We analyse the scalar potentials of maximal gauged three-dimensional supergravities which reveal a surprisingly rich structure. In contrast to maximal supergravities in dimensions D ≥ 4, all these theories possess a maximally supersymmetric (N = 16) ground state with negative cosmological constant Λ < 0, except for the SO(4, 4)² gauged theory, whose maximally supersymmetric groundstate has Λ = 0. We compute the mass spectra of bosonic and fermionic fluctuations around these vacua and identify the unitary irreducible representations of the relevant background (super)isometry groups to which they belong.

In addition, we find several stationary points which are not maximally supersymmetric, and determine their complete mass spectra as well. In particular, we show that there are analogues of all stationary points found in higher dimensions, among them are de Sitter (dS) vacua in the theories with noncompact gauge groups SO(5, 3)² and SO(4, 4)², as well as anti-de Sitter (AdS) vacua in the compact gauged theory preserving 1/4 and 1/8 of the supersymmetries. All the dS vacua have tachyonic instabilities, whereas there do exist nonsupersymmetric AdS vacua which are stable, again in contrast to the D ≥ 4 theories.