Finite Group Databasebeta

← D8×#90673 #20299634

Subgroups — D8×#90673 #20299634

Order 7232.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#90673C212yesmaximal, complemented
2#16813691C211yesmaximal, characteristic, complemented
3#16813684C212yesmaximal, complemented
4C8×#90673C211yesmaximal, characteristic, complemented
5D8×D113C211yesmaximal, characteristic
6C22×#90673—22no—
7#14268655C2211yescharacteristic
8C4⋊#90673C2212yes—
9C22⋊#90673—22no—
10C4×#90673C2211yescharacteristic
11D4×D113C2212yes—
12D904C411yescharacteristic, complemented
13#14268632C412yescomplemented
14C8×D113C2211yescharacteristic
15D8×C113C411yescharacteristic, complemented
16C22×D113—22no—
17C2×#90673—22no—
18C2×#90673—44no—
19C2×#90673D411yescharacteristic
20C2×#90673D411yescharacteristic
21D4×C113C2×C412yescomplemented
22C22⋊D113—22no—
23D452C2×C412yescomplemented
24C4×D113C2311yescharacteristic
25#11744753—21no—
26C8×C113C2×C411yescharacteristic, complemented
27#11744751C2×C411yescharacteristic, complemented
28C22×C113—22no—
29C2×D113—22no—
30C2×D113—42no—
31C2×D113—42no—
32C2×D113C2×D411yescharacteristic
33#90673—21no—
34#90673—42no—
35#90673D812yesdirect product factor
36C4×C113C22×C411yescharacteristic
37Dic113#4111yescharacteristic
38C2×C113—42no—
39C2×C113C4×D411yescharacteristic
40D113—42no—
41D113C2×D811yescharacteristic
42D113#13511yescharacteristic
43C113C4×D811yescharacteristic, complemented, Sylow
44C4×D8—1131nomaximal, Sylow
45C2×D8—1131no—
46C4×D4—1132no—
47#107—1131no—
48#102—1132no—
49C4×C8—1131no—
50C2×D4—1132no—
51C22×C4—2262no—
52D8—1132no—
53D8—1131no—
54D8#9067311yescharacteristic, direct product factor
55C2×C8—1131no—
56C2×C8—1131no—
57C4⋊C4—1132no—
58C22⋊C4—2262no—
59C42—1131no—
60C23—2262no—
61D4—1132no—
62D4—2262no—
63D4C2×#9067312yescomplemented
64C2×C4—1131no—
65C2×C4—1131no—
66C2×C4—1131no—
67C2×C4—4524no—
68C2×C4—2262no—
69C8—1131no—
70C8—2261no—
71C8C2×#9067311yescharacteristic, complemented
72C22—22no—
73C22—1131no—
74C22—4522no—
75C22—4522no—
76C22—2262no—
77C4—1132no—
78C4—1131no—
79C4—4522no—
80C4—2261no—
81C4C22×#9067311yescharacteristic
82C2—42no—
83C2—1131no—
84C2—1131no—
85C2—4522no—
86C2D4×#9067311yescharacteristic
subgroupG/H
centerC2D4×#90673
commutatorC4×C113C22×C4
FrattiniC4C22×#90673
FittingD8×C113C4
socleC2×C113C4×D4
hypercenterD8#90673
hypocenterC113C4×D8
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C4 ◁ D8

Complements

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

NH ≅ G/Ntype
1. D4×#90673C2semidirect
2. #16813691C2semidirect
3. #16813684C2semidirect
4. C8×#90673C2semidirect
12. D904C4semidirect
13. #14268632C4semidirect
15. D8×C113C4semidirect
21. D4×C113C2×C4semidirect
23. D452C2×C4semidirect
26. C8×C113C2×C4semidirect
27. #11744751C2×C4semidirect
35. #90673D8direct (N × H)
43. C113C4×D8semidirect
54. D8#90673direct (N × H)
63. D4C2×#90673semidirect
71. C8C2×#90673semidirect