Mode always contain the median?

No. Mode and median are two different descriptive statistics.

The mode is the value that occurs most often. The median is the middle value (the value below which 50 % of the cases lie and above which 50 % of the cases lie). Here is an example. Consider the set of data. 2,3,3,5,5,5,6,8,10 3 occurs most often (3 times), Jeune mannequin so 3 is the mode.

5 is the median. There are 4 cases below 5 and 4 cases above 5.