# Groups of order 48

From Groupprops

This article gives information about, and links to more details on, groups of order 48

See pages on algebraic structures of order 48| See pages on groups of a particular order

This article gives basic information comparing and contrasting groups of order .

## Statistics at a glance

Quantity | Value |
---|---|

Total number of groups | 52 |

Number of abelian groups | 5 |

Number of nilpotent groups | 14 |

Number of solvable groups | 52 |

Number of simple groups | 0 |

## Sylow subgroups

### 2-Sylow subgroups

Here is the occurrence summary:

Group of order 16 | GAP ID (second part) | Number of groups of order 48 in which it is a 2-Sylow subgroup | List of these groups | Second part of GAP ID of these groups |
---|---|---|---|---|

cyclic group:Z16 | 1 | 2 | 1, 2 | |

direct product of Z4 and Z4 | 2 | 3 | 3, 11, 20 | |

SmallGroup(16,3) | 3 | 4 | 14, 19, 21, 30 | |

nontrivial semidirect product of Z4 and Z4 | 4 | 3 | 12, 13, 22 | |

direct product of Z8 and Z2 | 5 | 3 | 4, 9, 23 | |

M16 | 6 | 3 | 5, 10, 24 | |

dihedral group:D16 | 7 | 3 | 7, 15, 25 | |

semidihedral group:SD16 | 8 | 5 | 6, 16, 17, 26, 29 | |

generalized quaternion group:Q16 | 9 | 4 | 8, 18, 27, 28 | |

direct product of Z4 and V4 | 10 | 4 | 31, 35, 42, 44 | |

direct product of D8 and Z2 | 11 | 5 | 36, 38, 43, 45, 48 | |

direct product of Q8 and Z2 | 12 | 4 | 32, 34, 40, 46 | |

central product of D8 and Z4 | 13 | 5 | 33, 37, 39, 41, 47 | |

elementary abelian group:E16 | 14 | 4 | 49, 50, 51, 52 |