Finite Group DatabasebetaFinite Group DatabasebetaOrder 64.
59 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #95 | C2 | 1 | 7 | yes | maximal |
| 2 | C22×C4 | C22 | 1 | 7 | yes | — |
| 3 | C23 | C23 | 1 | 1 | yes | characteristic |
| 4 | C2×C4 | — | 2 | 21 | no | — |
| 5 | C22 | #41 | 1 | 7 | yes | — |
| 6 | C4 | — | 4 | 7 | no | — |
| 7 | C2 | #126 | 1 | 7 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, prime radical, cosocle | C23 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #95 | 2 |