Finite Group Databasebeta

← #15784698

Subgroups — #15784698

Order 3328.

1246 conjugacy classes of subgroups; only the 427 normal subgroups are shown.

normal subgroups only

This group has 1246 conjugacy classes of subgroups — too many to draw. Only its 427 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13113098C218yesmaximal
2C4×#88071C216yesmaximal
3C2×C13×#376C211yesmaximal, characteristic
4C22×C42×C13C2213yes—
5C22×C4×Dic13C2214yes—
6C13×#376C418yescomplemented
7C2×C13×#95C2214yes—
8C2×#88071C22124yes—
9C23×C4×C13C2316yes—
10C23×C4×C13C2311yescharacteristic
11C23×Dic13C2318yes—
12C2×C42×C13—212no—
13C2×C42×C13C2×C4112yes—
14C2×C4×Dic13—224no—
15C13×#95C2×C4116yes—
16#88071—248no—
17#13855—131nomaximal, Sylow
18C24×C13C2411yescharacteristic
19C22×C4×C13—224no—
20C22×C4×C13—212no—
21C22×C4×C13C22×C4112yes—
22C22×C4×C13C22×C412yes—
23C22×C4×C13#41112yes—
24C22×Dic13—224no—
25C22×Dic13—224no—
26C22×Dic13#41116yes—
27C42×C13—224no—
28C4×Dic13—416no—
29C2×#376D1311yescharacteristic
30#1443—138no—
31C4×#95—136no—
32C23×C13C23×C411yescharacteristic
33C23×C13C2×#4116yes—
34C23×C13C2×#4118yes—
35C2×C4×C13—212no—
36C2×C4×C13—224no—
37C2×C4×C13—424no—
38C2×C4×C13#117112yes—
39C2×C4×C13#126116yes—
40C2×Dic13—248no—
41C2×Dic13—48no—
42C2×Dic13—424no—
43C22×C42—134no—
44C22×C42C2×D1313yes—
45#376Dic1318yescomplemented
46C2×#95—1324no—
47C2×#95C2×D1314yes—
48C22×C13C2×#11713yes—
49C22×C13C4×#4114yes—
50C22×C13C2×#12614yes—
51C22×C13#529124yes—
52C4×C13—412no—
53C4×C13#38318yes—
54Dic13—416no—
55C23×C4—138no—
56C23×C4C22×D1316yes—
57C23×C4C22×D1311yescharacteristic
58C2×C42—212no—
59C2×C42—2624no—
60C2×C42C2×Dic13112yes—
61#95—2648no—
62#95C2×Dic13116yes—
63C2×C13C2×#38311yescharacteristic
64C2×C13#229816yes—
65C2×C13#240118yes—
66C24C23×D1311yescharacteristic
67C22×C4—212no—
68C22×C4—224no—
69C22×C4—1316no—
70C22×C4—2624no—
71C22×C4—2624no—
72C22×C4#6127112yes—
73C22×C4C22×Dic13112yes—
74C22×C4C22×Dic1312yes—
75C42—224no—
76C42—5216no—
77C13#1385511yescharacteristic, complemented, Sylow
78C23C2×#612716yes—
79C23#41×D1318yes—
80C23C23×Dic1311yescharacteristic
81C2×C4—212no—
82C2×C4—224no—
83C2×C4—424no—
84C2×C4—2648no—
85C2×C4—528no—
86C2×C4—5224no—
87C2×C4#88130116yes—
88C2×C4#88180112yes—
89C22C2×#8813014yes—
90C22#11719233124yes—
91C22C2×#8818013yes—
92C22#41×Dic1314yes—
93C4—412no—
94C4—5216no—
95C4#1171859818yes—
96C2C2×#1171859811yescharacteristic
97C2#1311733416yes—
98C2#1311813418yes—
subgroupG/H
centerC23×C4C22×D13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC2×C13×#376C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×#376D13
hypocenterC13#13855
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
6. C13×#376C4semidirect
45. #376Dic13semidirect
77. C13#13855semidirect

Maximal subgroups

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

subgroupindex
#131130982
C4×#880712
C2×C13×#3762
#1385513