Finite Group Databasebeta

← D4×D1052 #30682574

Subgroups — D4×D1052 #30682574

Order 16832.

428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C22×D1052C212yesmaximal, complemented
2C2×D4×D263C212yesmaximal, complemented
3#22554467C211yesmaximal, characteristic, complemented
4#22554445C212yesmaximal, complemented
5#22554444C212yesmaximal, complemented
6#22554440C214yesmaximal, complemented
7C4×D1052C211yesmaximal, characteristic, complemented
8C4×D4×C263C211yesmaximal, characteristic, complemented
9C23×D263C2214yescomplemented
10C2×D1052—28no—
11C2×D1052C2211yescharacteristic
12C2×D1052C2214yescomplemented
13C2×D1052C2212yescomplemented
14C2×D1052C2212yescomplemented
15C2×D1052C2212yescomplemented
16C2×C22⋊D263C2214yescomplemented
17D4×D263—28no—
18C2×C4×D263C2212yescomplemented
19C4⋊Dic263C2211yescharacteristic, complemented
20(C2×D263)⋊C4C2212yescomplemented
21(C2×D263)⋊C4C2214yescomplemented
22C2×D4×C263C2211yescharacteristic
23C22×C4×C263C2212yescomplemented
24C4⋊C4×C263C2211yescharacteristic, complemented
25C22⋊C4×C263C2212yescomplemented
26C42×C263C2211yescharacteristic, complemented
27C22×D263—28no—
28C22×D263—28no—
29C22×D263—44no—
30C22×D263C2314yes—
31C22×D263C2312yes—
32D1052—28no—
33D1052—24no—
34D1052—24no—
35D1052—42no—
36D1052D414yesdirect product factor
37C22⋊D263—28no—
38C2×Dic263C2312yes—
39C4×D263—24no—
40C23×C263C2312yes—
41D4×C263D414yescomplemented
42C2×C4×C263—24no—
43C2×C4×C263C2311yescharacteristic
44C2×C4×C263C2312yes—
45C2×C4×C263C2311yescharacteristic
46C2×C4×C263C2311yescharacteristic
47C22×C263—22no—
48C22×C263—22no—
49C22×C263C2×D414yescomplemented
50C22×C263C2411yescharacteristic
51C2×D263—22no—
52C2×D263—22no—
53C2×D263—24no—
54C2×D263—24no—
55C2×D263—24no—
56C2×D263—416no—
57C2×D263C2×D414yescomplemented
58C4×C263—22no—
59C4×C263—21no—
60C4×C263C2×D412yescomplemented
61C4×C263C2×D412yescomplemented
62Dic263—22no—
63C2×C263—24no—
64C2×C263C22×D411yescharacteristic
65C2×C263C22×D411yescharacteristic
66C2×C263H(5,𝔽2)11yescharacteristic
67D263—24no—
68D263—44no—
69C263D4211yescharacteristic, complemented, Sylow
70D42—2631nomaximal, Sylow
71C22×D4—2632no—
72C22×D4—2632no—
73#127—2631no—
74#121—2632no—
75#121—2632no—
76#120—2634no—
77C4×D4—2631no—
78C4×D4D26311yescharacteristic, complemented
79C24—2634no—
80C2×D4—2634no—
81C2×D4—2631no—
82C2×D4—2634no—
83C2×D4—2632no—
84C2×D4—2632no—
85C2×D4—2632no—
86C2×D4—5268no—
87C2×D4—5268no—
88C2×D4C2×D26311yescharacteristic
89C22×C4—2632no—
90C22×C4C2×D26312yescomplemented
91C4⋊C4—2631no—
92C4⋊C4C2×D26311yescharacteristic, complemented
93C22⋊C4—2632no—
94C22⋊C4—2634no—
95C22⋊C4C2×D26312yescomplemented
96C42C2×D26311yescharacteristic, complemented
97C23—2632no—
98C23—2634no—
99C23—5268no—
100C23—5268no—
101C23—10524no—
102C23C22×D26312yes—
103D4—2634no—
104D4—5268no—
105D4—5268no—
106D4—5264no—
107D4—5264no—
108D4—10522no—
109D4D105214yesdirect product factor
110C2×C4—24no—
111C2×C4—2632no—
112C2×C4—5264no—
113C2×C4C22×D26311yescharacteristic
114C2×C4C22×D26312yes—
115C2×C4C22×D26311yescharacteristic
116C2×C4C22×D26311yescharacteristic
117C22—22no—
118C22—22no—
119C22—2634no—
120C22—5262no—
121C22—5262no—
122C22—5264no—
123C22—5264no—
124C22—5264no—
125C22—105216no—
126C22C2×D105214yescomplemented
127C22C23×D26311yescharacteristic
128C4—22no—
129C4—21no—
130C4—5262no—
131C4D4×D26312yescomplemented
132C4C2×D105212yescomplemented
133C2—24no—
134C2—5264no—
135C2—10524no—
136C2C2×D4×D26311yescharacteristic
137C2C22×D105211yescharacteristic
138C2#2255451611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D263
commutator, socle, cosocleC22×C263C24
FittingC4×D4×C263C2
hypercenterC4×D4D263
hypocenterC263D42
LCSG ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D1052C2semidirect
2. C2×D4×D263C2semidirect
3. #22554467C2semidirect
4. #22554445C2semidirect
5. #22554444C2semidirect
6. #22554440C2semidirect
7. C4×D1052C2semidirect
8. C4×D4×C263C2semidirect
9. C23×D263C22semidirect
12. C2×D1052C22semidirect
13. C2×D1052C22semidirect
14. C2×D1052C22semidirect
15. C2×D1052C22semidirect
16. C2×C22⋊D263C22semidirect
18. C2×C4×D263C22semidirect
19. C4⋊Dic263C22semidirect
20. (C2×D263)⋊C4C22semidirect
21. (C2×D263)⋊C4C22semidirect
23. C22×C4×C263C22semidirect
24. C4⋊C4×C263C22semidirect
25. C22⋊C4×C263C22semidirect
26. C42×C263C22semidirect
36. D1052D4direct (N × H)
41. D4×C263D4semidirect
49. C22×C263C2×D4semidirect
57. C2×D263C2×D4semidirect
60. C4×C263C2×D4semidirect
61. C4×C263C2×D4semidirect
69. C263D42semidirect
78. C4×D4D263semidirect
90. C22×C4C2×D263semidirect
92. C4⋊C4C2×D263semidirect
95. C22⋊C4C2×D263semidirect
96. C42C2×D263semidirect
109. D4D1052direct (N × H)
126. C22C2×D1052semidirect
131. C4D4×D263semidirect
132. C4C2×D1052semidirect

Maximal subgroups

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

subgroupindex
C22×D10522
C2×D4×D2632
#225544672
#225544452
#225544442
#225544402
C4×D10522
C4×D4×C2632
D42263