Finite Group Databasebeta

← D4×D2012 #44566917

Subgroups — D4×D2012 #44566917

Order 32192.

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×D2012C212yesmaximal, complemented
2C2×D4×D503C212yesmaximal, complemented
3#30632861C211yesmaximal, characteristic, complemented
4#30632839C212yesmaximal, complemented
5#30632838C212yesmaximal, complemented
6#30632834C214yesmaximal, complemented
7C4×D2012C211yesmaximal, characteristic, complemented
8C4×D4×C503C211yesmaximal, characteristic, complemented
9C23×D503C2214yescomplemented
10C2×D2012—28no—
11C2×D2012C2211yescharacteristic
12C2×D2012C2214yescomplemented
13C2×D2012C2212yescomplemented
14C2×D2012C2212yescomplemented
15C2×D2012C2212yescomplemented
16C2×C22⋊D503C2214yescomplemented
17D4×D503—28no—
18C2×C4×D503C2212yescomplemented
19C4⋊Dic503C2211yescharacteristic, complemented
20(C2×D503)⋊C4C2212yescomplemented
21(C2×D503)⋊C4C2214yescomplemented
22C2×D4×C503C2211yescharacteristic
23C22×C4×C503C2212yescomplemented
24C4⋊C4×C503C2211yescharacteristic, complemented
25C22⋊C4×C503C2212yescomplemented
26C42×C503C2211yescharacteristic, complemented
27C22×D503—28no—
28C22×D503—28no—
29C22×D503—44no—
30C22×D503C2314yes—
31C22×D503C2312yes—
32D2012—28no—
33D2012—24no—
34D2012—24no—
35D2012—42no—
36D2012D414yesdirect product factor
37C22⋊D503—28no—
38C2×Dic503C2312yes—
39C4×D503—24no—
40C23×C503C2312yes—
41D4×C503D414yescomplemented
42C2×C4×C503—24no—
43C2×C4×C503C2311yescharacteristic
44C2×C4×C503C2312yes—
45C2×C4×C503C2311yescharacteristic
46C2×C4×C503C2311yescharacteristic
47C22×C503—22no—
48C22×C503—22no—
49C22×C503C2×D414yescomplemented
50C22×C503C2411yescharacteristic
51C2×D503—22no—
52C2×D503—22no—
53C2×D503—24no—
54C2×D503—24no—
55C2×D503—24no—
56C2×D503—416no—
57C2×D503C2×D414yescomplemented
58C4×C503—22no—
59C4×C503—21no—
60C4×C503C2×D412yescomplemented
61C4×C503C2×D412yescomplemented
62Dic503—22no—
63C2×C503—24no—
64C2×C503C22×D411yescharacteristic
65C2×C503C22×D411yescharacteristic
66C2×C503H(5,𝔽2)11yescharacteristic
67D503—24no—
68D503—44no—
69C503D4211yescharacteristic, complemented, Sylow
70D42—5031nomaximal, Sylow
71C22×D4—5032no—
72C22×D4—5032no—
73#127—5031no—
74#121—5032no—
75#121—5032no—
76#120—5034no—
77C4×D4—5031no—
78C4×D4D50311yescharacteristic, complemented
79C24—5034no—
80C2×D4—10068no—
81C2×D4—10068no—
82C2×D4—5034no—
83C2×D4—5032no—
84C2×D4—5034no—
85C2×D4—5032no—
86C2×D4—5032no—
87C2×D4—5031no—
88C2×D4C2×D50311yescharacteristic
89C22×C4—5032no—
90C22×C4C2×D50312yescomplemented
91C4⋊C4—5031no—
92C4⋊C4C2×D50311yescharacteristic, complemented
93C22⋊C4—5032no—
94C22⋊C4—5034no—
95C22⋊C4C2×D50312yescomplemented
96C42C2×D50311yescharacteristic, complemented
97C23—20124no—
98C23—10068no—
99C23—10068no—
100C23—5034no—
101C23—5032no—
102C23C22×D50312yes—
103D4—20122no—
104D4—10068no—
105D4—10068no—
106D4—10064no—
107D4—10064no—
108D4—5034no—
109D4D201214yesdirect product factor
110C2×C4—24no—
111C2×C4—10064no—
112C2×C4—5032no—
113C2×C4C22×D50311yescharacteristic
114C2×C4C22×D50312yes—
115C2×C4C22×D50311yescharacteristic
116C2×C4C22×D50311yescharacteristic
117C22—22no—
118C22—22no—
119C22—201216no—
120C22—10064no—
121C22—10064no—
122C22—10064no—
123C22—10062no—
124C22—10062no—
125C22—5034no—
126C22C2×D201214yescomplemented
127C22C23×D50311yescharacteristic
128C4—22no—
129C4—21no—
130C4—10062no—
131C4D4×D50312yescomplemented
132C4C2×D201212yescomplemented
133C2—24no—
134C2—20124no—
135C2—10064no—
136C2C2×D4×D50311yescharacteristic
137C2C22×D201211yescharacteristic
138C2#3063291011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D503
commutator, socle, cosocleC22×C503C24
FittingC4×D4×C503C2
hypercenterC4×D4D503
hypocenterC503D42
LCSG ▷ C22×C503 ▷ C503
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D2012C2semidirect
2. C2×D4×D503C2semidirect
3. #30632861C2semidirect
4. #30632839C2semidirect
5. #30632838C2semidirect
6. #30632834C2semidirect
7. C4×D2012C2semidirect
8. C4×D4×C503C2semidirect
9. C23×D503C22semidirect
12. C2×D2012C22semidirect
13. C2×D2012C22semidirect
14. C2×D2012C22semidirect
15. C2×D2012C22semidirect
16. C2×C22⋊D503C22semidirect
18. C2×C4×D503C22semidirect
19. C4⋊Dic503C22semidirect
20. (C2×D503)⋊C4C22semidirect
21. (C2×D503)⋊C4C22semidirect
23. C22×C4×C503C22semidirect
24. C4⋊C4×C503C22semidirect
25. C22⋊C4×C503C22semidirect
26. C42×C503C22semidirect
36. D2012D4direct (N × H)
41. D4×C503D4semidirect
49. C22×C503C2×D4semidirect
57. C2×D503C2×D4semidirect
60. C4×C503C2×D4semidirect
61. C4×C503C2×D4semidirect
69. C503D42semidirect
78. C4×D4D503semidirect
90. C22×C4C2×D503semidirect
92. C4⋊C4C2×D503semidirect
95. C22⋊C4C2×D503semidirect
96. C42C2×D503semidirect
109. D4D2012direct (N × H)
126. C22C2×D2012semidirect
131. C4D4×D503semidirect
132. C4C2×D2012semidirect

Maximal subgroups

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

subgroupindex
C22×D20122
C2×D4×D5032
#306328612
#306328392
#306328382
#306328342
C4×D20122
C4×D4×C5032
D42503