Subgroups — C₃²×C₄×Dic₃ #88824

Order 432.

244 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×Dic₃	C₂	1	2	yes	maximal
3	C₃²×C₄²	—	3	1	no	maximal
4	C₃×C₄×Dic₃	C₃	1	4	yes	maximal, direct product factor
5	C₂²×C₃³	C₂²	1	1	yes	characteristic
6	C₃³×C₄	C₄	1	2	yes	complemented
7	C₃²×Dic₃	C₄	1	4	yes	direct product factor
8	C₂×C₃²×C₄	—	2	4	no	—
9	C₂×C₃²×C₄	—	3	2	no	—
10	C₂×C₃²×C₄	D₃	1	1	yes	characteristic
11	C₂×C₃²×C₄	C₂×C₃	1	4	yes	—
12	C₂×C₃×Dic₃	C₂×C₃	1	8	yes	—
13	C₂×C₃³	C₂×C₄	1	2	yes	—
14	C₂×C₃³	C₂×C₄	1	1	yes	characteristic
15	C₃×C₄²	—	3	4	no	—
16	C₄×Dic₃	C₃²	1	1	yes	characteristic, direct product factor
17	C₂²×C₃²	—	2	4	no	—
18	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
19	C₂²×C₃²	C₂²×C₃	1	4	yes	—
20	C₃²×C₄	—	2	8	no	—
21	C₃²×C₄	—	3	4	no	—
22	C₃²×C₄	Dic₃	1	2	yes	direct product factor
23	C₃²×C₄	C₃×C₄	1	8	yes	complemented
24	C₃×Dic₃	C₃×C₄	1	16	yes	direct product factor
25	C₃³	C₄²	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃×C₄	—	2	4	no	—
27	C₂×C₃×C₄	—	3	8	no	—
28	C₂×C₃×C₄	C₃×D₃	1	4	yes	—
29	C₂×C₃×C₄	C₂×C₃²	1	1	yes	characteristic
30	C₂×Dic₃	C₂×C₃²	1	2	yes	—
31	C₂×C₃²	—	2	8	no	—
32	C₂×C₃²	—	2	4	no	—
33	C₂×C₃²	C₄×D₃	1	2	yes	—
34	C₂×C₃²	C₂×Dic₃	1	1	yes	characteristic
35	C₂×C₃²	C₂×C₃×C₄	1	8	yes	—
36	C₂×C₃²	C₂×C₃×C₄	1	4	yes	—
37	C₄²	—	3	1	no	Sylow
38	C₂²×C₃	—	2	4	no	—
39	C₂²×C₃	C₂×C₃×D₃	1	4	yes	—
40	C₂²×C₃	C₂²×C₃²	1	1	yes	characteristic
41	C₃×C₄	—	2	8	no	—
42	C₃×C₄	—	3	16	no	—
43	C₃×C₄	C₃×Dic₃	1	8	yes	direct product factor
44	C₃×C₄	C₃²×C₄	1	2	yes	complemented
45	Dic₃	C₃²×C₄	1	4	yes	direct product factor
46	C₃²	—	2	4	no	—
47	C₃²	C₄×Dic₃	1	1	yes	characteristic, direct product factor
48	C₃²	C₃×C₄²	1	4	yes	complemented
49	C₂×C₄	—	3	2	no	—
50	C₂×C₄	C₃²×D₃	1	1	yes	characteristic
51	C₂×C₃	—	2	8	no	—
52	C₂×C₃	—	2	4	no	—
53	C₂×C₃	C₃×C₄×D₃	1	8	yes	—
54	C₂×C₃	C₂×C₃×Dic₃	1	4	yes	—
55	C₂×C₃	C₂×C₃²×C₄	1	2	yes	—
56	C₂×C₃	C₂×C₃²×C₄	1	1	yes	characteristic
57	C₂²	C₂×C₃²×D₃	1	1	yes	characteristic
58	C₄	—	3	4	no	—
59	C₄	C₃²×Dic₃	1	2	yes	direct product factor
60	C₃	—	2	4	no	—
61	C₃	C₃×C₄×Dic₃	1	4	yes	direct product factor
62	C₃	C₃²×C₄²	1	1	yes	characteristic, complemented
63	C₂	C₃²×C₄×D₃	1	2	yes	—
64	C₂	C₂×C₃²×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₄	D₃
commutator, hypocenter	C₃	C₃²×C₄²
Frattini	C₂²	C₂×C₃²×D₃
Fitting	C₂×C₃³×C₄	C₂
socle, prime radical	C₂²×C₃³	C₂²
cosocle	C₂²×C₃	C₂²×C₃²
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₄

Complements

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

N	H ≅ G/N	type
4. C₃×C₄×Dic₃	C₃	direct (N × H)
6. C₃³×C₄	C₄	semidirect
7. C₃²×Dic₃	C₄	direct (N × H)
16. C₄×Dic₃	C₃²	direct (N × H)
22. C₃²×C₄	Dic₃	direct (N × H)
23. C₃²×C₄	C₃×C₄	semidirect
24. C₃×Dic₃	C₃×C₄	direct (N × H)
25. C₃³	C₄²	semidirect
43. C₃×C₄	C₃×Dic₃	direct (N × H)
44. C₃×C₄	C₃²×C₄	semidirect
45. Dic₃	C₃²×C₄	direct (N × H)
47. C₃²	C₄×Dic₃	direct (N × H)
48. C₃²	C₃×C₄²	semidirect
59. C₄	C₃²×Dic₃	direct (N × H)
61. C₃	C₃×C₄×Dic₃	direct (N × H)
62. C₃	C₃²×C₄²	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃³×C₄	2
C₂×C₃²×Dic₃	2
C₃²×C₄²	3
C₃×C₄×Dic₃	3

Subgroups — C32×C4×Dic3 #88824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₄×Dic₃ #88824