Question

Let D(subscript12) = (x,y : x^2 = e ; y^6 = e ; xy =(y^-1) x)
a) Which of the following subsets are subgroups of D(subscript12) ? Justify your answer.
i) (x,y,xy,y^2,y^3,e) ii) (xy,xy^2,y^2^e) iii) (x,y^3,xy^3,e)