Subgroups — C₃²×#4208 #13091701

Order 1458.

1868 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×#4208	C₃	1	12	yes	maximal, direct product factor
3	C₃²×#272	C₃	1	1	yes	maximal, characteristic
4	C₃²×D₃×C₉	—	3	4	no	maximal
5	C₃×#737	—	2	48	no	—
6	C₃×#737	C₂×C₃	1	12	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	C₃³×D₃	—	3	4	no	—
11	C₂×C₃²×C₉	—	9	1	no	—
12	#4208	C₃²	1	9	yes	direct product factor
13	C₃×#272	C₃²	1	4	yes	—
14	C₃×D₃×C₉	—	3	48	no	—
15	C₃⁴	C₃×D₃	1	4	yes	—
16	#737	—	2	216	no	—
17	#737	—	2	144	no	—
18	#737	C₂×C₃²	1	9	yes	complemented
19	C₃×3₋¹⁺²	—	2	96	no	—
20	C₃×3₋¹⁺²	—	2	48	no	—
21	C₃×H(3,𝔽₃)	—	2	16	no	—
22	C₃×H(3,𝔽₃)	C₂×C₃²	1	4	yes	—
23	C₃²×C₉	—	2	4	no	—
24	C₃²×C₉	—	2	48	no	—
25	C₃²×C₉	C₃×D₃	1	48	yes	complemented
26	C₃²×C₉	C₃⋊D₃	1	1	yes	characteristic
27	C₂×C₃³	—	9	1	no	—
28	C₃²×D₃	—	3	36	no	—
29	C₃²×D₃	—	3	16	no	—
30	C₂×C₃×C₉	—	9	12	no	—
31	#272	C₃³	1	1	yes	characteristic
32	D₃×C₉	—	3	36	no	—
33	C₃³	—	2	16	no	—
34	C₃³	—	3	36	no	—
35	C₃³	C₃²×D₃	1	16	yes	—
36	C₃³	C₃×C₃⋊D₃	1	1	yes	characteristic
37	3₋¹⁺²	—	2	288	no	—
38	3₋¹⁺²	—	2	36	no	—
39	H(3,𝔽₃)	—	2	24	no	—
40	H(3,𝔽₃)	—	2	16	no	—
41	H(3,𝔽₃)	C₂×C₃³	1	1	yes	characteristic
42	C₃×C₉	—	2	48	no	—
43	C₃×C₉	—	2	144	no	—
44	C₃×C₉	C₃²×D₃	1	36	yes	complemented
45	C₃×C₉	C₃×C₃⋊D₃	1	12	yes	—
46	C₂×C₃²	—	9	9	no	—
47	C₂×C₃²	—	9	4	no	—
48	C₃×D₃	—	3	48	no	—
49	C₃×D₃	—	3	4	no	—
50	C₂×C₉	—	9	9	no	—
51	C₃²	—	2	16	no	—
52	C₃²	—	3	48	no	—
53	C₃²	—	6	48	no	—
54	C₃²	#4208	1	9	yes	direct product factor
55	C₃²	C₃³×D₃	1	4	yes	—
56	C₃²	C₃²×C₃⋊D₃	1	4	yes	—
57	C₉	—	2	36	no	—
58	C₉	C₃²×C₃⋊D₃	1	9	yes	—
59	C₂×C₃	—	9	12	no	—
60	C₂×C₃	—	9	1	no	—
61	D₃	—	3	4	no	—
62	C₃	—	3	4	no	—
63	C₃	—	6	16	no	—
64	C₃	C₃×#4208	1	12	yes	direct product factor
65	C₃	C₃³×C₃⋊D₃	1	1	yes	characteristic
66	C₂	—	9	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃²×#737	C₂	semidirect
2. C₃×#4208	C₃	direct (N × H)
6. C₃×#737	C₂×C₃	semidirect
9. C₃³×C₉	D₃	semidirect
12. #4208	C₃²	direct (N × H)
18. #737	C₂×C₃²	semidirect
25. C₃²×C₉	C₃×D₃	semidirect
44. C₃×C₉	C₃²×D₃	semidirect
54. C₃²	#4208	direct (N × H)
64. C₃	C₃×#4208	direct (N × H)

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×#4208	3
C₃²×#272	3
C₃²×D₃×C₉	3

Subgroups — C32×#4208 #13091701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#4208 #13091701