In the laboratory analysis of maize grains, we have the following components of dry matter:

Carbohydrates: 30.0 parts, Ash: 3.3 parts, Fibre: 13.8 parts, Protein: 1.7 parts

First, calculate the total parts of the components: \(\text{Total parts} = 30.0 + 3.3 + 13.8 + 1.7 = 48.8 \text{ parts}\)

The remainder of the dry matter is oil: \(\text{Oil parts} = 100 - 48.8 = 51.2 \text{ parts}\)

Now, to find the percentage of oil in the dry matter:

\(\text{Percentage of oil} = \left( \frac{51.2}{80} \right) \times 100 \approx 64.0\%\)

Thus, the percentage of oil in the dry matter is \( \boxed{64.0\%} \).