Subgroups — D₇×D₃₅₇ #23756256

Order 9996.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₇⋊D₁₁₉)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₃₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₇×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₁₁₉	—	3	1	no	maximal, Hall
5	C₃×C₇²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇⋊D₁₁₉	—	3	1	no	—
7	C₇×D₁₁₉	—	3	1	no	—
8	C₇×D₇×C₁₇	D₃	1	1	yes	characteristic, complemented
9	C₂×D₃₅₇	—	7	1	no	maximal
10	D₇×D₅₁	—	7	1	no	maximal
11	C₇²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₇×C₁₇	—	7	1	no	—
13	D₃₅₇	—	7	1	no	—
14	D₃₅₇	—	7	1	no	—
15	D₃₅₇	—	14	3	no	—
16	D₃₅₇	D₇	1	1	yes	characteristic, direct product factor
17	C₇×D₅₁	—	7	1	no	—
18	C₃×D₇×C₁₇	D₇	1	1	yes	characteristic, complemented
19	D₇×D₂₁	—	17	1	no	maximal, Hall
20	C₂×D₁₁₉	—	21	1	no	—
21	D₇×D₁₇	—	21	1	no	—
22	C₃×C₇×C₁₇	—	2	3	no	—
23	C₃×C₇×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented
24	C₃×C₇×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented
25	C₃⋊(C₇⋊D₇)	—	17	1	no	—
26	C₇×D₂₁	—	17	1	no	—
27	C₃×C₇×D₇	D₁₇	1	1	yes	characteristic, complemented
28	C₂×C₇×C₁₇	—	7	1	no	—
29	D₁₁₉	—	3	1	no	—
30	D₁₁₉	—	21	1	no	—
31	D₁₁₉	—	21	1	no	—
32	D₁₁₉	—	42	3	no	—
33	C₇×D₁₇	—	21	1	no	—
34	D₇×C₁₇	D₂₁	1	1	yes	characteristic, complemented
35	C₂×D₅₁	—	49	1	no	Hall
36	D₇²	—	51	1	no	Hall
37	C₃×C₇²	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
38	C₇×C₁₇	—	2	3	no	—
39	C₇×C₁₇	D₃×D₇	1	1	yes	characteristic, complemented
40	C₇×C₁₇	C₂×D₂₁	1	1	yes	characteristic, complemented
41	C₂×C₃×C₁₇	—	7	1	no	—
42	D₅₁	—	7	1	no	—
43	D₅₁	—	49	1	no	—
44	C₇⋊D₇	—	51	1	no	—
45	C₇×D₇	—	51	1	no	—
46	C₇×D₇	D₅₁	1	1	yes	characteristic, complemented
47	C₂×D₂₁	—	119	1	no	—
48	D₃×D₇	—	119	1	no	—
49	C₂×D₁₇	—	147	1	no	Hall
50	C₃×C₁₇	D₇²	1	1	yes	characteristic, complemented, Hall
51	C₇²	C₂×D₅₁	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₃×C₇	—	7	1	no	—
53	D₂₁	—	17	1	no	—
54	D₂₁	—	119	1	no	—
55	D₂₁	—	119	1	no	—
56	D₂₁	—	238	3	no	—
57	C₃×D₇	D₁₁₉	1	1	yes	characteristic, complemented
58	D₃×C₇	—	119	1	no	—
59	C₂×C₁₇	—	7	1	no	—
60	D₁₇	—	21	1	no	—
61	D₁₇	—	147	1	no	—
62	C₂×D₇	—	357	1	no	—
63	C₂×D₇	—	357	1	no	—
64	C₃×C₇	—	2	3	no	—
65	C₃×C₇	D₇×D₁₇	1	1	yes	characteristic, complemented
66	C₃×C₇	C₂×D₁₁₉	1	1	yes	characteristic, complemented
67	C₁₇	D₇×D₂₁	1	1	yes	characteristic, complemented, Sylow
68	C₂×C₇	—	7	1	no	—
69	C₂×C₇	—	357	1	no	—
70	D₇	—	51	1	no	—
71	D₇	—	357	1	no	—
72	D₇	—	357	1	no	—
73	D₇	—	714	3	no	—
74	D₇	D₃₅₇	1	1	yes	characteristic, direct product factor
75	C₂×D₃	—	833	1	no	Hall
76	C₇	—	2	3	no	—
77	C₇	D₇×D₅₁	1	1	yes	characteristic, complemented
78	C₇	C₂×D₃₅₇	1	1	yes	characteristic, complemented
79	C₂×C₃	—	7	1	no	—
80	D₃	—	833	1	no	—
81	D₃	—	119	1	no	—
82	C₂²	—	2499	1	no	Sylow
83	C₃	D₇×D₁₁₉	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	7	1	no	—
85	C₂	—	357	1	no	—
86	C₂	—	2499	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₇⋊D₁₁₉)	C₂	semidirect
2. C₇×D₃₅₇	C₂	semidirect
3. C₃×C₇×D₇×C₁₇	C₂	semidirect
5. C₃×C₇²×C₁₇	C₂²	semidirect
8. C₇×D₇×C₁₇	D₃	semidirect
11. C₇²×C₁₇	C₂×D₃	semidirect
16. D₃₅₇	D₇	direct (N × H)
18. C₃×D₇×C₁₇	D₇	semidirect
23. C₃×C₇×C₁₇	C₂×D₇	semidirect
24. C₃×C₇×C₁₇	C₂×D₇	semidirect
27. C₃×C₇×D₇	D₁₇	semidirect
34. D₇×C₁₇	D₂₁	semidirect
37. C₃×C₇²	C₂×D₁₇	semidirect
39. C₇×C₁₇	D₃×D₇	semidirect
40. C₇×C₁₇	C₂×D₂₁	semidirect
46. C₇×D₇	D₅₁	semidirect
50. C₃×C₁₇	D₇²	semidirect
51. C₇²	C₂×D₅₁	semidirect
57. C₃×D₇	D₁₁₉	semidirect
65. C₃×C₇	D₇×D₁₇	semidirect
66. C₃×C₇	C₂×D₁₁₉	semidirect
67. C₁₇	D₇×D₂₁	semidirect
74. D₇	D₃₅₇	direct (N × H)
77. C₇	D₇×D₅₁	semidirect
78. C₇	C₂×D₃₅₇	semidirect
83. C₃	D₇×D₁₁₉	semidirect

Subgroups — D7×D357 #23756256

Conjugacy classes of subgroups

Complements

Subgroups — D₇×D₃₅₇ #23756256