Subgroups — D₃₁×AGL(1,𝔽₂₃) #44535877

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	1	yes	maximal, characteristic, complemented
2	C₃₁×AGL(1,𝔽₂₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₁×C₂₃⋊C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×C₂₃⋊C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₃×D₃₁	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
6	D₇₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented
7	C₂₃×D₃₁	C₂×C₁₁	1	1	yes	characteristic, complemented
8	C₃₁×D₂₃	C₂×C₁₁	1	1	yes	characteristic, complemented
9	C₂×C₁₁×D₃₁	—	23	1	no	maximal, Hall
10	C₂×AGL(1,𝔽₂₃)	—	31	1	no	maximal, Hall
11	C₂₃×C₃₁	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×C₃₁	—	23	1	no	—
13	C₁₁×D₃₁	—	23	1	no	—
14	C₁₁×D₃₁	—	23	1	no	—
15	C₂×C₂₃⋊C₁₁	—	31	1	no	—
16	AGL(1,𝔽₂₃)	—	31	1	no	—
17	AGL(1,𝔽₂₃)	D₃₁	1	1	yes	characteristic, direct product factor
18	C₁₁×C₃₁	—	23	1	no	Hall
19	C₂₃⋊C₁₁	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃₁	—	23	1	no	Hall
21	C₂×D₂₃	—	31	1	no	Hall
22	C₂×C₃₁	—	23	1	no	—
23	D₃₁	—	23	1	no	—
24	D₃₁	AGL(1,𝔽₂₃)	1	1	yes	characteristic, direct product factor
25	C₂×C₂₃	—	31	1	no	—
26	D₂₃	—	31	1	no	—
27	D₂₃	C₁₁×D₃₁	1	1	yes	characteristic, complemented
28	C₂²×C₁₁	—	713	1	no	Hall
29	C₃₁	C₂×AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented, Sylow
30	C₂₃	C₂×C₁₁×D₃₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₁₁	—	23	1	no	—
32	C₂×C₁₁	—	713	1	no	—
33	C₂×C₁₁	—	713	1	no	—
34	C₁₁	—	23	1	no	Sylow
35	C₂²	—	713	1	no	Sylow
36	C₂	—	23	1	no	—
37	C₂	—	31	1	no	—
38	C₂	—	713	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₃×C₃₁	C₂²×C₁₁
LCS	G ▷ C₂₃×C₃₁
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃₁⋊AGL(1,𝔽₂₃)	C₂	semidirect
2. C₃₁×AGL(1,𝔽₂₃)	C₂	semidirect
3. D₃₁×C₂₃⋊C₁₁	C₂	semidirect
4. C₃₁×C₂₃⋊C₁₁	C₂²	semidirect
5. D₂₃×D₃₁	C₁₁	semidirect
6. D₇₁₃	C₂×C₁₁	semidirect
7. C₂₃×D₃₁	C₂×C₁₁	semidirect
8. C₃₁×D₂₃	C₂×C₁₁	semidirect
11. C₂₃×C₃₁	C₂²×C₁₁	semidirect
17. AGL(1,𝔽₂₃)	D₃₁	direct (N × H)
19. C₂₃⋊C₁₁	C₂×D₃₁	semidirect
24. D₃₁	AGL(1,𝔽₂₃)	direct (N × H)
27. D₂₃	C₁₁×D₃₁	semidirect
29. C₃₁	C₂×AGL(1,𝔽₂₃)	semidirect
30. C₂₃	C₂×C₁₁×D₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁⋊AGL(1,𝔽₂₃)	2
C₃₁×AGL(1,𝔽₂₃)	2
D₃₁×C₂₃⋊C₁₁	2
D₂₃×D₃₁	11
C₂×C₁₁×D₃₁	23
C₂×AGL(1,𝔽₂₃)	31

Subgroups — D31×AGL(1,𝔽23) #44535877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₁×AGL(1,𝔽₂₃) #44535877