This element is 啇, U+5547 in Unicode, and it is used primarily for its sound テキ in these kanji. It is hardly used as a character on its own in Japanese, but you should be able to find it listed in larger 漢和辞典.
In 新漢語林, for example, this character is listed under the radical 口 plus 8 strokes (11 total) with the following meanings:
The former meaning is presumably what semantic sense, if any, can be found in characters containing 啇 as an element.
In Henshall's book A Guide to Remembering Japanese Characters, he says this character means 'base; starting point' (p.236) as part of other characters. Wiktionary lists its meanings in English as 'stem; root'.
Henshall suggests that 啇 is a variant form of 啻, but he says the origin of this character is unclear. It seems that the top part is 帝 'emperor/altar', and the bottom part is 口, which may represent a block at the bottom of the altar; or 口 may represent 'mouth/say', the compound giving 'emperor's words', which were seen as the basis or starting point of all actions, hence 'starting point'. These are just theories, and I'm not sure which if either is correct.
Note that in addition to the 漢音 reading テキ, this character also has the 呉音 reading チャク, which you can see mainly in the derived character 嫡, as in the word 嫡子 (read ちゃくし).