The formal State consists of Elected Officials, but political authority and government decision-making power is also exercised by the Military and Intelligence "services" and the central Law Enforcement agency. One special cartel enforcement agency is the Central Bank (the Fed), which maintains the State's money monopoly. All other power-wielding government employees and agents are subsumed under Technocracy, including bureaucrats in federal courts (e.g. Supreme Court justices), tax/extortion agents (IRS), and the various trade cartel enforcers ("regulatory" agencies).
The Elected Officals are not necessarily the most powerful. For example, most foreign policy is driven by the military and intelligence branches, which are often at odds with one another. Sometimes the executive ruler (president) plays these two blocs against each other to protect his own power. For example, the US ruler Trump cozied up to the military bloc, adopting their policies, after the intelligence bloc attempted to subvert his regime.
The law enforcement bloc tends to be in a coalition with the military bloc, benefitting from both retired military personnel and gifts of military-grade weapons, surveillance devices, and equipment. The technocracy bloc, on the other hand, is more likely to receive aid from the intelligence community.
Special interests lobby all of these blocs. Some of the major special interests are: big environment, the munitions industry (military industrial complex), the prison industrial complex, authoritarian moralist groups of both "right" and "left" such as anti-abortionists, anti-immigrationists, gun-grabbers, and social justice warriors. Also, there is lobbying by foreign States, such as Israel through its AIPEC lobby. Finally, there are those firms (political or crony capitalist) which lobby for special favors, such as barriers for competitors and government contracts.
In some cases, it can be hard to draw a line between blocs of the Deep State and lobbies for special interests. For example, the banking industry has been cartelized for over a century, with the Central Bank substantially determining how much profit subordinate banks make, through policy, regulation, and fiat money-creation. Is an association of underling banks trying to influence the Central Bank a faction of the Money bloc, or is it a lobby?
The Deep State is not a secret. You don't have to be an anarchist to see its danger. Eisenhower called it "the military industrial complex" in 1961. Kennedy talked about it the same year.
It is a system which has conscripted vast human and material resources into the building of a tightly knit, highly efficient machine that combines military, diplomatic, intelligence, economic, scientific and political operations. Its preparations are concealed, not published. Its mistakes are buried, not headlined. Its dissenters are silenced, not praised. No expenditure is questioned, no rumor is printed, no secret is revealed. - John F. Kennedy
When even the most ardent statists worry about the Deep State, there might be something to it.
There is another point of view popular among "conspiracy theorists" which claims that formal rulers do not matter, and everything is run by a cabal of rich families, or an Occultocracy, or the Khazarian Mafia, or even "white hat" or "black hat" aliens from outer space. These views ignore the fact that the government has virtually all the guns, so other entities can only rent power and privilege from the State. At right is an example of that view.
Those rich guys only have the power they can purchase from States - i.e. formal rulers and bureaucrats. Without a State, they would either go broke, or at the very least have their volence-based political power eliminated and transmogrified into the good kind of power - economic power. These rich political sucklings are merely buyers of government power. No government - no power to buy.