Finite Group Databasebeta

← #44529481

Subgroups — #44529481

Order 31168.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#29510238C211yesmaximal, characteristic, complemented
2#29510234C211yesmaximal, characteristic, complemented
3#29510161C211yesmaximal, characteristic, complemented
4#29510160C211yesmaximal, characteristic, complemented
5#29510156C211yesmaximal, characteristic, complemented
6C16×D487C211yesmaximal, characteristic, complemented
7SD32×C487C211yesmaximal, characteristic, complemented
8#21441262—21no—
9#21441260—21no—
10Dic1948C2211yescharacteristic
11#21441249—21no—
12#21441248—21no—
13D3896C2211yescharacteristic
14C8×D487C2211yescharacteristic
15C487⋊C16C2211yescharacteristic
16Q16×C487C2211yescharacteristic
17D8×C487C2211yescharacteristic
18C16×C487C2211yescharacteristic
19Dic974—21no—
20D1948—21no—
21D1948—41no—
22C22⋊D487—41no—
23C2×Dic487—41no—
24C4×D487—41no—
25C4×D487D411yescharacteristic
26C487⋊C8D411yescharacteristic
27Q8×C487—21no—
28D4×C487—21no—
29C8×C487C2311yescharacteristic
30C22×C487—41no—
31C2×D487—41no—
32C2×D487D811yescharacteristic
33C4×C487—41no—
34C4×C487C2×D411yescharacteristic
35Dic487—41no—
36Dic487D811yescharacteristic
37C2×C487—81no—
38C2×C487C2×D811yescharacteristic
39D487—21no—
40D487—81no—
41C487#50811yescharacteristic, complemented, Sylow
42#508—4871nomaximal, Sylow
43#135—4871no—
44#135—4871no—
45Q32—4871no—
46SD32—4871no—
47SD32D48711yescharacteristic, complemented
48D16—4871no—
49C2×C16—4871no—
50#41—9741no—
51#41—9741no—
52Q16—4871no—
53Q16C2×D48711yescharacteristic
54SD16—9741no—
55SD16—9741no—
56D8—4871no—
57D8C2×D48711yescharacteristic
58C2×C8—4871no—
59C16—4871no—
60C16C2×D48711yescharacteristic
61Q8—21no—
62Q8—9741no—
63D4—21no—
64D4—19481no—
65D4—19481no—
66D4—9741no—
67C2×C4—19481no—
68C2×C4—19481no—
69C2×C4—4871no—
70C8—4871no—
71C8C22×D48711yescharacteristic
72C22—41no—
73C22—19481no—
74C22—4871no—
75C4—41no—
76C4—19481no—
77C4—4871no—
78C4D4×D48711yescharacteristic
79C2—81no—
80C2—38961no—
81C2—9741no—
82C2D8×D48711yescharacteristic
subgroupG/H
centerC2D8×D487
commutator, cosocleC8×C487C23
FrattiniC8C22×D487
FittingSD32×C487C2
socleC2×C487C2×D8
hypercenterSD32D487
hypocenterC487#508
LCSG ▷ C8×C487 ▷ C4×C487 ▷ C2×C487 ▷ C487
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. #29510238C2semidirect
2. #29510234C2semidirect
3. #29510161C2semidirect
4. #29510160C2semidirect
5. #29510156C2semidirect
6. C16×D487C2semidirect
7. SD32×C487C2semidirect
41. C487#508semidirect
47. SD32D487semidirect

Maximal subgroups

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

subgroupindex
#295102382
#295102342
#295101612
#295101602
#295101562
C16×D4872
SD32×C4872
#508487