Subgroups — C₃×C₇₃×AGL(1,𝔽₁₁) #37562801

Order 24090.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁⋊C₅×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇₃×AGL(1,𝔽₁₁)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₁₁×C₇₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁⋊C₅×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₇₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₅×C₇₃	—	11	1	no	maximal, Hall
7	D₁₁×C₇₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃×C₅×C₇₃	—	11	1	no	Hall
9	C₁₁×C₇₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₇₃	—	11	1	no	Hall
11	C₂×C₃×C₇₃	—	11	1	no	Hall
12	C₅×C₇₃	—	11	1	no	Hall
13	C₃×AGL(1,𝔽₁₁)	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×C₇₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₁⋊C₅	C₂×C₇₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇₃	—	11	1	no	Hall
17	AGL(1,𝔽₁₁)	C₃×C₇₃	1	1	yes	characteristic, direct product factor, Hall
18	C₇₃	C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×D₁₁	C₅×C₇₃	1	1	yes	characteristic, complemented, Hall
20	C₁₁⋊C₅	C₂×C₃×C₇₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁	C₂×C₅×C₇₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₅	—	11	1	no	Hall
23	D₁₁	C₃×C₅×C₇₃	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅	—	11	1	no	Hall
25	C₁₁	C₂×C₃×C₅×C₇₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	11	1	no	Hall
27	C₂×C₃	—	11	1	no	Hall
28	C₅	—	11	1	no	Sylow
29	C₃	C₇₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇₃	AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₁₁	C₂×C₃×C₅×C₇₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₇₃	C₂×C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₃×C₇₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁⋊C₅×C₇₃	C₂	semidirect
2. C₇₃×AGL(1,𝔽₁₁)	C₃	direct (N × H)
3. C₃×D₁₁×C₇₃	C₅	semidirect
4. C₁₁⋊C₅×C₇₃	C₂×C₃	semidirect
5. C₃×C₁₁×C₇₃	C₂×C₅	semidirect
7. D₁₁×C₇₃	C₃×C₅	semidirect
9. C₁₁×C₇₃	C₂×C₃×C₅	semidirect
13. C₃×AGL(1,𝔽₁₁)	C₇₃	direct (N × H)
14. C₃×C₇₃	AGL(1,𝔽₁₁)	direct (N × H)
15. C₃×C₁₁⋊C₅	C₂×C₇₃	semidirect
17. AGL(1,𝔽₁₁)	C₃×C₇₃	direct (N × H)
18. C₇₃	C₃×AGL(1,𝔽₁₁)	direct (N × H)
19. C₃×D₁₁	C₅×C₇₃	semidirect
20. C₁₁⋊C₅	C₂×C₃×C₇₃	semidirect
21. C₃×C₁₁	C₂×C₅×C₇₃	semidirect
23. D₁₁	C₃×C₅×C₇₃	semidirect
25. C₁₁	C₂×C₃×C₅×C₇₃	semidirect
29. C₃	C₇₃×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
C₃×C₁₁⋊C₅×C₇₃	2
C₇₃×AGL(1,𝔽₁₁)	3
C₃×D₁₁×C₇₃	5
C₂×C₃×C₅×C₇₃	11
C₃×AGL(1,𝔽₁₁)	73

Subgroups — C3×C73×AGL(1,𝔽11) #37562801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇₃×AGL(1,𝔽₁₁) #37562801