Finite Group Databasebeta

← D4×C22⋊D41 #14580969

Subgroups — D4×C22⋊D41 #14580969

Order 2624.

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×C22⋊D41C212yesmaximal, complemented
2C2×D4×D41C211yesmaximal, characteristic, complemented
3#13050160C211yesmaximal, characteristic, complemented
4#13050138C211yesmaximal, characteristic, complemented
5#13050136C212yesmaximal, complemented
6#13050135C211yesmaximal, characteristic, complemented
7#13050133C212yesmaximal, complemented
8#13050132C212yesmaximal, complemented
9D4×Dic41C211yesmaximal, characteristic, complemented
10C4×C22⋊D41C211yesmaximal, characteristic, complemented
11C22×D4×C41C211yesmaximal, characteristic, complemented
12C24×C41C2212yescomplemented
13C23×D41C2212yescomplemented
14C2×D4×C41—24no—
15C2×D4×C41C2211yescharacteristic
16C2×D4×C41C2212yescomplemented
17C2×D4×C41C2211yescharacteristic, complemented
18C22×C4×C41C2211yescharacteristic, complemented
19C2×C22⋊D41—28no—
20C2×C22⋊D41C2211yescharacteristic
21C2×C22⋊D41C2212yescomplemented
22C2×C22⋊D41C2212yescomplemented
23C2×C22⋊D41C2212yescomplemented
24C2×C22⋊D41C2212yescomplemented
25C2×C22⋊D41C2212yescomplemented
26C22×Dic41C2212yescomplemented
27D4×D41—24no—
28C2×D164C2211yescharacteristic, complemented
29C2×C4×D41C2211yescharacteristic, complemented
30C22⋊Dic41C2211yescharacteristic, complemented
31C22⋊Dic41C2212yescomplemented
32C22⋊Dic41C2212yescomplemented
33#10620281C2211yescharacteristic, complemented
34#10620281C2212yescomplemented
35C4⋊Dic41C2211yescharacteristic, complemented
36#10620279C2211yescharacteristic, complemented
37C4×Dic41C2211yescharacteristic, complemented
38C23×C41—24no—
39C23×C41—24no—
40C23×C41—42no—
41C23×C41C2312yes—
42C23×C41C2312yes—
43C23×C41C2311yescharacteristic
44C22×D41—24no—
45C22×D41—24no—
46C22×D41—42no—
47C22×D41C2312yes—
48C22×D41C2311yescharacteristic
49D4×C41—24no—
50D4×C41—22no—
51D4×C41D414yescomplemented
52C2×C4×C41—22no—
53C2×C4×C41C2311yescharacteristic
54C2×C4×C41C2311yescharacteristic
55C22⋊D41—24no—
56C22⋊D41—24no—
57C22⋊D41—24no—
58C22⋊D41—24no—
59C22⋊D41—42no—
60C22⋊D41D414yesdirect product factor
61C2×Dic41—24no—
62C2×Dic41C2311yescharacteristic
63C2×Dic41C2311yescharacteristic
64C2×Dic41C2312yes—
65C2×Dic41C2311yescharacteristic
66D164—22no—
67C4×D41—22no—
68C22×C41—22no—
69C22×C41—21no—
70C22×C41—22no—
71C22×C41—21no—
72C22×C41—22no—
73C22×C41—22no—
74C22×C41—22no—
75C22×C41—48no—
76C22×C41C2×D412yescomplemented
77C22×C41C2×D414yescomplemented
78C22×C41C2411yescharacteristic
79C2×D41—21no—
80C2×D41—21no—
81C2×D41—22no—
82C2×D41—22no—
83C2×D41—22no—
84C2×D41—48no—
85C2×D41C2×D412yescomplemented
86C4×C41—21no—
87C4×C41C2×D412yescomplemented
88Dic41—21no—
89Dic41—22no—
90Dic41—21no—
91Dic41C2×D412yescomplemented
92C2×C41—24no—
93C2×C41—22no—
94C2×C41—42no—
95C2×C41C22×D411yescharacteristic
96C2×C41C22×D411yescharacteristic
97C2×C41H(5,𝔽2)11yescharacteristic
98D41—22no—
99D41—42no—
100D42—411nomaximal, Sylow
101C41D4211yescharacteristic, complemented, Sylow
102C22×D4—412no—
103C22×D4—411no—
104C22×D4D4111yescharacteristic, complemented
105#127—411no—
106#121—411no—
107#121—412no—
108#121—411no—
109#120—412no—
110#120—412no—
111C4×D4—411no—
112C4×D4—411no—
113C24—412no—
114C24C2×D4112yescomplemented
115C2×D4—24no—
116C2×D4—411no—
117C2×D4—412no—
118C2×D4—412no—
119C2×D4—412no—
120C2×D4—412no—
121C2×D4—412no—
122C2×D4—411no—
123C2×D4—828no—
124C2×D4—824no—
125C2×D4C2×D4111yescharacteristic
126C2×D4C2×D4112yescomplemented
127C2×D4C2×D4111yescharacteristic, complemented
128C22×C4—412no—
129C22×C4—411no—
130C22×C4C2×D4111yescharacteristic, complemented
131C4⋊C4—411no—
132C4⋊C4—411no—
133C22⋊C4—411no—
134C22⋊C4—412no—
135C22⋊C4—412no—
136C22⋊C4—411no—
137C22⋊C4—412no—
138C42—411no—
139C23—24no—
140C23—24no—
141C23—42no—
142C23—411no—
143C23—412no—
144C23—824no—
145C23—824no—
146C23—1642no—
147C23C22×D4112yes—
148C23C22×D4111yescharacteristic
149C23C22×D4112yes—
150D4—24no—
151D4—22no—
152D4—414no—
153D4—824no—
154D4—824no—
155D4—824no—
156D4—824no—
157D4—822no—
158D4—1642no—
159D4C22⋊D4114yesdirect product factor
160C2×C4—22no—
161C2×C4—411no—
162C2×C4—411no—
163C2×C4—412no—
164C2×C4—411no—
165C2×C4—824no—
166C2×C4—822no—
167C2×C4C22×D4111yescharacteristic
168C2×C4C22×D4111yescharacteristic
169C22—22no—
170C22—21no—
171C22—21no—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—48no—
177C22—412no—
178C22—821no—
179C22—821no—
180C22—822no—
181C22—822no—
182C22—822no—
183C22—1648no—
184C22D4×D4112yescomplemented
185C22C2×C22⋊D4114yescomplemented
186C22C23×D4111yescharacteristic
187C4—21no—
188C4—412no—
189C4—822no—
190C4—821no—
191C4—821no—
192C4C2×C22⋊D4112yescomplemented
193C2—22no—
194C2—24no—
195C2—42no—
196C2—822no—
197C2—1642no—
198C2C2×D4×D4111yescharacteristic
199C2C22×C22⋊D4111yescharacteristic
200C2#1305020911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D41
commutator, socle, cosocleC22×C41C24
FittingC22×D4×C41C2
hypercenterC22×D4D41
hypocenterC41D42
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D41C2semidirect
2. C2×D4×D41C2semidirect
3. #13050160C2semidirect
4. #13050138C2semidirect
5. #13050136C2semidirect
6. #13050135C2semidirect
7. #13050133C2semidirect
8. #13050132C2semidirect
9. D4×Dic41C2semidirect
10. C4×C22⋊D41C2semidirect
11. C22×D4×C41C2semidirect
12. C24×C41C22semidirect
13. C23×D41C22semidirect
16. C2×D4×C41C22semidirect
17. C2×D4×C41C22semidirect
18. C22×C4×C41C22semidirect
21. C2×C22⋊D41C22semidirect
22. C2×C22⋊D41C22semidirect
23. C2×C22⋊D41C22semidirect
24. C2×C22⋊D41C22semidirect
25. C2×C22⋊D41C22semidirect
26. C22×Dic41C22semidirect
28. C2×D164C22semidirect
29. C2×C4×D41C22semidirect
30. C22⋊Dic41C22semidirect
31. C22⋊Dic41C22semidirect
32. C22⋊Dic41C22semidirect
33. #10620281C22semidirect
34. #10620281C22semidirect
35. C4⋊Dic41C22semidirect
36. #10620279C22semidirect
37. C4×Dic41C22semidirect
51. D4×C41D4semidirect
60. C22⋊D41D4direct (N × H)
76. C22×C41C2×D4semidirect
77. C22×C41C2×D4semidirect
85. C2×D41C2×D4semidirect
87. C4×C41C2×D4semidirect
91. Dic41C2×D4semidirect
101. C41D42semidirect
104. C22×D4D41semidirect
114. C24C2×D41semidirect
126. C2×D4C2×D41semidirect
127. C2×D4C2×D41semidirect
130. C22×C4C2×D41semidirect
159. D4C22⋊D41direct (N × H)
184. C22D4×D41semidirect
185. C22C2×C22⋊D41semidirect
192. C4C2×C22⋊D41semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D412
C2×D4×D412
#130501602
#130501382
#130501362
#130501352
#130501332
#130501322
D4×Dic412
C4×C22⋊D412
C22×D4×C412
D4241