Finite Group Databasebeta

← #27135690

Subgroups — #27135690

Order 12352.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20259922C211yesmaximal, characteristic, complemented
2#20259918C211yesmaximal, characteristic, complemented
3#20259845C211yesmaximal, characteristic, complemented
4#20259844C211yesmaximal, characteristic, complemented
5#20259840C211yesmaximal, characteristic, complemented
6C16×D193C211yesmaximal, characteristic, complemented
7SD32×C193C211yesmaximal, characteristic, complemented
8#15690556—21no—
9#15690554—21no—
10Dic772C2211yescharacteristic
11#15690543—21no—
12#15690542—21no—
13D1544C2211yescharacteristic
14C8×D193C2211yescharacteristic
15#15690530C2211yescharacteristic
16Q16×C193C2211yescharacteristic
17D8×C193C2211yescharacteristic
18C16×C193C2211yescharacteristic
19Dic386—21no—
20D772—21no—
21D772—41no—
22C22⋊D193—41no—
23C2×Dic193—41no—
24C4×D193—41no—
25C4×D193D411yescharacteristic
26#13095393D411yescharacteristic
27Q8×C193—21no—
28D4×C193—21no—
29C8×C193C2311yescharacteristic
30C22×C193—41no—
31C2×D193—41no—
32C2×D193D811yescharacteristic
33C4×C193—41no—
34C4×C193C2×D411yescharacteristic
35Dic193—41no—
36Dic193D811yescharacteristic
37C2×C193—81no—
38C2×C193C2×D811yescharacteristic
39D193—21no—
40D193—81no—
41C193#50811yescharacteristic, complemented, Sylow
42#508—1931nomaximal, Sylow
43#135—1931no—
44#135—1931no—
45Q32—1931no—
46SD32—1931no—
47SD32D19311yescharacteristic, complemented
48D16—1931no—
49C2×C16—1931no—
50#41—3861no—
51#41—3861no—
52Q16—1931no—
53Q16C2×D19311yescharacteristic
54SD16—3861no—
55SD16—3861no—
56D8—1931no—
57D8C2×D19311yescharacteristic
58C2×C8—1931no—
59C16—1931no—
60C16C2×D19311yescharacteristic
61Q8—21no—
62Q8—3861no—
63D4—21no—
64D4—7721no—
65D4—7721no—
66D4—3861no—
67C2×C4—7721no—
68C2×C4—7721no—
69C2×C4—1931no—
70C8—1931no—
71C8C22×D19311yescharacteristic
72C22—41no—
73C22—7721no—
74C22—1931no—
75C4—41no—
76C4—7721no—
77C4—1931no—
78C4D4×D19311yescharacteristic
79C2—81no—
80C2—15441no—
81C2—3861no—
82C2D8×D19311yescharacteristic
subgroupG/H
centerC2D8×D193
commutator, cosocleC8×C193C23
FrattiniC8C22×D193
FittingSD32×C193C2
socleC2×C193C2×D8
hypercenterSD32D193
hypocenterC193#508
LCSG ▷ C8×C193 ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. #20259922C2semidirect
2. #20259918C2semidirect
3. #20259845C2semidirect
4. #20259844C2semidirect
5. #20259840C2semidirect
6. C16×D193C2semidirect
7. SD32×C193C2semidirect
41. C193#508semidirect
47. SD32D193semidirect

Maximal subgroups

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

subgroupindex
#202599222
#202599182
#202598452
#202598442
#202598402
C16×D1932
SD32×C1932
#508193