Finite Group Databasebeta

← C2×C3×SL(2,ℤ/4) #64257

Subgroups — C2×C3×SL(2,ℤ/4) #64257

Order 288.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×A4C211yesmaximal, characteristic
2C3×SL(2,ℤ/4)C212yesmaximal, direct product factor
3C2×SL(2,ℤ/4)C311yesmaximal, characteristic, direct product factor
4C2×C3×C22⋊C4—31nomaximal
5C2×C3×A4C412yescomplemented
6C2×C3×A4C2211yescharacteristic
7C2×C3×Dic3—41nomaximal
8C24×C3D311yescharacteristic
9C22×A4—21no—
10C22×A4C2×C311yescharacteristic
11C22×C3×C4—31no—
12C22×C3×C4—31no—
13SL(2,ℤ/4)C2×C312yesdirect product factor
14C3×C22⋊C4—32no—
15C3×C22⋊C4—32no—
16C22×C32—41no—
17C3×A4C2×C411yescharacteristic, complemented
18C3×Dic3—42no—
19C2×C22⋊C4—31noSylow
20C23×C3—31no—
21C23×C3—31no—
22C23×C3—32no—
23C23×C3Dic312yescomplemented
24C23×C3C2×D311yescharacteristic
25C2×A4—22no—
26C2×A4—21no—
27C2×A4C3×C412yescomplemented
28C2×A4C22×C311yescharacteristic
29C2×C3×C4—32no—
30C2×C3×C4—32no—
31C2×C3×C4—62no—
32C2×C3×C4—61no—
33C2×C3×C4—61no—
34C2×Dic3—41no—
35C2×C32—42no—
36C2×C32—41no—
37C24C3×D311yescharacteristic
38C22×C4—31no—
39C22×C4—31no—
40C22⋊C4—32no—
41C22⋊C4—32no—
42C22×C3—32no—
43C22×C3—31no—
44C22×C3—32no—
45C22×C3—32no—
46C22×C3—31no—
47C22×C3—31no—
48C22×C3—41no—
49C22×C3—61no—
50C22×C3—81no—
51C22×C3C2×Dic311yescharacteristic, complemented
52C22×C3S411yescharacteristic
53A4—21no—
54A4C2×C3×C411yescharacteristic, complemented
55C3×C4—62no—
56C3×C4—62no—
57Dic3—42no—
58C32—41noSylow
59C23—31no—
60C23—31no—
61C23—32no—
62C23C3×Dic312yescomplemented
63C23C2×C3×D311yescharacteristic
64C2×C4—32no—
65C2×C4—32no—
66C2×C4—62no—
67C2×C4—61no—
68C2×C4—61no—
69C2×C3—31no—
70C2×C3—31no—
71C2×C3—32no—
72C2×C3—41no—
73C2×C3—42no—
74C2×C3—81no—
75C2×C3—82no—
76C2×C3SL(2,ℤ/4)12yesdirect product factor
77C2×C3C2×S411yescharacteristic
78C22—32no—
79C22—31no—
80C22—31no—
81C22—31no—
82C22—32no—
83C22—32no—
84C22—61no—
85C22C2×C3×Dic311yescharacteristic, complemented
86C22C3×S411yescharacteristic
87C4—62no—
88C4—62no—
89C3—41no—
90C3—81no—
91C3C2×SL(2,ℤ/4)11yescharacteristic, direct product factor
92C2—31no—
93C2—31no—
94C2—32no—
95C2C3×SL(2,ℤ/4)12yesdirect product factor
96C2C2×C3×S411yescharacteristic
subgroupG/H
center, hypercenterC22×C3S4
commutator, hypocenterA4C2×C3×C4
FrattiniC2C2×C3×S4
Fitting, socleC24×C3D3
prime radicalC22×C3×A4C2
cosocleC2×A4C22×C3
LCSG ▷ A4
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
2. C3×SL(2,ℤ/4)C2direct (N × H)
3. C2×SL(2,ℤ/4)C3direct (N × H)
5. C2×C3×A4C4semidirect
13. SL(2,ℤ/4)C2×C3direct (N × H)
17. C3×A4C2×C4semidirect
23. C23×C3Dic3semidirect
27. C2×A4C3×C4semidirect
51. C22×C3C2×Dic3semidirect
54. A4C2×C3×C4semidirect
62. C23C3×Dic3semidirect
76. C2×C3SL(2,ℤ/4)direct (N × H)
85. C22C2×C3×Dic3semidirect
91. C3C2×SL(2,ℤ/4)direct (N × H)
95. C2C3×SL(2,ℤ/4)direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×A42
C3×SL(2,ℤ/4)2
C2×SL(2,ℤ/4)3
C2×C3×C22⋊C43
C2×C3×Dic34