Subgroups — C₅₉×C₃⋊AGL(1,𝔽₁₁) #34085702

Order 19470.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁⋊C₅×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅₉×AGL(1,𝔽₁₁)	—	3	1	no	maximal, Hall
3	C₅₉×D₃₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁⋊C₅×C₅₉	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₅₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×D₃×C₅₉	—	11	1	no	maximal, Hall
7	D₁₁×C₅₉	—	3	1	no	Hall
8	C₃×C₅×C₅₉	—	11	1	no	Hall
9	C₁₁×C₅₉	C₅×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₅₉	—	33	1	no	Hall
11	D₃×C₅₉	—	11	1	no	Hall
12	C₃⋊AGL(1,𝔽₁₁)	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅×C₅₉	—	11	1	no	Hall
14	C₃×C₅₉	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₁⋊C₅	C₂×C₅₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅₉	—	33	1	no	Hall
17	AGL(1,𝔽₁₁)	—	3	1	no	Hall
18	D₃₃	C₅×C₅₉	1	1	yes	characteristic, complemented, Hall
19	C₅₉	C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor, Sylow
20	C₁₁⋊C₅	D₃×C₅₉	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁	C₂×C₅×C₅₉	1	1	yes	characteristic, complemented, Hall
22	C₅×D₃	—	11	1	no	Hall
23	D₁₁	—	3	1	no	Hall
24	C₃×C₅	—	11	1	no	Hall
25	C₁₁	C₅×D₃×C₅₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	33	1	no	Hall
27	D₃	—	11	1	no	Hall
28	C₅	—	11	1	no	Sylow
29	C₃	C₅₉×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	33	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅₉	C₃⋊AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₃×C₁₁	C₂×C₅×C₅₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₅₉	C₂×C₅
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₅₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁⋊C₅×C₅₉	C₂	semidirect
3. C₅₉×D₃₃	C₅	semidirect
4. C₁₁⋊C₅×C₅₉	D₃	semidirect
5. C₃×C₁₁×C₅₉	C₂×C₅	semidirect
9. C₁₁×C₅₉	C₅×D₃	semidirect
12. C₃⋊AGL(1,𝔽₁₁)	C₅₉	direct (N × H)
14. C₃×C₅₉	AGL(1,𝔽₁₁)	semidirect
15. C₃×C₁₁⋊C₅	C₂×C₅₉	semidirect
18. D₃₃	C₅×C₅₉	semidirect
19. C₅₉	C₃⋊AGL(1,𝔽₁₁)	direct (N × H)
20. C₁₁⋊C₅	D₃×C₅₉	semidirect
21. C₃×C₁₁	C₂×C₅×C₅₉	semidirect
25. C₁₁	C₅×D₃×C₅₉	semidirect
29. C₃	C₅₉×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×C₁₁⋊C₅×C₅₉	2
C₅₉×AGL(1,𝔽₁₁)	3
C₅₉×D₃₃	5
C₅×D₃×C₅₉	11
C₃⋊AGL(1,𝔽₁₁)	59

Subgroups — C59×C3⋊AGL(1,𝔽11) #34085702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×C₃⋊AGL(1,𝔽₁₁) #34085702