Finite Group Databasebeta

← D4×C22⋊D509 #45655871

Subgroups — D4×C22⋊D509 #45655871

Order 32576.

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⋊D509C212yesmaximal, complemented
2C2×D4×D509C211yesmaximal, characteristic, complemented
3#30654211C211yesmaximal, characteristic, complemented
4#30654189C211yesmaximal, characteristic, complemented
5#30654187C212yesmaximal, complemented
6#30654186C211yesmaximal, characteristic, complemented
7#30654184C212yesmaximal, complemented
8#30654183C212yesmaximal, complemented
9D4×Dic509C211yesmaximal, characteristic, complemented
10C4×C22⋊D509C211yesmaximal, characteristic, complemented
11C22×D4×C509C211yesmaximal, characteristic, complemented
12C23×D509C2212yescomplemented
13C2×D2036C2211yescharacteristic, complemented
14C2×C22⋊D509—28no—
15C2×C22⋊D509C2211yescharacteristic
16C2×C22⋊D509C2212yescomplemented
17C2×C22⋊D509C2212yescomplemented
18C2×C22⋊D509C2212yescomplemented
19C2×C22⋊D509C2212yescomplemented
20C2×C22⋊D509C2212yescomplemented
21D4×D509—24no—
22C22×Dic509C2212yescomplemented
23C2×C4×D509C2211yescharacteristic, complemented
24C4⋊Dic509C2211yescharacteristic, complemented
25#22550840C2211yescharacteristic, complemented
26C22⋊Dic509C2211yescharacteristic, complemented
27C22⋊Dic509C2212yescomplemented
28C22⋊Dic509C2212yescomplemented
29#22550838C2211yescharacteristic, complemented
30#22550838C2212yescomplemented
31C4×Dic509C2211yescharacteristic, complemented
32C24×C509C2212yescomplemented
33C2×D4×C509—24no—
34C2×D4×C509C2211yescharacteristic
35C2×D4×C509C2211yescharacteristic, complemented
36C2×D4×C509C2212yescomplemented
37C22×C4×C509C2211yescharacteristic, complemented
38C22×D509—24no—
39C22×D509—24no—
40C22×D509—42no—
41C22×D509C2312yes—
42C22×D509C2311yescharacteristic
43D2036—22no—
44C22⋊D509—24no—
45C22⋊D509—24no—
46C22⋊D509—24no—
47C22⋊D509—24no—
48C22⋊D509—42no—
49C22⋊D509D414yesdirect product factor
50C2×Dic509—24no—
51C2×Dic509C2311yescharacteristic
52C2×Dic509C2312yes—
53C2×Dic509C2311yescharacteristic
54C2×Dic509C2311yescharacteristic
55C4×D509—22no—
56C23×C509—24no—
57C23×C509—24no—
58C23×C509—42no—
59C23×C509C2312yes—
60C23×C509C2311yescharacteristic
61C23×C509C2312yes—
62D4×C509—24no—
63D4×C509—22no—
64D4×C509D414yescomplemented
65C2×C4×C509—22no—
66C2×C4×C509C2311yescharacteristic
67C2×C4×C509C2311yescharacteristic
68C22×C509—21no—
69C22×C509—22no—
70C22×C509—21no—
71C22×C509—22no—
72C22×C509—22no—
73C22×C509—22no—
74C22×C509—22no—
75C22×C509—48no—
76C22×C509C2×D412yescomplemented
77C22×C509C2×D414yescomplemented
78C22×C509C2411yescharacteristic
79C2×D509—21no—
80C2×D509—21no—
81C2×D509—22no—
82C2×D509—22no—
83C2×D509—22no—
84C2×D509—48no—
85C2×D509C2×D412yescomplemented
86C4×C509—21no—
87C4×C509C2×D412yescomplemented
88Dic509—21no—
89Dic509—22no—
90Dic509—21no—
91Dic509C2×D412yescomplemented
92C2×C509—24no—
93C2×C509—22no—
94C2×C509—42no—
95C2×C509C22×D411yescharacteristic
96C2×C509C22×D411yescharacteristic
97C2×C509H(5,𝔽2)11yescharacteristic
98D509—22no—
99D509—42no—
100C509D4211yescharacteristic, complemented, Sylow
101D42—5091nomaximal, Sylow
102C22×D4—5092no—
103C22×D4—5091no—
104C22×D4D50911yescharacteristic, complemented
105#127—5091no—
106#121—5091no—
107#121—5092no—
108#121—5091no—
109#120—5092no—
110#120—5092no—
111C4×D4—5091no—
112C4×D4—5091no—
113C24—5092no—
114C24C2×D50912yescomplemented
115C2×D4—24no—
116C2×D4—10188no—
117C2×D4—10184no—
118C2×D4—5092no—
119C2×D4—5092no—
120C2×D4—5092no—
121C2×D4—5092no—
122C2×D4—5092no—
123C2×D4—5091no—
124C2×D4—5091no—
125C2×D4C2×D50911yescharacteristic
126C2×D4C2×D50912yescomplemented
127C2×D4C2×D50911yescharacteristic, complemented
128C22×C4—5092no—
129C22×C4—5091no—
130C22×C4C2×D50911yescharacteristic, complemented
131C4⋊C4—5091no—
132C4⋊C4—5091no—
133C22⋊C4—5091no—
134C22⋊C4—5092no—
135C22⋊C4—5092no—
136C22⋊C4—5091no—
137C22⋊C4—5092no—
138C42—5091no—
139C23—24no—
140C23—24no—
141C23—42no—
142C23—20362no—
143C23—10184no—
144C23—10184no—
145C23—5092no—
146C23—5091no—
147C23C22×D50912yes—
148C23C22×D50911yescharacteristic
149C23C22×D50912yes—
150D4—24no—
151D4—22no—
152D4—20362no—
153D4—10184no—
154D4—10184no—
155D4—10184no—
156D4—10184no—
157D4—10182no—
158D4—5094no—
159D4C22⋊D50914yesdirect product factor
160C2×C4—22no—
161C2×C4—10184no—
162C2×C4—10182no—
163C2×C4—5091no—
164C2×C4—5092no—
165C2×C4—5091no—
166C2×C4—5091no—
167C2×C4C22×D50911yescharacteristic
168C2×C4C22×D50911yescharacteristic
169C22—22no—
170C22—21no—
171C22—21no—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—48no—
177C22—20368no—
178C22—10182no—
179C22—10182no—
180C22—10182no—
181C22—10181no—
182C22—10181no—
183C22—5092no—
184C22D4×D50912yescomplemented
185C22C2×C22⋊D50914yescomplemented
186C22C23×D50911yescharacteristic
187C4—21no—
188C4—10182no—
189C4—10181no—
190C4—10181no—
191C4—5092no—
192C4C2×C22⋊D50912yescomplemented
193C2—22no—
194C2—24no—
195C2—42no—
196C2—20362no—
197C2—10182no—
198C2C2×D4×D50911yescharacteristic
199C2C22×C22⋊D50911yescharacteristic
200C2#3065426011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D509
commutator, socle, cosocleC22×C509C24
FittingC22×D4×C509C2
hypercenterC22×D4D509
hypocenterC509D42
LCSG ▷ C22×C509 ▷ C509
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D509C2semidirect
2. C2×D4×D509C2semidirect
3. #30654211C2semidirect
4. #30654189C2semidirect
5. #30654187C2semidirect
6. #30654186C2semidirect
7. #30654184C2semidirect
8. #30654183C2semidirect
9. D4×Dic509C2semidirect
10. C4×C22⋊D509C2semidirect
11. C22×D4×C509C2semidirect
12. C23×D509C22semidirect
13. C2×D2036C22semidirect
16. C2×C22⋊D509C22semidirect
17. C2×C22⋊D509C22semidirect
18. C2×C22⋊D509C22semidirect
19. C2×C22⋊D509C22semidirect
20. C2×C22⋊D509C22semidirect
22. C22×Dic509C22semidirect
23. C2×C4×D509C22semidirect
24. C4⋊Dic509C22semidirect
25. #22550840C22semidirect
26. C22⋊Dic509C22semidirect
27. C22⋊Dic509C22semidirect
28. C22⋊Dic509C22semidirect
29. #22550838C22semidirect
30. #22550838C22semidirect
31. C4×Dic509C22semidirect
32. C24×C509C22semidirect
35. C2×D4×C509C22semidirect
36. C2×D4×C509C22semidirect
37. C22×C4×C509C22semidirect
49. C22⋊D509D4direct (N × H)
64. D4×C509D4semidirect
76. C22×C509C2×D4semidirect
77. C22×C509C2×D4semidirect
85. C2×D509C2×D4semidirect
87. C4×C509C2×D4semidirect
91. Dic509C2×D4semidirect
100. C509D42semidirect
104. C22×D4D509semidirect
114. C24C2×D509semidirect
126. C2×D4C2×D509semidirect
127. C2×D4C2×D509semidirect
130. C22×C4C2×D509semidirect
159. D4C22⋊D509direct (N × H)
184. C22D4×D509semidirect
185. C22C2×C22⋊D509semidirect
192. C4C2×C22⋊D509semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D5092
C2×D4×D5092
#306542112
#306541892
#306541872
#306541862
#306541842
#306541832
D4×Dic5092
C4×C22⋊D5092
C22×D4×C5092
D42509