Finite Group Databasebeta

← #44500826

Subgroups — #44500826

Order 30656.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#29506405C211yesmaximal, characteristic, complemented
2#29506401C211yesmaximal, characteristic, complemented
3#29506328C211yesmaximal, characteristic, complemented
4#29506327C211yesmaximal, characteristic, complemented
5#29506323C211yesmaximal, characteristic, complemented
6C16×D479C211yesmaximal, characteristic, complemented
7SD32×C479C211yesmaximal, characteristic, complemented
8#21440163—21no—
9#21440161—21no—
10Dic1916C2211yescharacteristic
11#21440150—21no—
12#21440149—21no—
13D3832C2211yescharacteristic
14C8×D479C2211yescharacteristic
15C479⋊C16C2211yescharacteristic
16Q16×C479C2211yescharacteristic
17D8×C479C2211yescharacteristic
18C16×C479C2211yescharacteristic
19Dic958—21no—
20D1916—21no—
21D1916—41no—
22C22⋊D479—41no—
23C2×Dic479—41no—
24C4×D479—41no—
25C4×D479D411yescharacteristic
26C479⋊C8D411yescharacteristic
27Q8×C479—21no—
28D4×C479—21no—
29C8×C479C2311yescharacteristic
30C22×C479—41no—
31C2×D479—41no—
32C2×D479D811yescharacteristic
33C4×C479—41no—
34C4×C479C2×D411yescharacteristic
35Dic479—41no—
36Dic479D811yescharacteristic
37C2×C479—81no—
38C2×C479C2×D811yescharacteristic
39D479—21no—
40D479—81no—
41C479#50811yescharacteristic, complemented, Sylow
42#508—4791nomaximal, Sylow
43#135—4791no—
44#135—4791no—
45Q32—4791no—
46SD32—4791no—
47SD32D47911yescharacteristic, complemented
48D16—4791no—
49C2×C16—4791no—
50#41—9581no—
51#41—9581no—
52Q16—4791no—
53Q16C2×D47911yescharacteristic
54SD16—9581no—
55SD16—9581no—
56D8—4791no—
57D8C2×D47911yescharacteristic
58C2×C8—4791no—
59C16—4791no—
60C16C2×D47911yescharacteristic
61Q8—21no—
62Q8—9581no—
63D4—21no—
64D4—19161no—
65D4—19161no—
66D4—9581no—
67C2×C4—19161no—
68C2×C4—19161no—
69C2×C4—4791no—
70C8—4791no—
71C8C22×D47911yescharacteristic
72C22—41no—
73C22—19161no—
74C22—4791no—
75C4—41no—
76C4—19161no—
77C4—4791no—
78C4D4×D47911yescharacteristic
79C2—81no—
80C2—9581no—
81C2—38321no—
82C2D8×D47911yescharacteristic
subgroupG/H
centerC2D8×D479
commutator, cosocleC8×C479C23
FrattiniC8C22×D479
FittingSD32×C479C2
socleC2×C479C2×D8
hypercenterSD32D479
hypocenterC479#508
LCSG ▷ C8×C479 ▷ C4×C479 ▷ C2×C479 ▷ C479
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. #29506405C2semidirect
2. #29506401C2semidirect
3. #29506328C2semidirect
4. #29506327C2semidirect
5. #29506323C2semidirect
6. C16×D479C2semidirect
7. SD32×C479C2semidirect
41. C479#508semidirect
47. SD32D479semidirect

Maximal subgroups

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

subgroupindex
#295064052
#295064012
#295063282
#295063272
#295063232
C16×D4792
SD32×C4792
#508479