Subgroups — C₇×(C₃⋊D₃)⋊D₉₇ #37567969

Order 24444.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₂₉₁	C₂	1	2	yes	maximal, complemented
2	C₇×C₃⋊D₃×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×C₇×D₉₇	—	3	2	no	maximal
4	C₃²×C₇×C₉₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₂₉₁	D₃	1	2	yes	complemented
6	D₃×C₇×C₉₇	—	3	2	no	—
7	D₃×C₇×C₉₇	—	6	1	no	—
8	C₃×C₇×D₉₇	—	3	2	no	—
9	(C₃⋊D₃)⋊D₉₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₇×D₉₇	—	9	1	no	Hall
11	C₃×C₇×C₉₇	—	2	1	no	—
12	C₃×C₇×C₉₇	C₂×D₃	1	2	yes	complemented
13	C₃⋊D₃×C₉₇	C₂×C₇	1	1	yes	characteristic, complemented
14	C₃×D₂₉₁	C₂×C₇	1	2	yes	complemented
15	C₂×C₇×C₉₇	—	9	1	no	—
16	C₇×D₉₇	—	3	2	no	—
17	D₃×D₉₇	—	3	2	no	—
18	C₃²×C₉₇	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
19	C₇×C₉₇	D₃²	1	1	yes	characteristic, complemented, Hall
20	D₂₉₁	D₃×C₇	1	2	yes	complemented
21	C₃×D₉₇	—	3	2	no	—
22	D₃×C₉₇	—	3	2	no	—
23	D₃×C₉₇	—	6	1	no	—
24	C₂×D₉₇	—	9	1	no	Hall
25	C₃×C₉₇	—	2	1	no	—
26	C₃×C₉₇	C₂×D₃×C₇	1	2	yes	complemented
27	D₃²×C₇	—	97	1	no	maximal, Hall
28	C₂×C₉₇	—	9	1	no	—
29	D₉₇	—	3	2	no	—
30	C₇×C₃⋊D₃	D₉₇	1	1	yes	characteristic, complemented
31	C₃×D₃×C₇	—	97	2	no	—
32	C₉₇	D₃²×C₇	1	1	yes	characteristic, complemented, Sylow
33	C₂×D₃×C₇	—	291	2	no	—
34	C₃²×C₇	C₂×D₉₇	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₇	—	291	2	no	—
36	D₃×C₇	—	3	2	no	—
37	D₃×C₇	—	6	1	no	—
38	D₃×C₇	—	97	2	no	—
39	D₃²	—	97	1	no	Hall
40	C₂²×C₇	—	873	1	no	Hall
41	C₃×C₇	—	2	1	no	—
42	C₃×C₇	D₃×D₉₇	1	2	yes	complemented
43	C₃⋊D₃	C₇×D₉₇	1	1	yes	characteristic, complemented
44	C₃×D₃	—	97	2	no	—
45	C₂×C₇	—	9	1	no	—
46	C₂×C₇	—	291	2	no	—
47	C₂×D₃	—	291	2	no	—
48	C₃²	C₂×C₇×D₉₇	1	1	yes	characteristic, complemented, Sylow
49	C₇	(C₃⋊D₃)⋊D₉₇	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₃	—	291	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	—	97	2	no	—
54	C₂²	—	873	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×C₇×D₉₇	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	291	2	no	—

	subgroup	G/H
center, hypercenter	C₇	(C₃⋊D₃)⋊D₉₇
commutator, cosocle, hypocenter	C₃²×C₉₇	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₉₇	C₂²
LCS	G ▷ C₃²×C₉₇
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×D₂₉₁	C₂	semidirect
2. C₇×C₃⋊D₃×C₉₇	C₂	semidirect
4. C₃²×C₇×C₉₇	C₂²	semidirect
5. C₇×D₂₉₁	D₃	semidirect
9. (C₃⋊D₃)⋊D₉₇	C₇	direct (N × H)
12. C₃×C₇×C₉₇	C₂×D₃	semidirect
13. C₃⋊D₃×C₉₇	C₂×C₇	semidirect
14. C₃×D₂₉₁	C₂×C₇	semidirect
18. C₃²×C₉₇	C₂²×C₇	semidirect
19. C₇×C₉₇	D₃²	semidirect
20. D₂₉₁	D₃×C₇	semidirect
26. C₃×C₉₇	C₂×D₃×C₇	semidirect
30. C₇×C₃⋊D₃	D₉₇	semidirect
32. C₉₇	D₃²×C₇	semidirect
34. C₃²×C₇	C₂×D₉₇	semidirect
42. C₃×C₇	D₃×D₉₇	semidirect
43. C₃⋊D₃	C₇×D₉₇	semidirect
48. C₃²	C₂×C₇×D₉₇	semidirect
49. C₇	(C₃⋊D₃)⋊D₉₇	direct (N × H)
56. C₃	D₃×C₇×D₉₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×D₂₉₁	2
C₇×C₃⋊D₃×C₉₇	2
D₃×C₇×D₉₇	3
(C₃⋊D₃)⋊D₉₇	7
D₃²×C₇	97

Subgroups — C7×(C3⋊D3)⋊D97 #37567969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×(C₃⋊D₃)⋊D₉₇ #37567969