Finite Group Databasebeta

← #23782104

Subgroups — #23782104

Order 10432.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19104754C211yesmaximal, characteristic
2Q16×D163C211yesmaximal, characteristic, complemented
3Dic1304C211yesmaximal, characteristic, complemented
4#19104681C211yesmaximal, characteristic, complemented
5#19104679C211yesmaximal, characteristic, complemented
6#19104674C211yesmaximal, characteristic, complemented
7SD32×C163C211yesmaximal, characteristic, complemented
8#14579698—21no—
9Q8×D163—21no—
10Dic652C2211yescharacteristic
11Dic652C2211yescharacteristic
12#14579689—21no—
13#14579687—21no—
14C8×D163C2211yescharacteristic
15C163⋊C16C2211yescharacteristic
16Q16×C163C2211yescharacteristic
17D8×C163C2211yescharacteristic
18C16×C163C2211yescharacteristic
19Dic326—21no—
20Dic326—21no—
21Dic326—41no—
22C22⋊D163—41no—
23C2×Dic163—41no—
24C4×D163—41no—
25C4×D163D411yescharacteristic
26C163⋊C8D411yescharacteristic
27Q8×C163—21no—
28D4×C163—21no—
29C8×C163C2311yescharacteristic
30C22×C163—41no—
31C2×D163D811yescharacteristic
32C4×C163—41no—
33C4×C163C2×D411yescharacteristic
34Dic163—41no—
35Dic163—41no—
36Dic163D811yescharacteristic
37C2×C163—81no—
38C2×C163C2×D811yescharacteristic
39D163—21no—
40C163#51011yescharacteristic, complemented, Sylow
41#510—1631nomaximal, Sylow
42#135—1631no—
43C2×Q16—1631no—
44Q32—1631no—
45Q32—1631no—
46SD32—1631no—
47SD32D16311yescharacteristic, complemented
48M32—1631no—
49#41—3261no—
50C2×Q8—3261no—
51Q16—3261no—
52Q16—1631no—
53Q16—1631no—
54Q16C2×D16311yescharacteristic
55SD16—3261no—
56D8C2×D16311yescharacteristic
57C2×C8—1631no—
58C16—1631no—
59C16C2×D16311yescharacteristic
60Q8—21no—
61Q8—3261no—
62Q8—3261no—
63Q8—6521no—
64D4—21no—
65D4—6521no—
66C2×C4—6521no—
67C2×C4—6521no—
68C2×C4—1631no—
69C8—1631no—
70C8C22×D16311yescharacteristic
71C22—41no—
72C22—1631no—
73C4—41no—
74C4—6521no—
75C4—6521no—
76C4—1631no—
77C4D4×D16311yescharacteristic
78C2—81no—
79C2—3261no—
80C2D8×D16311yescharacteristic
subgroupG/H
centerC2D8×D163
commutator, cosocleC8×C163C23
FrattiniC8C22×D163
FittingSD32×C163C2
socleC2×C163C2×D8
prime radical#19104754C2
hypercenterSD32D163
hypocenterC163#510
LCSG ▷ C8×C163 ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
2. Q16×D163C2semidirect
3. Dic1304C2semidirect
4. #19104681C2semidirect
5. #19104679C2semidirect
6. #19104674C2semidirect
7. SD32×C163C2semidirect
40. C163#510semidirect
47. SD32D163semidirect