Subgroups — C₄×D₃² #3800

Order 144.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃²	C₂	1	1	yes	maximal, characteristic
2	C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×D₃	C₂	1	2	yes	maximal, complemented
4	#624	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×Dic₃	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×D₃	—	3	2	no	maximal
7	C₂×C₃⋊D₃	C₂²	1	1	yes	characteristic
8	C₂×C₃×D₃	C₂²	1	2	yes	—
9	D₃²	C₄	1	4	yes	direct product factor
10	C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
11	C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
12	C₃×Dic₃	C₂²	1	2	yes	complemented
13	C₂²×D₃	—	3	2	no	—
14	C₂×C₃×C₄	—	3	2	no	—
15	C₂×Dic₃	—	3	2	no	—
16	C₄×D₃	—	3	2	no	—
17	C₄×D₃	—	3	2	no	—
18	C₄×D₃	—	3	2	no	—
19	C₄×D₃	—	6	1	no	—
20	C₄×D₃	D₃	1	2	yes	direct product factor
21	C₂×C₃²	C₂³	1	1	yes	characteristic
22	C₃⋊D₃	C₂×C₄	1	2	yes	complemented
23	C₃×D₃	C₂×C₄	1	4	yes	complemented
24	C₂²×C₄	—	9	1	no	Sylow
25	C₂²×C₃	—	3	2	no	—
26	C₂×D₃	—	3	2	no	—
27	C₂×D₃	—	3	8	no	—
28	C₂×D₃	—	6	1	no	—
29	C₂×D₃	C₂×D₃	1	2	yes	—
30	C₃×C₄	—	2	1	no	—
31	C₃×C₄	—	3	2	no	—
32	C₃×C₄	C₂×D₃	1	2	yes	complemented
33	Dic₃	—	3	2	no	—
34	Dic₃	—	6	1	no	—
35	Dic₃	C₂×D₃	1	2	yes	complemented
36	C₃²	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
37	C₂³	—	9	1	no	—
38	C₂×C₄	—	3	2	no	—
39	C₂×C₄	—	9	1	no	—
40	C₂×C₄	—	9	2	no	—
41	C₂×C₄	—	9	1	no	—
42	C₂×C₃	—	2	1	no	—
43	C₂×C₃	—	3	4	no	—
44	C₂×C₃	C₂²×D₃	1	2	yes	—
45	D₃	—	3	4	no	—
46	D₃	—	6	2	no	—
47	D₃	C₄×D₃	1	4	yes	direct product factor
48	C₂²	—	3	2	no	—
49	C₂²	—	9	4	no	—
50	C₂²	—	9	1	no	—
51	C₄	—	3	2	no	—
52	C₄	—	9	1	no	—
53	C₄	D₃²	1	1	yes	characteristic, direct product factor
54	C₃	—	2	1	no	—
55	C₃	C₂×C₄×D₃	1	2	yes	complemented
56	C₂	—	3	4	no	—
57	C₂	—	9	2	no	—
58	C₂	C₂×D₃²	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	D₃²
commutator, hypocenter	C₃²	C₂²×C₄
Frattini	C₂	C₂×D₃²
Fitting	C₃²×C₄	C₂²
socle, cosocle	C₂×C₃²	C₂³
prime radical	C₂×D₃²	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₄×C₃⋊D₃	C₂	semidirect
3. C₃×C₄×D₃	C₂	semidirect
4. #624	C₂	semidirect
5. D₃×Dic₃	C₂	semidirect
9. D₃²	C₄	direct (N × H)
10. C₃²×C₄	C₂²	semidirect
11. C₃⋊Dic₃	C₂²	semidirect
12. C₃×Dic₃	C₂²	semidirect
20. C₄×D₃	D₃	direct (N × H)
22. C₃⋊D₃	C₂×C₄	semidirect
23. C₃×D₃	C₂×C₄	semidirect
32. C₃×C₄	C₂×D₃	semidirect
35. Dic₃	C₂×D₃	semidirect
36. C₃²	C₂²×C₄	semidirect
47. D₃	C₄×D₃	direct (N × H)
53. C₄	D₃²	direct (N × H)
55. C₃	C₂×C₄×D₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃²	2
C₄×C₃⋊D₃	2
C₃×C₄×D₃	2
#624	2
D₃×Dic₃	2
C₂×C₄×D₃	3

Subgroups — C4×D32 #3800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₃² #3800