Finite Group Databasebeta

← D4×D1492 #37560058

Subgroups — D4×D1492 #37560058

Order 23872.

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×D1492C212yesmaximal, complemented
2C2×D4×D373C212yesmaximal, complemented
3#26045789C211yesmaximal, characteristic, complemented
4#26045767C212yesmaximal, complemented
5#26045766C212yesmaximal, complemented
6#26045762C214yesmaximal, complemented
7C4×D1492C211yesmaximal, characteristic, complemented
8C4×D4×C373C211yesmaximal, characteristic, complemented
9C23×D373C2214yescomplemented
10C2×D1492—28no—
11C2×D1492C2211yescharacteristic
12C2×D1492C2214yescomplemented
13C2×D1492C2212yescomplemented
14C2×D1492C2212yescomplemented
15C2×D1492C2212yescomplemented
16C2×C22⋊D373C2214yescomplemented
17D4×D373—28no—
18C2×C4×D373C2212yescomplemented
19C4⋊Dic373C2211yescharacteristic, complemented
20#20238587C2212yescomplemented
21#20238587C2214yescomplemented
22C2×D4×C373C2211yescharacteristic
23C22×C4×C373C2212yescomplemented
24C4⋊C4×C373C2211yescharacteristic, complemented
25C22⋊C4×C373C2212yescomplemented
26C42×C373C2211yescharacteristic, complemented
27C22×D373—28no—
28C22×D373—28no—
29C22×D373—44no—
30C22×D373C2314yes—
31C22×D373C2312yes—
32D1492—28no—
33D1492—24no—
34D1492—24no—
35D1492—42no—
36D1492D414yesdirect product factor
37C22⋊D373—28no—
38C2×Dic373C2312yes—
39C4×D373—24no—
40C23×C373C2312yes—
41D4×C373D414yescomplemented
42C2×C4×C373—24no—
43C2×C4×C373C2311yescharacteristic
44C2×C4×C373C2312yes—
45C2×C4×C373C2311yescharacteristic
46C2×C4×C373C2311yescharacteristic
47C22×C373—22no—
48C22×C373—22no—
49C22×C373C2×D414yescomplemented
50C22×C373C2411yescharacteristic
51C2×D373—22no—
52C2×D373—22no—
53C2×D373—24no—
54C2×D373—24no—
55C2×D373—24no—
56C2×D373—416no—
57C2×D373C2×D414yescomplemented
58C4×C373—22no—
59C4×C373—21no—
60C4×C373C2×D412yescomplemented
61C4×C373C2×D412yescomplemented
62Dic373—22no—
63C2×C373—24no—
64C2×C373C22×D411yescharacteristic
65C2×C373C22×D411yescharacteristic
66C2×C373H(5,𝔽2)11yescharacteristic
67D373—24no—
68D373—44no—
69C373D4211yescharacteristic, complemented, Sylow
70D42—3731nomaximal, Sylow
71C22×D4—3732no—
72C22×D4—3732no—
73#127—3731no—
74#121—3732no—
75#121—3732no—
76#120—3734no—
77C4×D4—3731no—
78C4×D4D37311yescharacteristic, complemented
79C24—3734no—
80C2×D4—3734no—
81C2×D4—3731no—
82C2×D4—3732no—
83C2×D4—3734no—
84C2×D4—3732no—
85C2×D4—3732no—
86C2×D4—7468no—
87C2×D4—7468no—
88C2×D4C2×D37311yescharacteristic
89C22×C4—3732no—
90C22×C4C2×D37312yescomplemented
91C4⋊C4—3731no—
92C4⋊C4C2×D37311yescharacteristic, complemented
93C22⋊C4—3732no—
94C22⋊C4—3734no—
95C22⋊C4C2×D37312yescomplemented
96C42C2×D37311yescharacteristic, complemented
97C23—3732no—
98C23—3734no—
99C23—14924no—
100C23—7468no—
101C23—7468no—
102C23C22×D37312yes—
103D4—3734no—
104D4—14922no—
105D4—7468no—
106D4—7468no—
107D4—7464no—
108D4—7464no—
109D4D149214yesdirect product factor
110C2×C4—24no—
111C2×C4—3732no—
112C2×C4—7464no—
113C2×C4C22×D37311yescharacteristic
114C2×C4C22×D37312yes—
115C2×C4C22×D37311yescharacteristic
116C2×C4C22×D37311yescharacteristic
117C22—22no—
118C22—22no—
119C22—3734no—
120C22—149216no—
121C22—7464no—
122C22—7464no—
123C22—7464no—
124C22—7462no—
125C22—7462no—
126C22C2×D149214yescomplemented
127C22C23×D37311yescharacteristic
128C4—22no—
129C4—21no—
130C4—7462no—
131C4D4×D37312yescomplemented
132C4C2×D149212yescomplemented
133C2—24no—
134C2—14924no—
135C2—7464no—
136C2C2×D4×D37311yescharacteristic
137C2C22×D149211yescharacteristic
138C2#2604583811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D373
commutator, socle, cosocleC22×C373C24
FittingC4×D4×C373C2
hypercenterC4×D4D373
hypocenterC373D42
LCSG ▷ C22×C373 ▷ C373
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D1492C2semidirect
2. C2×D4×D373C2semidirect
3. #26045789C2semidirect
4. #26045767C2semidirect
5. #26045766C2semidirect
6. #26045762C2semidirect
7. C4×D1492C2semidirect
8. C4×D4×C373C2semidirect
9. C23×D373C22semidirect
12. C2×D1492C22semidirect
13. C2×D1492C22semidirect
14. C2×D1492C22semidirect
15. C2×D1492C22semidirect
16. C2×C22⋊D373C22semidirect
18. C2×C4×D373C22semidirect
19. C4⋊Dic373C22semidirect
20. #20238587C22semidirect
21. #20238587C22semidirect
23. C22×C4×C373C22semidirect
24. C4⋊C4×C373C22semidirect
25. C22⋊C4×C373C22semidirect
26. C42×C373C22semidirect
36. D1492D4direct (N × H)
41. D4×C373D4semidirect
49. C22×C373C2×D4semidirect
57. C2×D373C2×D4semidirect
60. C4×C373C2×D4semidirect
61. C4×C373C2×D4semidirect
69. C373D42semidirect
78. C4×D4D373semidirect
90. C22×C4C2×D373semidirect
92. C4⋊C4C2×D373semidirect
95. C22⋊C4C2×D373semidirect
96. C42C2×D373semidirect
109. D4D1492direct (N × H)
126. C22C2×D1492semidirect
131. C4D4×D373semidirect
132. C4C2×D1492semidirect

Maximal subgroups

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

subgroupindex
C22×D14922
C2×D4×D3732
#260457892
#260457672
#260457662
#260457622
C4×D14922
C4×D4×C3732
D42373