Subgroups — D₃×Dic₁₂ #63799

Order 288.

129 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×Dic₆	C₂	1	2	yes	maximal
2	#3746	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic
5	#3719	C₂	1	2	yes	maximal, complemented
6	D₃×Q₁₆	—	3	1	no	maximal
7	C₂×Dic₁₂	—	3	1	no	maximal
8	#634	C₂²	1	2	yes	—
9	C₃×C₄×D₃	C₂²	1	1	yes	characteristic
10	C₃×Dic₆	C₂²	1	2	yes	—
11	#627	—	2	2	no	—
12	D₃×Dic₃	—	2	2	no	—
13	C₃²×C₈	C₂²	1	1	yes	characteristic
14	C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	D₃×Q₈	—	3	2	no	—
16	C₂×Dic₆	—	3	2	no	—
17	C₃×Q₁₆	—	3	1	no	—
18	C₂×C₃×C₈	—	3	1	no	—
19	#216	—	3	2	no	—
20	Dic₁₂	—	3	2	no	—
21	Dic₁₂	—	3	1	no	—
22	Dic₁₂	—	3	1	no	—
23	Dic₁₂	—	6	1	no	—
24	Dic₁₂	D₃	1	1	yes	characteristic, direct product factor
25	D₃×C₈	D₃	1	1	yes	characteristic
26	C₂×C₃×D₃	D₄	1	1	yes	characteristic
27	C₃²×C₄	C₂³	1	1	yes	characteristic
28	C₃⋊Dic₃	—	2	2	no	—
29	C₃×Dic₃	—	2	2	no	—
30	C₃×Dic₃	D₄	1	1	yes	characteristic
31	C₂×Q₁₆	—	9	1	no	Sylow
32	C₃×Q₈	—	3	2	no	—
33	C₂×C₃×C₄	—	3	1	no	—
34	C₂×Dic₃	—	6	2	no	—
35	C₄×D₃	—	6	2	no	—
36	C₄×D₃	C₂×D₃	1	1	yes	characteristic
37	Dic₆	—	3	2	no	—
38	Dic₆	—	3	2	no	—
39	Dic₆	—	6	2	no	—
40	Dic₆	—	6	2	no	—
41	Dic₆	—	6	2	no	—
42	Dic₆	C₂×D₃	1	2	yes	—
43	C₃×C₈	—	2	1	no	—
44	C₃×C₈	—	3	1	no	—
45	C₃×C₈	C₂×D₃	1	1	yes	characteristic
46	C₃×C₈	C₂×D₃	1	1	yes	characteristic
47	C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
48	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
49	C₃×D₃	Q₁₆	1	2	yes	complemented
50	C₂×Q₈	—	9	2	no	—
51	Q₁₆	—	3	1	no	—
52	Q₁₆	—	9	2	no	—
53	Q₁₆	—	9	1	no	—
54	C₂×C₈	—	3	1	no	—
55	C₂²×C₃	—	3	1	no	—
56	C₂×D₃	D₁₂	1	1	yes	characteristic
57	C₃×C₄	—	2	1	no	—
58	C₃×C₄	—	3	1	no	—
59	C₃×C₄	—	6	2	no	—
60	C₃×C₄	C₂²×D₃	1	1	yes	characteristic
61	C₃×C₄	C₂²×D₃	1	1	yes	characteristic
62	Dic₃	—	2	2	no	—
63	Dic₃	—	6	2	no	—
64	Dic₃	—	6	2	no	—
65	Dic₃	—	12	2	no	—
66	Dic₃	D₁₂	1	1	yes	characteristic
67	C₃²	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
68	Q₈	—	3	2	no	—
69	Q₈	—	9	2	no	—
70	Q₈	—	18	2	no	—
71	C₂×C₄	—	3	1	no	—
72	C₂×C₄	—	18	2	no	—
73	C₈	—	3	1	no	—
74	C₈	D₃²	1	1	yes	characteristic
75	C₂×C₃	—	2	1	no	—
76	C₂×C₃	—	3	2	no	—
77	C₂×C₃	C₂×D₁₂	1	1	yes	characteristic
78	C₂×C₃	D₃×D₄	1	1	yes	characteristic
79	D₃	Dic₁₂	1	2	yes	direct product factor
80	C₂²	—	3	1	no	—
81	C₄	—	3	1	no	—
82	C₄	—	6	2	no	—
83	C₄	—	18	2	no	—
84	C₄	C₂×D₃²	1	1	yes	characteristic
85	C₃	—	2	1	no	—
86	C₃	C₂×Dic₁₂	1	1	yes	characteristic, complemented
87	C₃	D₃×Q₁₆	1	1	yes	characteristic, complemented
88	C₂	—	3	2	no	—
89	C₂	D₃×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃×D₁₂
commutator, cosocle	C₃²×C₄	C₂³
Frattini	C₄	C₂×D₃²
Fitting	C₃²×C₈	C₂²
socle	C₂×C₃²	C₂×D₄
prime radical	C₂×C₃×D₃	D₄
hypercenter	C₈	D₃²
hypocenter	C₃²	C₂×Q₁₆
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. #3746	C₂	semidirect
3. C₃×Dic₁₂	C₂	semidirect
5. #3719	C₂	semidirect
24. Dic₁₂	D₃	direct (N × H)
49. C₃×D₃	Q₁₆	semidirect
67. C₃²	C₂×Q₁₆	semidirect
79. D₃	Dic₁₂	direct (N × H)
86. C₃	C₂×Dic₁₂	semidirect
87. C₃	D₃×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
D₃×Dic₆	2
#3746	2
C₃×Dic₁₂	2
C₃×D₃×C₈	2
#3719	2
D₃×Q₁₆	3
C₂×Dic₁₂	3

Subgroups — D3×Dic12 #63799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×Dic₁₂ #63799