Finite Group Databasebeta

← #31826904

Subgroups — #31826904

Order 18112.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22583629C211yesmaximal, characteristic
2Q16×D283C211yesmaximal, characteristic, complemented
3Dic2264C211yesmaximal, characteristic, complemented
4#22583556C211yesmaximal, characteristic, complemented
5#22583554C211yesmaximal, characteristic, complemented
6#22583549C211yesmaximal, characteristic, complemented
7SD32×C283C211yesmaximal, characteristic, complemented
8#17985391—21no—
9Q8×D283—21no—
10Dic1132C2211yescharacteristic
11Dic1132C2211yescharacteristic
12#17985382—21no—
13#17985380—21no—
14C8×D283C2211yescharacteristic
15C283⋊C16C2211yescharacteristic
16Q16×C283C2211yescharacteristic
17D8×C283C2211yescharacteristic
18C16×C283C2211yescharacteristic
19Dic566—21no—
20Dic566—21no—
21Dic566—41no—
22C22⋊D283—41no—
23C2×Dic283—41no—
24C4×D283—41no—
25C4×D283D411yescharacteristic
26C283⋊C8D411yescharacteristic
27Q8×C283—21no—
28D4×C283—21no—
29C8×C283C2311yescharacteristic
30C22×C283—41no—
31C2×D283D811yescharacteristic
32C4×C283—41no—
33C4×C283C2×D411yescharacteristic
34Dic283—41no—
35Dic283—41no—
36Dic283D811yescharacteristic
37C2×C283—81no—
38C2×C283C2×D811yescharacteristic
39D283—21no—
40C283#51011yescharacteristic, complemented, Sylow
41#510—2831nomaximal, Sylow
42#135—2831no—
43C2×Q16—2831no—
44Q32—2831no—
45Q32—2831no—
46SD32—2831no—
47SD32D28311yescharacteristic, complemented
48M32—2831no—
49#41—5661no—
50C2×Q8—5661no—
51Q16—2831no—
52Q16—2831no—
53Q16—5661no—
54Q16C2×D28311yescharacteristic
55SD16—5661no—
56D8C2×D28311yescharacteristic
57C2×C8—2831no—
58C16—2831no—
59C16C2×D28311yescharacteristic
60Q8—21no—
61Q8—5661no—
62Q8—5661no—
63Q8—11321no—
64D4—21no—
65D4—11321no—
66C2×C4—2831no—
67C2×C4—11321no—
68C2×C4—11321no—
69C8—2831no—
70C8C22×D28311yescharacteristic
71C22—41no—
72C22—2831no—
73C4—41no—
74C4—2831no—
75C4—11321no—
76C4—11321no—
77C4D4×D28311yescharacteristic
78C2—81no—
79C2—5661no—
80C2D8×D28311yescharacteristic
subgroupG/H
centerC2D8×D283
commutator, cosocleC8×C283C23
FrattiniC8C22×D283
FittingSD32×C283C2
socleC2×C283C2×D8
prime radical#22583629C2
hypercenterSD32D283
hypocenterC283#510
LCSG ▷ C8×C283 ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
2. Q16×D283C2semidirect
3. Dic2264C2semidirect
4. #22583556C2semidirect
5. #22583554C2semidirect
6. #22583549C2semidirect
7. SD32×C283C2semidirect
40. C283#510semidirect
47. SD32D283semidirect

Maximal subgroups

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

subgroupindex
#225836292
Q16×D2832
Dic22642
#225835562
#225835542
#225835492
SD32×C2832
#510283