Subgroups — #22582576

Order 8991.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#66524	C₃	1	1	yes	maximal, characteristic
2	#15688505	C₃	1	3	yes	maximal, complemented
3	#15688504	C₃	1	6	yes	maximal, complemented
4	C₃²⋊#66524	C₃	1	2	yes	maximal
5	C₃₇×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
6	C₃³×C₃₇	C₃²	1	1	yes	characteristic
7	C₃×C₉×C₃₇	C₃²	1	3	yes	—
8	C₃×#66524	—	3	3	no	—
9	C₃×#66524	C₃²	1	6	yes	—
10	C₃×#66524	C₃²	1	2	yes	—
11	C₃×#66524	C₃²	1	1	yes	characteristic
12	C₃²×C₃₇	—	3	1	no	—
13	C₃²×C₃₇	—	3	2	no	—
14	C₃²×C₃₇	3₋¹⁺²	1	3	yes	—
15	C₃²×C₃₇	C₃³	1	1	yes	characteristic
16	C₉×C₃₇	—	3	3	no	—
17	#66524	—	3	2	no	—
18	#66524	—	3	1	no	—
19	#66524	—	3	6	no	—
20	#6895	—	37	1	no	maximal, Sylow
21	C₃×C₃₇	—	3	3	no	—
22	C₃×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
23	C₃×C₃₇	#737	1	1	yes	characteristic
24	C₃×C₃₇	#737	1	2	yes	—
25	C₃²×C₉	—	37	1	no	—
26	C₉⋊C₉	—	37	6	no	—
27	C₉⋊C₉	—	37	3	no	—
28	C₃²⋊C₉	—	37	2	no	—
29	C₃²⋊C₉	C₃₇⋊C₃	1	1	yes	characteristic
30	C₃₇	#6895	1	1	yes	characteristic, complemented, Sylow
31	C₃³	C₃×C₃₇⋊C₃	1	1	yes	characteristic
32	C₃×C₉	—	37	6	no	—
33	C₃×C₉	—	37	2	no	—
34	C₃×C₉	—	37	1	no	—
35	C₃×C₉	—	111	3	no	—
36	C₃×C₉	C₃×C₃₇⋊C₃	1	3	yes	—
37	C₃²	—	3	1	no	—
38	C₃²	—	3	2	no	—
39	C₃²	#11758605	1	3	yes	—
40	C₃²	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
41	C₉	—	3	3	no	—
42	C₉	—	111	2	no	—
43	C₉	—	111	1	no	—
44	C₉	—	111	6	no	—
45	C₃	—	3	3	no	—
46	C₃	C₃×#11758605	1	1	yes	characteristic
47	C₃	#15688530	1	1	yes	characteristic
48	C₃	#15688532	1	2	yes	—

	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	#6895
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
2. #15688505	C₃	semidirect
3. #15688504	C₃	semidirect
30. C₃₇	#6895	semidirect