Find a subgroup H of sigma_8 ( permutation of {1,2,.......,8} ) such that

H =~ Q_8 ( H is isomorphic to the quanternion group of 8)

This is what I do:

Draw the table of Q_8, and find the elements of the group, they are:

. I dont know how to find the subgroup H.1 , -1 , i , -i , k, -k , j ,-j

Can somebody please show me what i should do next in order to find the subgroup H?

Thanks very much for your replies