Finite Group Databasebeta

← #20261169

Subgroups — #20261169

Order 6208.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15690829C211yesmaximal, characteristic, complemented
2D8×D97C211yesmaximal, characteristic, complemented
3#15690755C211yesmaximal, characteristic, complemented
4#15690754C211yesmaximal, characteristic, complemented
5#15690751C211yesmaximal, characteristic, complemented
6#15690749C211yesmaximal, characteristic, complemented
7D16×C97C211yesmaximal, characteristic, complemented
8#13095510—21no—
9D4×D97—21no—
10Dic388C2211yescharacteristic, complemented
11#13095499—21no—
12D776C2211yescharacteristic
13#13095496—21no—
14C8×D97C2211yescharacteristic
15#13095486C2211yescharacteristic, complemented
16D8×C97C2211yescharacteristic
17D8×C97C2211yescharacteristic, complemented
18C16×C97C2211yescharacteristic, complemented
19C22×D97—41no—
20D4×C97—21no—
21D4×C97—21no—
22C22⋊D97—41no—
23C22⋊D97—41no—
24C2×Dic97—41no—
25D388—21no—
26C4×D97D411yescharacteristic
27Dic194—21no—
28C8×C97C2311yescharacteristic
29#11715895D411yescharacteristic
30C22×C97—41no—
31C22×C97—41no—
32C2×D97—41no—
33C2×D97—82no—
34C2×D97D811yescharacteristic
35C4×C97C2×D411yescharacteristic
36Dic97—41no—
37Dic97D811yescharacteristic
38C2×C97—81no—
39C2×C97—81no—
40C2×C97C2×D811yescharacteristic
41D97—21no—
42D97—81no—
43C97#50911yescharacteristic, complemented, Sylow
44#509—971nomaximal, Sylow
45#135—971no—
46C2×D8—971no—
47SD32—971no—
48SD32—971no—
49D16—971no—
50D16D9711yescharacteristic, complemented
51M32—971no—
52#41—1941no—
53C2×D4—1941no—
54Q16—971no—
55SD16—1941no—
56D8—971no—
57D8—1941no—
58D8C2×D9711yescharacteristic
59D8C2×D9711yescharacteristic, complemented
60C2×C8—971no—
61C16—971no—
62C16C2×D9711yescharacteristic, complemented
63C23—3881no—
64Q8—1941no—
65D4—21no—
66D4—21no—
67D4—3881no—
68D4—3881no—
69D4—1941no—
70C2×C4—971no—
71C2×C4—3881no—
72C8—971no—
73C8C22×D9711yescharacteristic
74C22—41no—
75C22—41no—
76C22—7762no—
77C22—971no—
78C22—3881no—
79C4—971no—
80C4—3881no—
81C4D4×D9711yescharacteristic
82C2—81no—
83C2—81no—
84C2—7761no—
85C2—1941no—
86C2D8×D9711yescharacteristic
subgroupG/H
centerC2D8×D97
commutatorC8×C97C23
FrattiniC8C22×D97
FittingD16×C97C2
socleC2×C97C2×D8
hypercenterD16D97
hypocenterC97#509
LCSG ▷ C8×C97 ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D16

Complements

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

NH ≅ G/Ntype
1. #15690829C2semidirect
2. D8×D97C2semidirect
3. #15690755C2semidirect
4. #15690754C2semidirect
5. #15690751C2semidirect
6. #15690749C2semidirect
7. D16×C97C2semidirect
10. Dic388C22semidirect
15. #13095486C22semidirect
17. D8×C97C22semidirect
18. C16×C97C22semidirect
43. C97#509semidirect
50. D16D97semidirect
59. D8C2×D97semidirect
62. C16C2×D97semidirect