Finite Group Databasebeta

← #20261835

Subgroups — #20261835

Order 6208.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15690907C211yesmaximal, characteristic, complemented
2#15690905C211yesmaximal, characteristic, complemented
3#15690897C211yesmaximal, characteristic
4#13095523—21no—
5#13095523—21no—
6#13095521C411yescharacteristic
7#13095520—21no—
8#13095519C2211yescharacteristic
9C2×#11715897—21no—
10#13095510C411yescharacteristic
11D4×C97C811yescharacteristic
12C22⋊D97—21no—
13C2×Dic97—21no—
14C4×D97C2×C411yescharacteristic
15Dic194C811yescharacteristic
16#11715897—21no—
17#11715897D411yescharacteristic
18#11715897D411yescharacteristic
19C22×C97—21no—
20C2×D97M1611yescharacteristic
21C4×C97C2×C811yescharacteristic
22Dic97—21no—
23Dic97C22⋊C411yescharacteristic
24C2×C97—41no—
25C2×C97C22⋊C811yescharacteristic
26D97—21no—
27C97#35011yescharacteristic, complemented, Sylow
28#350—971nomaximal, Sylow
29#131—971no—
30M32—971no—
31C2×C16—971no—
32#41—971no—
33M16—971no—
34M16—1941no—
35C2×C8—971no—
36C2×C8—1941no—
37C16—1941no—
38C16—1941no—
39Q8—971no—
40D4—1941no—
41D4#1171590611yescharacteristic
42C2×C4—971no—
43C2×C4—1941no—
44C8—971no—
45C8—971no—
46C8—1941no—
47C22—21no—
48C22—971no—
49C4—971no—
50C4—1941no—
51C4C2×#1171590611yescharacteristic
52C2—41no—
53C2—1941no—
54C2C22⋊#1171590611yescharacteristic
subgroupG/H
centerC2C22⋊#11715906
commutatorC4×C97C2×C8
FrattiniC4C2×#11715906
FittingD4×C97C8
socleC2×C97C22⋊C8
hypercenterD4#11715906
hypocenterC97#350
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C4 ◁ D4

Complements

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

NH ≅ G/Ntype
1. #15690907C2semidirect
2. #15690905C2semidirect
27. C97#350semidirect