Subgroups — C₃×C₄×Dic₃ #3733

Order 144.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₃	C₂	1	2	yes	maximal
3	C₃×C₄²	—	3	1	no	maximal
4	C₄×Dic₃	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂²×C₃²	C₂²	1	1	yes	characteristic
6	C₃²×C₄	C₄	1	2	yes	complemented
7	C₃×Dic₃	C₄	1	4	yes	direct product factor
8	C₂×C₃×C₄	—	2	1	no	—
9	C₂×C₃×C₄	—	3	2	no	—
10	C₂×C₃×C₄	D₃	1	1	yes	characteristic
11	C₂×C₃×C₄	C₂×C₃	1	1	yes	characteristic
12	C₂×Dic₃	C₂×C₃	1	2	yes	—
13	C₂×C₃²	C₂×C₄	1	2	yes	—
14	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
15	C₄²	—	3	1	no	Sylow
16	C₂²×C₃	—	2	1	no	—
17	C₂²×C₃	C₂×D₃	1	1	yes	characteristic
18	C₂²×C₃	C₂²×C₃	1	1	yes	characteristic
19	C₃×C₄	—	2	2	no	—
20	C₃×C₄	—	3	4	no	—
21	C₃×C₄	Dic₃	1	2	yes	direct product factor
22	C₃×C₄	C₃×C₄	1	2	yes	complemented
23	Dic₃	C₃×C₄	1	4	yes	direct product factor
24	C₃²	C₄²	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₄	—	3	2	no	—
26	C₂×C₄	C₃×D₃	1	1	yes	characteristic
27	C₂×C₃	—	2	2	no	—
28	C₂×C₃	—	2	1	no	—
29	C₂×C₃	C₄×D₃	1	2	yes	—
30	C₂×C₃	C₂×Dic₃	1	1	yes	characteristic
31	C₂×C₃	C₂×C₃×C₄	1	2	yes	—
32	C₂×C₃	C₂×C₃×C₄	1	1	yes	characteristic
33	C₂²	C₂×C₃×D₃	1	1	yes	characteristic
34	C₄	—	3	4	no	—
35	C₄	C₃×Dic₃	1	2	yes	direct product factor
36	C₃	—	2	1	no	—
37	C₃	C₄×Dic₃	1	1	yes	characteristic, direct product factor
38	C₃	C₃×C₄²	1	1	yes	characteristic, complemented
39	C₂	C₃×C₄×D₃	1	2	yes	—
40	C₂	C₂×C₃×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄	D₃
commutator, hypocenter	C₃	C₃×C₄²
Frattini	C₂²	C₂×C₃×D₃
Fitting	C₂×C₃²×C₄	C₂
socle, prime radical	C₂²×C₃²	C₂²
cosocle	C₂²×C₃	C₂²×C₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄

Complements

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

N	H ≅ G/N	type
4. C₄×Dic₃	C₃	direct (N × H)
6. C₃²×C₄	C₄	semidirect
7. C₃×Dic₃	C₄	direct (N × H)
21. C₃×C₄	Dic₃	direct (N × H)
22. C₃×C₄	C₃×C₄	semidirect
23. Dic₃	C₃×C₄	direct (N × H)
24. C₃²	C₄²	semidirect
35. C₄	C₃×Dic₃	direct (N × H)
37. C₃	C₄×Dic₃	direct (N × H)
38. C₃	C₃×C₄²	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₄	2
C₂×C₃×Dic₃	2
C₃×C₄²	3
C₄×Dic₃	3

Subgroups — C3×C4×Dic3 #3733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×Dic₃ #3733