Finite Group Databasebeta

← D4×C22⋊D23 #13093050

Subgroups — D4×C22⋊D23 #13093050

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
1C22×D4×C23C211yesmaximal, characteristic, complemented
2C22×C22⋊D23C212yesmaximal, complemented
3C2×D4×D23C211yesmaximal, characteristic, complemented
4#10625124C212yesmaximal, complemented
5#10625111C211yesmaximal, characteristic, complemented
6#10625110C212yesmaximal, complemented
7#10625109C211yesmaximal, characteristic, complemented
8#10625108C212yesmaximal, complemented
9D4×Dic23C211yesmaximal, characteristic, complemented
10#10625101C211yesmaximal, characteristic, complemented
11C4×C22⋊D23C211yesmaximal, characteristic, complemented
12C24×C23C2212yescomplemented
13C23×D23C2212yescomplemented
14C2×D4×C23—24no—
15C2×D4×C23C2211yescharacteristic
16C2×D4×C23C2212yescomplemented
17C2×D4×C23C2211yescharacteristic, complemented
18C22×C4×C23C2211yescharacteristic, complemented
19C2×C22⋊D23—28no—
20C2×C22⋊D23C2211yescharacteristic
21C2×C22⋊D23C2212yescomplemented
22C2×C22⋊D23C2212yescomplemented
23C2×C22⋊D23C2212yescomplemented
24C2×C22⋊D23C2212yescomplemented
25C2×C22⋊D23C2212yescomplemented
26C22×Dic23C2212yescomplemented
27D4×D23—24no—
28C2×D92C2211yescharacteristic, complemented
29C2×C4×D23C2211yescharacteristic, complemented
30C22⋊Dic23C2211yescharacteristic, complemented
31C22⋊Dic23C2212yescomplemented
32C22⋊Dic23C2212yescomplemented
33(C2×D23)⋊C4C2211yescharacteristic, complemented
34(C2×D23)⋊C4C2212yescomplemented
35C4⋊Dic23C2211yescharacteristic, complemented
36Dic23⋊C4C2211yescharacteristic, complemented
37C4×Dic23C2211yescharacteristic, complemented
38C23×C23—24no—
39C23×C23—24no—
40C23×C23—42no—
41C23×C23C2312yes—
42C23×C23C2312yes—
43C23×C23C2311yescharacteristic
44C22×D23—24no—
45C22×D23—24no—
46C22×D23—42no—
47C22×D23C2312yes—
48C22×D23C2311yescharacteristic
49D4×C23—24no—
50D4×C23—22no—
51D4×C23D414yescomplemented
52C2×C4×C23—22no—
53C2×C4×C23C2311yescharacteristic
54C2×C4×C23C2311yescharacteristic
55C22⋊D23—24no—
56C22⋊D23—24no—
57C22⋊D23—24no—
58C22⋊D23—24no—
59C22⋊D23—42no—
60C22⋊D23D414yesdirect product factor
61C2×Dic23—24no—
62C2×Dic23C2311yescharacteristic
63C2×Dic23C2311yescharacteristic
64C2×Dic23C2312yes—
65C2×Dic23C2311yescharacteristic
66D92—22no—
67C4×D23—22no—
68C22×C23—22no—
69C22×C23—21no—
70C22×C23—22no—
71C22×C23—21no—
72C22×C23—22no—
73C22×C23—22no—
74C22×C23—22no—
75C22×C23—48no—
76C22×C23C2×D412yescomplemented
77C22×C23C2×D414yescomplemented
78C22×C23C2411yescharacteristic
79C2×D23—21no—
80C2×D23—21no—
81C2×D23—22no—
82C2×D23—22no—
83C2×D23—22no—
84C2×D23—48no—
85C2×D23C2×D412yescomplemented
86C4×C23—21no—
87C4×C23C2×D412yescomplemented
88Dic23—21no—
89Dic23—22no—
90Dic23—21no—
91Dic23C2×D412yescomplemented
92D42—231nomaximal, Sylow
93C2×C23—24no—
94C2×C23—22no—
95C2×C23—42no—
96C2×C23C22×D411yescharacteristic
97C2×C23C22×D411yescharacteristic
98C2×C23H(5,𝔽2)11yescharacteristic
99D23—22no—
100D23—42no—
101C22×D4—232no—
102C22×D4—231no—
103C22×D4D2311yescharacteristic, complemented
104#127—231no—
105#121—231no—
106#121—232no—
107#121—231no—
108#120—232no—
109#120—232no—
110C4×D4—231no—
111C4×D4—231no—
112C23D4211yescharacteristic, complemented, Sylow
113C24—232no—
114C24C2×D2312yescomplemented
115C2×D4—24no—
116C2×D4—231no—
117C2×D4—232no—
118C2×D4—232no—
119C2×D4—232no—
120C2×D4—232no—
121C2×D4—232no—
122C2×D4—231no—
123C2×D4—468no—
124C2×D4—464no—
125C2×D4C2×D2311yescharacteristic
126C2×D4C2×D2312yescomplemented
127C2×D4C2×D2311yescharacteristic, complemented
128C22×C4—232no—
129C22×C4—231no—
130C22×C4C2×D2311yescharacteristic, complemented
131C4⋊C4—231no—
132C4⋊C4—231no—
133C22⋊C4—231no—
134C22⋊C4—232no—
135C22⋊C4—232no—
136C22⋊C4—231no—
137C22⋊C4—232no—
138C42—231no—
139C23—24no—
140C23—24no—
141C23—42no—
142C23—231no—
143C23—232no—
144C23—464no—
145C23—464no—
146C23—922no—
147C23C22×D2312yes—
148C23C22×D2311yescharacteristic
149C23C22×D2312yes—
150D4—24no—
151D4—22no—
152D4—234no—
153D4—464no—
154D4—464no—
155D4—464no—
156D4—464no—
157D4—462no—
158D4—922no—
159D4C22⋊D2314yesdirect product factor
160C2×C4—22no—
161C2×C4—231no—
162C2×C4—231no—
163C2×C4—232no—
164C2×C4—231no—
165C2×C4—464no—
166C2×C4—462no—
167C2×C4C22×D2311yescharacteristic
168C2×C4C22×D2311yescharacteristic
169C22—22no—
170C22—21no—
171C22—22no—
172C22—21no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—48no—
177C22—232no—
178C22—461no—
179C22—461no—
180C22—462no—
181C22—462no—
182C22—462no—
183C22—928no—
184C22D4×D2312yescomplemented
185C22C2×C22⋊D2314yescomplemented
186C22C23×D2311yescharacteristic
187C4—21no—
188C4—232no—
189C4—462no—
190C4—461no—
191C4—461no—
192C4C2×C22⋊D2312yescomplemented
193C2—22no—
194C2—24no—
195C2—42no—
196C2—462no—
197C2—922no—
198C2C2×D4×D2311yescharacteristic
199C2#1062515511yescharacteristic
200C2C22×C22⋊D2311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D23
commutator, socle, cosocleC22×C23C24
FittingC22×D4×C23C2
hypercenterC22×D4D23
hypocenterC23D42
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×D4×C23C2semidirect
2. C22×C22⋊D23C2semidirect
3. C2×D4×D23C2semidirect
4. #10625124C2semidirect
5. #10625111C2semidirect
6. #10625110C2semidirect
7. #10625109C2semidirect
8. #10625108C2semidirect
9. D4×Dic23C2semidirect
10. #10625101C2semidirect
11. C4×C22⋊D23C2semidirect
12. C24×C23C22semidirect
13. C23×D23C22semidirect
16. C2×D4×C23C22semidirect
17. C2×D4×C23C22semidirect
18. C22×C4×C23C22semidirect
21. C2×C22⋊D23C22semidirect
22. C2×C22⋊D23C22semidirect
23. C2×C22⋊D23C22semidirect
24. C2×C22⋊D23C22semidirect
25. C2×C22⋊D23C22semidirect
26. C22×Dic23C22semidirect
28. C2×D92C22semidirect
29. C2×C4×D23C22semidirect
30. C22⋊Dic23C22semidirect
31. C22⋊Dic23C22semidirect
32. C22⋊Dic23C22semidirect
33. (C2×D23)⋊C4C22semidirect
34. (C2×D23)⋊C4C22semidirect
35. C4⋊Dic23C22semidirect
36. Dic23⋊C4C22semidirect
37. C4×Dic23C22semidirect
51. D4×C23D4semidirect
60. C22⋊D23D4direct (N × H)
76. C22×C23C2×D4semidirect
77. C22×C23C2×D4semidirect
85. C2×D23C2×D4semidirect
87. C4×C23C2×D4semidirect
91. Dic23C2×D4semidirect
103. C22×D4D23semidirect
112. C23D42semidirect
114. C24C2×D23semidirect
126. C2×D4C2×D23semidirect
127. C2×D4C2×D23semidirect
130. C22×C4C2×D23semidirect
159. D4C22⋊D23direct (N × H)
184. C22D4×D23semidirect
185. C22C2×C22⋊D23semidirect
192. C4C2×C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
C22×D4×C232
C22×C22⋊D232
C2×D4×D232
#106251242
#106251112
#106251102
#106251092
#106251082
D4×Dic232
#106251012
C4×C22⋊D232
D4223