Subgroups — D₉×3₋¹⁺² #92256

Order 486.

73 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	D₃×3₋¹⁺²	—	3	1	no	maximal
3	C₃²×D₉	C₃	1	1	yes	maximal, characteristic
4	C₉×D₉	C₃	1	3	yes	maximal, complemented
5	C₃×3₋¹⁺²	D₃	1	1	yes	characteristic
6	C₃²×C₉	C₂×C₃	1	1	yes	characteristic
7	C₉⋊C₉	—	2	3	no	—
8	C₃²⋊C₉	—	2	1	no	—
9	C₉²	C₂×C₃	1	3	yes	complemented
10	C₃²×D₃	—	3	1	no	—
11	C₂×3₋¹⁺²	—	9	1	no	—
12	D₃×C₉	—	3	3	no	—
13	C₃×D₉	—	3	1	no	—
14	C₃×D₉	C₃²	1	1	yes	characteristic
15	C₃³	C₃×D₃	1	1	yes	characteristic
16	3₋¹⁺²	—	2	1	no	—
17	3₋¹⁺²	—	2	3	no	—
18	3₋¹⁺²	D₉	1	1	yes	characteristic, direct product factor
19	C₃×C₉	—	2	3	no	—
20	C₃×C₉	—	2	1	no	—
21	C₃×C₉	—	3	1	no	—
22	C₃×C₉	—	6	1	no	—
23	C₃×C₉	C₃×D₃	1	3	yes	—
24	C₃×C₉	C₂×C₃²	1	1	yes	characteristic
25	C₂×C₃²	—	9	1	no	—
26	C₃×D₃	—	3	1	no	—
27	C₃×D₃	—	9	1	no	—
28	C₂×C₉	—	9	3	no	—
29	D₉	3₋¹⁺²	1	1	yes	characteristic, direct product factor
30	C₃²	—	2	1	no	—
31	C₃²	—	3	1	no	—
32	C₃²	—	6	1	no	—
33	C₃²	C₃×D₉	1	1	yes	characteristic
34	C₃²	C₃²×D₃	1	1	yes	characteristic
35	C₉	—	2	3	no	—
36	C₉	—	2	1	no	—
37	C₉	—	6	3	no	—
38	C₉	—	6	1	no	—
39	C₉	C₃×D₉	1	3	yes	complemented
40	C₉	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
41	C₂×C₃	—	9	1	no	—
42	C₂×C₃	—	27	1	no	—
43	D₃	—	3	1	no	—
44	C₃	—	2	1	no	—
45	C₃	—	3	1	no	—
46	C₃	—	6	1	no	—
47	C₃	C₃²×D₉	1	1	yes	characteristic
48	C₃	D₃×3₋¹⁺²	1	1	yes	characteristic
49	C₂	—	9	1	no	Sylow

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.