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List all subgroups of $\Bbb Z_{12}$

$\Bbb Z_{12}$ is cyclic so all its subgroups are also cyclic

$$\begin{aligned} <1> &= Z_{12} \\<2> &= \{ 0,2,4,6,8,10\} \\<3> &= \{ 0,3,6,9\} \\<4> &= \{ 0,4,8 \} \\<6> &= \{ 6 ,0\} \end{aligned}$$

are there more???

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    No, those are all. – 2017-02-07
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    There's also $\{0\}$. Note that there is one subgroup for each possible value of $\gcd(n,12)$. – 2017-02-07

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In general you have:

In the cyclic group of order $n$, there is exactly one subgroup for each divisor of $n$.

Since the divisors of $12$ are $1,2,3,4,6,12$, you have found all subgroups except the subgroup $\langle 12 \rangle$ corresponding to $12$, which is the trivial subgroup.