Subgroups — #22582642

Order 8991.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11758608	C₃	1	2	yes	maximal, complemented
2	C₃×#11758608	C₃	1	1	yes	maximal, characteristic, complemented
3	#15688515	C₃	1	9	yes	maximal, complemented
4	C₃×H(3,𝔽₃)×C₃₇	C₃	1	1	yes	maximal, characteristic
5	C₃³×C₃₇	—	3	1	no	—
6	C₃³×C₃₇	C₃²	1	1	yes	characteristic
7	H(3,𝔽₃)×C₃₇	—	3	2	no	—
8	H(3,𝔽₃)×C₃₇	C₃²	1	3	yes	—
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	complemented
14	C₃×#66524	—	3	2	no	—
15	C₃×#66524	C₃²	1	3	yes	complemented
16	C₃²×C₃₇	—	3	3	no	—
17	C₃²×C₃₇	—	9	1	no	—
18	C₃²×C₃₇	—	9	3	no	—
19	C₃²×C₃₇	H(3,𝔽₃)	1	2	yes	—
20	C₃²×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃²×C₃₇	C₃³	1	1	yes	characteristic
22	#66524	—	3	6	no	—
23	#66524	—	3	3	no	—
24	#6910	—	37	1	no	maximal, Sylow
25	C₃×C₃₇	—	3	1	no	—
26	C₃×C₃₇	—	3	2	no	—
27	C₃×C₃₇	—	3	1	no	—
28	C₃×C₃₇	—	9	3	no	—
29	C₃×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
30	C₃×3₋¹⁺²	—	37	1	no	—
31	C₃×3₋¹⁺²	—	37	2	no	—
32	C₃×H(3,𝔽₃)	C₃₇⋊C₃	1	1	yes	characteristic
33	#731	—	37	9	no	—
34	C₃₇	#6910	1	1	yes	characteristic, complemented, Sylow
35	C₃³	—	3	1	no	—
36	C₃³	C₃×C₃₇⋊C₃	1	1	yes	characteristic
37	3₋¹⁺²	—	37	6	no	—
38	3₋¹⁺²	—	111	2	no	—
39	3₋¹⁺²	—	111	1	no	—
40	3₋¹⁺²	—	111	2	no	—
41	3₋¹⁺²	—	111	2	no	—
42	H(3,𝔽₃)	—	3	2	no	—
43	H(3,𝔽₃)	C₃×C₃₇⋊C₃	1	3	yes	—
44	C₃×C₉	—	37	3	no	—
45	C₃×C₉	—	111	2	no	—
46	C₃²	—	3	3	no	—
47	C₃²	—	9	1	no	—
48	C₃²	—	9	3	no	—
49	C₃²	C₃²⋊(C₃₇⋊C₃)	1	2	yes	—
50	C₃²	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
51	C₃²	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
52	C₉	—	111	3	no	—
53	C₉	—	111	6	no	—
54	C₃	—	3	1	no	—
55	C₃	—	3	2	no	—
56	C₃	—	3	1	no	—
57	C₃	—	9	3	no	—
58	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×H(3,𝔽₃)×C₃₇	C₃
socle	C₃×C₃₇	C₃×H(3,𝔽₃)
hypercenter	C₃×H(3,𝔽₃)	C₃₇⋊C₃
hypocenter	C₃₇	#6910
LCS	G ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃×#11758608	C₃	semidirect
2. C₃×#11758608	C₃	semidirect
3. #15688515	C₃	semidirect
13. #11758608	C₃²	semidirect
15. C₃×#66524	C₃²	semidirect
34. C₃₇	#6910	semidirect