Subgroups — C₁₂₀₁⋊C₂₇ #44569804

Order 32427.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₂₀₁	C₃	1	1	yes	maximal, characteristic
2	C₃×C₁₂₀₁	C₉	1	1	yes	characteristic
3	C₁₂₀₁	C₂₇	1	1	yes	characteristic, complemented, Sylow
4	C₂₇	—	1201	1	no	maximal, Sylow
5	C₉	C₁₂₀₁⋊C₃	1	1	yes	characteristic
6	C₃	C₁₂₀₁⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₉	C₁₂₀₁⋊C₃
commutator, hypocenter	C₁₂₀₁	C₂₇
Fitting, cosocle	C₉×C₁₂₀₁	C₃
socle, prime radical	C₃×C₁₂₀₁	C₉
LCS	G ▷ C₁₂₀₁
UCS	C₁ ◁ C₉

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

N	H ≅ G/N	type
3. C₁₂₀₁	C₂₇	semidirect

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

subgroup	index
C₉×C₁₂₀₁	3
C₂₇	1201