There are many different political systems, some of which can coexist, while some cannot.
Explanation:
On the political spectrum there are lot of variations and options. Some of them are democracy, monarchy, dictatorship, oligarchy, theocracy and all of them have their own unique characteristics. All of them can be divided into two broad groups, left wing and right wing political systems.
A monarchy can act as a dictatorship, and Saudi Arabia is an example of this, or it can be part of a democracy, where it usually doesn't have any real political power, like in the UK.
A dictatorship, on the other hand, can not be a democracy, as both of them are the total opposites and can not coexist.
While it is not common, there are examples, like Switzerland, where there is both representative and direct democracy. They can coexist because in principle they have the same purpose, but can only be practiced in countries that are not too populated.
An oligarchy can not include representative democracy, as they are two opposites, with the oligarchy practically being a dictatorship led by several people  or families.
A government can be a monarchy, and there are many examples of this, mostly in Arabia, but a government can not be an anarchy, as anarchy is a a system where there is no government or any authority.
The theocracy has been and still is a perfect match with the monarchy, as the goals are pretty much the same, they complement each other well, and use the same methods for control of the people. The Arab world
A theocracy, which is practically a religious dictatorship, can not coexist with the democracy, as one of them promotes freedom while the other forbids it.
An oligarchy can be a dictatorship, and in fact it pretty much always is. The only difference is that in a dictatorship there is usually only one leader, while in oligarchy there is several leaders.
