Subgroups — C₂×C₃₁⋊AGL(1,𝔽₂₃) #44535879

Order 31372.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁⋊AGL(1,𝔽₂₃)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃₁×C₂₃⋊C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×C₂₃⋊C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₇₁₃	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₂₃×C₃₁	C₂×C₁₁	1	1	yes	characteristic, complemented
6	D₇₁₃	C₂×C₁₁	1	2	yes	complemented
7	C₂×C₁₁×D₃₁	—	23	1	no	maximal, Hall
8	C₂×AGL(1,𝔽₂₃)	—	31	1	no	maximal, Hall
9	C₂₃×C₃₁	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁×C₃₁	—	23	1	no	—
11	C₁₁×D₃₁	—	23	2	no	—
12	C₂×C₂₃⋊C₁₁	D₃₁	1	1	yes	characteristic, complemented
13	AGL(1,𝔽₂₃)	—	31	2	no	—
14	C₁₁×C₃₁	—	23	1	no	Hall
15	C₂₃⋊C₁₁	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
16	C₂×D₃₁	—	23	1	no	Hall
17	C₂×D₂₃	—	31	1	no	Hall
18	C₂×C₃₁	AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented
19	D₃₁	—	23	2	no	—
20	C₂×C₂₃	C₁₁×D₃₁	1	1	yes	characteristic, complemented
21	D₂₃	—	31	2	no	—
22	C₂²×C₁₁	—	713	1	no	Hall
23	C₃₁	C₂×AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented, Sylow
24	C₂₃	C₂×C₁₁×D₃₁	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₁₁	—	23	1	no	—
26	C₂×C₁₁	—	713	2	no	—
27	C₁₁	—	23	1	no	Sylow
28	C₂²	—	713	1	no	Sylow
29	C₂	—	713	2	no	—
30	C₂	C₃₁⋊AGL(1,𝔽₂₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃₁⋊AGL(1,𝔽₂₃)
commutator, cosocle, hypocenter	C₂₃×C₃₁	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₂₃×C₃₁	C₂×C₁₁
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.