Subgroups — C₂×C₇×C₁₁×D₅₁ #30628175

Order 15708.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁×D₅₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×C₁₁×D₁₇	—	3	1	no	maximal, Hall
4	C₃×C₇×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₁×D₁₇	—	3	2	no	—
6	C₂×C₇×C₁₁×C₁₇	D₃	1	1	yes	characteristic, complemented
7	C₂×C₁₁×D₅₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×D₅₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₁₁×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₁₁×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented
11	C₁₁×D₅₁	C₂×C₇	1	2	yes	direct product factor
12	C₂×D₃×C₇×C₁₁	—	17	1	no	maximal, Hall
13	C₂×C₁₁×D₁₇	—	3	1	no	Hall
14	C₂×C₃×C₇×C₁₇	C₂×C₁₁	1	1	yes	characteristic, complemented
15	C₇×D₅₁	C₂×C₁₁	1	2	yes	direct product factor
16	C₃×C₁₁×C₁₇	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₇×D₁₇	—	3	1	no	Hall
18	C₂×C₃×C₇×C₁₁	D₁₇	1	1	yes	characteristic, complemented
19	D₃×C₇×C₁₁	—	17	2	no	—
20	C₂×C₁₁×C₁₇	D₃×C₇	1	1	yes	characteristic, complemented
21	C₁₁×D₁₇	—	3	2	no	—
22	C₃×C₇×C₁₇	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
23	C₂²×C₇×C₁₁	—	51	1	no	Hall
24	C₂×C₇×C₁₇	D₃×C₁₁	1	1	yes	characteristic, complemented
25	C₇×D₁₇	—	3	2	no	—
26	C₃×C₇×C₁₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
27	C₂×D₅₁	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
28	C₁₁×C₁₇	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
29	C₂×C₇×C₁₁	—	51	2	no	—
30	C₂×C₇×C₁₁	D₅₁	1	1	yes	characteristic, direct product factor
31	C₂×D₃×C₁₁	—	17	1	no	Hall
32	C₇×C₁₇	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₁₇	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented
34	D₅₁	C₂×C₇×C₁₁	1	2	yes	direct product factor
35	C₂×D₃×C₇	—	17	1	no	Hall
36	C₇×C₁₁	C₂×D₅₁	1	1	yes	characteristic, direct product factor, Hall
37	C₂×D₁₇	—	3	1	no	Hall
38	C₂×C₃×C₁₁	C₇×D₁₇	1	1	yes	characteristic, complemented
39	D₃×C₁₁	—	17	2	no	—
40	C₃×C₁₇	C₂²×C₇×C₁₁	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₁₁	—	51	1	no	Hall
42	C₂×C₃×C₇	C₁₁×D₁₇	1	1	yes	characteristic, complemented
43	D₃×C₇	—	17	2	no	—
44	C₂×C₁₇	D₃×C₇×C₁₁	1	1	yes	characteristic, complemented
45	D₁₇	—	3	2	no	—
46	C₃×C₁₁	C₂×C₇×D₁₇	1	1	yes	characteristic, complemented, Hall
47	C₂²×C₇	—	51	1	no	Hall
48	C₂×C₁₁	—	51	2	no	—
49	C₂×C₁₁	C₇×D₅₁	1	1	yes	characteristic, direct product factor
50	C₃×C₇	C₂×C₁₁×D₁₇	1	1	yes	characteristic, complemented, Hall
51	C₁₇	C₂×D₃×C₇×C₁₁	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₇	—	51	2	no	—
53	C₂×C₇	C₁₁×D₅₁	1	1	yes	characteristic, direct product factor
54	C₂×D₃	—	17	1	no	Hall
55	C₁₁	C₂×C₇×D₅₁	1	1	yes	characteristic, direct product factor, Sylow
56	C₇	C₂×C₁₁×D₅₁	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₃	C₇×C₁₁×D₁₇	1	1	yes	characteristic, complemented
58	D₃	—	17	2	no	—
59	C₂²	—	51	1	no	Sylow
60	C₃	C₂×C₇×C₁₁×D₁₇	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	51	2	no	—
62	C₂	C₇×C₁₁×D₅₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₁	D₅₁
commutator, cosocle, hypocenter	C₃×C₁₇	C₂²×C₇×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₁×C₁₇	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₂×C₇×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₁×D₅₁	C₂	direct (N × H)
2. C₂×C₃×C₇×C₁₁×C₁₇	C₂	semidirect
4. C₃×C₇×C₁₁×C₁₇	C₂²	semidirect
6. C₂×C₇×C₁₁×C₁₇	D₃	semidirect
7. C₂×C₁₁×D₅₁	C₇	direct (N × H)
8. C₂×C₇×D₅₁	C₁₁	direct (N × H)
9. C₇×C₁₁×C₁₇	C₂×D₃	semidirect
10. C₂×C₃×C₁₁×C₁₇	C₂×C₇	semidirect
11. C₁₁×D₅₁	C₂×C₇	direct (N × H)
14. C₂×C₃×C₇×C₁₇	C₂×C₁₁	semidirect
15. C₇×D₅₁	C₂×C₁₁	direct (N × H)
16. C₃×C₁₁×C₁₇	C₂²×C₇	semidirect
18. C₂×C₃×C₇×C₁₁	D₁₇	semidirect
20. C₂×C₁₁×C₁₇	D₃×C₇	semidirect
22. C₃×C₇×C₁₇	C₂²×C₁₁	semidirect
24. C₂×C₇×C₁₇	D₃×C₁₁	semidirect
26. C₃×C₇×C₁₁	C₂×D₁₇	semidirect
27. C₂×D₅₁	C₇×C₁₁	direct (N × H)
28. C₁₁×C₁₇	C₂×D₃×C₇	semidirect
30. C₂×C₇×C₁₁	D₅₁	direct (N × H)
32. C₇×C₁₇	C₂×D₃×C₁₁	semidirect
33. C₂×C₃×C₁₇	C₂×C₇×C₁₁	semidirect
34. D₅₁	C₂×C₇×C₁₁	direct (N × H)
36. C₇×C₁₁	C₂×D₅₁	direct (N × H)
38. C₂×C₃×C₁₁	C₇×D₁₇	semidirect
40. C₃×C₁₇	C₂²×C₇×C₁₁	semidirect
42. C₂×C₃×C₇	C₁₁×D₁₇	semidirect
44. C₂×C₁₇	D₃×C₇×C₁₁	semidirect
46. C₃×C₁₁	C₂×C₇×D₁₇	semidirect
49. C₂×C₁₁	C₇×D₅₁	direct (N × H)
50. C₃×C₇	C₂×C₁₁×D₁₇	semidirect
51. C₁₇	C₂×D₃×C₇×C₁₁	semidirect
53. C₂×C₇	C₁₁×D₅₁	direct (N × H)
55. C₁₁	C₂×C₇×D₅₁	direct (N × H)
56. C₇	C₂×C₁₁×D₅₁	direct (N × H)
57. C₂×C₃	C₇×C₁₁×D₁₇	semidirect
60. C₃	C₂×C₇×C₁₁×D₁₇	semidirect
62. C₂	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
C₇×C₁₁×D₅₁	2
C₂×C₃×C₇×C₁₁×C₁₇	2
C₂×C₇×C₁₁×D₁₇	3
C₂×C₁₁×D₅₁	7
C₂×C₇×D₅₁	11
C₂×D₃×C₇×C₁₁	17

Subgroups — C2×C7×C11×D51 #30628175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₁₁×D₅₁ #30628175