Context : The solar-like pulsator HD 49385 was observed with the CoRoT Based on data obtained from the CoRoT ( Convection , Rotation and planetary Transits ) space mission , developed by the French Space agency CNES in collaboration with the Science Programs of ESA , Austria , Belgium , Brazil , Germany and Spain . satellite during 137 days .
The analysis of its oscillation spectrum yielded precise estimates of the mode frequencies over nine radial orders and pointed out some unusual characteristics : there exist some modes outside the identified ridges in the échelle diagram and the curvature of the \ell = 1 ridge significantly differs from that of the \ell = 0 ridge .

Aims : We first search for stellar models reproducing the peculiar features of the oscillation spectrum of HD 49385 .
Having shown that they can be accounted for only by a low-frequency \ell = 1 avoided crossing , we investigate the information which is brought by the mixed modes about the structure of the core of HD 49385 .

Methods : We propose a toy-model to study the case of avoided crossings with a strong coupling between the p-mode and g-mode cavities in order to establish the presence of mixed modes in the spectrum of HD 49385 .
We then show that traditional optimization techniques are ill-suited for stars with mixed modes in avoided crossing .
We propose a new approach to the computation of grids of models which we apply to HD 49385 .

Results : The detection of mixed modes leads us to establish the post-main-sequence status of HD 49385 .
The mixed mode frequencies suggest a strong coupling between the p-mode and g-mode cavities .
As a result , we show that the amount of core overshooting in HD 49385 is either very low ( 0 < \alpha _ { ov } < 0.05 ) or moderate ( 0.18 < \alpha _ { ov } < 0.20 ) .
The mixing length parameter is found to be significantly lower than the solar one ( \alpha _ { CGM } = 0.55 \pm 0.04 compared to the solar value \alpha _ { \odot } = 0.64 ) .
Finally , we show that the revised solar abundances of Asplund give a better agreement than the classical ones of Grevesse & Noels .
At each step , we investigate the origin and meaning of these seismic diagnostics in terms of the physical structure of the star .

Conclusions : The subgiant HD 49385 is the first star for which a thorough modeling was led , trying to reproduce all the properties of an avoided crossing .
It gave the opportunity to show that the study of the coupling between the cavities in these stars can provide valuable contribution to the questions of core overshooting , the efficiency of convection and the abundances of heavy elements in stars .