Subgroups — C₃₁⋊(Dic₂₃⋊C₁₁) #44535875

Order 31372.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×C₂₃⋊C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₃₁×C₂₃⋊C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₇₁₃	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₂₃×C₃₁	C₂×C₁₁	1	1	yes	characteristic
5	C₁₁×Dic₃₁	—	23	1	no	maximal, Hall
6	Dic₂₃⋊C₁₁	—	31	1	no	maximal, Hall
7	C₂₃×C₃₁	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₁×C₃₁	—	23	1	no	—
9	C₂×C₂₃⋊C₁₁	D₃₁	1	1	yes	characteristic
10	C₁₁×C₃₁	—	23	1	no	Hall
11	C₂₃⋊C₁₁	Dic₃₁	1	1	yes	characteristic, complemented, Hall
12	Dic₃₁	—	23	1	no	Hall
13	Dic₂₃	—	31	1	no	Hall
14	C₂×C₃₁	AGL(1,𝔽₂₃)	1	1	yes	characteristic
15	C₂×C₂₃	C₁₁×D₃₁	1	1	yes	characteristic
16	C₄×C₁₁	—	713	1	no	Hall
17	C₃₁	Dic₂₃⋊C₁₁	1	1	yes	characteristic, complemented, Sylow
18	C₂₃	C₁₁×Dic₃₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₁₁	—	23	1	no	—
20	C₁₁	—	23	1	no	Sylow
21	C₄	—	713	1	no	Sylow
22	C₂	C₃₁⋊AGL(1,𝔽₂₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃₁⋊AGL(1,𝔽₂₃)
commutator, hypocenter	C₂₃×C₃₁	C₄×C₁₁
Fitting, socle, cosocle	C₂×C₂₃×C₃₁	C₂×C₁₁
prime radical	C₂×C₃₁×C₂₃⋊C₁₁	C₂
LCS	G ▷ C₂₃×C₃₁
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.