Subgroups — C₉⋊#16811779 #44501697

Order 30690.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#13133722	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊#16811779	—	3	1	no	maximal
3	C₃₁×D₉₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×#13133722	D₃	1	1	yes	characteristic
5	#16811779	—	9	1	no	Hall
6	C₉×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	D₉×ΓL(1,𝔽₃₂)	—	11	1	no	maximal, Hall
8	C₃₁×D₃₃	—	3	1	no	—
9	#13133722	D₉	1	1	yes	characteristic, complemented, Hall
10	C₉×ΓL(1,𝔽₃₂)	—	11	1	no	Hall
11	C₃×C₁₁×C₃₁	C₅×D₃	1	1	yes	characteristic
12	C₉⋊AGL(1,𝔽₁₁)	—	31	1	no	maximal, Hall
13	D₃×ΓL(1,𝔽₃₂)	—	33	1	no	—
14	D₁₁×C₃₁	—	9	1	no	Hall
15	D₉×C₃₁	—	11	1	no	Hall
16	C₉×C₁₁⋊C₅	—	31	1	no	Hall
17	C₃×ΓL(1,𝔽₃₂)	—	11	1	no	—
18	C₁₁×C₃₁	C₅×D₉	1	1	yes	characteristic, complemented, Hall
19	C₃⋊AGL(1,𝔽₁₁)	—	93	1	no	—
20	C₂×ΓL(1,𝔽₃₂)	—	99	1	no	Hall
21	C₉×C₃₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
22	D₉₉	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Hall
23	D₃×C₃₁	—	33	1	no	—
24	C₃×C₁₁⋊C₅	—	31	1	no	—
25	ΓL(1,𝔽₃₂)	—	11	1	no	Hall
26	AGL(1,𝔽₁₁)	—	279	1	no	Hall
27	C₉×C₁₁	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Hall
28	C₃×C₃₁	C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
29	C₅×D₉	—	341	1	no	Hall
30	D₃₃	—	3	1	no	—
31	C₂×C₃₁	—	99	1	no	Hall
32	C₁₁⋊C₅	—	31	1	no	Hall
33	C₅×C₉	—	341	1	no	Hall
34	C₃×C₁₁	D₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
35	C₃₁	C₉⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
36	C₅×D₃	—	1023	1	no	—
37	D₁₁	—	9	1	no	Hall
38	D₉	—	11	1	no	Hall
39	C₃×C₅	—	341	1	no	—
40	C₁₁	D₉×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	3069	1	no	Hall
42	C₉	#16811779	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	33	1	no	—
44	C₅	—	341	1	no	Sylow
45	C₃	C₃⋊#16811779	1	1	yes	characteristic
46	C₂	—	99	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₁×C₃₁	C₂×C₅
Frattini	C₃	C₃⋊#16811779
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×#13133722	C₂	semidirect
3. C₃₁×D₉₉	C₅	semidirect
6. C₉×C₁₁×C₃₁	C₂×C₅	semidirect
9. #13133722	D₉	semidirect
18. C₁₁×C₃₁	C₅×D₉	semidirect
21. C₉×C₃₁	AGL(1,𝔽₁₁)	semidirect
22. D₉₉	ΓL(1,𝔽₃₂)	semidirect
27. C₉×C₁₁	C₂×ΓL(1,𝔽₃₂)	semidirect
35. C₃₁	C₉⋊AGL(1,𝔽₁₁)	semidirect
40. C₁₁	D₉×ΓL(1,𝔽₃₂)	semidirect
42. C₉	#16811779	semidirect

Maximal subgroups

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

subgroup	index
C₉×#13133722	2
C₃⋊#16811779	3
C₃₁×D₉₉	5
D₉×ΓL(1,𝔽₃₂)	11
C₉⋊AGL(1,𝔽₁₁)	31

Subgroups — C9⋊#16811779 #44501697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊#16811779 #44501697