Subgroups — #22582651

Order 8991.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11758608	C₃	1	2	yes	maximal
2	C₃×#11758608	C₃	1	1	yes	maximal, characteristic
3	#15688520	C₃	1	9	yes	maximal, complemented
4	C₃×3₋¹⁺²×C₃₇	C₃	1	1	yes	maximal, characteristic
5	C₃³×C₃₇	C₃²	1	1	yes	characteristic
6	3₋¹⁺²×C₃₇	—	3	2	no	—
7	3₋¹⁺²×C₃₇	C₃²	1	3	yes	—
8	C₃×C₉×C₃₇	—	3	1	no	—
9	#11758608	—	3	2	no	—
10	#11758608	—	3	2	no	—
11	#11758608	—	3	2	no	—
12	#11758608	—	3	1	no	—
13	#11758608	C₃²	1	6	yes	—
14	C₃×#66524	—	3	2	no	—
15	C₃×#66524	C₃²	1	3	yes	—
16	C₃²×C₃₇	—	9	1	no	—
17	C₃²×C₃₇	H(3,𝔽₃)	1	2	yes	—
18	C₃²×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
19	C₃²×C₃₇	C₃³	1	1	yes	characteristic
20	C₉×C₃₇	—	3	3	no	—
21	#66524	—	3	6	no	—
22	#66524	—	3	3	no	—
23	#6912	—	37	1	no	maximal, Sylow
24	C₃×C₃₇	—	3	2	no	—
25	C₃×C₃₇	—	3	1	no	—
26	C₃×C₃₇	—	3	1	no	—
27	C₃×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₃×3₋¹⁺²	—	37	1	no	—
29	C₃×3₋¹⁺²	—	37	2	no	—
30	C₃×3₋¹⁺²	C₃₇⋊C₃	1	1	yes	characteristic
31	#733	—	37	9	no	—
32	C₃₇	#6912	1	1	yes	characteristic, complemented, Sylow
33	C₃³	C₃×C₃₇⋊C₃	1	1	yes	characteristic
34	3₋¹⁺²	—	3	2	no	—
35	3₋¹⁺²	—	37	6	no	—
36	3₋¹⁺²	—	111	1	no	—
37	3₋¹⁺²	—	111	2	no	—
38	3₋¹⁺²	—	111	2	no	—
39	3₋¹⁺²	—	111	2	no	—
40	3₋¹⁺²	C₃×C₃₇⋊C₃	1	3	yes	—
41	C₃×C₉	—	3	1	no	—
42	C₃×C₉	—	37	3	no	—
43	C₃×C₉	—	111	2	no	—
44	C₃²	—	9	1	no	—
45	C₃²	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
46	C₃²	C₃²⋊(C₃₇⋊C₃)	1	2	yes	—
47	C₃²	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
48	C₉	—	3	3	no	—
49	C₉	—	111	3	no	—
50	C₉	—	111	6	no	—
51	C₃	—	3	1	no	—
52	C₃	—	3	2	no	—
53	C₃	—	3	1	no	—
54	C₃	C₃×C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×C₃²⋊(C₃₇⋊C₃)
commutator	C₃²×C₃₇	C₃³
Frattini	C₃²	C₃²×C₃₇⋊C₃
Fitting	C₃×3₋¹⁺²×C₃₇	C₃
socle	C₃×C₃₇	C₃×H(3,𝔽₃)
hypercenter	C₃×3₋¹⁺²	C₃₇⋊C₃
hypocenter	C₃₇	#6912
LCS	G ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
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. #15688520	C₃	semidirect
32. C₃₇	#6912	semidirect