Finite Group Databasebeta

← #20261165

Subgroups — #20261165

Order 6208.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15690832C211yesmaximal, characteristic, complemented
2#15690756C211yesmaximal, characteristic, complemented
3#15690754C211yesmaximal, characteristic, complemented
4#15690753C211yesmaximal, characteristic, complemented
5#15690751C211yesmaximal, characteristic, complemented
6C2×#13095486C211yesmaximal, characteristic, complemented
7#135×C97C211yesmaximal, characteristic, complemented
8#13095511—21no—
9Dic388C2211yescharacteristic
10#13095500—21no—
11D776C2211yescharacteristic
12#13095486C2211yescharacteristic
13#13095486C2211yescharacteristic
14#41×C97—21no—
15Q16×C97C2211yescharacteristic
16SD16×C97—21no—
17D8×C97C2211yescharacteristic
18C2×C8×C97C2211yescharacteristic
19Q8×C97—21no—
20D4×C97—21no—
21D4×C97—41no—
22C2×C4×C97—41no—
23C2×C4×C97D411yescharacteristic
24C22⋊D97—41no—
25D388—21no—
26C4×D97—41no—
27Dic194—21no—
28C8×C97D411yescharacteristic
29C8×C97C2311yescharacteristic
30C22×C97—41no—
31C22×C97D811yescharacteristic
32C2×D97—41no—
33C4×C97—41no—
34C4×C97D811yescharacteristic
35C4×C97C2×D411yescharacteristic
36Dic97—41no—
37C2×C97—21no—
38C2×C97—81no—
39C2×C97C2×D811yescharacteristic
40D97—81no—
41C97#50811yescharacteristic, complemented, Sylow
42#508—971nomaximal, Sylow
43#135—971no—
44#135D9711yescharacteristic, complemented
45Q32—971no—
46SD32—971no—
47SD32—971no—
48D16—971no—
49C2×C16—971no—
50#41—21no—
51#41—1941no—
52Q16—971no—
53Q16C2×D9711yescharacteristic
54SD16—21no—
55SD16—1941no—
56D8—971no—
57D8C2×D9711yescharacteristic
58C2×C8C2×D9711yescharacteristic
59C16—971no—
60C16—971no—
61Q8—21no—
62Q8—1941no—
63D4—21no—
64D4—41no—
65D4—3881no—
66D4—1941no—
67C2×C4—41no—
68C2×C4—3881no—
69C2×C4C22⋊D9711yescharacteristic
70C8C22⋊D9711yescharacteristic
71C8C22×D9711yescharacteristic
72C22—41no—
73C22—3881no—
74C22#1309549611yescharacteristic
75C4—41no—
76C4—3881no—
77C4#1309549611yescharacteristic
78C4C2×C22⋊D9711yescharacteristic
79C2—21no—
80C2—81no—
81C2—7761no—
82C2C2×#1309549611yescharacteristic
subgroupG/H
centerC4#13095496
commutatorC8×C97C23
FrattiniC8C22×D97
Fitting#135×C97C2
socleC2×C97C2×D8
hypercenter#135D97
hypocenterC97#508
LCSG ▷ C8×C97 ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #15690832C2semidirect
2. #15690756C2semidirect
3. #15690754C2semidirect
4. #15690753C2semidirect
5. #15690751C2semidirect
6. C2×#13095486C2semidirect
7. #135×C97C2semidirect
41. C97#508semidirect
44. #135D97semidirect