Finite Group Databasebeta

← #11928138

Subgroups — #11928138

Order 1248.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C13×D8C211yesmaximal, characteristic, complemented
2D312C211yesmaximal, characteristic, complemented
3C3⋊#6090C211yesmaximal, characteristic, complemented
4#88066—31nomaximal, Hall
5C3×D4×C13—21no—
6D156—21no—
7C3×C8×C13C2211yescharacteristic
8C13×D8D311yescharacteristic, complemented
9D104—31no—
10#6090—31no—
11C22×C3×C13—41no—
12C2×D39—41no—
13C3×C4×C13D411yescharacteristic
14D4×C13—21no—
15D52—61no—
16C8×C13C2×D311yescharacteristic
17#826—131nomaximal, Hall
18C2×C3×C13—81no—
19C2×C3×C13D811yescharacteristic
20D39—81no—
21C22×C13—41no—
22C2×D13—121no—
23C4×C13#6711yescharacteristic
24C3×D8D1311yescharacteristic, complemented
25D24—131no—
26C3⋊C16—131no—
27C3×C13D1611yescharacteristic, complemented, Hall
28D16—391noSylow
29C2×C13—81no—
30C2×C13#21311yescharacteristic
31D13—241no—
32C3×D4—21no—
33D12—261no—
34C3×C8C2×D1311yescharacteristic
35D8—391no—
36D8D3911yescharacteristic, complemented
37C16—391no—
38C13#82611yescharacteristic, complemented, Sylow
39C22×C3—41no—
40C2×D3—521no—
41C3×C4C22⋊D1311yescharacteristic
42D4—21no—
43D4—781no—
44C8C2×D3911yescharacteristic
45C2×C3—81no—
46C2×C3#610411yescharacteristic
47D3—1041no—
48C22—41no—
49C22—1561no—
50C4#6462511yescharacteristic
51C3#8806611yescharacteristic, complemented, Sylow
52C2—81no—
53C2—3121no—
54C2#1059766711yescharacteristic
subgroupG/H
centerC2#10597667
commutator, cosocleC3×C8×C13C22
FrattiniC8C2×D39
FittingC3×C13×D8C2
socleC2×C3×C13D8
hypercenterD8D39
hypocenterC3×C13D16
LCSG ▷ C3×C8×C13 ▷ C3×C4×C13 ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D8

Complements

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

NH ≅ G/Ntype
1. C3×C13×D8C2semidirect
2. D312C2semidirect
3. C3⋊#6090C2semidirect
8. C13×D8D3semidirect
24. C3×D8D13semidirect
27. C3×C13D16semidirect
36. D8D39semidirect
38. C13#826semidirect
51. C3#88066semidirect

Maximal subgroups

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

subgroupindex
C3×C13×D82
D3122
C3⋊#60902
#880663
#82613