Subgroups — D₉×Dic₉ #10619527

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	1	yes	maximal, characteristic
2	C₉⋊Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×Dic₉	—	3	1	no	maximal
5	Dic₃×D₉	—	3	1	no	maximal
6	C₂×C₉²	C₂²	1	1	yes	characteristic
7	C₉×D₉	C₄	1	2	yes	complemented
8	C₂×D₃×C₉	—	3	1	no	—
9	C₂×C₃×D₉	D₃	1	1	yes	characteristic
10	C₃⋊Dic₉	—	3	1	no	—
11	C₃⋊Dic₉	—	3	1	no	—
12	C₃⋊Dic₉	—	6	1	no	—
13	C₉×Dic₃	—	3	1	no	—
14	C₃×Dic₉	D₃	1	1	yes	characteristic
15	C₉²	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
16	D₃×Dic₃	—	9	1	no	—
17	C₂×Dic₉	—	9	1	no	—
18	C₄×D₉	—	9	1	no	—
19	C₂×C₃×C₉	—	2	1	no	—
20	C₂×C₃×C₉	C₂×D₃	1	1	yes	characteristic
21	C₂×C₃×C₉	C₂×D₃	1	1	yes	characteristic
22	D₃×C₉	—	3	2	no	—
23	C₃×D₉	Dic₃	1	2	yes	—
24	C₂×C₃×D₃	—	3	1	no	—
25	C₃⋊Dic₃	—	9	1	no	—
26	C₃×Dic₃	—	3	1	no	—
27	C₂²×C₉	—	9	1	no	—
28	C₂×D₉	D₉	1	1	yes	characteristic
29	C₄×C₉	—	9	1	no	—
30	Dic₉	—	9	1	no	—
31	Dic₉	—	9	1	no	—
32	Dic₉	—	18	1	no	—
33	Dic₉	—	18	1	no	—
34	Dic₉	—	18	3	no	—
35	Dic₉	D₉	1	1	yes	characteristic, direct product factor
36	C₃×C₉	—	2	1	no	—
37	C₃×C₉	C₄×D₃	1	1	yes	characteristic
38	C₃×C₉	C₂×Dic₃	1	1	yes	characteristic
39	C₂×Dic₃	—	27	1	no	—
40	C₄×D₃	—	27	1	no	—
41	C₂×C₃²	D₃²	1	1	yes	characteristic
42	C₃×D₃	—	3	2	no	—
43	C₂×C₉	—	2	3	no	—
44	C₂×C₉	—	2	1	no	—
45	C₂×C₉	—	2	1	no	—
46	C₂×C₉	—	9	2	no	—
47	C₂×C₉	C₂×D₉	1	1	yes	characteristic
48	C₂×C₉	C₂×D₉	1	1	yes	characteristic
49	D₉	Dic₉	1	2	yes	direct product factor
50	C₂²×C₃	—	9	1	no	—
51	C₂×D₃	—	3	1	no	—
52	C₃×C₄	—	9	1	no	—
53	Dic₃	—	3	1	no	—
54	Dic₃	—	27	1	no	—
55	Dic₃	—	27	1	no	—
56	Dic₃	—	54	1	no	—
57	C₃²	D₃×Dic₃	1	1	yes	characteristic
58	C₉	—	2	3	no	—
59	C₉	—	2	1	no	—
60	C₉	—	2	1	no	—
61	C₉	C₄×D₉	1	1	yes	characteristic, complemented
62	C₉	C₂×Dic₉	1	1	yes	characteristic, complemented
63	C₂×C₄	—	81	1	no	Sylow
64	C₂×C₃	—	2	1	no	—
65	C₂×C₃	—	9	2	no	—
66	C₂×C₃	D₃×D₉	1	1	yes	characteristic
67	C₂×C₃	D₃×D₉	1	1	yes	characteristic
68	D₃	—	3	2	no	—
69	C₂²	—	9	1	no	—
70	C₄	—	9	1	no	—
71	C₄	—	81	1	no	—
72	C₃	—	2	1	no	—
73	C₃	Dic₃×D₉	1	1	yes	characteristic
74	C₃	D₃×Dic₉	1	1	yes	characteristic
75	C₂	—	9	2	no	—
76	C₂	D₉²	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₉²
commutator, hypocenter	C₉²	C₂×C₄
Frattini, socle	C₂×C₃²	D₃²
Fitting, cosocle	C₂×C₉²	C₂²
prime radical	C₂×C₃×D₉	D₃
LCS	G ▷ C₉²
UCS	C₁ ◁ C₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₉⋊Dic₉	C₂	semidirect
3. C₉×Dic₉	C₂	semidirect
7. C₉×D₉	C₄	semidirect
15. C₉²	C₂×C₄	semidirect
35. Dic₉	D₉	direct (N × H)
49. D₉	Dic₉	direct (N × H)
61. C₉	C₄×D₉	semidirect
62. C₉	C₂×Dic₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₉×D₉	2
C₉⋊Dic₉	2
C₉×Dic₉	2
D₃×Dic₉	3
Dic₃×D₉	3

Subgroups — D9×Dic9 #10619527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×Dic₉ #10619527