Finite Group Databasebeta

← #20259919

Subgroups — #20259919

Order 6176.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15690555C211yesmaximal, characteristic, complemented
2#15690545C211yesmaximal, characteristic, complemented
3#15690543C211yesmaximal, characteristic, complemented
4#15690542C211yesmaximal, characteristic, complemented
5#15690540C211yesmaximal, characteristic, complemented
6C2×#13095393C211yesmaximal, characteristic, complemented
7#41×C193C211yesmaximal, characteristic, complemented
8Dic386C2211yescharacteristic
9D772C2211yescharacteristic
10C22⋊D193—21no—
11C4×D193—21no—
12#13095393C2211yescharacteristic
13#13095393C2211yescharacteristic
14Q8×C193C2211yescharacteristic
15D4×C193—21no—
16D4×C193C2211yescharacteristic
17C2×C4×C193—21no—
18C2×C4×C193C2211yescharacteristic
19C22×C193—21no—
20C22×C193D411yescharacteristic
21C2×D193—21no—
22C4×C193—21no—
23C4×C193D411yescharacteristic
24C4×C193C2311yescharacteristic
25Dic193—21no—
26C2×C193—21no—
27C2×C193—41no—
28C2×C193C2×D411yescharacteristic
29D193—41no—
30C193#13511yescharacteristic, complemented, Sylow
31#135—1931nomaximal, Sylow
32#41—1931no—
33#41D19311yescharacteristic, complemented
34Q16—1931no—
35SD16—1931no—
36SD16—1931no—
37D8—1931no—
38C2×C8—1931no—
39Q8—1931no—
40Q8C2×D19311yescharacteristic
41D4—21no—
42D4—3861no—
43D4—1931no—
44D4C2×D19311yescharacteristic
45C2×C4—21no—
46C2×C4—3861no—
47C2×C4C2×D19311yescharacteristic
48C8—1931no—
49C8—1931no—
50C22—21no—
51C22—3861no—
52C22C22⋊D19311yescharacteristic
53C4—21no—
54C4—3861no—
55C4C22⋊D19311yescharacteristic
56C4C22×D19311yescharacteristic
57C2—21no—
58C2—41no—
59C2—7721no—
60C2C2×C22⋊D19311yescharacteristic
subgroupG/H
centerC4C22⋊D193
commutatorC4×C193C23
FrattiniC4C22×D193
Fitting#41×C193C2
socleC2×C193C2×D4
hypercenter#41D193
hypocenterC193#135
LCSG ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. #15690555C2semidirect
2. #15690545C2semidirect
3. #15690543C2semidirect
4. #15690542C2semidirect
5. #15690540C2semidirect
6. C2×#13095393C2semidirect
7. #41×C193C2semidirect
30. C193#135semidirect
33. #41D193semidirect