Subgroups — C₃³×#66848 #23748608

Order 9477.

7208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₁₃⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₃²×#66848	C₃	1	117	yes	maximal, direct product factor
3	C₃³×C₁₃⋊C₉	C₃	1	2	yes	maximal, complemented
4	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³×C₁₃⋊C₃	—	3	27	no	—
6	C₃³×C₁₃⋊C₃	C₃²	1	39	yes	—
7	C₃×#66848	C₃²	1	1053	yes	direct product factor
8	C₃²×C₁₃⋊C₉	C₃²	1	78	yes	complemented
9	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
10	C₃²×C₉×C₁₃	C₃²	1	39	yes	complemented
11	C₃³×3₋¹⁺²	—	13	1	no	maximal, Sylow
12	C₃³×C₁₃	3₋¹⁺²	1	27	yes	complemented
13	C₃³×C₁₃	C₃³	1	13	yes	—
14	C₃²×C₁₃⋊C₃	—	3	351	no	—
15	C₃²×C₁₃⋊C₃	C₃³	1	117	yes	—
16	C₃×C₉×C₁₃	C₃³	1	117	yes	complemented
17	C₃×C₁₃⋊C₉	C₃³	1	234	yes	complemented
18	#66848	C₃³	1	729	yes	direct product factor
19	C₃⁵	—	13	1	no	—
20	C₃²×3₋¹⁺²	—	13	117	no	—
21	C₃³×C₉	—	13	2	no	—
22	C₃³×C₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented
23	C₃²×C₁₃	C₃×3₋¹⁺²	1	117	yes	complemented
24	C₃²×C₁₃	C₃⁴	1	13	yes	—
25	C₃×C₁₃⋊C₃	—	3	351	no	—
26	C₃×C₁₃⋊C₃	C₃⁴	1	27	yes	—
27	C₉×C₁₃	C₃⁴	1	27	yes	complemented
28	C₁₃⋊C₉	C₃⁴	1	54	yes	complemented
29	C₃⁴	—	13	39	no	—
30	C₃⁴	—	39	27	no	—
31	C₃⁴	C₃×C₁₃⋊C₃	1	1	yes	characteristic
32	C₃×3₋¹⁺²	—	13	1053	no	—
33	C₃²×C₉	—	13	78	no	—
34	C₃²×C₉	C₃×C₁₃⋊C₃	1	39	yes	complemented
35	C₃×C₁₃	C₃²×3₋¹⁺²	1	39	yes	complemented
36	C₃×C₁₃	C₃⁵	1	1	yes	characteristic
37	C₁₃⋊C₃	—	3	27	no	—
38	C₃³	—	13	117	no	—
39	C₃³	—	39	351	no	—
40	C₃³	#66848	1	27	yes	direct product factor
41	C₃³	C₃²×C₁₃⋊C₃	1	13	yes	—
42	3₋¹⁺²	—	13	729	no	—
43	C₃×C₉	—	13	234	no	—
44	C₃×C₉	C₃²×C₁₃⋊C₃	1	117	yes	complemented
45	C₁₃	C₃³×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
46	C₃²	—	13	27	no	—
47	C₃²	—	39	351	no	—
48	C₃²	C₃×#66848	1	117	yes	direct product factor
49	C₃²	C₃³×C₁₃⋊C₃	1	13	yes	—
50	C₉	—	13	54	no	—
51	C₉	C₃³×C₁₃⋊C₃	1	27	yes	complemented
52	C₃	—	39	27	no	—
53	C₃	C₃²×#66848	1	39	yes	direct product factor
54	C₃	C₃⁴×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃⁴	C₃×C₁₃⋊C₃
commutator, cosocle	C₃×C₁₃	C₃⁵
Frattini	C₃	C₃⁴×C₁₃⋊C₃
Fitting	C₃³×C₉×C₁₃	C₃
socle	C₃⁴×C₁₃	C₃²
prime radical	C₃⁴×C₁₃⋊C₃	C₃
hypercenter	C₃³×C₉	C₁₃⋊C₃
hypocenter	C₁₃	C₃³×3₋¹⁺²
LCS	G ▷ C₃×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃⁴ ◁ C₃³×C₉

Complements

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

N	H ≅ G/N	type
2. C₃²×#66848	C₃	direct (N × H)
3. C₃³×C₁₃⋊C₉	C₃	semidirect
4. C₃³×C₉×C₁₃	C₃	semidirect
7. C₃×#66848	C₃²	direct (N × H)
8. C₃²×C₁₃⋊C₉	C₃²	semidirect
10. C₃²×C₉×C₁₃	C₃²	semidirect
12. C₃³×C₁₃	3₋¹⁺²	semidirect
16. C₃×C₉×C₁₃	C₃³	semidirect
17. C₃×C₁₃⋊C₉	C₃³	semidirect
18. #66848	C₃³	direct (N × H)
22. C₃³×C₉	C₁₃⋊C₃	semidirect
23. C₃²×C₁₃	C₃×3₋¹⁺²	semidirect
27. C₉×C₁₃	C₃⁴	semidirect
28. C₁₃⋊C₉	C₃⁴	semidirect
34. C₃²×C₉	C₃×C₁₃⋊C₃	semidirect
35. C₃×C₁₃	C₃²×3₋¹⁺²	semidirect
40. C₃³	#66848	direct (N × H)
44. C₃×C₉	C₃²×C₁₃⋊C₃	semidirect
45. C₁₃	C₃³×3₋¹⁺²	semidirect
48. C₃²	C₃×#66848	direct (N × H)
51. C₉	C₃³×C₁₃⋊C₃	semidirect
53. C₃	C₃²×#66848	direct (N × H)

Subgroups — C33×#66848 #23748608

Conjugacy classes of subgroups

Complements

Subgroups — C₃³×#66848 #23748608