Subgroups — #22582691

Order 8991.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊#66526	C₃	1	3	yes	maximal, complemented
2	C₃³×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₃³×C₃₇	C₉	1	1	yes	characteristic, complemented
4	C₃²×C₃₇⋊C₃	—	3	1	no	—
5	C₃²×C₃₇⋊C₃	—	3	2	no	—
6	C₃²×C₃₇⋊C₃	—	3	9	no	—
7	C₃²×C₃₇⋊C₃	C₉	1	2	yes	complemented
8	C₃²×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
9	C₃×#66526	—	3	3	no	—
10	C₃²×C₃₇	—	3	3	no	—
11	C₃²×C₃₇	—	3	1	no	—
12	C₃²×C₃₇	C₃×C₉	1	1	yes	characteristic
13	C₃×C₃₇⋊C₃	—	3	18	no	—
14	C₃×C₃₇⋊C₃	—	3	2	no	—
15	C₃×C₃₇⋊C₃	—	3	9	no	—
16	C₃×C₃₇⋊C₃	—	3	3	no	—
17	C₃×C₃₇⋊C₃	—	3	6	no	—
18	C₃×C₃₇⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
19	C₃×C₃₇⋊C₃	3₋¹⁺²	1	2	yes	—
20	#66526	—	9	3	no	—
21	#6866	—	37	1	no	maximal, Sylow
22	C₃×C₃₇	—	3	3	no	—
23	C₃×C₃₇	—	3	1	no	—
24	C₃×C₃₇	C₃²⋊C₉	1	1	yes	characteristic
25	C₃₇⋊C₃	—	3	6	no	—
26	C₃₇⋊C₃	—	3	2	no	—
27	C₃₇⋊C₃	AΣL(1,𝔽₂₇)	1	3	yes	—
28	C₃⁴	—	37	1	no	—
29	C₃²⋊C₉	—	37	3	no	—
30	C₃₇	#6866	1	1	yes	characteristic, complemented, Sylow
31	C₃³	—	37	1	no	—
32	C₃³	—	37	2	no	—
33	C₃³	—	111	1	no	—
34	C₃³	—	111	2	no	—
35	C₃³	—	111	9	no	—
36	C₃³	#66526	1	1	yes	characteristic, complemented
37	C₃×C₉	—	111	3	no	—
38	C₃²	—	3	3	no	—
39	C₃²	—	3	1	no	—
40	C₃²	—	37	1	no	—
41	C₃²	—	37	2	no	—
42	C₃²	—	111	3	no	—
43	C₃²	—	111	9	no	—
44	C₃²	—	111	6	no	—
45	C₃²	—	111	18	no	—
46	C₃²	—	111	2	no	—
47	C₃²	C₃×#66526	1	1	yes	characteristic
48	C₉	—	333	3	no	—
49	C₃	—	3	1	no	—
50	C₃	—	3	3	no	—
51	C₃	—	37	3	no	—
52	C₃	—	111	2	no	—
53	C₃	—	111	6	no	—
54	C₃	C₃²⋊#66526	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃²⋊#66526
commutator	C₃²×C₃₇	C₃×C₉
Frattini	C₃²	C₃×#66526
Fitting	C₃³×C₃₇	C₉
socle	C₃×C₃₇	C₃²⋊C₉
hypercenter	C₃³	#66526
hypocenter	C₃₇	#6866
LCS	G ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃³

Complements

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

N	H ≅ G/N	type
1. C₃²⋊#66526	C₃	semidirect
3. C₃³×C₃₇	C₉	semidirect
7. C₃²×C₃₇⋊C₃	C₉	semidirect
30. C₃₇	#6866	semidirect
36. C₃³	#66526	semidirect