Subgroups — C₁₁×C₃⋊D₃×ΓL(1,𝔽₃₂) #44501822

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₁×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₁₁×ΓL(1,𝔽₃₂)	—	3	4	no	maximal
3	C₁₁×C₃⋊D₃×C₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×C₁₁×ΓL(1,𝔽₃₂)	D₃	1	4	yes	complemented
5	C₂×C₁₁×ΓL(1,𝔽₃₂)	—	9	1	no	Hall
6	C₃²×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃⋊D₃×ΓL(1,𝔽₃₂)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	D₃×C₁₁×C₃₁	—	3	4	no	—
9	C₁₁×ΓL(1,𝔽₃₂)	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
10	C₃²×ΓL(1,𝔽₃₂)	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₁×C₃₁	C₅×D₃	1	4	yes	complemented
12	C₅×C₁₁×C₃⋊D₃	—	31	1	no	maximal, Hall
13	D₃×ΓL(1,𝔽₃₂)	—	3	4	no	—
14	C₂×C₁₁×C₃₁	—	9	1	no	Hall
15	C₃⋊D₃×C₃₁	C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₅×C₁₁	—	31	1	no	Hall
17	C₃×ΓL(1,𝔽₃₂)	D₃×C₁₁	1	4	yes	complemented
18	C₁₁×C₃₁	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
19	C₅×D₃×C₁₁	—	93	4	no	—
20	C₂×ΓL(1,𝔽₃₂)	—	9	1	no	Hall
21	C₃²×C₃₁	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
22	C₁₁×C₃⋊D₃	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Hall
23	D₃×C₃₁	—	3	4	no	—
24	C₃×C₅×C₁₁	—	31	4	no	—
25	ΓL(1,𝔽₃₂)	C₁₁×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₅×C₁₁	—	279	1	no	Hall
27	C₃²×C₁₁	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Hall
28	C₃×C₃₁	C₅×D₃×C₁₁	1	4	yes	complemented
29	C₅×C₃⋊D₃	—	31	1	no	Hall
30	D₃×C₁₁	—	3	4	no	—
31	C₂×C₃₁	—	9	1	no	Hall
32	C₅×C₁₁	—	31	1	no	Hall
33	C₃²×C₅	—	31	1	no	Hall
34	C₃×C₁₁	D₃×ΓL(1,𝔽₃₂)	1	4	yes	complemented
35	C₃₁	C₅×C₁₁×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
36	C₅×D₃	—	93	4	no	—
37	C₂×C₁₁	—	9	1	no	Hall
38	C₃⋊D₃	C₁₁×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Hall
39	C₃×C₅	—	31	4	no	—
40	C₁₁	C₃⋊D₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	—	279	1	no	Hall
42	C₃²	C₂×C₁₁×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	3	4	no	—
44	C₅	—	31	1	no	Sylow
45	C₃	D₃×C₁₁×ΓL(1,𝔽₃₂)	1	4	yes	complemented
46	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	C₃⋊D₃×ΓL(1,𝔽₃₂)
commutator, cosocle, hypocenter	C₃²×C₃₁	C₂×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₃₁	C₂×C₅
LCS	G ▷ C₃²×C₃₁
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₁×ΓL(1,𝔽₃₂)	C₂	semidirect
3. C₁₁×C₃⋊D₃×C₃₁	C₅	semidirect
4. C₃×C₁₁×ΓL(1,𝔽₃₂)	D₃	semidirect
6. C₃²×C₁₁×C₃₁	C₂×C₅	semidirect
7. C₃⋊D₃×ΓL(1,𝔽₃₂)	C₁₁	direct (N × H)
9. C₁₁×ΓL(1,𝔽₃₂)	C₃⋊D₃	direct (N × H)
10. C₃²×ΓL(1,𝔽₃₂)	C₂×C₁₁	semidirect
11. C₃×C₁₁×C₃₁	C₅×D₃	semidirect
15. C₃⋊D₃×C₃₁	C₅×C₁₁	semidirect
17. C₃×ΓL(1,𝔽₃₂)	D₃×C₁₁	semidirect
18. C₁₁×C₃₁	C₅×C₃⋊D₃	semidirect
21. C₃²×C₃₁	C₂×C₅×C₁₁	semidirect
22. C₁₁×C₃⋊D₃	ΓL(1,𝔽₃₂)	direct (N × H)
25. ΓL(1,𝔽₃₂)	C₁₁×C₃⋊D₃	direct (N × H)
27. C₃²×C₁₁	C₂×ΓL(1,𝔽₃₂)	semidirect
28. C₃×C₃₁	C₅×D₃×C₁₁	semidirect
34. C₃×C₁₁	D₃×ΓL(1,𝔽₃₂)	semidirect
35. C₃₁	C₅×C₁₁×C₃⋊D₃	semidirect
38. C₃⋊D₃	C₁₁×ΓL(1,𝔽₃₂)	direct (N × H)
40. C₁₁	C₃⋊D₃×ΓL(1,𝔽₃₂)	direct (N × H)
42. C₃²	C₂×C₁₁×ΓL(1,𝔽₃₂)	semidirect
45. C₃	D₃×C₁₁×ΓL(1,𝔽₃₂)	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₁×ΓL(1,𝔽₃₂)	2
D₃×C₁₁×ΓL(1,𝔽₃₂)	3
C₁₁×C₃⋊D₃×C₃₁	5
C₃⋊D₃×ΓL(1,𝔽₃₂)	11
C₅×C₁₁×C₃⋊D₃	31

Subgroups — C11×C3⋊D3×ΓL(1,𝔽32) #44501822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₃⋊D₃×ΓL(1,𝔽₃₂) #44501822