Subgroups — C₂×C₉⋊AGL(1,𝔽₁₁) #14520392

Order 1980.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉⋊AGL(1,𝔽₁₁)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃⋊AGL(1,𝔽₁₁)	—	3	1	no	maximal
4	C₉×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₉₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂×C₃×C₁₁⋊C₅	D₃	1	1	yes	characteristic
7	C₃⋊AGL(1,𝔽₁₁)	—	3	2	no	—
8	C₂×AGL(1,𝔽₁₁)	—	9	1	no	Hall
9	C₂×C₉×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
10	D₉₉	C₂×C₅	1	2	yes	complemented
11	C₂×C₅×D₉	—	11	1	no	maximal, Hall
12	C₃×C₁₁⋊C₅	C₂×D₃	1	1	yes	characteristic
13	C₂×D₃₃	—	3	1	no	—
14	C₂×C₁₁⋊C₅	D₉	1	1	yes	characteristic, complemented
15	AGL(1,𝔽₁₁)	—	9	2	no	—
16	C₉×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₉	—	11	1	no	—
18	C₅×D₉	—	11	2	no	—
19	C₂×C₃×C₁₁	C₅×D₃	1	1	yes	characteristic
20	D₃₃	—	3	2	no	—
21	C₂×C₅×D₃	—	33	1	no	—
22	C₁₁⋊C₅	C₂×D₉	1	1	yes	characteristic, complemented, Hall
23	C₅×C₉	—	11	1	no	Hall
24	C₂×D₁₁	—	9	1	no	Hall
25	C₂×D₉	—	11	1	no	Hall
26	C₃×C₁₁	C₂×C₅×D₃	1	1	yes	characteristic
27	C₂×C₃×C₅	—	11	1	no	—
28	C₅×D₃	—	33	2	no	—
29	C₂×C₁₁	C₅×D₉	1	1	yes	characteristic, complemented
30	D₁₁	—	9	2	no	—
31	C₂²×C₅	—	99	1	no	Hall
32	C₂×C₉	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
33	D₉	—	11	2	no	—
34	C₃×C₅	—	11	1	no	—
35	C₂×D₃	—	33	1	no	—
36	C₁₁	C₂×C₅×D₉	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₅	—	11	1	no	—
38	C₂×C₅	—	99	2	no	—
39	C₉	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃	C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
41	D₃	—	33	2	no	—
42	C₅	—	11	1	no	Sylow
43	C₂²	—	99	1	no	Sylow
44	C₃	C₂×C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
45	C₂	—	99	2	no	—
46	C₂	C₉⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₉⋊AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₉×C₁₁	C₂²×C₅
Frattini	C₃	C₂×C₃⋊AGL(1,𝔽₁₁)
Fitting	C₂×C₉×C₁₁	C₂×C₅
socle	C₂×C₃×C₁₁	C₅×D₃
LCS	G ▷ C₉×C₁₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×C₁₁⋊C₅	C₂	semidirect
2. C₉⋊AGL(1,𝔽₁₁)	C₂	direct (N × H)
4. C₉×C₁₁⋊C₅	C₂²	semidirect
5. C₂×D₉₉	C₅	semidirect
9. C₂×C₉×C₁₁	C₂×C₅	semidirect
10. D₉₉	C₂×C₅	semidirect
14. C₂×C₁₁⋊C₅	D₉	semidirect
16. C₉×C₁₁	C₂²×C₅	semidirect
22. C₁₁⋊C₅	C₂×D₉	semidirect
29. C₂×C₁₁	C₅×D₉	semidirect
32. C₂×C₉	AGL(1,𝔽₁₁)	semidirect
36. C₁₁	C₂×C₅×D₉	semidirect
39. C₉	C₂×AGL(1,𝔽₁₁)	semidirect
46. C₂	C₉⋊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×C₉×C₁₁⋊C₅	2
C₉⋊AGL(1,𝔽₁₁)	2
C₂×C₃⋊AGL(1,𝔽₁₁)	3
C₂×D₉₉	5
C₂×C₅×D₉	11

Subgroups — C2×C9⋊AGL(1,𝔽11) #14520392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉⋊AGL(1,𝔽₁₁) #14520392