6. Let the non-empty set $A \subseteq\{1,2,3,4,5,6,7\}$, when $a \in A$ it must also have $8-a \in A$, there are $\qquad$ such $A$.

将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。
6. 15 .

From the problem, we know that 1 and 7, 2 and 6, 3 and 5 must appear in pairs. Construct 4 sets $A_{1}=\{1,7\}, A_{2}=\{2,6\}$, $A_{3}=\{3,5\}, A_{4}=\{4\}$. The set $A$ we are looking for is formed by the union of $A_{1}, A_{2}, A_{3}, A_{4}$ or some of them. There are $C_{4}^{1}+C_{4}^{e}+C_{4}^{3}+C_{4}^{4}=2^{4}-1=15$