Subgroups — C₃²×C₄⋊Dic₃ #88826

Order 432.

220 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×C₄⋊C₄	—	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	—	2	2	no	—
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	1	yes	characteristic
14	C₂×C₃³	D₄	1	1	yes	characteristic
15	C₂×C₃³	Q₈	1	1	yes	characteristic
16	C₃×C₄⋊C₄	—	3	4	no	—
17	C₄⋊Dic₃	C₃²	1	1	yes	characteristic, direct product factor
18	C₂²×C₃²	—	2	4	no	—
19	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
20	C₂²×C₃²	C₂²×C₃	1	4	yes	—
21	C₃²×C₄	—	2	8	no	—
22	C₃²×C₄	—	6	2	no	—
23	C₃²×C₄	Dic₃	1	2	yes	complemented
24	C₃²×C₄	C₃×C₄	1	8	yes	complemented
25	C₃×Dic₃	—	2	8	no	—
26	C₃³	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃×C₄	—	2	4	no	—
28	C₂×C₃×C₄	—	3	8	no	—
29	C₂×C₃×C₄	C₃×D₃	1	4	yes	—
30	C₂×C₃×C₄	C₂×C₃²	1	1	yes	characteristic
31	C₂×Dic₃	C₂×C₃²	1	2	yes	—
32	C₂×C₃²	—	2	4	no	—
33	C₂×C₃²	—	2	4	no	—
34	C₂×C₃²	—	2	4	no	—
35	C₂×C₃²	Dic₆	1	1	yes	characteristic
36	C₂×C₃²	D₁₂	1	1	yes	characteristic
37	C₂×C₃²	C₂×Dic₃	1	1	yes	characteristic
38	C₂×C₃²	C₂×C₃×C₄	1	4	yes	—
39	C₂×C₃²	C₃×D₄	1	4	yes	—
40	C₂×C₃²	C₃×Q₈	1	4	yes	—
41	C₄⋊C₄	—	3	1	no	Sylow
42	C₂²×C₃	—	2	4	no	—
43	C₂²×C₃	C₂×C₃×D₃	1	4	yes	—
44	C₂²×C₃	C₂²×C₃²	1	1	yes	characteristic
45	C₃×C₄	—	2	8	no	—
46	C₃×C₄	—	6	8	no	—
47	C₃×C₄	C₃×Dic₃	1	8	yes	complemented
48	C₃×C₄	C₃²×C₄	1	2	yes	complemented
49	Dic₃	—	2	2	no	—
50	C₃²	—	2	4	no	—
51	C₃²	C₄⋊Dic₃	1	1	yes	characteristic, direct product factor
52	C₃²	C₃×C₄⋊C₄	1	4	yes	complemented
53	C₂×C₄	—	3	2	no	—
54	C₂×C₄	C₃²×D₃	1	1	yes	characteristic
55	C₂×C₃	—	2	4	no	—
56	C₂×C₃	—	2	4	no	—
57	C₂×C₃	—	2	4	no	—
58	C₂×C₃	C₃×Dic₆	1	4	yes	—
59	C₂×C₃	C₃×D₁₂	1	4	yes	—
60	C₂×C₃	C₂×C₃×Dic₃	1	4	yes	—
61	C₂×C₃	C₂×C₃²×C₄	1	1	yes	characteristic
62	C₂×C₃	C₃²×D₄	1	1	yes	characteristic
63	C₂×C₃	C₃²×Q₈	1	1	yes	characteristic
64	C₂²	C₂×C₃²×D₃	1	1	yes	characteristic
65	C₄	—	6	2	no	—
66	C₄	C₃²×Dic₃	1	2	yes	complemented
67	C₃	—	2	4	no	—
68	C₃	C₃×C₄⋊Dic₃	1	4	yes	direct product factor
69	C₃	C₃²×C₄⋊C₄	1	1	yes	characteristic, complemented
70	C₂	C₃²×Dic₆	1	1	yes	characteristic
71	C₂	C₃²×D₁₂	1	1	yes	characteristic
72	C₂	C₂×C₃²×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂×D₃
commutator	C₂×C₃	C₂×C₃²×C₄
Frattini	C₂²	C₂×C₃²×D₃
Fitting	C₂×C₃³×C₄	C₂
socle, prime radical	C₂²×C₃³	C₂²
cosocle	C₂²×C₃	C₂²×C₃²
hypercenter	C₂×C₃²×C₄	D₃
hypocenter	C₃	C₃²×C₄⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ 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
17. C₄⋊Dic₃	C₃²	direct (N × H)
23. C₃²×C₄	Dic₃	semidirect
24. C₃²×C₄	C₃×C₄	semidirect
26. C₃³	C₄⋊C₄	semidirect
47. C₃×C₄	C₃×Dic₃	semidirect
48. C₃×C₄	C₃²×C₄	semidirect
51. C₃²	C₄⋊Dic₃	direct (N × H)
52. C₃²	C₃×C₄⋊C₄	semidirect
66. C₄	C₃²×Dic₃	semidirect
68. C₃	C₃×C₄⋊Dic₃	direct (N × H)
69. C₃	C₃²×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×C₃³×C₄	2
C₂×C₃²×Dic₃	2
C₃²×C₄⋊C₄	3
C₃×C₄⋊Dic₃	3

Subgroups — C32×C4⋊Dic3 #88826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₄⋊Dic₃ #88826