We use a realistic molecular model to study the interfacial behavior of hydrocarbon sulfate surfactants within a self-consistent field model and consider the adsorption both at the air-water interface and at a hydrophobic solid-water interface. We focus on the structural properties of the hemimicelles at the critical interface aggregation concentration (CIAC) for the air-water system and the critical surface aggregation concentration (CSAC) for the solid-water system. The major difference between the two systems is that the liquid interface is penetrable but the solid surface is intrinsically impenetrable for the molecular species. At the LG interface the hemimicelles have a lens shape with their centers of mass positioned slightly toward the aqueous side and feature an aspect ratio of approximately 2, with the long dimension parallel to the interface. Hemimicelle formation occurs below a critical (interfacial) area per molecule and above a critical surface pressure depending on tail length and ionic strength. Hemimicelles are not expected at air-water interfaces for a surfactant with a tail length ( t) lower than 15 CH2 units. In contrast, at a hydrophobic solid the formation of laterally inhomogeneous micelles even takes place for surfactants with the tail length as short as t = 12. This difference is attributed to the screening of the lateral interactions in the vapor phase. The shape of surface hemimicelles is caplike (or half-lens) with an aspect ratio lower than 2 and the long dimension parallel to the solid surface. The tail length, the ionic strength, the adsorption energies, and the surfactant concentration have an effect on the surface micelle properties such as the aggregation number and size and shape.