Generate all permutations of a list and permutations of the possible lists within that list?

Your expected result does not contain all possible permutations, so not sure this is what you want, or you missed some. But to get all possible permutations of a list of different lengths, you can do as follows:

from itertools import permutations
a_list = [1,2,3]
perm_list = [p for l in range(1, len(a_list)+1) for p in permutations(a_list,l)]
print(perm_list)

The result is:

[(1,), (2,), (3,), (1, 2), (1, 3), (2, 1), (2, 3), (3, 1), (3, 2), (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1)]

If the input list is large though, probably it would be better to use generator expression, e.g.

perm_list_gen = (p for l in range(1, len(a_list)+1) for p in permutations(a_list,l))
print(perm_list_gen)
#prints:  <generator object <genexpr> at 0x7f176bbd88b8>

And than just go one by one, instead of everything at once:

for perm in perm_list_gen:
    print(perm)

from itertools import permutations
lst = [1, 2, 3]
per = list(permutations(lst, 1)) + list(permutations(lst, 2)) + list(permutations(lst, 3))

output:

>>> [(1,), (2,), (3,), (1, 2), (1, 3), (2, 1), (2, 3), (3, 1), (3, 2), (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1)]