Subgroups — #22582595

Order 8991.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11758606	C₃	1	1	yes	maximal, characteristic
2	#15688506	C₃	1	2	yes	maximal, complemented
3	#15688504	C₃	1	6	yes	maximal, complemented
4	#15688502	C₃	1	3	yes	maximal
5	C₉²×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
7	C₃×C₉×C₃₇	C₃²	1	3	yes	—
8	C₃×C₉×C₃₇	C₃²	1	1	yes	characteristic
9	C₃×#66524	C₃²	1	6	yes	—
10	C₃×#66524	C₃²	1	2	yes	—
11	#11758606	—	3	3	no	—
12	C₃²×C₃₇	C₃³	1	1	yes	characteristic
13	C₃×C₃₇⋊C₃	—	3	1	no	—
14	C₃×C₃₇⋊C₃	—	3	3	no	—
15	C₉×C₃₇	—	3	3	no	—
16	C₉×C₃₇	3₋¹⁺²	1	3	yes	—
17	#66524	—	3	2	no	—
18	#66524	—	3	6	no	—
19	#6899	—	37	1	no	maximal, Sylow
20	C₃×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
21	C₃×C₃₇	#737	1	3	yes	—
22	C₃₇⋊C₃	—	9	1	no	—
23	C₃×3₋¹⁺²	—	37	1	no	—
24	C₉⋊C₉	—	37	6	no	—
25	C₉⋊C₉	—	37	2	no	—
26	C₃²⋊C₉	—	37	3	no	—
27	C₉²	C₃₇⋊C₃	1	1	yes	characteristic, complemented
28	C₃₇	#6899	1	1	yes	characteristic, complemented, Sylow
29	C₃³	—	37	1	no	—
30	3₋¹⁺²	—	111	3	no	—
31	C₃×C₉	—	37	6	no	—
32	C₃×C₉	—	37	2	no	—
33	C₃×C₉	C₃×C₃₇⋊C₃	1	3	yes	—
34	C₃×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
35	C₃²	—	111	1	no	—
36	C₃²	—	111	3	no	—
37	C₃²	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
38	C₉	—	3	3	no	—
39	C₉	—	111	2	no	—
40	C₉	—	111	6	no	—
41	C₉	#11758606	1	3	yes	—
42	C₃	—	333	1	no	—
43	C₃	C₃×#11758606	1	1	yes	characteristic
44	C₃	#15688531	1	3	yes	—

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