Subgroups — D₉×Dic₆ #88633

Order 432.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6226	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×D₉	C₂	1	1	yes	maximal, characteristic
3	C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₃×D₉	C₂	1	2	yes	maximal
5	#6189	C₂	1	2	yes	maximal, complemented
6	D₃×Dic₆	—	3	1	no	maximal
7	Q₈×D₉	—	3	1	no	maximal
8	C₂×C₃×D₉	C₂²	1	1	yes	characteristic
9	C₃×C₄×C₉	C₂²	1	1	yes	characteristic
10	C₃⋊Dic₉	C₂²	1	2	yes	—
11	C₉×Dic₃	C₂²	1	2	yes	—
12	C₃×Dic₉	C₂²	1	1	yes	characteristic
13	#634	—	3	1	no	—
14	C₃×C₄×D₃	—	3	1	no	—
15	C₃×Dic₆	D₃	1	1	yes	characteristic
16	#627	—	3	2	no	—
17	D₃×Dic₃	—	3	2	no	—
18	Q₈×C₉	—	3	1	no	—
19	C₄×D₉	—	3	2	no	—
20	C₄×D₉	D₃	1	1	yes	characteristic
21	Dic₁₈	—	3	1	no	—
22	Dic₁₈	—	3	2	no	—
23	Dic₁₈	—	6	1	no	—
24	C₂×C₃×C₉	C₂³	1	1	yes	characteristic
25	C₃×D₉	Q₈	1	2	yes	complemented
26	D₃×Q₈	—	9	1	no	—
27	C₂×Dic₆	—	9	1	no	—
28	C₂×C₃×D₃	—	3	1	no	—
29	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
30	C₃⋊Dic₃	—	3	2	no	—
31	C₃×Dic₃	—	3	1	no	—
32	C₃×Dic₃	C₂×D₃	1	2	yes	—
33	C₂×D₉	C₂×D₃	1	1	yes	characteristic
34	C₄×C₉	—	2	1	no	—
35	C₄×C₉	—	3	2	no	—
36	C₄×C₉	C₂×D₃	1	1	yes	characteristic
37	Dic₉	—	3	2	no	—
38	Dic₉	—	6	2	no	—
39	Dic₉	C₂×D₃	1	1	yes	characteristic
40	C₃×C₉	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
41	C₃×Q₈	—	3	1	no	—
42	C₂×C₃×C₄	—	9	1	no	—
43	C₂×Dic₃	—	9	2	no	—
44	C₄×D₃	—	3	1	no	—
45	C₄×D₃	—	9	2	no	—
46	Dic₆	—	9	2	no	—
47	Dic₆	—	9	1	no	—
48	Dic₆	—	9	1	no	—
49	Dic₆	—	9	2	no	—
50	Dic₆	—	18	1	no	—
51	Dic₆	D₉	1	1	yes	characteristic, direct product factor
52	C₂×C₃²	C₂²×D₃	1	1	yes	characteristic
53	C₃×D₃	—	3	2	no	—
54	C₂×C₉	—	2	1	no	—
55	C₂×C₉	C₂²×D₃	1	1	yes	characteristic
56	D₉	Dic₆	1	2	yes	direct product factor
57	C₂×Q₈	—	27	1	no	Sylow
58	C₂²×C₃	—	9	1	no	—
59	C₂×D₃	—	3	1	no	—
60	C₃×C₄	—	2	1	no	—
61	C₃×C₄	—	3	2	no	—
62	C₃×C₄	—	9	1	no	—
63	C₃×C₄	C₂×D₉	1	1	yes	characteristic
64	C₃×C₄	D₃²	1	1	yes	characteristic
65	Dic₃	—	3	1	no	—
66	Dic₃	—	9	2	no	—
67	Dic₃	—	9	2	no	—
68	Dic₃	—	18	2	no	—
69	Dic₃	C₂×D₉	1	2	yes	—
70	C₃²	D₃×Q₈	1	1	yes	characteristic
71	C₉	—	2	1	no	—
72	C₉	C₂×Dic₆	1	1	yes	characteristic, complemented
73	Q₈	—	3	1	no	—
74	Q₈	—	27	2	no	—
75	Q₈	—	27	1	no	—
76	C₂×C₄	—	9	1	no	—
77	C₂×C₄	—	27	2	no	—
78	C₂×C₃	—	2	1	no	—
79	C₂×C₃	—	9	2	no	—
80	C₂×C₃	C₂²×D₉	1	1	yes	characteristic
81	C₂×C₃	C₂×D₃²	1	1	yes	characteristic
82	D₃	—	3	2	no	—
83	C₂²	—	9	1	no	—
84	C₄	—	3	2	no	—
85	C₄	—	9	1	no	—
86	C₄	—	27	2	no	—
87	C₄	D₃×D₉	1	1	yes	characteristic
88	C₃	—	2	1	no	—
89	C₃	Q₈×D₉	1	1	yes	characteristic, complemented
90	C₃	D₃×Dic₆	1	1	yes	characteristic
91	C₂	—	9	2	no	—
92	C₂	C₂×D₃×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₃×D₉
commutator, cosocle	C₂×C₃×C₉	C₂³
Frattini	C₂×C₃	C₂×D₃²
Fitting	C₃×C₄×C₉	C₂²
socle	C₂×C₃²	C₂²×D₃
prime radical	C₂×C₃×D₉	C₂²
hypercenter	C₄	D₃×D₉
hypocenter	C₃×C₉	C₂×Q₈
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. #6226	C₂	semidirect
3. C₉×Dic₆	C₂	semidirect
5. #6189	C₂	semidirect
25. C₃×D₉	Q₈	semidirect
40. C₃×C₉	C₂×Q₈	semidirect
51. Dic₆	D₉	direct (N × H)
56. D₉	Dic₆	direct (N × H)
72. C₉	C₂×Dic₆	semidirect
89. C₃	Q₈×D₉	semidirect

Maximal subgroups

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

subgroup	index
#6226	2
C₃×C₄×D₉	2
C₉×Dic₆	2
Dic₃×D₉	2
#6189	2
D₃×Dic₆	3
Q₈×D₉	3

Subgroups — D9×Dic6 #88633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×Dic₆ #88633