Finite Group Databasebeta

← SD32×D283 #31826887

Subgroups — SD32×D283 #31826887

Order 18112.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q16×D283C211yesmaximal, characteristic, complemented
2D8×D283C211yesmaximal, characteristic
3#22583555C211yesmaximal, characteristic, complemented
4#22583554C211yesmaximal, characteristic, complemented
5#22583553C211yesmaximal, characteristic, complemented
6C16×D283C211yesmaximal, characteristic, complemented
7SD32×C283C211yesmaximal, characteristic, complemented
8Q8×D283—21no—
9D4×D283—21no—
10Dic1132C2211yescharacteristic, complemented
11#17985382—21no—
12D2264C2211yescharacteristic
13#17985377—21no—
14C8×D283C2211yescharacteristic
15C283⋊C16C2211yescharacteristic, complemented
16Q16×C283C2211yescharacteristic, complemented
17D8×C283C2211yescharacteristic
18C16×C283C2211yescharacteristic, complemented
19C22×D283—41no—
20Dic566—21no—
21Dic566—41no—
22D1132—21no—
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—82no—
33C2×D283D811yescharacteristic
34C4×C283—41no—
35C4×C283C2×D411yescharacteristic
36Dic283—41no—
37Dic283D811yescharacteristic
38C2×C283—81no—
39C2×C283C2×D811yescharacteristic
40D283—81no—
41D283SD3212yesdirect product factor
42C283C2×SD3211yescharacteristic, complemented, Sylow
43C2×SD32—2831nomaximal, Sylow
44C2×Q16—2831no—
45C2×D8—2831no—
46SD32—2831no—
47SD32—2831no—
48SD32—2831no—
49SD32D28311yescharacteristic, direct product factor
50C2×C16—2831no—
51C2×Q8—5661no—
52C2×D4—5661no—
53Q16—2831no—
54Q16—5661no—
55Q16C2×D28311yescharacteristic, complemented
56D8—2831no—
57D8—5661no—
58D8C2×D28311yescharacteristic
59C2×C8—2831no—
60C16—2831no—
61C16C2×D28311yescharacteristic, complemented
62C23—11321no—
63Q8—21no—
64Q8—5661no—
65Q8—11321no—
66D4—21no—
67D4—5661no—
68D4—11321no—
69C2×C4—2831no—
70C2×C4—11321no—
71C8—2831no—
72C8C22×D28311yescharacteristic
73C22—41no—
74C22—2831no—
75C22—11321no—
76C22—22642no—
77C4—41no—
78C4—2831no—
79C4—11321no—
80C4D4×D28311yescharacteristic
81C2—81no—
82C2—2832no—
83C2—22641no—
84C2D8×D28311yescharacteristic
subgroupG/H
centerC2D8×D283
commutator, cosocleC8×C283C23
FrattiniC8C22×D283
FittingSD32×C283C2
socleC2×C283C2×D8
prime radicalD8×D283C2
hypercenterSD32D283
hypocenterC283C2×SD32
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. Q16×D283C2semidirect
3. #22583555C2semidirect
4. #22583554C2semidirect
5. #22583553C2semidirect
6. C16×D283C2semidirect
7. SD32×C283C2semidirect
10. Dic1132C22semidirect
15. C283⋊C16C22semidirect
16. Q16×C283C22semidirect
18. C16×C283C22semidirect
41. D283SD32direct (N × H)
42. C283C2×SD32semidirect
49. SD32D283direct (N × H)
55. Q16C2×D283semidirect
61. C16C2×D283semidirect

Maximal subgroups

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

subgroupindex
Q16×D2832
D8×D2832
#225835552
#225835542
#225835532
C16×D2832
SD32×C2832
C2×SD32283