Subgroups — D₇×C₃⋊D₃×C₉₇ #37567981

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⋊D₃×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉₇×C₃⋊D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₇×C₉₇	—	3	4	no	maximal
5	C₃²×C₇×C₉₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₁×C₉₇	—	3	4	no	—
7	D₃×C₇×C₉₇	—	3	4	no	—
8	C₃×D₇×C₉₇	D₃	1	4	yes	complemented
9	C₂×C₃⋊D₃×C₉₇	—	7	1	no	maximal, Hall
10	C₂×D₇×C₉₇	—	9	1	no	Hall
11	C₃×C₇×C₉₇	C₂×D₃	1	4	yes	complemented
12	C₂×C₃²×C₉₇	—	7	1	no	—
13	C₃⋊D₃×C₉₇	—	7	1	no	—
14	C₃⋊D₃×C₉₇	D₇	1	1	yes	characteristic, direct product factor
15	C₂×C₇×C₉₇	—	9	1	no	—
16	D₇×C₉₇	—	9	1	no	—
17	D₇×C₉₇	C₃⋊D₃	1	1	yes	characteristic, direct product factor
18	C₂×D₃×C₉₇	—	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	D₃×C₉₇	—	3	4	no	—
23	D₃×C₉₇	—	21	4	no	—
24	C₂²×C₉₇	—	63	1	no	Hall
25	C₃×C₉₇	D₃×D₇	1	4	yes	complemented
26	D₇×C₃⋊D₃	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₉₇	—	7	1	no	—
28	C₂×C₉₇	—	9	1	no	—
29	C₂×C₉₇	—	63	1	no	—
30	C₃⋊D₂₁	C₂×C₉₇	1	1	yes	characteristic, complemented
31	C₇×C₃⋊D₃	C₂×C₉₇	1	1	yes	characteristic, complemented
32	C₃²×D₇	C₂×C₉₇	1	1	yes	characteristic, complemented
33	C₉₇	D₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
34	D₃×D₇	—	3	4	no	—
35	C₃²×C₇	C₂²×C₉₇	1	1	yes	characteristic, complemented, Hall
36	D₂₁	—	3	4	no	—
37	C₃×D₇	D₃×C₉₇	1	4	yes	complemented
38	D₃×C₇	—	3	4	no	—
39	C₂×C₃⋊D₃	—	7	1	no	Hall
40	C₂×D₇	—	9	1	no	Hall
41	C₃×C₇	C₂×D₃×C₉₇	1	4	yes	complemented
42	C₂×C₃²	—	7	1	no	—
43	C₃⋊D₃	—	7	1	no	—
44	C₃⋊D₃	D₇×C₉₇	1	1	yes	characteristic, direct product factor
45	C₂×C₇	—	9	1	no	—
46	D₇	—	9	1	no	—
47	D₇	C₃⋊D₃×C₉₇	1	1	yes	characteristic, direct product factor
48	C₂×D₃	—	21	4	no	—
49	C₃²	C₂×D₇×C₉₇	1	1	yes	characteristic, complemented, Sylow
50	C₇	C₂×C₃⋊D₃×C₉₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	7	4	no	—
52	D₃	—	3	4	no	—
53	D₃	—	21	4	no	—
54	C₂²	—	63	1	no	Sylow
55	C₃	D₃×D₇×C₉₇	1	4	yes	complemented
56	C₂	—	7	1	no	—
57	C₂	—	9	1	no	—
58	C₂	—	63	1	no	—

	subgroup	G/H
center, hypercenter	C₉₇	D₇×C₃⋊D₃
commutator, cosocle, hypocenter	C₃²×C₇	C₂²×C₉₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₉₇	C₂²
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₉₇

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⋊D₃×C₉₇	C₂	semidirect
3. C₉₇×C₃⋊D₂₁	C₂	semidirect
5. C₃²×C₇×C₉₇	C₂²	semidirect
8. C₃×D₇×C₉₇	D₃	semidirect
11. C₃×C₇×C₉₇	C₂×D₃	semidirect
14. C₃⋊D₃×C₉₇	D₇	direct (N × H)
17. D₇×C₉₇	C₃⋊D₃	direct (N × H)
19. C₃²×C₉₇	C₂×D₇	semidirect
20. C₇×C₉₇	C₂×C₃⋊D₃	semidirect
25. C₃×C₉₇	D₃×D₇	semidirect
26. D₇×C₃⋊D₃	C₉₇	direct (N × H)
30. C₃⋊D₂₁	C₂×C₉₇	semidirect
31. C₇×C₃⋊D₃	C₂×C₉₇	semidirect
32. C₃²×D₇	C₂×C₉₇	semidirect
33. C₉₇	D₇×C₃⋊D₃	direct (N × H)
35. C₃²×C₇	C₂²×C₉₇	semidirect
37. C₃×D₇	D₃×C₉₇	semidirect
41. C₃×C₇	C₂×D₃×C₉₇	semidirect
44. C₃⋊D₃	D₇×C₉₇	direct (N × H)
47. D₇	C₃⋊D₃×C₉₇	direct (N × H)
49. C₃²	C₂×D₇×C₉₇	semidirect
50. C₇	C₂×C₃⋊D₃×C₉₇	semidirect
55. C₃	D₃×D₇×C₉₇	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⋊D₃×C₉₇	2
C₉₇×C₃⋊D₂₁	2
D₃×D₇×C₉₇	3
C₂×C₃⋊D₃×C₉₇	7
D₇×C₃⋊D₃	97

Subgroups — D7×C3⋊D3×C97 #37567981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₃⋊D₃×C₉₇ #37567981