Subgroups — C₃⋊(C₃⋊#4208) #13091703

Order 1458.

2228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#737	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊(C₃⋊#272)	C₃	1	1	yes	maximal, characteristic
3	C₃⋊#4208	—	3	36	no	maximal
4	C₉×C₃⋊(C₃⋊D₃)	—	3	4	no	maximal
5	C₃×#737	—	2	36	no	—
6	C₃×#737	D₃	1	36	yes	complemented
7	C₃²×3₋¹⁺²	—	2	4	no	—
8	C₃²×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
9	C₃³×C₉	D₃	1	4	yes	complemented
10	C₃×C₃⋊(C₃⋊D₃)	—	3	4	no	—
11	C₃⋊#272	—	3	36	no	—
12	#4208	—	9	81	no	—
13	C₉×C₃⋊D₃	—	9	1	no	—
14	C₉×C₃⋊D₃	—	9	48	no	—
15	C₃⁴	C₃×D₃	1	4	yes	—
16	#737	—	2	324	no	—
17	#737	C₃⋊D₃	1	81	yes	complemented
18	C₃×3₋¹⁺²	—	2	144	no	—
19	C₃×H(3,𝔽₃)	C₃×D₃	1	36	yes	—
20	C₃²×C₉	—	2	4	no	—
21	C₃²×C₉	—	2	48	no	—
22	C₃²×C₉	C₃⋊D₃	1	1	yes	characteristic
23	C₃²×C₉	C₃⋊D₃	1	48	yes	complemented
24	C₃⋊(C₃⋊D₃)	—	3	4	no	—
25	C₃×C₃⋊D₃	—	9	48	no	—
26	C₃×C₃⋊D₃	—	9	1	no	—
27	#272	—	9	81	no	—
28	D₃×C₉	—	27	4	no	—
29	D₃×C₉	—	27	36	no	—
30	C₃³	—	3	4	no	—
31	C₃³	—	6	16	no	—
32	C₃³	C₃×C₃⋊D₃	1	1	yes	characteristic
33	C₃³	C₃×C₃⋊D₃	1	48	yes	—
34	3₋¹⁺²	—	2	324	no	—
35	H(3,𝔽₃)	C₃×C₃⋊D₃	1	81	yes	—
36	C₃×C₉	—	2	4	no	—
37	C₃×C₉	—	2	48	no	—
38	C₃×C₉	—	2	144	no	—
39	C₃×C₉	C₃⋊(C₃⋊D₃)	1	4	yes	—
40	C₃×C₉	C₃⋊(C₃⋊D₃)	1	36	yes	complemented
41	C₃⋊D₃	—	9	48	no	—
42	C₃⋊D₃	—	9	1	no	—
43	C₃×D₃	—	27	36	no	—
44	C₃×D₃	—	27	4	no	—
45	C₂×C₉	—	81	1	no	—
46	C₃²	—	2	4	no	—
47	C₃²	—	3	48	no	—
48	C₃²	—	6	48	no	—
49	C₃²	#4208	1	1	yes	characteristic, complemented
50	C₃²	C₃×C₃⋊(C₃⋊D₃)	1	4	yes	—
51	C₃²	C₃×C₃⋊(C₃⋊D₃)	1	36	yes	—
52	C₉	—	2	4	no	—
53	C₉	—	2	36	no	—
54	C₉	C₃⋊(C₃⋊(C₃⋊D₃))	1	1	yes	characteristic
55	C₂×C₃	—	81	1	no	—
56	D₃	—	27	36	no	—
57	D₃	—	27	4	no	—
58	C₃	—	2	4	no	—
59	C₃	—	3	36	no	—
60	C₃	C₃⋊#4208	1	4	yes	complemented
61	C₃	C₃×C₃⋊(C₃⋊(C₃⋊D₃))	1	1	yes	characteristic
62	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉	C₃⋊(C₃⋊(C₃⋊D₃))
commutator, cosocle, hypocenter	C₃²×H(3,𝔽₃)	C₂×C₃
Frattini	C₃	C₃×C₃⋊(C₃⋊(C₃⋊D₃))
Fitting	C₃²×#737	C₂
socle	C₃³	C₃×C₃⋊D₃
prime radical	C₃⋊(C₃⋊#272)	C₃
LCS	G ▷ C₃²×H(3,𝔽₃)
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
1. C₃²×#737	C₂	semidirect
6. C₃×#737	D₃	semidirect
9. C₃³×C₉	D₃	semidirect
17. #737	C₃⋊D₃	semidirect
23. C₃²×C₉	C₃⋊D₃	semidirect
40. C₃×C₉	C₃⋊(C₃⋊D₃)	semidirect
49. C₃²	#4208	semidirect
60. C₃	C₃⋊#4208	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#737	2
C₃⋊(C₃⋊#272)	3
C₃⋊#4208	3
C₉×C₃⋊(C₃⋊D₃)	3

Subgroups — C3⋊(C3⋊#4208) #13091703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊#4208) #13091703