Finite Group Databasebeta

← #31826896

Subgroups — #31826896

Order 18112.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22583633C211yesmaximal, characteristic, complemented
2#22583629C211yesmaximal, characteristic, complemented
3#22583556C211yesmaximal, characteristic, complemented
4#22583555C211yesmaximal, characteristic, complemented
5#22583551C211yesmaximal, characteristic, complemented
6C16×D283C211yesmaximal, characteristic, complemented
7SD32×C283C211yesmaximal, characteristic, complemented
8#17985393—21no—
9#17985391—21no—
10Dic1132C2211yescharacteristic
11#17985380—21no—
12#17985379—21no—
13D2264C2211yescharacteristic
14C8×D283C2211yescharacteristic
15C283⋊C16C2211yescharacteristic
16Q16×C283C2211yescharacteristic
17D8×C283C2211yescharacteristic
18C16×C283C2211yescharacteristic
19Dic566—21no—
20D1132—21no—
21D1132—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×D283—41no—
32C2×D283D811yescharacteristic
33C4×C283—41no—
34C4×C283C2×D411yescharacteristic
35Dic283—41no—
36Dic283D811yescharacteristic
37C2×C283—81no—
38C2×C283C2×D811yescharacteristic
39D283—21no—
40D283—81no—
41C283#50811yescharacteristic, complemented, Sylow
42#508—2831nomaximal, Sylow
43#135—2831no—
44#135—2831no—
45Q32—2831no—
46SD32—2831no—
47SD32D28311yescharacteristic, complemented
48D16—2831no—
49C2×C16—2831no—
50#41—5661no—
51#41—5661no—
52Q16—2831no—
53Q16C2×D28311yescharacteristic
54SD16—5661no—
55SD16—5661no—
56D8—2831no—
57D8C2×D28311yescharacteristic
58C2×C8—2831no—
59C16—2831no—
60C16C2×D28311yescharacteristic
61Q8—21no—
62Q8—5661no—
63D4—21no—
64D4—5661no—
65D4—11321no—
66D4—11321no—
67C2×C4—2831no—
68C2×C4—11321no—
69C2×C4—11321no—
70C8—2831no—
71C8C22×D28311yescharacteristic
72C22—41no—
73C22—2831no—
74C22—11321no—
75C4—41no—
76C4—2831no—
77C4—11321no—
78C4D4×D28311yescharacteristic
79C2—81no—
80C2—5661no—
81C2—22641no—
82C2D8×D28311yescharacteristic
subgroupG/H
centerC2D8×D283
commutator, cosocleC8×C283C23
FrattiniC8C22×D283
FittingSD32×C283C2
socleC2×C283C2×D8
hypercenterSD32D283
hypocenterC283#508
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
1. #22583633C2semidirect
2. #22583629C2semidirect
3. #22583556C2semidirect
4. #22583555C2semidirect
5. #22583551C2semidirect
6. C16×D283C2semidirect
7. SD32×C283C2semidirect
41. C283#508semidirect
47. SD32D283semidirect

Maximal subgroups

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

subgroupindex
#225836332
#225836292
#225835562
#225835552
#225835512
C16×D2832
SD32×C2832
#508283