Subgroups — #36370604

Order 22148.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊D₇₉₁	C₂	1	1	yes	maximal, characteristic
2	C₇²×C₁₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	D₇₉₁	—	14	4	no	—
4	C₇×C₁₁₃	—	2	4	no	—
5	#90673	—	49	1	no	maximal, Hall
6	D₁₁₃	—	49	1	no	—
7	#5997	—	113	1	no	maximal, Hall
8	C₁₁₃	#5997	1	1	yes	characteristic, complemented, Sylow
9	C₇⋊D₇	—	113	1	no	—
10	C₇²	#90673	1	1	yes	characteristic, complemented, Sylow
11	D₇	—	1582	4	no	—
12	C₇	—	2	4	no	—
13	C₄	—	5537	1	no	Sylow
14	C₂	—	5537	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₁₁₃	C₄
prime radical, cosocle	C₇⋊D₇₉₁	C₂
LCS	G ▷ C₇²×C₁₁₃
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.