The minimum and maximum LOD (mip) supported for specific game TextureGroups is defined in a number of engine configuration files.
The source set of configuration settings files is located in the [Unreal Engine 4 Install Location]\Engine\Config\BaseEngine.ini file under the [SystemSettings] section.
For developing games, the [your_game]\Config\DefaultEngine.ini file also contains a mirror set of the base properties in the Engine\Config\ folder and should be the copy that is normally modified for your game's specific settings.
Note that there are independent sets of TextureGroup entries for the Unreal Editor and in-game. These two sets are respectively located in the [SystemSettingsEditor] and [SystemSettings] sections in the config files.
The TextureGroup settings entries in the BaseEngine.ini file will look similar to this. Note that older QA versions may not include the MinMagFilter and MipFilter properties for each setting.