Subgroups — C₇×C₃⋊D₂₃₁ #23753381

Order 9702.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₂₃₁	—	3	4	no	maximal
3	C₃×C₇²×C₁₁	D₃	1	4	yes	complemented
4	C₃⋊D₂₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₇×C₃⋊D₃₃	—	7	1	no	maximal
6	C₇×D₇₇	—	9	1	no	Hall
7	C₇×C₃⋊D₂₁	—	11	1	no	maximal, Hall
8	C₃²×C₇×C₁₁	—	2	3	no	—
9	C₃²×C₇×C₁₁	D₇	1	1	yes	characteristic, complemented
10	C₃²×C₇×C₁₁	C₂×C₇	1	1	yes	characteristic, complemented
11	C₇²×C₁₁	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
12	D₂₃₁	—	3	4	no	—
13	C₇×D₃₃	—	21	4	no	—
14	C₃²×C₇²	D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₇×D₂₁	—	33	4	no	—
16	C₃×C₇×C₁₁	—	2	12	no	—
17	C₃×C₇×C₁₁	D₃×C₇	1	4	yes	complemented
18	C₃×C₇×C₁₁	D₂₁	1	4	yes	complemented
19	C₃⋊D₃₃	—	7	1	no	Hall
20	D₇₇	—	9	1	no	—
21	C₇×D₁₁	—	63	1	no	—
22	C₃×C₇²	D₃₃	1	4	yes	complemented
23	C₃⋊D₂₁	—	11	1	no	—
24	C₇×C₃⋊D₃	—	77	1	no	—
25	C₃²×C₁₁	C₇×D₇	1	1	yes	characteristic, complemented, Hall
26	C₇×D₇	—	99	1	no	Hall
27	C₇×C₁₁	—	2	3	no	—
28	C₇×C₁₁	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented
29	C₇×C₁₁	C₃⋊D₂₁	1	1	yes	characteristic, complemented
30	D₃₃	—	21	4	no	—
31	C₃²×C₇	—	2	3	no	—
32	C₃²×C₇	C₇×D₁₁	1	1	yes	characteristic, complemented
33	C₃²×C₇	D₇₇	1	1	yes	characteristic, complemented
34	C₇²	C₃⋊D₃₃	1	1	yes	characteristic, complemented, Sylow
35	D₂₁	—	33	4	no	—
36	D₃×C₇	—	231	4	no	—
37	C₃×C₁₁	C₇×D₂₁	1	4	yes	complemented
38	D₁₁	—	63	1	no	Hall
39	C₃×C₇	—	2	12	no	—
40	C₃×C₇	C₇×D₃₃	1	4	yes	complemented
41	C₃×C₇	D₂₃₁	1	4	yes	complemented
42	C₃⋊D₃	—	77	1	no	Hall
43	C₂×C₇	—	693	1	no	—
44	D₇	—	99	1	no	—
45	C₁₁	C₇×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Sylow
46	C₃²	C₇×D₇₇	1	1	yes	characteristic, complemented, Sylow
47	C₇	—	2	3	no	—
48	C₇	C₇×C₃⋊D₃₃	1	1	yes	characteristic, complemented
49	C₇	C₃⋊D₂₃₁	1	1	yes	characteristic, direct product factor
50	D₃	—	231	4	no	—
51	C₃	C₇×D₂₃₁	1	4	yes	complemented
52	C₂	—	693	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₃⋊D₂₃₁
commutator, cosocle, hypocenter	C₃²×C₇×C₁₁	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₁	C₂
LCS	G ▷ C₃²×C₇×C₁₁
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇²×C₁₁	C₂	semidirect
3. C₃×C₇²×C₁₁	D₃	semidirect
4. C₃⋊D₂₃₁	C₇	direct (N × H)
9. C₃²×C₇×C₁₁	D₇	semidirect
10. C₃²×C₇×C₁₁	C₂×C₇	semidirect
11. C₇²×C₁₁	C₃⋊D₃	semidirect
14. C₃²×C₇²	D₁₁	semidirect
17. C₃×C₇×C₁₁	D₃×C₇	semidirect
18. C₃×C₇×C₁₁	D₂₁	semidirect
22. C₃×C₇²	D₃₃	semidirect
25. C₃²×C₁₁	C₇×D₇	semidirect
28. C₇×C₁₁	C₇×C₃⋊D₃	semidirect
29. C₇×C₁₁	C₃⋊D₂₁	semidirect
32. C₃²×C₇	C₇×D₁₁	semidirect
33. C₃²×C₇	D₇₇	semidirect
34. C₇²	C₃⋊D₃₃	semidirect
37. C₃×C₁₁	C₇×D₂₁	semidirect
40. C₃×C₇	C₇×D₃₃	semidirect
41. C₃×C₇	D₂₃₁	semidirect
45. C₁₁	C₇×C₃⋊D₂₁	semidirect
46. C₃²	C₇×D₇₇	semidirect
48. C₇	C₇×C₃⋊D₃₃	semidirect
49. C₇	C₃⋊D₂₃₁	direct (N × H)
51. C₃	C₇×D₂₃₁	semidirect

Subgroups — C7×C3⋊D231 #23753381

Conjugacy classes of subgroups

Complements

Subgroups — C₇×C₃⋊D₂₃₁ #23753381