Subgroups — C₉×C₄⋊Dic₃ #88486

Order 432.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
6. C₃×C₄×C₉	C₄	semidirect
17. C₄⋊Dic₃	C₉	direct (N × H)
25. C₄×C₉	Dic₃	semidirect
26. C₃×C₉	C₄⋊C₄	semidirect
47. C₃×C₄	C₄×C₉	semidirect
52. C₉	C₄⋊Dic₃	direct (N × H)
66. C₄	C₉×Dic₃	semidirect
68. C₃	C₉×C₄⋊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×C₄×C₉	2
C₂×C₉×Dic₃	2
C₃×C₄⋊Dic₃	3
C₉×C₄⋊C₄	3

Subgroups — C9×C4⋊Dic3 #88486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₄⋊Dic₃ #88486