Finite Group Databasebeta

← #11928144

Subgroups — #11928144

Order 1248.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C13C211yesmaximal, characteristic
2#10597671C212yesmaximal, complemented
3#88074—31nomaximal, Hall
4C23×C3×C13C411yescharacteristic, complemented
5C23×C3×C13C2211yescharacteristic
6C3×D4×C13—22no—
7C2×C3×C4×C13C411yescharacteristic, complemented
8C2×Dic39—22no—
9C2×D4×C13D311yescharacteristic
10C22⋊Dic13—32no—
11C22×C3×C13—21no—
12C22×C3×C13—41no—
13C22×C3×C13—41no—
14C22×C3×C13C2×C411yescharacteristic
15C22×C3×C13D412yes—
16C3×C4×C13—21no—
17Dic39—42no—
18C23×C13Dic311yescharacteristic, complemented
19C23×C13C2×D311yescharacteristic
20D4×C13—22no—
21C2×C4×C13Dic311yescharacteristic, complemented
22C2×Dic13—62no—
23#834—131nomaximal, Hall
24C2×C3×C13—22no—
25C2×C3×C13—21no—
26C2×C3×C13—41no—
27C2×C3×C13C22⋊C411yescharacteristic
28C22×C13—21no—
29C22×C13—41no—
30C22×C13—41no—
31C22×C13C2×Dic311yescharacteristic
32C22×C13#6712yes—
33C4×C13—21no—
34Dic13—122no—
35C2×C3×D4D1311yescharacteristic
36#217—132no—
37C3×C13#9911yescharacteristic, complemented, Hall
38#99—391noSylow
39C2×C13—22no—
40C2×C13—21no—
41C2×C13—41no—
42C2×C13#21711yescharacteristic
43C23×C3Dic1311yescharacteristic, complemented
44C23×C3C2×D1311yescharacteristic
45C3×D4—22no—
46C2×C3×C4Dic1311yescharacteristic, complemented
47C2×Dic3—262no—
48C2×D4D3911yescharacteristic
49C22⋊C4—392no—
50C13#83411yescharacteristic, complemented, Sylow
51C22×C3—21no—
52C22×C3—41no—
53C22×C3—41no—
54C22×C3C2×Dic1311yescharacteristic
55C22×C3C22⋊D1312yes—
56C3×C4—21no—
57Dic3—522no—
58C23Dic3911yescharacteristic, complemented
59C23C2×D3911yescharacteristic
60D4—22no—
61C2×C4—782no—
62C2×C4Dic3911yescharacteristic, complemented
63C2×C3—22no—
64C2×C3—21no—
65C2×C3—41no—
66C2×C3C22⋊Dic1311yescharacteristic
67C22—21no—
68C22—41no—
69C22—41no—
70C22C2×Dic3911yescharacteristic
71C22#6462512yes—
72C4—21no—
73C4—1562no—
74C3#8807411yescharacteristic, complemented, Sylow
75C2—22no—
76C2—21no—
77C2—41no—
78C2#1059767111yescharacteristic
subgroupG/H
centerC2#10597671
commutatorC22×C3×C13C2×C4
FrattiniC23C2×D39
Fitting, prime radicalC2×C3×D4×C13C2
socleC2×C3×C13C22⋊C4
cosocleC23×C3×C13C22
hypercenterC2×D4D39
hypocenterC3×C13#99
LCSG ▷ C22×C3×C13 ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2 ◁ C23 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #10597671C2semidirect
4. C23×C3×C13C4semidirect
7. C2×C3×C4×C13C4semidirect
18. C23×C13Dic3semidirect
21. C2×C4×C13Dic3semidirect
37. C3×C13#99semidirect
43. C23×C3Dic13semidirect
46. C2×C3×C4Dic13semidirect
50. C13#834semidirect
58. C23Dic39semidirect
62. C2×C4Dic39semidirect
74. C3#88074semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×C132
#105976712
#880743
#83413