The rotational characteristics of the solar photospheric magnetic field at four flux ranges are investigated together with the total flux of active regions (MFar) and quiet regions (MFqr). The first four ranges (MF1-4) are (1.5-2.9) × 1018, (2.9-32.0) × 1018, (3.20-4.27) × 1019, and (4.27-38.01) × 1019, respectively (the unit is Mx per element). Daily values of the flux data are extracted from magnetograms of the Michelson Doppler Imager on board the Solar and Heliospheric Observatory. Lomb-Scargle periodograms show that only MF2, MF4, MFqr, and MFar exhibit rotational periods. The periods of the first three types of flux are very similar, i.e., 26.20, 26.23, and 26.24 days, respectively, while that of MFar is longer, 26.66 days. This indicates that active regions rotate more slowly than quiet regions on average, and strong magnetic fields tend to repress the surface rotation. Sinusoidal function fittings and cross-correlation analyses reveal that MFar leads MF2 and MF4 by 5 and 1 days, respectively. This is speculated to be related with the decaying of active regions. MF2 and MFar are negatively correlated, while both MF4 and MFqr are positively correlated with MFar. At the timescale of the solar activity cycle, MFar leads (negatively) MF2 by around one year (350 days), and leads MF4 by about 3 rotation periods (82 days). The relation between MF2 and MFar may be explained by the possibility that the former mainly comes from a higher latitude, or emerges from the subsurface shear layer. We conjecture that MF4 may partly come from the magnetic flux of active regions; this verifies previous results that were obtained with indirect solar magnetic indices.