Subgroups — D₃×AGL(1,𝔽₁₁) #10620345

Order 660.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊AGL(1,𝔽₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×AGL(1,𝔽₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×AGL(1,𝔽₁₁)	—	3	1	no	maximal, Hall
5	C₃×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
7	C₂×C₁₁⋊C₅	—	3	1	no	—
8	AGL(1,𝔽₁₁)	—	3	1	no	—
9	AGL(1,𝔽₁₁)	D₃	1	1	yes	characteristic, direct product factor
10	D₃₃	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃×D₁₁	C₂×C₅	1	1	yes	characteristic, complemented
12	D₃×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
13	C₂×C₅×D₃	—	11	1	no	maximal, Hall
14	C₁₁⋊C₅	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₂×D₁₁	—	3	1	no	Hall
16	C₃×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₅	—	11	1	no	—
18	C₅×D₃	—	11	1	no	—
19	C₅×D₃	—	11	1	no	—
20	C₂×C₁₁	—	3	1	no	—
21	D₁₁	—	3	1	no	—
22	D₁₁	C₅×D₃	1	1	yes	characteristic, complemented
23	C₂²×C₅	—	33	1	no	Hall
24	C₃×C₅	—	11	1	no	Hall
25	C₂×D₃	—	11	1	no	Hall
26	C₁₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₅	—	11	1	no	—
28	C₂×C₅	—	33	1	no	—
29	C₂×C₅	—	33	1	no	—
30	C₂×C₃	—	11	1	no	—
31	D₃	—	11	1	no	—
32	D₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
33	C₅	—	11	1	no	Sylow
34	C₂²	—	33	1	no	Sylow
35	C₃	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	11	1	no	—
38	C₂	—	33	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁	C₂²×C₅
LCS	G ▷ C₃×C₁₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊AGL(1,𝔽₁₁)	C₂	semidirect
2. D₃×C₁₁⋊C₅	C₂	semidirect
3. C₃×AGL(1,𝔽₁₁)	C₂	semidirect
5. C₃×C₁₁⋊C₅	C₂²	semidirect
6. D₃×D₁₁	C₅	semidirect
9. AGL(1,𝔽₁₁)	D₃	direct (N × H)
10. D₃₃	C₂×C₅	semidirect
11. C₃×D₁₁	C₂×C₅	semidirect
12. D₃×C₁₁	C₂×C₅	semidirect
14. C₁₁⋊C₅	C₂×D₃	semidirect
16. C₃×C₁₁	C₂²×C₅	semidirect
22. D₁₁	C₅×D₃	semidirect
26. C₁₁	C₂×C₅×D₃	semidirect
32. D₃	AGL(1,𝔽₁₁)	direct (N × H)
35. C₃	C₂×AGL(1,𝔽₁₁)	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊AGL(1,𝔽₁₁)	2
D₃×C₁₁⋊C₅	2
C₃×AGL(1,𝔽₁₁)	2
C₂×AGL(1,𝔽₁₁)	3
D₃×D₁₁	5
C₂×C₅×D₃	11

Subgroups — D3×AGL(1,𝔽11) #10620345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×AGL(1,𝔽₁₁) #10620345