Subgroups — D₃×Dic₆ #3794

Order 144.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#634	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×D₃	C₂	1	1	yes	maximal, characteristic
3	C₃×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#627	C₂	1	2	yes	maximal, complemented
5	D₃×Dic₃	C₂	1	2	yes	maximal
6	D₃×Q₈	—	3	1	no	maximal
7	C₂×Dic₆	—	3	1	no	maximal
8	C₂×C₃×D₃	C₂²	1	1	yes	characteristic
9	C₃²×C₄	C₂²	1	1	yes	characteristic
10	C₃⋊Dic₃	C₂²	1	2	yes	—
11	C₃×Dic₃	C₂²	1	2	yes	—
12	C₃×Dic₃	C₂²	1	1	yes	characteristic
13	C₃×Q₈	—	3	1	no	—
14	C₂×C₃×C₄	—	3	1	no	—
15	C₂×Dic₃	—	3	2	no	—
16	C₄×D₃	—	3	2	no	—
17	C₄×D₃	D₃	1	1	yes	characteristic
18	Dic₆	—	3	1	no	—
19	Dic₆	—	3	1	no	—
20	Dic₆	—	3	2	no	—
21	Dic₆	—	3	2	no	—
22	Dic₆	—	6	1	no	—
23	Dic₆	D₃	1	1	yes	characteristic, direct product factor
24	C₂×C₃²	C₂³	1	1	yes	characteristic
25	C₃×D₃	Q₈	1	2	yes	complemented
26	C₂×Q₈	—	9	1	no	Sylow
27	C₂²×C₃	—	3	1	no	—
28	C₂×D₃	C₂×D₃	1	1	yes	characteristic
29	C₃×C₄	—	2	1	no	—
30	C₃×C₄	—	3	1	no	—
31	C₃×C₄	—	3	2	no	—
32	C₃×C₄	C₂×D₃	1	1	yes	characteristic
33	C₃×C₄	C₂×D₃	1	1	yes	characteristic
34	Dic₃	—	3	2	no	—
35	Dic₃	—	3	2	no	—
36	Dic₃	—	6	2	no	—
37	Dic₃	C₂×D₃	1	1	yes	characteristic
38	Dic₃	C₂×D₃	1	2	yes	—
39	C₃²	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
40	Q₈	—	3	1	no	—
41	Q₈	—	9	2	no	—
42	Q₈	—	9	1	no	—
43	C₂×C₄	—	3	1	no	—
44	C₂×C₄	—	9	2	no	—
45	C₂×C₃	—	2	1	no	—
46	C₂×C₃	—	3	2	no	—
47	C₂×C₃	C₂²×D₃	1	1	yes	characteristic
48	C₂×C₃	C₂²×D₃	1	1	yes	characteristic
49	D₃	Dic₆	1	2	yes	direct product factor
50	C₂²	—	3	1	no	—
51	C₄	—	3	1	no	—
52	C₄	—	3	2	no	—
53	C₄	—	9	2	no	—
54	C₄	D₃²	1	1	yes	characteristic
55	C₃	—	2	1	no	—
56	C₃	C₂×Dic₆	1	1	yes	characteristic, complemented
57	C₃	D₃×Q₈	1	1	yes	characteristic, complemented
58	C₂	—	3	2	no	—
59	C₂	C₂×D₃²	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₃²
commutator, socle, cosocle	C₂×C₃²	C₂³
Fitting	C₃²×C₄	C₂²
prime radical	C₂×C₃×D₃	C₂²
hypercenter	C₄	D₃²
hypocenter	C₃²	C₂×Q₈
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. #634	C₂	semidirect
3. C₃×Dic₆	C₂	semidirect
4. #627	C₂	semidirect
23. Dic₆	D₃	direct (N × H)
25. C₃×D₃	Q₈	semidirect
39. C₃²	C₂×Q₈	semidirect
49. D₃	Dic₆	direct (N × H)
56. C₃	C₂×Dic₆	semidirect
57. C₃	D₃×Q₈	semidirect

Maximal subgroups

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

subgroup	index
#634	2
C₃×C₄×D₃	2
C₃×Dic₆	2
#627	2
D₃×Dic₃	2
D₃×Q₈	3
C₂×Dic₆	3

Subgroups — D3×Dic6 #3794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×Dic₆ #3794