Finite Group Databasebeta

← #31826902

Subgroups — #31826902

Order 18112.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22583633C211yesmaximal, characteristic, complemented
2D8×D283C211yesmaximal, characteristic, complemented
3#22583553C211yesmaximal, characteristic, complemented
4D4528C211yesmaximal, characteristic, complemented
5#22583551C211yesmaximal, characteristic, complemented
6#22583549C211yesmaximal, characteristic, complemented
7SD32×C283C211yesmaximal, characteristic, complemented
8#17985393—21no—
9D4×D283—21no—
10#17985379—21no—
11D2264C2211yescharacteristic
12D2264C2211yescharacteristic, complemented
13#17985377—21no—
14C8×D283C2211yescharacteristic
15C283⋊C16C2211yescharacteristic, complemented
16Q16×C283C2211yescharacteristic, complemented
17D8×C283C2211yescharacteristic
18C16×C283C2211yescharacteristic, complemented
19C22×D283—41no—
20D1132—21no—
21D1132—21no—
22D1132—41no—
23C22⋊D283—41no—
24C4×D283—41no—
25C4×D283D411yescharacteristic
26C283⋊C8D411yescharacteristic
27Q8×C283—21no—
28D4×C283—21no—
29C8×C283C2311yescharacteristic
30C22×C283—41no—
31C2×D283—41no—
32C2×D283—41no—
33C2×D283—82no—
34C2×D283D811yescharacteristic
35C4×C283—41no—
36C4×C283C2×D411yescharacteristic
37Dic283D811yescharacteristic
38C2×C283—81no—
39C2×C283C2×D811yescharacteristic
40D283—21no—
41D283—81no—
42D283—81no—
43C283#50911yescharacteristic, complemented, Sylow
44#509—2831nomaximal, Sylow
45#135—2831no—
46C2×D8—2831no—
47SD32—2831no—
48SD32D28311yescharacteristic, complemented
49D16—2831no—
50D16—2831no—
51M32—2831no—
52#41—5661no—
53C2×D4—5661no—
54Q16C2×D28311yescharacteristic, complemented
55SD16—5661no—
56D8—2831no—
57D8—2831no—
58D8—5661no—
59D8C2×D28311yescharacteristic
60C2×C8—2831no—
61C16—2831no—
62C16C2×D28311yescharacteristic, complemented
63C23—11321no—
64Q8—21no—
65D4—21no—
66D4—5661no—
67D4—5661no—
68D4—11321no—
69D4—11321no—
70C2×C4—2831no—
71C2×C4—11321no—
72C8—2831no—
73C8C22×D28311yescharacteristic
74C22—41no—
75C22—2831no—
76C22—11321no—
77C22—11321no—
78C22—22642no—
79C4—41no—
80C4—2831no—
81C4D4×D28311yescharacteristic
82C2—81no—
83C2—5661no—
84C2—22641no—
85C2—22641no—
86C2D8×D28311yescharacteristic
subgroupG/H
centerC2D8×D283
commutator, cosocleC8×C283C23
FrattiniC8C22×D283
FittingSD32×C283C2
socleC2×C283C2×D8
hypercenterSD32D283
hypocenterC283#509
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. D8×D283C2semidirect
3. #22583553C2semidirect
4. D4528C2semidirect
5. #22583551C2semidirect
6. #22583549C2semidirect
7. SD32×C283C2semidirect
12. D2264C22semidirect
15. C283⋊C16C22semidirect
16. Q16×C283C22semidirect
18. C16×C283C22semidirect
43. C283#509semidirect
48. SD32D283semidirect
54. Q16C2×D283semidirect
62. C16C2×D283semidirect

Maximal subgroups

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

subgroupindex
#225836332
D8×D2832
#225835532
D45282
#225835512
#225835492
SD32×C2832
#509283