  The knowledge of the binary properties of metal-poor and solar-metallicity
stars can shed light on the potential differences between the formation
processes responsible for both types of objects.
  The aim of the project is to determine the binary properties (separation,
mass ratio, frequency of companions) for M subdwarfs, the low-metallicity
counterparts of field M dwarfs, and investigate any potential differences
between both populations.
  We have obtained high-resolution imaging in the optical for a sample of 24
early-M subdwarfs and nine extreme subdwarfs with the ``Lucky Imaging''
technique using the AstraLux instrument on the Calar Alto 2.2-m telescope.
  We are sensitive to companions at separations larger than 0.1 arcsec and
differences of ~2 magnitudes at 0.1 arcsec and ~5 mag at 1 arcsec. We have
found no companion around the 24 subdwarfs under study and one close binary out
of nine extreme subdwarfs. A second image of LHS 182 taken three months later
with the same instrument confirms the common proper motion of the binary
separated by about 0.7 arcsec. Moreover, we do not confirm the common proper
motion of the faint source reported by Riaz and collaborators at ~2 arcsec from
LHS 1074. We derive a binary frequency of 3+/-3% for M subdwarfs from our
sample of 33 objects for separations larger than about five astronomical units.
Adding to our sample the additional 28 metal-poor early-M dwarfs observed with
the Hubble Space Telescope by Riaz and collaborators, we infer a binary
fraction of 3.7+/-2.6% (with a 1 sigma confidence limit), significantly lower
than the fraction of resolved binary M dwarfs (~20%) over the same mass and
separation ranges (abridged).
