How program a particilar algorithm ?

[Michel Bonnifait]

Hello,
I think my question is more on programming than specifically on programming
with Python.
I want to generate all possible lists with elements from another one. For
example, from a list like [1,2,3,4] i want to program an algorithm which
will give this result
[[1,2],[1,3],[1,4],[1,2,3],[1,2,4],[1,3,4],[1,2,3,4],[2,3],[2,4],[2,3,4],[3,
4]]
It's seems to me it should be a recursive programming answer but i can't
find it.
thanks in advance for your help !