  We consider four supergravities with 16+16, 32+32, 64+64, 128+128 degrees of
freedom displaying some curious properties: (1) They exhibit minimal
supersymmetry (N=1, 2, 2, 1) but maximal rank (r=7, 6, 4, 0) of the scalar
coset in D=4, 5, 7, 11. (2) They couple naturally to supermembranes and admit
these membranes as solutions. (3) Although the D=4, 5, 7 supergravities follow
from truncating the maximally supersymmetric ones, there nevertheless exist
M-theory compactifications with G2, SU(3), SU(2) holonomy having these
supergravities as their massless sectors. (4) They reduce to N=1, 2, 4, 8
theories all with maximum rank 7 in D=4 which (5) correspond to 0, 1, 3, 7
lines of the Fano plane and hence admit a division algebra (R,C,H,O)
interpretation consistent with the black-hole/qubit correspondence, (6) are
generalized self-mirror and hence (7) have vanishing on-shell trace anomaly.
