Finite Group Databasebeta

← #22581384

Subgroups — #22581384

Order 8896.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17984865C211yesmaximal, characteristic, complemented
2#17984861C211yesmaximal, characteristic, complemented
3#17984788C211yesmaximal, characteristic, complemented
4#17984787C211yesmaximal, characteristic, complemented
5#17984783C211yesmaximal, characteristic, complemented
6C16×D139C211yesmaximal, characteristic, complemented
7SD32×C139C211yesmaximal, characteristic, complemented
8#14555786—21no—
9#14555784—21no—
10Dic556C2211yescharacteristic
11#14555773—21no—
12#14555772—21no—
13D1112C2211yescharacteristic
14C8×D139C2211yescharacteristic
15C139⋊C16C2211yescharacteristic
16Q16×C139C2211yescharacteristic
17D8×C139C2211yescharacteristic
18C16×C139C2211yescharacteristic
19Dic278—21no—
20D556—21no—
21D556—41no—
22C22⋊D139—41no—
23C2×Dic139—41no—
24C4×D139—41no—
25C4×D139D411yescharacteristic
26C139⋊C8D411yescharacteristic
27Q8×C139—21no—
28D4×C139—21no—
29C8×C139C2311yescharacteristic
30C22×C139—41no—
31C2×D139—41no—
32C2×D139D811yescharacteristic
33C4×C139—41no—
34C4×C139C2×D411yescharacteristic
35Dic139—41no—
36Dic139D811yescharacteristic
37C2×C139—81no—
38C2×C139C2×D811yescharacteristic
39D139—21no—
40D139—81no—
41C139#50811yescharacteristic, complemented, Sylow
42#508—1391nomaximal, Sylow
43#135—1391no—
44#135—1391no—
45Q32—1391no—
46SD32—1391no—
47SD32D13911yescharacteristic, complemented
48D16—1391no—
49C2×C16—1391no—
50#41—2781no—
51#41—2781no—
52Q16—1391no—
53Q16C2×D13911yescharacteristic
54SD16—2781no—
55SD16—2781no—
56D8—1391no—
57D8C2×D13911yescharacteristic
58C2×C8—1391no—
59C16—1391no—
60C16C2×D13911yescharacteristic
61Q8—21no—
62Q8—2781no—
63D4—21no—
64D4—2781no—
65D4—5561no—
66D4—5561no—
67C2×C4—5561no—
68C2×C4—5561no—
69C2×C4—1391no—
70C8—1391no—
71C8C22×D13911yescharacteristic
72C22—41no—
73C22—5561no—
74C22—1391no—
75C4—41no—
76C4—5561no—
77C4—1391no—
78C4D4×D13911yescharacteristic
79C2—81no—
80C2—2781no—
81C2—11121no—
82C2D8×D13911yescharacteristic
subgroupG/H
centerC2D8×D139
commutatorC8×C139C23
FrattiniC8C22×D139
FittingSD32×C139C2
socleC2×C139C2×D8
hypercenterSD32D139
hypocenterC139#508
LCSG ▷ C8×C139 ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. #17984865C2semidirect
2. #17984861C2semidirect
3. #17984788C2semidirect
4. #17984787C2semidirect
5. #17984783C2semidirect
6. C16×D139C2semidirect
7. SD32×C139C2semidirect
41. C139#508semidirect
47. SD32D139semidirect