Subgroups — C₁₁×(D₃₁⋊C₅)⋊C₉ #44501712

Order 30690.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×ΓL(1,𝔽₃₂)⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₁×D₃₁⋊C₅	C₃	1	1	yes	maximal, characteristic
3	C₁₁×D₃₁⋊C₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×C₁₁×ΓL(1,𝔽₃₂)	C₂×C₃	1	1	yes	characteristic
5	C₁₁×D₃₁⋊C₅	C₉	1	1	yes	characteristic, complemented, Hall
6	C₁₁×C₃₁⋊C₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	(D₃₁⋊C₅)⋊C₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₁₁×D₃₁	C₃×C₅	1	1	yes	characteristic
9	C₁₁×ΓL(1,𝔽₃₂)	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	ΓL(1,𝔽₃₂)⋊C₉	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₁×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic
12	C₂×C₅×C₉×C₁₁	—	31	1	no	maximal, Hall
13	C₃×D₃₁⋊C₅	C₃×C₁₁	1	1	yes	characteristic
14	C₁₁×D₃₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
15	D₃₁⋊C₉	C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₅×C₉×C₁₁	—	31	1	no	Hall
17	C₃×ΓL(1,𝔽₃₂)	C₂×C₃×C₁₁	1	1	yes	characteristic
18	C₁₁×C₃₁	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₅×C₁₁	—	31	1	no	—
20	D₃₁⋊C₅	C₉×C₁₁	1	1	yes	characteristic, complemented, Hall
21	C₃₁⋊C₉	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
22	C₂×C₉×C₁₁	—	31	1	no	Hall
23	C₃×D₃₁	C₃×C₅×C₁₁	1	1	yes	characteristic
24	C₃×C₅×C₁₁	—	31	1	no	—
25	ΓL(1,𝔽₃₂)	C₂×C₉×C₁₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅×C₁₁	—	31	1	no	Hall
27	C₉×C₁₁	—	31	1	no	Hall
28	C₃×C₃₁	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic
29	C₂×C₅×C₉	—	31	1	no	Hall
30	C₂×C₃×C₁₁	—	31	1	no	—
31	D₃₁	C₅×C₉×C₁₁	1	1	yes	characteristic, complemented, Hall
32	C₅×C₁₁	—	31	1	no	Hall
33	C₅×C₉	—	31	1	no	Hall
34	C₃×C₁₁	AGL(1,𝔽₃₁)	1	1	yes	characteristic
35	C₃₁	C₂×C₅×C₉×C₁₁	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₅	—	31	1	no	—
37	C₂×C₁₁	—	31	1	no	Hall
38	C₂×C₉	—	31	1	no	Hall
39	C₃×C₅	—	31	1	no	—
40	C₁₁	(D₃₁⋊C₅)⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	—	31	1	no	Hall
42	C₉	—	31	1	no	Sylow
43	C₂×C₃	—	31	1	no	—
44	C₅	—	31	1	no	Sylow
45	C₃	C₁₁×AGL(1,𝔽₃₁)	1	1	yes	characteristic
46	C₂	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₁	AGL(1,𝔽₃₁)
commutator, hypocenter	C₃₁	C₂×C₅×C₉×C₁₁
Frattini	C₃	C₁₁×AGL(1,𝔽₃₁)
Fitting, socle	C₃×C₁₁×C₃₁	C₂×C₃×C₅
prime radical	C₃×C₁₁×D₃₁⋊C₅	C₃
cosocle	C₃×C₃₁	C₂×C₃×C₅×C₁₁
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×ΓL(1,𝔽₃₂)⋊C₉	C₂	semidirect
3. C₁₁×D₃₁⋊C₉	C₅	semidirect
5. C₁₁×D₃₁⋊C₅	C₉	semidirect
6. C₁₁×C₃₁⋊C₉	C₂×C₅	semidirect
7. (D₃₁⋊C₅)⋊C₉	C₁₁	direct (N × H)
9. C₁₁×ΓL(1,𝔽₃₂)	C₂×C₉	semidirect
10. ΓL(1,𝔽₃₂)⋊C₉	C₂×C₁₁	semidirect
14. C₁₁×D₃₁	C₅×C₉	semidirect
15. D₃₁⋊C₉	C₅×C₁₁	semidirect
18. C₁₁×C₃₁	C₂×C₅×C₉	semidirect
20. D₃₁⋊C₅	C₉×C₁₁	semidirect
21. C₃₁⋊C₉	C₂×C₅×C₁₁	semidirect
25. ΓL(1,𝔽₃₂)	C₂×C₉×C₁₁	semidirect
31. D₃₁	C₅×C₉×C₁₁	semidirect
35. C₃₁	C₂×C₅×C₉×C₁₁	semidirect
40. C₁₁	(D₃₁⋊C₅)⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×ΓL(1,𝔽₃₂)⋊C₉	2
C₃×C₁₁×D₃₁⋊C₅	3
C₁₁×D₃₁⋊C₉	5
(D₃₁⋊C₅)⋊C₉	11
C₂×C₅×C₉×C₁₁	31

Subgroups — C11×(D31⋊C5)⋊C9 #44501712

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×(D₃₁⋊C₅)⋊C₉ #44501712