Finite Group Databasebeta

← #20259920

Subgroups — #20259920

Order 6176.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15690556C211yesmaximal, characteristic, complemented
2#15690554C211yesmaximal, characteristic, complemented
3#15690545C211yesmaximal, characteristic, complemented
4#15690544C211yesmaximal, characteristic, complemented
5#15690540C211yesmaximal, characteristic, complemented
6C8×D193C211yesmaximal, characteristic, complemented
7SD16×C193C211yesmaximal, characteristic, complemented
8Dic386C2211yescharacteristic
9D772—21no—
10D772C2211yescharacteristic
11C22⋊D193—21no—
12C2×Dic193—21no—
13C4×D193—21no—
14C4×D193C2211yescharacteristic
15#13095393C2211yescharacteristic
16Q8×C193C2211yescharacteristic
17D4×C193C2211yescharacteristic
18C8×C193C2211yescharacteristic
19C22×C193—21no—
20C2×D193—21no—
21C2×D193D411yescharacteristic
22C4×C193—21no—
23C4×C193C2311yescharacteristic
24Dic193—21no—
25Dic193D411yescharacteristic
26C2×C193—41no—
27C2×C193C2×D411yescharacteristic
28D193—21no—
29D193—41no—
30C193#13511yescharacteristic, complemented, Sylow
31#135—1931nomaximal, Sylow
32#41—1931no—
33#41—1931no—
34Q16—1931no—
35SD16—1931no—
36SD16D19311yescharacteristic, complemented
37D8—1931no—
38C2×C8—1931no—
39Q8—1931no—
40Q8C2×D19311yescharacteristic
41D4—3861no—
42D4—3861no—
43D4—1931no—
44D4C2×D19311yescharacteristic
45C2×C4—3861no—
46C2×C4—3861no—
47C2×C4—1931no—
48C8—1931no—
49C8C2×D19311yescharacteristic
50C22—21no—
51C22—3861no—
52C22—1931no—
53C4—21no—
54C4—3861no—
55C4—1931no—
56C4C22×D19311yescharacteristic
57C2—41no—
58C2—7721no—
59C2—3861no—
60C2D4×D19311yescharacteristic
subgroupG/H
centerC2D4×D193
commutatorC4×C193C23
FrattiniC4C22×D193
FittingSD16×C193C2
socleC2×C193C2×D4
hypercenterSD16D193
hypocenterC193#135
LCSG ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C2 ◁ C4 ◁ SD16

Complements

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

NH ≅ G/Ntype
1. #15690556C2semidirect
2. #15690554C2semidirect
3. #15690545C2semidirect
4. #15690544C2semidirect
5. #15690540C2semidirect
6. C8×D193C2semidirect
7. SD16×C193C2semidirect
30. C193#135semidirect
36. SD16D193semidirect