Symmetry of molecular oligomers

Often protein molecules are composed of several identical chains arranged in a symmetrical way. Dimers usually have 2-fold rotational symmetry, trimers 3-fold rotational symmetry, while tetramers can have both 4-fold rotational symmetry (although this is unusual) and 2-fold symmetry about each of three perpendicular directions (222 symmetry, see here:

The kind of symmetry that can be possessed by a local assembly of objects are called the point groups. Because of the constraints of the crystal lattice, crystals can only accommodate certain kinds of symmetry. The only rotational symmetries which a crystal can have are 2-, 3-, 4-, and 6-fold symmetry. Therefore, there are a limited number of crystallographic point groups, and for chiral units there are 11:

1, 2, 3, 322, 4, 422, 6, 622, 222, 23, 432

For a complete list of animated point groups see this page:

When (often) oligomeric molecules crystallize with the oligomer as the repeating unit, the internal symmetry of the oligomer is not evident from the crystal symmetry. If for example trimeric subunits are arranged symmetrically about a 3-fold symmetry that does not apply to the whole crystal but only locally, then we talk about local or non-crystallographic symmetry (NCS). More on NCS here:
NCS is very common. First important task once NCS has been detected (or suspected) is to find out how subunits are arranged. For this we use the self-rotation function that allows us to determine the rotation of one subunit to another by rotating the Patterson function upon itself.