Subgroups — C₉⋊(ΓL(1,𝔽₃₂)⋊D₁₁) #44501699

Order 30690.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₁×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(ΓL(1,𝔽₃₂)⋊D₁₁)	—	3	1	no	maximal
3	D₃₀₆₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×C₁₁×ΓL(1,𝔽₃₂)	D₃	1	1	yes	characteristic
5	ΓL(1,𝔽₃₂)⋊D₁₁	—	9	1	no	Hall
6	C₉×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₉⋊(D₃₁⋊C₅)	—	11	1	no	maximal, Hall
8	D₁₀₂₃	—	3	1	no	—
9	C₁₁×ΓL(1,𝔽₃₂)	D₉	1	1	yes	characteristic, complemented, Hall
10	C₉×ΓL(1,𝔽₃₂)	D₁₁	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₁×C₃₁	C₅×D₃	1	1	yes	characteristic
12	C₅×D₉₉	—	31	1	no	maximal, Hall
13	C₃⋊(D₃₁⋊C₅)	—	33	1	no	—
14	D₃₄₁	—	9	1	no	Hall
15	D₂₇₉	—	11	1	no	Hall
16	C₅×C₉×C₁₁	—	31	1	no	Hall
17	C₃×ΓL(1,𝔽₃₂)	D₃₃	1	1	yes	characteristic
18	C₁₁×C₃₁	C₅×D₉	1	1	yes	characteristic, complemented, Hall
19	C₅×D₃₃	—	93	1	no	—
20	D₃₁⋊C₅	—	99	1	no	Hall
21	C₉×C₃₁	C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
22	D₉₉	—	31	1	no	Hall
23	D₉₃	—	33	1	no	—
24	C₃×C₅×C₁₁	—	31	1	no	—
25	ΓL(1,𝔽₃₂)	D₉₉	1	1	yes	characteristic, complemented, Hall
26	C₅×D₁₁	—	279	1	no	Hall
27	C₉×C₁₁	D₃₁⋊C₅	1	1	yes	characteristic, complemented, Hall
28	C₃×C₃₁	C₅×D₃₃	1	1	yes	characteristic
29	C₅×D₉	—	341	1	no	Hall
30	D₃₃	—	93	1	no	—
31	D₃₁	—	99	1	no	Hall
32	C₅×C₁₁	—	31	1	no	Hall
33	C₅×C₉	—	31	1	no	Hall
34	C₃×C₁₁	C₃⋊(D₃₁⋊C₅)	1	1	yes	characteristic
35	C₃₁	C₅×D₉₉	1	1	yes	characteristic, complemented, Sylow
36	C₅×D₃	—	1023	1	no	—
37	D₁₁	—	279	1	no	Hall
38	D₉	—	341	1	no	Hall
39	C₃×C₅	—	31	1	no	—
40	C₁₁	C₉⋊(D₃₁⋊C₅)	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	3069	1	no	Hall
42	C₉	ΓL(1,𝔽₃₂)⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	1023	1	no	—
44	C₅	—	31	1	no	Sylow
45	C₃	C₃⋊(ΓL(1,𝔽₃₂)⋊D₁₁)	1	1	yes	characteristic
46	C₂	—	3069	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₁×C₃₁	C₂×C₅
Frattini	C₃	C₃⋊(ΓL(1,𝔽₃₂)⋊D₁₁)
socle	C₃×C₁₁×C₃₁	C₅×D₃
LCS	G ▷ C₉×C₁₁×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₉×C₁₁×ΓL(1,𝔽₃₂)	C₂	semidirect
3. D₃₀₆₉	C₅	semidirect
6. C₉×C₁₁×C₃₁	C₂×C₅	semidirect
9. C₁₁×ΓL(1,𝔽₃₂)	D₉	semidirect
10. C₉×ΓL(1,𝔽₃₂)	D₁₁	semidirect
18. C₁₁×C₃₁	C₅×D₉	semidirect
21. C₉×C₃₁	C₅×D₁₁	semidirect
25. ΓL(1,𝔽₃₂)	D₉₉	semidirect
27. C₉×C₁₁	D₃₁⋊C₅	semidirect
35. C₃₁	C₅×D₉₉	semidirect
40. C₁₁	C₉⋊(D₃₁⋊C₅)	semidirect
42. C₉	ΓL(1,𝔽₃₂)⋊D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₁₁×ΓL(1,𝔽₃₂)	2
C₃⋊(ΓL(1,𝔽₃₂)⋊D₁₁)	3
D₃₀₆₉	5
C₉⋊(D₃₁⋊C₅)	11
C₅×D₉₉	31

Subgroups — C9⋊(ΓL(1,𝔽32)⋊D11) #44501699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊(ΓL(1,𝔽₃₂)⋊D₁₁) #44501699