2018 AMC 12A Problem 15

A scanning code consists of a 7 \times 7 grid of squares, with some of its squares colored black and the rest colored white. There must be at least one square of each color in this grid of 49 squares. A scanning code is called \textit{symmetric} if its look does not change when the entire square is rotated by a multiple of 90 ^{\circ} counterclockwise around its center, nor when it is reflected across a line joining opposite corners or a line joining midpoints of opposite sides. What is the total number of possible symmetric scanning codes?

\textbf{(A)} \text{ 510} \qquad \textbf{(B)} \text{ 1022} \qquad \textbf{(C)} \text{ 8190} \qquad \textbf{(D)} \text{ 8192} \qquad \textbf{(E)} \text{ 65,534}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.