Subgroups — #401⋊C₇ #89417

Order 448.

14 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#401	C₇	1	1	yes	maximal, characteristic, complemented, Sylow
2	AGL(1,𝔽₈)	—	8	1	no	maximal
3	#95	—	7	1	no	—
4	C₂²×C₄	—	7	1	no	—
5	C₂³	AGL(1,𝔽₈)	1	1	yes	characteristic
6	C₂×C₄	—	14	3	no	—
7	C₇	—	64	1	no	Sylow
8	C₂²	—	7	1	no	—
9	C₄	—	28	1	no	—
10	C₂	—	7	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	#401	C₇
Frattini, socle	C₂³	AGL(1,𝔽₈)
LCS	G ▷ #401
UCS	C₁

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

N	H ≅ G/N	type
1. #401	C₇	semidirect

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

subgroup	index
#401	7
AGL(1,𝔽₈)	8