Subgroups — (C₇⋊C₉)⋊Dic₈₉ #36375830

Order 22428.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇⋊C₉×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₆₂₃	C₃	1	1	yes	maximal, characteristic
3	C₇⋊C₉×C₈₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₈₉	C₂×C₃	1	1	yes	characteristic
5	C₉×Dic₈₉	—	7	1	no	maximal, Hall
6	Dic₆₂₃	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇×C₈₉	C₃×C₄	1	1	yes	characteristic
8	C₂×C₉×C₈₉	—	7	1	no	—
9	C₂×C₇×C₈₉	C₂×C₉	1	1	yes	characteristic
10	C₃×Dic₈₉	—	21	1	no	—
11	C₉×C₈₉	—	7	1	no	Hall
12	C₇×C₈₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₈₉	AGL(1,𝔽₇)	1	1	yes	characteristic
14	Dic₈₉	—	21	1	no	Hall
15	C₃×C₈₉	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
16	Dic₇⋊C₉	—	89	1	no	maximal, Hall
17	C₂×C₈₉	D₇⋊C₉	1	1	yes	characteristic
18	C₂×C₇⋊C₉	D₈₉	1	1	yes	characteristic
19	C₈₉	Dic₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
20	C₃×Dic₇	—	89	1	no	—
21	C₇⋊C₉	Dic₈₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	C₃×D₈₉	1	1	yes	characteristic
23	C₄×C₉	—	623	1	no	Hall
24	Dic₇	—	89	1	no	Hall
25	C₃×C₇	C₃×Dic₈₉	1	1	yes	characteristic
26	C₂×C₉	—	7	1	no	—
27	C₂×C₇	C₉×D₈₉	1	1	yes	characteristic
28	C₃×C₄	—	1869	1	no	—
29	C₉	—	7	1	no	Sylow
30	C₇	C₉×Dic₈₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	ΓL(1,𝔽₈)⋊D₈₉	1	1	yes	characteristic
32	C₄	—	1869	1	no	Sylow
33	C₃	ΓL(1,𝔽₈)⋊Dic₈₉	1	1	yes	characteristic
34	C₂	(C₇⋊C₉)⋊D₈₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	ΓL(1,𝔽₈)⋊D₈₉
commutator, hypocenter	C₇×C₈₉	C₄×C₉
Fitting, socle, prime radical, cosocle	C₂×C₃×C₇×C₈₉	C₂×C₃
LCS	G ▷ C₇×C₈₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
3. C₇⋊C₉×C₈₉	C₄	semidirect
6. Dic₆₂₃	C₉	semidirect
12. C₇×C₈₉	C₄×C₉	semidirect
19. C₈₉	Dic₇⋊C₉	semidirect
21. C₇⋊C₉	Dic₈₉	semidirect
30. C₇	C₉×Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇⋊C₉×C₈₉	2
C₃×Dic₆₂₃	3
C₉×Dic₈₉	7
Dic₇⋊C₉	89

Subgroups — (C7⋊C9)⋊Dic89 #36375830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₇⋊C₉)⋊Dic₈₉ #36375830