Subgroup structure of nontrivial semidirect product of Z4 and Z4
This article gives specific information, namely, subgroup structure, about a particular group, namely: nontrivial semidirect product of Z4 and Z4.
View subgroup structure of particular groups | View other specific information about nontrivial semidirect product of Z4 and Z4
The elements are:
Tables for quick information
FACTS TO CHECK AGAINST FOR SUBGROUP STRUCTURE: (group of prime power order)
Lagrange's theorem (order of subgroup times index of subgroup equals order of whole group, so all subgroups have prime power orders)|order of quotient group divides order of group (and equals index of corresponding normal subgroup, so all quotients have prime power orders)
prime power order implies not centerless | prime power order implies nilpotent | prime power order implies center is normality-large
size of conjugacy class of subgroups divides index of center
congruence condition on number of subgroups of given prime power order: The total number of subgroups of any fixed prime power order is congruent to 1 mod the prime.
Table classifying subgroups up to automorphisms
In case a single equivalence class of subgroups under automorphisms comprises multiple conjugacy classes of subgroups, outer curly braces are used to bucket the conjugacy classes.