Subgroups — #23748571

Order 9477.

936 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15691698	C₃	1	3	yes	maximal
2	#15691670	C₃	1	24	yes	maximal, complemented
3	C₃×#11760443	C₃	1	12	yes	maximal, complemented
4	C₃×C₁₃×#737	C₃	1	1	yes	maximal, characteristic
5	#11760452	—	3	27	no	—
6	C₃×#66851	C₃²	1	36	yes	—
7	#11760443	C₃²	1	9	yes	—
8	#11760443	C₃²	1	72	yes	—
9	C₁₃×#737	—	3	9	no	—
10	C₃×C₁₃×3₋¹⁺²	C₃²	1	8	yes	—
11	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
12	C₃²×C₉×C₁₃	C₃²	1	4	yes	—
13	#10624933	—	13	1	no	maximal, Sylow
14	C₃³×C₁₃	C₃³	1	4	yes	—
15	C₁₃×3₋¹⁺²	—	3	24	no	—
16	C₁₃×H(3,𝔽₃)	H(3,𝔽₃)	1	9	yes	—
17	C₃×C₉×C₁₃	—	3	12	no	—
18	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
19	C₃×C₉×C₁₃	C₃³	1	8	yes	—
20	#66851	—	3	72	no	—
21	#66851	C₃³	1	27	yes	—
22	C₃×C₁₃⋊C₉	—	3	36	no	—
23	3₋¹⁺⁴	—	13	3	no	—
24	C₃×#737	C₁₃⋊C₃	1	1	yes	characteristic
25	#6912	—	13	24	no	—
26	C₃×#733	—	13	12	no	—
27	C₃²×C₁₃	—	9	4	no	—
28	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	12	yes	—
29	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
30	C₉×C₁₃	—	3	1	no	—
31	C₉×C₁₃	—	3	8	no	—
32	C₁₃⋊C₉	—	3	27	no	—
33	#737	—	3	9	no	—
34	#737	—	39	27	no	—
35	C₃×3₋¹⁺²	—	13	36	no	—
36	C₃×3₋¹⁺²	C₃×C₁₃⋊C₃	1	8	yes	—
37	C₃×H(3,𝔽₃)	C₃×C₁₃⋊C₃	1	1	yes	characteristic
38	C₃²×C₉	C₃×C₁₃⋊C₃	1	4	yes	—
39	#733	—	13	72	no	—
40	#733	—	13	9	no	—
41	C₃×C₁₃	—	3	1	no	—
42	C₃×C₁₃	—	3	12	no	—
43	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
44	C₃³	C₃²×C₁₃⋊C₃	1	4	yes	—
45	3₋¹⁺²	—	3	24	no	—
46	3₋¹⁺²	—	13	27	no	—
47	3₋¹⁺²	—	39	72	no	—
48	H(3,𝔽₃)	C₃²⋊(C₁₃⋊C₃)	1	9	yes	—
49	C₃×C₉	—	3	12	no	—
50	C₃×C₉	—	39	36	no	—
51	C₃×C₉	C₃²×C₁₃⋊C₃	1	1	yes	characteristic
52	C₃×C₉	C₃²×C₁₃⋊C₃	1	8	yes	—
53	C₁₃	#10624933	1	1	yes	characteristic, complemented, Sylow
54	C₃²	—	9	4	no	—
55	C₃²	C₃×C₃²⋊(C₁₃⋊C₃)	1	12	yes	—
56	C₃²	C₃³×C₁₃⋊C₃	1	1	yes	characteristic
57	C₉	—	3	1	no	—
58	C₉	—	3	8	no	—
59	C₉	—	39	27	no	—
60	C₃	—	3	1	no	—
61	C₃	—	3	12	no	—
62	C₃	C₃²×C₃²⋊(C₁₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃²×C₃²⋊(C₁₃⋊C₃)
commutator, cosocle	C₃²×C₁₃	C₃⁴
Frattini	C₃²	C₃³×C₁₃⋊C₃
Fitting	C₃×C₁₃×#737	C₃
socle	C₃×C₁₃	C₃²×H(3,𝔽₃)
prime radical	C₃×C₁₃×H(3,𝔽₃)	C₃²
hypercenter	C₃×#737	C₁₃⋊C₃
hypocenter	C₁₃	#10624933
LCS	G ▷ C₃²×C₁₃ ▷ C₃×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃ ◁ C₃×H(3,𝔽₃) ◁ C₃×#737

Complements

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

N	H ≅ G/N	type
2. #15691670	C₃	semidirect
3. C₃×#11760443	C₃	semidirect
53. C₁₃	#10624933	semidirect