Finite Group Databasebeta

← #20268230

Subgroups — #20268230

Order 6592.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15693040C211yesmaximal, characteristic
2Q16×D103C211yesmaximal, characteristic, complemented
3Dic824C211yesmaximal, characteristic, complemented
4#15692967C211yesmaximal, characteristic, complemented
5#15692965C211yesmaximal, characteristic, complemented
6#15692960C211yesmaximal, characteristic, complemented
7SD32×C103C211yesmaximal, characteristic, complemented
8#13110104—21no—
9Q8×D103—21no—
10Dic412C2211yescharacteristic
11Dic412C2211yescharacteristic
12#13110095—21no—
13#13110093—21no—
14C8×D103C2211yescharacteristic
15C103⋊C16C2211yescharacteristic
16Q16×C103C2211yescharacteristic
17D8×C103C2211yescharacteristic
18C16×C103C2211yescharacteristic
19Q8×C103—21no—
20D4×C103—21no—
21C22⋊D103—41no—
22C2×Dic103—41no—
23C4×D103—41no—
24C4×D103D411yescharacteristic
25Dic206—21no—
26Dic206—21no—
27Dic206—41no—
28C8×C103C2311yescharacteristic
29C103⋊C8D411yescharacteristic
30C22×C103—41no—
31C2×D103D811yescharacteristic
32C4×C103—41no—
33C4×C103C2×D411yescharacteristic
34Dic103—41no—
35Dic103—41no—
36Dic103D811yescharacteristic
37C2×C103—81no—
38C2×C103C2×D811yescharacteristic
39D103—21no—
40C103#51011yescharacteristic, complemented, Sylow
41#510—1031nomaximal, Sylow
42#135—1031no—
43C2×Q16—1031no—
44Q32—1031no—
45Q32—1031no—
46SD32—1031no—
47SD32D10311yescharacteristic, complemented
48M32—1031no—
49#41—2061no—
50C2×Q8—2061no—
51Q16—1031no—
52Q16—1031no—
53Q16—2061no—
54Q16C2×D10311yescharacteristic
55SD16—2061no—
56D8C2×D10311yescharacteristic
57C2×C8—1031no—
58C16—1031no—
59C16C2×D10311yescharacteristic
60Q8—21no—
61Q8—4121no—
62Q8—2061no—
63Q8—2061no—
64D4—21no—
65D4—4121no—
66C2×C4—1031no—
67C2×C4—4121no—
68C2×C4—4121no—
69C8—1031no—
70C8C22×D10311yescharacteristic
71C22—41no—
72C22—1031no—
73C4—41no—
74C4—1031no—
75C4—4121no—
76C4—4121no—
77C4D4×D10311yescharacteristic
78C2—81no—
79C2—2061no—
80C2D8×D10311yescharacteristic
subgroupG/H
centerC2D8×D103
commutatorC8×C103C23
FrattiniC8C22×D103
FittingSD32×C103C2
socleC2×C103C2×D8
hypercenterSD32D103
hypocenterC103#510
LCSG ▷ C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
2. Q16×D103C2semidirect
3. Dic824C2semidirect
4. #15692967C2semidirect
5. #15692965C2semidirect
6. #15692960C2semidirect
7. SD32×C103C2semidirect
40. C103#510semidirect
47. SD32D103semidirect