Subgroups — C₂×C₇⋊D₁₁₉₇ #45691707

Order 33516.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊D₁₁₉₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇²×C₉×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃⋊(C₇⋊D₁₃₃)	—	3	1	no	maximal
4	C₇²×C₉×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃⋊(C₇⋊D₁₃₃)	—	3	2	no	—
6	C₂×C₃×C₇²×C₁₉	D₃	1	1	yes	characteristic
7	C₂×D₁₁₉₇	—	7	8	no	maximal
8	C₂×C₇⋊D₁₃₃	—	9	1	no	Hall
9	C₃×C₇²×C₁₉	C₂×D₃	1	1	yes	characteristic
10	D₁₁₉₇	—	7	16	no	—
11	C₂×C₇×C₉×C₁₉	D₇	1	8	yes	complemented
12	C₂×C₇²×C₁₉	D₉	1	1	yes	characteristic, complemented
13	C₇⋊D₁₃₃	—	9	2	no	—
14	C₂×C₇⋊D₆₃	—	19	1	no	maximal, Hall
15	C₂×D₃₉₉	—	21	8	no	—
16	C₇×C₉×C₁₉	C₂×D₇	1	8	yes	complemented
17	C₇²×C₁₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇²×C₉	D₁₉	1	1	yes	characteristic, complemented
19	C₇⋊D₆₃	—	19	2	no	—
20	C₂×C₃×C₇×C₁₉	D₂₁	1	8	yes	—
21	D₃₉₉	—	21	16	no	—
22	C₂×D₁₇₁	—	49	1	no	Hall
23	C₂×C₃⋊(C₇⋊D₇)	—	57	1	no	—
24	C₂×D₁₃₃	—	63	8	no	—
25	C₇²×C₉	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
26	C₃×C₇×C₁₉	C₂×D₂₁	1	8	yes	—
27	C₂×C₉×C₁₉	C₇⋊D₇	1	1	yes	characteristic, complemented
28	D₁₇₁	—	49	2	no	—
29	C₂×C₃×C₇²	D₅₇	1	1	yes	characteristic
30	C₃⋊(C₇⋊D₇)	—	57	2	no	—
31	C₂×C₇×C₁₉	D₆₃	1	8	yes	complemented
32	D₁₃₃	—	63	16	no	—
33	C₂×D₆₃	—	133	8	no	—
34	C₂×D₅₇	—	147	1	no	—
35	C₂×C₇⋊D₇	—	171	1	no	Hall
36	C₉×C₁₉	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
37	C₃×C₇²	C₂×D₅₇	1	1	yes	characteristic
38	C₇×C₁₉	C₂×D₆₃	1	8	yes	complemented
39	C₂×C₇×C₉	D₁₃₃	1	8	yes	complemented
40	D₆₃	—	133	16	no	—
41	C₂×C₃×C₁₉	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
42	D₅₇	—	147	2	no	—
43	C₂×C₇²	D₁₇₁	1	1	yes	characteristic, complemented
44	C₇⋊D₇	—	171	2	no	—
45	C₂×D₂₁	—	399	8	no	—
46	C₂×D₁₉	—	441	1	no	Hall
47	C₇×C₉	C₂×D₁₃₃	1	8	yes	complemented
48	C₃×C₁₉	C₂×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
49	C₇²	C₂×D₁₇₁	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃×C₇	D₃₉₉	1	8	yes	—
51	D₂₁	—	399	16	no	—
52	C₂×C₁₉	C₇⋊D₆₃	1	1	yes	characteristic, complemented
53	D₁₉	—	441	2	no	—
54	C₂×D₉	—	931	1	no	Hall
55	C₂×D₇	—	1197	8	no	—
56	C₃×C₇	C₂×D₃₉₉	1	8	yes	—
57	C₁₉	C₂×C₇⋊D₆₃	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₉	C₇⋊D₁₃₃	1	1	yes	characteristic, complemented
59	D₉	—	931	2	no	—
60	C₂×C₇	D₁₁₉₇	1	8	yes	complemented
61	D₇	—	1197	16	no	—
62	C₂×D₃	—	2793	1	no	—
63	C₉	C₂×C₇⋊D₁₃₃	1	1	yes	characteristic, complemented, Sylow
64	C₇	C₂×D₁₁₉₇	1	8	yes	complemented
65	C₂×C₃	C₃⋊(C₇⋊D₁₃₃)	1	1	yes	characteristic
66	D₃	—	2793	2	no	—
67	C₂²	—	8379	1	no	Sylow
68	C₃	C₂×C₃⋊(C₇⋊D₁₃₃)	1	1	yes	characteristic
69	C₂	—	8379	2	no	—
70	C₂	C₇⋊D₁₁₉₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₇⋊D₁₁₉₇
commutator, cosocle, hypocenter	C₇²×C₉×C₁₉	C₂²
Frattini	C₃	C₂×C₃⋊(C₇⋊D₁₃₃)
Fitting	C₂×C₇²×C₉×C₁₉	C₂
socle	C₂×C₃×C₇²×C₁₉	D₃
LCS	G ▷ C₇²×C₉×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₇⋊D₁₁₉₇	C₂	direct (N × H)
2. C₂×C₇²×C₉×C₁₉	C₂	semidirect
4. C₇²×C₉×C₁₉	C₂²	semidirect
11. C₂×C₇×C₉×C₁₉	D₇	semidirect
12. C₂×C₇²×C₁₉	D₉	semidirect
16. C₇×C₉×C₁₉	C₂×D₇	semidirect
17. C₇²×C₁₉	C₂×D₉	semidirect
18. C₂×C₇²×C₉	D₁₉	semidirect
25. C₇²×C₉	C₂×D₁₉	semidirect
27. C₂×C₉×C₁₉	C₇⋊D₇	semidirect
31. C₂×C₇×C₁₉	D₆₃	semidirect
36. C₉×C₁₉	C₂×C₇⋊D₇	semidirect
38. C₇×C₁₉	C₂×D₆₃	semidirect
39. C₂×C₇×C₉	D₁₃₃	semidirect
43. C₂×C₇²	D₁₇₁	semidirect
47. C₇×C₉	C₂×D₁₃₃	semidirect
49. C₇²	C₂×D₁₇₁	semidirect
52. C₂×C₁₉	C₇⋊D₆₃	semidirect
57. C₁₉	C₂×C₇⋊D₆₃	semidirect
58. C₂×C₉	C₇⋊D₁₃₃	semidirect
60. C₂×C₇	D₁₁₉₇	semidirect
63. C₉	C₂×C₇⋊D₁₃₃	semidirect
64. C₇	C₂×D₁₁₉₇	semidirect
70. C₂	C₇⋊D₁₁₉₇	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⋊D₁₁₉₇	2
C₂×C₇²×C₉×C₁₉	2
C₂×C₃⋊(C₇⋊D₁₃₃)	3
C₂×D₁₁₉₇	7
C₂×C₇⋊D₆₃	19

Subgroups — C2×C7⋊D1197 #45691707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇⋊D₁₁₉₇ #45691707