Subgroups — C₃×C₄⋊Dic₃ #3735

Order 144.

60 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×C₄⋊C₄	—	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	—	2	2	no	—
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	1	yes	characteristic
14	C₂×C₃²	D₄	1	1	yes	characteristic
15	C₂×C₃²	Q₈	1	1	yes	characteristic
16	C₄⋊C₄	—	3	1	no	Sylow
17	C₂²×C₃	—	2	1	no	—
18	C₂²×C₃	C₂×D₃	1	1	yes	characteristic
19	C₂²×C₃	C₂²×C₃	1	1	yes	characteristic
20	C₃×C₄	—	2	2	no	—
21	C₃×C₄	—	6	2	no	—
22	C₃×C₄	Dic₃	1	2	yes	complemented
23	C₃×C₄	C₃×C₄	1	2	yes	complemented
24	Dic₃	—	2	2	no	—
25	C₃²	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₄	—	3	2	no	—
27	C₂×C₄	C₃×D₃	1	1	yes	characteristic
28	C₂×C₃	—	2	1	no	—
29	C₂×C₃	—	2	1	no	—
30	C₂×C₃	—	2	1	no	—
31	C₂×C₃	Dic₆	1	1	yes	characteristic
32	C₂×C₃	D₁₂	1	1	yes	characteristic
33	C₂×C₃	C₂×Dic₃	1	1	yes	characteristic
34	C₂×C₃	C₂×C₃×C₄	1	1	yes	characteristic
35	C₂×C₃	C₃×D₄	1	1	yes	characteristic
36	C₂×C₃	C₃×Q₈	1	1	yes	characteristic
37	C₂²	C₂×C₃×D₃	1	1	yes	characteristic
38	C₄	—	6	2	no	—
39	C₄	C₃×Dic₃	1	2	yes	complemented
40	C₃	—	2	1	no	—
41	C₃	C₄⋊Dic₃	1	1	yes	characteristic, direct product factor
42	C₃	C₃×C₄⋊C₄	1	1	yes	characteristic, complemented
43	C₂	C₃×Dic₆	1	1	yes	characteristic
44	C₂	C₃×D₁₂	1	1	yes	characteristic
45	C₂	C₂×C₃×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₃
commutator	C₂×C₃	C₂×C₃×C₄
Frattini	C₂²	C₂×C₃×D₃
Fitting	C₂×C₃²×C₄	C₂
socle, prime radical	C₂²×C₃²	C₂²
cosocle	C₂²×C₃	C₂²×C₃
hypercenter	C₂×C₃×C₄	D₃
hypocenter	C₃	C₃×C₄⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ 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
22. C₃×C₄	Dic₃	semidirect
23. C₃×C₄	C₃×C₄	semidirect
25. C₃²	C₄⋊C₄	semidirect
39. C₄	C₃×Dic₃	semidirect
41. C₃	C₄⋊Dic₃	direct (N × H)
42. C₃	C₃×C₄⋊C₄	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×C₄⋊C₄	3
C₄⋊Dic₃	3

Subgroups — C3×C4⋊Dic3 #3735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄⋊Dic₃ #3735