The largest segmental script is probably an abugida, Devanagari. When written in Devanagari, Vedic Sanskrit has an alphabet of 53 letters, including the visarga mark for final aspiration and special letters for kš and jñ, though one of the letters is theoretical and not actually used. The Hindi alphabet must represent both Sanskrit and modern vocabulary, and so has been expanded to 58 with the khutma letters (letters with a dot added) to represent sounds from Persian and English.
The largest known abjad is Sindhi, with 51 letters. The largest alphabets in the narrow sense include Kabardian and Abkhaz (for Cyrillic), with 58 and 56 letters, respectively, and Slovak (for the Latin alphabet), with 46. However, these scripts either count di- and tri-graphs as separate letters, as Spanish does with ch and ll, or uses diacritics like Slovak č. The largest true alphabet where each letter is graphically independent is probably Georgian, with 41 letters.