Subgroups — #45682005

Order 32949.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₅₂₃⋊C₃	C₃	1	1	yes	maximal, characteristic
2	#17989922	—	7	1	no	maximal, Hall
3	C₇×C₅₂₃	C₉	1	1	yes	characteristic, complemented, Hall
4	C₅₂₃⋊C₃	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	—	523	1	no	—
8	C₉	—	3661	1	no	Sylow
9	C₇	#17989922	1	1	yes	characteristic, complemented, Sylow
10	C₃	—	523	1	no	—

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

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.