Subgroups — C₄²×C₃⋊D₃ #64080

Order 288.

324 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₃²×C₄²	C₂	semidirect
3. C₄×C₃⋊Dic₃	C₂	semidirect
8. C₄×C₃⋊D₃	C₄	direct (N × H)
10. C₃×C₄²	D₃	semidirect
14. C₃²×C₄	C₂×C₄	semidirect
15. C₃⋊Dic₃	C₂×C₄	semidirect
22. C₃⋊D₃	C₄²	direct (N × H)
25. C₄²	C₃⋊D₃	direct (N × H)
28. C₃×C₄	C₄×D₃	semidirect
30. C₃²	C₂×C₄²	semidirect
40. C₄	C₄×C₃⋊D₃	direct (N × H)
41. C₃	C₄²×D₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₃⋊D₃	2
C₃²×C₄²	2
C₄×C₃⋊Dic₃	2
C₄²×D₃	3

Subgroups — C42×C3⋊D3 #64080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×C₃⋊D₃ #64080