Subgroups — C₃²×C₁₃×C₃²⋊C₉ #23745007

Order 9477.

2996 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁵×C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₃³×C₉×C₁₃	C₃	1	3	yes	maximal, complemented
3	C₃×C₁₃×C₃²⋊C₉	C₃	1	36	yes	maximal, direct product factor
4	C₃⁴×C₁₃	—	3	9	no	—
5	C₃⁴×C₁₃	—	3	18	no	—
6	C₃⁴×C₁₃	C₉	1	27	yes	complemented
7	C₃⁴×C₁₃	C₃²	1	12	yes	—
8	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
9	C₃²×C₉×C₁₃	—	3	27	no	—
10	C₃²×C₉×C₁₃	C₃²	1	36	yes	complemented
11	C₁₃×C₃²⋊C₉	C₃²	1	81	yes	direct product factor
12	C₃²×C₃²⋊C₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃³×C₁₃	—	3	243	no	—
14	C₃³×C₁₃	—	3	36	no	—
15	C₃³×C₁₃	—	3	72	no	—
16	C₃³×C₁₃	C₃×C₉	1	9	yes	—
17	C₃³×C₁₃	C₃×C₉	1	108	yes	complemented
18	C₃³×C₁₃	H(3,𝔽₃)	1	9	yes	—
19	C₃³×C₁₃	3₋¹⁺²	1	18	yes	—
20	C₃³×C₁₃	C₃³	1	9	yes	—
21	C₃³×C₁₃	C₃³	1	4	yes	—
22	C₃×C₉×C₁₃	—	3	108	no	—
23	C₃×C₉×C₁₃	C₃³	1	27	yes	complemented
24	C₃⁵	C₃×C₁₃	1	1	yes	characteristic
25	C₃³×C₉	C₃×C₁₃	1	3	yes	complemented
26	C₃×C₃²⋊C₉	C₃×C₁₃	1	36	yes	direct product factor
27	C₃²×C₁₃	—	3	9	no	—
28	C₃²×C₁₃	—	3	18	no	—
29	C₃²×C₁₃	—	3	324	no	—
30	C₃²×C₁₃	C₃²⋊C₉	1	81	yes	direct product factor
31	C₃²×C₁₃	C₃²×C₉	1	12	yes	—
32	C₃²×C₁₃	C₃²×C₉	1	27	yes	complemented
33	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	12	yes	—
34	C₃²×C₁₃	C₃×3₋¹⁺²	1	24	yes	—
35	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
36	C₉×C₁₃	—	3	27	no	—
37	C₃⁴	—	3	9	no	—
38	C₃⁴	—	3	18	no	—
39	C₃⁴	C₉×C₁₃	1	27	yes	complemented
40	C₃⁴	C₃²×C₁₃	1	12	yes	—
41	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
42	C₃²×C₉	—	3	27	no	—
43	C₃²×C₉	C₃²×C₁₃	1	36	yes	complemented
44	C₃²⋊C₉	C₃²×C₁₃	1	81	yes	direct product factor
45	C₃×C₁₃	—	3	27	no	—
46	C₃×C₁₃	C₃×C₃²⋊C₉	1	36	yes	direct product factor
47	C₃×C₁₃	C₃³×C₉	1	1	yes	characteristic
48	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
49	C₃×C₁₃	C₃²×3₋¹⁺²	1	2	yes	—
50	C₃³	—	3	243	no	—
51	C₃³	—	3	36	no	—
52	C₃³	—	3	72	no	—
53	C₃³	C₃×C₉×C₁₃	1	9	yes	—
54	C₃³	C₃×C₉×C₁₃	1	108	yes	complemented
55	C₃³	C₁₃×H(3,𝔽₃)	1	9	yes	—
56	C₃³	C₁₃×3₋¹⁺²	1	18	yes	—
57	C₃³	C₃³×C₁₃	1	9	yes	—
58	C₃³	C₃³×C₁₃	1	4	yes	—
59	C₃×C₉	—	3	108	no	—
60	C₃×C₉	C₃³×C₁₃	1	27	yes	complemented
61	C₁₃	C₃²×C₃²⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
62	C₃²	—	3	324	no	—
63	C₃²	—	3	9	no	—
64	C₃²	—	3	18	no	—
65	C₃²	C₁₃×C₃²⋊C₉	1	81	yes	direct product factor
66	C₃²	C₃²×C₉×C₁₃	1	12	yes	—
67	C₃²	C₃²×C₉×C₁₃	1	27	yes	complemented
68	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	12	yes	—
69	C₃²	C₃×C₁₃×3₋¹⁺²	1	24	yes	—
70	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
71	C₉	—	3	27	no	—
72	C₃	—	3	27	no	—
73	C₃	C₃×C₁₃×C₃²⋊C₉	1	36	yes	direct product factor
74	C₃	C₃³×C₉×C₁₃	1	1	yes	characteristic
75	C₃	C₃²×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
76	C₃	C₃²×C₁₃×3₋¹⁺²	1	2	yes	—

	subgroup	G/H
center, socle	C₃⁴×C₁₃	C₃²
commutator	C₃	C₃³×C₉×C₁₃
Frattini, cosocle	C₃²	C₃⁴×C₁₃
prime radical	C₃⁵×C₁₃	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃³×C₉×C₁₃	C₃	semidirect
3. C₃×C₁₃×C₃²⋊C₉	C₃	direct (N × H)
6. C₃⁴×C₁₃	C₉	semidirect
10. C₃²×C₉×C₁₃	C₃²	semidirect
11. C₁₃×C₃²⋊C₉	C₃²	direct (N × H)
12. C₃²×C₃²⋊C₉	C₁₃	direct (N × H)
17. C₃³×C₁₃	C₃×C₉	semidirect
23. C₃×C₉×C₁₃	C₃³	semidirect
25. C₃³×C₉	C₃×C₁₃	semidirect
26. C₃×C₃²⋊C₉	C₃×C₁₃	direct (N × H)
30. C₃²×C₁₃	C₃²⋊C₉	direct (N × H)
32. C₃²×C₁₃	C₃²×C₉	semidirect
39. C₃⁴	C₉×C₁₃	semidirect
43. C₃²×C₉	C₃²×C₁₃	semidirect
44. C₃²⋊C₉	C₃²×C₁₃	direct (N × H)
46. C₃×C₁₃	C₃×C₃²⋊C₉	direct (N × H)
54. C₃³	C₃×C₉×C₁₃	semidirect
60. C₃×C₉	C₃³×C₁₃	semidirect
61. C₁₃	C₃²×C₃²⋊C₉	direct (N × H)
65. C₃²	C₁₃×C₃²⋊C₉	direct (N × H)
67. C₃²	C₃²×C₉×C₁₃	semidirect
73. C₃	C₃×C₁₃×C₃²⋊C₉	direct (N × H)

Subgroups — C32×C13×C32⋊C9 #23745007

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₁₃×C₃²⋊C₉ #23745007