Subgroups — D₇×C₃⋊D₂₉₁ #37567982

Order 24444.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₇×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₃⋊D₂₉₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₂₀₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₂₉₁	—	3	4	no	maximal
5	C₃²×C₇×C₉₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₀₃₇	—	3	4	no	—
7	C₇×D₂₉₁	—	3	4	no	—
8	C₃×D₇×C₉₇	D₃	1	4	yes	complemented
9	C₂×C₃⋊D₂₉₁	—	7	1	no	maximal, Hall
10	D₇×D₉₇	—	9	1	no	Hall
11	C₃×C₇×C₉₇	C₂×D₃	1	4	yes	complemented
12	C₂×C₃²×C₉₇	—	7	1	no	—
13	C₃⋊D₂₉₁	—	7	1	no	—
14	C₃⋊D₂₉₁	D₇	1	1	yes	characteristic, direct product factor
15	D₆₇₉	—	9	1	no	—
16	C₇×D₉₇	—	9	1	no	—
17	D₇×C₉₇	C₃⋊D₃	1	1	yes	characteristic, complemented
18	C₂×D₂₉₁	—	21	4	no	—
19	C₃²×C₉₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	C₇×C₉₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₉₇	—	7	4	no	—
22	D₂₉₁	—	3	4	no	—
23	D₂₉₁	—	21	4	no	—
24	C₂×D₉₇	—	63	1	no	Hall
25	C₃×C₉₇	D₃×D₇	1	4	yes	complemented
26	D₇×C₃⋊D₃	—	97	1	no	maximal, Hall
27	C₂×C₉₇	—	7	1	no	—
28	D₉₇	—	9	1	no	—
29	D₉₇	—	63	1	no	—
30	C₃⋊D₂₁	—	97	1	no	—
31	C₇×C₃⋊D₃	—	97	1	no	—
32	C₃²×D₇	D₉₇	1	1	yes	characteristic, complemented
33	C₉₇	D₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
34	D₃×D₇	—	291	4	no	—
35	C₃²×C₇	C₂×D₉₇	1	1	yes	characteristic, complemented, Hall
36	D₂₁	—	291	4	no	—
37	C₃×D₇	D₂₉₁	1	4	yes	complemented
38	D₃×C₇	—	291	4	no	—
39	C₂×C₃⋊D₃	—	679	1	no	Hall
40	C₂×D₇	—	873	1	no	Hall
41	C₃×C₇	C₂×D₂₉₁	1	4	yes	complemented
42	C₂×C₃²	—	7	1	no	—
43	C₃⋊D₃	—	97	1	no	—
44	C₃⋊D₃	—	679	1	no	—
45	C₂×C₇	—	873	1	no	—
46	D₇	—	873	1	no	—
47	D₇	C₃⋊D₂₉₁	1	1	yes	characteristic, direct product factor
48	C₂×D₃	—	2037	4	no	—
49	C₃²	D₇×D₉₇	1	1	yes	characteristic, complemented, Sylow
50	C₇	C₂×C₃⋊D₂₉₁	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	7	4	no	—
52	D₃	—	291	4	no	—
53	D₃	—	2037	4	no	—
54	C₂²	—	6111	1	no	Sylow
55	C₃	D₇×D₂₉₁	1	4	yes	complemented
56	C₂	—	7	1	no	—
57	C₂	—	873	1	no	—
58	C₂	—	6111	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇×C₉₇	C₂²
LCS	G ▷ C₃²×C₇×C₉₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×D₇×C₉₇	C₂	semidirect
2. C₇×C₃⋊D₂₉₁	C₂	semidirect
3. C₃⋊D₂₀₃₇	C₂	semidirect
5. C₃²×C₇×C₉₇	C₂²	semidirect
8. C₃×D₇×C₉₇	D₃	semidirect
11. C₃×C₇×C₉₇	C₂×D₃	semidirect
14. C₃⋊D₂₉₁	D₇	direct (N × H)
17. D₇×C₉₇	C₃⋊D₃	semidirect
19. C₃²×C₉₇	C₂×D₇	semidirect
20. C₇×C₉₇	C₂×C₃⋊D₃	semidirect
25. C₃×C₉₇	D₃×D₇	semidirect
32. C₃²×D₇	D₉₇	semidirect
33. C₉₇	D₇×C₃⋊D₃	semidirect
35. C₃²×C₇	C₂×D₉₇	semidirect
37. C₃×D₇	D₂₉₁	semidirect
41. C₃×C₇	C₂×D₂₉₁	semidirect
47. D₇	C₃⋊D₂₉₁	direct (N × H)
49. C₃²	D₇×D₉₇	semidirect
50. C₇	C₂×C₃⋊D₂₉₁	semidirect
55. C₃	D₇×D₂₉₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×D₇×C₉₇	2
C₇×C₃⋊D₂₉₁	2
C₃⋊D₂₀₃₇	2
D₇×D₂₉₁	3
C₂×C₃⋊D₂₉₁	7
D₇×C₃⋊D₃	97

Subgroups — D7×C3⋊D291 #37567982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₃⋊D₂₉₁ #37567982