Context : 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 .

Aims : 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 .

Methods : 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 .

Results : We are sensitive to companions at separations larger than 0.1 arcsec and differences of \sim 2 magnitudes at 0.1 arcsec and \sim 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 \sim 2 arcsec from LHS 1074 .

Conclusions : We derive a binary frequency of 3 \pm 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 \pm 2.6 % ( with a 1 \sigma confidence limit ) , significantly lower than the fraction of resolved binary M dwarfs ( \sim 20 % ) over the same mass and separation ranges .
This result suggests a sharp cut-off in the multiplicity fraction from G to M subdwarfs , indicating that the metallicity plays a role at lower masses and/or an environmental effect governing the formation of metal-poor M dwarfs compared to their metallicity counterparts .