Subgroups — C₂×C₃×Dic₆ #3815

Order 144.

84 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×Dic₆	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃×Q₈	—	3	1	no	maximal
5	C₂×Dic₆	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₃²	C₂²	1	1	yes	characteristic
7	C₃²×C₄	C₂²	1	2	yes	—
8	C₃×Dic₃	C₂²	1	4	yes	—
9	C₃×Q₈	—	3	4	no	—
10	C₂×C₃×C₄	—	2	1	no	—
11	C₂×C₃×C₄	—	3	2	no	—
12	C₂×C₃×C₄	D₃	1	1	yes	characteristic
13	C₂×C₃×C₄	C₂×C₃	1	1	yes	characteristic
14	C₂×Dic₃	C₂×C₃	1	2	yes	—
15	Dic₆	C₂×C₃	1	4	yes	direct product factor
16	C₂×C₃²	Q₈	1	2	yes	complemented
17	C₂×C₃²	C₂³	1	1	yes	characteristic
18	C₂×Q₈	—	3	1	no	Sylow
19	C₂²×C₃	—	2	1	no	—
20	C₂²×C₃	C₂×D₃	1	1	yes	characteristic
21	C₂²×C₃	C₂²×C₃	1	1	yes	characteristic
22	C₃×C₄	—	2	2	no	—
23	C₃×C₄	—	3	4	no	—
24	C₃×C₄	C₂×D₃	1	2	yes	—
25	C₃×C₄	C₂²×C₃	1	2	yes	—
26	Dic₃	C₂²×C₃	1	4	yes	—
27	C₃²	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
28	Q₈	—	3	4	no	—
29	C₂×C₄	—	3	2	no	—
30	C₂×C₄	C₃×D₃	1	1	yes	characteristic
31	C₂×C₃	—	2	2	no	—
32	C₂×C₃	—	2	1	no	—
33	C₂×C₃	Dic₆	1	2	yes	direct product factor
34	C₂×C₃	C₃×Q₈	1	2	yes	complemented
35	C₂×C₃	C₂²×D₃	1	1	yes	characteristic
36	C₂×C₃	C₂³×C₃	1	1	yes	characteristic
37	C₂²	C₂×C₃×D₃	1	1	yes	characteristic
38	C₄	—	3	4	no	—
39	C₄	C₂×C₃×D₃	1	2	yes	—
40	C₃	—	2	1	no	—
41	C₃	C₂×Dic₆	1	1	yes	characteristic, direct product factor
42	C₃	C₂×C₃×Q₈	1	1	yes	characteristic, complemented
43	C₂	C₃×Dic₆	1	2	yes	direct product factor
44	C₂	C₂²×C₃×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₃
commutator, cosocle	C₂×C₃	C₂³×C₃
Frattini	C₂	C₂²×C₃×D₃
Fitting	C₂×C₃²×C₄	C₂
socle, prime radical	C₂²×C₃²	C₂²
hypercenter	C₂×C₃×C₄	D₃
hypocenter	C₃	C₂×C₃×Q₈
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
3. C₃×Dic₆	C₂	direct (N × H)
5. C₂×Dic₆	C₃	direct (N × H)
15. Dic₆	C₂×C₃	direct (N × H)
16. C₂×C₃²	Q₈	semidirect
27. C₃²	C₂×Q₈	semidirect
33. C₂×C₃	Dic₆	direct (N × H)
34. C₂×C₃	C₃×Q₈	semidirect
41. C₃	C₂×Dic₆	direct (N × H)
42. C₃	C₂×C₃×Q₈	semidirect
43. C₂	C₃×Dic₆	direct (N × H)

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×Dic₆	2
C₂×C₃×Q₈	3
C₂×Dic₆	3

Subgroups — C2×C3×Dic6 #3815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×Dic₆ #3815