Subgroups — D₃₃×D₇₇ #23779068

Order 10164.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₇⋊(C₁₁⋊D₁₁))	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	D₁₁×D₇₇	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇⋊(C₁₁⋊D₁₁)	—	3	1	no	—
7	C₁₁×D₇₇	D₃	1	1	yes	characteristic, complemented
8	C₇×C₁₁×D₁₁	—	3	1	no	—
9	D₁₁×D₃₃	—	7	1	no	maximal, Hall
10	D₃×D₇₇	—	11	1	no	maximal
11	D₇×D₃₃	—	11	1	no	maximal
12	C₇×C₁₁²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃⋊(C₁₁⋊D₁₁)	—	7	1	no	—
14	C₁₁×D₃₃	D₇	1	1	yes	characteristic, complemented
15	C₃×C₁₁×D₁₁	—	7	1	no	—
16	D₁₁²	—	21	1	no	Hall
17	D₂₃₁	—	11	1	no	—
18	D₂₃₁	—	11	1	no	—
19	D₂₃₁	—	22	5	no	—
20	C₇×D₃₃	D₁₁	1	1	yes	characteristic, complemented
21	D₃×C₇×C₁₁	—	11	1	no	—
22	C₃×D₇₇	D₁₁	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	—	33	1	no	—
26	D₇×D₁₁	—	33	1	no	—
27	C₁₁⋊D₁₁	—	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	C₂×D₁₁	1	1	yes	characteristic, complemented
33	C₂×C₇×C₁₁	—	33	1	no	—
34	D₇₇	—	33	1	no	—
35	D₇₇	—	33	1	no	—
36	D₇₇	—	66	5	no	—
37	D₇₇	D₃₃	1	1	yes	characteristic, direct product factor
38	C₇×D₁₁	—	3	1	no	—
39	C₁₁×D₇	—	11	1	no	—
40	C₂×D₃₃	—	77	1	no	—
41	D₃×D₁₁	—	77	1	no	—
42	C₁₁²	D₃×D₇	1	1	yes	characteristic, complemented, Sylow
43	D₃×D₇	—	121	1	no	Hall
44	C₇×C₁₁	—	2	5	no	—
45	C₇×C₁₁	D₃×D₁₁	1	1	yes	characteristic, complemented
46	C₇×C₁₁	C₂×D₃₃	1	1	yes	characteristic, complemented
47	C₂×C₃×C₁₁	—	77	1	no	—
48	D₃₃	—	77	1	no	—
49	D₃₃	—	77	1	no	—
50	D₃₃	—	154	5	no	—
51	D₃₃	D₇₇	1	1	yes	characteristic, direct product factor
52	C₃×D₁₁	—	7	1	no	—
53	D₃×C₁₁	—	11	1	no	—
54	C₂×D₁₁	—	231	1	no	—
55	C₂×D₁₁	—	231	1	no	—
56	D₂₁	—	121	1	no	—
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×D₇₇	1	1	yes	characteristic, complemented
62	C₂×D₇	—	363	1	no	Hall
63	C₂×C₁₁	—	33	1	no	—
64	C₂×C₁₁	—	77	1	no	—
65	D₁₁	—	3	1	no	—
66	D₁₁	—	7	1	no	—
67	D₁₁	—	462	5	no	—
68	D₁₁	—	231	1	no	—
69	D₁₁	—	231	1	no	—
70	C₃×C₇	D₁₁²	1	1	yes	characteristic, complemented, Hall
71	C₂×C₇	—	33	1	no	—
72	D₇	—	11	1	no	—
73	D₇	—	363	1	no	—
74	C₂×D₃	—	847	1	no	Hall
75	C₁₁	—	2	5	no	—
76	C₁₁	D₇×D₃₃	1	1	yes	characteristic, complemented
77	C₁₁	D₃×D₇₇	1	1	yes	characteristic, complemented
78	C₇	D₁₁×D₃₃	1	1	yes	characteristic, complemented, Sylow
79	C₂×C₃	—	77	1	no	—
80	D₃	—	11	1	no	—
81	D₃	—	847	1	no	—
82	C₂²	—	2541	1	no	Sylow
83	C₃	D₁₁×D₇₇	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	33	1	no	—
85	C₂	—	77	1	no	—
86	C₂	—	2541	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₇⋊(C₁₁⋊D₁₁))	C₂	semidirect
2. C₇×C₁₁×D₃₃	C₂	semidirect
3. C₃×C₁₁×D₇₇	C₂	semidirect
5. C₃×C₇×C₁₁²	C₂²	semidirect
7. C₁₁×D₇₇	D₃	semidirect
12. C₇×C₁₁²	C₂×D₃	semidirect
14. C₁₁×D₃₃	D₇	semidirect
20. C₇×D₃₃	D₁₁	semidirect
22. C₃×D₇₇	D₁₁	semidirect
24. C₃×C₁₁²	C₂×D₇	semidirect
31. C₃×C₇×C₁₁	C₂×D₁₁	semidirect
32. C₃×C₇×C₁₁	C₂×D₁₁	semidirect
37. D₇₇	D₃₃	direct (N × H)
42. C₁₁²	D₃×D₇	semidirect
45. C₇×C₁₁	D₃×D₁₁	semidirect
46. C₇×C₁₁	C₂×D₃₃	semidirect
51. D₃₃	D₇₇	direct (N × H)
60. C₃×C₁₁	D₇×D₁₁	semidirect
61. C₃×C₁₁	C₂×D₇₇	semidirect
70. C₃×C₇	D₁₁²	semidirect
76. C₁₁	D₇×D₃₃	semidirect
77. C₁₁	D₃×D₇₇	semidirect
78. C₇	D₁₁×D₃₃	semidirect
83. C₃	D₁₁×D₇₇	semidirect

Subgroups — D33×D77 #23779068

Conjugacy classes of subgroups

Complements

Subgroups — D₃₃×D₇₇ #23779068