Subgroups — C₉⋊#16814878 #45686033

Order 33300.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₅⋊D₁₈₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#16814878	—	3	1	no	maximal
3	C₅²×C₉×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉⋊#10625192	—	5	6	no	maximal
5	C₃×C₅⋊D₁₈₅	D₃	1	1	yes	characteristic
6	#16814878	—	9	1	no	Hall
7	C₉×D₁₈₅	—	5	6	no	—
8	C₃×C₅²×C₃₇	Dic₃	1	1	yes	characteristic
9	C₃⋊#10625192	—	15	6	no	—
10	C₅⋊D₁₈₅	D₉	1	1	yes	characteristic
11	C₅×C₉×C₃₇	AGL(1,𝔽₅)	1	6	yes	complemented
12	C₉⋊#3866	—	25	1	no	Hall
13	C₃×D₁₈₅	—	5	6	no	—
14	C₅²×C₃₇	Dic₉	1	1	yes	characteristic, complemented, Hall
15	C₉⋊#1043	—	37	1	no	maximal, Hall
16	#10625192	—	45	6	no	—
17	C₉×D₃₇	—	25	1	no	—
18	C₃×C₅×C₃₇	ΓL(1,𝔽₁₆)	1	6	yes	—
19	C₉×C₅⋊D₅	—	37	1	no	—
20	C₃⋊#3866	—	75	1	no	—
21	D₁₈₅	—	5	6	no	—
22	C₉×C₃₇	#1043	1	1	yes	characteristic, complemented, Hall
23	C₃⋊#1043	—	111	1	no	—
24	C₅²×C₉	#3866	1	1	yes	characteristic, complemented, Hall
25	C₃×D₃₇	—	25	1	no	—
26	C₅×C₃₇	C₉⋊AGL(1,𝔽₅)	1	6	yes	complemented
27	C₉⋊AGL(1,𝔽₅)	—	185	6	no	—
28	C₃×C₅⋊D₅	—	37	1	no	—
29	#3866	—	225	1	no	Hall
30	C₃×C₃₇	C₃⋊#1043	1	1	yes	characteristic
31	#1043	—	333	1	no	Hall
32	C₉×D₅	—	185	6	no	—
33	C₃×C₅²	C₃⋊#3866	1	1	yes	characteristic
34	D₃₇	—	25	1	no	—
35	ΓL(1,𝔽₁₆)	—	555	6	no	—
36	C₅⋊D₅	—	37	1	no	—
37	C₅×C₉	#10625192	1	6	yes	complemented
38	C₃₇	C₉⋊#1043	1	1	yes	characteristic, complemented, Sylow
39	Dic₉	—	925	1	no	Hall
40	C₃×D₅	—	185	6	no	—
41	C₅²	C₉⋊#3866	1	1	yes	characteristic, complemented, Sylow
42	AGL(1,𝔽₅)	—	1665	6	no	—
43	C₂×C₉	—	925	1	no	—
44	C₃×C₅	C₃⋊#10625192	1	6	yes	—
45	Dic₃	—	2775	1	no	—
46	D₅	—	185	6	no	—
47	C₉	#16814878	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	925	1	no	—
49	C₅	C₉⋊#10625192	1	6	yes	complemented
50	C₄	—	8325	1	no	Sylow
51	C₃	C₃⋊#16814878	1	1	yes	characteristic
52	C₂	—	925	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅²×C₉×C₃₇	C₄
Frattini	C₃	C₃⋊#16814878
socle	C₃×C₅²×C₃₇	Dic₃
prime radical	C₃×C₅⋊D₁₈₅	D₃
cosocle	C₉×C₅⋊D₁₈₅	C₂
LCS	G ▷ C₅²×C₉×C₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₅²×C₉×C₃₇	C₄	semidirect
11. C₅×C₉×C₃₇	AGL(1,𝔽₅)	semidirect
14. C₅²×C₃₇	Dic₉	semidirect
22. C₉×C₃₇	#1043	semidirect
24. C₅²×C₉	#3866	semidirect
26. C₅×C₃₇	C₉⋊AGL(1,𝔽₅)	semidirect
37. C₅×C₉	#10625192	semidirect
38. C₃₇	C₉⋊#1043	semidirect
41. C₅²	C₉⋊#3866	semidirect
47. C₉	#16814878	semidirect
49. C₅	C₉⋊#10625192	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₅⋊D₁₈₅	2
C₃⋊#16814878	3
C₉⋊#10625192	5
C₉⋊#1043	37

Subgroups — C9⋊#16814878 #45686033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊#16814878 #45686033