Finite Group Databasebeta

← #27135689

Subgroups — #27135689

Order 12352.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20259921C211yesmaximal, characteristic, complemented
2#20259845C211yesmaximal, characteristic, complemented
3#20259843C211yesmaximal, characteristic, complemented
4#20259842C211yesmaximal, characteristic, complemented
5#20259840C211yesmaximal, characteristic, complemented
6C2×#15690530C211yesmaximal, characteristic, complemented
7#135×C193C211yesmaximal, characteristic, complemented
8#15690555—21no—
9Dic772C2211yescharacteristic
10#15690544—21no—
11D1544C2211yescharacteristic
12#15690530C2211yescharacteristic
13#15690530C2211yescharacteristic
14#41×C193—21no—
15Q16×C193C2211yescharacteristic
16SD16×C193—21no—
17D8×C193C2211yescharacteristic
18C2×C8×C193C2211yescharacteristic
19Dic386—21no—
20D772—21no—
21C22⋊D193—41no—
22C4×D193—41no—
23Q8×C193—21no—
24D4×C193—21no—
25D4×C193—41no—
26C2×C4×C193—41no—
27C2×C4×C193D411yescharacteristic
28C8×C193D411yescharacteristic
29C8×C193C2311yescharacteristic
30C22×C193—41no—
31C22×C193D811yescharacteristic
32C2×D193—41no—
33C4×C193—41no—
34C4×C193D811yescharacteristic
35C4×C193C2×D411yescharacteristic
36Dic193—41no—
37C2×C193—21no—
38C2×C193—81no—
39C2×C193C2×D811yescharacteristic
40D193—81no—
41C193#50811yescharacteristic, complemented, Sylow
42#508—1931nomaximal, Sylow
43#135—1931no—
44#135D19311yescharacteristic, complemented
45Q32—1931no—
46SD32—1931no—
47SD32—1931no—
48D16—1931no—
49C2×C16—1931no—
50#41—21no—
51#41—3861no—
52Q16—1931no—
53Q16C2×D19311yescharacteristic
54SD16—21no—
55SD16—3861no—
56D8—1931no—
57D8C2×D19311yescharacteristic
58C2×C8C2×D19311yescharacteristic
59C16—1931no—
60C16—1931no—
61Q8—21no—
62Q8—3861no—
63D4—21no—
64D4—41no—
65D4—7721no—
66D4—3861no—
67C2×C4—41no—
68C2×C4—7721no—
69C2×C4C22⋊D19311yescharacteristic
70C8C22⋊D19311yescharacteristic
71C8C22×D19311yescharacteristic
72C22—41no—
73C22—7721no—
74C22#1569054011yescharacteristic
75C4—41no—
76C4—7721no—
77C4#1569054011yescharacteristic
78C4C2×C22⋊D19311yescharacteristic
79C2—21no—
80C2—81no—
81C2—15441no—
82C2C2×#1569054011yescharacteristic
subgroupG/H
centerC4#15690540
commutator, cosocleC8×C193C23
FrattiniC8C22×D193
Fitting#135×C193C2
socleC2×C193C2×D8
hypercenter#135D193
hypocenterC193#508
LCSG ▷ C8×C193 ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #20259921C2semidirect
2. #20259845C2semidirect
3. #20259843C2semidirect
4. #20259842C2semidirect
5. #20259840C2semidirect
6. C2×#15690530C2semidirect
7. #135×C193C2semidirect
41. C193#508semidirect
44. #135D193semidirect

Maximal subgroups

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

subgroupindex
#202599212
#202598452
#202598432
#202598422
#202598402
C2×#156905302
#135×C1932
#508193