The functional group that is nonpolar among the options given is the methyl group. Methyl groups consist of carbon and hydrogen atoms and do not have significant electronegativity differences that would create a dipole moment, making them nonpolar.
In contrast, the carbonyl, sulfhydryl, and hydroxyl groups have polar characters due to the presence of more electronegative atoms (like oxygen and sulfur) bonded to carbon, which can create polar covalent bonds.