Which lower extremity muscle groups are most important to sprinting speed in an athlete? According to the research it would appear to be the hamstrings and glutes. In this article by Chris Beasley, he breaks down the studies analyzing sprinting performance.
In the study he breaks down, the authors found that the hip extensor and knee flexor muscles had the greatest workload during terminal swing. What that indicates is that these muscle groups are vital to strengthen for improved sprinting ability, according to the study.
Additionally, it was found that peak knee extension torque during stance phase of gait were not affected with increased running speed. Check out the review by Chris for more details.