Subgroups — C₃×C₄×Dic₉ #88481

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×C₃×Dic₉	C₂	1	2	yes	maximal
3	C₃×C₄×Dic₃	—	3	1	no	maximal
4	C₄×Dic₉	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂²×C₃×C₉	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₉	C₄	1	2	yes	complemented
7	C₃×Dic₉	C₄	1	4	yes	direct product factor
8	C₂×C₃²×C₄	D₃	1	1	yes	characteristic
9	C₂×C₃×Dic₃	—	3	2	no	—
10	C₂×C₄×C₉	—	2	1	no	—
11	C₂×C₄×C₉	C₂×C₃	1	1	yes	characteristic
12	C₂×Dic₉	C₂×C₃	1	2	yes	—
13	C₂×C₃×C₉	C₂×C₄	1	2	yes	—
14	C₂×C₃×C₉	C₂×C₄	1	1	yes	characteristic
15	C₃×C₄²	—	9	1	no	—
16	C₄×Dic₃	—	3	1	no	—
17	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
18	C₃²×C₄	Dic₃	1	2	yes	—
19	C₃×Dic₃	—	3	4	no	—
20	C₂²×C₉	—	2	1	no	—
21	C₂²×C₉	C₂²×C₃	1	1	yes	characteristic
22	C₄×C₉	—	2	2	no	—
23	C₄×C₉	C₃×C₄	1	2	yes	complemented
24	Dic₉	C₃×C₄	1	4	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	—	9	2	no	—
28	C₂×C₃×C₄	D₉	1	1	yes	characteristic
29	C₂×C₃×C₄	C₃×D₃	1	1	yes	characteristic
30	C₂×Dic₃	—	3	2	no	—
31	C₂×C₃²	C₄×D₃	1	2	yes	—
32	C₂×C₃²	C₂×Dic₃	1	1	yes	characteristic
33	C₂×C₉	—	2	2	no	—
34	C₂×C₉	—	2	1	no	—
35	C₂×C₉	C₂×C₃×C₄	1	2	yes	—
36	C₂×C₉	C₂×C₃×C₄	1	1	yes	characteristic
37	C₄²	—	9	1	no	Sylow
38	C₂²×C₃	—	2	1	no	—
39	C₂²×C₃	C₂×D₉	1	1	yes	characteristic
40	C₂²×C₃	C₂×C₃×D₃	1	1	yes	characteristic
41	C₃×C₄	—	2	2	no	—
42	C₃×C₄	—	9	4	no	—
43	C₃×C₄	Dic₉	1	2	yes	direct product factor
44	C₃×C₄	C₃×Dic₃	1	2	yes	—
45	Dic₃	—	3	4	no	—
46	C₃²	C₄×Dic₃	1	1	yes	characteristic
47	C₉	—	2	1	no	—
48	C₉	C₃×C₄²	1	1	yes	characteristic, complemented
49	C₂×C₄	—	9	2	no	—
50	C₂×C₄	C₃×D₉	1	1	yes	characteristic
51	C₂×C₃	—	2	2	no	—
52	C₂×C₃	—	2	1	no	—
53	C₂×C₃	C₄×D₉	1	2	yes	—
54	C₂×C₃	C₂×Dic₉	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×C₃×D₉	1	1	yes	characteristic
58	C₄	—	9	4	no	—
59	C₄	C₃×Dic₉	1	2	yes	direct product factor
60	C₃	—	2	1	no	—
61	C₃	C₄×Dic₉	1	1	yes	characteristic, direct product factor
62	C₃	C₃×C₄×Dic₃	1	1	yes	characteristic
63	C₂	C₃×C₄×D₉	1	2	yes	—
64	C₂	C₂×C₃×Dic₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄	D₉
commutator, hypocenter	C₉	C₃×C₄²
Frattini	C₂²×C₃	C₂×C₃×D₃
Fitting	C₂×C₃×C₄×C₉	C₂
socle, prime radical	C₂²×C₃²	C₂×D₃
cosocle	C₂²×C₉	C₂²×C₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₃×C₄

Complements

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

N	H ≅ G/N	type
4. C₄×Dic₉	C₃	direct (N × H)
6. C₃×C₄×C₉	C₄	semidirect
7. C₃×Dic₉	C₄	direct (N × H)
23. C₄×C₉	C₃×C₄	semidirect
24. Dic₉	C₃×C₄	direct (N × H)
25. C₃×C₉	C₄²	semidirect
43. C₃×C₄	Dic₉	direct (N × H)
48. C₉	C₃×C₄²	semidirect
59. C₄	C₃×Dic₉	direct (N × H)
61. C₃	C₄×Dic₉	direct (N × H)

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×C₃×Dic₉	2
C₃×C₄×Dic₃	3
C₄×Dic₉	3

Subgroups — C3×C4×Dic9 #88481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×Dic₉ #88481