  The measurement of the internal rotation of post-main sequence stars using
data from space-based photometry missions has demonstrated the need for an
efficient angular momentum transport in stellar interiors. So far, no clear
solution has emerged and explaining the observed trends remain a challenge for
stellar modellers. We aim at constraining both the shape of the internal
rotation profile of six Kepler subgiants studied in details in 2014 and the
properties of the missing angular momentum transport process acting in stellar
interiors from MCMC inversions of the internal rotation. We apply a new MCMC
inversion technique to existing Kepler subgiant targets and test various shapes
of the internal rotation profile of all six original subgiants observed in
2014. We also constrain the limitations on the number of free parameters that
can be used in the MCMC inversion, showing the limitations in the amount of
information in the seismic data. First, we show that large-scale fossil
magnetic fields are not able to explain the internal rotation of subgiants,
similarly to what was determined from detailed studies of Kepler red giants. We
are also able to constrain the location of the transition in the internal
rotation profile for the most evolved stars in the available set of subgiants.
We find that some of them exhibit a transition located close to the border of
the helium core while one clearly does not. We conclude that it might be
possible that various processes might be at play to explain our observations,
but that revealing the physical nature of the angular momentum process will
require a consistent detailed modelling of all subgiants available,
particularly the least evolved. In addition, increasing the number of stars for
which such inferences are possible (e.g. with the future PLATO mission) is
paramount given the key role they play in validating transport process
candidates.
