Subgroups — C₂²×C₉×Dic₃ #88726

Order 432.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×Dic₃	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃×Dic₃	C₃	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₉	—	3	1	no	maximal
5	C₂²×C₃×C₉	C₄	1	4	yes	complemented
6	C₂²×C₃×C₉	C₂²	1	3	yes	—
7	C₉×Dic₃	C₂²	1	4	yes	direct product factor
8	C₂³×C₃²	C₂×C₃	1	1	yes	characteristic
9	C₂×C₃×Dic₃	C₂×C₃	1	6	yes	—
10	C₂³×C₉	—	2	1	no	—
11	C₂³×C₉	D₃	1	1	yes	characteristic
12	C₂×C₄×C₉	—	3	6	no	—
13	C₂×C₃×C₉	C₂×C₄	1	6	yes	complemented
14	C₂×C₃×C₉	C₂³	1	1	yes	characteristic
15	C₂²×C₃×C₄	—	3	1	no	—
16	C₂²×Dic₃	C₉	1	1	yes	characteristic, direct product factor
17	C₂²×C₃²	C₃×C₄	1	4	yes	—
18	C₂²×C₃²	C₂²×C₃	1	3	yes	—
19	C₃×Dic₃	C₂²×C₃	1	4	yes	—
20	C₂²×C₉	—	2	4	no	—
21	C₂²×C₉	—	2	3	no	—
22	C₂²×C₉	Dic₃	1	4	yes	direct product factor
23	C₂²×C₉	C₂×D₃	1	3	yes	—
24	C₄×C₉	—	3	4	no	—
25	C₃×C₉	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
26	C₂³×C₃	—	2	1	no	—
27	C₂³×C₃	C₂×C₉	1	1	yes	characteristic
28	C₂³×C₃	C₃×D₃	1	1	yes	characteristic
29	C₂×C₃×C₄	—	3	6	no	—
30	C₂×Dic₃	C₂×C₉	1	6	yes	direct product factor
31	C₂×C₃²	C₂×C₃×C₄	1	6	yes	—
32	C₂×C₃²	C₂³×C₃	1	1	yes	characteristic
33	C₂×C₉	—	2	6	no	—
34	C₂×C₉	—	2	1	no	—
35	C₂×C₉	C₂×Dic₃	1	6	yes	direct product factor
36	C₂×C₉	C₂²×D₃	1	1	yes	characteristic
37	C₂²×C₄	—	3	1	no	Sylow
38	C₂²×C₃	—	2	4	no	—
39	C₂²×C₃	—	2	3	no	—
40	C₂²×C₃	C₄×C₉	1	4	yes	complemented
41	C₂²×C₃	C₂²×C₉	1	3	yes	—
42	C₂²×C₃	C₃×Dic₃	1	4	yes	—
43	C₂²×C₃	C₂×C₃×D₃	1	3	yes	—
44	C₃×C₄	—	3	4	no	—
45	Dic₃	C₂²×C₉	1	4	yes	direct product factor
46	C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
47	C₉	—	2	1	no	—
48	C₉	C₂²×Dic₃	1	1	yes	characteristic, direct product factor
49	C₂³	D₃×C₉	1	1	yes	characteristic
50	C₂×C₄	—	3	6	no	—
51	C₂×C₃	—	2	6	no	—
52	C₂×C₃	—	2	1	no	—
53	C₂×C₃	C₂×C₄×C₉	1	6	yes	complemented
54	C₂×C₃	C₂³×C₉	1	1	yes	characteristic
55	C₂×C₃	C₂×C₃×Dic₃	1	6	yes	—
56	C₂×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
57	C₂²	C₉×Dic₃	1	4	yes	direct product factor
58	C₂²	C₂×D₃×C₉	1	3	yes	—
59	C₄	—	3	4	no	—
60	C₃	—	2	1	no	—
61	C₃	C₂²×C₄×C₉	1	1	yes	characteristic, complemented
62	C₃	C₂²×C₃×Dic₃	1	1	yes	characteristic
63	C₂	C₂×C₉×Dic₃	1	6	yes	direct product factor
64	C₂	C₂²×D₃×C₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₉×Dic₃	C₂	direct (N × H)
5. C₂²×C₃×C₉	C₄	semidirect
7. C₉×Dic₃	C₂²	direct (N × H)
13. C₂×C₃×C₉	C₂×C₄	semidirect
16. C₂²×Dic₃	C₉	direct (N × H)
22. C₂²×C₉	Dic₃	direct (N × H)
25. C₃×C₉	C₂²×C₄	semidirect
30. C₂×Dic₃	C₂×C₉	direct (N × H)
35. C₂×C₉	C₂×Dic₃	direct (N × H)
40. C₂²×C₃	C₄×C₉	semidirect
45. Dic₃	C₂²×C₉	direct (N × H)
48. C₉	C₂²×Dic₃	direct (N × H)
53. C₂×C₃	C₂×C₄×C₉	semidirect
57. C₂²	C₉×Dic₃	direct (N × H)
61. C₃	C₂²×C₄×C₉	semidirect
63. C₂	C₂×C₉×Dic₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₉	2
C₂×C₉×Dic₃	2
C₂²×C₃×Dic₃	3
C₂²×C₄×C₉	3

Subgroups — C22×C9×Dic3 #88726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₉×Dic₃ #88726