Application that Generates subgrouop of a group

Hello there
I have been confronted with a challenge to develop an application that generates the subgroup of a diheldra group of order 8. this is a under group theory in Abstract Algebra, mathematics.
so please i want to give it a try and see what I can do to develop it but where do I start? which platform will I use and How do I go about it
please help me thanks. I strongly belief its under the catergory of Algorithms.