Subgroups — #41008448

Order 26973.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₃×#66526)⋊C₉	C₃	1	12	yes	maximal
2	C₉²×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₃²×#66526	C₃²	1	9	yes	—
4	C₃×C₉×C₃₇⋊C₃	C₃²	1	4	yes	—
5	C₉×#66524	C₉	1	8	yes	complemented
6	C₉²×C₃₇	C₉	1	1	yes	characteristic, complemented
7	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
8	C₃×#66526	—	3	36	no	—
9	C₃×C₉×C₃₇	C₃×C₉	1	4	yes	—
10	C₃×#66524	C₃×C₉	1	8	yes	—
11	C₉×C₃₇⋊C₃	—	3	12	no	—
12	#10624552	—	37	1	no	maximal, Sylow
13	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
14	C₃×C₃₇⋊C₃	#737	1	12	yes	—
15	#66526	—	9	9	no	—
16	C₉×C₃₇	—	3	4	no	—
17	#66524	—	3	8	no	—
18	C₃×C₉²	—	37	1	no	—
19	#6855	—	37	12	no	—
20	C₃×C₃₇	#6887	1	4	yes	—
21	C₃₇⋊C₃	#6898	1	9	yes	—
22	C₃²×C₉	—	37	4	no	—
23	C₃²×C₉	—	37	9	no	—
24	C₉²	—	37	8	no	—
25	C₉²	#66526	1	1	yes	characteristic, complemented
26	C₃₇	#10624552	1	1	yes	characteristic, complemented, Sylow
27	C₃³	—	37	1	no	—
28	C₃×C₉	—	37	8	no	—
29	C₃×C₉	—	111	12	no	—
30	C₃×C₉	—	111	36	no	—
31	C₃×C₉	C₃×#66526	1	4	yes	—
32	C₃²	—	37	12	no	—
33	C₃²	C₃²×#66526	1	1	yes	characteristic
34	C₉	—	3	4	no	—
35	C₉	—	333	9	no	—
36	C₉	—	111	8	no	—
37	C₃	—	37	9	no	—
38	C₃	#22582722	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.