Finite Group Databasebeta

← C₇⋊(C₇⋊#67063) #31775313

Subgroups — C₇⋊(C₇⋊#67063) #31775313

Order 17444.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₈₉	C₂	1	1	yes	maximal, characteristic
2	C₇²×C₈₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇⋊#67063	—	7	8	no	maximal
4	C₇×D₈₉	D₇	1	8	yes	—
5	C₇×C₈₉	Dic₇	1	8	yes	complemented
6	#67063	—	49	1	no	Hall
7	C₇⋊Dic₇	—	89	1	no	maximal, Hall
8	D₈₉	C₇⋊D₇	1	1	yes	characteristic
9	C₂×C₇²	—	89	1	no	—
10	C₈₉	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Sylow
11	C₇²	#67063	1	1	yes	characteristic, complemented, Sylow
12	Dic₇	—	623	8	no	—
13	C₂×C₇	—	89	8	no	—
14	C₇	C₇⋊#67063	1	8	yes	complemented
15	C₄	—	4361	1	no	Sylow
16	C₂	—	89	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₈₉	C₄
prime radical, cosocle	C₇²×D₈₉	C₂
LCS	G ▷ C₇²×C₈₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₇²×C₈₉	C₄	semidirect
5. C₇×C₈₉	Dic₇	semidirect
10. C₈₉	C₇⋊Dic₇	semidirect
11. C₇²	#67063	semidirect
14. C₇	C₇⋊#67063	semidirect

Maximal subgroups

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

subgroup	index
C₇²×D₈₉	2
C₇⋊#67063	7
C₇⋊Dic₇	89