Subgroups — C₃²×C₁₃×#731 #23745071

Order 9477.

1160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×3₋¹⁺²	C₃	1	2	yes	maximal, complemented
2	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×#731	C₃	1	36	yes	maximal, direct product factor
5	C₃⁴×C₁₃	—	3	1	no	—
6	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
7	C₃×C₁₃×3₋¹⁺²	—	3	16	no	—
8	C₃×C₁₃×3₋¹⁺²	C₃²	1	24	yes	complemented
9	C₃×C₁₃×H(3,𝔽₃)	—	3	8	no	—
10	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	12	yes	—
11	C₃²×C₉×C₁₃	—	3	8	no	—
12	C₃²×C₉×C₁₃	—	3	1	no	—
13	C₃²×C₉×C₁₃	—	3	2	no	—
14	C₃²×C₉×C₁₃	C₃²	1	12	yes	complemented
15	C₁₃×#731	C₃²	1	81	yes	direct product factor
16	C₃²×#731	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃³×C₁₃	—	3	9	no	—
18	C₃³×C₁₃	—	3	12	no	—
19	C₃³×C₁₃	—	9	9	no	—
20	C₃³×C₁₃	H(3,𝔽₃)	1	8	yes	—
21	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
22	C₃³×C₁₃	C₃³	1	4	yes	—
23	C₁₃×3₋¹⁺²	—	3	48	no	—
24	C₁₃×3₋¹⁺²	C₃³	1	18	yes	complemented
25	C₁₃×H(3,𝔽₃)	—	3	24	no	—
26	C₁₃×H(3,𝔽₃)	C₃³	1	9	yes	—
27	C₃×C₉×C₁₃	—	3	24	no	—
28	C₃×C₉×C₁₃	—	3	12	no	—
29	C₃×C₉×C₁₃	—	3	24	no	—
30	C₃×C₉×C₁₃	C₃³	1	9	yes	complemented
31	C₃²×3₋¹⁺²	C₃×C₁₃	1	2	yes	complemented
32	C₃²×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
33	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic, complemented
34	C₃×#731	C₃×C₁₃	1	36	yes	direct product factor
35	C₃²×C₁₃	—	3	24	no	—
36	C₃²×C₁₃	—	3	12	no	—
37	C₃²×C₁₃	—	3	9	no	—
38	C₃²×C₁₃	—	9	36	no	—
39	C₃²×C₁₃	#731	1	9	yes	direct product factor
40	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	8	yes	—
41	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	4	yes	—
42	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
43	C₉×C₁₃	—	3	9	no	—
44	C₉×C₁₃	—	3	18	no	—
45	C₃⁴	—	3	1	no	—
46	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
47	C₃×3₋¹⁺²	—	3	16	no	—
48	C₃×3₋¹⁺²	C₃²×C₁₃	1	24	yes	complemented
49	C₃×H(3,𝔽₃)	—	3	8	no	—
50	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	12	yes	—
51	C₃²×C₉	—	3	8	no	—
52	C₃²×C₉	—	3	1	no	—
53	C₃²×C₉	—	3	2	no	—
54	C₃²×C₉	C₃²×C₁₃	1	12	yes	complemented
55	#731	C₃²×C₁₃	1	81	yes	direct product factor
56	C₃×C₁₃	—	3	8	no	—
57	C₃×C₁₃	—	3	1	no	—
58	C₃×C₁₃	—	9	9	no	—
59	C₃×C₁₃	C₃×#731	1	12	yes	direct product factor
60	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
61	C₃³	—	3	9	no	—
62	C₃³	—	3	12	no	—
63	C₃³	—	9	9	no	—
64	C₃³	C₁₃×H(3,𝔽₃)	1	8	yes	—
65	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
66	C₃³	C₃³×C₁₃	1	4	yes	—
67	3₋¹⁺²	—	3	48	no	—
68	3₋¹⁺²	C₃³×C₁₃	1	18	yes	complemented
69	H(3,𝔽₃)	—	3	24	no	—
70	H(3,𝔽₃)	C₃³×C₁₃	1	9	yes	—
71	C₃×C₉	—	3	24	no	—
72	C₃×C₉	—	3	12	no	—
73	C₃×C₉	—	3	24	no	—
74	C₃×C₉	C₃³×C₁₃	1	9	yes	complemented
75	C₁₃	C₃²×#731	1	1	yes	characteristic, direct product factor, Sylow
76	C₃²	—	3	24	no	—
77	C₃²	—	3	12	no	—
78	C₃²	—	3	9	no	—
79	C₃²	—	9	36	no	—
80	C₃²	C₁₃×#731	1	9	yes	direct product factor
81	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	8	yes	—
82	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	4	yes	—
83	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
84	C₉	—	3	9	no	—
85	C₉	—	3	18	no	—
86	C₃	—	3	8	no	—
87	C₃	—	3	1	no	—
88	C₃	—	9	9	no	—
89	C₃	C₃×C₁₃×#731	1	12	yes	direct product factor
90	C₃	C₃²×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃³×C₁₃	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃²	C₃⁴×C₁₃
prime radical	C₃²×C₁₃×H(3,𝔽₃)	C₃
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃³×C₁₃ ◁ C₃⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×3₋¹⁺²	C₃	semidirect
3. C₃³×C₉×C₁₃	C₃	semidirect
4. C₃×C₁₃×#731	C₃	direct (N × H)
8. C₃×C₁₃×3₋¹⁺²	C₃²	semidirect
14. C₃²×C₉×C₁₃	C₃²	semidirect
15. C₁₃×#731	C₃²	direct (N × H)
16. C₃²×#731	C₁₃	direct (N × H)
24. C₁₃×3₋¹⁺²	C₃³	semidirect
30. C₃×C₉×C₁₃	C₃³	semidirect
31. C₃²×3₋¹⁺²	C₃×C₁₃	semidirect
33. C₃³×C₉	C₃×C₁₃	semidirect
34. C₃×#731	C₃×C₁₃	direct (N × H)
39. C₃²×C₁₃	#731	direct (N × H)
48. C₃×3₋¹⁺²	C₃²×C₁₃	semidirect
54. C₃²×C₉	C₃²×C₁₃	semidirect
55. #731	C₃²×C₁₃	direct (N × H)
59. C₃×C₁₃	C₃×#731	direct (N × H)
68. 3₋¹⁺²	C₃³×C₁₃	semidirect
74. C₃×C₉	C₃³×C₁₃	semidirect
75. C₁₃	C₃²×#731	direct (N × H)
80. C₃²	C₁₃×#731	direct (N × H)
89. C₃	C₃×C₁₃×#731	direct (N × H)

Subgroups — C32×C13×#731 #23745071

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₁₃×#731 #23745071