Finite Group Databasebeta

← #20261836

Subgroups — #20261836

Order 6208.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15690907C211yesmaximal, characteristic, complemented
2#15690905C211yesmaximal, characteristic, complemented
3#15690898C211yesmaximal, characteristic
4#13095523—21no—
5#13095523—21no—
6#13095521—21no—
7#13095521C411yescharacteristic
8#13095519—21no—
9#13095519C2211yescharacteristic
10#13095512C411yescharacteristic
11Q8×C97C811yescharacteristic
12D388—21no—
13D388C811yescharacteristic
14C4×D97—21no—
15C4×D97C2×C411yescharacteristic
16#11715897—21no—
17#11715897D411yescharacteristic
18#11715897D411yescharacteristic
19C2×D97—21no—
20C2×D97M1611yescharacteristic
21C4×C97—21no—
22C4×C97C2×C811yescharacteristic
23Dic97C22⋊C411yescharacteristic
24C2×C97C22⋊C811yescharacteristic
25D97—21no—
26D97—41no—
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#1171590611yescharacteristic
40D4—971no—
41D4—1941no—
42C2×C4—971no—
43C2×C4—1941no—
44C8—971no—
45C8—971no—
46C8—1941no—
47C22—971no—
48C22—1941no—
49C4—21no—
50C4—971no—
51C4C2×#1171590611yescharacteristic
52C2—3881no—
53C2—1941no—
54C2C22⋊#1171590611yescharacteristic
subgroupG/H
centerC2C22⋊#11715906
commutatorC4×C97C2×C8
FrattiniC4C2×#11715906
FittingQ8×C97C8
socleC2×C97C22⋊C8
hypercenterQ8#11715906
hypocenterC97#350
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C4 ◁ Q8

Complements

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

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