Subgroups — D₃×C₁₁×D₇₇ #23779063

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	D₃×C₇×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁×D₇₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×D₇₇	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₇×C₁₁²	—	3	1	no	—
7	C₁₁×D₇₇	—	3	1	no	—
8	C₁₁×D₇₇	D₃	1	1	yes	characteristic, direct product factor
9	D₃×C₁₁×D₁₁	—	7	1	no	maximal, Hall
10	D₃×D₇₇	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	—	7	1	no	—
14	D₃×C₁₁²	D₇	1	1	yes	characteristic, complemented
15	C₃×C₁₁×D₁₁	—	7	1	no	—
16	C₂×C₁₁×D₁₁	—	21	1	no	Hall
17	D₂₃₁	C₂×C₁₁	1	1	yes	characteristic, complemented
18	C₁₁×D₂₁	—	11	1	no	—
19	D₃×C₇×C₁₁	—	2	5	no	—
20	D₃×C₇×C₁₁	D₁₁	1	1	yes	characteristic, complemented
21	D₃×C₇×C₁₁	C₂×C₁₁	1	1	yes	characteristic, complemented
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×D₇₇	—	3	1	no	—
26	C₂×C₁₁×D₇	—	33	1	no	—
27	C₂×C₁₁²	—	3	1	no	—
28	C₁₁×D₁₁	—	7	1	no	—
29	C₁₁×D₁₁	—	21	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	—	3	1	no	—
34	C₂×C₇×C₁₁	—	3	1	no	—
35	C₂×C₇×C₁₁	—	6	5	no	—
36	D₇₇	—	3	1	no	—
37	D₇₇	D₃×C₁₁	1	1	yes	characteristic, direct product factor
38	C₁₁×D₇	—	11	1	no	—
39	C₁₁×D₇	—	33	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	—	7	1	no	—
49	C₃×D₁₁	—	7	1	no	—
50	D₃×C₁₁	—	2	5	no	—
51	D₃×C₁₁	—	77	1	no	—
52	D₃×C₁₁	C₁₁×D₇	1	1	yes	characteristic, complemented
53	D₃×C₁₁	D₇₇	1	1	yes	characteristic, direct product factor
54	C₂²×C₁₁	—	231	1	no	—
55	C₂×D₁₁	—	21	1	no	—
56	D₂₁	—	11	1	no	—
57	C₃×D₇	—	11	1	no	—
58	D₃×C₇	C₁₁×D₁₁	1	1	yes	characteristic, complemented
59	C₃×C₁₁	—	2	5	no	—
60	C₃×C₁₁	C₂×C₁₁×D₇	1	1	yes	characteristic, complemented
61	C₃×C₁₁	C₂×D₇₇	1	1	yes	characteristic, complemented
62	C₂×D₇	—	33	1	no	Hall
63	C₂×C₁₁	—	3	1	no	—
64	C₂×C₁₁	—	3	1	no	—
65	C₂×C₁₁	—	6	5	no	—
66	C₂×C₁₁	—	77	1	no	—
67	C₂×C₁₁	—	231	1	no	—
68	D₁₁	—	7	1	no	—
69	D₁₁	—	21	1	no	—
70	C₃×C₇	C₂×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
71	C₂×C₇	—	3	1	no	—
72	D₇	—	11	1	no	—
73	D₇	—	33	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	D₃×D₇₇	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	—	77	1	no	—
81	D₃	C₁₁×D₇₇	1	1	yes	characteristic, direct product factor
82	C₂²	—	231	1	no	Sylow
83	C₃	C₂×C₁₁×D₇₇	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	3	1	no	—
85	C₂	—	77	1	no	—
86	C₂	—	231	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	D₃×D₇₇
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. D₃×C₇×C₁₁²	C₂	semidirect
3. C₃×C₁₁×D₇₇	C₂	semidirect
5. C₃×C₇×C₁₁²	C₂²	semidirect
8. C₁₁×D₇₇	D₃	direct (N × H)
10. D₃×D₇₇	C₁₁	direct (N × H)
12. C₇×C₁₁²	C₂×D₃	semidirect
14. D₃×C₁₁²	D₇	semidirect
17. D₂₃₁	C₂×C₁₁	semidirect
20. D₃×C₇×C₁₁	D₁₁	semidirect
21. D₃×C₇×C₁₁	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
37. D₇₇	D₃×C₁₁	direct (N × H)
42. C₁₁²	D₃×D₇	semidirect
45. C₇×C₁₁	D₃×D₁₁	semidirect
46. C₇×C₁₁	C₂×D₃×C₁₁	semidirect
52. D₃×C₁₁	C₁₁×D₇	semidirect
53. D₃×C₁₁	D₇₇	direct (N × H)
58. D₃×C₇	C₁₁×D₁₁	semidirect
60. C₃×C₁₁	C₂×C₁₁×D₇	semidirect
61. C₃×C₁₁	C₂×D₇₇	semidirect
70. C₃×C₇	C₂×C₁₁×D₁₁	semidirect
76. C₁₁	D₃×C₁₁×D₇	semidirect
77. C₁₁	D₃×D₇₇	direct (N × H)
78. C₇	D₃×C₁₁×D₁₁	semidirect
81. D₃	C₁₁×D₇₇	direct (N × H)
83. C₃	C₂×C₁₁×D₇₇	semidirect

Subgroups — D3×C11×D77 #23779063

Conjugacy classes of subgroups

Complements

Subgroups — D₃×C₁₁×D₇₇ #23779063