Finite Group Databasebeta

← #27156884

Subgroups — #27156884

Order 12416.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20261644C211yesmaximal, characteristic
2#20261642C211yesmaximal, characteristic
3#20261090C211yesmaximal, characteristic
4#15690871—21no—
5#15690869—21no—
6#15690802C411yescharacteristic, complemented
7#15690798C2211yescharacteristic
8#15690735—21no—
9#15690732—21no—
10C4×C8×C97C411yescharacteristic, complemented
11#13095520—41no—
12C22⋊#87604—41no—
13C2×Dic194D411yescharacteristic
14C2×D388D411yescharacteristic
15C4⋊Dic97—21no—
16#13095490—41no—
17#13095488—41no—
18C2×C8×C97—21no—
19C42×C97C2×C411yescharacteristic
20C22×D97—21no—
21C2×#87604—81no—
22C2×C4×C97—21no—
23C2×C4×C97C22⋊C411yescharacteristic
24C2×Dic97—21no—
25C2×Dic97—41no—
26D388—41no—
27Dic194—41no—
28#11715897—81no—
29C8×C97—41no—
30C22×C97#9911yescharacteristic
31C2×D97—41no—
32C2×D97—81no—
33#87604—161no—
34C4×C97—21no—
35C4×C97—41no—
36Dic97—41no—
37Dic97—81no—
38C2×C97—21no—
39C2×C97#35411yescharacteristic
40D97—81no—
41#1414—971nomaximal, Sylow
42C97#141411yescharacteristic, complemented, Sylow
43#488—971no—
44#355—971no—
45#354—971no—
46#125—971no—
47#124—971no—
48#103—1941no—
49#102—1941no—
50#101—1941no—
51#99—1941no—
52C4×C8#8760411yescharacteristic, complemented
53C2×Q8—971no—
54C2×D4—971no—
55M16—3881no—
56C2×C8—21no—
57C4⋊C4—3881no—
58C4⋊C4—1941no—
59C22⋊C4—3881no—
60C22⋊C4—3881no—
61C42C2×#8760411yescharacteristic
62C23—1941no—
63Q8—3881no—
64D4—3881no—
65C2×C4—21no—
66C2×C4—7761no—
67C2×C4—3881no—
68C2×C4—1941no—
69C2×C4C22⋊#8760411yescharacteristic
70C8—41no—
71C8—7761no—
72C22—7761no—
73C22—3881no—
74C22#1569086911yescharacteristic
75C4—21no—
76C4—41no—
77C4—7761no—
78C4—15521no—
79C4—3881no—
80C2—21no—
81C2—7761no—
82C2#2026164211yescharacteristic
subgroupG/H
centerC2#20261642
commutatorC42×C97C2×C4
FrattiniC42C2×#87604
FittingC4×C8×C97C4
socleC2×C97#354
prime radicalC2×D388D4
cosocle#15690798C22
hypercenterC4×C8#87604
hypocenterC97#1414
LCSG ▷ C42×C97 ▷ C2×C4×C97 ▷ C22×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
6. #15690802C4semidirect
10. C4×C8×C97C4semidirect
42. C97#1414semidirect
52. C4×C8#87604semidirect

Maximal subgroups

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

subgroupindex
#202616442
#202616422
#202610902
#141497