Finite Group Databasebeta

← #20261776

Subgroups — #20261776

Order 6208.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#87604C212yesmaximal, complemented
2#15690878C211yesmaximal, characteristic, complemented
3#15690872C212yesmaximal, complemented
4#15690864C211yesmaximal, characteristic, complemented
5D8×D97C211yesmaximal, characteristic
6C22×#87604—22no—
7#13095519C2211yescharacteristic
8C4⋊#87604C2212yes—
9C22⋊#87604—22no—
10C4×#87604C2211yescharacteristic
11D4×D97C2212yes—
12D776C411yescharacteristic, complemented
13#13095496C412yescomplemented
14C8×D97C2211yescharacteristic
15D8×C97C411yescharacteristic, complemented
16C22×D97—22no—
17C2×#87604—22no—
18C2×#87604—44no—
19C2×#87604D412yes—
20D4×C97C2×C412yescomplemented
21C22⋊D97—22no—
22D388C2×C412yescomplemented
23C4×D97C2311yescharacteristic
24#11715897—21no—
25C8×C97C2×C411yescharacteristic, complemented
26#11715895C2×C411yescharacteristic, complemented
27C22×C97—22no—
28C2×D97—22no—
29C2×D97—42no—
30C2×D97—42no—
31C2×D97C2×D411yescharacteristic
32#87604—22no—
33#87604—42no—
34C4×C97C22×C411yescharacteristic
35Dic97#4111yescharacteristic
36C2×C97—42no—
37C2×C97C4×D411yescharacteristic
38D97—42no—
39D97AGL(1,ℤ/8)12yes—
40C97#44211yescharacteristic, complemented, Sylow
41#442—971nomaximal, Sylow
42C2×D8—971no—
43C4×D4—972no—
44#106—971no—
45#102—972no—
46#97—971no—
47C2×D4—972no—
48C22×C4—1942no—
49D8—972no—
50D8—971no—
51D8#8760411yescharacteristic, complemented
52C2×C8—971no—
53C2×C8—971no—
54C4⋊C4—972no—
55C22⋊C4—1942no—
56C42—971no—
57C23—1942no—
58D4—972no—
59D4—1942no—
60D4C2×#8760412yescomplemented
61C2×C4—971no—
62C2×C4—972no—
63C2×C4—3884no—
64C2×C4—1942no—
65C8—971no—
66C8—1941no—
67C8C2×#8760411yescharacteristic, complemented
68C22—22no—
69C22—971no—
70C22—3882no—
71C22—3882no—
72C22—1942no—
73C4—971no—
74C4—3882no—
75C4—1942no—
76C4C22×#8760411yescharacteristic
77C2—42no—
78C2—972no—
79C2—3882no—
80C2D4×#8760411yescharacteristic
subgroupG/H
centerC2D4×#87604
commutatorC4×C97C22×C4
FrattiniC4C22×#87604
FittingD8×C97C4
socleC2×C97C4×D4
hypercenterD8#87604
hypocenterC97#442
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C4 ◁ D8

Complements

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

NH ≅ G/Ntype
1. D4×#87604C2semidirect
2. #15690878C2semidirect
3. #15690872C2semidirect
4. #15690864C2semidirect
12. D776C4semidirect
13. #13095496C4semidirect
15. D8×C97C4semidirect
20. D4×C97C2×C4semidirect
22. D388C2×C4semidirect
25. C8×C97C2×C4semidirect
26. #11715895C2×C4semidirect
40. C97#442semidirect
51. D8#87604semidirect
60. D4C2×#87604semidirect
67. C8C2×#87604semidirect