Finite Group Databasebeta

← D4×C22⋊D467 #44470670

Subgroups — D4×C22⋊D467 #44470670

Order 29888.

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⋊D467C212yesmaximal, complemented
2C2×D4×D467C211yesmaximal, characteristic, complemented
3#28417949C211yesmaximal, characteristic, complemented
4#28417927C211yesmaximal, characteristic, complemented
5#28417925C212yesmaximal, complemented
6#28417924C211yesmaximal, characteristic, complemented
7#28417922C212yesmaximal, complemented
8#28417921C212yesmaximal, complemented
9D4×Dic467C211yesmaximal, characteristic, complemented
10C4×C22⋊D467C211yesmaximal, characteristic, complemented
11C22×D4×C467C211yesmaximal, characteristic, complemented
12C23×D467C2212yescomplemented
13C2×D1868C2211yescharacteristic, complemented
14C2×C22⋊D467—28no—
15C2×C22⋊D467C2211yescharacteristic
16C2×C22⋊D467C2212yescomplemented
17C2×C22⋊D467C2212yescomplemented
18C2×C22⋊D467C2212yescomplemented
19C2×C22⋊D467C2212yescomplemented
20C2×C22⋊D467C2212yescomplemented
21D4×D467—24no—
22C22×Dic467C2212yescomplemented
23C2×C4×D467C2211yescharacteristic, complemented
24C4⋊Dic467C2211yescharacteristic, complemented
25Dic467⋊C4C2211yescharacteristic, complemented
26C22⋊Dic467C2211yescharacteristic, complemented
27C22⋊Dic467C2212yescomplemented
28C22⋊Dic467C2212yescomplemented
29(C2×D467)⋊C4C2211yescharacteristic, complemented
30(C2×D467)⋊C4C2212yescomplemented
31C4×Dic467C2211yescharacteristic, complemented
32C24×C467C2212yescomplemented
33C2×D4×C467—24no—
34C2×D4×C467C2211yescharacteristic
35C2×D4×C467C2212yescomplemented
36C2×D4×C467C2211yescharacteristic, complemented
37C22×C4×C467C2211yescharacteristic, complemented
38C22×D467—24no—
39C22×D467—24no—
40C22×D467—42no—
41C22×D467C2312yes—
42C22×D467C2311yescharacteristic
43D1868—22no—
44C22⋊D467—24no—
45C22⋊D467—24no—
46C22⋊D467—24no—
47C22⋊D467—24no—
48C22⋊D467—42no—
49C22⋊D467D414yesdirect product factor
50C2×Dic467—24no—
51C2×Dic467C2311yescharacteristic
52C2×Dic467C2312yes—
53C2×Dic467C2311yescharacteristic
54C2×Dic467C2311yescharacteristic
55C4×D467—22no—
56C23×C467—24no—
57C23×C467—24no—
58C23×C467—42no—
59C23×C467C2312yes—
60C23×C467C2311yescharacteristic
61C23×C467C2312yes—
62D4×C467—24no—
63D4×C467—22no—
64D4×C467D414yescomplemented
65C2×C4×C467—22no—
66C2×C4×C467C2311yescharacteristic
67C2×C4×C467C2311yescharacteristic
68C22×C467—21no—
69C22×C467—22no—
70C22×C467—21no—
71C22×C467—22no—
72C22×C467—22no—
73C22×C467—22no—
74C22×C467—22no—
75C22×C467—48no—
76C22×C467C2×D412yescomplemented
77C22×C467C2×D414yescomplemented
78C22×C467C2411yescharacteristic
79C2×D467—21no—
80C2×D467—21no—
81C2×D467—22no—
82C2×D467—22no—
83C2×D467—22no—
84C2×D467—48no—
85C2×D467C2×D412yescomplemented
86C4×C467—21no—
87C4×C467C2×D412yescomplemented
88Dic467—21no—
89Dic467—22no—
90Dic467—21no—
91Dic467C2×D412yescomplemented
92C2×C467—24no—
93C2×C467—22no—
94C2×C467—42no—
95C2×C467C22×D411yescharacteristic
96C2×C467C22×D411yescharacteristic
97C2×C467H(5,𝔽2)11yescharacteristic
98D467—22no—
99D467—42no—
100C467D4211yescharacteristic, complemented, Sylow
101D42—4671nomaximal, Sylow
102C22×D4—4672no—
103C22×D4—4671no—
104C22×D4D46711yescharacteristic, complemented
105#127—4671no—
106#121—4671no—
107#121—4672no—
108#121—4671no—
109#120—4672no—
110#120—4672no—
111C4×D4—4671no—
112C4×D4—4671no—
113C24—4672no—
114C24C2×D46712yescomplemented
115C2×D4—24no—
116C2×D4—9348no—
117C2×D4—9344no—
118C2×D4—4672no—
119C2×D4—4672no—
120C2×D4—4672no—
121C2×D4—4672no—
122C2×D4—4672no—
123C2×D4—4671no—
124C2×D4—4671no—
125C2×D4C2×D46711yescharacteristic
126C2×D4C2×D46712yescomplemented
127C2×D4C2×D46711yescharacteristic, complemented
128C22×C4—4672no—
129C22×C4—4671no—
130C22×C4C2×D46711yescharacteristic, complemented
131C4⋊C4—4671no—
132C4⋊C4—4671no—
133C22⋊C4—4671no—
134C22⋊C4—4672no—
135C22⋊C4—4672no—
136C22⋊C4—4671no—
137C22⋊C4—4672no—
138C42—4671no—
139C23—24no—
140C23—24no—
141C23—42no—
142C23—18682no—
143C23—9344no—
144C23—9344no—
145C23—4672no—
146C23—4671no—
147C23C22×D46712yes—
148C23C22×D46711yescharacteristic
149C23C22×D46712yes—
150D4—24no—
151D4—22no—
152D4—18682no—
153D4—9344no—
154D4—9344no—
155D4—9344no—
156D4—9344no—
157D4—9342no—
158D4—4674no—
159D4C22⋊D46714yesdirect product factor
160C2×C4—22no—
161C2×C4—9344no—
162C2×C4—9342no—
163C2×C4—4671no—
164C2×C4—4672no—
165C2×C4—4671no—
166C2×C4—4671no—
167C2×C4C22×D46711yescharacteristic
168C2×C4C22×D46711yescharacteristic
169C22—22no—
170C22—21no—
171C22—21no—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—48no—
177C22—18688no—
178C22—9342no—
179C22—9342no—
180C22—9342no—
181C22—9341no—
182C22—9341no—
183C22—4672no—
184C22D4×D46712yescomplemented
185C22C2×C22⋊D46714yescomplemented
186C22C23×D46711yescharacteristic
187C4—21no—
188C4—9342no—
189C4—9341no—
190C4—9341no—
191C4—4672no—
192C4C2×C22⋊D46712yescomplemented
193C2—22no—
194C2—24no—
195C2—42no—
196C2—18682no—
197C2—9342no—
198C2C2×D4×D46711yescharacteristic
199C2C22×C22⋊D46711yescharacteristic
200C2#2841799811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D467
commutator, socle, cosocleC22×C467C24
FittingC22×D4×C467C2
hypercenterC22×D4D467
hypocenterC467D42
LCSG ▷ C22×C467 ▷ C467
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D467C2semidirect
2. C2×D4×D467C2semidirect
3. #28417949C2semidirect
4. #28417927C2semidirect
5. #28417925C2semidirect
6. #28417924C2semidirect
7. #28417922C2semidirect
8. #28417921C2semidirect
9. D4×Dic467C2semidirect
10. C4×C22⋊D467C2semidirect
11. C22×D4×C467C2semidirect
12. C23×D467C22semidirect
13. C2×D1868C22semidirect
16. C2×C22⋊D467C22semidirect
17. C2×C22⋊D467C22semidirect
18. C2×C22⋊D467C22semidirect
19. C2×C22⋊D467C22semidirect
20. C2×C22⋊D467C22semidirect
22. C22×Dic467C22semidirect
23. C2×C4×D467C22semidirect
24. C4⋊Dic467C22semidirect
25. Dic467⋊C4C22semidirect
26. C22⋊Dic467C22semidirect
27. C22⋊Dic467C22semidirect
28. C22⋊Dic467C22semidirect
29. (C2×D467)⋊C4C22semidirect
30. (C2×D467)⋊C4C22semidirect
31. C4×Dic467C22semidirect
32. C24×C467C22semidirect
35. C2×D4×C467C22semidirect
36. C2×D4×C467C22semidirect
37. C22×C4×C467C22semidirect
49. C22⋊D467D4direct (N × H)
64. D4×C467D4semidirect
76. C22×C467C2×D4semidirect
77. C22×C467C2×D4semidirect
85. C2×D467C2×D4semidirect
87. C4×C467C2×D4semidirect
91. Dic467C2×D4semidirect
100. C467D42semidirect
104. C22×D4D467semidirect
114. C24C2×D467semidirect
126. C2×D4C2×D467semidirect
127. C2×D4C2×D467semidirect
130. C22×C4C2×D467semidirect
159. D4C22⋊D467direct (N × H)
184. C22D4×D467semidirect
185. C22C2×C22⋊D467semidirect
192. C4C2×C22⋊D467semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D4672
C2×D4×D4672
#284179492
#284179272
#284179252
#284179242
#284179222
#284179212
D4×Dic4672
C4×C22⋊D4672
C22×D4×C4672
D42467