Subgroups — D₄×C₃⋊D₃ #3829

Order 144.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
2	C₃²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#638	C₂	1	2	yes	maximal, complemented
4	C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
6	D₃×D₄	—	3	4	no	maximal
7	C₂²×C₃²	C₂²	1	2	yes	complemented
8	C₂×C₃⋊D₃	—	2	4	no	—
9	C₂×C₃⋊D₃	C₂²	1	1	yes	characteristic
10	C₂×C₃⋊D₃	C₂²	1	2	yes	complemented
11	C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
12	C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₃	—	3	8	no	—
14	C₃×D₄	D₃	1	4	yes	complemented
15	#67	—	3	8	no	—
16	D₁₂	—	3	4	no	—
17	C₄×D₃	—	3	4	no	—
18	C₂×C₃²	—	2	2	no	—
19	C₂×C₃²	C₂³	1	1	yes	characteristic
20	C₃⋊D₃	—	2	2	no	—
21	C₃⋊D₃	D₄	1	2	yes	direct product factor
22	C₂×D₄	—	9	1	no	Sylow
23	C₂²×C₃	C₂×D₃	1	8	yes	complemented
24	C₂×D₃	—	3	4	no	—
25	C₂×D₃	—	3	8	no	—
26	C₂×D₃	—	6	16	no	—
27	C₃×C₄	C₂×D₃	1	4	yes	complemented
28	Dic₃	—	3	4	no	—
29	C₃²	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
30	C₂³	—	9	2	no	—
31	D₄	—	9	2	no	—
32	D₄	—	9	1	no	—
33	D₄	C₃⋊D₃	1	1	yes	characteristic, direct product factor
34	C₂×C₄	—	9	1	no	—
35	C₂×C₃	—	2	8	no	—
36	C₂×C₃	C₂²×D₃	1	4	yes	—
37	D₃	—	3	8	no	—
38	D₃	—	6	8	no	—
39	C₂²	—	9	1	no	—
40	C₂²	—	9	2	no	—
41	C₂²	—	18	4	no	—
42	C₂²	C₂×C₃⋊D₃	1	2	yes	complemented
43	C₄	—	9	1	no	—
44	C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
45	C₃	D₃×D₄	1	4	yes	complemented
46	C₂	—	2	2	no	—
47	C₂	—	9	2	no	—
48	C₂	—	18	2	no	—
49	C₂	C₂²×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×C₃⋊D₃
commutator, socle, cosocle	C₂×C₃²	C₂³
Fitting	C₃²×D₄	C₂
hypercenter	D₄	C₃⋊D₃
hypocenter	C₃²	C₂×D₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃⋊D₃	C₂	semidirect
2. C₃²×D₄	C₂	semidirect
3. #638	C₂	semidirect
4. C₄⋊(C₃⋊D₃)	C₂	semidirect
5. C₄×C₃⋊D₃	C₂	semidirect
7. C₂²×C₃²	C₂²	semidirect
10. C₂×C₃⋊D₃	C₂²	semidirect
11. C₃²×C₄	C₂²	semidirect
12. C₃⋊Dic₃	C₂²	semidirect
14. C₃×D₄	D₃	semidirect
21. C₃⋊D₃	D₄	direct (N × H)
23. C₂²×C₃	C₂×D₃	semidirect
27. C₃×C₄	C₂×D₃	semidirect
29. C₃²	C₂×D₄	semidirect
33. D₄	C₃⋊D₃	direct (N × H)
42. C₂²	C₂×C₃⋊D₃	semidirect
44. C₄	C₂×C₃⋊D₃	semidirect
45. C₃	D₃×D₄	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
C₃²×D₄	2
#638	2
C₄⋊(C₃⋊D₃)	2
C₄×C₃⋊D₃	2
D₃×D₄	3

Subgroups — D4×C3⋊D3 #3829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₃⋊D₃ #3829