Subgroups — C₄×C₇×C₉₇⋊C₉ #37567739

Order 24444.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₉₇⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₇×C₉₇	C₃	1	1	yes	maximal, characteristic
3	C₇×C₉₇⋊C₉	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇×C₉₇	C₂×C₃	1	1	yes	characteristic
5	C₄×C₉₇⋊C₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₄×C₇×C₉₇	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇×C₉₇	C₃×C₄	1	1	yes	characteristic
8	C₂×C₉₇⋊C₉	C₂×C₇	1	1	yes	characteristic
9	C₂×C₇×C₉₇	C₂×C₉	1	1	yes	characteristic
10	C₃×C₄×C₉₇	C₃×C₇	1	1	yes	characteristic
11	C₉₇⋊C₉	C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
12	C₇×C₉₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₉₇	C₂×C₃×C₇	1	1	yes	characteristic
14	C₄×C₉₇	C₇×C₉	1	1	yes	characteristic, complemented, Hall
15	C₃×C₉₇	C₃×C₄×C₇	1	1	yes	characteristic
16	C₄×C₇×C₉	—	97	1	no	maximal, Hall
17	C₂×C₉₇	C₂×C₇×C₉	1	1	yes	characteristic
18	C₂×C₇×C₉	—	97	1	no	—
19	C₉₇	C₄×C₇×C₉	1	1	yes	characteristic, complemented, Sylow
20	C₃×C₄×C₇	C₉₇⋊C₃	1	1	yes	characteristic
21	C₇×C₉	—	97	1	no	Hall
22	C₂×C₃×C₇	C₂×C₉₇⋊C₃	1	1	yes	characteristic
23	C₄×C₉	—	97	1	no	Hall
24	C₄×C₇	C₉₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₇	C₄×C₉₇⋊C₃	1	1	yes	characteristic
26	C₂×C₉	—	97	1	no	—
27	C₂×C₇	C₂×C₉₇⋊C₉	1	1	yes	characteristic
28	C₃×C₄	C₇×C₉₇⋊C₃	1	1	yes	characteristic
29	C₉	—	97	1	no	Sylow
30	C₇	C₄×C₉₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₂×C₇×C₉₇⋊C₃	1	1	yes	characteristic
32	C₄	C₇×C₉₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₄×C₇×C₉₇⋊C₃	1	1	yes	characteristic
34	C₂	C₂×C₇×C₉₇⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄×C₇	C₉₇⋊C₃
commutator, hypocenter	C₉₇	C₄×C₇×C₉
Frattini	C₂×C₃	C₂×C₇×C₉₇⋊C₃
Fitting	C₃×C₄×C₇×C₉₇	C₃
socle, prime radical	C₂×C₃×C₇×C₉₇	C₂×C₃
cosocle	C₂×C₃×C₉₇	C₂×C₃×C₇
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₃×C₄×C₇

Complements

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

N	H ≅ G/N	type
3. C₇×C₉₇⋊C₉	C₄	direct (N × H)
5. C₄×C₉₇⋊C₉	C₇	direct (N × H)
6. C₄×C₇×C₉₇	C₉	semidirect
11. C₉₇⋊C₉	C₄×C₇	direct (N × H)
12. C₇×C₉₇	C₄×C₉	semidirect
14. C₄×C₉₇	C₇×C₉	semidirect
19. C₉₇	C₄×C₇×C₉	semidirect
24. C₄×C₇	C₉₇⋊C₉	direct (N × H)
30. C₇	C₄×C₉₇⋊C₉	direct (N × H)
32. C₄	C₇×C₉₇⋊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
C₂×C₇×C₉₇⋊C₉	2
C₃×C₄×C₇×C₉₇	3
C₄×C₉₇⋊C₉	7
C₄×C₇×C₉	97

Subgroups — C4×C7×C97⋊C9 #37567739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×C₉₇⋊C₉ #37567739