Subgroups — (C₂×D₃)⋊Dic₃ #3721

Order 144.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#217	—	3	1	no	maximal
5	(C₂×D₃)⋊C₄	—	3	1	no	maximal
6	C₂²×C₃²	C₂²	1	1	yes	characteristic
7	C₂×C₃×D₃	—	2	1	no	—
8	C₂×C₃×D₃	—	2	1	no	—
9	C₂×C₃×D₃	C₄	1	2	yes	complemented
10	C₃⋊Dic₃	—	2	1	no	—
11	C₃×Dic₃	—	2	1	no	—
12	C₂³×C₃	—	3	1	no	—
13	C₂²×D₃	D₃	1	1	yes	characteristic
14	C₂×C₃×C₄	—	3	1	no	—
15	C₂×Dic₃	—	3	1	no	—
16	C₂×Dic₃	—	3	1	no	—
17	C₂×Dic₃	—	6	1	no	—
18	C₂×Dic₃	D₃	1	1	yes	characteristic, complemented
19	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
20	C₂×C₃²	D₄	1	1	yes	characteristic
21	C₂×C₃²	D₄	1	1	yes	characteristic
22	C₃×D₃	—	2	2	no	—
23	C₂²⋊C₄	—	9	1	no	Sylow
24	C₂²×C₃	—	2	1	no	—
25	C₂²×C₃	—	3	2	no	—
26	C₂²×C₃	—	6	1	no	—
27	C₂²×C₃	—	6	1	no	—
28	C₂²×C₃	C₂×D₃	1	1	yes	characteristic
29	C₂²×C₃	C₂×D₃	1	1	yes	characteristic
30	C₂×D₃	—	2	1	no	—
31	C₂×D₃	—	2	1	no	—
32	C₂×D₃	Dic₃	1	2	yes	complemented
33	C₃×C₄	—	6	1	no	—
34	Dic₃	—	2	1	no	—
35	Dic₃	—	6	2	no	—
36	Dic₃	—	6	1	no	—
37	Dic₃	—	6	1	no	—
38	C₃²	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
39	C₂³	—	3	1	no	—
40	C₂×C₄	—	3	1	no	—
41	C₂×C₄	—	9	1	no	—
42	C₂×C₃	—	2	1	no	—
43	C₂×C₃	—	2	1	no	—
44	C₂×C₃	—	2	1	no	—
45	C₂×C₃	—	6	2	no	—
46	C₂×C₃	C₄×D₃	1	1	yes	characteristic
47	C₂×C₃	D₁₂	1	1	yes	characteristic
48	C₂×C₃	C₂×Dic₃	1	1	yes	characteristic
49	C₂×C₃	#67	1	1	yes	characteristic
50	C₂×C₃	#67	1	1	yes	characteristic
51	C₂×C₃	#67	1	1	yes	characteristic
52	D₃	—	2	2	no	—
53	C₂²	—	3	2	no	—
54	C₂²	—	6	1	no	—
55	C₂²	—	6	1	no	—
56	C₂²	D₃²	1	1	yes	characteristic
57	C₄	—	6	1	no	—
58	C₄	—	18	1	no	—
59	C₃	—	2	1	no	—
60	C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic, complemented
61	C₃	#217	1	1	yes	characteristic, complemented
62	C₂	—	6	2	no	—
63	C₂	D₃×Dic₃	1	1	yes	characteristic
64	C₂	#625	1	1	yes	characteristic
65	C₂	#626	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₃⋊Dic₃	C₂	semidirect
3. C₂×C₃×Dic₃	C₂	semidirect
9. C₂×C₃×D₃	C₄	semidirect
18. C₂×Dic₃	D₃	semidirect
32. C₂×D₃	Dic₃	semidirect
38. C₃²	C₂²⋊C₄	semidirect
60. C₃	(C₂×D₃)⋊C₄	semidirect
61. C₃	#217	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₃	2
C₂×C₃⋊Dic₃	2
C₂×C₃×Dic₃	2
#217	3
(C₂×D₃)⋊C₄	3

Subgroups — (C2×D3)⋊Dic3 #3721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×D₃)⋊Dic₃ #3721