Subgroups — #21419409

Order 7533.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11719689	C₃	1	2	yes	maximal
2	C₃×#11719689	C₃	1	1	yes	maximal, characteristic
3	#14578901	C₃	1	9	yes	maximal, complemented
4	C₃×3₋¹⁺²×C₃₁	C₃	1	1	yes	maximal, characteristic
5	C₃³×C₃₁	C₃²	1	1	yes	characteristic
6	3₋¹⁺²×C₃₁	—	3	2	no	—
7	3₋¹⁺²×C₃₁	C₃²	1	3	yes	—
8	C₃×C₉×C₃₁	—	3	1	no	—
9	#11719689	—	3	2	no	—
10	#11719689	—	3	2	no	—
11	#11719689	—	3	2	no	—
12	#11719689	—	3	1	no	—
13	#11719689	C₃²	1	6	yes	—
14	C₃×C₃₁⋊C₉	—	3	2	no	—
15	C₃×C₃₁⋊C₉	C₃²	1	3	yes	—
16	C₃²×C₃₁	—	9	1	no	—
17	C₃²×C₃₁	H(3,𝔽₃)	1	2	yes	—
18	C₃²×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
19	C₃²×C₃₁	C₃³	1	1	yes	characteristic
20	C₉×C₃₁	—	3	3	no	—
21	C₃₁⋊C₉	—	3	6	no	—
22	C₃₁⋊C₉	—	3	3	no	—
23	#6912	—	31	1	no	maximal, Sylow
24	C₃×C₃₁	—	3	2	no	—
25	C₃×C₃₁	—	3	1	no	—
26	C₃×C₃₁	—	3	1	no	—
27	C₃×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₃×3₋¹⁺²	—	31	1	no	—
29	C₃×3₋¹⁺²	—	31	2	no	—
30	C₃×3₋¹⁺²	C₃₁⋊C₃	1	1	yes	characteristic
31	#733	—	31	9	no	—
32	C₃₁	#6912	1	1	yes	characteristic, complemented, Sylow
33	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic
34	3₋¹⁺²	—	3	2	no	—
35	3₋¹⁺²	—	31	6	no	—
36	3₋¹⁺²	—	93	1	no	—
37	3₋¹⁺²	—	93	2	no	—
38	3₋¹⁺²	—	93	2	no	—
39	3₋¹⁺²	—	93	2	no	—
40	3₋¹⁺²	C₃×C₃₁⋊C₃	1	3	yes	—
41	C₃×C₉	—	3	1	no	—
42	C₃×C₉	—	31	3	no	—
43	C₃×C₉	—	93	2	no	—
44	C₃²	—	9	1	no	—
45	C₃²	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
46	C₃²	C₃²⋊(C₃₁⋊C₃)	1	2	yes	—
47	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
48	C₉	—	3	3	no	—
49	C₉	—	93	3	no	—
50	C₉	—	93	6	no	—
51	C₃	—	3	1	no	—
52	C₃	—	3	2	no	—
53	C₃	—	3	1	no	—
54	C₃	C₃×C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×C₃²⋊(C₃₁⋊C₃)
commutator	C₃²×C₃₁	C₃³
Frattini	C₃²	C₃²×C₃₁⋊C₃
Fitting	C₃×3₋¹⁺²×C₃₁	C₃
socle	C₃×C₃₁	C₃×H(3,𝔽₃)
hypercenter	C₃×3₋¹⁺²	C₃₁⋊C₃
hypocenter	C₃₁	#6912
LCS	G ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
3. #14578901	C₃	semidirect
32. C₃₁	#6912	semidirect