We know that sufficient statistic is not necessarily minimal. For example, consider a random sample $X_1,\cdots,X_n \sim \text{Bernoulli}(\theta) $. It can be shown easily that both $T'(X_1,\cdots,X_n) = (X_1,\cdots,X_n)$ and $T(X_1,\cdots,X_n) = \sum_{i=1}^n X_i$ are sufficient statistic. However, $T'$ is not minimal. This is not surprising because after all, $T'$ has "more dimensions" than $T$ , and thus achieve less data reduction. More specifically, range of $T'$ is in $\mathbb{R}^n$ and range of $T$ is in $\mathbb{R}$.
In general, we consider a random sample $X_1,\cdots,X_n \sim f_X (x\mid\theta)$. Does there exist a sufficient statistic $S$ for $\theta$ such that it is sufficient, its range is in $\mathbb{R}$, but it is not minimal?