Subgroups — #36379870

Order 22599.

458 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14578886	C₃	1	12	yes	maximal
2	C₃×C₉²×C₃₁	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₃₁⋊C₉	C₃²	1	9	yes	—
4	#14578886	—	3	36	no	—
5	C₃²×C₉×C₃₁	C₃²	1	4	yes	—
6	C₉²×C₃₁	C₉	1	9	yes	complemented
7	C₃³×C₃₁	C₃³	1	1	yes	characteristic
8	C₃×C₉×C₃₁	C₃×C₉	1	12	yes	—
9	C₃×C₉×C₃₁	3₋¹⁺²	1	36	yes	—
10	C₃×C₃₁⋊C₉	—	3	36	no	—
11	#10624554	—	31	1	no	maximal, Sylow
12	C₃²×C₃₁	C₃²×C₉	1	1	yes	characteristic
13	C₃²×C₃₁	C₃×3₋¹⁺²	1	12	yes	—
14	C₉×C₃₁	C₉⋊C₉	1	36	yes	complemented
15	C₃₁⋊C₉	—	9	9	no	—
16	C₃×C₉⋊C₉	—	31	12	no	—
17	C₃×C₉²	C₃₁⋊C₃	1	1	yes	characteristic
18	C₃×C₃₁	C₃×C₉⋊C₉	1	4	yes	—
19	C₃×C₃₁	#6900	1	9	yes	—
20	C₃²×C₉	—	31	9	no	—
21	C₃²×C₉	C₃×C₃₁⋊C₃	1	4	yes	—
22	C₉⋊C₉	—	93	36	no	—
23	C₉²	C₃₁⋊C₉	1	9	yes	complemented
24	C₃₁	#10624554	1	1	yes	characteristic, complemented, Sylow
25	C₃³	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
26	C₃×C₉	—	93	36	no	—
27	C₃×C₉	#11719686	1	36	yes	—
28	C₃×C₉	C₃×C₃₁⋊C₉	1	12	yes	—
29	C₃²	C₃²×C₃₁⋊C₉	1	1	yes	characteristic
30	C₃²	C₃×#11719686	1	12	yes	—
31	C₉	—	279	9	no	—
32	C₉	#14578886	1	36	yes	complemented
33	C₃	C₃×#14578886	1	4	yes	—
34	C₃	#21419360	1	9	yes	—

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.