What will come at the place of question mark ? 2816, ? , 176, 44, 11.

The answer is $\boxed{1408}$.

The sequence is a geometric sequence with a common ratio of $\frac{1}{2}$. In other words, each term is $\frac{1}{2}$ of the term before it. Therefore, the missing term is $2816 \cdot \frac{1}{2} = 1408$.

Option A, $704$, is incorrect because it is not a multiple of $2816$. Option B, $1408$, is correct because it is a multiple of $2816$ and it is also the product of $2816$ and the common ratio, $\frac{1}{2}$. Option C, $352$, is incorrect because it is not a multiple of $2816$. Option D, $2640$, is incorrect because it is not a multiple of $2816$.