【Conquer】 , 【defeat】 , 【vanquish】 , 【overcome】 , 【surmount】 , 【subdue】 ,  【subjugate】 , 【reduce】 , 【overthrow】 , 【rout】 , 【beat】 , 【lick】 all mean to get the better of or to bring into subjection whether by the exercise of force or of strategy.

【Conquer】 and 【defeat】  are perhaps the most general.

【Defeat】 usually signifies merely the fact of getting the better of or winning against and may imply no more than a temporary checking or frustrating.

【Conquer】 , however, usually implies a large and significant action (as of a large force in war) or an action involving an all-inclusive effort and a more or less permanent result.

【Vanquish】 suggests a significant action of a certain dignity usually in the 【defeat】 of a person rather than a thing and usually carrying the suggestion of complete 【defeat】 .

【Overcome】  usually implies an opposing, more or less fixed obstacle to be dealt with and a high degree of effectiveness in dealing therewith whether by direct conflict or perhaps more often by indirect means (as evasion or substitution).

【Surmount】 , like 【overcome】 , implies an opposing, more or less fixed obstacle but carries the idea of surpassing or exceeding rather than overcoming in face-to-face conflict.

【Subdue】 ,  【subjugate】 , and 【reduce】 all throw emphasis upon the condition of subjection resulting from 【defeat】 .

【Subdue】 signifies to bring under control by or as if by overpowering.

【Subjugate】  signifies to bring into and keep in subjection, often as a slave is in subjection.

【Reduce】 signifies surrender and submission but usually of a town or fortress under attack or siege.

【Overthrow】 is much like  【overcome】 but carries the strong idea of disaster to the overthrown.

【Rout】 always suggests a 【defeat】 so complete as to cause flight or the complete dispersion of the opposition.

【Beat】 and 【lick】 are characteristic of a less formal style of expression or level of usage than the preceding verbs.

Both come close to 【defeat】 in meaning but distinctively 【beat】 (see also 【BEAT】 1) is rather neutral in this sense, except that occasionally it may imply the finality though not the scope of 【vanquish】 while  【lick】 usually implies a complete humbling or reduction to impotency and ineffectiveness of the one defeated.