Finite Group Databasebeta

← C23×#13095520 #27158721

Subgroups — C23×#13095520 #27158721

Order 12416.

1720 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13095520C2128yesmaximal, direct product factor
2C23×#11715897C212yesmaximal, complemented
3C24×Dic97C211yesmaximal, characteristic
4C2×#13095520C221112yesdirect product factor
5C22×#11715897C22128yescomplemented
6C23×Dic97C4114yes—
7C23×Dic97C411yescharacteristic
8C23×Dic97C2211yescharacteristic
9C23×Dic97C22114yes—
10C25×C97C411yescharacteristic
11#13095520C23164yesdirect product factor
12C2×#11715897C23156yescomplemented
13C22×Dic97C2×C4184yes—
14C22×Dic97C2×C417yes—
15C22×Dic97C2×C4114yes—
16C22×Dic97C2317yes—
17C22×Dic97C23128yes—
18C24×C97—28no—
19C24×C97C2×C4114yes—
20C24×C97C2×C411yescharacteristic
21C23×C97—256no—
22C23×C97M1618yescomplemented
23C23×C97C22×C4128yes—
24C23×C97C22×C417yes—
25C2×Dic97C22×C4156yes—
26C2×Dic97C22×C4121yes—
27C2×Dic97C22×C4128yes—
28C2×Dic97C2417yes—
29C2×Dic97C2418yes—
30#11715897C24116yescomplemented
31C22×C97—256no—
32C22×C97C2×M16128yescomplemented
33C22×C97C23×C418yes—
34C22×C97C23×C417yes—
35Dic97C23×C417yes—
36Dic97C23×C418yes—
37Dic97C2511yescharacteristic
38C2×C97—28no—
39C2×C97C22×M16114yescomplemented
40C2×C97C24×C411yescharacteristic
41C23×M16—971nomaximal, Sylow
42C97C23×M1611yescharacteristic, complemented, Sylow
43C24×C4—971no—
44C22×M16—9728no—
45C23×C8—972no—
46C25#8760411yescharacteristic
47C23×C4—9714no—
48C23×C4—9714no—
49C23×C4—971no—
50C23×C4—971no—
51C2×M16—97112no—
52C22×C8—9728no—
53C24—28no—
54C24C2×#87604114yes—
55C24C2×#8760411yescharacteristic
56C22×C4—9784no—
57C22×C4—9714no—
58C22×C4—977no—
59C22×C4—977no—
60C22×C4—9728no—
61M16—9764no—
62C2×C8—9756no—
63C23—256no—
64C23#1309552018yesdirect product factor
65C23C22×#87604128yes—
66C23C22×#8760417yes—
67C2×C4—977no—
68C2×C4—978no—
69C2×C4—9756no—
70C2×C4—9721no—
71C2×C4—9728no—
72C8—9716no—
73C22—256no—
74C22C2×#13095520128yesdirect product factor
75C22C23×#8760418yes—
76C22C23×#8760417yes—
77C4—971no—
78C4—977no—
79C4—978no—
80C2—28no—
81C2C22×#13095520114yesdirect product factor
82C2C24×#8760411yescharacteristic
subgroupG/H
centerC24C2×#87604
commutatorC2×C97C24×C4
FrattiniC2C24×#87604
Fitting, prime radicalC25×C97C4
socleC24×C97C2×C4
cosocleDic97C25
hypercenterC25#87604
hypocenterC97C23×M16
LCSG ▷ C2×C97 ▷ C97
UCSC1 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C22×#13095520C2direct (N × H)
2. C23×#11715897C2semidirect
4. C2×#13095520C22direct (N × H)
5. C22×#11715897C22semidirect
11. #13095520C23direct (N × H)
12. C2×#11715897C23semidirect
22. C23×C97M16semidirect
30. #11715897C24semidirect
32. C22×C97C2×M16semidirect
39. C2×C97C22×M16semidirect
42. C97C23×M16semidirect
64. C23#13095520direct (N × H)
74. C22C2×#13095520direct (N × H)
81. C2C22×#13095520direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130955202
C23×#117158972
C24×Dic972
C23×M1697