Finite Group Databasebeta

← #27213576

Subgroups — #27213576

Order 13504.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20269999C211yesmaximal, characteristic, complemented
2#20269923C211yesmaximal, characteristic, complemented
3#20269921C211yesmaximal, characteristic, complemented
4#20269920C211yesmaximal, characteristic, complemented
5#20269918C211yesmaximal, characteristic, complemented
6C2×C211⋊C16C211yesmaximal, characteristic, complemented
7#135×C211C211yesmaximal, characteristic, complemented
8#16809962—21no—
9Dic844C2211yescharacteristic
10#16809951—21no—
11D1688C2211yescharacteristic
12C211⋊C16C2211yescharacteristic
13C211⋊C16C2211yescharacteristic
14#41×C211—21no—
15Q16×C211C2211yescharacteristic
16SD16×C211—21no—
17D8×C211C2211yescharacteristic
18C2×C8×C211C2211yescharacteristic
19Dic422—21no—
20D844—21no—
21C22⋊D211—41no—
22C4×D211—41no—
23Q8×C211—21no—
24D4×C211—21no—
25D4×C211—41no—
26C2×C4×C211—41no—
27C2×C4×C211D411yescharacteristic
28C8×C211D411yescharacteristic
29C8×C211C2311yescharacteristic
30C22×C211—41no—
31C22×C211D811yescharacteristic
32C2×D211—41no—
33C4×C211—41no—
34C4×C211D811yescharacteristic
35C4×C211C2×D411yescharacteristic
36Dic211—41no—
37C2×C211—21no—
38C2×C211—81no—
39C2×C211C2×D811yescharacteristic
40D211—81no—
41C211#50811yescharacteristic, complemented, Sylow
42#508—2111nomaximal, Sylow
43#135—2111no—
44#135D21111yescharacteristic, complemented
45Q32—2111no—
46SD32—2111no—
47SD32—2111no—
48D16—2111no—
49C2×C16—2111no—
50#41—21no—
51#41—4221no—
52Q16—2111no—
53Q16C2×D21111yescharacteristic
54SD16—21no—
55SD16—4221no—
56D8—2111no—
57D8C2×D21111yescharacteristic
58C2×C8C2×D21111yescharacteristic
59C16—2111no—
60C16—2111no—
61Q8—21no—
62Q8—4221no—
63D4—21no—
64D4—41no—
65D4—8441no—
66D4—4221no—
67C2×C4—41no—
68C2×C4—8441no—
69C2×C4C22⋊D21111yescharacteristic
70C8C22⋊D21111yescharacteristic
71C8C22×D21111yescharacteristic
72C22—41no—
73C22—8441no—
74C22#1680994711yescharacteristic
75C4—41no—
76C4—8441no—
77C4#1680994711yescharacteristic
78C4C2×C22⋊D21111yescharacteristic
79C2—21no—
80C2—81no—
81C2—16881no—
82C2C2×#1680994711yescharacteristic
subgroupG/H
centerC4#16809947
commutator, cosocleC8×C211C23
FrattiniC8C22×D211
Fitting#135×C211C2
socleC2×C211C2×D8
hypercenter#135D211
hypocenterC211#508
LCSG ▷ C8×C211 ▷ C4×C211 ▷ C2×C211 ▷ C211
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #20269999C2semidirect
2. #20269923C2semidirect
3. #20269921C2semidirect
4. #20269920C2semidirect
5. #20269918C2semidirect
6. C2×C211⋊C16C2semidirect
7. #135×C211C2semidirect
41. C211#508semidirect
44. #135D211semidirect

Maximal subgroups

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

subgroupindex
#202699992
#202699232
#202699212
#202699202
#202699182
C2×C211⋊C162
#135×C2112
#508211