Subgroups — #22582573

Order 8991.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11758608	C₃	1	1	yes	maximal, characteristic
2	C₃²×#66524	C₃	1	1	yes	maximal, characteristic
3	#15688506	C₃	1	3	yes	maximal, complemented
4	#15688504	C₃	1	3	yes	maximal, complemented
5	#15688504	C₃	1	3	yes	maximal, complemented
6	C₃²⋊#66524	C₃	1	1	yes	maximal, characteristic
7	C₃₇×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
8	C₃³×C₃₇	C₃²	1	1	yes	characteristic
9	C₃×C₉×C₃₇	C₃²	1	3	yes	—
10	#11758608	—	3	3	no	—
11	C₃×#66524	—	3	3	no	—
12	C₃×#66524	C₃²	1	3	yes	—
13	C₃×#66524	C₃²	1	1	yes	characteristic
14	C₃×#66524	C₃²	1	3	yes	—
15	C₃×#66524	C₃²	1	1	yes	characteristic
16	C₃×#66524	C₃²	1	1	yes	characteristic
17	C₃²×C₃₇	—	3	1	no	—
18	C₃²×C₃₇	—	3	1	no	—
19	C₃²×C₃₇	—	3	1	no	—
20	C₃²×C₃₇	3₋¹⁺²	1	3	yes	—
21	C₃²×C₃₇	C₃³	1	1	yes	characteristic
22	C₉×C₃₇	—	3	3	no	—
23	#66524	—	3	1	no	—
24	#66524	—	3	1	no	—
25	#66524	—	3	3	no	—
26	#66524	—	3	3	no	—
27	#66524	3₋¹⁺²	1	3	yes	complemented
28	#6894	—	37	1	no	maximal, Sylow
29	C₃×C₃₇	—	3	3	no	—
30	C₃×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
31	C₃×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
32	C₃×C₃₇	#737	1	1	yes	characteristic
33	C₃×C₃₇	#737	1	1	yes	characteristic
34	C₃×3₋¹⁺²	—	37	1	no	—
35	C₃²×C₉	—	37	1	no	—
36	C₉⋊C₉	—	37	3	no	—
37	C₉⋊C₉	—	37	3	no	—
38	C₉⋊C₉	—	37	3	no	—
39	C₃²⋊C₉	—	37	1	no	—
40	C₃²⋊C₉	C₃₇⋊C₃	1	1	yes	characteristic
41	C₃₇	#6894	1	1	yes	characteristic, complemented, Sylow
42	C₃³	C₃×C₃₇⋊C₃	1	1	yes	characteristic
43	3₋¹⁺²	—	111	3	no	—
44	C₃×C₉	—	37	1	no	—
45	C₃×C₉	—	37	3	no	—
46	C₃×C₉	—	37	1	no	—
47	C₃×C₉	—	37	1	no	—
48	C₃×C₉	—	37	3	no	—
49	C₃×C₉	—	111	3	no	—
50	C₃×C₉	C₃×C₃₇⋊C₃	1	3	yes	—
51	C₃²	—	3	1	no	—
52	C₃²	—	3	1	no	—
53	C₃²	—	3	1	no	—
54	C₃²	#11758606	1	3	yes	—
55	C₃²	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
56	C₉	—	3	3	no	—
57	C₉	—	37	3	no	—
58	C₉	—	111	1	no	—
59	C₉	—	111	1	no	—
60	C₉	—	111	3	no	—
61	C₉	—	111	3	no	—
62	C₃	—	3	3	no	—
63	C₃	3₋¹⁺²×C₃₇⋊C₃	1	1	yes	characteristic
64	C₃	C₃×#11758606	1	1	yes	characteristic
65	C₃	#15688530	1	1	yes	characteristic
66	C₃	#15688532	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₃₇⋊C₃
commutator, socle	C₃²×C₃₇	C₃³
Fitting	C₃₇×C₃²⋊C₉	C₃
hypercenter	C₃²⋊C₉	C₃₇⋊C₃
hypocenter	C₃₇	#6894
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
3. #15688506	C₃	semidirect
4. #15688504	C₃	semidirect
5. #15688504	C₃	semidirect
27. #66524	3₋¹⁺²	semidirect
41. C₃₇	#6894	semidirect