Subgroups — C₃⋊(C₃⋊#16861520) #49147197

Order 36900.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄₁×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#16861520	—	3	4	no	maximal
3	C₃²×C₅²×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊#11717963)	—	5	6	no	maximal
5	C₃×C₄₁×C₅⋊D₅	D₃	1	4	yes	—
6	#16861520	—	9	1	no	Hall
7	C₃²×D₅×C₄₁	—	5	6	no	—
8	C₃×C₅²×C₄₁	Dic₃	1	4	yes	complemented
9	C₃⋊#11717963	—	15	24	no	—
10	C₄₁×C₅⋊D₅	C₃⋊D₃	1	1	yes	characteristic
11	C₃²×C₅×C₄₁	AGL(1,𝔽₅)	1	6	yes	complemented
12	C₃⋊Dic₁₂₃	—	25	1	no	Hall
13	C₃×D₅×C₄₁	—	5	24	no	—
14	C₅²×C₄₁	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
15	C₃⋊(C₃⋊#1043)	—	41	1	no	maximal, Hall
16	#11717963	—	45	6	no	—
17	C₂×C₃²×C₄₁	—	25	1	no	—
18	C₃×C₅×C₄₁	ΓL(1,𝔽₁₆)	1	24	yes	complemented
19	Dic₁₂₃	—	75	4	no	—
20	C₃²×C₅⋊D₅	D₄₁	1	1	yes	characteristic
21	D₅×C₄₁	—	5	6	no	—
22	C₃²×C₄₁	#1043	1	1	yes	characteristic, complemented, Hall
23	C₃⋊#1043	—	123	4	no	—
24	C₂×C₃×C₄₁	—	25	4	no	—
25	C₃²×C₅²	Dic₄₁	1	1	yes	characteristic, complemented, Hall
26	C₅×C₄₁	C₃⋊ΓL(1,𝔽₁₆)	1	6	yes	complemented
27	C₃⋊ΓL(1,𝔽₁₆)	—	205	6	no	—
28	Dic₄₁	—	225	1	no	Hall
29	C₃×C₅⋊D₅	D₁₂₃	1	4	yes	—
30	C₃×C₄₁	C₃⋊#1043	1	4	yes	complemented
31	#1043	—	369	1	no	Hall
32	C₃²×D₅	—	5	6	no	—
33	C₂×C₄₁	—	25	1	no	—
34	C₃×C₅²	Dic₁₂₃	1	4	yes	complemented
35	ΓL(1,𝔽₁₆)	—	615	24	no	—
36	C₅⋊D₅	C₃⋊D₁₂₃	1	1	yes	characteristic
37	C₃²×C₅	#11717963	1	6	yes	complemented
38	C₄₁	C₃⋊(C₃⋊#1043)	1	1	yes	characteristic, complemented, Sylow
39	C₃⋊Dic₃	—	1025	1	no	Hall
40	C₃×D₅	—	5	24	no	—
41	C₅²	C₃⋊Dic₁₂₃	1	1	yes	characteristic, complemented, Sylow
42	AGL(1,𝔽₅)	—	1845	6	no	—
43	C₂×C₃²	—	25	1	no	—
44	C₃×C₅	C₃⋊#11717963	1	24	yes	complemented
45	Dic₃	—	3075	4	no	—
46	D₅	—	5	6	no	—
47	C₃²	#16861520	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	25	4	no	—
49	C₅	C₃⋊(C₃⋊#11717963)	1	6	yes	complemented
50	C₄	—	9225	1	no	Sylow
51	C₃	C₃⋊#16861520	1	4	yes	complemented
52	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₄₁	C₄
prime radical, cosocle	C₃²×C₄₁×C₅⋊D₅	C₂
LCS	G ▷ C₃²×C₅²×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅²×C₄₁	C₄	semidirect
8. C₃×C₅²×C₄₁	Dic₃	semidirect
11. C₃²×C₅×C₄₁	AGL(1,𝔽₅)	semidirect
14. C₅²×C₄₁	C₃⋊Dic₃	semidirect
18. C₃×C₅×C₄₁	ΓL(1,𝔽₁₆)	semidirect
22. C₃²×C₄₁	#1043	semidirect
25. C₃²×C₅²	Dic₄₁	semidirect
26. C₅×C₄₁	C₃⋊ΓL(1,𝔽₁₆)	semidirect
30. C₃×C₄₁	C₃⋊#1043	semidirect
34. C₃×C₅²	Dic₁₂₃	semidirect
37. C₃²×C₅	#11717963	semidirect
38. C₄₁	C₃⋊(C₃⋊#1043)	semidirect
41. C₅²	C₃⋊Dic₁₂₃	semidirect
44. C₃×C₅	C₃⋊#11717963	semidirect
47. C₃²	#16861520	semidirect
49. C₅	C₃⋊(C₃⋊#11717963)	semidirect
51. C₃	C₃⋊#16861520	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₄₁×C₅⋊D₅	2
C₃⋊#16861520	3
C₃⋊(C₃⋊#11717963)	5
C₃⋊(C₃⋊#1043)	41

Subgroups — C3⋊(C3⋊#16861520) #49147197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊#16861520) #49147197