Subgroups — C₂⁴×C₃×D₃ #64395

Order 288.

1563 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×D₃	C₂	1	30	yes	maximal, direct product factor
3	C₂⁵×C₃	—	3	1	no	maximal
4	C₂⁴×D₃	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂³×C₃²	C₂²	1	15	yes	complemented
6	C₂²×C₃×D₃	C₂²	1	140	yes	direct product factor
7	C₂⁴×C₃	—	2	1	no	—
8	C₂⁴×C₃	—	3	30	no	—
9	C₂⁴×C₃	D₃	1	1	yes	characteristic, direct product factor
10	C₂⁴×C₃	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂³×D₃	C₂×C₃	1	30	yes	direct product factor
12	C₂²×C₃²	C₂³	1	35	yes	complemented
13	C₂×C₃×D₃	C₂³	1	120	yes	direct product factor
14	C₂⁵	—	3	1	no	Sylow
15	C₂³×C₃	—	2	15	no	—
16	C₂³×C₃	—	3	140	no	—
17	C₂³×C₃	C₂×D₃	1	15	yes	direct product factor
18	C₂³×C₃	C₂²×C₃	1	15	yes	complemented
19	C₂²×D₃	C₂²×C₃	1	140	yes	direct product factor
20	C₂×C₃²	C₂⁴	1	15	yes	complemented
21	C₃×D₃	C₂⁴	1	16	yes	direct product factor
22	C₂⁴	—	3	30	no	—
23	C₂⁴	C₃×D₃	1	1	yes	characteristic, direct product factor
24	C₂²×C₃	—	2	35	no	—
25	C₂²×C₃	—	3	120	no	—
26	C₂²×C₃	C₂²×D₃	1	35	yes	direct product factor
27	C₂²×C₃	C₂³×C₃	1	35	yes	complemented
28	C₂×D₃	C₂³×C₃	1	120	yes	direct product factor
29	C₃²	C₂⁵	1	1	yes	characteristic, complemented, Sylow
30	C₂³	—	3	140	no	—
31	C₂³	C₂×C₃×D₃	1	15	yes	direct product factor
32	C₂×C₃	—	2	15	no	—
33	C₂×C₃	—	3	16	no	—
34	C₂×C₃	C₂³×D₃	1	15	yes	direct product factor
35	C₂×C₃	C₂⁴×C₃	1	15	yes	complemented
36	D₃	C₂⁴×C₃	1	16	yes	direct product factor
37	C₂²	—	3	120	no	—
38	C₂²	C₂²×C₃×D₃	1	35	yes	direct product factor
39	C₃	—	2	1	no	—
40	C₃	C₂⁴×D₃	1	1	yes	characteristic, direct product factor
41	C₃	C₂⁵×C₃	1	1	yes	characteristic, complemented
42	C₂	—	3	16	no	—
43	C₂	C₂³×C₃×D₃	1	15	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁴×C₃	D₃
commutator, cosocle, hypocenter	C₃	C₂⁵×C₃
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃²	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂⁴×C₃

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃²	C₂	semidirect
2. C₂³×C₃×D₃	C₂	direct (N × H)
4. C₂⁴×D₃	C₃	direct (N × H)
5. C₂³×C₃²	C₂²	semidirect
6. C₂²×C₃×D₃	C₂²	direct (N × H)
9. C₂⁴×C₃	D₃	direct (N × H)
10. C₂⁴×C₃	C₂×C₃	semidirect
11. C₂³×D₃	C₂×C₃	direct (N × H)
12. C₂²×C₃²	C₂³	semidirect
13. C₂×C₃×D₃	C₂³	direct (N × H)
17. C₂³×C₃	C₂×D₃	direct (N × H)
18. C₂³×C₃	C₂²×C₃	semidirect
19. C₂²×D₃	C₂²×C₃	direct (N × H)
20. C₂×C₃²	C₂⁴	semidirect
21. C₃×D₃	C₂⁴	direct (N × H)
23. C₂⁴	C₃×D₃	direct (N × H)
26. C₂²×C₃	C₂²×D₃	direct (N × H)
27. C₂²×C₃	C₂³×C₃	semidirect
28. C₂×D₃	C₂³×C₃	direct (N × H)
29. C₃²	C₂⁵	semidirect
31. C₂³	C₂×C₃×D₃	direct (N × H)
34. C₂×C₃	C₂³×D₃	direct (N × H)
35. C₂×C₃	C₂⁴×C₃	semidirect
36. D₃	C₂⁴×C₃	direct (N × H)
38. C₂²	C₂²×C₃×D₃	direct (N × H)
40. C₃	C₂⁴×D₃	direct (N × H)
41. C₃	C₂⁵×C₃	semidirect
43. C₂	C₂³×C₃×D₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃²	2
C₂³×C₃×D₃	2
C₂⁵×C₃	3
C₂⁴×D₃	3

Subgroups — C24×C3×D3 #64395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₃×D₃ #64395