Finite Group Databasebeta

← #27213577

Subgroups — #27213577

Order 13504.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20270000C211yesmaximal, characteristic, complemented
2#20269996C211yesmaximal, characteristic, complemented
3#20269923C211yesmaximal, characteristic, complemented
4#20269922C211yesmaximal, characteristic, complemented
5#20269918C211yesmaximal, characteristic, complemented
6C16×D211C211yesmaximal, characteristic, complemented
7SD32×C211C211yesmaximal, characteristic, complemented
8#16809963—21no—
9#16809961—21no—
10Dic844C2211yescharacteristic
11#16809950—21no—
12#16809949—21no—
13D1688C2211yescharacteristic
14C8×D211C2211yescharacteristic
15C211⋊C16C2211yescharacteristic
16Q16×C211C2211yescharacteristic
17D8×C211C2211yescharacteristic
18C16×C211C2211yescharacteristic
19Dic422—21no—
20D844—21no—
21D844—41no—
22C22⋊D211—41no—
23C2×Dic211—41no—
24C4×D211—41no—
25C4×D211D411yescharacteristic
26C211⋊C8D411yescharacteristic
27Q8×C211—21no—
28D4×C211—21no—
29C8×C211C2311yescharacteristic
30C22×C211—41no—
31C2×D211—41no—
32C2×D211D811yescharacteristic
33C4×C211—41no—
34C4×C211C2×D411yescharacteristic
35Dic211—41no—
36Dic211D811yescharacteristic
37C2×C211—81no—
38C2×C211C2×D811yescharacteristic
39D211—21no—
40D211—81no—
41C211#50811yescharacteristic, complemented, Sylow
42#508—2111nomaximal, Sylow
43#135—2111no—
44#135—2111no—
45Q32—2111no—
46SD32—2111no—
47SD32D21111yescharacteristic, complemented
48D16—2111no—
49C2×C16—2111no—
50#41—4221no—
51#41—4221no—
52Q16—2111no—
53Q16C2×D21111yescharacteristic
54SD16—4221no—
55SD16—4221no—
56D8—2111no—
57D8C2×D21111yescharacteristic
58C2×C8—2111no—
59C16—2111no—
60C16C2×D21111yescharacteristic
61Q8—21no—
62Q8—4221no—
63D4—21no—
64D4—8441no—
65D4—8441no—
66D4—4221no—
67C2×C4—8441no—
68C2×C4—8441no—
69C2×C4—2111no—
70C8—2111no—
71C8C22×D21111yescharacteristic
72C22—41no—
73C22—8441no—
74C22—2111no—
75C4—41no—
76C4—8441no—
77C4—2111no—
78C4D4×D21111yescharacteristic
79C2—81no—
80C2—16881no—
81C2—4221no—
82C2D8×D21111yescharacteristic
subgroupG/H
centerC2D8×D211
commutator, cosocleC8×C211C23
FrattiniC8C22×D211
FittingSD32×C211C2
socleC2×C211C2×D8
hypercenterSD32D211
hypocenterC211#508
LCSG ▷ C8×C211 ▷ C4×C211 ▷ C2×C211 ▷ C211
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. #20270000C2semidirect
2. #20269996C2semidirect
3. #20269923C2semidirect
4. #20269922C2semidirect
5. #20269918C2semidirect
6. C16×D211C2semidirect
7. SD32×C211C2semidirect
41. C211#508semidirect
47. SD32D211semidirect

Maximal subgroups

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

subgroupindex
#202700002
#202699962
#202699232
#202699222
#202699182
C16×D2112
SD32×C2112
#508211