  The size of convective cores remains uncertain, despite its substantial
influence on stellar evolution, and thus on stellar ages. The seismic modeling
of young subgiants can be used to obtain indirect constraints on the core
structure during main sequence, thanks to the high probing potential of mixed
modes. We selected the young subgiant KIC10273246, observed by Kepler, based on
its mixed-mode properties. We thoroughly modeled this star, with the aim of
placing constraints on the size of its main sequence convective core. We first
extracted the parameters of the oscillation modes of the star using the full
Kepler data set. To overcome the challenges posed by the seismic modeling of
subgiants, we proposed a method which is specifically tailored for subgiants
with mixed modes and consists in a nested optimization. We then applied this
method to perform a detailed seismic modeling of KIC10273246. We obtained
models that show good statistical agreements with the observations, both
seismic and non-seismic. We showed that including core overshooting in the
models significantly improves the quality of the seismic fit, optimal models
being found for $\alpha_{\mathrm{ov}} = 0.15$. Higher amounts of core
overshooting strongly worsen the agreement with the observations and are thus
firmly ruled out. We also found that having access to two g-dominated mixed
modes in young subgiants allows us to place stronger constraints on the
gradient of molecular weight in the core and on the central density. This study
confirms the high potential of young subgiants with mixed modes to investigate
the size of main-sequence convective cores. It paves the way for a more general
study including the subgiants observed with Kepler, TESS, and eventually PLATO.
