quantum mechanics - $SO(4,2)$ symmetry of the hydrogen atom

The hydrogen atom with Hamiltonian obviously has $SO(3)$ symmetry since it just depends on the radius.

$$H = \frac{\mathbf{p}^2}{2m} - \frac{k}{r}$$

This is generated by angular momentum $\mathbf{L} = \mathbf{r}\times \mathbf{p}$.

In quantum mechanics class we learn there is $SO(4)$ symmetry due to the Runge-Lenz vector:

$$\mathbf{A}= \frac{1}{2m}(\mathbf{p} \times \mathbf{L} - \mathbf{L} \times \mathbf{p}) - k \frac{\mathbf{r}}{r}$$

Even classical symmetry like gravity has this kind of symmetry.

I remember reading one time there is even greater symmetry for hydrogen atom. Possibly $SO(4,2)$ as in this article by Hagen Kleinert.

Has anyone heard of this?

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How can one see that the Hydrogen atom has $SO(4)$ symmetry?