Subgroups — #10619528

Order 648.

107 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉⋊D₉	C₂	1	1	yes	maximal, characteristic
2	C₉×Dic₉	C₂	1	2	yes	maximal, complemented
3	(C₃⋊D₉)⋊C₄	—	3	2	no	maximal
4	C₂×C₉²	C₂²	1	1	yes	characteristic
5	C₉⋊D₉	C₄	1	2	yes	complemented
6	C₂×C₃⋊D₉	—	3	2	no	—
7	C₂×C₃⋊D₉	—	6	1	no	—
8	C₉×Dic₃	—	3	2	no	—
9	C₃×Dic₉	D₃	1	2	yes	—
10	C₉²	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
11	#624	—	9	1	no	—
12	C₄×D₉	—	9	2	no	—
13	C₂×C₃×C₉	—	2	1	no	—
14	C₂×C₃×C₉	C₂×D₃	1	2	yes	—
15	C₃⋊D₉	—	3	4	no	—
16	C₃⋊D₉	—	6	2	no	—
17	C₂×C₃⋊D₃	—	9	1	no	—
18	C₃×Dic₃	—	3	2	no	—
19	C₂×D₉	—	9	2	no	—
20	C₂×D₉	—	18	2	no	—
21	C₂×D₉	—	18	3	no	—
22	C₄×C₉	—	9	2	no	—
23	Dic₉	D₉	1	2	yes	complemented
24	C₃×C₉	—	2	1	no	—
25	C₃×C₉	C₄×D₃	1	2	yes	—
26	C₄×D₃	—	27	2	no	—
27	C₂×C₃²	D₃²	1	1	yes	characteristic
28	C₃⋊D₃	—	9	2	no	—
29	C₂×C₉	—	2	3	no	—
30	C₂×C₉	—	2	2	no	—
31	C₂×C₉	C₂×D₉	1	2	yes	—
32	D₉	—	9	4	no	—
33	D₉	—	18	4	no	—
34	D₉	—	18	6	no	—
35	C₂×D₃	—	27	2	no	—
36	C₂×D₃	—	54	1	no	—
37	C₃×C₄	—	9	2	no	—
38	Dic₃	—	3	2	no	—
39	C₃²	#624	1	1	yes	characteristic
40	C₉	—	2	3	no	—
41	C₉	—	2	2	no	—
42	C₉	C₄×D₉	1	2	yes	complemented
43	C₂×C₄	—	81	1	no	Sylow
44	C₂×C₃	—	2	1	no	—
45	C₂×C₃	D₃×D₉	1	2	yes	—
46	D₃	—	27	4	no	—
47	D₃	—	54	2	no	—
48	C₂²	—	81	1	no	—
49	C₄	—	9	2	no	—
50	C₃	—	2	1	no	—
51	C₃	(C₃⋊D₉)⋊C₄	1	2	yes	—
52	C₂	—	81	2	no	—
53	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.