Finite Group Databasebeta

← D4×C22⋊D227 #28409665

Subgroups — D4×C22⋊D227 #28409665

Order 14528.

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⋊D227C212yesmaximal, complemented
2C2×D4×D227C211yesmaximal, characteristic, complemented
3#20300284C211yesmaximal, characteristic, complemented
4#20300262C211yesmaximal, characteristic, complemented
5#20300260C212yesmaximal, complemented
6#20300259C211yesmaximal, characteristic, complemented
7#20300257C212yesmaximal, complemented
8#20300256C212yesmaximal, complemented
9D4×Dic227C211yesmaximal, characteristic, complemented
10C4×C22⋊D227C211yesmaximal, characteristic, complemented
11C22×D4×C227C211yesmaximal, characteristic, complemented
12C23×D227C2212yescomplemented
13C2×D908C2211yescharacteristic, complemented
14C2×C22⋊D227—28no—
15C2×C22⋊D227C2211yescharacteristic
16C2×C22⋊D227C2212yescomplemented
17C2×C22⋊D227C2212yescomplemented
18C2×C22⋊D227C2212yescomplemented
19C2×C22⋊D227C2212yescomplemented
20C2×C22⋊D227C2212yescomplemented
21D4×D227—24no—
22C22×Dic227C2212yescomplemented
23C2×C4×D227C2211yescharacteristic, complemented
24C4⋊Dic227C2211yescharacteristic, complemented
25Dic227⋊C4C2211yescharacteristic, complemented
26C22⋊Dic227C2211yescharacteristic, complemented
27C22⋊Dic227C2212yescomplemented
28C22⋊Dic227C2212yescomplemented
29(C2×D227)⋊C4C2211yescharacteristic, complemented
30(C2×D227)⋊C4C2212yescomplemented
31C4×Dic227C2211yescharacteristic, complemented
32C24×C227C2212yescomplemented
33C2×D4×C227—24no—
34C2×D4×C227C2211yescharacteristic
35C2×D4×C227C2212yescomplemented
36C2×D4×C227C2211yescharacteristic, complemented
37C22×C4×C227C2211yescharacteristic, complemented
38C22×D227—24no—
39C22×D227—24no—
40C22×D227—42no—
41C22×D227C2312yes—
42C22×D227C2311yescharacteristic
43D908—22no—
44C22⋊D227—24no—
45C22⋊D227—24no—
46C22⋊D227—24no—
47C22⋊D227—24no—
48C22⋊D227—42no—
49C22⋊D227D414yesdirect product factor
50C2×Dic227—24no—
51C2×Dic227C2311yescharacteristic
52C2×Dic227C2312yes—
53C2×Dic227C2311yescharacteristic
54C2×Dic227C2311yescharacteristic
55C4×D227—22no—
56C23×C227—24no—
57C23×C227—24no—
58C23×C227—42no—
59C23×C227C2312yes—
60C23×C227C2311yescharacteristic
61C23×C227C2312yes—
62D4×C227—24no—
63D4×C227—22no—
64D4×C227D414yescomplemented
65C2×C4×C227—22no—
66C2×C4×C227C2311yescharacteristic
67C2×C4×C227C2311yescharacteristic
68C22×C227—21no—
69C22×C227—22no—
70C22×C227—21no—
71C22×C227—22no—
72C22×C227—22no—
73C22×C227—22no—
74C22×C227—22no—
75C22×C227—48no—
76C22×C227C2×D412yescomplemented
77C22×C227C2×D414yescomplemented
78C22×C227C2411yescharacteristic
79C2×D227—21no—
80C2×D227—21no—
81C2×D227—22no—
82C2×D227—22no—
83C2×D227—22no—
84C2×D227—48no—
85C2×D227C2×D412yescomplemented
86C4×C227—21no—
87C4×C227C2×D412yescomplemented
88Dic227—21no—
89Dic227—22no—
90Dic227—21no—
91Dic227C2×D412yescomplemented
92C2×C227—24no—
93C2×C227—22no—
94C2×C227—42no—
95C2×C227C22×D411yescharacteristic
96C2×C227C22×D411yescharacteristic
97C2×C227H(5,𝔽2)11yescharacteristic
98D227—22no—
99D227—42no—
100C227D4211yescharacteristic, complemented, Sylow
101D42—2271nomaximal, Sylow
102C22×D4—2272no—
103C22×D4—2271no—
104C22×D4D22711yescharacteristic, complemented
105#127—2271no—
106#121—2271no—
107#121—2272no—
108#121—2271no—
109#120—2272no—
110#120—2272no—
111C4×D4—2271no—
112C4×D4—2271no—
113C24—2272no—
114C24C2×D22712yescomplemented
115C2×D4—24no—
116C2×D4—4548no—
117C2×D4—4544no—
118C2×D4—2272no—
119C2×D4—2272no—
120C2×D4—2272no—
121C2×D4—2272no—
122C2×D4—2272no—
123C2×D4—2271no—
124C2×D4—2271no—
125C2×D4C2×D22711yescharacteristic
126C2×D4C2×D22712yescomplemented
127C2×D4C2×D22711yescharacteristic, complemented
128C22×C4—2272no—
129C22×C4—2271no—
130C22×C4C2×D22711yescharacteristic, complemented
131C4⋊C4—2271no—
132C4⋊C4—2271no—
133C22⋊C4—2271no—
134C22⋊C4—2272no—
135C22⋊C4—2272no—
136C22⋊C4—2271no—
137C22⋊C4—2272no—
138C42—2271no—
139C23—24no—
140C23—24no—
141C23—42no—
142C23—9082no—
143C23—4544no—
144C23—4544no—
145C23—2272no—
146C23—2271no—
147C23C22×D22712yes—
148C23C22×D22711yescharacteristic
149C23C22×D22712yes—
150D4—24no—
151D4—22no—
152D4—9082no—
153D4—4544no—
154D4—4544no—
155D4—4544no—
156D4—4544no—
157D4—4542no—
158D4—2274no—
159D4C22⋊D22714yesdirect product factor
160C2×C4—22no—
161C2×C4—4544no—
162C2×C4—4542no—
163C2×C4—2271no—
164C2×C4—2272no—
165C2×C4—2271no—
166C2×C4—2271no—
167C2×C4C22×D22711yescharacteristic
168C2×C4C22×D22711yescharacteristic
169C22—22no—
170C22—21no—
171C22—21no—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—48no—
177C22—9088no—
178C22—4542no—
179C22—4542no—
180C22—4542no—
181C22—4541no—
182C22—4541no—
183C22—2272no—
184C22D4×D22712yescomplemented
185C22C2×C22⋊D22714yescomplemented
186C22C23×D22711yescharacteristic
187C4—21no—
188C4—4542no—
189C4—4541no—
190C4—4541no—
191C4—2272no—
192C4C2×C22⋊D22712yescomplemented
193C2—22no—
194C2—24no—
195C2—42no—
196C2—9082no—
197C2—4542no—
198C2C2×D4×D22711yescharacteristic
199C2C22×C22⋊D22711yescharacteristic
200C2#2030033311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D227
commutator, socle, cosocleC22×C227C24
FittingC22×D4×C227C2
hypercenterC22×D4D227
hypocenterC227D42
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D227C2semidirect
2. C2×D4×D227C2semidirect
3. #20300284C2semidirect
4. #20300262C2semidirect
5. #20300260C2semidirect
6. #20300259C2semidirect
7. #20300257C2semidirect
8. #20300256C2semidirect
9. D4×Dic227C2semidirect
10. C4×C22⋊D227C2semidirect
11. C22×D4×C227C2semidirect
12. C23×D227C22semidirect
13. C2×D908C22semidirect
16. C2×C22⋊D227C22semidirect
17. C2×C22⋊D227C22semidirect
18. C2×C22⋊D227C22semidirect
19. C2×C22⋊D227C22semidirect
20. C2×C22⋊D227C22semidirect
22. C22×Dic227C22semidirect
23. C2×C4×D227C22semidirect
24. C4⋊Dic227C22semidirect
25. Dic227⋊C4C22semidirect
26. C22⋊Dic227C22semidirect
27. C22⋊Dic227C22semidirect
28. C22⋊Dic227C22semidirect
29. (C2×D227)⋊C4C22semidirect
30. (C2×D227)⋊C4C22semidirect
31. C4×Dic227C22semidirect
32. C24×C227C22semidirect
35. C2×D4×C227C22semidirect
36. C2×D4×C227C22semidirect
37. C22×C4×C227C22semidirect
49. C22⋊D227D4direct (N × H)
64. D4×C227D4semidirect
76. C22×C227C2×D4semidirect
77. C22×C227C2×D4semidirect
85. C2×D227C2×D4semidirect
87. C4×C227C2×D4semidirect
91. Dic227C2×D4semidirect
100. C227D42semidirect
104. C22×D4D227semidirect
114. C24C2×D227semidirect
126. C2×D4C2×D227semidirect
127. C2×D4C2×D227semidirect
130. C22×C4C2×D227semidirect
159. D4C22⋊D227direct (N × H)
184. C22D4×D227semidirect
185. C22C2×C22⋊D227semidirect
192. C4C2×C22⋊D227semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D2272
C2×D4×D2272
#203002842
#203002622
#203002602
#203002592
#203002572
#203002562
D4×Dic2272
C4×C22⋊D2272
C22×D4×C2272
D42227