Finite Group Databasebeta

← #46855432

Subgroups — #46855432

Order 35008.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31776025C211yesmaximal, characteristic, complemented
2#31776021C211yesmaximal, characteristic, complemented
3#31775948C211yesmaximal, characteristic, complemented
4#31775947C211yesmaximal, characteristic, complemented
5#31775943C211yesmaximal, characteristic, complemented
6C16×D547C211yesmaximal, characteristic, complemented
7SD32×C547C211yesmaximal, characteristic, complemented
8#22576777—21no—
9#22576775—21no—
10Dic2188C2211yescharacteristic
11#22576764—21no—
12#22576763—21no—
13D4376C2211yescharacteristic
14C8×D547C2211yescharacteristic
15C547⋊C16C2211yescharacteristic
16Q16×C547C2211yescharacteristic
17D8×C547C2211yescharacteristic
18C16×C547C2211yescharacteristic
19Dic1094—21no—
20D2188—21no—
21D2188—41no—
22C22⋊D547—41no—
23C2×Dic547—41no—
24C4×D547—41no—
25C4×D547D411yescharacteristic
26C547⋊C8D411yescharacteristic
27Q8×C547—21no—
28D4×C547—21no—
29C8×C547C2311yescharacteristic
30C22×C547—41no—
31C2×D547—41no—
32C2×D547D811yescharacteristic
33C4×C547—41no—
34C4×C547C2×D411yescharacteristic
35Dic547—41no—
36Dic547D811yescharacteristic
37C2×C547—81no—
38C2×C547C2×D811yescharacteristic
39D547—21no—
40D547—81no—
41C547#50811yescharacteristic, complemented, Sylow
42#508—5471nomaximal, Sylow
43#135—5471no—
44#135—5471no—
45Q32—5471no—
46SD32—5471no—
47SD32D54711yescharacteristic, complemented
48D16—5471no—
49C2×C16—5471no—
50#41—10941no—
51#41—10941no—
52Q16—5471no—
53Q16C2×D54711yescharacteristic
54SD16—10941no—
55SD16—10941no—
56D8—5471no—
57D8C2×D54711yescharacteristic
58C2×C8—5471no—
59C16—5471no—
60C16C2×D54711yescharacteristic
61Q8—21no—
62Q8—10941no—
63D4—21no—
64D4—10941no—
65D4—21881no—
66D4—21881no—
67C2×C4—5471no—
68C2×C4—21881no—
69C2×C4—21881no—
70C8—5471no—
71C8C22×D54711yescharacteristic
72C22—41no—
73C22—5471no—
74C22—21881no—
75C4—41no—
76C4—5471no—
77C4—21881no—
78C4D4×D54711yescharacteristic
79C2—81no—
80C2—43761no—
81C2—10941no—
82C2D8×D54711yescharacteristic
subgroupG/H
centerC2D8×D547
commutator, cosocleC8×C547C23
FrattiniC8C22×D547
FittingSD32×C547C2
socleC2×C547C2×D8
hypercenterSD32D547
hypocenterC547#508
LCSG ▷ C8×C547 ▷ C4×C547 ▷ C2×C547 ▷ C547
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. #31776025C2semidirect
2. #31776021C2semidirect
3. #31775948C2semidirect
4. #31775947C2semidirect
5. #31775943C2semidirect
6. C16×D547C2semidirect
7. SD32×C547C2semidirect
41. C547#508semidirect
47. SD32D547semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#317760252
#317760212
#317759482
#317759472
#317759432
C16×D5472
SD32×C5472
#508547