Finite Group Databasebeta

← A4⋊SL(2,ℤ/4) #10596401

Subgroups — A4⋊SL(2,ℤ/4) #10596401

Order 576.

191 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 191 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×A42C211yesmaximal, characteristic
2#5936—32nomaximal
3#5432—32nomaximal
4A42C411yescharacteristic, complemented
5C3⋊SL(2,ℤ/4)—42nomaximal
6C2×C22⋊A4D312yes—
7C23×A4D312yes—
8C2×SL(2,ℤ/4)—32no—
9C2×SL(2,ℤ/4)—32no—
10C2×C3×A4—42no—
11#379—91noSylow
12C22⋊A4Dic312yescomplemented
13C22×A4—32no—
14C22×A4—32no—
15C22×A4Dic312yescomplemented
16SL(2,ℤ/4)—62no—
17SL(2,ℤ/4)—62no—
18SL(2,ℤ/4)—124no—
19SL(2,ℤ/4)—122no—
20#217—122no—
21C3×A4—42no—
22C3⋊Dic3—161no—
23C25C3⋊D311yescharacteristic
24C2×C22⋊C4—92no—
25C2×C22⋊C4—92no—
26C2×C22⋊C4—91no—
27C2×C22⋊C4—91no—
28C23×C3—42no—
29C2×A4—32no—
30C2×A4—32no—
31C2×A4—44no—
32C2×A4—122no—
33C2×A4S412yes—
34C2×Dic3—122no—
35C2×Dic3—122no—
36C2×C32—161no—
37C24—32no—
38C24—32no—
39C24—91no—
40C24—91no—
41C24C3⋊Dic311yescharacteristic, complemented
42C22×C4—91no—
43C22×C4—92no—
44C22×C4—91no—
45C22⋊C4—182no—
46C22⋊C4—182no—
47C22⋊C4—182no—
48C22⋊C4—182no—
49C22⋊C4—182no—
50C22⋊C4—182no—
51C22×C3—42no—
52C22×C3—122no—
53C22×C3—122no—
54A4—44no—
55A4—122no—
56A4SL(2,ℤ/4)12yescomplemented
57Dic3—242no—
58Dic3—242no—
59Dic3—482no—
60C32—161noSylow
61C23—32no—
62C23—32no—
63C23—32no—
64C23—91no—
65C23—91no—
66C23—92no—
67C23—92no—
68C23—92no—
69C23—92no—
70C23—91no—
71C23—182no—
72C23C3⋊S412yes—
73C2×C4—182no—
74C2×C4—182no—
75C2×C4—182no—
76C2×C4—182no—
77C2×C4—182no—
78C2×C4—181no—
79C2×C4—181no—
80C2×C3—42no—
81C2×C3—122no—
82C2×C3—122no—
83C2×C3—162no—
84C22—32no—
85C22—32no—
86C22—32no—
87C22—92no—
88C22—91no—
89C22—91no—
90C22—92no—
91C22—92no—
92C22—92no—
93C22—91no—
94C22—182no—
95C22C3⋊SL(2,ℤ/4)12yescomplemented
96C4—362no—
97C4—361no—
98C4—361no—
99C3—42no—
100C3—162no—
101C2—32no—
102C2—32no—
103C2—91no—
104C2—91no—
105C2A4⋊S411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2A4⋊S4
commutator, hypocenterA42C4
Fitting, socleC25C3⋊D3
prime radical, cosocleC2×A42C2
LCSG ▷ A42
UCSC1 ◁ C2

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. A42C4semidirect
12. C22⋊A4Dic3semidirect
15. C22×A4Dic3semidirect
41. C24C3⋊Dic3semidirect
56. A4SL(2,ℤ/4)semidirect
95. C22C3⋊SL(2,ℤ/4)semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×A422
#59363
#54323
C3⋊SL(2,ℤ/4)4