Finite Group Databasebeta

← C24×C4×#261 #16809624

Subgroups — C24×C4×#261 #16809624

Order 3328.

24030 conjugacy classes of subgroups; only the 12696 normal subgroups are shown.

normal subgroups only

This group has 24030 conjugacy classes of subgroups — too many to draw. Only its 12696 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
1C25×#261C212yesmaximal
2C23×C4×#261C2160yesmaximal, direct product factor
3C24×C4×D13C211yesmaximal, characteristic
4C25×D13C2211yescharacteristic
5C24×#261C4164yesdirect product factor
6C24×#261C22160yes—
7C24×C4×C13C411yescharacteristic, complemented
8C24×Dic13C411yescharacteristic, complemented
9C23×C4×D13C4130yescomplemented
10C23×C4×D13C22130yes—
11C22×C4×#261C221560yesdirect product factor
12C25×C13C2×C411yescharacteristic
13C24×D13C2×C4115yes—
14C24×D13C2×C4132yes—
15C24×D13C23115yes—
16C23×#261C2×C41960yesdirect product factor
17C23×#261C231280yes—
18C23×C4×C13C2×C4130yescomplemented
19C23×Dic13C2×C4130yescomplemented
20C22×C4×D13C2×C41420yescomplemented
21C22×C4×D13C231140yes—
22C2×C4×#261C231960yesdirect product factor
23C24×C42—131nomaximal, Sylow
24C24×C13C42116yescomplemented
25C24×C13C22×C4115yes—
26C23×D13C421240yescomplemented
27C23×D13C22×C41105yes—
28C23×D13C22×C41240yes—
29C23×D13C24135yes—
30C22×#261C22×C412240yesdirect product factor
31C22×#261C241240yes—
32C22×C4×C13C22×C41140yescomplemented
33C22×Dic13C22×C41140yescomplemented
34C2×C4×D13C22×C41840yescomplemented
35C2×C4×D13C241120yes—
36C4×#261C241256yesdirect product factor
37C25×C4—132no—
38C25×C4—131no—
39C23×C42—1360no—
40C23×C13C2×C421120yescomplemented
41C23×C13C23×C4135yes—
42C22×D13C2×C421840yescomplemented
43C22×D13C23×C41280yes—
44C22×D13C23×C41105yes—
45C22×D13C25115yes—
46C2×#261C23×C41960yesdirect product factor
47C2×#261C25132yes—
48C2×C4×C13C23×C41120yescomplemented
49C2×Dic13C23×C41120yescomplemented
50C4×D13C23×C41240yescomplemented
51C4×D13C25116yes—
52C26—131no—
53C24×C4—1360no—
54C24×C4—1364no—
55C24×C4—131no—
56C24×C4—1330no—
57C24×C4—1330no—
58C24×C4#26111yescharacteristic, direct product factor
59C22×C42—13560no—
60C22×C13C22×C421140yescomplemented
61C22×C13C24×C4115yes—
62C2×D13C22×C421420yescomplemented
63C2×D13C24×C4160yes—
64C2×D13C24×C4115yes—
65C2×D13C2611yescharacteristic
66#261C24×C4164yesdirect product factor
67C4×C13C24×C4116yescomplemented
68Dic13C24×C4116yescomplemented
69C25—1332no—
70C25—1315no—
71C25—1315no—
72C25C2×#26111yescharacteristic
73C23×C4—13960no—
74C23×C4—13280no—
75C23×C4—1330no—
76C23×C4—13420no—
77C23×C4—13140no—
78C23×C4C2×#261130yesdirect product factor
79C2×C42—13960no—
80C2×C13C23×C42130yescomplemented
81C2×C13C25×C411yescharacteristic
82D13C23×C42130yescomplemented
83D13C25×C412yes—
84C24—13240no—
85C24—13240no—
86C24—1335no—
87C24—13105no—
88C24C4×#261116yesdirect product factor
89C24C22×#261115yes—
90C22×C4—13240no—
91C22×C4—132240no—
92C22×C4—13140no—
93C22×C4—13120no—
94C22×C4—13840no—
95C22×C4C22×#2611140yesdirect product factor
96C42—13256no—
97C13C24×C4211yescharacteristic, complemented, Sylow
98C23—13280no—
99C23—13840no—
100C23—1315no—
101C23—13105no—
102C23C2×C4×#2611120yesdirect product factor
103C23C23×#261135yes—
104C2×C4—1332no—
105C2×C4—13960no—
106C2×C4—13120no—
107C2×C4—1316no—
108C2×C4—13240no—
109C2×C4C23×#2611120yesdirect product factor
110C22—1360no—
111C22—13420no—
112C22—1315no—
113C22—131no—
114C22C22×C4×#2611140yesdirect product factor
115C22C24×#261115yes—
116C4—1364no—
117C4—1316no—
118C4C24×#261116yesdirect product factor
119C2—132no—
120C2—1330no—
121C2C23×C4×#261130yesdirect product factor
122C2C25×#26111yescharacteristic
subgroupG/H
center, hypercenterC24×C4#261
commutator, hypocenterC13C24×C42
FrattiniC2C25×#261
FittingC24×C4×C13C4
socleC25×C13C2×C4
prime radicalC25×D13C22
cosocleC2×D13C26
LCSG ▷ C13
UCSC1 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
2. C23×C4×#261C2direct (N × H)
5. C24×#261C4direct (N × H)
7. C24×C4×C13C4semidirect
8. C24×Dic13C4semidirect
9. C23×C4×D13C4semidirect
11. C22×C4×#261C22direct (N × H)
16. C23×#261C2×C4direct (N × H)
18. C23×C4×C13C2×C4semidirect
19. C23×Dic13C2×C4semidirect
20. C22×C4×D13C2×C4semidirect
22. C2×C4×#261C23direct (N × H)
24. C24×C13C42semidirect
26. C23×D13C42semidirect
30. C22×#261C22×C4direct (N × H)
32. C22×C4×C13C22×C4semidirect
33. C22×Dic13C22×C4semidirect
34. C2×C4×D13C22×C4semidirect
36. C4×#261C24direct (N × H)
40. C23×C13C2×C42semidirect
42. C22×D13C2×C42semidirect
46. C2×#261C23×C4direct (N × H)
48. C2×C4×C13C23×C4semidirect
49. C2×Dic13C23×C4semidirect
50. C4×D13C23×C4semidirect
58. C24×C4#261direct (N × H)
60. C22×C13C22×C42semidirect
62. C2×D13C22×C42semidirect
66. #261C24×C4direct (N × H)
67. C4×C13C24×C4semidirect
68. Dic13C24×C4semidirect
78. C23×C4C2×#261direct (N × H)
80. C2×C13C23×C42semidirect
82. D13C23×C42semidirect
88. C24C4×#261direct (N × H)
95. C22×C4C22×#261direct (N × H)
97. C13C24×C42semidirect
102. C23C2×C4×#261direct (N × H)
109. C2×C4C23×#261direct (N × H)
114. C22C22×C4×#261direct (N × H)
118. C4C24×#261direct (N × H)
121. C2C23×C4×#261direct (N × H)

Maximal subgroups

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

subgroupindex
C25×#2612
C23×C4×#2612
C24×C4×D132
C24×C4213