The Combine Symbol
The Combine Empire doesn't seem to be in its own control, it seems to be controlled by the Universal Union and its leaders, the Advisors.
It also doesn't seem to have perfect portal technology. The Combine technology and their military forces can be teleported into different universes, yet they cannot teleport from one place in a universe to another place in the same universe, meaning that they can only move from places on planets to other planets and between planets themselves via vehicles. That is possibly the reason of why they want to get a hold of the Borealis, an Aperture Science vessel that might contain better portal technology.