# Question: 8 a make a table whose first row are the...

###### Question details

8. (a) Make a table, whose first row are the 8 elements of
D_{4} and whose 2nd row is the order of each element.

(Recall, this group is the group of symmetries of a 4-gon, a.k.a.
square.)

(b) How many subgroups of each order does the group D_{4}
have? Give a list of the orders, with multiplicity.

(c) List them all (the subgroups), from smallest order to largest
order.