Subgroups — #10619529

Order 648.

93 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×D₉	C₂	1	2	yes	maximal, complemented
2	C₉⋊Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#6194	—	3	2	no	maximal
4	C₂×C₉²	C₂²	1	1	yes	characteristic
5	C₉×D₉	—	2	2	no	—
6	C₂×D₃×C₉	—	3	2	no	—
7	C₂×C₃×D₉	D₃	1	2	yes	—
8	C₃⋊Dic₉	—	3	2	no	—
9	C₃⋊Dic₉	—	6	1	no	—
10	C₉²	D₄	1	1	yes	characteristic, complemented, Sylow
11	#625	—	9	1	no	—
12	#611	—	9	2	no	—
13	C₂×C₃×C₉	—	2	1	no	—
14	C₂×C₃×C₉	C₂×D₃	1	2	yes	—
15	D₃×C₉	—	6	2	no	—
16	C₃×D₉	—	2	2	no	—
17	C₂×C₃×D₃	—	3	2	no	—
18	C₃⋊Dic₃	—	9	1	no	—
19	C₂²×C₉	—	9	2	no	—
20	C₂×D₉	D₉	1	2	yes	complemented
21	Dic₉	—	9	2	no	—
22	Dic₉	—	18	2	no	—
23	Dic₉	—	18	3	no	—
24	C₃×C₉	—	2	1	no	—
25	C₃×C₉	#67	1	2	yes	—
26	#67	—	27	2	no	—
27	C₂×C₃²	D₃²	1	1	yes	characteristic
28	C₃×D₃	—	6	2	no	—
29	C₂×C₉	—	2	3	no	—
30	C₂×C₉	—	2	2	no	—
31	C₂×C₉	—	18	2	no	—
32	C₂×C₉	C₂×D₉	1	2	yes	—
33	D₉	—	2	2	no	—
34	C₂²×C₃	—	9	2	no	—
35	C₂×D₃	—	3	2	no	—
36	Dic₃	—	27	2	no	—
37	Dic₃	—	54	1	no	—
38	C₃²	#625	1	1	yes	characteristic
39	C₉	—	2	3	no	—
40	C₉	—	2	2	no	—
41	C₉	#611	1	2	yes	complemented
42	D₄	—	81	1	no	Sylow
43	C₂×C₃	—	2	1	no	—
44	C₂×C₃	—	18	2	no	—
45	C₂×C₃	D₃×D₉	1	2	yes	—
46	D₃	—	6	2	no	—
47	C₂²	—	9	2	no	—
48	C₄	—	81	1	no	—
49	C₃	—	2	1	no	—
50	C₃	#6194	1	2	yes	—
51	C₂	—	18	2	no	—
52	C₂	D₉²	1	1	yes	characteristic

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.