Finite Group Databasebeta

← D4×D1868 #44470673

Subgroups — D4×D1868 #44470673

Order 29888.

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×D1868C212yesmaximal, complemented
2C2×D4×D467C212yesmaximal, complemented
3#28417950C211yesmaximal, characteristic, complemented
4#28417928C212yesmaximal, complemented
5#28417927C212yesmaximal, complemented
6#28417923C214yesmaximal, complemented
7C4×D1868C211yesmaximal, characteristic, complemented
8C4×D4×C467C211yesmaximal, characteristic, complemented
9C23×D467C2214yescomplemented
10C2×D1868—28no—
11C2×D1868C2211yescharacteristic
12C2×D1868C2214yescomplemented
13C2×D1868C2212yescomplemented
14C2×D1868C2212yescomplemented
15C2×D1868C2212yescomplemented
16C2×C22⋊D467C2214yescomplemented
17D4×D467—28no—
18C2×C4×D467C2212yescomplemented
19C4⋊Dic467C2211yescharacteristic, complemented
20(C2×D467)⋊C4C2212yescomplemented
21(C2×D467)⋊C4C2214yescomplemented
22C2×D4×C467C2211yescharacteristic
23C22×C4×C467C2212yescomplemented
24C4⋊C4×C467C2211yescharacteristic, complemented
25C22⋊C4×C467C2212yescomplemented
26C42×C467C2211yescharacteristic, complemented
27C22×D467—28no—
28C22×D467—28no—
29C22×D467—44no—
30C22×D467C2314yes—
31C22×D467C2312yes—
32D1868—28no—
33D1868—24no—
34D1868—24no—
35D1868—42no—
36D1868D414yesdirect product factor
37C22⋊D467—28no—
38C2×Dic467C2312yes—
39C4×D467—24no—
40C23×C467C2312yes—
41D4×C467D414yescomplemented
42C2×C4×C467—24no—
43C2×C4×C467C2311yescharacteristic
44C2×C4×C467C2312yes—
45C2×C4×C467C2311yescharacteristic
46C2×C4×C467C2311yescharacteristic
47C22×C467—22no—
48C22×C467—22no—
49C22×C467C2×D414yescomplemented
50C22×C467C2411yescharacteristic
51C2×D467—22no—
52C2×D467—22no—
53C2×D467—24no—
54C2×D467—24no—
55C2×D467—24no—
56C2×D467—416no—
57C2×D467C2×D414yescomplemented
58C4×C467—22no—
59C4×C467—21no—
60C4×C467C2×D412yescomplemented
61C4×C467C2×D412yescomplemented
62Dic467—22no—
63C2×C467—24no—
64C2×C467C22×D411yescharacteristic
65C2×C467C22×D411yescharacteristic
66C2×C467H(5,𝔽2)11yescharacteristic
67D467—24no—
68D467—44no—
69C467D4211yescharacteristic, complemented, Sylow
70D42—4671nomaximal, Sylow
71C22×D4—4672no—
72C22×D4—4672no—
73#127—4671no—
74#121—4672no—
75#121—4672no—
76#120—4674no—
77C4×D4—4671no—
78C4×D4D46711yescharacteristic, complemented
79C24—4674no—
80C2×D4—9348no—
81C2×D4—9348no—
82C2×D4—4674no—
83C2×D4—4672no—
84C2×D4—4674no—
85C2×D4—4672no—
86C2×D4—4672no—
87C2×D4—4671no—
88C2×D4C2×D46711yescharacteristic
89C22×C4—4672no—
90C22×C4C2×D46712yescomplemented
91C4⋊C4—4671no—
92C4⋊C4C2×D46711yescharacteristic, complemented
93C22⋊C4—4672no—
94C22⋊C4—4674no—
95C22⋊C4C2×D46712yescomplemented
96C42C2×D46711yescharacteristic, complemented
97C23—18684no—
98C23—9348no—
99C23—9348no—
100C23—4674no—
101C23—4672no—
102C23C22×D46712yes—
103D4—18682no—
104D4—9348no—
105D4—9348no—
106D4—9344no—
107D4—9344no—
108D4—4674no—
109D4D186814yesdirect product factor
110C2×C4—24no—
111C2×C4—9344no—
112C2×C4—4672no—
113C2×C4C22×D46711yescharacteristic
114C2×C4C22×D46712yes—
115C2×C4C22×D46711yescharacteristic
116C2×C4C22×D46711yescharacteristic
117C22—22no—
118C22—22no—
119C22—186816no—
120C22—9344no—
121C22—9344no—
122C22—9344no—
123C22—9342no—
124C22—9342no—
125C22—4674no—
126C22C2×D186814yescomplemented
127C22C23×D46711yescharacteristic
128C4—22no—
129C4—21no—
130C4—9342no—
131C4D4×D46712yescomplemented
132C4C2×D186812yescomplemented
133C2—24no—
134C2—18684no—
135C2—9344no—
136C2C2×D4×D46711yescharacteristic
137C2C22×D186811yescharacteristic
138C2#2841799911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D467
commutator, socle, cosocleC22×C467C24
FittingC4×D4×C467C2
hypercenterC4×D4D467
hypocenterC467D42
LCSG ▷ C22×C467 ▷ C467
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D1868C2semidirect
2. C2×D4×D467C2semidirect
3. #28417950C2semidirect
4. #28417928C2semidirect
5. #28417927C2semidirect
6. #28417923C2semidirect
7. C4×D1868C2semidirect
8. C4×D4×C467C2semidirect
9. C23×D467C22semidirect
12. C2×D1868C22semidirect
13. C2×D1868C22semidirect
14. C2×D1868C22semidirect
15. C2×D1868C22semidirect
16. C2×C22⋊D467C22semidirect
18. C2×C4×D467C22semidirect
19. C4⋊Dic467C22semidirect
20. (C2×D467)⋊C4C22semidirect
21. (C2×D467)⋊C4C22semidirect
23. C22×C4×C467C22semidirect
24. C4⋊C4×C467C22semidirect
25. C22⋊C4×C467C22semidirect
26. C42×C467C22semidirect
36. D1868D4direct (N × H)
41. D4×C467D4semidirect
49. C22×C467C2×D4semidirect
57. C2×D467C2×D4semidirect
60. C4×C467C2×D4semidirect
61. C4×C467C2×D4semidirect
69. C467D42semidirect
78. C4×D4D467semidirect
90. C22×C4C2×D467semidirect
92. C4⋊C4C2×D467semidirect
95. C22⋊C4C2×D467semidirect
96. C42C2×D467semidirect
109. D4D1868direct (N × H)
126. C22C2×D1868semidirect
131. C4D4×D467semidirect
132. C4C2×D1868semidirect

Maximal subgroups

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

subgroupindex
C22×D18682
C2×D4×D4672
#284179502
#284179282
#284179272
#284179232
C4×D18682
C4×D4×C4672
D42467