Subgroups — #22582602

Order 8991.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11758605	C₃	1	4	yes	maximal
2	#15688505	C₃	1	8	yes	maximal, complemented
3	C₉²×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
5	C₃×C₉×C₃₇	C₃²	1	4	yes	—
6	C₃×#66524	C₃²	1	8	yes	—
7	#11758605	—	3	12	no	—
8	C₃²×C₃₇	C₃³	1	1	yes	characteristic
9	C₃×C₃₇⋊C₃	—	3	4	no	—
10	C₉×C₃₇	3₋¹⁺²	1	12	yes	complemented
11	#66524	—	3	8	no	—
12	#6900	—	37	1	no	maximal, Sylow
13	C₃×C₃₇	C₃×3₋¹⁺²	1	4	yes	—
14	C₃₇⋊C₃	—	9	1	no	—
15	C₃×3₋¹⁺²	—	37	4	no	—
16	C₉⋊C₉	—	37	8	no	—
17	C₉²	C₃₇⋊C₃	1	1	yes	characteristic, complemented
18	C₃₇	#6900	1	1	yes	characteristic, complemented, Sylow
19	C₃³	—	37	1	no	—
20	3₋¹⁺²	—	111	12	no	—
21	C₃×C₉	—	37	8	no	—
22	C₃×C₉	C₃×C₃₇⋊C₃	1	4	yes	—
23	C₃²	—	111	4	no	—
24	C₃²	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
25	C₉	—	111	8	no	—
26	C₉	#11758605	1	12	yes	complemented
27	C₃	—	333	1	no	—
28	C₃	C₃×#11758605	1	4	yes	—

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