Subgroups — C₇⋊C₈ #282

Order 56.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇	C₄	1	1	yes	characteristic
3	C₈	—	7	1	no	maximal, Sylow
4	C₇	C₈	1	1	yes	characteristic, complemented, Sylow
5	C₄	D₇	1	1	yes	characteristic
6	C₂	Dic₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₇
commutator, hypocenter	C₇	C₈
Fitting, cosocle	C₄×C₇	C₂
socle, prime radical	C₂×C₇	C₄
LCS	G ▷ C₇
UCS	C₁ ◁ C₄

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

N	H ≅ G/N	type
4. C₇	C₈	semidirect

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

subgroup	index
C₄×C₇	2
C₈	7