Subgroups — Dic₉⋊Dic₃ #88441

Order 432.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊Dic₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×Dic₉	C₂	1	1	yes	maximal, characteristic
4	Dic₃⋊Dic₃	—	3	1	no	maximal
5	Dic₉⋊C₄	—	3	1	no	maximal
6	C₂²×C₃×C₉	C₂²	1	1	yes	characteristic
7	C₃⋊Dic₉	—	2	1	no	—
8	C₉×Dic₃	—	2	1	no	—
9	C₃×Dic₉	C₄	1	2	yes	complemented
10	C₂×C₃⋊Dic₃	—	3	1	no	—
11	C₂×C₃×Dic₃	—	3	1	no	—
12	C₂×C₃×Dic₃	D₃	1	1	yes	characteristic
13	C₂×C₄×C₉	—	3	1	no	—
14	C₂×Dic₉	—	3	1	no	—
15	C₂×Dic₉	—	6	1	no	—
16	C₂×Dic₉	D₃	1	1	yes	characteristic
17	C₂×C₃×C₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃×C₉	D₄	1	1	yes	characteristic
19	C₂×C₃×C₉	Q₈	1	1	yes	characteristic
20	C₄⋊Dic₃	—	9	1	no	—
21	Dic₃⋊C₄	—	9	1	no	—
22	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
23	C₃⋊Dic₃	—	6	1	no	—
24	C₃×Dic₃	—	2	1	no	—
25	C₃×Dic₃	—	3	2	no	—
26	C₂²×C₉	—	2	1	no	—
27	C₂²×C₉	C₂×D₃	1	1	yes	characteristic
28	C₄×C₉	—	6	1	no	—
29	Dic₉	—	6	2	no	—
30	Dic₉	—	6	1	no	—
31	Dic₉	Dic₃	1	2	yes	complemented
32	C₃×C₉	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃×C₄	—	3	1	no	—
34	C₂×C₃×C₄	—	9	1	no	—
35	C₂×Dic₃	—	3	1	no	—
36	C₂×Dic₃	—	9	1	no	—
37	C₂×Dic₃	—	9	1	no	—
38	C₂×Dic₃	—	18	1	no	—
39	C₂×Dic₃	D₉	1	1	yes	characteristic
40	C₂×C₃²	Dic₆	1	1	yes	characteristic
41	C₂×C₃²	C₄×D₃	1	1	yes	characteristic
42	C₂×C₃²	#67	1	1	yes	characteristic
43	C₂×C₉	—	2	1	no	—
44	C₂×C₉	—	2	1	no	—
45	C₂×C₉	—	2	1	no	—
46	C₂×C₉	Dic₆	1	1	yes	characteristic
47	C₂×C₉	D₁₂	1	1	yes	characteristic
48	C₂×C₉	C₂×Dic₃	1	1	yes	characteristic
49	C₄⋊C₄	—	27	1	no	Sylow
50	C₂²×C₃	—	2	1	no	—
51	C₂²×C₃	C₂×D₉	1	1	yes	characteristic
52	C₂²×C₃	D₃²	1	1	yes	characteristic
53	C₃×C₄	—	6	1	no	—
54	C₃×C₄	—	9	2	no	—
55	Dic₃	—	2	1	no	—
56	Dic₃	—	3	2	no	—
57	Dic₃	—	18	2	no	—
58	Dic₃	—	18	1	no	—
59	Dic₃	—	18	1	no	—
60	C₃²	Dic₃⋊C₄	1	1	yes	characteristic
61	C₉	—	2	1	no	—
62	C₉	C₄⋊Dic₃	1	1	yes	characteristic, complemented
63	C₂×C₄	—	3	1	no	—
64	C₂×C₄	—	9	1	no	—
65	C₂×C₄	—	27	1	no	—
66	C₂×C₃	—	2	1	no	—
67	C₂×C₃	—	2	1	no	—
68	C₂×C₃	—	2	1	no	—
69	C₂×C₃	Dic₁₈	1	1	yes	characteristic
70	C₂×C₃	C₄×D₉	1	1	yes	characteristic
71	C₂×C₃	#611	1	1	yes	characteristic
72	C₂×C₃	D₃×Dic₃	1	1	yes	characteristic
73	C₂×C₃	#626	1	1	yes	characteristic
74	C₂×C₃	#627	1	1	yes	characteristic
75	C₂²	D₃×D₉	1	1	yes	characteristic
76	C₄	—	6	1	no	—
77	C₄	—	9	2	no	—
78	C₄	—	54	1	no	—
79	C₃	—	2	1	no	—
80	C₃	Dic₉⋊C₄	1	1	yes	characteristic, complemented
81	C₃	Dic₃⋊Dic₃	1	1	yes	characteristic
82	C₂	#6189	1	1	yes	characteristic
83	C₂	Dic₃×D₉	1	1	yes	characteristic
84	C₂	#6195	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃×D₉
commutator	C₂×C₃×C₉	C₂×C₄
Frattini	C₂²×C₃	D₃²
Fitting, cosocle	C₂²×C₃×C₉	C₂²
socle, prime radical	C₂²×C₃²	C₂×D₃
hypocenter	C₃×C₉	C₄⋊C₄
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
9. C₃×Dic₉	C₄	semidirect
31. Dic₉	Dic₃	semidirect
32. C₃×C₉	C₄⋊C₄	semidirect
62. C₉	C₄⋊Dic₃	semidirect
80. C₃	Dic₉⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊Dic₉	2
C₂×C₉×Dic₃	2
C₂×C₃×Dic₉	2
Dic₃⋊Dic₃	3
Dic₉⋊C₄	3

Subgroups — Dic9⋊Dic3 #88441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₉⋊Dic₃ #88441