Subgroups — C₃×C₃⋊AGL(1,𝔽₂₃) #17986913

Order 4554.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₃⋊C₁₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊AGL(1,𝔽₂₃)	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×AGL(1,𝔽₂₃)	—	3	1	no	maximal
4	C₃×C₂₃⋊C₁₁	—	2	1	no	—
5	C₃×C₂₃⋊C₁₁	D₃	1	1	yes	characteristic, complemented
6	C₃×C₂₃⋊C₁₁	C₂×C₃	1	1	yes	characteristic, complemented
7	AGL(1,𝔽₂₃)	—	3	1	no	Hall
8	C₃×D₆₉	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
9	C₂₃⋊C₁₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₂₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
11	C₃×D₃×C₁₁	—	23	1	no	maximal, Hall
12	D₆₉	C₃×C₁₁	1	1	yes	characteristic, complemented
13	C₃×D₂₃	—	3	1	no	—
14	C₃²×C₁₁	—	23	1	no	Hall
15	C₃×C₂₃	—	2	1	no	—
16	C₃×C₂₃	D₃×C₁₁	1	1	yes	characteristic, complemented
17	C₃×C₂₃	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
18	C₂×C₃×C₁₁	—	69	1	no	—
19	D₃×C₁₁	—	23	1	no	—
20	D₂₃	—	3	1	no	Hall
21	C₃×C₁₁	—	23	1	no	—
22	C₃×C₁₁	—	23	1	no	—
23	C₃×C₁₁	—	46	1	no	—
24	C₂₃	C₃×D₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₁₁	—	69	1	no	Hall
26	C₃×D₃	—	23	1	no	Hall
27	C₁₁	—	23	1	no	Sylow
28	C₃²	AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	69	1	no	—
30	D₃	—	23	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented
33	C₃	C₃⋊AGL(1,𝔽₂₃)	1	1	yes	characteristic, direct product factor
34	C₂	—	69	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₃⋊AGL(1,𝔽₂₃)
commutator, cosocle, hypocenter	C₃×C₂₃	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₂₃	C₂×C₁₁
LCS	G ▷ C₃×C₂₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₃⋊C₁₁	C₂	semidirect
2. C₃⋊AGL(1,𝔽₂₃)	C₃	direct (N × H)
5. C₃×C₂₃⋊C₁₁	D₃	semidirect
6. C₃×C₂₃⋊C₁₁	C₂×C₃	semidirect
8. C₃×D₆₉	C₁₁	semidirect
9. C₂₃⋊C₁₁	C₃×D₃	semidirect
10. C₃²×C₂₃	C₂×C₁₁	semidirect
12. D₆₉	C₃×C₁₁	semidirect
16. C₃×C₂₃	D₃×C₁₁	semidirect
17. C₃×C₂₃	C₂×C₃×C₁₁	semidirect
24. C₂₃	C₃×D₃×C₁₁	semidirect
28. C₃²	AGL(1,𝔽₂₃)	semidirect
32. C₃	C₃×AGL(1,𝔽₂₃)	semidirect
33. C₃	C₃⋊AGL(1,𝔽₂₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₂₃⋊C₁₁	2
C₃⋊AGL(1,𝔽₂₃)	3
C₃×AGL(1,𝔽₂₃)	3
C₃×D₆₉	11
C₃×D₃×C₁₁	23

Subgroups — C3×C3⋊AGL(1,𝔽23) #17986913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊AGL(1,𝔽₂₃) #17986913