Subgroups — C₁₁×D₂₁⋊D₁₁ #23779064

Order 10164.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₁₁×D₃₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁×D₇₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×D₇×D₁₁	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₁×D₇₇	D₃	1	1	yes	characteristic, complemented
7	C₁₁²×D₇	—	3	1	no	—
8	C₇×C₁₁×D₁₁	—	3	1	no	—
9	D₃×C₁₁×D₁₁	—	7	1	no	maximal, Hall
10	D₂₁⋊D₁₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor
11	D₃×C₁₁×D₇	—	11	1	no	maximal
12	C₇×C₁₁²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
13	C₁₁×D₃₃	D₇	1	1	yes	characteristic, complemented
14	D₃×C₁₁²	—	7	1	no	—
15	C₃×C₁₁×D₁₁	—	7	1	no	—
16	C₂×C₁₁×D₁₁	—	21	1	no	Hall
17	C₁₁×D₂₁	—	2	5	no	—
18	C₁₁×D₂₁	D₁₁	1	1	yes	characteristic, complemented
19	C₁₁×D₂₁	C₂×C₁₁	1	1	yes	characteristic, complemented
20	C₇×D₃₃	C₂×C₁₁	1	1	yes	characteristic, complemented
21	D₃×C₇×C₁₁	—	11	1	no	—
22	C₃×D₇₇	C₂×C₁₁	1	1	yes	characteristic, complemented
23	C₃×C₁₁×D₇	—	11	1	no	—
24	C₃×C₁₁²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
25	C₂×C₁₁×D₇	—	33	1	no	—
26	D₇×D₁₁	—	3	1	no	—
27	C₂×C₁₁²	—	21	1	no	—
28	C₁₁×D₁₁	—	3	1	no	—
29	C₁₁×D₁₁	—	7	1	no	—
30	C₃×C₇×C₁₁	—	2	5	no	—
31	C₃×C₇×C₁₁	C₂×D₁₁	1	1	yes	characteristic, complemented
32	C₃×C₇×C₁₁	C₂²×C₁₁	1	1	yes	characteristic, complemented
33	C₂×C₇×C₁₁	—	33	1	no	—
34	D₇₇	D₃×C₁₁	1	1	yes	characteristic, complemented
35	C₇×D₁₁	—	3	1	no	—
36	C₁₁×D₇	—	3	1	no	—
37	C₁₁×D₇	—	3	1	no	—
38	C₁₁×D₇	—	6	5	no	—
39	C₁₁×D₇	—	11	1	no	—
40	C₂×D₃×C₁₁	—	77	1	no	—
41	D₃×D₁₁	—	7	1	no	—
42	C₁₁²	D₃×D₇	1	1	yes	characteristic, complemented, Sylow
43	D₃×D₇	—	11	1	no	Hall
44	C₇×C₁₁	—	2	5	no	—
45	C₇×C₁₁	D₃×D₁₁	1	1	yes	characteristic, complemented
46	C₇×C₁₁	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented
47	C₂×C₃×C₁₁	—	77	1	no	—
48	D₃₃	C₁₁×D₇	1	1	yes	characteristic, complemented
49	C₃×D₁₁	—	7	1	no	—
50	D₃×C₁₁	—	7	1	no	—
51	D₃×C₁₁	—	7	1	no	—
52	D₃×C₁₁	—	11	1	no	—
53	D₃×C₁₁	—	14	5	no	—
54	C₂²×C₁₁	—	231	1	no	—
55	C₂×D₁₁	—	21	1	no	—
56	D₂₁	C₁₁×D₁₁	1	1	yes	characteristic, complemented
57	C₃×D₇	—	11	1	no	—
58	D₃×C₇	—	11	1	no	—
59	C₃×C₁₁	—	2	5	no	—
60	C₃×C₁₁	D₇×D₁₁	1	1	yes	characteristic, complemented
61	C₃×C₁₁	C₂×C₁₁×D₇	1	1	yes	characteristic, complemented
62	C₂×D₇	—	33	1	no	Hall
63	C₂×C₁₁	—	21	1	no	—
64	C₂×C₁₁	—	21	1	no	—
65	C₂×C₁₁	—	33	1	no	—
66	C₂×C₁₁	—	42	5	no	—
67	C₂×C₁₁	—	77	1	no	—
68	D₁₁	—	3	1	no	—
69	D₁₁	—	7	1	no	—
70	C₃×C₇	C₂×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
71	C₂×C₇	—	33	1	no	—
72	D₇	—	3	1	no	—
73	D₇	—	11	1	no	—
74	C₂×D₃	—	77	1	no	Hall
75	C₁₁	—	2	5	no	—
76	C₁₁	D₃×C₁₁×D₇	1	1	yes	characteristic, complemented
77	C₁₁	D₂₁⋊D₁₁	1	1	yes	characteristic, direct product factor
78	C₇	D₃×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Sylow
79	C₂×C₃	—	77	1	no	—
80	D₃	—	7	1	no	—
81	D₃	—	11	1	no	—
82	C₂²	—	231	1	no	Sylow
83	C₃	C₁₁×D₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	21	1	no	—
85	C₂	—	33	1	no	—
86	C₂	—	77	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	D₂₁⋊D₁₁
commutator, cosocle, hypocenter	C₃×C₇×C₁₁	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁²	C₂²
LCS	G ▷ C₃×C₇×C₁₁
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁²×D₂₁	C₂	semidirect
2. C₇×C₁₁×D₃₃	C₂	semidirect
3. C₃×C₁₁×D₇₇	C₂	semidirect
5. C₃×C₇×C₁₁²	C₂²	semidirect
6. C₁₁×D₇₇	D₃	semidirect
10. D₂₁⋊D₁₁	C₁₁	direct (N × H)
12. C₇×C₁₁²	C₂×D₃	semidirect
13. C₁₁×D₃₃	D₇	semidirect
18. C₁₁×D₂₁	D₁₁	semidirect
19. C₁₁×D₂₁	C₂×C₁₁	semidirect
20. C₇×D₃₃	C₂×C₁₁	semidirect
22. C₃×D₇₇	C₂×C₁₁	semidirect
24. C₃×C₁₁²	C₂×D₇	semidirect
31. C₃×C₇×C₁₁	C₂×D₁₁	semidirect
32. C₃×C₇×C₁₁	C₂²×C₁₁	semidirect
34. D₇₇	D₃×C₁₁	semidirect
42. C₁₁²	D₃×D₇	semidirect
45. C₇×C₁₁	D₃×D₁₁	semidirect
46. C₇×C₁₁	C₂×D₃×C₁₁	semidirect
48. D₃₃	C₁₁×D₇	semidirect
56. D₂₁	C₁₁×D₁₁	semidirect
60. C₃×C₁₁	D₇×D₁₁	semidirect
61. C₃×C₁₁	C₂×C₁₁×D₇	semidirect
70. C₃×C₇	C₂×C₁₁×D₁₁	semidirect
76. C₁₁	D₃×C₁₁×D₇	semidirect
77. C₁₁	D₂₁⋊D₁₁	direct (N × H)
78. C₇	D₃×C₁₁×D₁₁	semidirect
83. C₃	C₁₁×D₇×D₁₁	semidirect

Subgroups — C11×D21⋊D11 #23779064

Conjugacy classes of subgroups

Complements

Subgroups — C₁₁×D₂₁⋊D₁₁ #23779064