Finite Group Databasebeta

← D4×C22⋊D47 #15689756

Subgroups — D4×C22⋊D47 #15689756

Order 3008.

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⋊D47C212yesmaximal, complemented
2C2×D4×D47C211yesmaximal, characteristic, complemented
3#13094020C211yesmaximal, characteristic, complemented
4#13093998C211yesmaximal, characteristic, complemented
5#13093996C212yesmaximal, complemented
6#13093995C211yesmaximal, characteristic, complemented
7#13093993C212yesmaximal, complemented
8#13093992C212yesmaximal, complemented
9D4×Dic47C211yesmaximal, characteristic, complemented
10C4×C22⋊D47C211yesmaximal, characteristic, complemented
11C22×D4×C47C211yesmaximal, characteristic, complemented
12C24×C47C2212yescomplemented
13C23×D47C2212yescomplemented
14C2×D4×C47—24no—
15C2×D4×C47C2211yescharacteristic
16C2×D4×C47C2212yescomplemented
17C2×D4×C47C2211yescharacteristic, complemented
18C22×C4×C47C2211yescharacteristic, complemented
19C2×C22⋊D47—28no—
20C2×C22⋊D47C2211yescharacteristic
21C2×C22⋊D47C2212yescomplemented
22C2×C22⋊D47C2212yescomplemented
23C2×C22⋊D47C2212yescomplemented
24C2×C22⋊D47C2212yescomplemented
25C2×C22⋊D47C2212yescomplemented
26C22×Dic47C2212yescomplemented
27D4×D47—24no—
28C2×D188C2211yescharacteristic, complemented
29C2×C4×D47C2211yescharacteristic, complemented
30C22⋊Dic47C2211yescharacteristic, complemented
31C22⋊Dic47C2212yescomplemented
32C22⋊Dic47C2212yescomplemented
33(C2×D47)⋊C4C2211yescharacteristic, complemented
34(C2×D47)⋊C4C2212yescomplemented
35C4⋊Dic47C2211yescharacteristic, complemented
36Dic47⋊C4C2211yescharacteristic, complemented
37C4×Dic47C2211yescharacteristic, complemented
38C23×C47—24no—
39C23×C47—24no—
40C23×C47—42no—
41C23×C47C2312yes—
42C23×C47C2312yes—
43C23×C47C2311yescharacteristic
44C22×D47—24no—
45C22×D47—24no—
46C22×D47—42no—
47C22×D47C2312yes—
48C22×D47C2311yescharacteristic
49D4×C47—24no—
50D4×C47—22no—
51D4×C47D414yescomplemented
52C2×C4×C47—22no—
53C2×C4×C47C2311yescharacteristic
54C2×C4×C47C2311yescharacteristic
55C22⋊D47—24no—
56C22⋊D47—24no—
57C22⋊D47—24no—
58C22⋊D47—24no—
59C22⋊D47—42no—
60C22⋊D47D414yesdirect product factor
61C2×Dic47—24no—
62C2×Dic47C2311yescharacteristic
63C2×Dic47C2311yescharacteristic
64C2×Dic47C2312yes—
65C2×Dic47C2311yescharacteristic
66D188—22no—
67C4×D47—22no—
68C22×C47—22no—
69C22×C47—21no—
70C22×C47—22no—
71C22×C47—21no—
72C22×C47—22no—
73C22×C47—22no—
74C22×C47—22no—
75C22×C47—48no—
76C22×C47C2×D412yescomplemented
77C22×C47C2×D414yescomplemented
78C22×C47C2411yescharacteristic
79C2×D47—21no—
80C2×D47—21no—
81C2×D47—22no—
82C2×D47—22no—
83C2×D47—22no—
84C2×D47—48no—
85C2×D47C2×D412yescomplemented
86C4×C47—21no—
87C4×C47C2×D412yescomplemented
88Dic47—21no—
89Dic47—22no—
90Dic47—21no—
91Dic47C2×D412yescomplemented
92C2×C47—24no—
93C2×C47—22no—
94C2×C47—42no—
95C2×C47C22×D411yescharacteristic
96C2×C47C22×D411yescharacteristic
97C2×C47H(5,𝔽2)11yescharacteristic
98D47—22no—
99D47—42no—
100D42—471nomaximal, Sylow
101C47D4211yescharacteristic, complemented, Sylow
102C22×D4—472no—
103C22×D4—471no—
104C22×D4D4711yescharacteristic, complemented
105#127—471no—
106#121—471no—
107#121—472no—
108#121—471no—
109#120—472no—
110#120—472no—
111C4×D4—471no—
112C4×D4—471no—
113C24—472no—
114C24C2×D4712yescomplemented
115C2×D4—24no—
116C2×D4—471no—
117C2×D4—472no—
118C2×D4—472no—
119C2×D4—472no—
120C2×D4—472no—
121C2×D4—472no—
122C2×D4—471no—
123C2×D4—948no—
124C2×D4—944no—
125C2×D4C2×D4711yescharacteristic
126C2×D4C2×D4712yescomplemented
127C2×D4C2×D4711yescharacteristic, complemented
128C22×C4—472no—
129C22×C4—471no—
130C22×C4C2×D4711yescharacteristic, complemented
131C4⋊C4—471no—
132C4⋊C4—471no—
133C22⋊C4—471no—
134C22⋊C4—472no—
135C22⋊C4—472no—
136C22⋊C4—471no—
137C22⋊C4—472no—
138C42—471no—
139C23—24no—
140C23—24no—
141C23—42no—
142C23—471no—
143C23—472no—
144C23—944no—
145C23—944no—
146C23—1882no—
147C23C22×D4712yes—
148C23C22×D4711yescharacteristic
149C23C22×D4712yes—
150D4—24no—
151D4—22no—
152D4—474no—
153D4—944no—
154D4—944no—
155D4—944no—
156D4—944no—
157D4—942no—
158D4—1882no—
159D4C22⋊D4714yesdirect product factor
160C2×C4—22no—
161C2×C4—471no—
162C2×C4—471no—
163C2×C4—472no—
164C2×C4—471no—
165C2×C4—944no—
166C2×C4—942no—
167C2×C4C22×D4711yescharacteristic
168C2×C4C22×D4711yescharacteristic
169C22—22no—
170C22—21no—
171C22—21no—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—48no—
177C22—472no—
178C22—941no—
179C22—941no—
180C22—942no—
181C22—942no—
182C22—942no—
183C22—1888no—
184C22D4×D4712yescomplemented
185C22C2×C22⋊D4714yescomplemented
186C22C23×D4711yescharacteristic
187C4—21no—
188C4—472no—
189C4—942no—
190C4—941no—
191C4—941no—
192C4C2×C22⋊D4712yescomplemented
193C2—22no—
194C2—24no—
195C2—42no—
196C2—942no—
197C2—1882no—
198C2C2×D4×D4711yescharacteristic
199C2C22×C22⋊D4711yescharacteristic
200C2#1309406911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D47
commutator, socle, cosocleC22×C47C24
FittingC22×D4×C47C2
hypercenterC22×D4D47
hypocenterC47D42
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D47C2semidirect
2. C2×D4×D47C2semidirect
3. #13094020C2semidirect
4. #13093998C2semidirect
5. #13093996C2semidirect
6. #13093995C2semidirect
7. #13093993C2semidirect
8. #13093992C2semidirect
9. D4×Dic47C2semidirect
10. C4×C22⋊D47C2semidirect
11. C22×D4×C47C2semidirect
12. C24×C47C22semidirect
13. C23×D47C22semidirect
16. C2×D4×C47C22semidirect
17. C2×D4×C47C22semidirect
18. C22×C4×C47C22semidirect
21. C2×C22⋊D47C22semidirect
22. C2×C22⋊D47C22semidirect
23. C2×C22⋊D47C22semidirect
24. C2×C22⋊D47C22semidirect
25. C2×C22⋊D47C22semidirect
26. C22×Dic47C22semidirect
28. C2×D188C22semidirect
29. C2×C4×D47C22semidirect
30. C22⋊Dic47C22semidirect
31. C22⋊Dic47C22semidirect
32. C22⋊Dic47C22semidirect
33. (C2×D47)⋊C4C22semidirect
34. (C2×D47)⋊C4C22semidirect
35. C4⋊Dic47C22semidirect
36. Dic47⋊C4C22semidirect
37. C4×Dic47C22semidirect
51. D4×C47D4semidirect
60. C22⋊D47D4direct (N × H)
76. C22×C47C2×D4semidirect
77. C22×C47C2×D4semidirect
85. C2×D47C2×D4semidirect
87. C4×C47C2×D4semidirect
91. Dic47C2×D4semidirect
101. C47D42semidirect
104. C22×D4D47semidirect
114. C24C2×D47semidirect
126. C2×D4C2×D47semidirect
127. C2×D4C2×D47semidirect
130. C22×C4C2×D47semidirect
159. D4C22⋊D47direct (N × H)
184. C22D4×D47semidirect
185. C22C2×C22⋊D47semidirect
192. C4C2×C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D472
C2×D4×D472
#130940202
#130939982
#130939962
#130939952
#130939932
#130939922
D4×Dic472
C4×C22⋊D472
C22×D4×C472
D4247