According to RFC 4288 “Media Type Specifications and Registration Procedures”, type (eg. “application”) and subtype (eg “vnd…”) both can be max 127 characters. So including the slash, the maximum length is 255.
Edit: Meanwhile, that document has been obsoleted by RFC 6838, which does not alter the maximum size but adds a remark:
Also note that while this syntax allows names of up to 127
characters, implementation limits may make such long names
problematic. For this reason,<type-name>and<subtype-name>SHOULD
be limited to 64 characters.