Saying he never showed Aizen his second release, does not mean that Aizen did not only know about it, but most likely talked to Ulquiorra about it at some point, we have seen that while at times Aizen can get very arrogant at times, like in his final fight with Ichigo, he is a genius.
He would have figured out that while soul reapers have their skikai and bankai, arrancars would most likely be able to have their own version of bankai, just as their first release is similar to a soul reapers shikai. The way Ulquiorra spoke when he said he never showed Aizen his 2nd release was vague, as he didn't exactly have to show Aizen his power, but he might have told him and made a plan with Aizen to keep it hidden from Gin, Tosen, and the other espada in case they rebelled, much like how Nel regained her power as an espada and starting to fight, and how Grimmjow went against orders to fight Ichigo, except to a more extreme level like a full scale rebellion. Aizen had rarely fought, at first having his espada fight for him.
If most of the espada went into full scale rebellion and if he knew about Ulquiorra's second release before hand, he would be able to send Ulquiorra out to deal with the treasonous espada and end them. It would not be that far fetched, considering the fact that Aizen seemed to hold a special trust in Ulquiorra that he didn't have for the other espada, sending Ulquiorra with Yammy to the world of the living, sending Ulquiorra to get Orihime after letting him trick the treasonous arrancars to steal a fake hogyoku only to get killed in the world of the living, entrusting care of Orihime to Ulquiorra, and lastly ensuring the safety of Los Noches to Ulquiorra.
It's possible that he would have also used Ulquiorra to kill Tosen or Gin if they rebelled, sense Ulquiorra's second resurrection was powerful enough to completely stomp Ichigo when he was using bankai and hollowfication. And as several others have said, it is most likely that Ulquiorra was just the first espada to discover and use the second release, Aizen not revealing to other arrancars, or even just the other espada, that it is possible for them to do this as they all seemed to be more loyal to their fraccion or to more loyal to themselves, unlike Ulquiorra who seemed to not only have no faccion, but never wavered in his loyalty to lord Aizen, you could say that in comparison that Ulquiorra is like the perfect soldier.
Not to mention IF Ulquiorra did aspire to rebel against Aizen and take his place, he most likely could have done so before Aizen was able to finally use the hogyoku. Not only is Ulquiorra already an expert in sonido and extremely fast without any form of release, in his second release he got faster, more agile, stronger. If he truly wished to rebel against Aizen, sense as far as we know Aizen actually never showed the espada his zanpakto, he could have completely blind-sided Aizen when ever he pleased, releasing his second release and using a grand rey cero while in his second release.
If he did this quick enough he would have been able to completely destroy Aizen, as we saw how powerful Grimmjows ceros were when he was just using the standard at point blank range and without his first release, Grimmjow not being as strong as Ulquiorra and with Ulquiorras power being enhanced with the second release, a grand rey cero at point blank range in his second release and if Ulquiorra put everything he has into it, if Ulquiorra was able to do this and blindside Aizen, well Aizen would have had no chance to survive it. And the fact is, Ulquiorra is very intelligent and would most likely realize that if he wanted, he could kill Aizen if he did blind-side him. But he didn't and was trusted with many responsibilities that the other espada weren't.
In conclusion, yes, Aizen more then likely knew about it and talked to Ulquiorra about it, deciding to keep it between themselves, yet would keep Ulquiorra at number 4 sense it would seem strange if the 5th best espada, I say fifth because while Ulquiorra was numbered at 4 the numbering system for espada was 0-9. Even the image above "Aizen-sama has not seen me in this form", the wording meaning that while Aizen has literally not been shown the second release Ulquiorra most likely talked to him about it, its possible that Aizen is even the reason that Ulquiorra got his second release before the other espada and another reason why Ulquiorra could be so loyal to him. Sorry for the very long answer.