Subgroups — C₉²×#66526 #41008433

Order 26973.

890 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#66526	C₃	1	12	yes	maximal
2	C₉²×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₃²×#66526	C₃²	1	9	yes	—
4	C₉×#66526	C₉	1	108	yes	direct product factor
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	C₃×C₉	1	108	yes	—
10	C₃×C₉×C₃₇	C₃×C₉	1	4	yes	—
11	C₃×#66524	C₃×C₉	1	8	yes	—
12	C₉×C₃₇⋊C₃	C₃×C₉	1	36	yes	—
13	C₉³	—	37	1	no	maximal, Sylow
14	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
15	C₃×C₃₇⋊C₃	C₃²×C₉	1	12	yes	—
16	#66526	C₉²	1	81	yes	direct product factor
17	C₉×C₃₇	C₉²	1	12	yes	complemented
18	#66524	C₉²	1	24	yes	complemented
19	C₃×C₉²	—	37	12	no	—
20	C₃×C₉²	—	37	1	no	—
21	C₃×C₃₇	C₃×C₉²	1	4	yes	—
22	C₃₇⋊C₃	C₃×C₉²	1	9	yes	—
23	C₃²×C₉	—	37	9	no	—
24	C₃²×C₉	—	37	4	no	—
25	C₉²	—	37	108	no	—
26	C₉²	—	37	8	no	—
27	C₉²	#66526	1	1	yes	characteristic, direct product factor
28	C₃₇	C₉³	1	1	yes	characteristic, complemented, Sylow
29	C₃³	—	37	1	no	—
30	C₃×C₉	—	37	108	no	—
31	C₃×C₉	—	37	8	no	—
32	C₃×C₉	—	37	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	81	no	—
37	C₉	—	37	24	no	—
38	C₉	C₉×#66526	1	12	yes	direct product factor
39	C₃	—	37	9	no	—
40	C₃	C₃×C₉×#66526	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.