Introduction:
A Trie, also known as a prefix tree, is a tree-based data structure that is commonly used for efficient string storage and retrieval operations. It is particularly useful when dealing with large sets of strings where common prefixes occur frequently. The Trie organizes strings in a way that allows for fast searching, insertion, and deletion operations.

Operations supported by a Trie:
1. Insertion of a string: A Trie is typically used for efficient insertion of strings. Each character in the string is sequentially inserted into the Trie, creating new nodes as necessary. The last node representing the last character of the string is marked as a terminal node to indicate the end of the string.

2. Deletion of a string: Trie data structure supports the deletion of a string. To delete a string, we start from the root and traverse down the Trie until we reach the last character of the string. We then mark the terminal node for that character as non-terminal, effectively deleting the string from the Trie.

3. Search for a string: Trie supports efficient searching of strings. Starting from the root, we traverse down the Trie, character by character, following the path corresponding to the input string. If we successfully reach the end of the string and the last character's node is marked as a terminal node, it means the string is present in the Trie.

Operation NOT typically supported by a Trie:
4. Sorting the strings in lexicographic order: Tries are primarily designed for efficient retrieval, insertion, and deletion operations, rather than sorting. While it is possible to retrieve all strings stored in a Trie in lexicographic order, it is not an inherent property of the data structure. Sorting the strings in lexicographic order would require performing an additional sorting step after retrieving all the strings from the Trie.

Conclusion:
In conclusion, the operation that is NOT typically supported by a Trie is sorting the strings in lexicographic order. Tries excel at efficient string insertion, deletion, and retrieval operations, but sorting requires an additional step beyond the Trie's main purpose.