Finite Group Databasebeta

← D4×C22⋊D271 #31774530

Subgroups — D4×C22⋊D271 #31774530

Order 17344.

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⋊D271C212yesmaximal, complemented
2C2×D4×D271C211yesmaximal, characteristic, complemented
3#22576156C211yesmaximal, characteristic, complemented
4#22576134C211yesmaximal, characteristic, complemented
5#22576132C212yesmaximal, complemented
6#22576131C211yesmaximal, characteristic, complemented
7#22576129C212yesmaximal, complemented
8#22576128C212yesmaximal, complemented
9D4×Dic271C211yesmaximal, characteristic, complemented
10C4×C22⋊D271C211yesmaximal, characteristic, complemented
11C22×D4×C271C211yesmaximal, characteristic, complemented
12C23×D271C2212yescomplemented
13C2×D1084C2211yescharacteristic, complemented
14C2×C22⋊D271—28no—
15C2×C22⋊D271C2211yescharacteristic
16C2×C22⋊D271C2212yescomplemented
17C2×C22⋊D271C2212yescomplemented
18C2×C22⋊D271C2212yescomplemented
19C2×C22⋊D271C2212yescomplemented
20C2×C22⋊D271C2212yescomplemented
21D4×D271—24no—
22C22×Dic271C2212yescomplemented
23C2×C4×D271C2211yescharacteristic, complemented
24C4⋊Dic271C2211yescharacteristic, complemented
25Dic271⋊C4C2211yescharacteristic, complemented
26C22⋊Dic271C2212yescomplemented
27C22⋊Dic271C2211yescharacteristic, complemented
28C22⋊Dic271C2212yescomplemented
29(C2×D271)⋊C4C2211yescharacteristic, complemented
30(C2×D271)⋊C4C2212yescomplemented
31C4×Dic271C2211yescharacteristic, complemented
32C24×C271C2212yescomplemented
33C2×D4×C271—24no—
34C2×D4×C271C2211yescharacteristic
35C2×D4×C271C2212yescomplemented
36C2×D4×C271C2211yescharacteristic, complemented
37C22×C4×C271C2211yescharacteristic, complemented
38C22×D271—24no—
39C22×D271—24no—
40C22×D271—42no—
41C22×D271C2312yes—
42C22×D271C2311yescharacteristic
43D1084—22no—
44C22⋊D271—24no—
45C22⋊D271—24no—
46C22⋊D271—24no—
47C22⋊D271—24no—
48C22⋊D271—42no—
49C22⋊D271D414yesdirect product factor
50C2×Dic271—24no—
51C2×Dic271C2311yescharacteristic
52C2×Dic271C2312yes—
53C2×Dic271C2311yescharacteristic
54C2×Dic271C2311yescharacteristic
55C4×D271—22no—
56C23×C271—24no—
57C23×C271—24no—
58C23×C271—42no—
59C23×C271C2312yes—
60C23×C271C2311yescharacteristic
61C23×C271C2312yes—
62D4×C271—24no—
63D4×C271—22no—
64D4×C271D414yescomplemented
65C2×C4×C271—22no—
66C2×C4×C271C2311yescharacteristic
67C2×C4×C271C2311yescharacteristic
68C22×C271—21no—
69C22×C271—22no—
70C22×C271—21no—
71C22×C271—22no—
72C22×C271—22no—
73C22×C271—22no—
74C22×C271—22no—
75C22×C271—48no—
76C22×C271C2×D412yescomplemented
77C22×C271C2×D414yescomplemented
78C22×C271C2411yescharacteristic
79C2×D271—21no—
80C2×D271—21no—
81C2×D271—22no—
82C2×D271—22no—
83C2×D271—22no—
84C2×D271—48no—
85C2×D271C2×D412yescomplemented
86C4×C271—21no—
87C4×C271C2×D412yescomplemented
88Dic271—21no—
89Dic271—22no—
90Dic271—21no—
91Dic271C2×D412yescomplemented
92C2×C271—24no—
93C2×C271—22no—
94C2×C271—42no—
95C2×C271C22×D411yescharacteristic
96C2×C271C22×D411yescharacteristic
97C2×C271H(5,𝔽2)11yescharacteristic
98D271—22no—
99D271—42no—
100C271D4211yescharacteristic, complemented, Sylow
101D42—2711nomaximal, Sylow
102C22×D4—2712no—
103C22×D4—2711no—
104C22×D4D27111yescharacteristic, complemented
105#127—2711no—
106#121—2711no—
107#121—2712no—
108#121—2711no—
109#120—2712no—
110#120—2712no—
111C4×D4—2711no—
112C4×D4—2711no—
113C24—2712no—
114C24C2×D27112yescomplemented
115C2×D4—24no—
116C2×D4—2711no—
117C2×D4—2712no—
118C2×D4—2712no—
119C2×D4—2712no—
120C2×D4—2712no—
121C2×D4—2712no—
122C2×D4—2711no—
123C2×D4—5428no—
124C2×D4—5424no—
125C2×D4C2×D27111yescharacteristic
126C2×D4C2×D27112yescomplemented
127C2×D4C2×D27111yescharacteristic, complemented
128C22×C4—2712no—
129C22×C4—2711no—
130C22×C4C2×D27111yescharacteristic, complemented
131C4⋊C4—2711no—
132C4⋊C4—2711no—
133C22⋊C4—2711no—
134C22⋊C4—2712no—
135C22⋊C4—2712no—
136C22⋊C4—2711no—
137C22⋊C4—2712no—
138C42—2711no—
139C23—24no—
140C23—24no—
141C23—42no—
142C23—2711no—
143C23—2712no—
144C23—5424no—
145C23—5424no—
146C23—10842no—
147C23C22×D27112yes—
148C23C22×D27111yescharacteristic
149C23C22×D27112yes—
150D4—24no—
151D4—22no—
152D4—2714no—
153D4—5424no—
154D4—5424no—
155D4—5424no—
156D4—5424no—
157D4—5422no—
158D4—10842no—
159D4C22⋊D27114yesdirect product factor
160C2×C4—22no—
161C2×C4—2711no—
162C2×C4—2711no—
163C2×C4—2712no—
164C2×C4—2711no—
165C2×C4—5424no—
166C2×C4—5422no—
167C2×C4C22×D27111yescharacteristic
168C2×C4C22×D27111yescharacteristic
169C22—22no—
170C22—21no—
171C22—21no—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—48no—
177C22—2712no—
178C22—5421no—
179C22—5421no—
180C22—5422no—
181C22—5422no—
182C22—5422no—
183C22—10848no—
184C22D4×D27112yescomplemented
185C22C2×C22⋊D27114yescomplemented
186C22C23×D27111yescharacteristic
187C4—21no—
188C4—2712no—
189C4—5422no—
190C4—5421no—
191C4—5421no—
192C4C2×C22⋊D27112yescomplemented
193C2—22no—
194C2—24no—
195C2—42no—
196C2—5422no—
197C2—10842no—
198C2C2×D4×D27111yescharacteristic
199C2C22×C22⋊D27111yescharacteristic
200C2#2257620511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D271
commutator, socle, cosocleC22×C271C24
FittingC22×D4×C271C2
hypercenterC22×D4D271
hypocenterC271D42
LCSG ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D271C2semidirect
2. C2×D4×D271C2semidirect
3. #22576156C2semidirect
4. #22576134C2semidirect
5. #22576132C2semidirect
6. #22576131C2semidirect
7. #22576129C2semidirect
8. #22576128C2semidirect
9. D4×Dic271C2semidirect
10. C4×C22⋊D271C2semidirect
11. C22×D4×C271C2semidirect
12. C23×D271C22semidirect
13. C2×D1084C22semidirect
16. C2×C22⋊D271C22semidirect
17. C2×C22⋊D271C22semidirect
18. C2×C22⋊D271C22semidirect
19. C2×C22⋊D271C22semidirect
20. C2×C22⋊D271C22semidirect
22. C22×Dic271C22semidirect
23. C2×C4×D271C22semidirect
24. C4⋊Dic271C22semidirect
25. Dic271⋊C4C22semidirect
26. C22⋊Dic271C22semidirect
27. C22⋊Dic271C22semidirect
28. C22⋊Dic271C22semidirect
29. (C2×D271)⋊C4C22semidirect
30. (C2×D271)⋊C4C22semidirect
31. C4×Dic271C22semidirect
32. C24×C271C22semidirect
35. C2×D4×C271C22semidirect
36. C2×D4×C271C22semidirect
37. C22×C4×C271C22semidirect
49. C22⋊D271D4direct (N × H)
64. D4×C271D4semidirect
76. C22×C271C2×D4semidirect
77. C22×C271C2×D4semidirect
85. C2×D271C2×D4semidirect
87. C4×C271C2×D4semidirect
91. Dic271C2×D4semidirect
100. C271D42semidirect
104. C22×D4D271semidirect
114. C24C2×D271semidirect
126. C2×D4C2×D271semidirect
127. C2×D4C2×D271semidirect
130. C22×C4C2×D271semidirect
159. D4C22⋊D271direct (N × H)
184. C22D4×D271semidirect
185. C22C2×C22⋊D271semidirect
192. C4C2×C22⋊D271semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D2712
C2×D4×D2712
#225761562
#225761342
#225761322
#225761312
#225761292
#225761282
D4×Dic2712
C4×C22⋊D2712
C22×D4×C2712
D42271