Any updates to A007828?

[N. J. A. Sloane]

To extend A018216  Maximal number of subgroups in a group with n
elements, is there something better for a(16) than Fisher's group G
with 35 subgroups?

a(17) is of course 2.

There are only 3 nonabelian groups of order 18. Before I count
elements, let me cry plaintively: there must be people here who've
used Sylow's theorems more recently than I have.

This is not, I think, a "hard" sequence, to any real Group Theorist.
In front of you guys, I'm not afraid to show my ignorance, but I'd be
ashamed to drive down to Caltech and ask, say, Michael Aschbacher.



I think C2^4 has 67 subgroups (1 trivial, 15 C2, 35 C2^2, 15 C2^3, 1 itself).
I would suspect that's the largest case, but I'm not in the mood to check all
14 groups of order 16 (and to dig up a description of the more obsure ones.)

------ Original Message ------
<jvospost2 at yahoo.com>
elements

> To extend A018216  Maximal number of subgroups in a group with n
> elements, is there something better for a(16) than Fisher's group G
> with 35 subgroups?
> 
> a(17) is of course 2.
> 
> There are only 3 nonabelian groups of order 18. Before I count
> elements, let me cry plaintively: there must be people here who've
> used Sylow's theorems more recently than I have.
> 
> This is not, I think, a "hard" sequence, to any real Group Theorist.
> In front of you guys, I'm not afraid to show my ignorance, but I'd be
> ashamed to drive down to Caltech and ask, say, Michael Aschbacher.
> 







Christian Bower said:
I think C2^4 has 67 subgroups (1 trivial, 15 C2, 35 C2^2, 15 C2^3, 1 itself).

Neil