Subgroups — C₃×C₄⋊AGL(1,𝔽₁₁) #13050321

Order 1320.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×AGL(1,𝔽₁₁)	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊AGL(1,𝔽₁₁)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₁₁⋊C₅	C₂²	1	1	yes	characteristic
5	C₃×AGL(1,𝔽₁₁)	—	2	2	no	—
6	C₃×D₄₄	C₅	1	1	yes	maximal, characteristic, complemented, Hall
7	C₂×AGL(1,𝔽₁₁)	C₂×C₃	1	2	yes	complemented
8	C₄×C₁₁⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×C₁₁⋊C₅	D₄	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×D₁₁	C₂×C₅	1	2	yes	complemented
11	C₃×C₄×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×C₅×D₄	—	11	1	no	maximal, Hall
13	C₂×C₁₁⋊C₅	C₂²×C₃	1	1	yes	characteristic
14	AGL(1,𝔽₁₁)	—	2	2	no	—
15	D₄₄	C₃×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₁	C₂²×C₅	1	1	yes	characteristic
17	C₃×D₁₁	—	2	2	no	—
18	C₂²×C₃×C₅	—	11	2	no	—
19	C₃×C₄×C₅	—	11	1	no	—
20	C₁₁⋊C₅	C₃×D₄	1	1	yes	characteristic, complemented, Hall
21	C₂×D₁₁	C₂×C₃×C₅	1	2	yes	complemented
22	C₄×C₁₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
23	C₅×D₄	—	11	1	no	Hall
24	C₃×C₁₁	C₅×D₄	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₅	—	11	1	no	—
26	C₂×C₃×C₅	—	22	2	no	—
27	C₃×D₄	—	11	1	no	Hall
28	C₂×C₁₁	C₂²×C₃×C₅	1	1	yes	characteristic
29	D₁₁	—	2	2	no	—
30	C₂²×C₅	—	11	2	no	—
31	C₄×C₅	—	11	1	no	—
32	C₃×C₅	—	11	1	no	Hall
33	C₂²×C₃	—	11	2	no	—
34	C₃×C₄	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
35	C₁₁	C₃×C₅×D₄	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₅	—	11	1	no	—
37	C₂×C₅	—	22	2	no	—
38	D₄	—	11	1	no	Sylow
39	C₂×C₃	—	22	2	no	—
40	C₂×C₃	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic
41	C₅	—	11	1	no	Sylow
42	C₂²	—	11	2	no	—
43	C₄	C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
44	C₃	C₄⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	22	2	no	—
46	C₂	C₂×C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×AGL(1,𝔽₁₁)
commutator, cosocle	C₂×C₁₁	C₂²×C₃×C₅
Frattini	C₂	C₂×C₃×AGL(1,𝔽₁₁)
Fitting	C₃×C₄×C₁₁	C₂×C₅
socle	C₂×C₃×C₁₁	C₂²×C₅
hypercenter	C₃×C₄	AGL(1,𝔽₁₁)
hypocenter	C₁₁	C₃×C₅×D₄
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×AGL(1,𝔽₁₁)	C₂	semidirect
2. C₃×C₄×C₁₁⋊C₅	C₂	semidirect
3. C₄⋊AGL(1,𝔽₁₁)	C₃	direct (N × H)
6. C₃×D₄₄	C₅	semidirect
7. C₂×AGL(1,𝔽₁₁)	C₂×C₃	semidirect
8. C₄×C₁₁⋊C₅	C₂×C₃	semidirect
9. C₃×C₁₁⋊C₅	D₄	semidirect
10. C₂×C₃×D₁₁	C₂×C₅	semidirect
11. C₃×C₄×C₁₁	C₂×C₅	semidirect
15. D₄₄	C₃×C₅	semidirect
20. C₁₁⋊C₅	C₃×D₄	semidirect
21. C₂×D₁₁	C₂×C₃×C₅	semidirect
22. C₄×C₁₁	C₂×C₃×C₅	semidirect
24. C₃×C₁₁	C₅×D₄	semidirect
34. C₃×C₄	AGL(1,𝔽₁₁)	semidirect
35. C₁₁	C₃×C₅×D₄	semidirect
43. C₄	C₃×AGL(1,𝔽₁₁)	semidirect
44. C₃	C₄⋊AGL(1,𝔽₁₁)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×AGL(1,𝔽₁₁)	2
C₃×C₄×C₁₁⋊C₅	2
C₄⋊AGL(1,𝔽₁₁)	3
C₃×D₄₄	5
C₃×C₅×D₄	11

Subgroups — C3×C4⋊AGL(1,𝔽11) #13050321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄⋊AGL(1,𝔽₁₁) #13050321