Subgroups — #30633864

Order 16212.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22549226	C₂	1	1	yes	maximal, characteristic
2	C₇⋊#11715871	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#16860995	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×D₁₉₃	C₂×C₃	1	1	yes	characteristic
5	#11715871⋊C₃	—	7	1	no	maximal, Hall
6	C₇×C₁₉₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	D₁₉₃⋊C₃	—	14	1	no	—
8	#11715871	—	7	1	no	Hall
9	C₁₉₃⋊C₃	—	14	1	no	Hall
10	D₁₉₃	AGL(1,𝔽₇)	1	1	yes	characteristic
11	C₁₉₃	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic, complemented, Sylow
12	ΓL(1,𝔽₈)⋊C₄	—	193	1	no	maximal, Hall
13	C₂×ΓL(1,𝔽₈)	—	193	1	no	—
14	Dic₇	—	193	1	no	Hall
15	ΓL(1,𝔽₈)	—	772	1	no	Hall
16	C₂×C₇	—	193	1	no	—
17	C₃×C₄	—	1351	1	no	Hall
18	C₇	#11715871⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	2702	1	no	—
20	C₄	—	1351	1	no	Sylow
21	C₃	—	5404	1	no	Sylow
22	C₂	—	193	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇×C₁₉₃	C₃×C₄
prime radical	#22549226	C₂
cosocle	C₇×D₁₉₃	C₂×C₃
LCS	G ▷ C₇×C₁₉₃
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.