Finite Group Databasebeta

← D4×C22⋊D173 #26012124

Subgroups — D4×C22⋊D173 #26012124

Order 11072.

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⋊D173C212yesmaximal, complemented
2C2×D4×D173C211yesmaximal, characteristic, complemented
3#19149675C211yesmaximal, characteristic, complemented
4#19149653C211yesmaximal, characteristic, complemented
5#19149651C212yesmaximal, complemented
6#19149650C211yesmaximal, characteristic, complemented
7#19149648C212yesmaximal, complemented
8#19149647C212yesmaximal, complemented
9D4×Dic173C211yesmaximal, characteristic, complemented
10C4×C22⋊D173C211yesmaximal, characteristic, complemented
11C22×D4×C173C211yesmaximal, characteristic, complemented
12C23×D173C2212yescomplemented
13C2×D692C2211yescharacteristic, complemented
14C2×C22⋊D173—28no—
15C2×C22⋊D173C2211yescharacteristic
16C2×C22⋊D173C2212yescomplemented
17C2×C22⋊D173C2212yescomplemented
18C2×C22⋊D173C2212yescomplemented
19C2×C22⋊D173C2212yescomplemented
20C2×C22⋊D173C2212yescomplemented
21D4×D173—24no—
22C22×Dic173C2212yescomplemented
23C2×C4×D173C2211yescharacteristic, complemented
24C4⋊Dic173C2211yescharacteristic, complemented
25#14583805C2211yescharacteristic, complemented
26C22⋊Dic173C2211yescharacteristic, complemented
27C22⋊Dic173C2212yescomplemented
28C22⋊Dic173C2212yescomplemented
29#14583803C2211yescharacteristic, complemented
30#14583803C2212yescomplemented
31C4×Dic173C2211yescharacteristic, complemented
32C24×C173C2212yescomplemented
33C2×D4×C173—24no—
34C2×D4×C173C2211yescharacteristic
35C2×D4×C173C2212yescomplemented
36C2×D4×C173C2211yescharacteristic, complemented
37C22×C4×C173C2211yescharacteristic, complemented
38C22×D173—24no—
39C22×D173—24no—
40C22×D173—42no—
41C22×D173C2312yes—
42C22×D173C2311yescharacteristic
43D692—22no—
44C22⋊D173—24no—
45C22⋊D173—24no—
46C22⋊D173—24no—
47C22⋊D173—24no—
48C22⋊D173—42no—
49C22⋊D173D414yesdirect product factor
50C2×Dic173—24no—
51C2×Dic173C2311yescharacteristic
52C2×Dic173C2312yes—
53C2×Dic173C2311yescharacteristic
54C2×Dic173C2311yescharacteristic
55C4×D173—22no—
56C23×C173—24no—
57C23×C173—24no—
58C23×C173—42no—
59C23×C173C2312yes—
60C23×C173C2312yes—
61C23×C173C2311yescharacteristic
62D4×C173—24no—
63D4×C173—22no—
64D4×C173D414yescomplemented
65C2×C4×C173—22no—
66C2×C4×C173C2311yescharacteristic
67C2×C4×C173C2311yescharacteristic
68C22×C173—21no—
69C22×C173—22no—
70C22×C173—21no—
71C22×C173—22no—
72C22×C173—22no—
73C22×C173—22no—
74C22×C173—22no—
75C22×C173—48no—
76C22×C173C2×D412yescomplemented
77C22×C173C2×D414yescomplemented
78C22×C173C2411yescharacteristic
79C2×D173—21no—
80C2×D173—21no—
81C2×D173—22no—
82C2×D173—22no—
83C2×D173—22no—
84C2×D173—48no—
85C2×D173C2×D412yescomplemented
86C4×C173—21no—
87C4×C173C2×D412yescomplemented
88Dic173—21no—
89Dic173—22no—
90Dic173—21no—
91Dic173C2×D412yescomplemented
92C2×C173—24no—
93C2×C173—22no—
94C2×C173—42no—
95C2×C173C22×D411yescharacteristic
96C2×C173C22×D411yescharacteristic
97C2×C173H(5,𝔽2)11yescharacteristic
98D173—22no—
99D173—42no—
100C173D4211yescharacteristic, complemented, Sylow
101D42—1731nomaximal, Sylow
102C22×D4—1732no—
103C22×D4—1731no—
104C22×D4D17311yescharacteristic, complemented
105#127—1731no—
106#121—1731no—
107#121—1732no—
108#121—1731no—
109#120—1732no—
110#120—1732no—
111C4×D4—1731no—
112C4×D4—1731no—
113C24—1732no—
114C24C2×D17312yescomplemented
115C2×D4—24no—
116C2×D4—3468no—
117C2×D4—3464no—
118C2×D4—1732no—
119C2×D4—1732no—
120C2×D4—1732no—
121C2×D4—1732no—
122C2×D4—1731no—
123C2×D4—1732no—
124C2×D4—1731no—
125C2×D4C2×D17311yescharacteristic
126C2×D4C2×D17312yescomplemented
127C2×D4C2×D17311yescharacteristic, complemented
128C22×C4—1732no—
129C22×C4—1731no—
130C22×C4C2×D17311yescharacteristic, complemented
131C4⋊C4—1731no—
132C4⋊C4—1731no—
133C22⋊C4—1731no—
134C22⋊C4—1732no—
135C22⋊C4—1732no—
136C22⋊C4—1731no—
137C22⋊C4—1732no—
138C42—1731no—
139C23—24no—
140C23—24no—
141C23—42no—
142C23—3464no—
143C23—3464no—
144C23—1732no—
145C23—1731no—
146C23—6922no—
147C23C22×D17312yes—
148C23C22×D17311yescharacteristic
149C23C22×D17312yes—
150D4—24no—
151D4—22no—
152D4—3464no—
153D4—3464no—
154D4—3464no—
155D4—3464no—
156D4—3462no—
157D4—1734no—
158D4—6922no—
159D4C22⋊D17314yesdirect product factor
160C2×C4—22no—
161C2×C4—3464no—
162C2×C4—3462no—
163C2×C4—1731no—
164C2×C4—1732no—
165C2×C4—1731no—
166C2×C4—1731no—
167C2×C4C22×D17311yescharacteristic
168C2×C4C22×D17311yescharacteristic
169C22—22no—
170C22—21no—
171C22—21no—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—48no—
177C22—3461no—
178C22—3461no—
179C22—3462no—
180C22—3462no—
181C22—3462no—
182C22—1732no—
183C22—6928no—
184C22D4×D17312yescomplemented
185C22C2×C22⋊D17314yescomplemented
186C22C23×D17311yescharacteristic
187C4—21no—
188C4—3462no—
189C4—3461no—
190C4—3461no—
191C4—1732no—
192C4C2×C22⋊D17312yescomplemented
193C2—22no—
194C2—24no—
195C2—42no—
196C2—3462no—
197C2—6922no—
198C2C2×D4×D17311yescharacteristic
199C2C22×C22⋊D17311yescharacteristic
200C2#1914972411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D173
commutator, socle, cosocleC22×C173C24
FittingC22×D4×C173C2
hypercenterC22×D4D173
hypocenterC173D42
LCSG ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D173C2semidirect
2. C2×D4×D173C2semidirect
3. #19149675C2semidirect
4. #19149653C2semidirect
5. #19149651C2semidirect
6. #19149650C2semidirect
7. #19149648C2semidirect
8. #19149647C2semidirect
9. D4×Dic173C2semidirect
10. C4×C22⋊D173C2semidirect
11. C22×D4×C173C2semidirect
12. C23×D173C22semidirect
13. C2×D692C22semidirect
16. C2×C22⋊D173C22semidirect
17. C2×C22⋊D173C22semidirect
18. C2×C22⋊D173C22semidirect
19. C2×C22⋊D173C22semidirect
20. C2×C22⋊D173C22semidirect
22. C22×Dic173C22semidirect
23. C2×C4×D173C22semidirect
24. C4⋊Dic173C22semidirect
25. #14583805C22semidirect
26. C22⋊Dic173C22semidirect
27. C22⋊Dic173C22semidirect
28. C22⋊Dic173C22semidirect
29. #14583803C22semidirect
30. #14583803C22semidirect
31. C4×Dic173C22semidirect
32. C24×C173C22semidirect
35. C2×D4×C173C22semidirect
36. C2×D4×C173C22semidirect
37. C22×C4×C173C22semidirect
49. C22⋊D173D4direct (N × H)
64. D4×C173D4semidirect
76. C22×C173C2×D4semidirect
77. C22×C173C2×D4semidirect
85. C2×D173C2×D4semidirect
87. C4×C173C2×D4semidirect
91. Dic173C2×D4semidirect
100. C173D42semidirect
104. C22×D4D173semidirect
114. C24C2×D173semidirect
126. C2×D4C2×D173semidirect
127. C2×D4C2×D173semidirect
130. C22×C4C2×D173semidirect
159. D4C22⋊D173direct (N × H)
184. C22D4×D173semidirect
185. C22C2×C22⋊D173semidirect
192. C4C2×C22⋊D173semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D1732
C2×D4×D1732
#191496752
#191496532
#191496512
#191496502
#191496482
#191496472
D4×Dic1732
C4×C22⋊D1732
C22×D4×C1732
D42173