁	C₂×D₁₁	1	1	yes	characteristic, complemented
28	C₇²×C₁₁	C₂²×C₁₁	1	1	yes	characteristic, complemented
29	C₂×C₁₁×D₁₁	—	7	1	no	Hall
30	C₂²×C₇×C₁₁	—	77	1	no	—
31	C₂×C₁₁×D₇	—	11	1	no	—
32	C₂×C₇×D₁₁	—	7	1	no	—
33	D₇×D₁₁	C₇×C₁₁	1	1	yes	characteristic, direct product factor
34	C₂×C₁₁²	—	7	1	no	—
35	C₁₁×D₁₁	—	7	1	no	—
36	C₁₁×D₁₁	C₇×D₇	1	1	yes	characteristic, direct product factor
37	C₂×C₇×D₇	—	11	1	no	Hall
38	C₂×C₇×C₁₁	—	7	1	no	—
39	C₂×C₇×C₁₁	—	7	1	no	—
40	C₂×C₇×C₁₁	—	11	1	no	—
41	C₂×C₇×C₁₁	—	11	1	no	—
42	C₂×C₇×C₁₁	—	14	5	no	—
43	C₂×C₇×C₁₁	—	22	3	no	—
44	C₂×C₇×C₁₁	—	77	1	no	—
45	D₇₇	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented
46	C₇×D₁₁	—	2	3	no	—
47	C₇×D₁₁	—	7	1	no	—
48	C₇×D₁₁	C₁₁×D₇	1	1	yes	characteristic, direct product factor
49	C₇×D₁₁	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented
50	C₁₁×D₇	—	2	5	no	—
51	C₁₁×D₇	—	11	1	no	—
52	C₁₁×D₇	C₇×D₁₁	1	1	yes	characteristic, direct product factor
53	C₁₁×D₇	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented
54	C₁₁²	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₇²	—	11	1	no	—
56	C₇×D₇	—	11	1	no	—
57	C₇×D₇	C₁₁×D₁₁	1	1	yes	characteristic, direct product factor
58	C₇×C₁₁	—	2	3	no	—
59	C₇×C₁₁	—	2	3	no	—
60	C₇×C₁₁	—	2	5	no	—
61	C₇×C₁₁	—	2	5	no	—
62	C₇×C₁₁	—	4	15	no	—
63	C₇×C₁₁	D₇×D₁₁	1	1	yes	characteristic, direct product factor
64	C₇×C₁₁	C₂×C₇×D₁₁	1	1	yes	characteristic, complemented
65	C₇×C₁₁	C₂×C₁₁×D₇	1	1	yes	characteristic, complemented
66	C₇×C₁₁	C₂²×C₇×C₁₁	1	1	yes	characteristic, complemented
67	C₇²	C₂×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₁₁	—	77	1	no	—
69	C₂×D₁₁	—	7	1	no	—
70	C₂²×C₇	—	77	1	no	—
71	C₂×D₇	—	11	1	no	—
72	C₂×C₁₁	—	7	1	no	—
73	C₂×C₁₁	—	7	1	no	—
74	C₂×C₁₁	—	11	1	no	—
75	C₂×C₁₁	—	14	5	no	—
76	C₂×C₁₁	—	77	1	no	—
77	D₁₁	—	7	1	no	—
78	D₁₁	C₇×C₁₁×D₇	1	1	yes	characteristic, direct product factor
79	C₂×C₇	—	7	1	no	—
80	C₂×C₇	—	11	1	no	—
81	C₂×C₇	—	11	1	no	—
82	C₂×C₇	—	22	3	no	—
83	C₂×C₇	—	77	1	no	—
84	D₇	—	11	1	no	—
85	D₇	C₇×C₁₁×D₁₁	1	1	yes	characteristic, direct product factor
86	C₁₁	—	2	5	no	—
87	C₁₁	C₇×D₇×D₁₁	1	1	yes	characteristic, direct product factor
88	C₁₁	C₂×C₇×C₁₁×D₇	1	1	yes	characteristic, complemented
89	C₇	—	2	3	no	—
90	C₇	C₁₁×D₇×D₁₁	1	1	yes	characteristic, direct product factor
91	C₇	C₂×C₇×C₁₁×D₁₁	1	1	yes	characteristic, complemented
92	C₂²	—	77	1	no	Sylow
93	C₂	—	7	1	no	—
94	C₂	—	11	1	no	—
95	C₂	—	77	1	no	—

	subgroup	G/H
center, hypercenter	C₇×C₁₁	D₇×D₁₁
commutator, cosocle, hypocenter	C₇×C₁₁	C₂²×C₇×C₁₁
Frattini	C₁	G
Fitting, socle	C₇²×C₁₁²	C₂²
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₇×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₇²×C₁₁×D₁₁	C₂	semidirect
2. C₇×C₁₁²×D₇	C₂	semidirect
3. C₇×C₁₁×D₇₇	C₂	semidirect
4. C₇²×C₁₁²	C₂²	semidirect
6. C₁₁×D₇×D₁₁	C₇	direct (N × H)
8. C₇×D₇×D₁₁	C₁₁	direct (N × H)
10. C₁₁×D₇₇	C₂×C₇	semidirect
11. C₁₁²×D₇	C₂×C₇	semidirect
14. C₇×C₁₁×D₁₁	D₇	direct (N × H)
15. C₇×C₁₁×D₁₁	C₂×C₇	semidirect
17. C₇×D₇₇	C₂×C₁₁	semidirect
20. C₇×C₁₁×D₇	D₁₁	direct (N × H)
21. C₇×C₁₁×D₇	C₂×C₁₁	semidirect
22. C₇²×D₁₁	C₂×C₁₁	semidirect
24. C₇×C₁₁²	C₂×D₇	semidirect
25. C₇×C₁₁²	C₂²×C₇	semidirect
27. C₇²×C₁₁	C₂×D₁₁	semidirect
28. C₇²×C₁₁	C₂²×C₁₁	semidirect
33. D₇×D₁₁	C₇×C₁₁	direct (N × H)
36. C₁₁×D₁₁	C₇×D₇	direct (N × H)
45. D₇₇	C₂×C₇×C₁₁	semidirect
48. C₇×D₁₁	C₁₁×D₇	direct (N × H)
49. C₇×D₁₁	C₂×C₇×C₁₁	semidirect
52. C₁₁×D₇	C₇×D₁₁	direct (N × H)
53. C₁₁×D₇	C₂×C₇×C₁₁	semidirect
54. C₁₁²	C₂×C₇×D₇	semidirect
57. C₇×D₇	C₁₁×D₁₁	direct (N × H)
63. C₇×C₁₁	D₇×D₁₁	direct (N × H)
64. C₇×C₁₁	C₂×C₇×D₁₁	semidirect
65. C₇×C₁₁	C₂×C₁₁×D₇	semidirect
66. C₇×C₁₁	C₂²×C₇×C₁₁	semidirect
67. C₇²	C₂×C₁₁×D₁₁	semidirect
78. D₁₁	C₇×C₁₁×D₇	direct (N × H)
85. D₇	C₇×C₁₁×D₁₁	direct (N × H)
87. C₁₁	C₇×D₇×D₁₁	direct (N × H)
88. C₁₁	C₂×C₇×C₁₁×D₇	semidirect
90. C₇	C₁₁×D₇×D₁₁	direct (N × H)
91. C₇	C₂×C₇×C₁₁×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₇²×C₁₁×D₁₁	2
C₇×C₁₁²×D₇	2
C₇×C₁₁×D₇₇	2
C₂×C₇×C₁₁×D₁₁	7
C₁₁×D₇×D₁₁	7
C₂×C₇×C₁₁×D₇	11
C₇×D₇×D₁₁	11

Subgroups — C7×C11×D7×D11 #37557402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₁×D₇×D₁₁ #37557402