Subgroups — C₁₁×D₁₁×D₂₁ #23779056

Order 10164.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₂₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁²×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₁₁×D₁₁	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	—	3	1	no	—
7	C₁₁²×D₇	—	3	1	no	—
8	C₇×C₁₁×D₁₁	D₃	1	1	yes	characteristic, complemented
9	D₃×C₁₁×D₁₁	—	7	1	no	maximal, Hall
10	C₂×C₁₁×D₂₁	—	11	1	no	maximal
11	D₁₁×D₂₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor
12	C₇×C₁₁²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
13	C₁₁×D₃₃	—	7	1	no	—
14	D₃×C₁₁²	—	7	1	no	—
15	C₃×C₁₁×D₁₁	D₇	1	1	yes	characteristic, complemented
16	C₂×C₁₁×D₁₁	—	21	1	no	Hall
17	C₂×C₃×C₇×C₁₁	—	11	1	no	—
18	D₂₃₁	C₂×C₁₁	1	1	yes	characteristic, complemented
19	C₁₁×D₂₁	—	2	5	no	—
20	C₁₁×D₂₁	—	11	1	no	—
21	C₁₁×D₂₁	D₁₁	1	1	yes	characteristic, direct product factor
22	C₁₁×D₂₁	C₂×C₁₁	1	1	yes	characteristic, complemented
23	C₃×C₇×D₁₁	C₂×C₁₁	1	1	yes	characteristic, complemented
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	—	21	1	no	—
29	C₁₁×D₁₁	D₂₁	1	1	yes	characteristic, direct product factor
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	—	11	1	no	—
34	D₇₇	—	3	1	no	—
35	C₇×D₁₁	D₃×C₁₁	1	1	yes	characteristic, complemented
36	C₁₁×D₇	—	3	1	no	—
37	C₁₁×D₇	—	3	1	no	—
38	C₁₁×D₇	—	6	5	no	—
39	C₁₁×D₇	—	33	1	no	—
40	C₂×D₃×C₁₁	—	77	1	no	—
41	D₃×D₁₁	—	7	1	no	—
42	C₁₁²	C₂×D₂₁	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₂₁	—	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	—	11	1	no	—
48	D₃₃	—	7	1	no	—
49	C₃×D₁₁	C₁₁×D₇	1	1	yes	characteristic, complemented
50	D₃×C₁₁	—	7	1	no	—
51	D₃×C₁₁	—	7	1	no	—
52	D₃×C₁₁	—	14	5	no	—
53	D₃×C₁₁	—	77	1	no	—
54	C₂²×C₁₁	—	231	1	no	—
55	C₂×D₁₁	—	21	1	no	—
56	C₂×C₃×C₇	—	11	1	no	—
57	D₂₁	—	11	1	no	—
58	D₂₁	C₁₁×D₁₁	1	1	yes	characteristic, direct product factor
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	—	11	1	no	—
64	C₂×C₁₁	—	21	1	no	—
65	C₂×C₁₁	—	21	1	no	—
66	C₂×C₁₁	—	42	5	no	—
67	C₂×C₁₁	—	231	1	no	—
68	D₁₁	—	21	1	no	—
69	D₁₁	C₁₁×D₂₁	1	1	yes	characteristic, direct product factor
70	C₃×C₇	C₂×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
71	C₂×C₇	—	11	1	no	—
72	D₇	—	3	1	no	—
73	D₇	—	33	1	no	—
74	C₂×D₃	—	77	1	no	Hall
75	C₁₁	—	2	5	no	—
76	C₁₁	D₁₁×D₂₁	1	1	yes	characteristic, direct product factor
77	C₁₁	C₂×C₁₁×D₂₁	1	1	yes	characteristic, complemented
78	C₇	D₃×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Sylow
79	C₂×C₃	—	11	1	no	—
80	D₃	—	7	1	no	—
81	D₃	—	77	1	no	—
82	C₂²	—	231	1	no	Sylow
83	C₃	C₁₁×D₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	11	1	no	—
85	C₂	—	21	1	no	—
86	C₂	—	231	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	D₁₁×D₂₁
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. C₁₁×D₂₃₁	C₂	semidirect
2. C₁₁²×D₂₁	C₂	semidirect
3. C₃×C₇×C₁₁×D₁₁	C₂	semidirect
5. C₃×C₇×C₁₁²	C₂²	semidirect
8. C₇×C₁₁×D₁₁	D₃	semidirect
11. D₁₁×D₂₁	C₁₁	direct (N × H)
12. C₇×C₁₁²	C₂×D₃	semidirect
15. C₃×C₁₁×D₁₁	D₇	semidirect
18. D₂₃₁	C₂×C₁₁	semidirect
21. C₁₁×D₂₁	D₁₁	direct (N × H)
22. C₁₁×D₂₁	C₂×C₁₁	semidirect
23. C₃×C₇×D₁₁	C₂×C₁₁	semidirect
24. C₃×C₁₁²	C₂×D₇	semidirect
29. C₁₁×D₁₁	D₂₁	direct (N × H)
31. C₃×C₇×C₁₁	C₂×D₁₁	semidirect
32. C₃×C₇×C₁₁	C₂²×C₁₁	semidirect
35. C₇×D₁₁	D₃×C₁₁	semidirect
42. C₁₁²	C₂×D₂₁	semidirect
45. C₇×C₁₁	D₃×D₁₁	semidirect
46. C₇×C₁₁	C₂×D₃×C₁₁	semidirect
49. C₃×D₁₁	C₁₁×D₇	semidirect
58. D₂₁	C₁₁×D₁₁	direct (N × H)
60. C₃×C₁₁	D₇×D₁₁	semidirect
61. C₃×C₁₁	C₂×C₁₁×D₇	semidirect
69. D₁₁	C₁₁×D₂₁	direct (N × H)
70. C₃×C₇	C₂×C₁₁×D₁₁	semidirect
76. C₁₁	D₁₁×D₂₁	direct (N × H)
77. C₁₁	C₂×C₁₁×D₂₁	semidirect
78. C₇	D₃×C₁₁×D₁₁	semidirect
83. C₃	C₁₁×D₇×D₁₁	semidirect

Subgroups — C11×D11×D21 #23779056

Conjugacy classes of subgroups

Complements

Subgroups — C₁₁×D₁₁×D₂₁ #23779056