Finite Group Databasebeta

← C23×C42×D13 #16769467

Subgroups — C23×C42×D13 #16769467

Order 3328.

24030 conjugacy classes of subgroups; only the 13515 normal subgroups are shown.

normal subgroups only

This group has 24030 conjugacy classes of subgroups — too many to draw. Only its 13515 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
1C24×C4×D13C213yesmaximal
2C23×C4×Dic13C213yesmaximal, complemented
3C22×C42×D13C2156yesmaximal, direct product factor
4C23×C42×C13C211yesmaximal, characteristic, complemented
5C25×D13C2211yescharacteristic
6C24×C4×C13C2213yes—
7C24×Dic13C2213yes—
8C23×C4×D13C4196yesdirect product factor
9C23×C4×D13C22184yes—
10C22×C42×C13C22128yescomplemented
11C22×C4×Dic13C22184yescomplemented
12C2×C42×D13C221448yesdirect product factor
13C25×C13C2311yescharacteristic
14C24×D13C2×C4148yes—
15C24×D13C23114yes—
16C23×C4×C13C2×C4148yescomplemented
17C23×C4×C13C23142yes—
18C23×Dic13C2×C4148yescomplemented
19C23×Dic13C23142yes—
20C22×C4×D13C2×C411344yesdirect product factor
21C22×C4×D13C231336yes—
22C2×C42×C13C231112yescomplemented
23C2×C4×Dic13C231336yescomplemented
24C42×D13C231512yesdirect product factor
25C24×C42—131nomaximal, Sylow
26C24×C13C22×C4124yes—
27C24×C13C2417yes—
28C23×D13C421256yesdirect product factor
29C23×D13C22×C41336yes—
30C23×D13C24128yes—
31C22×C4×C13C22×C41336yescomplemented
32C22×C4×C13C24184yes—
33C22×Dic13C22×C41336yescomplemented
34C22×Dic13C24184yes—
35C2×C4×D13C22×C412688yesdirect product factor
36C2×C4×D13C241192yes—
37C42×C13C24164yescomplemented
38C4×Dic13C241192yescomplemented
39C25×C4—133no—
40C23×C42—1356no—
41C23×C42—133no—
42C23×C42D1311yescharacteristic, direct product factor
43C23×C13C2×C42164yescomplemented
44C23×C13C23×C4184yes—
45C23×C13C2517yes—
46C22×D13C2×C421896yesdirect product factor
47C22×D13C23×C41336yes—
48C22×D13C2518yes—
49C2×C4×C13C23×C41336yescomplemented
50C2×C4×C13C25124yes—
51C2×Dic13C23×C41336yescomplemented
52C2×Dic13C25124yes—
53C4×D13C23×C41768yesdirect product factor
54C26—131no—
55C24×C4—133no—
56C24×C4—1396no—
57C24×C4—1384no—
58C24×C4C2×D1313yes—
59C22×C42—1384no—
60C22×C42—13448no—
61C22×C42C2×D13128yesdirect product factor
62C22×C13C22×C421112yescomplemented
63C22×C13C24×C4142yes—
64C22×C13C2611yescharacteristic
65C2×D13C22×C421448yesdirect product factor
66C2×D13C24×C4148yes—
67C4×C13C24×C4148yescomplemented
68Dic13C24×C4148yescomplemented
69C25—1348no—
70C25—1314no—
71C25C22×D1311yescharacteristic
72C23×C4—1348no—
73C23×C4—1342no—
74C23×C4—131344no—
75C23×C4—13336no—
76C23×C4C4×D13148yesdirect product factor
77C23×C4C22×D13142yes—
78C2×C42—13336no—
79C2×C42—13512no—
80C2×C42C22×D131112yesdirect product factor
81C2×C13C23×C42128yescomplemented
82C2×C13C25×C413yes—
83D13C23×C42132yesdirect product factor
84C24—13256no—
85C24—13336no—
86C24—1328no—
87C24C2×C4×D13124yes—
88C24C23×D1317yes—
89C22×C4—13336no—
90C22×C4—1384no—
91C22×C4—132688no—
92C22×C4—13192no—
93C22×C4C2×C4×D131336yesdirect product factor
94C22×C4C23×D13184yes—
95C42—13192no—
96C42C23×D13164yesdirect product factor
97C13C24×C4211yescharacteristic, complemented, Sylow
98C23—13896no—
99C23—13336no—
100C23—138no—
101C23C42×D13164yesdirect product factor
102C23C22×C4×D13184yes—
103C23C24×D1317yes—
104C2×C4—13336no—
105C2×C4—1324no—
106C2×C4—13768no—
107C2×C4C22×C4×D131336yesdirect product factor
108C2×C4C24×D13124yes—
109C22—13448no—
110C22—1348no—
111C22C2×C42×D131112yesdirect product factor
112C22C23×C4×D13142yes—
113C22C25×D1311yescharacteristic
114C4—1348no—
115C4C23×C4×D13148yesdirect product factor
116C2—1332no—
117C2C22×C42×D13128yesdirect product factor
118C2C24×C4×D1313yes—
subgroupG/H
center, hypercenterC23×C42D13
commutator, hypocenterC13C24×C42
FrattiniC22C25×D13
FittingC23×C42×C13C2
socleC25×C13C23
prime radicalC25×D13C22
cosocleC22×C13C26
LCSG ▷ C13
UCSC1 ◁ C23×C42

Complements

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

NH ≅ G/Ntype
2. C23×C4×Dic13C2semidirect
3. C22×C42×D13C2direct (N × H)
4. C23×C42×C13C2semidirect
8. C23×C4×D13C4direct (N × H)
10. C22×C42×C13C22semidirect
11. C22×C4×Dic13C22semidirect
12. C2×C42×D13C22direct (N × H)
16. C23×C4×C13C2×C4semidirect
18. C23×Dic13C2×C4semidirect
20. C22×C4×D13C2×C4direct (N × H)
22. C2×C42×C13C23semidirect
23. C2×C4×Dic13C23semidirect
24. C42×D13C23direct (N × H)
28. C23×D13C42direct (N × H)
31. C22×C4×C13C22×C4semidirect
33. C22×Dic13C22×C4semidirect
35. C2×C4×D13C22×C4direct (N × H)
37. C42×C13C24semidirect
38. C4×Dic13C24semidirect
42. C23×C42D13direct (N × H)
43. C23×C13C2×C42semidirect
46. C22×D13C2×C42direct (N × H)
49. C2×C4×C13C23×C4semidirect
51. C2×Dic13C23×C4semidirect
53. C4×D13C23×C4direct (N × H)
61. C22×C42C2×D13direct (N × H)
62. C22×C13C22×C42semidirect
65. C2×D13C22×C42direct (N × H)
67. C4×C13C24×C4semidirect
68. Dic13C24×C4semidirect
76. C23×C4C4×D13direct (N × H)
80. C2×C42C22×D13direct (N × H)
81. C2×C13C23×C42semidirect
83. D13C23×C42direct (N × H)
93. C22×C4C2×C4×D13direct (N × H)
96. C42C23×D13direct (N × H)
97. C13C24×C42semidirect
101. C23C42×D13direct (N × H)
107. C2×C4C22×C4×D13direct (N × H)
111. C22C2×C42×D13direct (N × H)
115. C4C23×C4×D13direct (N × H)
117. C2C22×C42×D13direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C4×D132
C23×C4×Dic132
C22×C42×D132
C23×C42×C132
C24×C4213