Subgroups — C₄₉⋊C₉ #89199

Order 441.

9 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₉	C₃	1	1	yes	maximal, characteristic
2	C₇⋊C₉	—	7	1	no	maximal
3	C₄₉	C₉	1	1	yes	characteristic, complemented, Sylow
4	C₃×C₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
5	C₉	—	49	1	no	Sylow
6	C₇	C₇⋊C₉	1	1	yes	characteristic
7	C₃	C₄₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃	C₄₉⋊C₃
commutator, hypocenter	C₄₉	C₉
Frattini, socle, prime radical	C₃×C₇	ΓL(1,𝔽₈)
Fitting, cosocle	C₃×C₄₉	C₃
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₃

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

N	H ≅ G/N	type
3. C₄₉	C₉	semidirect

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

subgroup	index
C₃×C₄₉	3
C₇⋊C₉	7