Is a Corporal higher in rank than a Captain?

No, Corporals are non-commissioned officers (NCOs) commanding small units of men and usually quite junior (see exceptions below)

A Captain is a commissioned officer, typically in charge of a larger company of men.

In the Royal Marines and most regiments of the British Army a lance corporal is the second lowest rank, wears a single chevron on one or both arms and is and lowest ranking non-commissioned officer. A corporal is the next rank up, wears two chevrons and ranks below sergeant. The rank is also used at the same level in the RAF.

While duties may vary, in the infantry a corporal typically commands a section of eight soldiers including himself. The section may be divided into two units of four men Called as fireteams. A team known as Charlie will be commanded by the corporal and Delta commanded by a lance corporal.

In the Royal Artillery, the two ranks are instead known as lance bombardier and bombardier

The Household Cavalry made of the Blues & Royals and Lifeguard Regiments uses lance corporal and lance corporal of horse. As it has no sergeants, it also uses corporal of horse in place of sergeant, staff corporal in place of staff/colour sergeant in place staff corporal. Similarly, "corporal major" is used in some of the job titles of Warrant Officers where "Sergeant Major" would be used in the rest of the British Army.

A Captain in most armies is the third officer ran up after second lieutenant and lieutenant (first lieutenant in the US Military) and may command a company of soldiers (below or above around 100).

A Captain in the Navy is both: a more senior rank (equivalent to an army colonel, which is three ranks above an army captain) and the title of any officer while he is in command of a vessel.

Captain derives from the Word "Capo" which is head in Latin

Corporal comes from the Latin for "Corpus" meaning body. It is not agreed whether this came from the more senior soldiers appointed as body guards or the more figurative sense that they led 'a body of soldiers'

Army/Marine ranks in descending order:

Generals:

Five star ranks such as Field Marshal (UK) or General of the Army (US)

General (Commands an Army)

Lieutenant General (commands a Corps)

Major General (commands a Division)

Field Officers:

Brigadier (or Brigadier General in some countries) (commands a Brigade)

Colonel (traditional Regiment commander (now likely to serve as a staff officer)

Lieutenant Colonel (Commander of a Regiment in modern British Army)

Major

Company Officers:

Captain

Lieutenant (UK) 1st Lieutenant (US)

2nd Lieutenant

NCOs (British Army most regiments):

Warrant Officer class 1

Warrant Officer class 2

Warrant officers of both grades are known instead by job titles such as

Regimental Sergeant Major, Quartermaster Sergeant, Conductor etc.

Staff/Colour Sergeant

Sergeant

Corporal

Lance Corporal

Below NCOs:

Private - or any other regiment-specific title such as Gunner, Sapper, Trooper etc.