Subgroups — #16811778⋊C₉ #44501721

Order 30690.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13133723⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×#16811778	C₃	1	1	yes	maximal, characteristic
3	D₁₁×C₃₁⋊C₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×#13133723	C₂×C₃	1	1	yes	characteristic
5	#16811778	C₉	1	1	yes	characteristic, complemented, Hall
6	C₁₁×C₃₁⋊C₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×ΓL(1,𝔽₃₂)⋊C₉	—	11	1	no	maximal, Hall
8	C₃×D₁₁×C₃₁	C₃×C₅	1	1	yes	characteristic
9	#13133723	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	ΓL(1,𝔽₃₂)⋊C₉	—	11	1	no	Hall
11	C₃×C₁₁×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic
12	C₉×AGL(1,𝔽₁₁)	—	31	1	no	maximal, Hall
13	C₂×C₃×ΓL(1,𝔽₃₂)	—	11	1	no	—
14	D₁₁×C₃₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃₁⋊C₉	—	11	1	no	Hall
16	C₉×C₁₁⋊C₅	—	31	1	no	Hall
17	C₃×ΓL(1,𝔽₃₂)	—	11	1	no	—
18	C₁₁×C₃₁	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Hall
19	C₃×AGL(1,𝔽₁₁)	—	31	1	no	—
20	C₂×ΓL(1,𝔽₃₂)	—	11	1	no	Hall
21	C₃₁⋊C₉	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
22	C₉×D₁₁	—	31	1	no	Hall
23	C₂×C₃×C₃₁	—	11	1	no	—
24	C₃×C₁₁⋊C₅	—	31	1	no	—
25	ΓL(1,𝔽₃₂)	—	11	1	no	Hall
26	AGL(1,𝔽₁₁)	—	31	1	no	Hall
27	C₉×C₁₁	—	31	1	no	Hall
28	C₃×C₃₁	C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic
29	C₂×C₅×C₉	—	341	1	no	Hall
30	C₃×D₁₁	(C₃₁⋊C₃)⋊C₅	1	1	yes	characteristic
31	C₂×C₃₁	—	11	1	no	Hall
32	C₁₁⋊C₅	—	31	1	no	Hall
33	C₅×C₉	—	341	1	no	Hall
34	C₃×C₁₁	C₂×(C₃₁⋊C₃)⋊C₅	1	1	yes	characteristic
35	C₃₁	C₉×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₅	—	341	1	no	—
37	D₁₁	ΓL(1,𝔽₃₂)⋊C₉	1	1	yes	characteristic, complemented, Hall
38	C₂×C₉	—	341	1	no	Hall
39	C₃×C₅	—	341	1	no	—
40	C₁₁	C₂×ΓL(1,𝔽₃₂)⋊C₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	341	1	no	Hall
42	C₉	—	31	1	no	Sylow
43	C₂×C₃	—	11	1	no	—
44	C₅	—	341	1	no	Sylow
45	C₃	#16811778⋊C₃	1	1	yes	characteristic
46	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	#16811778⋊C₃
commutator, hypocenter	C₁₁×C₃₁	C₂×C₅×C₉
Fitting, socle, cosocle	C₃×C₁₁×C₃₁	C₂×C₃×C₅
prime radical	C₃×#16811778	C₃
LCS	G ▷ C₁₁×C₃₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. #13133723⋊C₉	C₂	semidirect
3. D₁₁×C₃₁⋊C₉	C₅	semidirect
5. #16811778	C₉	semidirect
6. C₁₁×C₃₁⋊C₉	C₂×C₅	semidirect
9. #13133723	C₂×C₉	semidirect
14. D₁₁×C₃₁	C₅×C₉	semidirect
18. C₁₁×C₃₁	C₂×C₅×C₉	semidirect
21. C₃₁⋊C₉	AGL(1,𝔽₁₁)	semidirect
35. C₃₁	C₉×AGL(1,𝔽₁₁)	semidirect
37. D₁₁	ΓL(1,𝔽₃₂)⋊C₉	semidirect
40. C₁₁	C₂×ΓL(1,𝔽₃₂)⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
#13133723⋊C₉	2
C₃×#16811778	3
D₁₁×C₃₁⋊C₉	5
C₂×ΓL(1,𝔽₃₂)⋊C₉	11
C₉×AGL(1,𝔽₁₁)	31

Subgroups — #16811778⋊C9 #44501721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #16811778⋊C₉ #44501721