The prefix super- means larger, bigger, better, higher, or greater. Almost always this prefix is used without hyphens, unlike the prefix self-.
Supra-, unlike hypo- and hyper-, is not an exact opposite of super-. In some cases, it has the same meaning and acts as a synonym, usually for words where the supra- formation exceeds the super- in popularity. Another definition of supra- is that the modified object rises above those around it or those before it.
It should be noted that there are some words that still use a hyphen in their spelling with the supra- prefix. It’s always good to double-check a dictionary if in doubt.
Some confusion arises because super and supra can be used as adjectives without being prefixes. Supra is rare, but it means to be mentioned above or earlier in the text. Super means exactly the same as its prefix form, bigger or better or greater in some way. People sometimes put a hyphen between super and the noun it modifies. Probably because they are torn between wanting to use super as a prefix and also knowing that whatever word they are forming is not a recognized term in the dictionary.
However, hyphens are generally out of favor and fading from general use. They should not be added to words modified by super.
The single exception to the above rule is the term super-duper.
The yuan reform was in line with Beijing’s strong wish that the International Monetary Fund include the yuan in October as a new reserve currency in its Special Drawing Rights, a supranational currency basket consisting of the US dollar, pound sterling, yen and euro. [South China Morning Post]
As we explain in Bain & Company’s Global Private Equity Report 2015, the conditions that made it possible for top PE fund managers to cruise from success to success have washed away in a flood of money-chasing assets in today’s world of superabundant capital. [Forbes]