Finite Group Databasebeta

← #11927989

Subgroups — #11927989

Order 1248.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10597790C211yesmaximal, characteristic
2C4×Dic3×C13C211yesmaximal, characteristic, complemented
3C3×#6099C211yesmaximal, characteristic, complemented
4#88045—31nomaximal, Hall
5C2×C3×C4×C13C2211yescharacteristic
6#64625—21no—
7D156C411yescharacteristic, complemented
8C4×D39—21no—
9Dic78C411yescharacteristic, complemented
10C2×Dic3×C13—21no—
11C3×#1055—21no—
12#6127—31no—
13C42×C13—31no—
14#6099D311yescharacteristic, complemented
15C22×C3×C13D411yescharacteristic
16C2×D39—21no—
17C3×C4×C13C2×C411yescharacteristic
18C3×C4×C13D411yescharacteristic
19Dic39—21no—
20Dic3×C13—22no—
21C2×C4×C13—61no—
22C2×C4×C13C2×D311yescharacteristic
23C22⋊D13—61no—
24D52—31no—
25C4×D13—61no—
26Dic26—31no—
27#1055—21no—
28#825—131nomaximal, Hall
29C2×C3×C13—21no—
30C2×C3×C13C22⋊C411yescharacteristic
31D39—41no—
32C22×C13D1211yescharacteristic
33C2×D13—61no—
34C4×C13—62no—
35C4×C13C4×D311yescharacteristic
36C4×C13#6711yescharacteristic
37Dic13—61no—
38#235—131no—
39C3×M16—131no—
40C4×Dic3D1311yescharacteristic, complemented
41C3×C13#10411yescharacteristic, complemented, Hall
42#104—391noSylow
43C2×C13—21no—
44C2×C13(C2×D3)⋊C411yescharacteristic
45D13—121no—
46C2×C3×C4C2×D1311yescharacteristic
47#67—261no—
48C2×Dic3—21no—
49D12—131no—
50C4×D3—261no—
51Dic6—131no—
52C3×C8—261no—
53#41—391no—
54M16—131no—
55C42—31no—
56C13#82511yescharacteristic, complemented, Sylow
57C22×C3C22⋊D1311yescharacteristic
58C2×D3—261no—
59C3×C4C4×D1311yescharacteristic
60C3×C4D5211yescharacteristic
61Dic3—22no—
62Dic3—261no—
63Q8—391no—
64D4—391no—
65D4—781no—
66C2×C4—61no—
67C2×C4—781no—
68C2×C4D3×D1311yescharacteristic
69C8—261no—
70C2×C3—21no—
71C2×C3#610311yescharacteristic
72D3—521no—
73C22—781no—
74C22#6460411yescharacteristic
75C4—62no—
76C4—781no—
77C4#6460111yescharacteristic
78C4#6460311yescharacteristic
79C3#8804511yescharacteristic, complemented, Sylow
80C2—21no—
81C2—1561no—
82C2#1059761011yescharacteristic
subgroupG/H
centerC4#64603
commutatorC3×C4×C13C2×C4
Frattini, hypercenterC2×C4D3×D13
Fitting, cosocleC2×C3×C4×C13C22
socleC2×C3×C13C22⋊C4
prime radical#10597790C2
hypocenterC3×C13#104
LCSG ▷ C3×C4×C13 ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C4×Dic3×C13C2semidirect
3. C3×#6099C2semidirect
7. D156C4semidirect
9. Dic78C4semidirect
14. #6099D3semidirect
40. C4×Dic3D13semidirect
41. C3×C13#104semidirect
56. C13#825semidirect
79. C3#88045semidirect

Maximal subgroups

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

subgroupindex
#105977902
C4×Dic3×C132
C3×#60992
#880453
#82513