Subgroups — C₃×(C₂×D₃)⋊C₄ #3736

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×C₃²×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₂²⋊C₄	—	3	1	no	maximal
5	(C₂×D₃)⋊C₄	C₃	1	1	yes	maximal, characteristic, direct product factor
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	C₃²×C₄	—	2	1	no	—
11	C₃×Dic₃	—	2	1	no	—
12	C₂³×C₃	—	3	1	no	—
13	C₂²×D₃	C₂×C₃	1	1	yes	characteristic
14	C₂×C₃×C₄	—	2	1	no	—
15	C₂×C₃×C₄	—	3	1	no	—
16	C₂×C₃×C₄	D₃	1	1	yes	characteristic, complemented
17	C₂×C₃×C₄	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂×Dic₃	C₂×C₃	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	—	3	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	C₂²×C₃	1	1	yes	characteristic
30	C₂×D₃	—	2	1	no	—
31	C₂×D₃	—	2	1	no	—
32	C₂×D₃	C₃×C₄	1	2	yes	complemented
33	C₃×C₄	—	2	2	no	—
34	C₃×C₄	—	2	1	no	—
35	C₃×C₄	—	2	1	no	—
36	C₃×C₄	—	6	1	no	—
37	Dic₃	—	2	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	C₃×D₃	1	1	yes	characteristic, complemented
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	#67	1	1	yes	characteristic
49	C₂×C₃	C₂×C₃×C₄	1	1	yes	characteristic
50	C₂×C₃	C₃×D₄	1	1	yes	characteristic
51	C₂×C₃	C₃×D₄	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	C₂×C₃×D₃	1	1	yes	characteristic
57	C₄	—	2	1	no	—
58	C₄	—	6	1	no	—
59	C₃	—	2	1	no	—
60	C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic, direct product factor
61	C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic, complemented
62	C₂	—	6	2	no	—
63	C₂	C₃×C₄×D₃	1	1	yes	characteristic
64	C₂	C₃×D₁₂	1	1	yes	characteristic
65	C₂	C₃×#67	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	C₂²×C₃²	C₂²
prime radical	C₂²×C₃×D₃	C₂
cosocle	C₂²×C₃	C₂²×C₃
hypercenter	C₂×C₃×C₄	D₃
hypocenter	C₃	C₃×C₂²⋊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
2. C₂×C₃²×C₄	C₂	semidirect
3. C₂×C₃×Dic₃	C₂	semidirect
5. (C₂×D₃)⋊C₄	C₃	direct (N × H)
9. C₂×C₃×D₃	C₄	semidirect
16. C₂×C₃×C₄	D₃	semidirect
17. C₂×C₃×C₄	C₂×C₃	semidirect
18. C₂×Dic₃	C₂×C₃	semidirect
32. C₂×D₃	C₃×C₄	semidirect
38. C₃²	C₂²⋊C₄	semidirect
41. C₂×C₄	C₃×D₃	semidirect
60. C₃	(C₂×D₃)⋊C₄	direct (N × H)
61. C₃	C₃×C₂²⋊C₄	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×C₃²×C₄	2
C₂×C₃×Dic₃	2
C₃×C₂²⋊C₄	3
(C₂×D₃)⋊C₄	3

Subgroups — C3×(C2×D3)⋊C4 #3736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×(C₂×D₃)⋊C₄ #3736