Finite Group Databasebeta

← D4×D1468 #37554822

Subgroups — D4×D1468 #37554822

Order 23488.

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×D1468C212yesmaximal, complemented
2C2×D4×D367C212yesmaximal, complemented
3#26044258C211yesmaximal, characteristic, complemented
4#26044236C212yesmaximal, complemented
5#26044235C212yesmaximal, complemented
6#26044231C214yesmaximal, complemented
7C4×D1468C211yesmaximal, characteristic, complemented
8C4×D4×C367C211yesmaximal, characteristic, complemented
9C23×D367C2214yescomplemented
10C2×D1468—28no—
11C2×D1468C2211yescharacteristic
12C2×D1468C2214yescomplemented
13C2×D1468C2212yescomplemented
14C2×D1468C2212yescomplemented
15C2×D1468C2212yescomplemented
16C2×C22⋊D367C2214yescomplemented
17D4×D367—28no—
18C2×C4×D367C2212yescomplemented
19C4⋊Dic367C2211yescharacteristic, complemented
20(C2×D367)⋊C4C2212yescomplemented
21(C2×D367)⋊C4C2214yescomplemented
22C2×D4×C367C2211yescharacteristic
23C22×C4×C367C2212yescomplemented
24C4⋊C4×C367C2211yescharacteristic, complemented
25C22⋊C4×C367C2212yescomplemented
26C42×C367C2211yescharacteristic, complemented
27C22×D367—28no—
28C22×D367—28no—
29C22×D367—44no—
30C22×D367C2314yes—
31C22×D367C2312yes—
32D1468—28no—
33D1468—24no—
34D1468—24no—
35D1468—42no—
36D1468D414yesdirect product factor
37C22⋊D367—28no—
38C2×Dic367C2312yes—
39C4×D367—24no—
40C23×C367C2312yes—
41D4×C367D414yescomplemented
42C2×C4×C367—24no—
43C2×C4×C367C2311yescharacteristic
44C2×C4×C367C2312yes—
45C2×C4×C367C2311yescharacteristic
46C2×C4×C367C2311yescharacteristic
47C22×C367—22no—
48C22×C367—22no—
49C22×C367C2×D414yescomplemented
50C22×C367C2411yescharacteristic
51C2×D367—22no—
52C2×D367—22no—
53C2×D367—24no—
54C2×D367—24no—
55C2×D367—24no—
56C2×D367—416no—
57C2×D367C2×D414yescomplemented
58C4×C367—22no—
59C4×C367—21no—
60C4×C367C2×D412yescomplemented
61C4×C367C2×D412yescomplemented
62Dic367—22no—
63C2×C367—24no—
64C2×C367C22×D411yescharacteristic
65C2×C367C22×D411yescharacteristic
66C2×C367H(5,𝔽2)11yescharacteristic
67D367—24no—
68D367—44no—
69C367D4211yescharacteristic, complemented, Sylow
70D42—3671nomaximal, Sylow
71C22×D4—3672no—
72C22×D4—3672no—
73#127—3671no—
74#121—3672no—
75#121—3672no—
76#120—3674no—
77C4×D4—3671no—
78C4×D4D36711yescharacteristic, complemented
79C24—3674no—
80C2×D4—3674no—
81C2×D4—3671no—
82C2×D4—3672no—
83C2×D4—3674no—
84C2×D4—3672no—
85C2×D4—3672no—
86C2×D4—7348no—
87C2×D4—7348no—
88C2×D4C2×D36711yescharacteristic
89C22×C4—3672no—
90C22×C4C2×D36712yescomplemented
91C4⋊C4—3671no—
92C4⋊C4C2×D36711yescharacteristic, complemented
93C22⋊C4—3672no—
94C22⋊C4—3674no—
95C22⋊C4C2×D36712yescomplemented
96C42C2×D36711yescharacteristic, complemented
97C23—3672no—
98C23—3674no—
99C23—14684no—
100C23—7348no—
101C23—7348no—
102C23C22×D36712yes—
103D4—3674no—
104D4—14682no—
105D4—7348no—
106D4—7348no—
107D4—7344no—
108D4—7344no—
109D4D146814yesdirect product factor
110C2×C4—24no—
111C2×C4—3672no—
112C2×C4—7344no—
113C2×C4C22×D36711yescharacteristic
114C2×C4C22×D36712yes—
115C2×C4C22×D36711yescharacteristic
116C2×C4C22×D36711yescharacteristic
117C22—22no—
118C22—22no—
119C22—3674no—
120C22—146816no—
121C22—7344no—
122C22—7344no—
123C22—7344no—
124C22—7342no—
125C22—7342no—
126C22C2×D146814yescomplemented
127C22C23×D36711yescharacteristic
128C4—22no—
129C4—21no—
130C4—7342no—
131C4D4×D36712yescomplemented
132C4C2×D146812yescomplemented
133C2—24no—
134C2—14684no—
135C2—7344no—
136C2C2×D4×D36711yescharacteristic
137C2C22×D146811yescharacteristic
138C2#2604430711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D367
commutator, socle, cosocleC22×C367C24
FittingC4×D4×C367C2
hypercenterC4×D4D367
hypocenterC367D42
LCSG ▷ C22×C367 ▷ C367
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D1468C2semidirect
2. C2×D4×D367C2semidirect
3. #26044258C2semidirect
4. #26044236C2semidirect
5. #26044235C2semidirect
6. #26044231C2semidirect
7. C4×D1468C2semidirect
8. C4×D4×C367C2semidirect
9. C23×D367C22semidirect
12. C2×D1468C22semidirect
13. C2×D1468C22semidirect
14. C2×D1468C22semidirect
15. C2×D1468C22semidirect
16. C2×C22⋊D367C22semidirect
18. C2×C4×D367C22semidirect
19. C4⋊Dic367C22semidirect
20. (C2×D367)⋊C4C22semidirect
21. (C2×D367)⋊C4C22semidirect
23. C22×C4×C367C22semidirect
24. C4⋊C4×C367C22semidirect
25. C22⋊C4×C367C22semidirect
26. C42×C367C22semidirect
36. D1468D4direct (N × H)
41. D4×C367D4semidirect
49. C22×C367C2×D4semidirect
57. C2×D367C2×D4semidirect
60. C4×C367C2×D4semidirect
61. C4×C367C2×D4semidirect
69. C367D42semidirect
78. C4×D4D367semidirect
90. C22×C4C2×D367semidirect
92. C4⋊C4C2×D367semidirect
95. C22⋊C4C2×D367semidirect
96. C42C2×D367semidirect
109. D4D1468direct (N × H)
126. C22C2×D1468semidirect
131. C4D4×D367semidirect
132. C4C2×D1468semidirect

Maximal subgroups

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

subgroupindex
C22×D14682
C2×D4×D3672
#260442582
#260442362
#260442352
#260442312
C4×D14682
C4×D4×C3672
D42367