Finite Group Databasebeta

← D4×D92 #13093053

Subgroups — D4×D92 #13093053

Order 1472.

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
1C2×D4×D23C212yesmaximal, complemented
2C22×D92C212yesmaximal, complemented
3C4×D4×C23C211yesmaximal, characteristic, complemented
4#10625101C212yesmaximal, complemented
5#10625066C212yesmaximal, complemented
6#10625053C214yesmaximal, complemented
7#10625045C211yesmaximal, characteristic, complemented
8C4×D92C211yesmaximal, characteristic, complemented
9C23×D23C2214yescomplemented
10C2×D4×C23C2211yescharacteristic
11C22×C4×C23C2212yescomplemented
12C2×C22⋊D23C2214yescomplemented
13D4×D23—28no—
14C2×D92—28no—
15C2×D92C2211yescharacteristic
16C2×D92C2212yescomplemented
17C2×D92C2212yescomplemented
18C2×D92C2214yescomplemented
19C2×D92C2212yescomplemented
20C2×C4×D23C2212yescomplemented
21C4⋊C4×C23C2211yescharacteristic, complemented
22C22⋊C4×C23C2212yescomplemented
23C42×C23C2211yescharacteristic, complemented
24(C2×D23)⋊C4C2212yescomplemented
25(C2×D23)⋊C4C2214yescomplemented
26C4⋊Dic23C2211yescharacteristic, complemented
27C23×C23C2312yes—
28C22×D23—28no—
29C22×D23—28no—
30C22×D23—44no—
31C22×D23C2314yes—
32C22×D23C2312yes—
33D4×C23D414yescomplemented
34C2×C4×C23—24no—
35C2×C4×C23C2311yescharacteristic
36C2×C4×C23C2312yes—
37C2×C4×C23C2311yescharacteristic
38C2×C4×C23C2311yescharacteristic
39C22⋊D23—28no—
40C2×Dic23C2312yes—
41D92—28no—
42D92—24no—
43D92—24no—
44D92—42no—
45D92D414yesdirect product factor
46C4×D23—24no—
47C22×C23—22no—
48C22×C23—22no—
49C22×C23C2×D414yescomplemented
50C22×C23C2411yescharacteristic
51C2×D23—22no—
52C2×D23—22no—
53C2×D23—24no—
54C2×D23—24no—
55C2×D23—24no—
56C2×D23—416no—
57C2×D23C2×D414yescomplemented
58C4×C23—22no—
59C4×C23—21no—
60C4×C23C2×D412yescomplemented
61C4×C23C2×D412yescomplemented
62Dic23—22no—
63D42—231nomaximal, Sylow
64C2×C23—24no—
65C2×C23C22×D411yescharacteristic
66C2×C23C22×D411yescharacteristic
67C2×C23H(5,𝔽2)11yescharacteristic
68D23—24no—
69D23—44no—
70C22×D4—232no—
71C22×D4—232no—
72#127—231no—
73#121—232no—
74#121—232no—
75#120—234no—
76C4×D4—231no—
77C4×D4D2311yescharacteristic, complemented
78C23D4211yescharacteristic, complemented, Sylow
79C24—234no—
80C2×D4—234no—
81C2×D4—231no—
82C2×D4—234no—
83C2×D4—232no—
84C2×D4—232no—
85C2×D4—232no—
86C2×D4—468no—
87C2×D4—468no—
88C2×D4C2×D2311yescharacteristic
89C22×C4—232no—
90C22×C4C2×D2312yescomplemented
91C4⋊C4—231no—
92C4⋊C4C2×D2311yescharacteristic, complemented
93C22⋊C4—232no—
94C22⋊C4—234no—
95C22⋊C4C2×D2312yescomplemented
96C42C2×D2311yescharacteristic, complemented
97C23—232no—
98C23—234no—
99C23—468no—
100C23—468no—
101C23—924no—
102C23C22×D2312yes—
103D4—234no—
104D4—468no—
105D4—468no—
106D4—464no—
107D4—464no—
108D4—922no—
109D4D9214yesdirect product factor
110C2×C4—24no—
111C2×C4—232no—
112C2×C4—464no—
113C2×C4C22×D2311yescharacteristic
114C2×C4C22×D2312yes—
115C2×C4C22×D2311yescharacteristic
116C2×C4C22×D2311yescharacteristic
117C22—22no—
118C22—22no—
119C22—234no—
120C22—462no—
121C22—462no—
122C22—464no—
123C22—464no—
124C22—464no—
125C22—9216no—
126C22C2×D9214yescomplemented
127C22C23×D2311yescharacteristic
128C4—22no—
129C4—21no—
130C4—462no—
131C4C2×D9212yescomplemented
132C4D4×D2312yescomplemented
133C2—24no—
134C2—464no—
135C2—924no—
136C2C22×D9211yescharacteristic
137C2C2×D4×D2311yescharacteristic
138C2#1062516011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D23
commutator, socle, cosocleC22×C23C24
FittingC4×D4×C23C2
hypercenterC4×D4D23
hypocenterC23D42
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×D23C2semidirect
2. C22×D92C2semidirect
3. C4×D4×C23C2semidirect
4. #10625101C2semidirect
5. #10625066C2semidirect
6. #10625053C2semidirect
7. #10625045C2semidirect
8. C4×D92C2semidirect
9. C23×D23C22semidirect
11. C22×C4×C23C22semidirect
12. C2×C22⋊D23C22semidirect
16. C2×D92C22semidirect
17. C2×D92C22semidirect
18. C2×D92C22semidirect
19. C2×D92C22semidirect
20. C2×C4×D23C22semidirect
21. C4⋊C4×C23C22semidirect
22. C22⋊C4×C23C22semidirect
23. C42×C23C22semidirect
24. (C2×D23)⋊C4C22semidirect
25. (C2×D23)⋊C4C22semidirect
26. C4⋊Dic23C22semidirect
33. D4×C23D4semidirect
45. D92D4direct (N × H)
49. C22×C23C2×D4semidirect
57. C2×D23C2×D4semidirect
60. C4×C23C2×D4semidirect
61. C4×C23C2×D4semidirect
77. C4×D4D23semidirect
78. C23D42semidirect
90. C22×C4C2×D23semidirect
92. C4⋊C4C2×D23semidirect
95. C22⋊C4C2×D23semidirect
96. C42C2×D23semidirect
109. D4D92direct (N × H)
126. C22C2×D92semidirect
131. C4C2×D92semidirect
132. C4D4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D232
C22×D922
C4×D4×C232
#106251012
#106250662
#106250532
#106250452
C4×D922
D4223