Subgroups — #23748639

Order 9477.

170 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₃³⋊C₁₃)⋊C₉	C₃	1	3	yes	maximal, complemented
2	C₃²×C₃³⋊C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₃³⋊C₁₃	—	3	1	no	—
4	C₃×C₃³⋊C₁₃	C₃²	1	1	yes	characteristic
5	#10624765	—	13	1	no	maximal, Sylow
6	C₃³⋊C₁₃	3₋¹⁺²	1	1	yes	characteristic, complemented
7	#66851	—	27	1	no	maximal
8	C₃⁵	C₁₃⋊C₃	1	1	yes	characteristic
9	#6891	—	13	1	no	—
10	#6891	—	13	2	no	—
11	#6866	—	13	6	no	—
12	#6866	—	13	3	no	—
13	C₃²×C₁₃	—	27	1	no	—
14	C₁₃⋊C₉	—	27	3	no	—
15	C₃⁴	—	3	1	no	—
16	C₃⁴	—	13	2	no	—
17	C₃⁴	—	13	1	no	—
18	C₃⁴	—	39	2	no	—
19	C₃⁴	C₃×C₁₃⋊C₃	1	1	yes	characteristic
20	C₃×3₋¹⁺²	—	39	2	no	—
21	C₃×3₋¹⁺²	—	39	1	no	—
22	C₃²⋊C₉	—	13	6	no	—
23	C₃²⋊C₉	—	13	3	no	—
24	C₃²⋊C₉	—	39	2	no	—
25	C₃²⋊C₉	—	39	2	no	—
26	C₃²⋊C₉	—	39	2	no	—
27	C₃×C₁₃	—	27	1	no	—
28	C₃×C₁₃	—	81	1	no	—
29	C₃³	—	13	2	no	—
30	C₃³	—	13	1	no	—
31	C₃³	—	13	1	no	—
32	C₃³	—	13	2	no	—
33	C₃³	—	13	6	no	—
34	C₃³	—	39	2	no	—
35	C₃³	—	39	2	no	—
36	C₃³	—	39	2	no	—
37	C₃³	—	39	1	no	—
38	C₃³	—	39	2	no	—
39	C₃³	—	39	6	no	—
40	C₃³	—	39	12	no	—
41	C₃³	#66851	1	1	yes	characteristic, complemented
42	3₋¹⁺²	—	117	6	no	—
43	3₋¹⁺²	—	117	2	no	—
44	3₋¹⁺²	—	117	1	no	—
45	C₃×C₉	—	39	6	no	—
46	C₃×C₉	—	39	3	no	—
47	C₁₃	—	27	1	no	Sylow
48	C₃²	—	13	1	no	—
49	C₃²	—	13	2	no	—
50	C₃²	—	13	1	no	—
51	C₃²	—	13	6	no	—
52	C₃²	—	13	2	no	—
53	C₃²	—	39	2	no	—
54	C₃²	—	39	1	no	—
55	C₃²	—	39	2	no	—
56	C₃²	—	39	2	no	—
57	C₃²	—	39	2	no	—
58	C₃²	—	39	12	no	—
59	C₃²	—	39	6	no	—
60	C₃²	(C₃³⋊C₁₃)⋊C₃	1	1	yes	characteristic
61	C₉	—	117	6	no	—
62	C₉	—	117	3	no	—
63	C₃	—	3	1	no	—
64	C₃	—	13	2	no	—
65	C₃	—	13	1	no	—
66	C₃	—	39	2	no	—
67	C₃	C₃×(C₃³⋊C₁₃)⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃	C₃×(C₃³⋊C₁₃)⋊C₃
commutator, cosocle	C₃×C₃³⋊C₁₃	C₃²
Fitting	C₃⁵	C₁₃⋊C₃
socle	C₃⁴	C₃×C₁₃⋊C₃
prime radical	C₃²×C₃³⋊C₁₃	C₃
hypercenter	C₃²	(C₃³⋊C₁₃)⋊C₃
hypocenter	C₃³⋊C₁₃	3₋¹⁺²
LCS	G ▷ C₃×C₃³⋊C₁₃ ▷ C₃³⋊C₁₃
UCS	C₁ ◁ C₃ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. (C₃³⋊C₁₃)⋊C₉	C₃	semidirect
6. C₃³⋊C₁₃	3₋¹⁺²	semidirect
41. C₃³	#66851	semidirect