Subgroups — C₃×#15691670 #23748531

Order 9477.

980 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#66851	C₃	1	3	yes	maximal
2	#15691670	C₃	1	27	yes	maximal, direct product factor
3	C₃×#11760443	C₃	1	9	yes	maximal, complemented
4	C₃²×C₁₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
5	C₃×#66851	—	3	6	no	—
6	C₃×#66851	—	3	18	no	—
7	C₃×#66851	C₃²	1	9	yes	—
8	C₃×#66851	C₃²	1	27	yes	—
9	C₃²×C₁₃⋊C₉	—	3	3	no	—
10	#11760443	C₃²	1	81	yes	complemented
11	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
12	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
13	C₃×C₁₃×3₋¹⁺²	—	3	6	no	—
14	C₃×C₁₃×3₋¹⁺²	C₃²	1	9	yes	—
15	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
16	C₃×#6912	—	13	1	no	maximal, Sylow
17	C₃³×C₁₃	—	9	3	no	—
18	C₃³×C₁₃	H(3,𝔽₃)	1	3	yes	—
19	C₃³×C₁₃	H(3,𝔽₃)	1	6	yes	—
20	C₃³×C₁₃	C₃³	1	1	yes	characteristic
21	C₃³×C₁₃	C₃³	1	3	yes	—
22	C₁₃×3₋¹⁺²	—	3	27	no	—
23	C₃×C₉×C₁₃	—	3	6	no	—
24	C₃×C₉×C₁₃	—	3	3	no	—
25	C₃×C₉×C₁₃	C₃³	1	9	yes	—
26	#66851	—	3	54	no	—
27	#66851	—	3	18	no	—
28	#66851	C₃³	1	27	yes	—
29	C₃×C₁₃⋊C₉	—	3	27	no	—
30	C₃×C₁₃⋊C₉	—	3	9	no	—
31	C₃²×3₋¹⁺²	—	13	3	no	—
32	C₃²×3₋¹⁺²	C₁₃⋊C₃	1	1	yes	characteristic
33	#6912	—	13	27	no	—
34	C₃×#733	—	13	9	no	—
35	C₃²×C₁₃	—	3	9	no	—
36	C₃²×C₁₃	—	3	3	no	—
37	C₃²×C₁₃	—	9	6	no	—
38	C₃²×C₁₃	—	9	3	no	—
39	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	9	yes	—
40	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	2	yes	—
41	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
42	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
43	C₉×C₁₃	—	3	9	no	—
44	C₁₃⋊C₉	—	3	27	no	—
45	C₃⁴	C₃×C₁₃⋊C₃	1	1	yes	characteristic
46	C₃×3₋¹⁺²	—	3	6	no	—
47	C₃×3₋¹⁺²	—	3	3	no	—
48	C₃×3₋¹⁺²	—	13	27	no	—
49	C₃×3₋¹⁺²	—	13	9	no	—
50	C₃×3₋¹⁺²	—	39	18	no	—
51	C₃×3₋¹⁺²	—	39	6	no	—
52	C₃×3₋¹⁺²	C₃×C₁₃⋊C₃	1	9	yes	—
53	C₃²×C₉	—	39	3	no	—
54	C₃²×C₉	C₃×C₁₃⋊C₃	1	3	yes	—
55	#733	—	13	81	no	—
56	C₃×C₁₃	—	3	9	no	—
57	C₃×C₁₃	—	3	2	no	—
58	C₃×C₁₃	—	3	1	no	—
59	C₃×C₁₃	#6912	1	3	yes	complemented
60	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
61	C₃³	—	9	3	no	—
62	C₃³	C₃²⋊(C₁₃⋊C₃)	1	3	yes	—
63	C₃³	C₃²⋊(C₁₃⋊C₃)	1	6	yes	—
64	C₃³	C₃²×C₁₃⋊C₃	1	1	yes	characteristic
65	C₃³	C₃²×C₁₃⋊C₃	1	3	yes	—
66	3₋¹⁺²	—	3	27	no	—
67	3₋¹⁺²	—	13	27	no	—
68	3₋¹⁺²	—	39	18	no	—
69	3₋¹⁺²	—	39	54	no	—
70	C₃×C₉	—	3	6	no	—
71	C₃×C₉	—	3	3	no	—
72	C₃×C₉	—	39	27	no	—
73	C₃×C₉	—	39	9	no	—
74	C₃×C₉	C₃²×C₁₃⋊C₃	1	9	yes	—
75	C₁₃	C₃×#6912	1	1	yes	characteristic, complemented, Sylow
76	C₃²	—	3	9	no	—
77	C₃²	—	3	3	no	—
78	C₃²	—	9	6	no	—
79	C₃²	—	9	3	no	—
80	C₃²	C₃×C₃²⋊(C₁₃⋊C₃)	1	2	yes	—
81	C₃²	C₃×C₃²⋊(C₁₃⋊C₃)	1	9	yes	—
82	C₃²	C₃×C₃²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
83	C₃²	C₃³×C₁₃⋊C₃	1	1	yes	characteristic
84	C₉	—	3	9	no	—
85	C₉	—	39	27	no	—
86	C₃	—	3	9	no	—
87	C₃	—	3	2	no	—
88	C₃	—	3	1	no	—
89	C₃	#15691670	1	3	yes	direct product factor
90	C₃	C₃²×C₃²⋊(C₁₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃×C₃²⋊(C₁₃⋊C₃)
commutator, cosocle	C₃²×C₁₃	C₃⁴
Frattini	C₃²	C₃³×C₁₃⋊C₃
Fitting	C₃²×C₁₃×3₋¹⁺²	C₃
socle	C₃²×C₁₃	C₃×H(3,𝔽₃)
prime radical	C₃⁴×C₁₃	C₃²
hypercenter	C₃²×3₋¹⁺²	C₁₃⋊C₃
hypocenter	C₁₃	C₃×#6912
LCS	G ▷ C₃²×C₁₃ ▷ C₃×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃² ◁ C₃⁴ ◁ C₃²×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
2. #15691670	C₃	direct (N × H)
3. C₃×#11760443	C₃	semidirect
10. #11760443	C₃²	semidirect
59. C₃×C₁₃	#6912	semidirect
75. C₁₃	C₃×#6912	semidirect
89. C₃	#15691670	direct (N × H)

Subgroups — C3×#15691670 #23748531

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#15691670 #23748531