Subgroups — #22582599

Order 8991.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11758605	C₃	1	1	yes	maximal, characteristic
2	#15688506	C₃	1	1	yes	maximal, characteristic, complemented
3	#15688505	C₃	1	3	yes	maximal, complemented
4	#15688504	C₃	1	3	yes	maximal, complemented
5	#15688502	C₃	1	3	yes	maximal
6	C₉×#66524	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃₇×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
9	C₃×C₉×C₃₇	C₃²	1	3	yes	—
10	C₃×C₉×C₃₇	C₃²	1	1	yes	characteristic
11	C₃×#66524	C₃²	1	3	yes	—
12	C₃×#66524	C₃²	1	3	yes	—
13	C₃×#66524	C₃²	1	1	yes	characteristic
14	C₃×#66524	C₃²	1	1	yes	characteristic
15	#11758605	—	3	3	no	—
16	C₃²×C₃₇	C₃³	1	1	yes	characteristic
17	C₃×C₃₇⋊C₃	—	3	1	no	—
18	C₃×C₃₇⋊C₃	—	3	3	no	—
19	C₉×C₃₇	—	3	3	no	—
20	C₉×C₃₇	3₋¹⁺²	1	3	yes	—
21	#66524	—	3	1	no	—
22	#66524	—	3	1	no	—
23	#66524	—	3	3	no	—
24	#66524	—	3	3	no	—
25	#6899	—	37	1	no	maximal, Sylow
26	C₃×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
27	C₃×C₃₇	#737	1	3	yes	—
28	C₃₇⋊C₃	—	9	1	no	—
29	C₃×3₋¹⁺²	—	37	1	no	—
30	C₉⋊C₉	—	37	3	no	—
31	C₉⋊C₉	—	37	3	no	—
32	C₉⋊C₉	—	37	1	no	—
33	C₉⋊C₉	C₃₇⋊C₃	1	1	yes	characteristic, complemented
34	C₃²⋊C₉	—	37	3	no	—
35	C₉²	—	37	1	no	—
36	C₃₇	#6899	1	1	yes	characteristic, complemented, Sylow
37	C₃³	—	37	1	no	—
38	3₋¹⁺²	—	111	3	no	—
39	C₃×C₉	—	37	3	no	—
40	C₃×C₉	—	37	3	no	—
41	C₃×C₉	—	37	1	no	—
42	C₃×C₉	—	37	1	no	—
43	C₃×C₉	C₃×C₃₇⋊C₃	1	3	yes	—
44	C₃×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
45	C₃²	—	111	1	no	—
46	C₃²	—	111	3	no	—
47	C₃²	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
48	C₉	—	3	3	no	—
49	C₉	—	111	1	no	—
50	C₉	—	111	1	no	—
51	C₉	—	111	3	no	—
52	C₉	—	111	3	no	—
53	C₉	#11758605	1	3	yes	—
54	C₃	—	333	1	no	—
55	C₃	C₃×#11758605	1	1	yes	characteristic
56	C₃	#15688532	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₃₇⋊C₃
commutator, socle	C₃²×C₃₇	C₃³
Fitting	C₃₇×C₉⋊C₉	C₃
hypercenter	C₉⋊C₉	C₃₇⋊C₃
hypocenter	C₃₇	#6899
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

Complements

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

N	H ≅ G/N	type
2. #15688506	C₃	semidirect
3. #15688505	C₃	semidirect
4. #15688504	C₃	semidirect
6. C₉×#66524	C₃	semidirect
7. C₃₇×C₉⋊C₉	C₃	semidirect
33. C₉⋊C₉	C₃₇⋊C₃	semidirect
36. C₃₇	#6899	semidirect