Subgroups — C₂×C₇×D₉₇⋊C₉ #37567775

Order 24444.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₉₇⋊C₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₉₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₇×D₉₇	C₃	1	1	yes	maximal, characteristic
4	C₇×C₉₇⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×D₉₇	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇×C₉₇	C₂×C₃	1	1	yes	characteristic
7	C₂×D₉₇⋊C₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×D₉₇	C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₉₇	C₂²×C₃	1	1	yes	characteristic
10	C₂×C₉₇⋊C₉	C₂×C₇	1	1	yes	characteristic, complemented
11	D₉₇⋊C₉	C₂×C₇	1	2	yes	direct product factor
12	C₂×C₇×C₉₇	C₂×C₉	1	1	yes	characteristic, complemented
13	C₇×D₉₇	C₂×C₉	1	2	yes	complemented
14	C₂×C₃×D₉₇	C₃×C₇	1	1	yes	characteristic
15	C₉₇⋊C₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₉₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₉₇	C₂×C₃×C₇	1	1	yes	characteristic
18	C₃×D₉₇	C₂×C₃×C₇	1	2	yes	—
19	C₂×D₉₇	C₇×C₉	1	1	yes	characteristic, complemented, Hall
20	C₃×C₉₇	C₂²×C₃×C₇	1	1	yes	characteristic
21	C₂²×C₇×C₉	—	97	1	no	maximal, Hall
22	C₂×C₉₇	C₂×C₇×C₉	1	1	yes	characteristic, complemented
23	D₉₇	C₂×C₇×C₉	1	2	yes	complemented
24	C₂×C₇×C₉	—	97	2	no	—
25	C₂×C₇×C₉	—	97	1	no	—
26	C₉₇	C₂²×C₇×C₉	1	1	yes	characteristic, complemented, Sylow
27	C₂²×C₃×C₇	—	291	1	no	—
28	C₇×C₉	—	97	1	no	Hall
29	C₂×C₃×C₇	—	291	2	no	—
30	C₂×C₃×C₇	D₉₇⋊C₃	1	1	yes	characteristic
31	C₂²×C₉	—	97	1	no	Hall
32	C₂²×C₇	—	291	1	no	Hall
33	C₃×C₇	C₂×D₉₇⋊C₃	1	1	yes	characteristic
34	C₂×C₉	—	97	2	no	—
35	C₂×C₉	—	97	1	no	—
36	C₂×C₇	—	291	2	no	—
37	C₂×C₇	D₉₇⋊C₉	1	1	yes	characteristic, direct product factor
38	C₂²×C₃	—	291	1	no	—
39	C₉	—	97	1	no	Sylow
40	C₇	C₂×D₉₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	—	291	2	no	—
42	C₂×C₃	C₇×D₉₇⋊C₃	1	1	yes	characteristic
43	C₂²	—	291	1	no	Sylow
44	C₃	C₂×C₇×D₉₇⋊C₃	1	1	yes	characteristic
45	C₂	—	291	2	no	—
46	C₂	C₇×D₉₇⋊C₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	D₉₇⋊C₃
commutator, hypocenter	C₉₇	C₂²×C₇×C₉
Frattini	C₃	C₂×C₇×D₉₇⋊C₃
Fitting, socle	C₂×C₃×C₇×C₉₇	C₂×C₃
prime radical	C₂×C₃×C₇×D₉₇	C₃
cosocle	C₃×C₉₇	C₂²×C₃×C₇
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₂×C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₉₇⋊C₉	C₂	direct (N × H)
2. C₂×C₇×C₉₇⋊C₉	C₂	semidirect
4. C₇×C₉₇⋊C₉	C₂²	semidirect
7. C₂×D₉₇⋊C₉	C₇	direct (N × H)
8. C₂×C₇×D₉₇	C₉	semidirect
10. C₂×C₉₇⋊C₉	C₂×C₇	semidirect
11. D₉₇⋊C₉	C₂×C₇	direct (N × H)
12. C₂×C₇×C₉₇	C₂×C₉	semidirect
13. C₇×D₉₇	C₂×C₉	semidirect
15. C₉₇⋊C₉	C₂²×C₇	semidirect
16. C₇×C₉₇	C₂²×C₉	semidirect
19. C₂×D₉₇	C₇×C₉	semidirect
22. C₂×C₉₇	C₂×C₇×C₉	semidirect
23. D₉₇	C₂×C₇×C₉	semidirect
26. C₉₇	C₂²×C₇×C₉	semidirect
37. C₂×C₇	D₉₇⋊C₉	direct (N × H)
40. C₇	C₂×D₉₇⋊C₉	direct (N × H)
46. C₂	C₇×D₉₇⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×D₉₇⋊C₉	2
C₂×C₇×C₉₇⋊C₉	2
C₂×C₃×C₇×D₉₇	3
C₂×D₉₇⋊C₉	7
C₂²×C₇×C₉	97

Subgroups — C2×C7×D97⋊C9 #37567775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₉₇⋊C₉ #37567775