Subgroups — #44501585

Order 30681.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₄₈₇	C₃	1	1	yes	maximal, characteristic
2	#17983938	—	7	1	no	maximal, Hall
3	C₇×C₄₈₇	C₉	1	1	yes	characteristic, complemented, Hall
4	C₃×C₄₈₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
5	C₄₈₇	C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
6	C₇⋊C₉	—	487	1	no	maximal, Hall
7	C₃×C₇	C₄₈₇⋊C₃	1	1	yes	characteristic
8	C₉	—	3409	1	no	Sylow
9	C₇	#17983938	1	1	yes	characteristic, complemented, Sylow
10	C₃	#23779394	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₃	#23779394
commutator, hypocenter	C₇×C₄₈₇	C₉
Fitting, socle, prime radical, cosocle	C₃×C₇×C₄₈₇	C₃
LCS	G ▷ C₇×C₄₈₇
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.