Subgroups — C₉²×#66524 #41005083

Order 26973.

890 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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