Subgroups — C₂×C₃²×Dic₃ #6301

Order 216.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³	C₂	1	1	yes	maximal, characteristic
2	C₃²×Dic₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃²×C₄	—	3	1	no	maximal
4	C₂×C₃×Dic₃	C₃	1	4	yes	maximal, direct product factor
5	C₂×C₃³	C₄	1	2	yes	complemented
6	C₂×C₃³	C₂²	1	1	yes	characteristic
7	C₂²×C₃²	—	2	4	no	—
8	C₂²×C₃²	D₃	1	1	yes	characteristic
9	C₂²×C₃²	C₂×C₃	1	4	yes	—
10	C₃²×C₄	—	3	2	no	—
11	C₃×Dic₃	C₂×C₃	1	8	yes	direct product factor
12	C₃³	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₃×C₄	—	3	4	no	—
14	C₂×Dic₃	C₃²	1	1	yes	characteristic, direct product factor
15	C₂×C₃²	—	2	8	no	—
16	C₂×C₃²	—	2	4	no	—
17	C₂×C₃²	Dic₃	1	2	yes	direct product factor
18	C₂×C₃²	C₃×C₄	1	8	yes	complemented
19	C₂×C₃²	C₂×D₃	1	1	yes	characteristic
20	C₂×C₃²	C₂²×C₃	1	4	yes	—
21	C₂²×C₃	—	2	4	no	—
22	C₂²×C₃	C₃×D₃	1	4	yes	—
23	C₂²×C₃	C₂×C₃²	1	1	yes	characteristic
24	C₃×C₄	—	3	8	no	—
25	Dic₃	C₂×C₃²	1	2	yes	direct product factor
26	C₃²	—	2	4	no	—
27	C₃²	C₂×Dic₃	1	1	yes	characteristic, direct product factor
28	C₃²	C₂×C₃×C₄	1	4	yes	complemented
29	C₂×C₄	—	3	1	no	Sylow
30	C₂×C₃	—	2	8	no	—
31	C₂×C₃	—	2	4	no	—
32	C₂×C₃	C₃×Dic₃	1	8	yes	direct product factor
33	C₂×C₃	C₃²×C₄	1	2	yes	complemented
34	C₂×C₃	C₂×C₃×D₃	1	4	yes	—
35	C₂×C₃	C₂²×C₃²	1	1	yes	characteristic
36	C₂²	C₃²×D₃	1	1	yes	characteristic
37	C₄	—	3	2	no	—
38	C₃	—	2	4	no	—
39	C₃	C₂×C₃×Dic₃	1	4	yes	direct product factor
40	C₃	C₂×C₃²×C₄	1	1	yes	characteristic, complemented
41	C₂	C₃²×Dic₃	1	2	yes	direct product factor
42	C₂	C₂×C₃²×D₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₃²	D₃
commutator, hypocenter	C₃	C₂×C₃²×C₄
Frattini	C₂	C₂×C₃²×D₃
Fitting, socle, prime radical	C₂²×C₃³	C₂
cosocle	C₂×C₃	C₂²×C₃²
LCS	G ▷ C₃
UCS	C₁ ◁ C₂²×C₃²

Complements

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

N	H ≅ G/N	type
2. C₃²×Dic₃	C₂	direct (N × H)
4. C₂×C₃×Dic₃	C₃	direct (N × H)
5. C₂×C₃³	C₄	semidirect
11. C₃×Dic₃	C₂×C₃	direct (N × H)
12. C₃³	C₂×C₄	semidirect
14. C₂×Dic₃	C₃²	direct (N × H)
17. C₂×C₃²	Dic₃	direct (N × H)
18. C₂×C₃²	C₃×C₄	semidirect
25. Dic₃	C₂×C₃²	direct (N × H)
27. C₃²	C₂×Dic₃	direct (N × H)
28. C₃²	C₂×C₃×C₄	semidirect
32. C₂×C₃	C₃×Dic₃	direct (N × H)
33. C₂×C₃	C₃²×C₄	semidirect
39. C₃	C₂×C₃×Dic₃	direct (N × H)
40. C₃	C₂×C₃²×C₄	semidirect
41. C₂	C₃²×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
C₂²×C₃³	2
C₃²×Dic₃	2
C₂×C₃²×C₄	3
C₂×C₃×Dic₃	3

Subgroups — C2×C32×Dic3 #6301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×Dic₃ #6301