The Standard Model of particle physics is a tad complicated.
Unfortunately, some folks love to make it appear even more complicated than it really is, by using a technically correct, but intentionally obfuscated representation of its Lagrangian. Yes, the model is complex but not as complex as they'd make it appear.
Following the superb book, The Standard Model, by Burgess and Moore, here is the Standard Model Lagrangian:
\begin{align*} \newcommand{\slashed}[1]{\big{/}\hspace{-6.5pt}{#1}} {\cal L}=&-\frac{1}{4}G_{\mu\nu}^\alpha G^{\alpha\mu\nu}-\frac{1}{4}W^{a\mu\nu}W_{\mu\nu}^a-\frac{1}{4}B_{\mu\nu}B^{\mu\nu}-\frac{g_3^2\Theta_3}{64\pi^2}\epsilon_{\mu\nu\lambda\rho}G^{\alpha\mu\nu}G^{\alpha\lambda\rho}\\ &-\frac{g_2^2\Theta_2}{64\pi^2}\epsilon_{\mu\nu\lambda\rho}W^{a\mu\nu}W^{a\lambda\rho}-\frac{g_1^2\Theta_1}{64\pi^2}\epsilon_{\mu\nu\lambda\rho}B^{\mu\nu}B^{\lambda\rho}-\frac{1}{2}{\overline L}_m\slashed{\rm D}L_m\\ &-\frac{1}{2}{\overline E}_m\slashed{\rm D}E_m-\frac{1}{2}{\overline Q}_m\slashed{\rm D}Q_m-\frac{1}{2}{\overline U}_m\slashed{\rm D}U_m-\frac{1}{2}{\overline D}_m\slashed{\rm D}D_m, \end{align*}
where
\begin{align*} G_{\mu\nu}^\alpha&=\partial_\mu G_\nu^\alpha-\partial_\nu G_\mu^\alpha+g_3f^\alpha_{\beta\gamma}G^\beta_\mu G^\gamma_\nu,\\ W_{\mu\nu}^a&=\partial_\mu W_\nu^a-\partial_\nu W_\mu^a+g_3\epsilon_{abc}W^b_\mu W^c_\nu,\\ B_{\mu\nu}&=\partial_\mu B_\nu-\partial_\nu B_\mu, \end{align*}
and
\begin{align*} D_\mu L_m=\partial_\mu L_m&+\left[\frac{\rm i}{2}g_1B_\mu - \frac{\rm i}{2}g_2W_\mu^a\tau_a\right]P_{\rm L}L_m\\ &+\left[-\frac{\rm i}{2}g_1B_\mu+\frac{\rm i}{2}g_2W_\mu^a\tau_a^*\right]P_{\rm R}L_m,\\ D_\mu E_m=\partial_\mu E_m&+{\rm i}g_1B_\mu(P_{\rm R}E_m)-{\rm i}g_1B_\mu(P_{\rm L}E_m),\\ D_\mu Q_m=\partial_\mu Q_m&+\left[-\frac{\rm i}{2}g_3G_\mu^\alpha\lambda_\alpha-\frac{\rm i}{2}g_2W_\mu^a\tau_a-\frac{\rm i}{6}g_1B_\mu\right]P_{\rm L}Q_m\\ &+\left[\frac{\rm i}{2}g_3G_\mu^\alpha\lambda_\alpha^*+\frac{i}{2}g_2W_\mu^a\tau_a^*+\frac{\rm i}{6}g_1B_\mu\right]P_{\rm R}Q_m,\\ D_\mu U_m=\partial_\mu U_m&+\left[-\frac{\rm i}{2}g_3G_\mu^\alpha\lambda_\alpha-\frac{2{\rm i}}{3}g_1B_\mu\right]P_{\rm R}U_m\\ &+\left[\frac{\rm i}{2}g_3G_\mu^\alpha\lambda_\alpha^*+\frac{2{\rm i}}{3}g_1B_\mu\right]P_{\rm L}U_m\\ D_\mu D_m=\partial_\mu D_m&+\left[-\frac{\rm i}{2}g_3G_\mu^\alpha\lambda_\alpha+\frac{\rm i}{3}g_1B_\mu\right]P_{\rm R}D_m\\ &+\left[\frac{\rm i}{2}g_3G_\mu^\alpha\lambda_\alpha^*-\frac{i}{3}g_1B_\mu\right]P_{\rm L}D_m. \end{align*}
What this expression represents are charged and uncharged electroweak fields and gluonic fields, along with their interactions with a family of fermions through gauge covariant derivatives. It does not explicitly account for there being three generations of fermions, though.
This representation does not include the Higgs boson and its interactions with other fields:
\begin{align*} {\cal L}_{\rm Higgs}=&-\frac{1}{2}\partial_\mu H\partial^\mu H-\lambda v^2H^2-\lambda vH^3-\frac{\lambda}{4}H^4\\ &-\frac{1}{8}g_2^2(v+H)^2|W_\mu^1-{\rm i}W_\mu^2|^2\\ &-\frac{1}{8}(v+H)^2(-g_2W_\mu^3+g_1B_\mu)^2\\ &-\frac{1}{\sqrt{2}}(v+H)[f_{mn}\bar{\cal E}P_RE_N+{\rm h.c.}]\\ &-\frac{1}{\sqrt{2}}(v+H)[g_{mn}\bar{\cal U}P_RU_N+{\rm h.c.}]\\ &-\frac{1}{\sqrt{2}}(v+H)[h_{mn}\bar{\cal D}P_RD_N+{\rm h.c.}], \end{align*}
with $v=\mu^2/\lambda$ and $H$ related to the Higgs complex scalar doublet by $\phi=[0,(v+H)/\sqrt{2}]$ in the unitary gauge.
Again, no big mystery: we just defined a scalar field with its funky Mexican hat potential, along with its symmetry-breaking and Yukawa interactions with the massive gauge bosons and charged fermions.
Omitted from this representation is any attempt to account for neutrino masses and the observed neutrino oscillations, along with neutrino handedness. Phenomenologically this could be accounted for by an explicit term involving a mass matrix, ${\cal L}_\nu=-\tfrac{1}{2}[m_{ij}(\bar{\nu}_iP_{\rm L}\nu_j)+\text{c.c.}]$ but, as Burgess and Moore explains, that's just a starting point and not a viable extension of the theory on its own right; there are several possible directions to take but no conclusive solution emerged for now.
There. Even with my (admittedly brief) explanatory comments, still occupying less screen real estate than the monstrous expression that some Internet cogniscenti love to shove under your nose to show you how stupid you are.
