Flying the F-105 Thunderchief from Yokota in the mid-60’s, the 6441st was one of the first USAF units to deploy to Vietnam. If the patch design looks like the more familiar 347th Tactical Fighter Wing that is because it is they who were created from units of the 6441st; the 347th simply continued the patch.
Note: As any student of USAF history can attest, four digit units (like the 6441st) are deemed “temporary” and therefore carry no permanent lineage. Researching them is always a challenge.