Does there exist a positive integer which is a power of two, such that by rearranging it's digits we can get another power of two?

Question

Does there exist a positive integer which is a power of two, such that by rearranging it's digits we can get another power of two? I know a quite good solution, that involves working with sum of digits, which is the same after rearrangement and seeing it in modulo 9, ... e.t.c Maybe someone can come up with another method of solution, which is shorter. Anyway want to see any other methods than my.