Finite Group Databasebeta

← D4×D908 #28409668

Subgroups — D4×D908 #28409668

Order 14528.

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×D908C212yesmaximal, complemented
2C2×D4×D227C212yesmaximal, complemented
3#20300285C211yesmaximal, characteristic, complemented
4#20300263C212yesmaximal, complemented
5#20300262C212yesmaximal, complemented
6#20300258C214yesmaximal, complemented
7C4×D908C211yesmaximal, characteristic, complemented
8C4×D4×C227C211yesmaximal, characteristic, complemented
9C23×D227C2214yescomplemented
10C2×D908—28no—
11C2×D908C2211yescharacteristic
12C2×D908C2212yescomplemented
13C2×D908C2214yescomplemented
14C2×D908C2212yescomplemented
15C2×D908C2212yescomplemented
16C2×C22⋊D227C2214yescomplemented
17D4×D227—28no—
18C2×C4×D227C2212yescomplemented
19C4⋊Dic227C2211yescharacteristic, complemented
20(C2×D227)⋊C4C2212yescomplemented
21(C2×D227)⋊C4C2214yescomplemented
22C2×D4×C227C2211yescharacteristic
23C22×C4×C227C2212yescomplemented
24C4⋊C4×C227C2211yescharacteristic, complemented
25C22⋊C4×C227C2212yescomplemented
26C42×C227C2211yescharacteristic, complemented
27C22×D227—28no—
28C22×D227—28no—
29C22×D227—44no—
30C22×D227C2314yes—
31C22×D227C2312yes—
32D908—28no—
33D908—24no—
34D908—24no—
35D908—42no—
36D908D414yesdirect product factor
37C22⋊D227—28no—
38C2×Dic227C2312yes—
39C4×D227—24no—
40C23×C227C2312yes—
41D4×C227D414yescomplemented
42C2×C4×C227—24no—
43C2×C4×C227C2311yescharacteristic
44C2×C4×C227C2312yes—
45C2×C4×C227C2311yescharacteristic
46C2×C4×C227C2311yescharacteristic
47C22×C227—22no—
48C22×C227—22no—
49C22×C227C2×D414yescomplemented
50C22×C227C2411yescharacteristic
51C2×D227—22no—
52C2×D227—22no—
53C2×D227—24no—
54C2×D227—24no—
55C2×D227—24no—
56C2×D227—416no—
57C2×D227C2×D414yescomplemented
58C4×C227—22no—
59C4×C227—21no—
60C4×C227C2×D412yescomplemented
61C4×C227C2×D412yescomplemented
62Dic227—22no—
63C2×C227—24no—
64C2×C227C22×D411yescharacteristic
65C2×C227C22×D411yescharacteristic
66C2×C227H(5,𝔽2)11yescharacteristic
67D227—24no—
68D227—44no—
69C227D4211yescharacteristic, complemented, Sylow
70D42—2271nomaximal, Sylow
71C22×D4—2272no—
72C22×D4—2272no—
73#127—2271no—
74#121—2272no—
75#121—2272no—
76#120—2274no—
77C4×D4—2271no—
78C4×D4D22711yescharacteristic, complemented
79C24—2274no—
80C2×D4—4548no—
81C2×D4—4548no—
82C2×D4—2274no—
83C2×D4—2272no—
84C2×D4—2274no—
85C2×D4—2272no—
86C2×D4—2272no—
87C2×D4—2271no—
88C2×D4C2×D22711yescharacteristic
89C22×C4—2272no—
90C22×C4C2×D22712yescomplemented
91C4⋊C4—2271no—
92C4⋊C4C2×D22711yescharacteristic, complemented
93C22⋊C4—2272no—
94C22⋊C4—2274no—
95C22⋊C4C2×D22712yescomplemented
96C42C2×D22711yescharacteristic, complemented
97C23—9084no—
98C23—4548no—
99C23—4548no—
100C23—2274no—
101C23—2272no—
102C23C22×D22712yes—
103D4—9082no—
104D4—4548no—
105D4—4548no—
106D4—4544no—
107D4—4544no—
108D4—2274no—
109D4D90814yesdirect product factor
110C2×C4—24no—
111C2×C4—4544no—
112C2×C4—2272no—
113C2×C4C22×D22711yescharacteristic
114C2×C4C22×D22712yes—
115C2×C4C22×D22711yescharacteristic
116C2×C4C22×D22711yescharacteristic
117C22—22no—
118C22—22no—
119C22—90816no—
120C22—4544no—
121C22—4544no—
122C22—4544no—
123C22—4542no—
124C22—4542no—
125C22—2274no—
126C22C2×D90814yescomplemented
127C22C23×D22711yescharacteristic
128C4—22no—
129C4—21no—
130C4—4542no—
131C4D4×D22712yescomplemented
132C4C2×D90812yescomplemented
133C2—24no—
134C2—9084no—
135C2—4544no—
136C2C2×D4×D22711yescharacteristic
137C2C22×D90811yescharacteristic
138C2#2030033411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D227
commutator, socle, cosocleC22×C227C24
FittingC4×D4×C227C2
hypercenterC4×D4D227
hypocenterC227D42
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D908C2semidirect
2. C2×D4×D227C2semidirect
3. #20300285C2semidirect
4. #20300263C2semidirect
5. #20300262C2semidirect
6. #20300258C2semidirect
7. C4×D908C2semidirect
8. C4×D4×C227C2semidirect
9. C23×D227C22semidirect
12. C2×D908C22semidirect
13. C2×D908C22semidirect
14. C2×D908C22semidirect
15. C2×D908C22semidirect
16. C2×C22⋊D227C22semidirect
18. C2×C4×D227C22semidirect
19. C4⋊Dic227C22semidirect
20. (C2×D227)⋊C4C22semidirect
21. (C2×D227)⋊C4C22semidirect
23. C22×C4×C227C22semidirect
24. C4⋊C4×C227C22semidirect
25. C22⋊C4×C227C22semidirect
26. C42×C227C22semidirect
36. D908D4direct (N × H)
41. D4×C227D4semidirect
49. C22×C227C2×D4semidirect
57. C2×D227C2×D4semidirect
60. C4×C227C2×D4semidirect
61. C4×C227C2×D4semidirect
69. C227D42semidirect
78. C4×D4D227semidirect
90. C22×C4C2×D227semidirect
92. C4⋊C4C2×D227semidirect
95. C22⋊C4C2×D227semidirect
96. C42C2×D227semidirect
109. D4D908direct (N × H)
126. C22C2×D908semidirect
131. C4D4×D227semidirect
132. C4C2×D908semidirect

Maximal subgroups

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

subgroupindex
C22×D9082
C2×D4×D2272
#203002852
#203002632
#203002622
#203002582
C4×D9082
C4×D4×C2272
D42227