Subgroups — C₃×#15691698 #23748620

Order 9477.

5588 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15691698	C₃	1	81	yes	maximal, direct product factor
2	C₃×#11760452	C₃	1	27	yes	maximal, complemented
3	C₃²×#66851	C₃	1	12	yes	maximal, complemented
4	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
5	#11760452	C₃²	1	729	yes	complemented
6	C₃×#66851	C₃²	1	9	yes	—
7	C₃×#66851	C₃²	1	72	yes	complemented
8	C₃×#66851	C₃²	1	324	yes	complemented
9	C₃²×C₁₃⋊C₉	C₃²	1	36	yes	complemented
10	C₃⁴×C₁₃	C₃²	1	4	yes	—
11	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	9	yes	—
12	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	27	yes	—
13	C₃×3₋¹⁺⁴	—	13	1	no	maximal, Sylow
14	C₃³×C₁₃	—	9	12	no	—
15	C₃³×C₁₃	C₃³	1	12	yes	—
16	C₃³×C₁₃	C₃³	1	1	yes	characteristic
17	C₃³×C₁₃	C₃³	1	36	yes	—
18	C₁₃×H(3,𝔽₃)	C₃³	1	81	yes	—
19	#66851	C₃³	1	81	yes	—
20	#66851	C₃³	1	648	yes	complemented
21	C₃×C₁₃⋊C₉	C₃³	1	27	yes	—
22	C₃×C₁₃⋊C₉	C₃³	1	324	yes	complemented
23	3₋¹⁺⁴	—	13	81	no	—
24	C₃×#737	—	13	27	no	—
25	C₃²×3₋¹⁺²	—	13	12	no	—
26	C₃²×H(3,𝔽₃)	C₁₃⋊C₃	1	1	yes	characteristic
27	C₃²×C₁₃	—	3	3	no	—
28	C₃²×C₁₃	—	3	36	no	—
29	C₃²×C₁₃	—	9	36	no	—
30	C₃²×C₁₃	C₃⁴	1	36	yes	—
31	C₃²×C₁₃	C₃⁴	1	3	yes	—
32	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
33	C₁₃⋊C₉	C₃⁴	1	81	yes	—
34	C₃⁴	C₃×C₁₃⋊C₃	1	4	yes	—
35	#737	—	13	729	no	—
36	C₃×3₋¹⁺²	—	13	9	no	—
37	C₃×3₋¹⁺²	—	13	72	no	—
38	C₃×3₋¹⁺²	—	13	324	no	—
39	C₃×H(3,𝔽₃)	C₃×C₁₃⋊C₃	1	9	yes	—
40	C₃×H(3,𝔽₃)	C₃×C₁₃⋊C₃	1	27	yes	—
41	C₃²×C₉	—	13	36	no	—
42	C₃×C₁₃	—	3	3	no	—
43	C₃×C₁₃	—	3	36	no	—
44	C₃×C₁₃	3₋¹⁺⁴	1	3	yes	complemented
45	C₃×C₁₃	C₃⁵	1	1	yes	characteristic
46	C₃³	—	9	12	no	—
47	C₃³	C₃²×C₁₃⋊C₃	1	12	yes	—
48	C₃³	C₃²×C₁₃⋊C₃	1	1	yes	characteristic
49	C₃³	C₃²×C₁₃⋊C₃	1	36	yes	—
50	3₋¹⁺²	—	13	81	no	—
51	3₋¹⁺²	—	13	648	no	—
52	H(3,𝔽₃)	C₃²×C₁₃⋊C₃	1	81	yes	—
53	C₃×C₉	—	13	324	no	—
54	C₃×C₉	—	13	27	no	—
55	C₁₃	C₃×3₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
56	C₃²	—	3	3	no	—
57	C₃²	—	3	36	no	—
58	C₃²	—	9	36	no	—
59	C₃²	C₃³×C₁₃⋊C₃	1	36	yes	—
60	C₃²	C₃³×C₁₃⋊C₃	1	3	yes	—
61	C₃²	C₃³×C₁₃⋊C₃	1	1	yes	characteristic
62	C₉	—	13	81	no	—
63	C₃	—	3	3	no	—
64	C₃	—	3	36	no	—
65	C₃	#15691698	1	3	yes	direct product factor
66	C₃	C₃⁴×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃³×C₁₃⋊C₃
commutator, cosocle	C₃×C₁₃	C₃⁵
Frattini	C₃	C₃⁴×C₁₃⋊C₃
Fitting, prime radical	C₃²×C₁₃×H(3,𝔽₃)	C₃
socle	C₃²×C₁₃	C₃⁴
hypercenter	C₃²×H(3,𝔽₃)	C₁₃⋊C₃
hypocenter	C₁₃	C₃×3₋¹⁺⁴
LCS	G ▷ C₃×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃² ◁ C₃²×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. #15691698	C₃	direct (N × H)
2. C₃×#11760452	C₃	semidirect
3. C₃²×#66851	C₃	semidirect
5. #11760452	C₃²	semidirect
7. C₃×#66851	C₃²	semidirect
8. C₃×#66851	C₃²	semidirect
9. C₃²×C₁₃⋊C₉	C₃²	semidirect
20. #66851	C₃³	semidirect
22. C₃×C₁₃⋊C₉	C₃³	semidirect
44. C₃×C₁₃	3₋¹⁺⁴	semidirect
55. C₁₃	C₃×3₋¹⁺⁴	semidirect
65. C₃	#15691698	direct (N × H)

Subgroups — C3×#15691698 #23748620

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#15691698 #23748620