Design a dental appointment system using Python, with the following requirements.

Appointment as a super class, which contains four variables $($M$,$D$,$Y$,$Desc$)$

Three sub classes $($Month$,$ Day, Date$).$

There should be appointments already created in a list and you are simply asking the users for a date to check against them. This mean that you need to create them ahead of time. When the user tries to search by month or day, all appointments that meet on that month$/$day should print.