Subgroups — C₄₉⋊C₃ #3858

Order 147.

6 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₉	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
2	ΓL(1,𝔽₈)	—	7	1	no	maximal
3	C₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
4	C₃	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₄₉	C₃
Frattini, socle	C₇	ΓL(1,𝔽₈)
LCS	G ▷ C₄₉
UCS	C₁

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

N	H ≅ G/N	type
1. C₄₉	C₃	semidirect

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

subgroup	index
C₄₉	3
ΓL(1,𝔽₈)	7