  Symmetry energy is an important part of the equation of state of isospin
asymmetry matter. However, the huge uncertainties of symmetry energy remain at
suprasaturation densities, where the phase transitions of strongly interacting
matter and the quark matter symmetry energy are likely to be taken into
account. In this work, we investigate the properties of symmetry energy by
using a hybrid star with the hadron-quark phase transition. The interaction
among strange quark matter (SQM) in hybrid stars is based on a 3-flavor NJL
model with different vector and isovector channels, while the equation of state
(EOS) of the nuclear matter is obtained by considering the ImMDI-ST interaction
by varying the parameters x, y, and z. Our results indicate that the various
parameters and coupling constants of the interactions from the ImMDI-ST and NJL
model can lead to widely different trends for the symmetry energy in the
hadron-quark mixed phase and the different onsets of the hadron-quark phase
transition. In addition, it has been found that the radii and tidal
deformabilities of hybrid stars constrain mostly the density dependence of
symmetry energy while the observed maximum masses of hybrid stars constrain
mostly the EOS of symmetric nuclear and quark matter.
