Finite Group Databasebeta

← #20259872

Subgroups — #20259872

Order 6176.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D772C211yesmaximal, characteristic, complemented
2C2×C22⋊D193C211yesmaximal, characteristic, complemented
3C2×C22⋊D193C211yesmaximal, characteristic, complemented
4C2×C4×D193C211yesmaximal, characteristic, complemented
5#15690534C211yesmaximal, characteristic, complemented
6#15690532C211yesmaximal, characteristic, complemented
7C22⋊C4×C193C211yesmaximal, characteristic, complemented
8C22×D193C2211yescharacteristic
9C22×D193C2211yescharacteristic
10D772—22no—
11C22⋊D193—22no—
12C22⋊D193—22no—
13C2×Dic193C2211yescharacteristic
14C2×Dic193C2211yescharacteristic
15C4×D193—22no—
16C23×C193C2211yescharacteristic
17C2×C4×C193C2211yescharacteristic
18C2×C4×C193C2211yescharacteristic
19C22×C193—21no—
20C22×C193—21no—
21C22×C193—21no—
22C22×C193C2311yescharacteristic
23C2×D193—21no—
24C2×D193—21no—
25C2×D193—21no—
26C2×D193—21no—
27C2×D193—21no—
28C2×D193D412yescomplemented
29C4×C193—21no—
30C4×C193—21no—
31Dic193—21no—
32Dic193D412yescomplemented
33C2×C193—41no—
34C2×C193C2×D411yescharacteristic
35C2×C193C2×D411yescharacteristic
36C2×C193#4111yescharacteristic
37D193—22no—
38D193—41no—
39C193#12111yescharacteristic, complemented, Sylow
40#121—1931nomaximal, Sylow
41C2×D4—1931no—
42C2×D4—1931no—
43C2×D4—1931no—
44C22×C4—1931no—
45C4⋊C4—1931no—
46C22⋊C4—1931no—
47C22⋊C4D19311yescharacteristic, complemented
48C23—1931no—
49C23—1931no—
50C23C2×D19311yescharacteristic
51D4—3862no—
52D4—3862no—
53D4—3862no—
54C2×C4—3862no—
55C2×C4—1931no—
56C2×C4—1931no—
57C2×C4C2×D19311yescharacteristic
58C2×C4C2×D19311yescharacteristic
59C22—21no—
60C22—21no—
61C22—21no—
62C22—3861no—
63C22—3861no—
64C22—3861no—
65C22—3861no—
66C22—3861no—
67C22—1932no—
68C22C22×D19311yescharacteristic
69C4—21no—
70C4—21no—
71C4—3861no—
72C4—1932no—
73C2—41no—
74C2—7721no—
75C2—3862no—
76C2D4×D19311yescharacteristic
77C2D4×D19311yescharacteristic
78C2#1569055511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D193
commutator, socleC22×C193C23
FittingC22⋊C4×C193C2
hypercenterC22⋊C4D193
hypocenterC193#121
LCSG ▷ C22×C193 ▷ C193
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D772C2semidirect
2. C2×C22⋊D193C2semidirect
3. C2×C22⋊D193C2semidirect
4. C2×C4×D193C2semidirect
5. #15690534C2semidirect
6. #15690532C2semidirect
7. C22⋊C4×C193C2semidirect
28. C2×D193D4semidirect
32. Dic193D4semidirect
39. C193#121semidirect
47. C22⋊C4D193semidirect