Finite Group Databasebeta

← D4×C22⋊D241 #29508350

Subgroups — D4×C22⋊D241 #29508350

Order 15424.

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⋊D241C212yesmaximal, complemented
2C2×D4×D241C211yesmaximal, characteristic, complemented
3#21440638C211yesmaximal, characteristic, complemented
4#21440616C211yesmaximal, characteristic, complemented
5#21440614C212yesmaximal, complemented
6#21440613C211yesmaximal, characteristic, complemented
7#21440611C212yesmaximal, complemented
8#21440610C212yesmaximal, complemented
9D4×Dic241C211yesmaximal, characteristic, complemented
10C4×C22⋊D241C211yesmaximal, characteristic, complemented
11C22×D4×C241C211yesmaximal, characteristic, complemented
12C23×D241C2212yescomplemented
13C2×D964C2211yescharacteristic, complemented
14C2×C22⋊D241—28no—
15C2×C22⋊D241C2211yescharacteristic
16C2×C22⋊D241C2212yescomplemented
17C2×C22⋊D241C2212yescomplemented
18C2×C22⋊D241C2212yescomplemented
19C2×C22⋊D241C2212yescomplemented
20C2×C22⋊D241C2212yescomplemented
21D4×D241—24no—
22C22×Dic241C2212yescomplemented
23C2×C4×D241C2211yescharacteristic, complemented
24C4⋊Dic241C2211yescharacteristic, complemented
25#16838749C2211yescharacteristic, complemented
26C22⋊Dic241C2211yescharacteristic, complemented
27C22⋊Dic241C2212yescomplemented
28C22⋊Dic241C2212yescomplemented
29#16838747C2211yescharacteristic, complemented
30#16838747C2212yescomplemented
31C4×Dic241C2211yescharacteristic, complemented
32C24×C241C2212yescomplemented
33C2×D4×C241—24no—
34C2×D4×C241C2211yescharacteristic
35C2×D4×C241C2212yescomplemented
36C2×D4×C241C2211yescharacteristic, complemented
37C22×C4×C241C2211yescharacteristic, complemented
38C22×D241—24no—
39C22×D241—24no—
40C22×D241—42no—
41C22×D241C2312yes—
42C22×D241C2311yescharacteristic
43D964—22no—
44C22⋊D241—24no—
45C22⋊D241—24no—
46C22⋊D241—24no—
47C22⋊D241—24no—
48C22⋊D241—42no—
49C22⋊D241D414yesdirect product factor
50C2×Dic241—24no—
51C2×Dic241C2311yescharacteristic
52C2×Dic241C2312yes—
53C2×Dic241C2311yescharacteristic
54C2×Dic241C2311yescharacteristic
55C4×D241—22no—
56C23×C241—24no—
57C23×C241—24no—
58C23×C241—42no—
59C23×C241C2312yes—
60C23×C241C2311yescharacteristic
61C23×C241C2312yes—
62D4×C241—24no—
63D4×C241—22no—
64D4×C241D414yescomplemented
65C2×C4×C241—22no—
66C2×C4×C241C2311yescharacteristic
67C2×C4×C241C2311yescharacteristic
68C22×C241—21no—
69C22×C241—22no—
70C22×C241—21no—
71C22×C241—22no—
72C22×C241—22no—
73C22×C241—22no—
74C22×C241—22no—
75C22×C241—48no—
76C22×C241C2×D412yescomplemented
77C22×C241C2×D414yescomplemented
78C22×C241C2411yescharacteristic
79C2×D241—21no—
80C2×D241—21no—
81C2×D241—22no—
82C2×D241—22no—
83C2×D241—22no—
84C2×D241—48no—
85C2×D241C2×D412yescomplemented
86C4×C241—21no—
87C4×C241C2×D412yescomplemented
88Dic241—21no—
89Dic241—22no—
90Dic241—21no—
91Dic241C2×D412yescomplemented
92C2×C241—24no—
93C2×C241—22no—
94C2×C241—42no—
95C2×C241C22×D411yescharacteristic
96C2×C241C22×D411yescharacteristic
97C2×C241H(5,𝔽2)11yescharacteristic
98D241—22no—
99D241—42no—
100C241D4211yescharacteristic, complemented, Sylow
101D42—2411nomaximal, Sylow
102C22×D4—2412no—
103C22×D4—2411no—
104C22×D4D24111yescharacteristic, complemented
105#127—2411no—
106#121—2411no—
107#121—2412no—
108#121—2411no—
109#120—2412no—
110#120—2412no—
111C4×D4—2411no—
112C4×D4—2411no—
113C24—2412no—
114C24C2×D24112yescomplemented
115C2×D4—24no—
116C2×D4—4828no—
117C2×D4—4824no—
118C2×D4—2412no—
119C2×D4—2412no—
120C2×D4—2412no—
121C2×D4—2412no—
122C2×D4—2412no—
123C2×D4—2411no—
124C2×D4—2411no—
125C2×D4C2×D24111yescharacteristic
126C2×D4C2×D24112yescomplemented
127C2×D4C2×D24111yescharacteristic, complemented
128C22×C4—2412no—
129C22×C4—2411no—
130C22×C4C2×D24111yescharacteristic, complemented
131C4⋊C4—2411no—
132C4⋊C4—2411no—
133C22⋊C4—2411no—
134C22⋊C4—2412no—
135C22⋊C4—2412no—
136C22⋊C4—2411no—
137C22⋊C4—2412no—
138C42—2411no—
139C23—24no—
140C23—24no—
141C23—42no—
142C23—9642no—
143C23—4824no—
144C23—4824no—
145C23—2412no—
146C23—2411no—
147C23C22×D24112yes—
148C23C22×D24111yescharacteristic
149C23C22×D24112yes—
150D4—24no—
151D4—22no—
152D4—9642no—
153D4—4824no—
154D4—4824no—
155D4—4824no—
156D4—4824no—
157D4—4822no—
158D4—2414no—
159D4C22⋊D24114yesdirect product factor
160C2×C4—22no—
161C2×C4—4824no—
162C2×C4—4822no—
163C2×C4—2411no—
164C2×C4—2412no—
165C2×C4—2411no—
166C2×C4—2411no—
167C2×C4C22×D24111yescharacteristic
168C2×C4C22×D24111yescharacteristic
169C22—22no—
170C22—21no—
171C22—21no—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—48no—
177C22—9648no—
178C22—4822no—
179C22—4822no—
180C22—4822no—
181C22—4821no—
182C22—4821no—
183C22—2412no—
184C22D4×D24112yescomplemented
185C22C2×C22⋊D24114yescomplemented
186C22C23×D24111yescharacteristic
187C4—21no—
188C4—4822no—
189C4—4821no—
190C4—4821no—
191C4—2412no—
192C4C2×C22⋊D24112yescomplemented
193C2—22no—
194C2—24no—
195C2—42no—
196C2—9642no—
197C2—4822no—
198C2C2×D4×D24111yescharacteristic
199C2C22×C22⋊D24111yescharacteristic
200C2#2144068711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D241
commutator, socle, cosocleC22×C241C24
FittingC22×D4×C241C2
hypercenterC22×D4D241
hypocenterC241D42
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D241C2semidirect
2. C2×D4×D241C2semidirect
3. #21440638C2semidirect
4. #21440616C2semidirect
5. #21440614C2semidirect
6. #21440613C2semidirect
7. #21440611C2semidirect
8. #21440610C2semidirect
9. D4×Dic241C2semidirect
10. C4×C22⋊D241C2semidirect
11. C22×D4×C241C2semidirect
12. C23×D241C22semidirect
13. C2×D964C22semidirect
16. C2×C22⋊D241C22semidirect
17. C2×C22⋊D241C22semidirect
18. C2×C22⋊D241C22semidirect
19. C2×C22⋊D241C22semidirect
20. C2×C22⋊D241C22semidirect
22. C22×Dic241C22semidirect
23. C2×C4×D241C22semidirect
24. C4⋊Dic241C22semidirect
25. #16838749C22semidirect
26. C22⋊Dic241C22semidirect
27. C22⋊Dic241C22semidirect
28. C22⋊Dic241C22semidirect
29. #16838747C22semidirect
30. #16838747C22semidirect
31. C4×Dic241C22semidirect
32. C24×C241C22semidirect
35. C2×D4×C241C22semidirect
36. C2×D4×C241C22semidirect
37. C22×C4×C241C22semidirect
49. C22⋊D241D4direct (N × H)
64. D4×C241D4semidirect
76. C22×C241C2×D4semidirect
77. C22×C241C2×D4semidirect
85. C2×D241C2×D4semidirect
87. C4×C241C2×D4semidirect
91. Dic241C2×D4semidirect
100. C241D42semidirect
104. C22×D4D241semidirect
114. C24C2×D241semidirect
126. C2×D4C2×D241semidirect
127. C2×D4C2×D241semidirect
130. C22×C4C2×D241semidirect
159. D4C22⋊D241direct (N × H)
184. C22D4×D241semidirect
185. C22C2×C22⋊D241semidirect
192. C4C2×C22⋊D241semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D2412
C2×D4×D2412
#214406382
#214406162
#214406142
#214406132
#214406112
#214406102
D4×Dic2412
C4×C22⋊D2412
C22×D4×C2412
D42241