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Presidential line of succession is;
1) V.President,
2) Speaker of the House of Representatives,
3) President Pro-Tempore of the U.S.Senate,
-—Cabinet Level (Oldest to Newest Dept.s)
4) Secretary of State,
5) Secretary of the Treasury,
6) Secretary of Defense,
7) Attorney General,
8) Secretary of the Interior,
9) Secretary of Agriculture,
10) Secretary of Commerce,
11) Secretary of Labor,
12) Secretary of Health and Human Services,
13) Secretary of Housing and Urban Development,
14) Secretary of Transportation,
15) Secretary of Energy,
16) Secretary of Education,
17) Secretary of Veterans Affairs,
18) Secretary of Homeland Security.

So which post be he? Agriculture?

According to Wikipedia: In the United States, a designated survivor (or designated successor) is an individual in the presidential line of succession, usually a member of the United States Cabinet, who is arranged to be at a physically distant, secure, and undisclosed location when the President and the country's other top leaders (e.g., Vice President and Cabinet members) are gathered at a single location, such as during State of the Union addresses and presidential inaugurations. This is intended to maintain continuity of government in the event of a catastrophic occurrence which kills many officials in the presidential line of succession. Were such an event to occur, killing both the President and Vice President, the surviving official highest in the line, possibly the designated survivor, would become the Acting President of the United States under the Presidential Succession Act.

The practice of naming a designated survivor originated during the Cold War amid fears of a nuclear attack. Only Cabinet members who are eligible to succeed to the presidency (i.e., natural-born citizens over the age of 35) are chosen as designated survivors. For example, Secretary of State Madeleine Albright was not a natural-born citizen (having emigrated to the United States at age 9 from Czechoslovakia) and was thus skipped in the official line of presidential succession. The designated survivor is provided presidential-level security and transport for the duration of the event. An aide carries a nuclear football with them. However, they are not given a briefing on what to do in the event that the other successors to the presidency are killed.

So, to answer your question, I imagine that anyone after the Sec. of Labor is open to be the 'designated survivor' There was one time when Hillary was Secretary of State where she was also out of the country in London at a conference. They had a DS for that event as well, but if something happened, Clinton would have gotten the nod over the DS because her position was higher up the line of succession.