Cool subdwarfs are the oldest members of the low-mass stellar population. Mostly present in the galactic halo, subdwarfs are characterized by their low-metallicity. Measuring their binary fraction and comparing it to solar-metallicity stars could give key insights into the star formation process early in the Milky Way's history. However, because of their low luminosity and relative rarity in the solar neighborhood, binarity surveys of cool subdwarfs have suffered from small sample sizes and incompleteness. Previous surveys have suggested that the binary fraction of red subdwarfs is much lower than for their main-sequence cousins. Using the highly efficient Robo-AO system, we present the largest high-resolution survey of subdwarfs, sensitive to angular separations ({rho}>=0.15") and contrast ratios ({Delta}_mi_<=6) invisible in past surveys. Of 344 target cool subdwarfs, 43 are in multiple systems, 19 of which are newly discovered, for a binary fraction of 12.5+/-1.9%. We also discovered seven triple star systems for a triplet fraction of 2.0+/-0.8%. Comparisons to similar surveys of solar-metallicity dwarf stars gives a ~3{sigma} disparity in luminosity between companion stars, with subdwarfs displaying a shortage of low-contrast companions. We also observe a lack of close subdwarf companions in comparison to similar-mass dwarf multiple systems.