Subgroups — #31799397

Order 17724.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17984521	C₂	1	1	yes	maximal, characteristic
2	Dic₁₄₇₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#17984521	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₂₁₁	C₂×C₃	1	1	yes	characteristic
5	(C₂₁₁⋊C₃)⋊C₄	—	7	1	no	maximal, Hall
6	C₇×C₂₁₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₂₁₁⋊C₃	—	14	1	no	—
8	Dic₂₁₁	—	7	1	no	Hall
9	C₂₁₁⋊C₃	—	14	1	no	Hall
10	C₂×C₂₁₁	AGL(1,𝔽₇)	1	1	yes	characteristic
11	C₂₁₁	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic, complemented, Sylow
12	ΓL(1,𝔽₈)⋊C₄	—	211	1	no	maximal, Hall
13	C₂×ΓL(1,𝔽₈)	—	422	1	no	—
14	Dic₇	—	211	1	no	Hall
15	ΓL(1,𝔽₈)	—	422	1	no	Hall
16	C₂×C₇	D₂₁₁⋊C₃	1	1	yes	characteristic
17	C₃×C₄	—	1477	1	no	Hall
18	C₇	(C₂₁₁⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	2954	1	no	—
20	C₄	—	1477	1	no	Sylow
21	C₃	—	2954	1	no	Sylow
22	C₂	#22579732	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#22579732
commutator, hypocenter	C₇×C₂₁₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₇×C₂₁₁	C₂×C₃
prime radical	C₂×#17984521	C₂
LCS	G ▷ C₇×C₂₁₁
UCS	C₁ ◁ C₂

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.