Groups of order 48

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 $48$.

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