Subgroups — D₃×C₉⋊C₉ #92252

Order 486.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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