This was something I hadn’t thought much about, but I was perusing a site I found where one of the projects was to find brothers killed in the war on the same day.
To my surprise the research has turned up 300 sets of brothers. Note- this was for the UK and the Commonwealth forces so doesn’t include the USA or other military forces such as Turkey, the then Russian Empire or Germany and her allies. It does include Canada.
I suppose it is understandable that brothers would serve in the same units, and in the Navy on the same ships- if they went down their could easily be family losses. The Sullivans of the USA navy in the Second World War is an example.
There were also 3 brothers lost on the Queen Mary at Jutland. Also rather strange losses like a father and son both being killed on the same day.
It was all pretty depressing.