Subgroups — C₂×C₁₁×D₇×C₅²⋊C₃ #37528577

Order 23100.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₁×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₇×C₅²⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅²×C₁₁×D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇×C₁₁×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅²×C₁₁×D₇	C₂×C₃	1	2	yes	complemented
6	C₂×C₅²×C₇×C₁₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂²×C₁₁×C₅²⋊C₃	—	7	1	no	maximal, Hall
8	C₂×D₇×C₅²⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅²×C₇×C₁₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁×C₅²⋊C₃	—	7	2	no	—
11	C₂×C₁₁×C₅²⋊C₃	D₇	1	1	yes	characteristic, direct product factor
12	C₂×C₅×C₁₁×D₇	—	3	2	no	—
13	C₂²×C₅²×C₁₁	—	7	1	no	Hall
14	C₂×C₇×C₅²⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented
15	D₇×C₅²⋊C₃	C₂×C₁₁	1	2	yes	direct product factor
16	C₂×C₃×C₁₁×D₇	—	25	1	no	maximal, Hall
17	C₁₁×C₅²⋊C₃	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₅×C₇×C₁₁	—	3	2	no	—
19	C₅×C₁₁×D₇	—	3	4	no	—
20	C₂×C₅²×D₇	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅²×C₁₁	—	7	2	no	—
22	C₂×C₅²×C₁₁	C₃×D₇	1	1	yes	characteristic, complemented
23	C₇×C₅²⋊C₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₇×C₁₁	—	25	1	no	—
25	C₃×C₁₁×D₇	—	25	2	no	—
26	C₅×C₇×C₁₁	—	3	2	no	—
27	C₂×C₅²×C₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
28	C₅²×D₇	C₂×C₃×C₁₁	1	2	yes	complemented
29	C₂×C₁₁×D₇	C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
30	C₂²×C₅²⋊C₃	—	7	1	no	Hall
31	C₅²×C₁₁	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
32	C₃×C₇×C₁₁	—	25	1	no	Hall
33	C₂²×C₅×C₁₁	—	21	2	no	—
34	C₅²×C₇	C₂²×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
35	C₂×C₇×C₁₁	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented
36	C₁₁×D₇	C₂×C₅²⋊C₃	1	2	yes	direct product factor
37	C₂×C₅²⋊C₃	—	7	2	no	—
38	C₂×C₅²⋊C₃	C₁₁×D₇	1	1	yes	characteristic, direct product factor
39	C₂×C₅×D₇	—	3	2	no	—
40	C₂²×C₃×C₁₁	—	175	1	no	Hall
41	C₂×C₅×C₁₁	—	3	2	no	—
42	C₂×C₅×C₁₁	—	21	4	no	—
43	C₂²×C₅²	—	7	1	no	Hall
44	C₂×C₃×D₇	—	25	1	no	Hall
45	C₇×C₁₁	C₂²×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
46	C₅²⋊C₃	C₂×C₁₁×D₇	1	1	yes	characteristic, direct product factor, Hall
47	C₂×C₅×C₇	—	3	2	no	—
48	C₅×D₇	—	3	4	no	—
49	C₂×C₃×C₁₁	—	25	1	no	—
50	C₂×C₃×C₁₁	—	175	2	no	—
51	C₅×C₁₁	—	3	2	no	—
52	C₂×C₅²	—	7	2	no	—
53	C₂×C₅²	C₃×C₁₁×D₇	1	1	yes	characteristic, complemented
54	C₂²×C₁₁	—	7	1	no	Hall
55	C₂×C₃×C₇	—	25	1	no	—
56	C₃×D₇	—	25	2	no	—
57	C₅×C₇	—	3	2	no	—
58	C₃×C₁₁	—	25	1	no	Hall
59	C₂×D₇	C₁₁×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
60	C₅²	C₂×C₃×C₁₁×D₇	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₁₁	—	7	2	no	—
62	C₂×C₁₁	D₇×C₅²⋊C₃	1	1	yes	characteristic, direct product factor
63	C₃×C₇	—	25	1	no	Hall
64	C₂²×C₅	—	21	2	no	—
65	C₂×C₇	C₂×C₁₁×C₅²⋊C₃	1	1	yes	characteristic, complemented
66	D₇	C₂×C₁₁×C₅²⋊C₃	1	2	yes	direct product factor
67	C₂²×C₃	—	175	1	no	Hall
68	C₁₁	C₂×D₇×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
69	C₂×C₅	—	3	2	no	—
70	C₂×C₅	—	21	4	no	—
71	C₇	C₂²×C₁₁×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	25	1	no	—
73	C₂×C₃	—	175	2	no	—
74	C₅	—	3	2	no	—
75	C₂²	—	7	1	no	Sylow
76	C₃	—	25	1	no	Sylow
77	C₂	—	7	2	no	—
78	C₂	C₁₁×D₇×C₅²⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₇×C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²×C₇	C₂²×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₇×C₁₁	C₂×C₃
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×C₁₁×C₅²⋊C₃	C₂	semidirect
2. C₁₁×D₇×C₅²⋊C₃	C₂	direct (N × H)
3. C₂×C₅²×C₁₁×D₇	C₃	semidirect
4. C₇×C₁₁×C₅²⋊C₃	C₂²	semidirect
5. C₅²×C₁₁×D₇	C₂×C₃	semidirect
6. C₂×C₅²×C₇×C₁₁	C₂×C₃	semidirect
8. C₂×D₇×C₅²⋊C₃	C₁₁	direct (N × H)
9. C₅²×C₇×C₁₁	C₂²×C₃	semidirect
11. C₂×C₁₁×C₅²⋊C₃	D₇	direct (N × H)
14. C₂×C₇×C₅²⋊C₃	C₂×C₁₁	semidirect
15. D₇×C₅²⋊C₃	C₂×C₁₁	direct (N × H)
17. C₁₁×C₅²⋊C₃	C₂×D₇	direct (N × H)
20. C₂×C₅²×D₇	C₃×C₁₁	semidirect
22. C₂×C₅²×C₁₁	C₃×D₇	semidirect
23. C₇×C₅²⋊C₃	C₂²×C₁₁	semidirect
27. C₂×C₅²×C₇	C₂×C₃×C₁₁	semidirect
28. C₅²×D₇	C₂×C₃×C₁₁	semidirect
29. C₂×C₁₁×D₇	C₅²⋊C₃	direct (N × H)
31. C₅²×C₁₁	C₂×C₃×D₇	semidirect
34. C₅²×C₇	C₂²×C₃×C₁₁	semidirect
35. C₂×C₇×C₁₁	C₂×C₅²⋊C₃	semidirect
36. C₁₁×D₇	C₂×C₅²⋊C₃	direct (N × H)
38. C₂×C₅²⋊C₃	C₁₁×D₇	direct (N × H)
45. C₇×C₁₁	C₂²×C₅²⋊C₃	semidirect
46. C₅²⋊C₃	C₂×C₁₁×D₇	direct (N × H)
53. C₂×C₅²	C₃×C₁₁×D₇	semidirect
59. C₂×D₇	C₁₁×C₅²⋊C₃	direct (N × H)
60. C₅²	C₂×C₃×C₁₁×D₇	semidirect
62. C₂×C₁₁	D₇×C₅²⋊C₃	direct (N × H)
65. C₂×C₇	C₂×C₁₁×C₅²⋊C₃	semidirect
66. D₇	C₂×C₁₁×C₅²⋊C₃	direct (N × H)
68. C₁₁	C₂×D₇×C₅²⋊C₃	direct (N × H)
71. C₇	C₂²×C₁₁×C₅²⋊C₃	semidirect
78. C₂	C₁₁×D₇×C₅²⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×C₁₁×C₅²⋊C₃	2
C₁₁×D₇×C₅²⋊C₃	2
C₂×C₅²×C₁₁×D₇	3
C₂²×C₁₁×C₅²⋊C₃	7
C₂×D₇×C₅²⋊C₃	11
C₂×C₃×C₁₁×D₇	25

Subgroups — C2×C11×D7×C52⋊C3 #37528577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₇×C₅²⋊C₃ #37528577