Subgroups — C₂×C₇×D₃₅₇ #23756274

Order 9996.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₃₅₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₁₁₉	—	3	1	no	maximal, Hall
4	C₃×C₇²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇²×C₁₇	D₃	1	1	yes	characteristic, complemented
6	C₇×D₁₁₉	—	3	2	no	—
7	C₂×D₃₅₇	C₇	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₇×D₅₁	—	7	1	no	maximal
9	C₇²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₇×C₁₇	—	2	3	no	—
11	C₂×C₃×C₇×C₁₇	D₇	1	1	yes	characteristic, complemented
12	C₂×C₃×C₇×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented
13	D₃₅₇	C₂×C₇	1	2	yes	direct product factor
14	C₇×D₅₁	—	7	2	no	—
15	C₂×C₇×D₂₁	—	17	1	no	maximal, Hall
16	C₂×D₁₁₉	—	3	1	no	—
17	C₂×C₇×D₁₇	—	21	1	no	—
18	C₃×C₇×C₁₇	—	2	3	no	—
19	C₃×C₇×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented
20	C₃×C₇×C₁₇	C₂²×C₇	1	1	yes	characteristic, complemented
21	C₂×C₃×C₇²	D₁₇	1	1	yes	characteristic, complemented
22	C₇×D₂₁	—	17	2	no	—
23	C₂×C₇×C₁₇	—	2	3	no	—
24	C₂×C₇×C₁₇	D₃×C₇	1	1	yes	characteristic, complemented
25	C₂×C₇×C₁₇	D₂₁	1	1	yes	characteristic, complemented
26	D₁₁₉	—	3	2	no	—
27	C₇×D₁₇	—	21	2	no	—
28	C₂×D₅₁	—	7	1	no	Hall
29	C₂×C₇×D₇	—	51	1	no	Hall
30	C₃×C₇²	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
31	C₇×C₁₇	—	2	3	no	—
32	C₇×C₁₇	C₂×D₃×C₇	1	1	yes	characteristic, complemented
33	C₇×C₁₇	C₂×D₂₁	1	1	yes	characteristic, complemented
34	C₂×C₃×C₁₇	C₇×D₇	1	1	yes	characteristic, complemented
35	D₅₁	—	7	2	no	—
36	C₂×C₇²	D₅₁	1	1	yes	characteristic, complemented
37	C₇×D₇	—	51	2	no	—
38	C₂×D₂₁	—	17	1	no	—
39	C₂×D₃×C₇	—	119	1	no	—
40	C₂×D₁₇	—	21	1	no	Hall
41	C₃×C₁₇	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
42	C₇²	C₂×D₅₁	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃×C₇	—	2	3	no	—
44	C₂×C₃×C₇	C₇×D₁₇	1	1	yes	characteristic, complemented
45	C₂×C₃×C₇	D₁₁₉	1	1	yes	characteristic, complemented
46	D₂₁	—	17	2	no	—
47	D₃×C₇	—	119	2	no	—
48	C₂×C₁₇	C₇×D₂₁	1	1	yes	characteristic, complemented
49	D₁₇	—	21	2	no	—
50	C₂²×C₇	—	357	1	no	—
51	C₂×D₇	—	51	1	no	—
52	C₃×C₇	—	2	3	no	—
53	C₃×C₇	C₂×C₇×D₁₇	1	1	yes	characteristic, complemented
54	C₃×C₇	C₂×D₁₁₉	1	1	yes	characteristic, complemented
55	C₁₇	C₂×C₇×D₂₁	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₇	—	2	3	no	—
57	C₂×C₇	—	357	2	no	—
58	C₂×C₇	C₇×D₅₁	1	1	yes	characteristic, complemented
59	C₂×C₇	D₃₅₇	1	1	yes	characteristic, direct product factor
60	D₇	—	51	2	no	—
61	C₂×D₃	—	119	1	no	Hall
62	C₇	—	2	3	no	—
63	C₇	C₂×C₇×D₅₁	1	1	yes	characteristic, complemented
64	C₇	C₂×D₃₅₇	1	1	yes	characteristic, direct product factor
65	C₂×C₃	C₇×D₁₁₉	1	1	yes	characteristic, complemented
66	D₃	—	119	2	no	—
67	C₂²	—	357	1	no	Sylow
68	C₃	C₂×C₇×D₁₁₉	1	1	yes	characteristic, complemented, Sylow
69	C₂	—	357	2	no	—
70	C₂	C₇×D₃₅₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₃₅₇
commutator, cosocle, hypocenter	C₃×C₇×C₁₇	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇²×C₁₇	C₂
LCS	G ▷ C₃×C₇×C₁₇
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₃₅₇	C₂	direct (N × H)
2. C₂×C₃×C₇²×C₁₇	C₂	semidirect
4. C₃×C₇²×C₁₇	C₂²	semidirect
5. C₂×C₇²×C₁₇	D₃	semidirect
7. C₂×D₃₅₇	C₇	direct (N × H)
9. C₇²×C₁₇	C₂×D₃	semidirect
11. C₂×C₃×C₇×C₁₇	D₇	semidirect
12. C₂×C₃×C₇×C₁₇	C₂×C₇	semidirect
13. D₃₅₇	C₂×C₇	direct (N × H)
19. C₃×C₇×C₁₇	C₂×D₇	semidirect
20. C₃×C₇×C₁₇	C₂²×C₇	semidirect
21. C₂×C₃×C₇²	D₁₇	semidirect
24. C₂×C₇×C₁₇	D₃×C₇	semidirect
25. C₂×C₇×C₁₇	D₂₁	semidirect
30. C₃×C₇²	C₂×D₁₇	semidirect
32. C₇×C₁₇	C₂×D₃×C₇	semidirect
33. C₇×C₁₇	C₂×D₂₁	semidirect
34. C₂×C₃×C₁₇	C₇×D₇	semidirect
36. C₂×C₇²	D₅₁	semidirect
41. C₃×C₁₇	C₂×C₇×D₇	semidirect
42. C₇²	C₂×D₅₁	semidirect
44. C₂×C₃×C₇	C₇×D₁₇	semidirect
45. C₂×C₃×C₇	D₁₁₉	semidirect
48. C₂×C₁₇	C₇×D₂₁	semidirect
53. C₃×C₇	C₂×C₇×D₁₇	semidirect
54. C₃×C₇	C₂×D₁₁₉	semidirect
55. C₁₇	C₂×C₇×D₂₁	semidirect
58. C₂×C₇	C₇×D₅₁	semidirect
59. C₂×C₇	D₃₅₇	direct (N × H)
63. C₇	C₂×C₇×D₅₁	semidirect
64. C₇	C₂×D₃₅₇	direct (N × H)
65. C₂×C₃	C₇×D₁₁₉	semidirect
68. C₃	C₂×C₇×D₁₁₉	semidirect
70. C₂	C₇×D₃₅₇	direct (N × H)

Subgroups — C2×C7×D357 #23756274

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₇×D₃₅₇ #23756274