Subgroups — C₃²×Dic₂₃⋊C₁₁ #22603443

Order 9108.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₂₃⋊C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₂₃⋊C₁₁	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₂₃⋊C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₂₃⋊C₁₁	C₂×C₃	1	4	yes	—
5	Dic₂₃⋊C₁₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×Dic₂₃	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
7	C₃×C₂₃⋊C₁₁	C₃×C₄	1	4	yes	complemented
8	C₂×C₂₃⋊C₁₁	C₂×C₃²	1	1	yes	characteristic
9	C₂×C₃²×C₂₃	C₂×C₁₁	1	1	yes	characteristic
10	C₃²×C₄×C₁₁	—	23	1	no	maximal, Hall
11	C₃×Dic₂₃	C₃×C₁₁	1	4	yes	complemented
12	C₂₃⋊C₁₁	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
13	C₃²×C₂₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃²×C₁₁	—	23	1	no	—
15	C₂×C₃×C₂₃	C₂×C₃×C₁₁	1	4	yes	—
16	C₃×C₄×C₁₁	—	23	4	no	—
17	C₃²×C₁₁	—	23	1	no	Hall
18	Dic₂₃	C₃²×C₁₁	1	1	yes	characteristic, complemented, Hall
19	C₃×C₂₃	C₃×C₄×C₁₁	1	4	yes	complemented
20	C₂×C₃×C₁₁	—	23	4	no	—
21	C₂×C₂₃	C₂×C₃²×C₁₁	1	1	yes	characteristic
22	C₄×C₁₁	—	23	1	no	Hall
23	C₃²×C₄	—	23	1	no	Hall
24	C₃×C₁₁	—	23	4	no	—
25	C₂₃	C₃²×C₄×C₁₁	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₁	—	23	1	no	—
27	C₂×C₃²	AGL(1,𝔽₂₃)	1	1	yes	characteristic
28	C₃×C₄	—	23	4	no	—
29	C₁₁	—	23	1	no	Sylow
30	C₃²	Dic₂₃⋊C₁₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₃×AGL(1,𝔽₂₃)	1	4	yes	—
32	C₄	—	23	1	no	Sylow
33	C₃	C₃×Dic₂₃⋊C₁₁	1	4	yes	direct product factor
34	C₂	C₃²×AGL(1,𝔽₂₃)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²	AGL(1,𝔽₂₃)
commutator, hypocenter	C₂₃	C₃²×C₄×C₁₁
Frattini	C₂	C₃²×AGL(1,𝔽₂₃)
Fitting, socle	C₂×C₃²×C₂₃	C₂×C₁₁
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
2. C₃×Dic₂₃⋊C₁₁	C₃	direct (N × H)
3. C₃²×C₂₃⋊C₁₁	C₄	semidirect
5. Dic₂₃⋊C₁₁	C₃²	direct (N × H)
6. C₃²×Dic₂₃	C₁₁	semidirect
7. C₃×C₂₃⋊C₁₁	C₃×C₄	semidirect
11. C₃×Dic₂₃	C₃×C₁₁	semidirect
12. C₂₃⋊C₁₁	C₃²×C₄	semidirect
13. C₃²×C₂₃	C₄×C₁₁	semidirect
18. Dic₂₃	C₃²×C₁₁	semidirect
19. C₃×C₂₃	C₃×C₄×C₁₁	semidirect
25. C₂₃	C₃²×C₄×C₁₁	semidirect
30. C₃²	Dic₂₃⋊C₁₁	direct (N × H)
33. C₃	C₃×Dic₂₃⋊C₁₁	direct (N × H)

Subgroups — C32×Dic23⋊C11 #22603443

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×Dic₂₃⋊C₁₁ #22603443