Finite Group Databasebeta

← #43244035

Subgroups — #43244035

Order 28096.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#28380766C211yesmaximal, characteristic, complemented
2#28380762C211yesmaximal, characteristic, complemented
3#28380689C211yesmaximal, characteristic, complemented
4#28380688C211yesmaximal, characteristic, complemented
5#28380684C211yesmaximal, characteristic, complemented
6C16×D439C211yesmaximal, characteristic, complemented
7SD32×C439C211yesmaximal, characteristic, complemented
8#20296330—21no—
9#20296328—21no—
10Dic1756C2211yescharacteristic
11#20296317—21no—
12#20296316—21no—
13D3512C2211yescharacteristic
14C8×D439C2211yescharacteristic
15C439⋊C16C2211yescharacteristic
16Q16×C439C2211yescharacteristic
17D8×C439C2211yescharacteristic
18C16×C439C2211yescharacteristic
19Dic878—21no—
20D1756—21no—
21D1756—41no—
22C22⋊D439—41no—
23C2×Dic439—41no—
24C4×D439—41no—
25C4×D439D411yescharacteristic
26C439⋊C8D411yescharacteristic
27Q8×C439—21no—
28D4×C439—21no—
29C8×C439C2311yescharacteristic
30C22×C439—41no—
31C2×D439—41no—
32C2×D439D811yescharacteristic
33C4×C439—41no—
34C4×C439C2×D411yescharacteristic
35Dic439—41no—
36Dic439D811yescharacteristic
37C2×C439—81no—
38C2×C439C2×D811yescharacteristic
39D439—21no—
40D439—81no—
41C439#50811yescharacteristic, complemented, Sylow
42#508—4391nomaximal, Sylow
43#135—4391no—
44#135—4391no—
45Q32—4391no—
46SD32—4391no—
47SD32D43911yescharacteristic, complemented
48D16—4391no—
49C2×C16—4391no—
50#41—8781no—
51#41—8781no—
52Q16—4391no—
53Q16C2×D43911yescharacteristic
54SD16—8781no—
55SD16—8781no—
56D8—4391no—
57D8C2×D43911yescharacteristic
58C2×C8—4391no—
59C16—4391no—
60C16C2×D43911yescharacteristic
61Q8—21no—
62Q8—8781no—
63D4—21no—
64D4—8781no—
65D4—17561no—
66D4—17561no—
67C2×C4—4391no—
68C2×C4—17561no—
69C2×C4—17561no—
70C8—4391no—
71C8C22×D43911yescharacteristic
72C22—41no—
73C22—4391no—
74C22—17561no—
75C4—41no—
76C4—4391no—
77C4—17561no—
78C4D4×D43911yescharacteristic
79C2—81no—
80C2—8781no—
81C2—35121no—
82C2D8×D43911yescharacteristic
subgroupG/H
centerC2D8×D439
commutator, cosocleC8×C439C23
FrattiniC8C22×D439
FittingSD32×C439C2
socleC2×C439C2×D8
hypercenterSD32D439
hypocenterC439#508
LCSG ▷ C8×C439 ▷ C4×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. #28380766C2semidirect
2. #28380762C2semidirect
3. #28380689C2semidirect
4. #28380688C2semidirect
5. #28380684C2semidirect
6. C16×D439C2semidirect
7. SD32×C439C2semidirect
41. C439#508semidirect
47. SD32D439semidirect

Maximal subgroups

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

subgroupindex
#283807662
#283807622
#283806892
#283806882
#283806842
C16×D4392
SD32×C4392
#508439