Subgroups — #28412653

Order 14661.

10 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19096556	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₈₁	C₉	1	1	yes	characteristic
3	C₃×C₁₈₁	C₂₇	1	1	yes	characteristic
4	C₁₈₁	C₈₁	1	1	yes	characteristic, complemented, Sylow
5	C₈₁	—	181	1	no	maximal, Sylow
6	C₂₇	—	181	1	no	—
7	C₉	#13108658	1	1	yes	characteristic
8	C₃	#19096564	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₉	#13108658
commutator, hypocenter	C₁₈₁	C₈₁
Fitting	C₉×C₁₈₁	C₉
socle, prime radical	C₃×C₁₈₁	C₂₇
cosocle	#19096556	C₃
LCS	G ▷ C₁₈₁
UCS	C₁ ◁ C₉

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

N	H ≅ G/N	type
4. C₁₈₁	C₈₁	semidirect

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

subgroup	index
#19096556	3
C₈₁	181