Subgroups — C₃×C₇×C₁₁×D₅₁ #37555656

Order 23562.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₁×D₅₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₇×C₁₁×D₁₇	—	3	1	no	maximal
4	C₃×C₇×C₁₁×C₁₇	—	2	1	no	—
5	C₃×C₇×C₁₁×C₁₇	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₁₁×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×C₁₁×D₅₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₁₁×D₁₇	—	3	1	no	Hall
9	C₃×C₇×D₅₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃²×C₁₁×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
11	C₃×D₃×C₇×C₁₁	—	17	1	no	maximal, Hall
12	C₇×C₁₁×C₁₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₁₁×D₅₁	C₃×C₇	1	1	yes	characteristic, direct product factor
14	C₃×C₁₁×D₁₇	—	3	1	no	—
15	C₃²×C₇×C₁₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₇×D₅₁	C₃×C₁₁	1	1	yes	characteristic, direct product factor
17	C₃×C₇×D₁₇	—	3	1	no	—
18	C₃²×C₇×C₁₁	D₁₇	1	1	yes	characteristic, complemented, Hall
19	C₃×C₁₁×C₁₇	—	2	1	no	—
20	C₃×C₁₁×C₁₇	D₃×C₇	1	1	yes	characteristic, complemented
21	C₃×C₁₁×C₁₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
22	C₂×C₃×C₇×C₁₁	—	51	1	no	—
23	D₃×C₇×C₁₁	—	17	1	no	—
24	C₁₁×D₁₇	—	3	1	no	Hall
25	C₃×C₇×C₁₇	—	2	1	no	—
26	C₃×C₇×C₁₇	D₃×C₁₁	1	1	yes	characteristic, complemented
27	C₃×C₇×C₁₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
28	C₃×D₅₁	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
29	C₇×D₁₇	—	3	1	no	Hall
30	C₃×C₇×C₁₁	—	2	1	no	—
31	C₃×C₇×C₁₁	C₃×D₁₇	1	1	yes	characteristic, complemented
32	C₃×C₇×C₁₁	D₅₁	1	1	yes	characteristic, direct product factor
33	C₃×D₃×C₁₁	—	17	1	no	Hall
34	C₁₁×C₁₇	C₃×D₃×C₇	1	1	yes	characteristic, complemented, Hall
35	C₂×C₇×C₁₁	—	51	1	no	Hall
36	C₃²×C₁₇	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented, Hall
37	C₃×D₃×C₇	—	17	1	no	Hall
38	C₇×C₁₇	C₃×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
39	D₅₁	C₃×C₇×C₁₁	1	1	yes	characteristic, direct product factor
40	C₃×D₁₇	—	3	1	no	—
41	C₃²×C₁₁	C₇×D₁₇	1	1	yes	characteristic, complemented, Hall
42	C₇×C₁₁	C₃×D₅₁	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₃×C₁₁	—	51	1	no	—
44	D₃×C₁₁	—	17	1	no	—
45	C₃²×C₇	C₁₁×D₁₇	1	1	yes	characteristic, complemented, Hall
46	C₃×C₁₇	—	2	1	no	—
47	C₃×C₁₇	D₃×C₇×C₁₁	1	1	yes	characteristic, complemented
48	C₃×C₁₇	C₂×C₃×C₇×C₁₁	1	1	yes	characteristic, complemented
49	C₂×C₃×C₇	—	51	1	no	—
50	D₃×C₇	—	17	1	no	—
51	D₁₇	—	3	1	no	Hall
52	C₃×C₁₁	—	2	1	no	—
53	C₃×C₁₁	C₃×C₇×D₁₇	1	1	yes	characteristic, complemented
54	C₃×C₁₁	C₇×D₅₁	1	1	yes	characteristic, direct product factor
55	C₂×C₁₁	—	51	1	no	Hall
56	C₃×C₇	—	2	1	no	—
57	C₃×C₇	C₃×C₁₁×D₁₇	1	1	yes	characteristic, complemented
58	C₃×C₇	C₁₁×D₅₁	1	1	yes	characteristic, direct product factor
59	C₃×D₃	—	17	1	no	Hall
60	C₁₇	C₃×D₃×C₇×C₁₁	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₇	—	51	1	no	Hall
62	C₁₁	C₃×C₇×D₅₁	1	1	yes	characteristic, direct product factor, Sylow
63	C₃²	C₇×C₁₁×D₁₇	1	1	yes	characteristic, complemented, Sylow
64	C₇	C₃×C₁₁×D₅₁	1	1	yes	characteristic, direct product factor, Sylow
65	C₂×C₃	—	51	1	no	—
66	D₃	—	17	1	no	—
67	C₃	—	2	1	no	—
68	C₃	C₃×C₇×C₁₁×D₁₇	1	1	yes	characteristic, complemented
69	C₃	C₇×C₁₁×D₅₁	1	1	yes	characteristic, direct product factor
70	C₂	—	51	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇×C₁₁	D₅₁
commutator, cosocle, hypocenter	C₃×C₁₇	C₂×C₃×C₇×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁×C₁₇	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₃×C₇×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁×C₁₇	C₂	semidirect
2. C₇×C₁₁×D₅₁	C₃	direct (N × H)
5. C₃×C₇×C₁₁×C₁₇	D₃	semidirect
6. C₃×C₇×C₁₁×C₁₇	C₂×C₃	semidirect
7. C₃×C₁₁×D₅₁	C₇	direct (N × H)
9. C₃×C₇×D₅₁	C₁₁	direct (N × H)
10. C₃²×C₁₁×C₁₇	C₂×C₇	semidirect
12. C₇×C₁₁×C₁₇	C₃×D₃	semidirect
13. C₁₁×D₅₁	C₃×C₇	direct (N × H)
15. C₃²×C₇×C₁₇	C₂×C₁₁	semidirect
16. C₇×D₅₁	C₃×C₁₁	direct (N × H)
18. C₃²×C₇×C₁₁	D₁₇	semidirect
20. C₃×C₁₁×C₁₇	D₃×C₇	semidirect
21. C₃×C₁₁×C₁₇	C₂×C₃×C₇	semidirect
26. C₃×C₇×C₁₇	D₃×C₁₁	semidirect
27. C₃×C₇×C₁₇	C₂×C₃×C₁₁	semidirect
28. C₃×D₅₁	C₇×C₁₁	direct (N × H)
31. C₃×C₇×C₁₁	C₃×D₁₇	semidirect
32. C₃×C₇×C₁₁	D₅₁	direct (N × H)
34. C₁₁×C₁₇	C₃×D₃×C₇	semidirect
36. C₃²×C₁₇	C₂×C₇×C₁₁	semidirect
38. C₇×C₁₇	C₃×D₃×C₁₁	semidirect
39. D₅₁	C₃×C₇×C₁₁	direct (N × H)
41. C₃²×C₁₁	C₇×D₁₇	semidirect
42. C₇×C₁₁	C₃×D₅₁	direct (N × H)
45. C₃²×C₇	C₁₁×D₁₇	semidirect
47. C₃×C₁₇	D₃×C₇×C₁₁	semidirect
48. C₃×C₁₇	C₂×C₃×C₇×C₁₁	semidirect
53. C₃×C₁₁	C₃×C₇×D₁₇	semidirect
54. C₃×C₁₁	C₇×D₅₁	direct (N × H)
57. C₃×C₇	C₃×C₁₁×D₁₇	semidirect
58. C₃×C₇	C₁₁×D₅₁	direct (N × H)
60. C₁₇	C₃×D₃×C₇×C₁₁	semidirect
62. C₁₁	C₃×C₇×D₅₁	direct (N × H)
63. C₃²	C₇×C₁₁×D₁₇	semidirect
64. C₇	C₃×C₁₁×D₅₁	direct (N × H)
68. C₃	C₃×C₇×C₁₁×D₁₇	semidirect
69. C₃	C₇×C₁₁×D₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₇×C₁₁×C₁₇	2
C₇×C₁₁×D₅₁	3
C₃×C₇×C₁₁×D₁₇	3
C₃×C₁₁×D₅₁	7
C₃×C₇×D₅₁	11
C₃×D₃×C₇×C₁₁	17

Subgroups — C3×C7×C11×D51 #37555656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₁₁×D₅₁ #37555656