Subgroups — C₄×C₉×Dic₃ #88484

Order 432.

106 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	C₄²×C₉	—	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	C₄	1	4	yes	direct product factor
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	2	yes	—
14	C₂×C₃×C₉	C₂×C₄	1	1	yes	characteristic
15	C₃×C₄²	—	3	1	no	—
16	C₄×Dic₃	C₉	1	1	yes	characteristic, direct product factor
17	C₂²×C₃²	C₂²×C₃	1	1	yes	characteristic
18	C₃²×C₄	C₃×C₄	1	2	yes	—
19	C₃×Dic₃	C₃×C₄	1	4	yes	—
20	C₂²×C₉	—	2	1	no	—
21	C₂²×C₉	C₂×D₃	1	1	yes	characteristic
22	C₄×C₉	—	2	2	no	—
23	C₄×C₉	—	3	4	no	—
24	C₄×C₉	Dic₃	1	2	yes	direct product factor
25	C₃×C₉	C₄²	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃×C₄	—	2	1	no	—
27	C₂×C₃×C₄	—	3	2	no	—
28	C₂×C₃×C₄	C₂×C₉	1	1	yes	characteristic
29	C₂×C₃×C₄	C₃×D₃	1	1	yes	characteristic
30	C₂×Dic₃	C₂×C₉	1	2	yes	—
31	C₂×C₃²	C₂×C₃×C₄	1	2	yes	—
32	C₂×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
33	C₂×C₉	—	2	2	no	—
34	C₂×C₉	—	2	1	no	—
35	C₂×C₉	C₄×D₃	1	2	yes	—
36	C₂×C₉	C₂×Dic₃	1	1	yes	characteristic
37	C₄²	—	3	1	no	Sylow
38	C₂²×C₃	—	2	1	no	—
39	C₂²×C₃	C₂²×C₉	1	1	yes	characteristic
40	C₂²×C₃	C₂×C₃×D₃	1	1	yes	characteristic
41	C₃×C₄	—	2	2	no	—
42	C₃×C₄	—	3	4	no	—
43	C₃×C₄	C₄×C₉	1	2	yes	complemented
44	C₃×C₄	C₃×Dic₃	1	2	yes	—
45	Dic₃	C₄×C₉	1	4	yes	direct product factor
46	C₃²	C₃×C₄²	1	1	yes	characteristic
47	C₉	—	2	1	no	—
48	C₉	C₄×Dic₃	1	1	yes	characteristic, direct product factor
49	C₂×C₄	—	3	2	no	—
50	C₂×C₄	D₃×C₉	1	1	yes	characteristic
51	C₂×C₃	—	2	2	no	—
52	C₂×C₃	—	2	1	no	—
53	C₂×C₃	C₂×C₄×C₉	1	2	yes	—
54	C₂×C₃	C₂×C₄×C₉	1	1	yes	characteristic
55	C₂×C₃	C₃×C₄×D₃	1	2	yes	—
56	C₂×C₃	C₂×C₃×Dic₃	1	1	yes	characteristic
57	C₂²	C₂×D₃×C₉	1	1	yes	characteristic
58	C₄	—	3	4	no	—
59	C₄	C₉×Dic₃	1	2	yes	direct product factor
60	C₃	—	2	1	no	—
61	C₃	C₄²×C₉	1	1	yes	characteristic, complemented
62	C₃	C₃×C₄×Dic₃	1	1	yes	characteristic
63	C₂	C₄×D₃×C₉	1	2	yes	—
64	C₂	C₂×C₉×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄×C₉	D₃
commutator, hypocenter	C₃	C₄²×C₉
Frattini	C₂²×C₃	C₂×C₃×D₃
Fitting	C₂×C₃×C₄×C₉	C₂
socle, prime radical, cosocle	C₂²×C₃²	C₂²×C₃
LCS	G ▷ C₃
UCS	C₁ ◁ 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
7. C₉×Dic₃	C₄	direct (N × H)
16. C₄×Dic₃	C₉	direct (N × H)
24. C₄×C₉	Dic₃	direct (N × H)
25. C₃×C₉	C₄²	semidirect
43. C₃×C₄	C₄×C₉	semidirect
45. Dic₃	C₄×C₉	direct (N × H)
48. C₉	C₄×Dic₃	direct (N × H)
59. C₄	C₉×Dic₃	direct (N × H)
61. C₃	C₄²×C₉	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
C₄²×C₉	3

Subgroups — C4×C9×Dic3 #88484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×Dic₃ #88484