Subgroups — C₄⋊(C₃⋊AGL(1,𝔽₁₁)) #13050331

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)	—	3	1	no	maximal, Hall
4	C₂×C₃×C₁₁⋊C₅	C₂²	1	1	yes	characteristic
5	C₃⋊AGL(1,𝔽₁₁)	—	2	2	no	—
6	D₁₃₂	C₅	1	1	yes	maximal, characteristic, complemented, Hall
7	C₂×AGL(1,𝔽₁₁)	—	3	2	no	—
8	C₄×C₁₁⋊C₅	D₃	1	1	yes	characteristic, complemented
9	C₃×C₁₁⋊C₅	D₄	1	1	yes	characteristic, complemented, Hall
10	C₂×D₃₃	C₂×C₅	1	2	yes	complemented
11	C₃×C₄×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
12	C₅×D₁₂	—	11	1	no	maximal, Hall
13	C₂×C₁₁⋊C₅	C₂×D₃	1	1	yes	characteristic
14	AGL(1,𝔽₁₁)	—	6	2	no	—
15	D₄₄	—	3	1	no	Hall
16	C₂×C₃×C₁₁	C₂²×C₅	1	1	yes	characteristic
17	D₃₃	—	2	2	no	—
18	C₂×C₅×D₃	—	11	2	no	—
19	C₃×C₄×C₅	—	11	1	no	—
20	C₁₁⋊C₅	D₁₂	1	1	yes	characteristic, complemented, Hall
21	C₂×D₁₁	—	3	2	no	—
22	C₄×C₁₁	C₅×D₃	1	1	yes	characteristic, complemented
23	C₅×D₄	—	33	1	no	Hall
24	C₃×C₁₁	C₅×D₄	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₅	—	11	1	no	—
26	C₅×D₃	—	22	2	no	—
27	D₁₂	—	11	1	no	Hall
28	C₂×C₁₁	C₂×C₅×D₃	1	1	yes	characteristic
29	D₁₁	—	6	2	no	—
30	C₂²×C₅	—	33	2	no	—
31	C₄×C₅	—	11	1	no	—
32	C₃×C₅	—	11	1	no	Hall
33	C₂×D₃	—	11	2	no	—
34	C₃×C₄	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
35	C₁₁	C₅×D₁₂	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₅	—	11	1	no	—
37	C₂×C₅	—	66	2	no	—
38	D₄	—	33	1	no	Sylow
39	C₂×C₃	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic
40	D₃	—	22	2	no	—
41	C₅	—	11	1	no	Sylow
42	C₂²	—	33	2	no	—
43	C₄	C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
44	C₃	C₄⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	66	2	no	—
46	C₂	C₂×C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×C₃⋊AGL(1,𝔽₁₁)
commutator, socle, cosocle	C₂×C₃×C₁₁	C₂²×C₅
Fitting	C₃×C₄×C₁₁	C₂×C₅
hypercenter	C₄	C₃⋊AGL(1,𝔽₁₁)
hypocenter	C₃×C₁₁	C₅×D₄
LCS	G ▷ C₂×C₃×C₁₁ ▷ C₃×C₁₁
UCS	C₁ ◁ C₂ ◁ 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
6. D₁₃₂	C₅	semidirect
8. C₄×C₁₁⋊C₅	D₃	semidirect
9. C₃×C₁₁⋊C₅	D₄	semidirect
10. C₂×D₃₃	C₂×C₅	semidirect
11. C₃×C₄×C₁₁	C₂×C₅	semidirect
20. C₁₁⋊C₅	D₁₂	semidirect
22. C₄×C₁₁	C₅×D₃	semidirect
24. C₃×C₁₁	C₅×D₄	semidirect
34. C₃×C₄	AGL(1,𝔽₁₁)	semidirect
35. C₁₁	C₅×D₁₂	semidirect
43. C₄	C₃⋊AGL(1,𝔽₁₁)	semidirect
44. C₃	C₄⋊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
C₂×C₃⋊AGL(1,𝔽₁₁)	2
C₃×C₄×C₁₁⋊C₅	2
C₄⋊AGL(1,𝔽₁₁)	3
D₁₃₂	5
C₅×D₁₂	11

Subgroups — C4⋊(C3⋊AGL(1,𝔽11)) #13050331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊(C₃⋊AGL(1,𝔽₁₁)) #13050331