Subgroups — C₄×D₇×D₁₁ #11927713

Order 1232.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇×D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₄×D₇₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₁×D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₇×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	D₇₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	D₇×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
7	D₁₁×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₇₇	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×D₇	C₂²	1	1	yes	characteristic
10	C₂×C₇×D₁₁	C₂²	1	1	yes	characteristic
11	D₇×D₁₁	C₄	1	4	yes	direct product factor
12	C₄×C₇×C₁₁	C₂²	1	1	yes	characteristic, complemented
13	Dic₇₇	C₂²	1	1	yes	characteristic, complemented
14	C₇×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
15	C₁₁×Dic₇	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₄×D₁₁	—	7	1	no	maximal, Hall
17	C₂×C₇×C₁₁	C₂³	1	1	yes	characteristic
18	D₇₇	C₂×C₄	1	2	yes	complemented
19	C₇×D₁₁	C₂×C₄	1	2	yes	complemented
20	C₁₁×D₇	C₂×C₄	1	2	yes	complemented
21	C₂×C₄×D₇	—	11	1	no	maximal, Hall
22	C₂²×D₁₁	—	7	1	no	—
23	C₂×C₄×C₁₁	—	7	1	no	—
24	C₂×Dic₁₁	—	7	1	no	—
25	C₄×D₁₁	—	7	1	no	—
26	C₄×D₁₁	—	7	1	no	—
27	C₄×D₁₁	—	7	1	no	—
28	C₄×D₁₁	D₇	1	1	yes	characteristic, direct product factor
29	C₇×C₁₁	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
30	C₂²×D₇	—	11	1	no	—
31	C₂×C₄×C₇	—	11	1	no	—
32	C₂×Dic₇	—	11	1	no	—
33	C₄×D₇	—	11	1	no	—
34	C₄×D₇	—	11	1	no	—
35	C₄×D₇	—	11	1	no	—
36	C₄×D₇	D₁₁	1	1	yes	characteristic, direct product factor
37	C₂²×C₁₁	—	7	1	no	—
38	C₂×D₁₁	—	7	1	no	—
39	C₂×D₁₁	—	7	4	no	—
40	C₂×D₁₁	C₂×D₇	1	1	yes	characteristic
41	C₄×C₁₁	—	7	1	no	—
42	C₄×C₁₁	C₂×D₇	1	1	yes	characteristic, complemented
43	Dic₁₁	—	7	1	no	—
44	Dic₁₁	C₂×D₇	1	1	yes	characteristic, complemented
45	C₂²×C₇	—	11	1	no	—
46	C₂×D₇	—	11	1	no	—
47	C₂×D₇	—	11	4	no	—
48	C₂×D₇	C₂×D₁₁	1	1	yes	characteristic
49	C₄×C₇	—	11	1	no	—
50	C₄×C₇	C₂×D₁₁	1	1	yes	characteristic, complemented
51	Dic₇	—	11	1	no	—
52	Dic₇	C₂×D₁₁	1	1	yes	characteristic, complemented
53	C₂×C₁₁	—	7	2	no	—
54	C₂×C₁₁	C₂²×D₇	1	1	yes	characteristic
55	D₁₁	—	7	2	no	—
56	D₁₁	C₄×D₇	1	2	yes	direct product factor
57	C₂²×C₄	—	77	1	no	Sylow
58	C₂×C₇	—	11	2	no	—
59	C₂×C₇	C₂²×D₁₁	1	1	yes	characteristic
60	D₇	—	11	2	no	—
61	D₇	C₄×D₁₁	1	2	yes	direct product factor
62	C₁₁	C₂×C₄×D₇	1	1	yes	characteristic, complemented, Sylow
63	C₂³	—	77	1	no	—
64	C₂×C₄	—	7	1	no	—
65	C₂×C₄	—	11	1	no	—
66	C₂×C₄	—	77	1	no	—
67	C₂×C₄	—	77	1	no	—
68	C₂×C₄	—	77	1	no	—
69	C₂×C₄	—	77	1	no	—
70	C₇	C₂×C₄×D₁₁	1	1	yes	characteristic, complemented, Sylow
71	C₂²	—	7	1	no	—
72	C₂²	—	11	1	no	—
73	C₂²	—	77	4	no	—
74	C₂²	—	77	1	no	—
75	C₄	—	7	1	no	—
76	C₄	—	11	1	no	—
77	C₄	—	77	1	no	—
78	C₄	D₇×D₁₁	1	1	yes	characteristic, direct product factor
79	C₂	—	7	2	no	—
80	C₂	—	11	2	no	—
81	C₂	—	77	2	no	—
82	C₂	C₂×D₇×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	D₇×D₁₁
commutator, hypocenter	C₇×C₁₁	C₂²×C₄
Frattini	C₂	C₂×D₇×D₁₁
Fitting	C₄×C₇×C₁₁	C₂²
socle, cosocle	C₂×C₇×C₁₁	C₂³
prime radical	C₂×D₇×D₁₁	C₂
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₄×D₇₇	C₂	semidirect
3. C₄×C₁₁×D₇	C₂	semidirect
4. C₄×C₇×D₁₁	C₂	semidirect
5. D₇₇⋊C₄	C₂	semidirect
6. D₇×Dic₁₁	C₂	semidirect
7. D₁₁×Dic₇	C₂	semidirect
11. D₇×D₁₁	C₄	direct (N × H)
12. C₄×C₇×C₁₁	C₂²	semidirect
13. Dic₇₇	C₂²	semidirect
14. C₇×Dic₁₁	C₂²	semidirect
15. C₁₁×Dic₇	C₂²	semidirect
18. D₇₇	C₂×C₄	semidirect
19. C₇×D₁₁	C₂×C₄	semidirect
20. C₁₁×D₇	C₂×C₄	semidirect
28. C₄×D₁₁	D₇	direct (N × H)
29. C₇×C₁₁	C₂²×C₄	semidirect
36. C₄×D₇	D₁₁	direct (N × H)
42. C₄×C₁₁	C₂×D₇	semidirect
44. Dic₁₁	C₂×D₇	semidirect
50. C₄×C₇	C₂×D₁₁	semidirect
52. Dic₇	C₂×D₁₁	semidirect
56. D₁₁	C₄×D₇	direct (N × H)
61. D₇	C₄×D₁₁	direct (N × H)
62. C₁₁	C₂×C₄×D₇	semidirect
70. C₇	C₂×C₄×D₁₁	semidirect
78. C₄	D₇×D₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₇×D₁₁	2
C₄×D₇₇	2
C₄×C₁₁×D₇	2
C₄×C₇×D₁₁	2
D₇₇⋊C₄	2
D₇×Dic₁₁	2
D₁₁×Dic₇	2
C₂×C₄×D₁₁	7
C₂×C₄×D₇	11

Subgroups — C4×D7×D11 #11927713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₇×D₁₁ #11927713