Subgroups — C₃²×#11760452 #23748611

Order 9477.

5804 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11760452	C₃	1	108	yes	maximal, direct product factor
2	C₃²×#66851	C₃	1	8	yes	maximal, complemented
3	C₃³×C₁₃⋊C₉	C₃	1	4	yes	maximal, complemented
4	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
5	#11760452	C₃²	1	729	yes	direct product factor
6	C₃×#66851	C₃²	1	288	yes	complemented
7	C₃²×C₁₃⋊C₉	C₃²	1	1	yes	characteristic
8	C₃²×C₁₃⋊C₉	C₃²	1	8	yes	—
9	C₃²×C₁₃⋊C₉	C₃²	1	144	yes	complemented
10	C₃⁴×C₁₃	C₃²	1	4	yes	—
11	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	36	yes	—
12	C₃²×#737	—	13	1	no	maximal, Sylow
13	C₃³×C₁₃	—	3	36	no	—
14	C₃³×C₁₃	C₃³	1	48	yes	—
15	C₃³×C₁₃	C₃³	1	1	yes	characteristic
16	C₁₃×H(3,𝔽₃)	C₃³	1	81	yes	—
17	#66851	C₃³	1	648	yes	complemented
18	C₃×C₁₃⋊C₉	C₃³	1	12	yes	—
19	C₃×C₁₃⋊C₉	C₃³	1	96	yes	—
20	C₃×C₁₃⋊C₉	C₃³	1	324	yes	complemented
21	C₃×#737	—	13	108	no	—
22	C₃²×3₋¹⁺²	—	13	8	no	—
23	C₃²×H(3,𝔽₃)	C₁₃⋊C₃	1	1	yes	characteristic
24	C₃³×C₉	—	13	4	no	—
25	C₃²×C₁₃	—	3	144	no	—
26	C₃²×C₁₃	#737	1	9	yes	complemented
27	C₃²×C₁₃	C₃⁴	1	36	yes	—
28	C₃²×C₁₃	C₃⁴	1	4	yes	—
29	C₁₃⋊C₉	C₃⁴	1	9	yes	—
30	C₁₃⋊C₉	C₃⁴	1	72	yes	—
31	C₃⁴	C₃×C₁₃⋊C₃	1	4	yes	—
32	#737	—	13	729	no	—
33	C₃×3₋¹⁺²	—	13	288	no	—
34	C₃×H(3,𝔽₃)	C₃×C₁₃⋊C₃	1	36	yes	—
35	C₃²×C₉	—	13	144	no	—
36	C₃²×C₉	—	13	1	no	—
37	C₃²×C₉	—	13	8	no	—
38	C₃×C₁₃	—	3	36	no	—
39	C₃×C₁₃	C₃×#737	1	12	yes	complemented
40	C₃×C₁₃	C₃⁵	1	1	yes	characteristic
41	C₃³	—	3	36	no	—
42	C₃³	C₃²×C₁₃⋊C₃	1	48	yes	—
43	C₃³	C₃²×C₁₃⋊C₃	1	1	yes	characteristic
44	3₋¹⁺²	—	13	648	no	—
45	H(3,𝔽₃)	C₃²×C₁₃⋊C₃	1	81	yes	—
46	C₃×C₉	—	13	12	no	—
47	C₃×C₉	—	13	96	no	—
48	C₃×C₉	—	13	324	no	—
49	C₁₃	C₃²×#737	1	1	yes	characteristic, complemented, Sylow
50	C₃²	—	3	144	no	—
51	C₃²	#11760452	1	9	yes	direct product factor
52	C₃²	C₃³×C₁₃⋊C₃	1	36	yes	—
53	C₃²	C₃³×C₁₃⋊C₃	1	4	yes	—
54	C₉	—	13	9	no	—
55	C₉	—	13	72	no	—
56	C₃	—	3	36	no	—
57	C₃	C₃×#11760452	1	12	yes	direct product factor
58	C₃	C₃⁴×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃³	C₃²×C₁₃⋊C₃
commutator, cosocle	C₃×C₁₃	C₃⁵
Frattini	C₃	C₃⁴×C₁₃⋊C₃
Fitting, prime radical	C₃²×C₁₃×H(3,𝔽₃)	C₃
socle	C₃³×C₁₃	C₃³
hypercenter	C₃²×H(3,𝔽₃)	C₁₃⋊C₃
hypocenter	C₁₃	C₃²×#737
LCS	G ▷ C₃×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃³ ◁ C₃²×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃×#11760452	C₃	direct (N × H)
2. C₃²×#66851	C₃	semidirect
3. C₃³×C₁₃⋊C₉	C₃	semidirect
5. #11760452	C₃²	direct (N × H)
6. C₃×#66851	C₃²	semidirect
9. C₃²×C₁₃⋊C₉	C₃²	semidirect
17. #66851	C₃³	semidirect
20. C₃×C₁₃⋊C₉	C₃³	semidirect
26. C₃²×C₁₃	#737	semidirect
39. C₃×C₁₃	C₃×#737	semidirect
49. C₁₃	C₃²×#737	semidirect
51. C₃²	#11760452	direct (N × H)
57. C₃	C₃×#11760452	direct (N × H)

Subgroups — C32×#11760452 #23748611

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×#11760452 #23748611