Most special fares (referred to as subclasses, since they are subclasses of the Coach class) are coded using other letters, such as M, B, H, K, Q, L, V, etc. Each airline generally has a hierarchical structure for the subclass codes - e.g. on one airline the order is generally MBHVQL, where M is usually close to a full Y fare and L is usually a deeply discounted fare. The hierarchical structure varies however from airline to airline (e.g. on another airline M may be heavily discounted).
When checking whether a particular flight is available, what you really want to know is what classes are available? If you are looking for a low fare requiring booking in Q class, then you must find a flight for which Q class is available. If Q class is sold out on that flight, then you will have to pay a higher fare to take that flight, or choose another flight.