Finite Group Databasebeta

← C24×C22⋊#261 #16809625

Subgroups — C24×C22⋊#261 #16809625

Order 3328.

43678 conjugacy classes of subgroups; only the 8408 normal subgroups are shown.

normal subgroups only

This group has 43678 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, complemented
2C23×C22⋊#261C2160yesmaximal, direct product factor
3C26×D13C211yesmaximal, characteristic
4C26×C13C411yescharacteristic, complemented
5C25×D13—232no—
6C25×D13C4130yescomplemented
7C25×D13C411yescharacteristic, complemented
8C25×D13C22130yes—
9C25×D13C2211yescharacteristic
10C24×#261—232no—
11C24×#261C22160yescomplemented
12C22×C22⋊#261C221560yesdirect product factor
13C25×C13—216no—
14C25×C13C2×C411yescharacteristic
15C25×C13C2×C4130yescomplemented
16C24×D13—216no—
17C24×D13—2480no—
18C24×D13—2480no—
19C24×D13C2×C4115yes—
20C24×D13C2×C41420yescomplemented
21C24×D13C2×C4130yescomplemented
22C24×D13D4132yes—
23C24×D13C231140yes—
24C24×D13C23115yes—
25C23×#261—2480no—
26C23×#261C231280yescomplemented
27C2×C22⋊#261C231960yesdirect product factor
28C24×C22⋊C4—131nomaximal, Sylow
29C24×C13—2240no—
30C24×C13C22⋊C4116yescomplemented
31C24×C13C22×C4115yes—
32C24×C13C22×C41140yescomplemented
33C23×D13—2240no—
34C23×D13—23360no—
35C23×D13—21120no—
36C23×D13C22⋊C41240yescomplemented
37C23×D13C22×C41105yes—
38C23×D13C22×C41840yescomplemented
39C23×D13C22×C41140yescomplemented
40C23×D13C2×D41240yes—
41C23×D13C241120yes—
42C23×D13C24135yes—
43C22×#261—21120no—
44C22×#261C241240yescomplemented
45C22⋊#261C241256yesdirect product factor
46C27—131no—
47C25×C4—132no—
48C23×C22⋊C4—1360no—
49C23×C13—2560no—
50C23×C13C2×C22⋊C41120yescomplemented
51C23×C13C23×C4135yes—
52C23×C13C23×C41120yescomplemented
53C22×D13—2560no—
54C22×D13—23360no—
55C22×D13—2480no—
56C22×D13C2×C22⋊C41840yescomplemented
57C22×D13C23×C41105yes—
58C22×D13C23×C41240yescomplemented
59C22×D13C23×C41120yescomplemented
60C22×D13C22×D41280yes—
61C22×D13C25116yes—
62C22×D13C25115yes—
63C2×#261—2480no—
64C2×#261C25132yescomplemented
65C26—131no—
66C26—131no—
67C26—1330no—
68C26—1330no—
69C26—2632no—
70C26#26111yescharacteristic, complemented
71C24×C4—1360no—
72C24×C4—2632no—
73C22×C22⋊C4—13560no—
74C22×C13—2240no—
75C22×C13C22×C22⋊C41140yescomplemented
76C22×C13C24×C4115yes—
77C22×C13C24×C4116yescomplemented
78C2×D13—2240no—
79C2×D13—232no—
80C2×D13—2480no—
81C2×D13C22×C22⋊C41420yescomplemented
82C2×D13C24×C4115yes—
83C2×D13C24×C4116yescomplemented
84C2×D13C23×D4160yes—
85C2×D13C2611yescharacteristic
86#261—232no—
87C25—216no—
88C25—1332no—
89C25—1315no—
90C25—1315no—
91C25—1330no—
92C25—13140no—
93C25—13420no—
94C25—26480no—
95C25—26480no—
96C25—2616no—
97C25C2×#26111yescharacteristic
98C25C2×#261130yescomplemented
99C23×C4—13280no—
100C23×C4—26480no—
101C2×C22⋊C4—13960no—
102C2×C13—216no—
103C2×C13C23×C22⋊C4130yescomplemented
104C2×C13C25×C411yescharacteristic
105D13—216no—
106D13C23×C22⋊C4130yescomplemented
107D13C24×D412yes—
108C24—2240no—
109C24—13240no—
110C24—13240no—
111C24—1335no—
112C24—13105no—
113C24—13140no—
114C24—13120no—
115C24—13840no—
116C24—261120no—
117C24—263360no—
118C24—26240no—
119C24C22⋊#261116yesdirect product factor
120C24C22×#261115yes—
121C24C22×#2611140yescomplemented
122C22×C4—13240no—
123C22×C4—261120no—
124C22⋊C4—13256no—
125C13C24×C22⋊C411yescharacteristic, complemented, Sylow
126C23—2560no—
127C23—13280no—
128C23—13840no—
129C23—1315no—
130C23—13105no—
131C23—13120no—
132C23—1316no—
133C23—13240no—
134C23—263360no—
135C23—26480no—
136C23—26560no—
137C23C2×C22⋊#2611120yesdirect product factor
138C23C23×#261135yes—
139C23C23×#2611120yescomplemented
140C2×C4—1332no—
141C2×C4—26480no—
142C22—2240no—
143C22—13420no—
144C22—1360no—
145C22—1315no—
146C22—131no—
147C22—1316no—
148C22—2632no—
149C22—26480no—
150C22—26240no—
151C22C22×C22⋊#2611140yesdirect product factor
152C22C24×#261115yes—
153C22C24×#261116yescomplemented
154C4—2632no—
155C2—216no—
156C2—132no—
157C2—1330no—
158C2—2616no—
159C2C23×C22⋊#261130yesdirect product factor
160C2C25×#26111yescharacteristic
subgroupG/H
centerC25C2×#261
commutatorC2×C13C25×C4
FrattiniC2C25×#261
FittingC26×C13C4
socleC25×C13C2×C4
prime radicalC26×D13C2
cosocleC2×D13C26
hypercenterC26#261
hypocenterC13C24×C22⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C25 ◁ C26

Complements

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

NH ≅ G/Ntype
1. C25×#261C2semidirect
2. C23×C22⋊#261C2direct (N × H)
4. C26×C13C4semidirect
6. C25×D13C4semidirect
7. C25×D13C4semidirect
11. C24×#261C22semidirect
12. C22×C22⋊#261C22direct (N × H)
15. C25×C13C2×C4semidirect
20. C24×D13C2×C4semidirect
21. C24×D13C2×C4semidirect
26. C23×#261C23semidirect
27. C2×C22⋊#261C23direct (N × H)
30. C24×C13C22⋊C4semidirect
32. C24×C13C22×C4semidirect
36. C23×D13C22⋊C4semidirect
38. C23×D13C22×C4semidirect
39. C23×D13C22×C4semidirect
44. C22×#261C24semidirect
45. C22⋊#261C24direct (N × H)
50. C23×C13C2×C22⋊C4semidirect
52. C23×C13C23×C4semidirect
56. C22×D13C2×C22⋊C4semidirect
58. C22×D13C23×C4semidirect
59. C22×D13C23×C4semidirect
64. C2×#261C25semidirect
70. C26#261semidirect
75. C22×C13C22×C22⋊C4semidirect
77. C22×C13C24×C4semidirect
81. C2×D13C22×C22⋊C4semidirect
83. C2×D13C24×C4semidirect
98. C25C2×#261semidirect
103. C2×C13C23×C22⋊C4semidirect
106. D13C23×C22⋊C4semidirect
119. C24C22⋊#261direct (N × H)
121. C24C22×#261semidirect
125. C13C24×C22⋊C4semidirect
137. C23C2×C22⋊#261direct (N × H)
139. C23C23×#261semidirect
151. C22C22×C22⋊#261direct (N × H)
153. C22C24×#261semidirect
159. C2C23×C22⋊#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×C22⋊#2612
C26×D132
C24×C22⋊C413