Subgroups — #45682000

Order 32949.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₅₂₃	C₃	1	1	yes	maximal, characteristic
2	#17989920	—	7	1	no	maximal, Hall
3	C₇×C₅₂₃	C₉	1	1	yes	characteristic, complemented, Hall
4	C₃×C₅₂₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
5	C₅₂₃	C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
6	C₇⋊C₉	—	523	1	no	maximal, Hall
7	C₃×C₇	C₅₂₃⋊C₃	1	1	yes	characteristic
8	C₉	—	3661	1	no	Sylow
9	C₇	#17989920	1	1	yes	characteristic, complemented, Sylow
10	C₃	#24926886	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₃	#24926886
commutator, hypocenter	C₇×C₅₂₃	C₉
Fitting, socle, prime radical, cosocle	C₃×C₇×C₅₂₃	C₃
LCS	G ▷ C₇×C₅₂₃
UCS	C₁ ◁ C₃

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

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