A cracked Esrog:
Crack on the length: A cracked Esrog is only invalid if all the following apply:
- The crack reaches from to top to bottom
- The depth of the crack is at least majority of the thick white flesh.
If the crack is not this deep throughout the entire length, but rather only in the middle, and the top and bottom of the crack is not this deep, the Esrog is Kosher. [Vetzaruch Iyun if only the top or bottom side is this deep and not the other.]
Crack in width: If there is a crack along the circumference of the Esrog then if there are two cracks, one on each side of the Esrog parallel to each other, than if there remains an un-cracked area between the two cracks the Esrog is valid. This applies even if the depth of the crack is majority of the width of the white thick peel. [If however a single crack carries through majority of the circumference it is implied from Admur that the Esrog is invalid.]
 Source of these invalidations: All of these invalidations of a hole, and crack is not due to Hiddur but rather because the Esrog is not considered Tam [complete] and the Torah states “Ulikachtem” and the Sages expounded this to mean a full and complete taking. [648/14]
 648/14; See Arba Haminim p. 156