Finite Group Databasebeta

← D8×#87938 #20266213

Subgroups — D8×#87938 #20266213

Order 6464.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#87938C212yesmaximal, complemented
2#15692324C211yesmaximal, characteristic, complemented
3#15692317C212yesmaximal, complemented
4C8×#87938C211yesmaximal, characteristic, complemented
5D8×D101C211yesmaximal, characteristic
6C22×#87938—22no—
7D101⋊C8C2211yescharacteristic
8C4⋊#87938C2212yes—
9C22⋊#87938—22no—
10C4×#87938C2211yescharacteristic
11D4×D101C2212yes—
12D808C411yescharacteristic, complemented
13#13108059C412yescomplemented
14C8×D101C2211yescharacteristic
15D8×C101C411yescharacteristic, complemented
16C22×D101—22no—
17C2×#87938—22no—
18C2×#87938—44no—
19C2×#87938D411yescharacteristic
20C2×#87938D411yescharacteristic
21D4×C101C2×C412yescomplemented
22C22⋊D101—22no—
23D404C2×C412yescomplemented
24C4×D101C2311yescharacteristic
25#11717581—21no—
26C8×C101C2×C411yescharacteristic, complemented
27#11717579C2×C411yescharacteristic, complemented
28C22×C101—22no—
29C2×D101—22no—
30C2×D101—42no—
31C2×D101—42no—
32C2×D101C2×D411yescharacteristic
33#87938—21no—
34#87938—42no—
35#87938D812yesdirect product factor
36C4×C101C22×C411yescharacteristic
37Dic101#4111yescharacteristic
38C2×C101—42no—
39C2×C101C4×D411yescharacteristic
40D101—42no—
41D101C2×D811yescharacteristic
42D101#13511yescharacteristic
43C101C4×D811yescharacteristic, complemented, Sylow
44C4×D8—1011nomaximal, Sylow
45C2×D8—1011no—
46C4×D4—1012no—
47#107—1011no—
48#102—1012no—
49C4×C8—1011no—
50C2×D4—1012no—
51C22×C4—2022no—
52D8—1012no—
53D8—1011no—
54D8#8793811yescharacteristic, direct product factor
55C2×C8—1011no—
56C2×C8—1011no—
57C4⋊C4—1012no—
58C22⋊C4—2022no—
59C42—1011no—
60C23—2022no—
61D4—1012no—
62D4—2022no—
63D4C2×#8793812yescomplemented
64C2×C4—1011no—
65C2×C4—1011no—
66C2×C4—1011no—
67C2×C4—4044no—
68C2×C4—2022no—
69C8—1011no—
70C8—2021no—
71C8C2×#8793811yescharacteristic, complemented
72C22—22no—
73C22—1011no—
74C22—4042no—
75C22—4042no—
76C22—2022no—
77C4—1012no—
78C4—1011no—
79C4—4042no—
80C4—2021no—
81C4C22×#8793811yescharacteristic
82C2—42no—
83C2—1011no—
84C2—1011no—
85C2—4042no—
86C2D4×#8793811yescharacteristic
subgroupG/H
centerC2D4×#87938
commutatorC4×C101C22×C4
FrattiniC4C22×#87938
FittingD8×C101C4
socleC2×C101C4×D4
hypercenterD8#87938
hypocenterC101C4×D8
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C4 ◁ D8

Complements

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

NH ≅ G/Ntype
1. D4×#87938C2semidirect
2. #15692324C2semidirect
3. #15692317C2semidirect
4. C8×#87938C2semidirect
12. D808C4semidirect
13. #13108059C4semidirect
15. D8×C101C4semidirect
21. D4×C101C2×C4semidirect
23. D404C2×C4semidirect
26. C8×C101C2×C4semidirect
27. #11717579C2×C4semidirect
35. #87938D8direct (N × H)
43. C101C4×D8semidirect
54. D8#87938direct (N × H)
63. D4C2×#87938semidirect
71. C8C2×#87938semidirect