Subgroups — #41008451

Order 26973.

458 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688537	C₃	1	12	yes	maximal
2	C₉²×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₃²×#66526	C₃²	1	9	yes	—
4	#15688537	—	3	36	no	—
5	C₃×C₉×C₃₇⋊C₃	C₃²	1	4	yes	—
6	C₉×#66524	C₉	1	8	yes	complemented
7	C₉²×C₃₇	C₉	1	1	yes	characteristic, complemented
8	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
9	C₃×#66526	—	3	36	no	—
10	C₃×C₉×C₃₇	C₃×C₉	1	4	yes	—
11	C₃×#66524	C₃×C₉	1	8	yes	—
12	C₉×C₃₇⋊C₃	3₋¹⁺²	1	36	yes	—
13	#10624554	—	37	1	no	maximal, Sylow
14	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
15	C₃×C₃₇⋊C₃	C₃×3₋¹⁺²	1	12	yes	—
16	#66526	—	9	9	no	—
17	C₉×C₃₇	C₉⋊C₉	1	12	yes	complemented
18	#66524	C₉⋊C₉	1	24	yes	complemented
19	C₃×C₉⋊C₉	—	37	12	no	—
20	C₃×C₉²	—	37	1	no	—
21	C₃×C₃₇	C₃×C₉⋊C₉	1	4	yes	—
22	C₃₇⋊C₃	#6900	1	9	yes	—
23	C₃²×C₉	—	37	4	no	—
24	C₃²×C₉	—	37	9	no	—
25	C₉⋊C₉	—	111	36	no	—
26	C₉²	—	37	8	no	—
27	C₉²	#66526	1	1	yes	characteristic, complemented
28	C₃₇	#10624554	1	1	yes	characteristic, complemented, Sylow
29	C₃³	—	37	1	no	—
30	C₃×C₉	—	37	8	no	—
31	C₃×C₉	—	37	36	no	—
32	C₃×C₉	—	111	36	no	—
33	C₃×C₉	C₃×#66526	1	4	yes	—
34	C₃²	—	37	12	no	—
35	C₃²	C₃²×#66526	1	1	yes	characteristic
36	C₉	—	37	24	no	—
37	C₉	—	333	9	no	—
38	C₉	#15688537	1	12	yes	complemented
39	C₃	—	37	9	no	—
40	C₃	C₃×#15688537	1	4	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.