Finite Group Databasebeta

← #44500825

Subgroups — #44500825

Order 30656.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#29506404C211yesmaximal, characteristic, complemented
2#29506328C211yesmaximal, characteristic, complemented
3#29506326C211yesmaximal, characteristic, complemented
4#29506325C211yesmaximal, characteristic, complemented
5#29506323C211yesmaximal, characteristic, complemented
6C2×C479⋊C16C211yesmaximal, characteristic, complemented
7#135×C479C211yesmaximal, characteristic, complemented
8#21440162—21no—
9Dic1916C2211yescharacteristic
10#21440151—21no—
11D3832C2211yescharacteristic
12C479⋊C16C2211yescharacteristic
13C479⋊C16C2211yescharacteristic
14#41×C479—21no—
15Q16×C479C2211yescharacteristic
16SD16×C479—21no—
17D8×C479C2211yescharacteristic
18C2×C8×C479C2211yescharacteristic
19Dic958—21no—
20D1916—21no—
21C22⋊D479—41no—
22C4×D479—41no—
23Q8×C479—21no—
24D4×C479—21no—
25D4×C479—41no—
26C2×C4×C479—41no—
27C2×C4×C479D411yescharacteristic
28C8×C479D411yescharacteristic
29C8×C479C2311yescharacteristic
30C22×C479—41no—
31C22×C479D811yescharacteristic
32C2×D479—41no—
33C4×C479—41no—
34C4×C479D811yescharacteristic
35C4×C479C2×D411yescharacteristic
36Dic479—41no—
37C2×C479—21no—
38C2×C479—81no—
39C2×C479C2×D811yescharacteristic
40D479—81no—
41C479#50811yescharacteristic, complemented, Sylow
42#508—4791nomaximal, Sylow
43#135—4791no—
44#135D47911yescharacteristic, complemented
45Q32—4791no—
46SD32—4791no—
47SD32—4791no—
48D16—4791no—
49C2×C16—4791no—
50#41—21no—
51#41—9581no—
52Q16—4791no—
53Q16C2×D47911yescharacteristic
54SD16—21no—
55SD16—9581no—
56D8—4791no—
57D8C2×D47911yescharacteristic
58C2×C8C2×D47911yescharacteristic
59C16—4791no—
60C16—4791no—
61Q8—21no—
62Q8—9581no—
63D4—21no—
64D4—41no—
65D4—19161no—
66D4—9581no—
67C2×C4—41no—
68C2×C4—19161no—
69C2×C4C22⋊D47911yescharacteristic
70C8C22⋊D47911yescharacteristic
71C8C22×D47911yescharacteristic
72C22—41no—
73C22—19161no—
74C22#2144014711yescharacteristic
75C4—41no—
76C4—19161no—
77C4#2144014711yescharacteristic
78C4C2×C22⋊D47911yescharacteristic
79C2—21no—
80C2—81no—
81C2—38321no—
82C2C2×#2144014711yescharacteristic
subgroupG/H
centerC4#21440147
commutator, cosocleC8×C479C23
FrattiniC8C22×D479
Fitting#135×C479C2
socleC2×C479C2×D8
hypercenter#135D479
hypocenterC479#508
LCSG ▷ C8×C479 ▷ C4×C479 ▷ C2×C479 ▷ C479
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #29506404C2semidirect
2. #29506328C2semidirect
3. #29506326C2semidirect
4. #29506325C2semidirect
5. #29506323C2semidirect
6. C2×C479⋊C16C2semidirect
7. #135×C479C2semidirect
41. C479#508semidirect
44. #135D479semidirect

Maximal subgroups

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

subgroupindex
#295064042
#295063282
#295063262
#295063252
#295063232
C2×C479⋊C162
#135×C4792
#508479