Submaximal subgroup

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed submaximal if there exists an ascending chain:

$$H = H_0 \le H_1 \le H_2 \le \ldots \le H_n = G$$

where each $$H_i$$ is a maximal subgroup of $$H_{i+1}$$.

Stronger properties

 * Maximal subgroup
 * Subgroup of finite index

Weaker properties

 * Subpronormal subgroup