Subgroups — C₂²×C₃×Dic₃ #3823

Order 144.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂³×C₃	D₃
commutator, hypocenter	C₃	C₂²×C₃×C₄
Frattini	C₂	C₂²×C₃×D₃
Fitting, socle, prime radical	C₂³×C₃²	C₂
cosocle	C₂×C₃	C₂³×C₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₂³×C₃

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×Dic₃	C₂	direct (N × H)
4. C₂²×Dic₃	C₃	direct (N × H)
5. C₂²×C₃²	C₄	semidirect
7. C₃×Dic₃	C₂²	direct (N × H)
12. C₂×Dic₃	C₂×C₃	direct (N × H)
13. C₂×C₃²	C₂×C₄	semidirect
18. C₂²×C₃	Dic₃	direct (N × H)
19. C₂²×C₃	C₃×C₄	semidirect
23. Dic₃	C₂²×C₃	direct (N × H)
24. C₃²	C₂²×C₄	semidirect
29. C₂×C₃	C₂×Dic₃	direct (N × H)
30. C₂×C₃	C₂×C₃×C₄	semidirect
33. C₂²	C₃×Dic₃	direct (N × H)
37. C₃	C₂²×Dic₃	direct (N × H)
38. C₃	C₂²×C₃×C₄	semidirect
39. C₂	C₂×C₃×Dic₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃²	2
C₂×C₃×Dic₃	2
C₂²×C₃×C₄	3
C₂²×Dic₃	3

Subgroups — C22×C3×Dic3 #3823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×Dic₃ #3823