Subgroups — #22582581

Order 8991.

120 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	C₃×#11758606	C₃	1	1	yes	maximal, characteristic
3	#15688506	C₃	1	2	yes	maximal, complemented
4	#15688505	C₃	1	2	yes	maximal, complemented
5	#15688504	C₃	1	4	yes	maximal, complemented
6	#15688502	C₃	1	2	yes	maximal
7	C₉²×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
9	C₃×C₉×C₃₇	C₃²	1	2	yes	—
10	C₃×C₉×C₃₇	C₃²	1	1	yes	characteristic
11	C₃×C₉×C₃₇	C₃²	1	1	yes	characteristic
12	C₃×#66524	C₃²	1	4	yes	—
13	C₃×#66524	C₃²	1	2	yes	—
14	C₃×#66524	C₃²	1	2	yes	—
15	#11758606	—	3	3	no	—
16	#11758605	—	3	3	no	—
17	C₃²×C₃₇	C₃³	1	1	yes	characteristic
18	C₃×C₃₇⋊C₃	—	3	1	no	—
19	C₃×C₃₇⋊C₃	—	3	1	no	—
20	C₃×C₃₇⋊C₃	—	3	2	no	—
21	C₉×C₃₇	—	3	2	no	—
22	C₉×C₃₇	3₋¹⁺²	1	3	yes	complemented
23	C₉×C₃₇	3₋¹⁺²	1	3	yes	complemented
24	#66524	—	3	2	no	—
25	#66524	—	3	2	no	—
26	#66524	—	3	4	no	—
27	#6896	—	37	1	no	maximal, Sylow
28	C₃×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
29	C₃×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
30	C₃×C₃₇	#737	1	2	yes	—
31	C₃₇⋊C₃	—	9	1	no	—
32	C₃×3₋¹⁺²	—	37	1	no	—
33	C₃×3₋¹⁺²	—	37	1	no	—
34	C₉⋊C₉	—	37	4	no	—
35	C₉⋊C₉	—	37	2	no	—
36	C₉⋊C₉	—	37	2	no	—
37	C₃²⋊C₉	—	37	2	no	—
38	C₉²	C₃₇⋊C₃	1	1	yes	characteristic, complemented
39	C₃₇	#6896	1	1	yes	characteristic, complemented, Sylow
40	C₃³	—	37	1	no	—
41	3₋¹⁺²	—	111	3	no	—
42	3₋¹⁺²	—	111	3	no	—
43	C₃×C₉	—	37	4	no	—
44	C₃×C₉	—	37	2	no	—
45	C₃×C₉	—	37	2	no	—
46	C₃×C₉	C₃×C₃₇⋊C₃	1	2	yes	—
47	C₃×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
48	C₃×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
49	C₃²	—	111	1	no	—
50	C₃²	—	111	1	no	—
51	C₃²	—	111	2	no	—
52	C₃²	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
53	C₉	—	3	2	no	—
54	C₉	—	111	2	no	—
55	C₉	—	111	2	no	—
56	C₉	—	111	4	no	—
57	C₉	#11758605	1	3	yes	complemented
58	C₉	#11758606	1	3	yes	complemented
59	C₃	—	333	1	no	—
60	C₃	C₃×#11758606	1	1	yes	characteristic
61	C₃	C₃×#11758605	1	1	yes	characteristic
62	C₃	#15688531	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₃₇⋊C₃
commutator, socle	C₃²×C₃₇	C₃³
Fitting	C₉²×C₃₇	C₃
hypercenter	C₉²	C₃₇⋊C₃
hypocenter	C₃₇	#6896
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₉²

Complements

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

N	H ≅ G/N	type
3. #15688506	C₃	semidirect
4. #15688505	C₃	semidirect
5. #15688504	C₃	semidirect
7. C₉²×C₃₇	C₃	semidirect
22. C₉×C₃₇	3₋¹⁺²	semidirect
23. C₉×C₃₇	3₋¹⁺²	semidirect
38. C₉²	C₃₇⋊C₃	semidirect
39. C₃₇	#6896	semidirect
57. C₉	#11758605	semidirect
58. C₉	#11758606	semidirect