Subgroups — C₂×C₄×C₃⋊Dic₃ #64131

Order 288.

324 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃⋊Dic₃	C₂	1	2	yes	maximal
3	C₄×C₃⋊Dic₃	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×Dic₃	—	3	4	no	maximal
5	C₂³×C₃²	C₂²	1	1	yes	characteristic
6	C₂×C₃²×C₄	C₄	1	4	yes	complemented
7	C₂×C₃²×C₄	C₂²	1	2	yes	—
8	C₂×C₃⋊Dic₃	C₄	1	8	yes	direct product factor
9	C₂×C₃⋊Dic₃	C₂²	1	4	yes	—
10	C₂²×C₃×C₄	D₃	1	4	yes	—
11	C₂²×Dic₃	—	3	8	no	—
12	C₄×Dic₃	—	3	16	no	—
13	C₂²×C₃²	C₂×C₄	1	4	yes	—
14	C₂²×C₃²	C₂×C₄	1	2	yes	—
15	C₂²×C₃²	C₂³	1	1	yes	characteristic
16	C₃²×C₄	C₂×C₄	1	4	yes	complemented
17	C₃⋊Dic₃	C₂×C₄	1	8	yes	direct product factor
18	C₂×C₄²	—	9	1	no	Sylow
19	C₂³×C₃	C₂×D₃	1	4	yes	—
20	C₂×C₃×C₄	Dic₃	1	16	yes	complemented
21	C₂×C₃×C₄	C₂×D₃	1	8	yes	—
22	C₂×Dic₃	—	3	32	no	—
23	C₂×Dic₃	—	3	16	no	—
24	C₂×C₃²	C₄²	1	4	yes	complemented
25	C₂×C₃²	C₂²×C₄	1	2	yes	—
26	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₄	—	9	2	no	—
28	C₂²×C₄	C₃⋊D₃	1	1	yes	characteristic
29	C₄²	—	9	4	no	—
30	C₂²×C₃	C₄×D₃	1	16	yes	—
31	C₂²×C₃	C₂×Dic₃	1	8	yes	—
32	C₂²×C₃	C₂²×D₃	1	4	yes	—
33	C₃×C₄	C₂×Dic₃	1	16	yes	complemented
34	Dic₃	—	3	32	no	—
35	C₃²	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
36	C₂³	C₂×C₃⋊D₃	1	1	yes	characteristic
37	C₂×C₄	—	9	8	no	—
38	C₂×C₄	—	9	4	no	—
39	C₂×C₄	C₃⋊Dic₃	1	4	yes	direct product factor
40	C₂×C₄	C₂×C₃⋊D₃	1	2	yes	—
41	C₂×C₃	C₄×Dic₃	1	16	yes	complemented
42	C₂×C₃	C₂×C₄×D₃	1	8	yes	—
43	C₂×C₃	C₂²×Dic₃	1	4	yes	—
44	C₂²	C₄×C₃⋊D₃	1	4	yes	—
45	C₂²	C₂×C₃⋊Dic₃	1	2	yes	—
46	C₂²	C₂²×C₃⋊D₃	1	1	yes	characteristic
47	C₄	—	9	8	no	—
48	C₄	C₂×C₃⋊Dic₃	1	4	yes	direct product factor
49	C₃	C₂×C₄×Dic₃	1	4	yes	complemented
50	C₂	C₄×C₃⋊Dic₃	1	4	yes	direct product factor
51	C₂	C₂×C₄×C₃⋊D₃	1	2	yes	—
52	C₂	C₂²×C₃⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₄²
Frattini	C₂²	C₂²×C₃⋊D₃
Fitting	C₂²×C₃²×C₄	C₂
socle, prime radical	C₂³×C₃²	C₂²
cosocle	C₂²×C₃²	C₂³
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
3. C₄×C₃⋊Dic₃	C₂	direct (N × H)
6. C₂×C₃²×C₄	C₄	semidirect
8. C₂×C₃⋊Dic₃	C₄	direct (N × H)
16. C₃²×C₄	C₂×C₄	semidirect
17. C₃⋊Dic₃	C₂×C₄	direct (N × H)
20. C₂×C₃×C₄	Dic₃	semidirect
24. C₂×C₃²	C₄²	semidirect
33. C₃×C₄	C₂×Dic₃	semidirect
35. C₃²	C₂×C₄²	semidirect
39. C₂×C₄	C₃⋊Dic₃	direct (N × H)
41. C₂×C₃	C₄×Dic₃	semidirect
48. C₄	C₂×C₃⋊Dic₃	direct (N × H)
49. C₃	C₂×C₄×Dic₃	semidirect
50. C₂	C₄×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
C₂²×C₃²×C₄	2
C₂²×C₃⋊Dic₃	2
C₄×C₃⋊Dic₃	2
C₂×C₄×Dic₃	3

Subgroups — C2×C4×C3⋊Dic3 #64131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₃⋊Dic₃ #64131