Subgroups — C₃×#15688515 #22582620

Order 8991.

144 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	C₃²×#66524	C₃	1	1	yes	maximal, characteristic, complemented
3	#15688515	C₃	1	9	yes	maximal, direct product factor
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	4	no	—
10	#11758608	C₃²	1	6	yes	complemented
11	C₃×#66524	—	3	2	no	—
12	C₃×#66524	—	3	1	no	—
13	C₃×#66524	—	3	2	no	—
14	C₃×#66524	C₃²	1	3	yes	complemented
15	C₃²×C₃₇	—	3	3	no	—
16	C₃²×C₃₇	—	3	3	no	—
17	C₃²×C₃₇	—	9	3	no	—
18	C₃²×C₃₇	H(3,𝔽₃)	1	2	yes	—
19	C₃²×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃²×C₃₇	C₃³	1	1	yes	characteristic
21	#66524	—	3	3	no	—
22	#66524	—	3	6	no	—
23	C₃×#731	—	37	1	no	maximal, Sylow
24	C₃×C₃₇	—	3	2	no	—
25	C₃×C₃₇	—	3	1	no	—
26	C₃×C₃₇	—	9	3	no	—
27	C₃×C₃₇	#731	1	3	yes	complemented
28	C₃×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
29	C₃×3₋¹⁺²	—	37	2	no	—
30	C₃×H(3,𝔽₃)	C₃₇⋊C₃	1	1	yes	characteristic
31	C₃²×C₉	—	37	1	no	—
32	#731	—	37	9	no	—
33	C₃₇	C₃×#731	1	1	yes	characteristic, complemented, Sylow
34	C₃³	—	3	1	no	—
35	C₃³	C₃×C₃₇⋊C₃	1	1	yes	characteristic
36	3₋¹⁺²	—	37	6	no	—
37	3₋¹⁺²	—	111	4	no	—
38	H(3,𝔽₃)	—	3	2	no	—
39	H(3,𝔽₃)	C₃×C₃₇⋊C₃	1	3	yes	—
40	C₃×C₉	—	37	3	no	—
41	C₃×C₉	—	111	2	no	—
42	C₃×C₉	—	111	1	no	—
43	C₃×C₉	—	111	2	no	—
44	C₃²	—	3	3	no	—
45	C₃²	—	3	3	no	—
46	C₃²	—	9	3	no	—
47	C₃²	C₃²⋊(C₃₇⋊C₃)	1	2	yes	—
48	C₃²	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
49	C₃²	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
50	C₉	—	111	3	no	—
51	C₉	—	111	6	no	—
52	C₃	—	3	2	no	—
53	C₃	—	3	1	no	—
54	C₃	—	9	3	no	—
55	C₃	#15688515	1	3	yes	direct product factor
56	C₃	C₃×C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊(C₃₇⋊C₃)
commutator	C₃²×C₃₇	C₃³
Frattini	C₃²	C₃²×C₃₇⋊C₃
Fitting	C₃×H(3,𝔽₃)×C₃₇	C₃
socle	C₃²×C₃₇	H(3,𝔽₃)
hypercenter	C₃×H(3,𝔽₃)	C₃₇⋊C₃
hypocenter	C₃₇	C₃×#731
LCS	G ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ 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. C₃²×#66524	C₃	semidirect
3. #15688515	C₃	direct (N × H)
10. #11758608	C₃²	semidirect
14. C₃×#66524	C₃²	semidirect
27. C₃×C₃₇	#731	semidirect
33. C₃₇	C₃×#731	semidirect
55. C₃	#15688515	direct (N × H)

Subgroups — C3×#15688515 #22582620

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#15688515 #22582620