Subgroups — C₃²×C₁₃×#733 #23745073

Order 9477.

1052 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×3₋¹⁺²	C₃	1	3	yes	maximal
2	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃×#733	C₃	1	36	yes	maximal, direct product factor
4	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
5	C₃×C₁₃×3₋¹⁺²	—	3	24	no	—
6	C₃×C₁₃×3₋¹⁺²	C₃²	1	36	yes	—
7	C₃²×C₉×C₁₃	—	3	8	no	—
8	C₃²×C₉×C₁₃	—	3	1	no	—
9	C₃²×C₉×C₁₃	—	3	3	no	—
10	C₃²×C₉×C₁₃	C₃²	1	12	yes	—
11	C₁₃×#733	C₃²	1	81	yes	direct product factor
12	C₃²×#733	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃³×C₁₃	—	3	9	no	—
14	C₃³×C₁₃	H(3,𝔽₃)	1	8	yes	—
15	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
16	C₃³×C₁₃	C₃³	1	4	yes	—
17	C₁₃×3₋¹⁺²	—	3	72	no	—
18	C₁₃×3₋¹⁺²	C₃³	1	27	yes	—
19	C₃×C₉×C₁₃	—	3	24	no	—
20	C₃×C₉×C₁₃	—	3	12	no	—
21	C₃×C₉×C₁₃	—	3	36	no	—
22	C₃×C₉×C₁₃	C₃³	1	9	yes	—
23	C₃²×3₋¹⁺²	C₃×C₁₃	1	3	yes	—
24	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
25	C₃×#733	C₃×C₁₃	1	36	yes	direct product factor
26	C₃²×C₁₃	—	3	24	no	—
27	C₃²×C₁₃	—	3	12	no	—
28	C₃²×C₁₃	#733	1	9	yes	direct product factor
29	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	8	yes	—
30	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	4	yes	—
31	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
32	C₉×C₁₃	—	3	9	no	—
33	C₉×C₁₃	—	3	27	no	—
34	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
35	C₃×3₋¹⁺²	—	3	24	no	—
36	C₃×3₋¹⁺²	C₃²×C₁₃	1	36	yes	—
37	C₃²×C₉	—	3	8	no	—
38	C₃²×C₉	—	3	1	no	—
39	C₃²×C₉	—	3	3	no	—
40	C₃²×C₉	C₃²×C₁₃	1	12	yes	—
41	#733	C₃²×C₁₃	1	81	yes	direct product factor
42	C₃×C₁₃	—	3	8	no	—
43	C₃×C₁₃	—	3	1	no	—
44	C₃×C₁₃	C₃×#733	1	12	yes	direct product factor
45	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
46	C₃³	—	3	9	no	—
47	C₃³	C₁₃×H(3,𝔽₃)	1	8	yes	—
48	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
49	C₃³	C₃³×C₁₃	1	4	yes	—
50	3₋¹⁺²	—	3	72	no	—
51	3₋¹⁺²	C₃³×C₁₃	1	27	yes	—
52	C₃×C₉	—	3	24	no	—
53	C₃×C₉	—	3	12	no	—
54	C₃×C₉	—	3	36	no	—
55	C₃×C₉	C₃³×C₁₃	1	9	yes	—
56	C₁₃	C₃²×#733	1	1	yes	characteristic, direct product factor, Sylow
57	C₃²	—	3	24	no	—
58	C₃²	—	3	12	no	—
59	C₃²	C₁₃×#733	1	9	yes	direct product factor
60	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	8	yes	—
61	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	4	yes	—
62	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
63	C₉	—	3	9	no	—
64	C₉	—	3	27	no	—
65	C₃	—	3	8	no	—
66	C₃	—	3	1	no	—
67	C₃	C₃×C₁₃×#733	1	12	yes	direct product factor
68	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	C₃⁴×C₁₃	C₃²
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
3. C₃×C₁₃×#733	C₃	direct (N × H)
11. C₁₃×#733	C₃²	direct (N × H)
12. C₃²×#733	C₁₃	direct (N × H)
25. C₃×#733	C₃×C₁₃	direct (N × H)
28. C₃²×C₁₃	#733	direct (N × H)
41. #733	C₃²×C₁₃	direct (N × H)
44. C₃×C₁₃	C₃×#733	direct (N × H)
56. C₁₃	C₃²×#733	direct (N × H)
59. C₃²	C₁₃×#733	direct (N × H)
67. C₃	C₃×C₁₃×#733	direct (N × H)

Subgroups — C32×C13×#733 #23745073

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₁₃×#733 #23745073