Geodesic
Arrangement of the subgroups that contain an unramified quadratic torus in the general linear group of degree~2 over a~local number field ($p\ne2$)
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 3, Tome 211 (1994), pp. 67-79

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Let $k$ be a nondyadic local number field and let $K=k(\sqrt\omega)$ be its unramifield quadratic extension. A complete description is suggested for the intermediate subgroups of the general linear group $\mathrm{G=GL}(2,k)$ of degree 2 over the field $k$ that contain the nonsplit maximal torus $T=T(\omega)$ (i.e., the image in $\mathrm G$ of the multiplicative group $K^*$ of the field $K$ under the regular embedding). In particular, the torus $T(\omega)$ is polynormal in $\mathrm{GL}(2,k)$. Bibliography: 11 titles. 
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     author = {A. A. Bongarenko},
     title = {Arrangement of the subgroups that contain an unramified quadratic torus in the general linear group of degree~2 over a~local number field ($p\ne2$)},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {67--79},
     publisher = {mathdoc},
     volume = {211},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_211_a3/}
}
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A. A. Bongarenko. Arrangement of the subgroups that contain an unramified quadratic torus in the general linear group of degree~2 over a~local number field ($p\ne2$). Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 3, Tome 211 (1994), pp. 67-79. http://geodesic.mathdoc.fr/item/ZNSL_1994_211_a3/