If hierarchy is a group of people exercising authority then in the Roman Catholic Church it is distributed amongst the bishops, priests and the deacons. The bishops clamour the highest authority and the deacons and the priests are their assistants.
The body of bishops are considered the successors of the apostles and they are the ones who have attained the highest form of priesthood and they comprise of the pastors of the Church or rather are the Church representation. Primarily a bishop controls the diocesan ordinaries and they meet up on a regular basis to discuss the current issues. The Liturgy or certain decisions of the Church are an exclusive agenda of these meetings. The bishops are normally ordained by another three, though only a single validity is good enough. Various ranks are distinguished amongst bishops where Pope is the head.
The Pope is the bishop of Rome and the direct successor of St Peter. He is reliable in matters like morals and faith. Also known as the Vicar of Christ he is but not an absolute authority and cant issue decrees whimsically. The Vatican City is the home of the Pope and the rules that govern his election procedure is found in the apostolic constitution. He definitely has the option of resigning too.
Patriarchs are the heads of particular autonomous churches who in turn consists of local churches under their periphery. They have complete authority over the bishops and the metropolitans of that particular church.
The autonomous churches are led by a major archbishop. Barring a few exceptions his functions are similar to that of a patriarch.
They are the princes of the Church and are appointed by the Pope himself. Generally they are the bishops heading departments of important Episcopal sees and as a group they advise the Pope and are also eligible to elect Pope’s successor in case of his death or resignation. The cardinalate is more of an honorific distinction and not an essential part of the theological structure of the Catholic Church.
Primate is a Latin Church title and in some countries is given to bishops of a particular metropolitan. This title is allotted to the ordinary of the archdiocese of the country.
A Latin church composed of several dioceses has a Bishop who is called a Metropolitan. He gets the pallium from the Pope symbolising his office. With limited oversight authority, this Metropolitan is also known as archbishop.
This title is held by bishops heading metropolitan sees and also by those heading archdioceses that aren’t either.
Though they don’t hold major titles like that of the Archbishop or Metropolitan but he surely is the centre of unity for his eparchy or diocese. He is not delegated by the Pope, instead he teaches, governs and sanctifies responsibility.
Administering most of the sacraments, he can belong to any of the religious orders like Baptism or Eucharist and is committed to serve any congregation.
In the transitional stage, he is a seminarian and is studying for priesthood and a permanent one can be married too. He normally assists a priest.