Subgroups — Dic₃⋊Dic₃ #3723

Order 144.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₃	—	3	1	no	maximal
5	Dic₃⋊C₄	—	3	1	no	maximal
6	C₂²×C₃²	C₂²	1	1	yes	characteristic
7	C₃⋊Dic₃	—	2	1	no	—
8	C₃×Dic₃	—	2	1	no	—
9	C₃×Dic₃	C₄	1	2	yes	complemented
10	C₂×C₃×C₄	—	3	1	no	—
11	C₂×C₃×C₄	—	3	1	no	—
12	C₂×Dic₃	—	3	1	no	—
13	C₂×Dic₃	—	3	1	no	—
14	C₂×Dic₃	—	6	1	no	—
15	C₂×Dic₃	D₃	1	1	yes	characteristic
16	C₂×Dic₃	D₃	1	1	yes	characteristic
17	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃²	D₄	1	1	yes	characteristic
19	C₂×C₃²	Q₈	1	1	yes	characteristic
20	C₄⋊C₄	—	9	1	no	Sylow
21	C₂²×C₃	—	2	1	no	—
22	C₂²×C₃	C₂×D₃	1	1	yes	characteristic
23	C₂²×C₃	C₂×D₃	1	1	yes	characteristic
24	C₃×C₄	—	3	2	no	—
25	C₃×C₄	—	6	1	no	—
26	Dic₃	—	2	1	no	—
27	Dic₃	—	6	2	no	—
28	Dic₃	—	6	1	no	—
29	Dic₃	—	6	1	no	—
30	Dic₃	Dic₃	1	2	yes	complemented
31	C₃²	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₄	—	3	1	no	—
33	C₂×C₄	—	3	1	no	—
34	C₂×C₄	—	9	1	no	—
35	C₂×C₃	—	2	1	no	—
36	C₂×C₃	—	2	1	no	—
37	C₂×C₃	—	2	1	no	—
38	C₂×C₃	Dic₆	1	1	yes	characteristic
39	C₂×C₃	Dic₆	1	1	yes	characteristic
40	C₂×C₃	C₄×D₃	1	1	yes	characteristic
41	C₂×C₃	D₁₂	1	1	yes	characteristic
42	C₂×C₃	C₂×Dic₃	1	1	yes	characteristic
43	C₂×C₃	#67	1	1	yes	characteristic
44	C₂²	D₃²	1	1	yes	characteristic
45	C₄	—	3	2	no	—
46	C₄	—	6	1	no	—
47	C₄	—	18	1	no	—
48	C₃	—	2	1	no	—
49	C₃	Dic₃⋊C₄	1	1	yes	characteristic, complemented
50	C₃	C₄⋊Dic₃	1	1	yes	characteristic, complemented
51	C₂	D₃×Dic₃	1	1	yes	characteristic
52	C₂	#626	1	1	yes	characteristic
53	C₂	#627	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₃²
commutator	C₂×C₃²	C₂×C₄
Fitting, socle, prime radical, cosocle	C₂²×C₃²	C₂²
hypocenter	C₃²	C₄⋊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
9. C₃×Dic₃	C₄	semidirect
30. Dic₃	Dic₃	semidirect
31. C₃²	C₄⋊C₄	semidirect
49. C₃	Dic₃⋊C₄	semidirect
50. C₃	C₄⋊Dic₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊Dic₃	2
C₂×C₃×Dic₃	2
C₄⋊Dic₃	3
Dic₃⋊C₄	3

Subgroups — Dic3⋊Dic3 #3723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃⋊Dic₃ #3723