Subgroups — C₇×D₁₁₉₇ #30660631

Order 16758.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₉×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₃₉₉	—	3	1	no	maximal
3	C₃×C₇²×C₁₉	D₃	1	1	yes	characteristic
4	D₁₁₉₇	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₇×D₁₇₁	—	7	1	no	maximal
6	C₇×D₁₃₃	—	9	1	no	Hall
7	C₇×C₉×C₁₉	—	2	3	no	—
8	C₇×C₉×C₁₉	D₇	1	1	yes	characteristic, complemented
9	C₇×C₉×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented
10	C₇²×C₁₉	D₉	1	1	yes	characteristic, complemented, Hall
11	C₇×D₆₃	—	19	1	no	maximal, Hall
12	D₃₉₉	—	3	1	no	—
13	C₇×D₅₇	—	21	1	no	—
14	C₇²×C₉	D₁₉	1	1	yes	characteristic, complemented, Hall
15	C₃×C₇×C₁₉	—	2	3	no	—
16	C₃×C₇×C₁₉	D₃×C₇	1	1	yes	characteristic
17	C₃×C₇×C₁₉	D₂₁	1	1	yes	characteristic
18	D₁₇₁	—	7	1	no	Hall
19	C₇×D₂₁	—	57	1	no	—
20	D₁₃₃	—	9	1	no	—
21	C₇×D₁₉	—	63	1	no	—
22	C₉×C₁₉	C₇×D₇	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇²	D₅₇	1	1	yes	characteristic
24	C₇×C₁₉	—	2	3	no	—
25	C₇×C₁₉	C₇×D₉	1	1	yes	characteristic, complemented
26	C₇×C₁₉	D₆₃	1	1	yes	characteristic, complemented
27	D₆₃	—	19	1	no	—
28	C₇×D₉	—	133	1	no	—
29	D₅₇	—	21	1	no	—
30	C₇×D₇	—	171	1	no	Hall
31	C₇×C₉	—	2	3	no	—
32	C₇×C₉	C₇×D₁₉	1	1	yes	characteristic, complemented
33	C₇×C₉	D₁₃₃	1	1	yes	characteristic, complemented
34	C₃×C₁₉	C₇×D₂₁	1	1	yes	characteristic
35	C₇²	D₁₇₁	1	1	yes	characteristic, complemented, Sylow
36	D₂₁	—	57	1	no	—
37	D₃×C₇	—	399	1	no	—
38	D₁₉	—	63	1	no	Hall
39	C₃×C₇	—	2	3	no	—
40	C₃×C₇	C₇×D₅₇	1	1	yes	characteristic
41	C₃×C₇	D₃₉₉	1	1	yes	characteristic
42	C₁₉	C₇×D₆₃	1	1	yes	characteristic, complemented, Sylow
43	D₉	—	133	1	no	Hall
44	C₂×C₇	—	1197	1	no	—
45	D₇	—	171	1	no	—
46	C₉	C₇×D₁₃₃	1	1	yes	characteristic, complemented, Sylow
47	C₇	—	2	3	no	—
48	C₇	C₇×D₁₇₁	1	1	yes	characteristic, complemented
49	C₇	D₁₁₉₇	1	1	yes	characteristic, direct product factor
50	D₃	—	399	1	no	—
51	C₃	C₇×D₃₉₉	1	1	yes	characteristic
52	C₂	—	1197	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₁₁₉₇
commutator, cosocle, hypocenter	C₇×C₉×C₁₉	C₂×C₇
Frattini	C₃	C₇×D₃₉₉
Fitting	C₇²×C₉×C₁₉	C₂
socle	C₃×C₇²×C₁₉	D₃
LCS	G ▷ C₇×C₉×C₁₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇²×C₉×C₁₉	C₂	semidirect
4. D₁₁₉₇	C₇	direct (N × H)
8. C₇×C₉×C₁₉	D₇	semidirect
9. C₇×C₉×C₁₉	C₂×C₇	semidirect
10. C₇²×C₁₉	D₉	semidirect
14. C₇²×C₉	D₁₉	semidirect
22. C₉×C₁₉	C₇×D₇	semidirect
25. C₇×C₁₉	C₇×D₉	semidirect
26. C₇×C₁₉	D₆₃	semidirect
32. C₇×C₉	C₇×D₁₉	semidirect
33. C₇×C₉	D₁₃₃	semidirect
35. C₇²	D₁₇₁	semidirect
42. C₁₉	C₇×D₆₃	semidirect
46. C₉	C₇×D₁₃₃	semidirect
48. C₇	C₇×D₁₇₁	semidirect
49. 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
C₇²×C₉×C₁₉	2
C₇×D₃₉₉	3
D₁₁₉₇	7
C₇×D₁₇₁	7
C₇×D₆₃	19

Subgroups — C7×D1197 #30660631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₁₁₉₇ #30660631