Subgroups — C₇⋊C₂₇ #4424

Order 189.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉	C₃	1	1	yes	maximal, characteristic
2	C₂₇	—	7	1	no	maximal, Sylow
3	C₃×C₇	C₉	1	1	yes	characteristic
4	C₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
5	C₇	C₂₇	1	1	yes	characteristic, complemented, Sylow
6	C₃	C₇⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₉	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₂₇
Fitting, cosocle	C₇×C₉	C₃
socle, prime radical	C₃×C₇	C₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₉

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

N	H ≅ G/N	type
5. C₇	C₂₇	semidirect

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

subgroup	index
C₇×C₉	3
C₂₇	7