Subgroups — C₂×C₇×D₁₁₁₃ #44528491

Order 31164.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₁₁₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇²×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₃₇₁	—	3	1	no	maximal, Hall
4	C₃×C₇²×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₃₇₁	—	3	2	no	—
6	C₂×C₇²×C₅₃	D₃	1	1	yes	characteristic, complemented
7	C₂×D₁₁₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₇×D₁₅₉	—	7	1	no	maximal
9	C₇²×C₅₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₁₁₁₃	C₂×C₇	1	2	yes	direct product factor
11	C₇×D₁₅₉	—	7	2	no	—
12	C₂×C₃×C₇×C₅₃	—	2	3	no	—
13	C₂×C₃×C₇×C₅₃	D₇	1	1	yes	characteristic, complemented
14	C₂×C₃×C₇×C₅₃	C₂×C₇	1	1	yes	characteristic, complemented
15	C₂×D₃₇₁	—	3	1	no	—
16	C₂×C₇×D₅₃	—	21	1	no	—
17	C₃×C₇×C₅₃	—	2	3	no	—
18	C₃×C₇×C₅₃	C₂×D₇	1	1	yes	characteristic, complemented
19	C₃×C₇×C₅₃	C₂²×C₇	1	1	yes	characteristic, complemented
20	C₂×C₇×C₅₃	—	2	3	no	—
21	C₂×C₇×C₅₃	D₃×C₇	1	1	yes	characteristic, complemented
22	C₂×C₇×C₅₃	D₂₁	1	1	yes	characteristic, complemented
23	D₃₇₁	—	3	2	no	—
24	C₇×D₅₃	—	21	2	no	—
25	C₂×D₁₅₉	—	7	1	no	Hall
26	C₂×C₇×D₂₁	—	53	1	no	maximal, Hall
27	C₇×C₅₃	—	2	3	no	—
28	C₇×C₅₃	C₂×D₃×C₇	1	1	yes	characteristic, complemented
29	C₇×C₅₃	C₂×D₂₁	1	1	yes	characteristic, complemented
30	C₂×C₃×C₅₃	C₇×D₇	1	1	yes	characteristic, complemented
31	D₁₅₉	—	7	2	no	—
32	C₂×C₃×C₇²	D₅₃	1	1	yes	characteristic, complemented
33	C₇×D₂₁	—	53	2	no	—
34	C₂×D₅₃	—	21	1	no	Hall
35	C₂×C₇×D₇	—	159	1	no	Hall
36	C₃×C₅₃	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
37	C₃×C₇²	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
38	C₂×C₅₃	C₇×D₂₁	1	1	yes	characteristic, complemented
39	D₅₃	—	21	2	no	—
40	C₂×C₇²	D₁₅₉	1	1	yes	characteristic, complemented
41	C₇×D₇	—	159	2	no	—
42	C₂×D₂₁	—	53	1	no	—
43	C₂×D₃×C₇	—	371	1	no	—
44	C₅₃	C₂×C₇×D₂₁	1	1	yes	characteristic, complemented, Sylow
45	C₇²	C₂×D₁₅₉	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃×C₇	—	2	3	no	—
47	C₂×C₃×C₇	C₇×D₅₃	1	1	yes	characteristic, complemented
48	C₂×C₃×C₇	D₃₇₁	1	1	yes	characteristic, complemented
49	D₂₁	—	53	2	no	—
50	D₃×C₇	—	371	2	no	—
51	C₂²×C₇	—	1113	1	no	—
52	C₂×D₇	—	159	1	no	—
53	C₃×C₇	—	2	3	no	—
54	C₃×C₇	C₂×C₇×D₅₃	1	1	yes	characteristic, complemented
55	C₃×C₇	C₂×D₃₇₁	1	1	yes	characteristic, complemented
56	C₂×C₇	—	2	3	no	—
57	C₂×C₇	—	1113	2	no	—
58	C₂×C₇	C₇×D₁₅₉	1	1	yes	characteristic, complemented
59	C₂×C₇	D₁₁₁₃	1	1	yes	characteristic, direct product factor
60	D₇	—	159	2	no	—
61	C₂×D₃	—	371	1	no	Hall
62	C₇	—	2	3	no	—
63	C₇	C₂×C₇×D₁₅₉	1	1	yes	characteristic, complemented
64	C₇	C₂×D₁₁₁₃	1	1	yes	characteristic, direct product factor
65	C₂×C₃	C₇×D₃₇₁	1	1	yes	characteristic, complemented
66	D₃	—	371	2	no	—
67	C₂²	—	1113	1	no	Sylow
68	C₃	C₂×C₇×D₃₇₁	1	1	yes	characteristic, complemented, Sylow
69	C₂	—	1113	2	no	—
70	C₂	C₇×D₁₁₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₁₁₁₃
commutator, cosocle, hypocenter	C₃×C₇×C₅₃	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇²×C₅₃	C₂
LCS	G ▷ C₃×C₇×C₅₃
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₁₁₁₃	C₂	direct (N × H)
2. C₂×C₃×C₇²×C₅₃	C₂	semidirect
4. C₃×C₇²×C₅₃	C₂²	semidirect
6. C₂×C₇²×C₅₃	D₃	semidirect
7. C₂×D₁₁₁₃	C₇	direct (N × H)
9. C₇²×C₅₃	C₂×D₃	semidirect
10. D₁₁₁₃	C₂×C₇	direct (N × H)
13. C₂×C₃×C₇×C₅₃	D₇	semidirect
14. C₂×C₃×C₇×C₅₃	C₂×C₇	semidirect
18. C₃×C₇×C₅₃	C₂×D₇	semidirect
19. C₃×C₇×C₅₃	C₂²×C₇	semidirect
21. C₂×C₇×C₅₃	D₃×C₇	semidirect
22. C₂×C₇×C₅₃	D₂₁	semidirect
28. C₇×C₅₃	C₂×D₃×C₇	semidirect
29. C₇×C₅₃	C₂×D₂₁	semidirect
30. C₂×C₃×C₅₃	C₇×D₇	semidirect
32. C₂×C₃×C₇²	D₅₃	semidirect
36. C₃×C₅₃	C₂×C₇×D₇	semidirect
37. C₃×C₇²	C₂×D₅₃	semidirect
38. C₂×C₅₃	C₇×D₂₁	semidirect
40. C₂×C₇²	D₁₅₉	semidirect
44. C₅₃	C₂×C₇×D₂₁	semidirect
45. C₇²	C₂×D₁₅₉	semidirect
47. C₂×C₃×C₇	C₇×D₅₃	semidirect
48. C₂×C₃×C₇	D₃₇₁	semidirect
54. C₃×C₇	C₂×C₇×D₅₃	semidirect
55. C₃×C₇	C₂×D₃₇₁	semidirect
58. C₂×C₇	C₇×D₁₅₉	semidirect
59. C₂×C₇	D₁₁₁₃	direct (N × H)
63. C₇	C₂×C₇×D₁₅₉	semidirect
64. C₇	C₂×D₁₁₁₃	direct (N × H)
65. C₂×C₃	C₇×D₃₇₁	semidirect
68. C₃	C₂×C₇×D₃₇₁	semidirect
70. C₂	C₇×D₁₁₁₃	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×D₁₁₁₃	2
C₂×C₃×C₇²×C₅₃	2
C₂×C₇×D₃₇₁	3
C₂×D₁₁₁₃	7
C₂×C₇×D₁₅₉	7
C₂×C₇×D₂₁	53

Subgroups — C2×C7×D1113 #44528491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₁₁₁₃ #44528491