documentclass[11pt]{article}
usepackage{caption}
usepackage{subcaption}
DeclareCaptionSubType*[arabic]{table}
captionsetup[subtable]{labelformat=simple,labelsep=space}

begin{document}

begin{table}[ht]
begin{subtable}{.5textwidth}
centering
$begin{array}{ | c | c | c | c | } hline
ast & ast & ast & ast \ hline
ast & ast & ast & ast \ hline
ast & ast & ast & ast \ hline
ast & ast & ast & ast \ hline
end{array}$
subcaption{Subtable 1}
label{lab1}
end{subtable}
begin{subtable}{.5textwidth}
centering
$begin{array}{ | c | c | c | c | } hline
ast & ast & ast & ast \ hline
ast & ast & ast & ast \ hline
ast & ast & ast & ast \ hline
ast & ast & ast & ast \ hline
end{array}$
subcaption{Subtable 1}
label{lab2}
end{subtable}
caption{Sub Tables}
label{lab3}
end{table}

end{document}

DeclareCaptionSubType*[alph]{table}

renewcommand{arraystretch}{2}

documentclass[11pt]{article}
usepackage{caption}
usepackage{subcaption}
DeclareCaptionSubType*[alph]{table}
captionsetup[subtable]{labelformat=simple,labelsep=space}
usepackage{array}
usepackage{bigstrut}

begin{document}


begin{table}[ht]
begin{subtable}{.5textwidth}
centering
$begin{array}{ | c | c | c | c | } hline
 parbox[c][3cm][b]{3cm}{$ast$} & ast & ast & ast bigstrut\ hline
ast & ast & ast & ast \ hline
ast & ast & ast & ast \ hline
ast & ast & ast & ast \ hline
end{array}$
subcaption{Subtable 1}
label{lab1}
end{subtable}
begin{subtable}{.5textwidth}
centering
renewcommand{arraystretch}{2}
$begin{array}{ | c | c | c | c | } hline
ast & ast & ast & ast \ hline
ast & ast & ast & ast \ hline
ast & ast & ast & ast \ hline
ast & ast & ast & ast \ hline
end{array}$
subcaption{Subtable 1}
label{lab2}
end{subtable}
caption{Sub Tables}
label{lab3}
end{table}

end{document}

newcommand{mycell}[1]{parbox[c][3cm][c]{3cm}{centering #1}}

mycell{$ast$}