Finite Group Databasebeta

← #11928377

Subgroups — #11928377

Order 1248.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#6129C211yesmaximal, characteristic
2C4×C3⋊#261C211yesmaximal, characteristic, complemented
3#10597724C211yesmaximal, characteristic, complemented
4#88116—31nomaximal, Hall
5C2×C3⋊#261—21no—
6C3×D4×C13C411yescharacteristic, complemented
7C3×C22⋊D13—21no—
8C2×C3×Dic13—21no—
9C3×C4×D13C2211yescharacteristic
10C3×Dic26C411yescharacteristic, complemented
11C3⋊#1057—21no—
12#6129D311yescharacteristic
13C4×#261—31no—
14#6118—31no—
15C22×C3×C13—21no—
16C2×C3×D13D411yescharacteristic
17C3⋊#261—22no—
18C3×C4×C13C2×C411yescharacteristic
19C3×Dic13—21no—
20C3×Dic13D411yescharacteristic
21C2×#261—61no—
22D4×C13Dic311yescharacteristic, complemented
23C22⋊D13—21no—
24C2×Dic13—21no—
25C4×D13C2×D311yescharacteristic
26Dic26Dic311yescharacteristic, complemented
27#1057—61no—
28#837—131nomaximal, Hall
29C2×C3×C13—41no—
30C2×C3×C13C22⋊C411yescharacteristic
31C3×D13—21no—
32C22×C13—21no—
33C2×D13#6711yescharacteristic
34#261—62no—
35C4×C13C2×Dic311yescharacteristic
36Dic13—21no—
37Dic13#6711yescharacteristic
38C3×#41—131no—
39C4×Dic3—131no—
40#208—131no—
41C3×C13#10411yescharacteristic, complemented, Hall
42#104—391noSylow
43C2×C13—41no—
44C2×C13#21711yescharacteristic
45D13—21no—
46C3×Q8—131no—
47C3×D4—261no—
48C3×D4#26111yescharacteristic, complemented
49C2×C3×C4—131no—
50C2×C3×C4—261no—
51C2×Dic3—261no—
52C3⋊C8—261no—
53#41—131no—
54M16—391no—
55C42—391no—
56C13#83711yescharacteristic, complemented, Sylow
57C22×C3—21no—
58C22×C3—131no—
59C3×C4—131no—
60C3×C4—261no—
61C3×C4C2×#26111yescharacteristic
62Dic3—262no—
63Q8—131no—
64D4—261no—
65D4C3⋊#26111yescharacteristic, complemented
66C2×C4—131no—
67C2×C4—261no—
68C2×C4—781no—
69C8—781no—
70C2×C3—41no—
71C2×C3—261no—
72C2×C3C22⋊#26111yescharacteristic
73C22—21no—
74C22—131no—
75C4—131no—
76C4—261no—
77C4—782no—
78C4C2×C3⋊#26111yescharacteristic
79C3#8811611yescharacteristic, complemented, Sylow
80C2—41no—
81C2—261no—
82C2#1059772911yescharacteristic
subgroupG/H
centerC2#10597729
commutatorC3×C4×C13C2×C4
FrattiniC4C2×C3⋊#261
FittingC3×D4×C13C4
socleC2×C3×C13C22⋊C4
prime radicalC3×#6129C2
cosocleC3×C4×D13C22
hypercenterD4C3⋊#261
hypocenterC3×C13#104
LCSG ▷ C3×C4×C13 ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2 ◁ C4 ◁ D4

Complements

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

NH ≅ G/Ntype
2. C4×C3⋊#261C2semidirect
3. #10597724C2semidirect
6. C3×D4×C13C4semidirect
10. C3×Dic26C4semidirect
22. D4×C13Dic3semidirect
26. Dic26Dic3semidirect
41. C3×C13#104semidirect
48. C3×D4#261semidirect
56. C13#837semidirect
65. D4C3⋊#261semidirect
79. C3#88116semidirect

Maximal subgroups

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

subgroupindex
C3×#61292
C4×C3⋊#2612
#105977242
#881163
#83713