Finite Group Databasebeta

← C24×C4⋊#261 #16809626

Subgroups — C24×C4⋊#261 #16809626

Order 3328.

19742 conjugacy classes of subgroups; only the 8408 normal subgroups are shown.

normal subgroups only

This group has 19742 conjugacy classes of subgroups — too many to draw. Only its 8408 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×#261—232no—
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×D13D4116yes—
15C24×D13Q8116yes—
16C24×D13C23115yes—
17C23×#261—2480no—
18C23×#261C231280yes—
19C23×C4×C13C2×C4130yescomplemented
20C23×Dic13C2×C4130yescomplemented
21C22×C4×D13C2×C41420yescomplemented
22C22×C4×D13C231140yes—
23C2×C4⋊#261C231960yesdirect product factor
24C24×C4⋊C4—131nomaximal, Sylow
25C24×C13C4⋊C4116yescomplemented
26C24×C13C22×C4115yes—
27C23×D13C4⋊C41240yescomplemented
28C23×D13C22×C41105yes—
29C23×D13C2×D41120yes—
30C23×D13C2×Q81120yes—
31C23×D13C24135yes—
32C22×#261—21120no—
33C22×#261C241240yes—
34C22×C4×C13C22×C41140yescomplemented
35C22×Dic13C22×C41140yescomplemented
36C2×C4×D13C22×C41840yescomplemented
37C2×C4×D13C241120yes—
38C4⋊#261C241256yesdirect product factor
39C25×C4—131no—
40C25×C4—132no—
41C23×C4⋊C4—1360no—
42C23×C13C2×C4⋊C41120yescomplemented
43C23×C13C23×C4135yes—
44C22×D13C2×C4⋊C41840yescomplemented
45C22×D13C23×C41105yes—
46C22×D13C22×D41140yes—
47C22×D13C22×Q81140yes—
48C22×D13C25115yes—
49C2×#261—2480no—
50C2×#261C25132yes—
51C2×C4×C13C23×C41120yescomplemented
52C2×Dic13C23×C41120yescomplemented
53C4×D13C23×C41240yescomplemented
54C4×D13C25116yes—
55C26—131no—
56C24×C4—131no—
57C24×C4—1330no—
58C24×C4—1330no—
59C24×C4—1360no—
60C24×C4—2632no—
61C24×C4#26111yescharacteristic, complemented
62C22×C4⋊C4—13560no—
63C22×C13C22×C4⋊C41140yescomplemented
64C22×C13C24×C4115yes—
65C2×D13C22×C4⋊C41420yescomplemented
66C2×D13C24×C4115yes—
67C2×D13C23×D4130yes—
68C2×D13C23×Q8130yes—
69C2×D13C2611yescharacteristic
70#261—232no—
71C4×C13C24×C4116yescomplemented
72Dic13C24×C4116yescomplemented
73C25—1316no—
74C25—1316no—
75C25—1315no—
76C25—1315no—
77C25C2×#26111yescharacteristic
78C23×C4—1330no—
79C23×C4—13140no—
80C23×C4—13420no—
81C23×C4—13280no—
82C23×C4—26480no—
83C23×C4C2×#261130yescomplemented
84C2×C4⋊C4—13960no—
85C2×C13C23×C4⋊C4130yescomplemented
86C2×C13C25×C411yescharacteristic
87D13C23×C4⋊C4130yescomplemented
88D13C24×D411yescharacteristic
89D13C24×Q811yescharacteristic
90C24—13120no—
91C24—13240no—
92C24—13120no—
93C24—1335no—
94C24—13105no—
95C24C4⋊#261116yesdirect product factor
96C24C22×#261115yes—
97C22×C4—13140no—
98C22×C4—13120no—
99C22×C4—13840no—
100C22×C4—13240no—
101C22×C4—261120no—
102C22×C4C22×#2611140yescomplemented
103C4⋊C4—13256no—
104C13C24×C4⋊C411yescharacteristic, complemented, Sylow
105C23—13140no—
106C23—13840no—
107C23—13140no—
108C23—1315no—
109C23—13105no—
110C23C2×C4⋊#2611120yesdirect product factor
111C23C23×#261135yes—
112C2×C4—13120no—
113C2×C4—1316no—
114C2×C4—13240no—
115C2×C4—1332no—
116C2×C4—26480no—
117C2×C4C23×#2611120yescomplemented
118C22—13420no—
119C22—1330no—
120C22—1330no—
121C22—1315no—
122C22—131no—
123C22C22×C4⋊#2611140yesdirect product factor
124C22C24×#261115yes—
125C4—1316no—
126C4—2632no—
127C4C24×#261116yescomplemented
128C2—131no—
129C2—131no—
130C2—1330no—
131C2C23×C4⋊#261130yesdirect product factor
132C2C25×#26111yescharacteristic
subgroupG/H
centerC25C2×#261
commutatorC2×C13C25×C4
FrattiniC2C25×#261
FittingC24×C4×C13C4
socleC25×C13C2×C4
prime radicalC25×D13C22
cosocleC2×D13C26
hypercenterC24×C4#261
hypocenterC13C24×C4⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C25 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
2. C23×C4⋊#261C2direct (N × H)
7. C24×C4×C13C4semidirect
8. C24×Dic13C4semidirect
9. C23×C4×D13C4semidirect
11. C22×C4⋊#261C22direct (N × H)
19. C23×C4×C13C2×C4semidirect
20. C23×Dic13C2×C4semidirect
21. C22×C4×D13C2×C4semidirect
23. C2×C4⋊#261C23direct (N × H)
25. C24×C13C4⋊C4semidirect
27. C23×D13C4⋊C4semidirect
34. C22×C4×C13C22×C4semidirect
35. C22×Dic13C22×C4semidirect
36. C2×C4×D13C22×C4semidirect
38. C4⋊#261C24direct (N × H)
42. C23×C13C2×C4⋊C4semidirect
44. C22×D13C2×C4⋊C4semidirect
51. C2×C4×C13C23×C4semidirect
52. C2×Dic13C23×C4semidirect
53. C4×D13C23×C4semidirect
61. C24×C4#261semidirect
63. C22×C13C22×C4⋊C4semidirect
65. C2×D13C22×C4⋊C4semidirect
71. C4×C13C24×C4semidirect
72. Dic13C24×C4semidirect
83. C23×C4C2×#261semidirect
85. C2×C13C23×C4⋊C4semidirect
87. D13C23×C4⋊C4semidirect
95. C24C4⋊#261direct (N × H)
102. C22×C4C22×#261semidirect
104. C13C24×C4⋊C4semidirect
110. C23C2×C4⋊#261direct (N × H)
117. C2×C4C23×#261semidirect
123. C22C22×C4⋊#261direct (N × H)
127. C4C24×#261semidirect
131. 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×C4⋊C413