Subgroups — #41005121

Order 26973.

458 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688506	C₃	1	12	yes	maximal
2	C₃×C₉²×C₃₇	C₃	1	1	yes	maximal, characteristic
3	C₃²×#66524	C₃²	1	9	yes	—
4	#15688506	—	3	36	no	—
5	C₃²×C₉×C₃₇	C₃²	1	4	yes	—
6	C₉²×C₃₇	C₉	1	9	yes	complemented
7	C₃³×C₃₇	C₃³	1	1	yes	characteristic
8	C₃×C₉×C₃₇	C₃×C₉	1	12	yes	—
9	C₃×C₉×C₃₇	3₋¹⁺²	1	36	yes	—
10	C₃×#66524	—	3	36	no	—
11	#10624554	—	37	1	no	maximal, Sylow
12	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
13	C₃²×C₃₇	C₃×3₋¹⁺²	1	12	yes	—
14	C₉×C₃₇	C₉⋊C₉	1	36	yes	complemented
15	#66524	—	9	9	no	—
16	C₃×C₉⋊C₉	—	37	12	no	—
17	C₃×C₉²	C₃₇⋊C₃	1	1	yes	characteristic
18	C₃×C₃₇	C₃×C₉⋊C₉	1	4	yes	—
19	C₃×C₃₇	#6900	1	9	yes	—
20	C₃²×C₉	—	37	9	no	—
21	C₃²×C₉	C₃×C₃₇⋊C₃	1	4	yes	—
22	C₉⋊C₉	—	111	36	no	—
23	C₉²	#66524	1	9	yes	complemented
24	C₃₇	#10624554	1	1	yes	characteristic, complemented, Sylow
25	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
26	C₃×C₉	—	111	36	no	—
27	C₃×C₉	#11758606	1	36	yes	—
28	C₃×C₉	C₃×#66524	1	12	yes	—
29	C₃²	C₃²×#66524	1	1	yes	characteristic
30	C₃²	C₃×#11758606	1	12	yes	—
31	C₉	—	333	9	no	—
32	C₉	#15688506	1	36	yes	complemented
33	C₃	C₃×#15688506	1	4	yes	—
34	C₃	#22582603	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.