Subgroups — C₃²×C₁₃×#732 #23745072

Order 9477.

1376 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	3	yes	maximal, complemented
2	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×#732	C₃	1	36	yes	maximal, direct product factor
4	C₃⁴×C₁₃	—	3	3	no	—
5	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
6	C₃×C₁₃×H(3,𝔽₃)	—	3	24	no	—
7	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	36	yes	complemented
8	C₃²×C₉×C₁₃	—	3	8	no	—
9	C₃²×C₉×C₁₃	—	3	1	no	—
10	C₃²×C₉×C₁₃	C₃²	1	12	yes	complemented
11	C₁₃×#732	C₃²	1	81	yes	direct product factor
12	C₃²×#732	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃³×C₁₃	—	3	9	no	—
14	C₃³×C₁₃	—	3	36	no	—
15	C₃³×C₁₃	—	9	27	no	—
16	C₃³×C₁₃	H(3,𝔽₃)	1	8	yes	—
17	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
18	C₃³×C₁₃	C₃³	1	4	yes	—
19	C₁₃×H(3,𝔽₃)	—	3	72	no	—
20	C₁₃×H(3,𝔽₃)	C₃³	1	27	yes	complemented
21	C₃×C₉×C₁₃	—	3	24	no	—
22	C₃×C₉×C₁₃	—	3	12	no	—
23	C₃×C₉×C₁₃	C₃³	1	9	yes	complemented
24	C₃²×H(3,𝔽₃)	C₃×C₁₃	1	3	yes	complemented
25	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic, complemented
26	C₃×#732	C₃×C₁₃	1	36	yes	direct product factor
27	C₃²×C₁₃	—	3	24	no	—
28	C₃²×C₁₃	—	3	12	no	—
29	C₃²×C₁₃	—	3	27	no	—
30	C₃²×C₁₃	—	9	108	no	—
31	C₃²×C₁₃	#732	1	9	yes	direct product factor
32	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	8	yes	—
33	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	4	yes	—
34	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
35	C₉×C₁₃	—	3	9	no	—
36	C₃⁴	—	3	3	no	—
37	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
38	C₃×H(3,𝔽₃)	—	3	24	no	—
39	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	36	yes	complemented
40	C₃²×C₉	—	3	8	no	—
41	C₃²×C₉	—	3	1	no	—
42	C₃²×C₉	C₃²×C₁₃	1	12	yes	complemented
43	#732	C₃²×C₁₃	1	81	yes	direct product factor
44	C₃×C₁₃	—	3	8	no	—
45	C₃×C₁₃	—	3	1	no	—
46	C₃×C₁₃	—	9	27	no	—
47	C₃×C₁₃	C₃×#732	1	12	yes	direct product factor
48	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
49	C₃³	—	3	9	no	—
50	C₃³	—	3	36	no	—
51	C₃³	—	9	27	no	—
52	C₃³	C₁₃×H(3,𝔽₃)	1	8	yes	—
53	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
54	C₃³	C₃³×C₁₃	1	4	yes	—
55	H(3,𝔽₃)	—	3	72	no	—
56	H(3,𝔽₃)	C₃³×C₁₃	1	27	yes	complemented
57	C₃×C₉	—	3	24	no	—
58	C₃×C₉	—	3	12	no	—
59	C₃×C₉	C₃³×C₁₃	1	9	yes	complemented
60	C₁₃	C₃²×#732	1	1	yes	characteristic, direct product factor, Sylow
61	C₃²	—	3	24	no	—
62	C₃²	—	3	12	no	—
63	C₃²	—	3	27	no	—
64	C₃²	—	9	108	no	—
65	C₃²	C₁₃×#732	1	9	yes	direct product factor
66	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	8	yes	—
67	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	4	yes	—
68	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
69	C₉	—	3	9	no	—
70	C₃	—	3	8	no	—
71	C₃	—	3	1	no	—
72	C₃	—	9	27	no	—
73	C₃	C₃×C₁₃×#732	1	12	yes	direct product factor
74	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
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×H(3,𝔽₃)	C₃	semidirect
2. C₃³×C₉×C₁₃	C₃	semidirect
3. C₃×C₁₃×#732	C₃	direct (N × H)
7. C₃×C₁₃×H(3,𝔽₃)	C₃²	semidirect
10. C₃²×C₉×C₁₃	C₃²	semidirect
11. C₁₃×#732	C₃²	direct (N × H)
12. C₃²×#732	C₁₃	direct (N × H)
20. C₁₃×H(3,𝔽₃)	C₃³	semidirect
23. C₃×C₉×C₁₃	C₃³	semidirect
24. C₃²×H(3,𝔽₃)	C₃×C₁₃	semidirect
25. C₃³×C₉	C₃×C₁₃	semidirect
26. C₃×#732	C₃×C₁₃	direct (N × H)
31. C₃²×C₁₃	#732	direct (N × H)
39. C₃×H(3,𝔽₃)	C₃²×C₁₃	semidirect
42. C₃²×C₉	C₃²×C₁₃	semidirect
43. #732	C₃²×C₁₃	direct (N × H)
47. C₃×C₁₃	C₃×#732	direct (N × H)
56. H(3,𝔽₃)	C₃³×C₁₃	semidirect
59. C₃×C₉	C₃³×C₁₃	semidirect
60. C₁₃	C₃²×#732	direct (N × H)
65. C₃²	C₁₃×#732	direct (N × H)
73. C₃	C₃×C₁₃×#732	direct (N × H)

Subgroups — C32×C13×#732 #23745072

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₁₃×#732 #23745072