Finite Group Databasebeta

← D4×C22⋊D107 #20293260

Subgroups — D4×C22⋊D107 #20293260

Order 6848.

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⋊D107C212yesmaximal, complemented
2C2×D4×D107C211yesmaximal, characteristic, complemented
3#16812105C211yesmaximal, characteristic, complemented
4#16812083C211yesmaximal, characteristic, complemented
5#16812081C212yesmaximal, complemented
6#16812080C211yesmaximal, characteristic, complemented
7#16812078C212yesmaximal, complemented
8#16812077C212yesmaximal, complemented
9D4×Dic107C211yesmaximal, characteristic, complemented
10C4×C22⋊D107C211yesmaximal, characteristic, complemented
11C22×D4×C107C211yesmaximal, characteristic, complemented
12C23×D107C2212yescomplemented
13C2×D428C2211yescharacteristic, complemented
14C2×C22⋊D107—28no—
15C2×C22⋊D107C2211yescharacteristic
16C2×C22⋊D107C2212yescomplemented
17C2×C22⋊D107C2212yescomplemented
18C2×C22⋊D107C2212yescomplemented
19C2×C22⋊D107C2212yescomplemented
20C2×C22⋊D107C2212yescomplemented
21D4×D107—24no—
22C22×Dic107C2212yescomplemented
23C2×C4×D107C2211yescharacteristic, complemented
24C4⋊Dic107C2211yescharacteristic, complemented
25Dic107⋊C4C2211yescharacteristic, complemented
26C22⋊Dic107C2211yescharacteristic, complemented
27C22⋊Dic107C2212yescomplemented
28C22⋊Dic107C2212yescomplemented
29(C2×D107)⋊C4C2211yescharacteristic, complemented
30(C2×D107)⋊C4C2212yescomplemented
31C4×Dic107C2211yescharacteristic, complemented
32C24×C107C2212yescomplemented
33C2×D4×C107—24no—
34C2×D4×C107C2211yescharacteristic
35C2×D4×C107C2212yescomplemented
36C2×D4×C107C2211yescharacteristic, complemented
37C22×C4×C107C2211yescharacteristic, complemented
38C23×C107—24no—
39C23×C107—24no—
40C23×C107—42no—
41C23×C107C2312yes—
42C23×C107C2311yescharacteristic
43C23×C107C2312yes—
44C22×D107—24no—
45C22×D107—24no—
46C22×D107—42no—
47C22×D107C2312yes—
48C22×D107C2311yescharacteristic
49D4×C107—24no—
50D4×C107—22no—
51D4×C107D414yescomplemented
52C2×C4×C107—22no—
53C2×C4×C107C2311yescharacteristic
54C2×C4×C107C2311yescharacteristic
55C22⋊D107—24no—
56C22⋊D107—24no—
57C22⋊D107—24no—
58C22⋊D107—24no—
59C22⋊D107—42no—
60C22⋊D107D414yesdirect product factor
61C2×Dic107—24no—
62C2×Dic107C2311yescharacteristic
63C2×Dic107C2312yes—
64C2×Dic107C2311yescharacteristic
65C2×Dic107C2311yescharacteristic
66D428—22no—
67C4×D107—22no—
68C22×C107—22no—
69C22×C107—21no—
70C22×C107—22no—
71C22×C107—21no—
72C22×C107—22no—
73C22×C107—22no—
74C22×C107—22no—
75C22×C107—48no—
76C22×C107C2×D412yescomplemented
77C22×C107C2×D414yescomplemented
78C22×C107C2411yescharacteristic
79C2×D107—21no—
80C2×D107—21no—
81C2×D107—22no—
82C2×D107—22no—
83C2×D107—22no—
84C2×D107—48no—
85C2×D107C2×D412yescomplemented
86C4×C107—21no—
87C4×C107C2×D412yescomplemented
88Dic107—21no—
89Dic107—22no—
90Dic107—21no—
91Dic107C2×D412yescomplemented
92C2×C107—24no—
93C2×C107—22no—
94C2×C107—42no—
95C2×C107C22×D411yescharacteristic
96C2×C107C22×D411yescharacteristic
97C2×C107H(5,𝔽2)11yescharacteristic
98D107—22no—
99D107—42no—
100C107D4211yescharacteristic, complemented, Sylow
101D42—1071nomaximal, Sylow
102C22×D4—1072no—
103C22×D4—1071no—
104C22×D4D10711yescharacteristic, complemented
105#127—1071no—
106#121—1071no—
107#121—1072no—
108#121—1071no—
109#120—1072no—
110#120—1072no—
111C4×D4—1071no—
112C4×D4—1071no—
113C24—1072no—
114C24C2×D10712yescomplemented
115C2×D4—24no—
116C2×D4—1071no—
117C2×D4—1072no—
118C2×D4—1072no—
119C2×D4—1072no—
120C2×D4—1072no—
121C2×D4—1072no—
122C2×D4—1071no—
123C2×D4—2148no—
124C2×D4—2144no—
125C2×D4C2×D10711yescharacteristic
126C2×D4C2×D10712yescomplemented
127C2×D4C2×D10711yescharacteristic, complemented
128C22×C4—1072no—
129C22×C4—1071no—
130C22×C4C2×D10711yescharacteristic, complemented
131C4⋊C4—1071no—
132C4⋊C4—1071no—
133C22⋊C4—1071no—
134C22⋊C4—1072no—
135C22⋊C4—1072no—
136C22⋊C4—1071no—
137C22⋊C4—1072no—
138C42—1071no—
139C23—24no—
140C23—24no—
141C23—42no—
142C23—1071no—
143C23—1072no—
144C23—4282no—
145C23—2144no—
146C23—2144no—
147C23C22×D10712yes—
148C23C22×D10711yescharacteristic
149C23C22×D10712yes—
150D4—24no—
151D4—22no—
152D4—1074no—
153D4—4282no—
154D4—2144no—
155D4—2144no—
156D4—2144no—
157D4—2144no—
158D4—2142no—
159D4C22⋊D10714yesdirect product factor
160C2×C4—22no—
161C2×C4—1071no—
162C2×C4—1071no—
163C2×C4—1072no—
164C2×C4—1071no—
165C2×C4—2144no—
166C2×C4—2142no—
167C2×C4C22×D10711yescharacteristic
168C2×C4C22×D10711yescharacteristic
169C22—22no—
170C22—21no—
171C22—21no—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—48no—
177C22—1072no—
178C22—4288no—
179C22—2142no—
180C22—2142no—
181C22—2142no—
182C22—2141no—
183C22—2141no—
184C22D4×D10712yescomplemented
185C22C2×C22⋊D10714yescomplemented
186C22C23×D10711yescharacteristic
187C4—21no—
188C4—1072no—
189C4—2142no—
190C4—2141no—
191C4—2141no—
192C4C2×C22⋊D10712yescomplemented
193C2—22no—
194C2—24no—
195C2—42no—
196C2—4282no—
197C2—2142no—
198C2C2×D4×D10711yescharacteristic
199C2C22×C22⋊D10711yescharacteristic
200C2#1681215411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D107
commutator, socleC22×C107C24
FittingC22×D4×C107C2
hypercenterC22×D4D107
hypocenterC107D42
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D107C2semidirect
2. C2×D4×D107C2semidirect
3. #16812105C2semidirect
4. #16812083C2semidirect
5. #16812081C2semidirect
6. #16812080C2semidirect
7. #16812078C2semidirect
8. #16812077C2semidirect
9. D4×Dic107C2semidirect
10. C4×C22⋊D107C2semidirect
11. C22×D4×C107C2semidirect
12. C23×D107C22semidirect
13. C2×D428C22semidirect
16. C2×C22⋊D107C22semidirect
17. C2×C22⋊D107C22semidirect
18. C2×C22⋊D107C22semidirect
19. C2×C22⋊D107C22semidirect
20. C2×C22⋊D107C22semidirect
22. C22×Dic107C22semidirect
23. C2×C4×D107C22semidirect
24. C4⋊Dic107C22semidirect
25. Dic107⋊C4C22semidirect
26. C22⋊Dic107C22semidirect
27. C22⋊Dic107C22semidirect
28. C22⋊Dic107C22semidirect
29. (C2×D107)⋊C4C22semidirect
30. (C2×D107)⋊C4C22semidirect
31. C4×Dic107C22semidirect
32. C24×C107C22semidirect
35. C2×D4×C107C22semidirect
36. C2×D4×C107C22semidirect
37. C22×C4×C107C22semidirect
51. D4×C107D4semidirect
60. C22⋊D107D4direct (N × H)
76. C22×C107C2×D4semidirect
77. C22×C107C2×D4semidirect
85. C2×D107C2×D4semidirect
87. C4×C107C2×D4semidirect
91. Dic107C2×D4semidirect
100. C107D42semidirect
104. C22×D4D107semidirect
114. C24C2×D107semidirect
126. C2×D4C2×D107semidirect
127. C2×D4C2×D107semidirect
130. C22×C4C2×D107semidirect
159. D4C22⋊D107direct (N × H)
184. C22D4×D107semidirect
185. C22C2×C22⋊D107semidirect
192. C4C2×C22⋊D107semidirect