Hi Mike!
According to statistics in Solar Influences Data Analysis Center (SIDC) http://sidc.oma.be/ the highest daily sunspot number reported since 1818 was 355 and occurred on 24-25 December 1957. This time was around the maximum of solar cycle 19 that had also the highest monthly sunspot number (201) since mid 1700s.
The sunspot number listed in SIDC does not indicate the number of individual sunspots but a “relative sunspot number” that takes into account the total number of individual spots, sunspot groups and efficiency of the observatory.