Subgroups — #50311069

Order 38619.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₆₁₃⋊C₃	C₃	1	1	yes	maximal, characteristic
2	#19149452	—	7	1	no	maximal, Hall
3	C₇×C₆₁₃	C₉	1	1	yes	characteristic, complemented, Hall
4	C₆₁₃⋊C₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
5	C₆₁₃	C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
6	C₇⋊C₉	—	613	1	no	maximal, Hall
7	C₃×C₇	—	613	1	no	—
8	C₉	—	4291	1	no	Sylow
9	C₇	#19149452	1	1	yes	characteristic, complemented, Sylow
10	C₃	—	613	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇×C₆₁₃	C₉
prime radical, cosocle	C₇×C₆₁₃⋊C₃	C₃
LCS	G ▷ C₇×C₆₁₃
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.