Subgroups — #22582567

Order 8991.

124 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×C₉×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#15688506	C₃	1	1	yes	maximal, characteristic, complemented
4	#15688505	C₃	1	1	yes	maximal, characteristic, complemented
5	#15688505	C₃	1	2	yes	maximal, complemented
6	#15688504	C₃	1	2	yes	maximal, complemented
7	#15688504	C₃	1	2	yes	maximal, complemented
8	#15688502	C₃	1	2	yes	maximal
9	C₃₇×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
10	C₃²×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
11	C₃×C₉×C₃₇	C₃²	1	2	yes	—
12	C₃×C₉×C₃₇	C₃²	1	1	yes	characteristic
13	C₃×C₉×C₃₇	C₃²	1	1	yes	characteristic
14	C₃×#66524	C₃²	1	2	yes	—
15	C₃×#66524	C₃²	1	2	yes	—
16	C₃×#66524	C₃²	1	2	yes	—
17	C₃×#66524	C₃²	1	1	yes	characteristic
18	C₃×#66524	C₃²	1	1	yes	characteristic
19	#11758605	—	3	3	no	—
20	C₉×C₃₇⋊C₃	—	3	3	no	—
21	C₃²×C₃₇	C₃³	1	1	yes	characteristic
22	C₃×C₃₇⋊C₃	—	3	1	no	—
23	C₃×C₃₇⋊C₃	—	3	2	no	—
24	C₃×C₃₇⋊C₃	3₋¹⁺²	1	3	yes	—
25	C₉×C₃₇	—	3	1	no	—
26	C₉×C₃₇	—	3	2	no	—
27	C₉×C₃₇	3₋¹⁺²	1	3	yes	complemented
28	#66524	—	3	2	no	—
29	#66524	—	3	1	no	—
30	#66524	—	3	1	no	—
31	#66524	—	3	2	no	—
32	#66524	—	3	2	no	—
33	#6894	—	37	1	no	maximal, Sylow
34	C₃×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
35	C₃×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
36	C₃×C₃₇	#737	1	2	yes	—
37	C₃₇⋊C₃	—	3	3	no	—
38	C₃×3₋¹⁺²	—	37	1	no	—
39	C₃²×C₉	—	37	1	no	—
40	C₉⋊C₉	—	37	2	no	—
41	C₉⋊C₉	—	37	2	no	—
42	C₉⋊C₉	—	37	1	no	—
43	C₉⋊C₉	—	37	2	no	—
44	C₉⋊C₉	—	37	1	no	—
45	C₉⋊C₉	C₃₇⋊C₃	1	1	yes	characteristic, complemented
46	C₃²⋊C₉	—	37	2	no	—
47	C₃₇	#6894	1	1	yes	characteristic, complemented, Sylow
48	C₃³	—	37	1	no	—
49	3₋¹⁺²	—	111	3	no	—
50	C₃×C₉	—	37	2	no	—
51	C₃×C₉	—	37	2	no	—
52	C₃×C₉	—	37	2	no	—
53	C₃×C₉	—	37	1	no	—
54	C₃×C₉	—	37	1	no	—
55	C₃×C₉	—	111	3	no	—
56	C₃×C₉	C₃×C₃₇⋊C₃	1	2	yes	—
57	C₃×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
58	C₃×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
59	C₃²	—	37	3	no	—
60	C₃²	—	111	1	no	—
61	C₃²	—	111	2	no	—
62	C₃²	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
63	C₉	—	3	1	no	—
64	C₉	—	3	2	no	—
65	C₉	—	111	1	no	—
66	C₉	—	111	1	no	—
67	C₉	—	111	2	no	—
68	C₉	—	111	2	no	—
69	C₉	—	111	2	no	—
70	C₉	#11758605	1	3	yes	complemented
71	C₃	—	111	3	no	—
72	C₃	3₋¹⁺²×C₃₇⋊C₃	1	1	yes	characteristic
73	C₃	C₃×#11758605	1	1	yes	characteristic
74	C₃	#15688532	1	2	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	#6894
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
3. #15688506	C₃	semidirect
4. #15688505	C₃	semidirect
5. #15688505	C₃	semidirect
6. #15688504	C₃	semidirect
7. #15688504	C₃	semidirect
9. C₃₇×C₉⋊C₉	C₃	semidirect
27. C₉×C₃₇	3₋¹⁺²	semidirect
45. C₉⋊C₉	C₃₇⋊C₃	semidirect
47. C₃₇	#6894	semidirect
70. C₉	#11758605	semidirect