Finite Group Databasebeta

← D4×C22⋊D479 #44501028

Subgroups — D4×C22⋊D479 #44501028

Order 30656.

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⋊D479C212yesmaximal, complemented
2C2×D4×D479C211yesmaximal, characteristic, complemented
3#29506378C211yesmaximal, characteristic, complemented
4#29506356C211yesmaximal, characteristic, complemented
5#29506354C212yesmaximal, complemented
6#29506353C211yesmaximal, characteristic, complemented
7#29506351C212yesmaximal, complemented
8#29506350C212yesmaximal, complemented
9D4×Dic479C211yesmaximal, characteristic, complemented
10C4×C22⋊D479C211yesmaximal, characteristic, complemented
11C22×D4×C479C211yesmaximal, characteristic, complemented
12C23×D479C2212yescomplemented
13C2×D1916C2211yescharacteristic, complemented
14C2×C22⋊D479—28no—
15C2×C22⋊D479C2211yescharacteristic
16C2×C22⋊D479C2212yescomplemented
17C2×C22⋊D479C2212yescomplemented
18C2×C22⋊D479C2212yescomplemented
19C2×C22⋊D479C2212yescomplemented
20C2×C22⋊D479C2212yescomplemented
21D4×D479—24no—
22C22×Dic479C2212yescomplemented
23C2×C4×D479C2211yescharacteristic, complemented
24C4⋊Dic479C2211yescharacteristic, complemented
25Dic479⋊C4C2211yescharacteristic, complemented
26C22⋊Dic479C2211yescharacteristic, complemented
27C22⋊Dic479C2212yescomplemented
28C22⋊Dic479C2212yescomplemented
29(C2×D479)⋊C4C2211yescharacteristic, complemented
30(C2×D479)⋊C4C2212yescomplemented
31C4×Dic479C2211yescharacteristic, complemented
32C24×C479C2212yescomplemented
33C2×D4×C479—24no—
34C2×D4×C479C2211yescharacteristic
35C2×D4×C479C2212yescomplemented
36C2×D4×C479C2211yescharacteristic, complemented
37C22×C4×C479C2211yescharacteristic, complemented
38C22×D479—24no—
39C22×D479—24no—
40C22×D479—42no—
41C22×D479C2312yes—
42C22×D479C2311yescharacteristic
43D1916—22no—
44C22⋊D479—24no—
45C22⋊D479—24no—
46C22⋊D479—24no—
47C22⋊D479—24no—
48C22⋊D479—42no—
49C22⋊D479D414yesdirect product factor
50C2×Dic479—24no—
51C2×Dic479C2311yescharacteristic
52C2×Dic479C2312yes—
53C2×Dic479C2311yescharacteristic
54C2×Dic479C2311yescharacteristic
55C4×D479—22no—
56C23×C479—24no—
57C23×C479—24no—
58C23×C479—42no—
59C23×C479C2312yes—
60C23×C479C2311yescharacteristic
61C23×C479C2312yes—
62D4×C479—24no—
63D4×C479—22no—
64D4×C479D414yescomplemented
65C2×C4×C479—22no—
66C2×C4×C479C2311yescharacteristic
67C2×C4×C479C2311yescharacteristic
68C22×C479—21no—
69C22×C479—22no—
70C22×C479—21no—
71C22×C479—22no—
72C22×C479—22no—
73C22×C479—22no—
74C22×C479—22no—
75C22×C479—48no—
76C22×C479C2×D412yescomplemented
77C22×C479C2×D414yescomplemented
78C22×C479C2411yescharacteristic
79C2×D479—21no—
80C2×D479—21no—
81C2×D479—22no—
82C2×D479—22no—
83C2×D479—22no—
84C2×D479—48no—
85C2×D479C2×D412yescomplemented
86C4×C479—21no—
87C4×C479C2×D412yescomplemented
88Dic479—21no—
89Dic479—22no—
90Dic479—21no—
91Dic479C2×D412yescomplemented
92C2×C479—24no—
93C2×C479—22no—
94C2×C479—42no—
95C2×C479C22×D411yescharacteristic
96C2×C479C22×D411yescharacteristic
97C2×C479H(5,𝔽2)11yescharacteristic
98D479—22no—
99D479—42no—
100C479D4211yescharacteristic, complemented, Sylow
101D42—4791nomaximal, Sylow
102C22×D4—4792no—
103C22×D4—4791no—
104C22×D4D47911yescharacteristic, complemented
105#127—4791no—
106#121—4791no—
107#121—4792no—
108#121—4791no—
109#120—4792no—
110#120—4792no—
111C4×D4—4791no—
112C4×D4—4791no—
113C24—4792no—
114C24C2×D47912yescomplemented
115C2×D4—24no—
116C2×D4—9588no—
117C2×D4—9584no—
118C2×D4—4792no—
119C2×D4—4792no—
120C2×D4—4792no—
121C2×D4—4792no—
122C2×D4—4792no—
123C2×D4—4791no—
124C2×D4—4791no—
125C2×D4C2×D47911yescharacteristic
126C2×D4C2×D47912yescomplemented
127C2×D4C2×D47911yescharacteristic, complemented
128C22×C4—4792no—
129C22×C4—4791no—
130C22×C4C2×D47911yescharacteristic, complemented
131C4⋊C4—4791no—
132C4⋊C4—4791no—
133C22⋊C4—4791no—
134C22⋊C4—4792no—
135C22⋊C4—4792no—
136C22⋊C4—4791no—
137C22⋊C4—4792no—
138C42—4791no—
139C23—24no—
140C23—24no—
141C23—42no—
142C23—19162no—
143C23—9584no—
144C23—9584no—
145C23—4792no—
146C23—4791no—
147C23C22×D47912yes—
148C23C22×D47911yescharacteristic
149C23C22×D47912yes—
150D4—24no—
151D4—22no—
152D4—19162no—
153D4—9584no—
154D4—9584no—
155D4—9584no—
156D4—9584no—
157D4—9582no—
158D4—4794no—
159D4C22⋊D47914yesdirect product factor
160C2×C4—22no—
161C2×C4—9584no—
162C2×C4—9582no—
163C2×C4—4791no—
164C2×C4—4792no—
165C2×C4—4791no—
166C2×C4—4791no—
167C2×C4C22×D47911yescharacteristic
168C2×C4C22×D47911yescharacteristic
169C22—22no—
170C22—21no—
171C22—21no—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—48no—
177C22—19168no—
178C22—9582no—
179C22—9582no—
180C22—9582no—
181C22—9581no—
182C22—9581no—
183C22—4792no—
184C22D4×D47912yescomplemented
185C22C2×C22⋊D47914yescomplemented
186C22C23×D47911yescharacteristic
187C4—21no—
188C4—9582no—
189C4—9581no—
190C4—9581no—
191C4—4792no—
192C4C2×C22⋊D47912yescomplemented
193C2—22no—
194C2—24no—
195C2—42no—
196C2—19162no—
197C2—9582no—
198C2C2×D4×D47911yescharacteristic
199C2C22×C22⋊D47911yescharacteristic
200C2#2950642711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D479
commutator, socle, cosocleC22×C479C24
FittingC22×D4×C479C2
hypercenterC22×D4D479
hypocenterC479D42
LCSG ▷ C22×C479 ▷ C479
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D479C2semidirect
2. C2×D4×D479C2semidirect
3. #29506378C2semidirect
4. #29506356C2semidirect
5. #29506354C2semidirect
6. #29506353C2semidirect
7. #29506351C2semidirect
8. #29506350C2semidirect
9. D4×Dic479C2semidirect
10. C4×C22⋊D479C2semidirect
11. C22×D4×C479C2semidirect
12. C23×D479C22semidirect
13. C2×D1916C22semidirect
16. C2×C22⋊D479C22semidirect
17. C2×C22⋊D479C22semidirect
18. C2×C22⋊D479C22semidirect
19. C2×C22⋊D479C22semidirect
20. C2×C22⋊D479C22semidirect
22. C22×Dic479C22semidirect
23. C2×C4×D479C22semidirect
24. C4⋊Dic479C22semidirect
25. Dic479⋊C4C22semidirect
26. C22⋊Dic479C22semidirect
27. C22⋊Dic479C22semidirect
28. C22⋊Dic479C22semidirect
29. (C2×D479)⋊C4C22semidirect
30. (C2×D479)⋊C4C22semidirect
31. C4×Dic479C22semidirect
32. C24×C479C22semidirect
35. C2×D4×C479C22semidirect
36. C2×D4×C479C22semidirect
37. C22×C4×C479C22semidirect
49. C22⋊D479D4direct (N × H)
64. D4×C479D4semidirect
76. C22×C479C2×D4semidirect
77. C22×C479C2×D4semidirect
85. C2×D479C2×D4semidirect
87. C4×C479C2×D4semidirect
91. Dic479C2×D4semidirect
100. C479D42semidirect
104. C22×D4D479semidirect
114. C24C2×D479semidirect
126. C2×D4C2×D479semidirect
127. C2×D4C2×D479semidirect
130. C22×C4C2×D479semidirect
159. D4C22⋊D479direct (N × H)
184. C22D4×D479semidirect
185. C22C2×C22⋊D479semidirect
192. C4C2×C22⋊D479semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D4792
C2×D4×D4792
#295063782
#295063562
#295063542
#295063532
#295063512
#295063502
D4×Dic4792
C4×C22⋊D4792
C22×D4×C4792
D42479