How to replace the number of each element of a matrix with a subscript?

I want to get the matrix as Figure 2. There should be two ways to achieve the result.

  1. There is a matrix as Figure 1, and change it to the form of Figure 2.

  2. Generating the matrix as Figure 2 directly.

How can I do it? Thanks.

Noteļ¼šThe matrix in Figure 2 is a symmetric matrix

Figure 1

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Figure 2

enter image description here

Codes

{{C11,C12,C13,C14,C15,C16},{0,C22,C23,C24,C25,C26},{0,0,C33,C34,C35,C36},{0,0,0,C44,C45,C46},{0,0,0,0,C55,C56},{0,0,0,0,0,C66}}