Let us first have a direct literal translation of 1 Cor 15:24-28:
 ειτα το τελος οταν παραδω την βασιλειαν τω θεω και πατρι οταν καταργηση πασαν αρχην και πασαν εξουσιαν και δυναμιν  δει γαρ αυτον βασιλευειν αχρις ου αν θη παντας τους εχθρους υπο τους ποδας αυτου  εσχατος εχθρος καταργειται ο θανατος  παντα γαρ υπεταξεν υπο τους ποδας αυτου οταν δε ειπη οτι παντα υποτετακται δηλον οτι εκτος του υποταξαντος αυτω τα παντα  οταν δε υποταγη αυτω τα παντα τοτε και αυτος ο υιος υποταγησεται τω υποταξαντι αυτω τα παντα ινα η ο θεος τα παντα εν πασιν
 and then [it is] the end, when [he] delivers up the kingdom to the God and father when [he] puts away every principality and every authority and power.  For [it] must [be] [that] he reigns until when [he] shall put all the enemies under his feet.  [The] last enemy, death, is put away.  For "[he] subjected all [things] under his feet", but when [it] says that all [things] have been subjected, [it] [is] evident that [it] [is] except the [one] who subjected all [things] to him.  Moreover when all [things] are subjected to him, then also the son himself will be subjected to the [one] who subjected all [things] to him, so that God may be all in all.
There are a number of notable points here.
Firstly, it not only explicitly says that God subjected "all things" to Christ Jesus, but also explicitly says that this "all things" does not refer to literally all things but evidently excludes God. Secondly, it explicitly says that Christ will at the end be subjected to God. In sum, God will not be subjected to Christ, but Christ will be subjected to God.
Thirdly, why did the author say it is evident? It clearly shows that in the author's time it was considered self-evident that when anyone grants authority over "all things" to someone else, it does not include authority over the one who grants that authority, and the author applies that to the quote "he subjected all things under his feet" to demonstrate that Christ Jesus was not God.
Fourthly, what is the purpose of the author in describing the hierarchy? It is to explain that although God is the highest authority, he has delegated authority to Christ (the anointed one), and will ultimately be the supreme authority, which is why the author made very clear in the final statement that the son of God himself will be subjected to God, so that God may be all in all.
Finally, just as "all things" does not mean "absolutely everything", the "be all in all" does not literally mean that God is everything, but rather that God has the final say in all things. This also implies that there is no other intermediate authority below God besides Christ, because that final statement says explicitly that the reason that the son will be subjected to God is to ensure that God is ultimately the final authority, which implies that everything apart from God and Christ would at that point have been subjected to the authority of Christ.
These already suffice to fully answer your inquiry. However, there is more. Compare this cited text to Gen 41:39-44:
 And Pharaoh said to Joseph, after [the] elohim let you know all this, no one [is] discerning and wise like you.  You shall be over my house, and according to your mouth [i.e. word] all my people shall kiss [i.e. submit]. Only the throne I shall have over you.  And Pharaoh said to Joseph, behold, I set you over all the land of Egypt.  and Pharaoh removed his ring from upon his hand and set it upon the hand of Joseph, and clothed him [in] garments of fine linen, and put the chain of the gold upon his neck,  and made him ride in the second chariot of [those] which [were] for him, and they called out [before] his face, kneel! and [he] set him over all the land of Egypt.  And Pharaoh said to Joseph, I [am] Pharaoh, and apart from you [a] man shall not lift up his hand and his foot in all the land of Egypt.
When the Pharaoh says, "[a] man ... in all the land of Egypt", it is evident that it is except him who subjected all the land of Egypt to Joseph! Notice how Pharaoh made it completely clear that Joseph is second but second only to him, and that Pharaoh has only the throne (meaning the final authority) over Joseph! Can you see the indisputable parallel with 1 Cor 15:24-28 in the notion of delegated and final authority?
Not just the author of 1 Cor 15:24-28 but also the author of Phlp 2:9-11 was completely clear on this notion. Here is Phlp 2:9-11:
 Hence also God lifted [him] up highly and granted to him [a] name above every name,  so that in the name of Jesus every knee might bow, of heavenly [ones] and of earthly [ones] and of [ones] under the earth,  and every tongue might clearly confess that Jesus Christ [is] lord, for [the] glory of God, [the] father.
It should be obvious to you that Phlp 2:9-11 is a crystal-clear parallel with Gen 41:39-44; Jesus Christ is the one whom YHWH set over his house, and to whom YHWH commands all his people to submit, enthroned over all except YHWH (verse 40), highly lifted up and granted a name above every name (verse 41-42), so that in the name of Jesus every knee might bow (verse 43), and every tongue might clearly confess that Jesus Christ is lord (verse 44).
Note that "in the name of X" in the NT always means "as an authorized representative of X". We see this very clearly here; Jesus is granted a name above every name (but of course evidently not above the name of God), meaning authority above every authority except that of God.