Subgroups — C₇×C₃⋊D₃×D₉₇ #37567978

Order 24444.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

Subgroups — C7×C3⋊D3×D97 #37567978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₃⋊D₃×D₉₇ #37567978