The Collaborative International Dictionary of English v.0.48:

Hierarchy \Hi"er*arch`y\ (h[imac]"[~e]r*[aum]rk`[y^]), n.; pl.
   Hierarchies (h[imac]"[~e]r*[aum]rk`[i^]z). [Gr.
   'ierarchi`a: cf. F. hi['e]rarchie.]
   1. Dominion or authority in sacred things.
      [1913 Webster]

   2. A body of officials disposed organically in ranks and
      orders each subordinate to the one above it; a body of
      ecclesiastical rulers.
      [1913 Webster]

   3. A form of government administered in the church by
      patriarchs, metropolitans, archbishops, bishops, and, in
      an inferior degree, by priests. --Shipley.
      [1913 Webster]

   4. A rank or order of holy beings.
      [1913 Webster]

            Standards and gonfalons . . . for distinction serve
            Of hierarchies, of orders, and degrees. --Milton.

   5. (Math., Logic, Computers) Any group of objects ranked so
      that every one but the topmost is subordinate to a
      specified one above it; also, the entire set of ordering
      relations between such objects. The ordering relation
      between each object and the one above is called a
      hierarchical relation.

   Note: Classification schemes, as in biology, usually form
         hierarchies.
         [PJC]

WordNet (r) 3.0 (2006):

hierarchy
    n 1: a series of ordered groupings of people or things within a
         system; "put honesty first in her hierarchy of values"
    2: the organization of people at different ranks in an
       administrative body [syn: hierarchy, power structure,
       pecking order]

Moby Thesaurus II by Grady Ward, 1.0:

193 Moby Thesaurus words for "hierarchy":
   absolute monarchy, aedileship, animal kingdom, archbishopric,
   archiepiscopacy, archiepiscopate, aristocracy, autarchy, autocracy,
   autonomy, bishopric, bureaucracy, caste, chain of being,
   chairmanship, chancellery, chancellorate, chancellorship, chiefery,
   chiefry, chieftaincy, chieftainry, chieftainship, class,
   class structure, coalition government, colonialism, commonwealth,
   condition, constitutional government, constitutional monarchy,
   consulate, consulship, continuity, deanery, degree, democracy,
   dictatorship, dictature, directorate, directorship, domain,
   dominion rule, duarchy, duumvirate, dyarchy, echelon, emirate,
   episcopacy, establishment, federal government, federation,
   feudal system, footing, garrison state, gerontocracy, governorship,
   gradation, headship, hegemony, heteronomy, hierocracy,
   higher echelons, higher-ups, home rule, kingdom, leadership,
   limited monarchy, lordship, magistracy, magistrateship,
   magistrature, management, martial law, masterdom, mastership,
   mastery, mayoralty, mayorship, meritocracy, metropolitanate,
   metropolitanship, militarism, military government, mineral kingdom,
   ministry, mob rule, mobocracy, monarchy, natural hierarchy,
   neocolonialism, nobility, ochlocracy, officialdom, oligarchy,
   order, pantisocracy, papacy, pashadom, pashalic, patriarchate,
   patriarchy, pecking order, place, police state, pontificality,
   pontificate, popedom, popehood, popeship, position,
   power structure, precedence, prefectship, prefecture, prelacy,
   premiership, presidency, presidentship, prime-ministership,
   prime-ministry, princedom, princeship, principality, proconsulate,
   proconsulship, protectorate, protectorship, provostry, provostship,
   pure democracy, pyramid, rank, rate, rating, realm, rectorate,
   rectorship, regency, regentship, representative democracy,
   representative government, republic, ruling class, ruling classes,
   seigniory, self-determination, self-government, seneschalship,
   seneschalsy, sequence, serial order, sheikhdom, sheriffalty,
   sheriffcy, sheriffdom, shrievalty, social democracy, sphere, stage,
   standing, station, status, stratocracy, subordination,
   supervisorship, suzerainship, suzerainty, technocracy,
   the Establishment, the administration, the authorities,
   the ingroup, the interests, the people upstairs, the power elite,
   the power structure, the top, thearchy, them, theocracy, they,
   top brass, totalitarian government, totalitarian regime, triarchy,
   tribunate, triumvirate, tyranny, vegetable kingdom, vizierate,
   viziership, welfare state



The Free On-line Dictionary of Computing (30 December 2018):

hierarchy

   An organisation with few things, or one thing, at the top and
   with several things below each other thing.  An inverted tree
   structure.  Examples in computing include a directory
   hierarchy where each directory may contain files or other
   directories; a hierarchical network (see hierarchical
   routing), a class hierarchy in object-oriented
   programming.

   (1994-10-11)


Bouvier's Law Dictionary, Revised 6th Ed (1856):

HIERARCHY, eccl. law. A hierarchy signified, originally, power of the
priest; for in the beginning of societies, the priests were entrusted with
all the power but, among the priests themselves, there were different
degrees of power and authority, at the summit of which was the sovereign
pontiff, and this was called the hierarchy. Now it signifies, not so much
the power of the priests as the border of power.