Finite Group Databasebeta

← D4×D904 #28402251

Subgroups — D4×D904 #28402251

Order 14464.

620 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 149 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×D904C212yesmaximal, complemented
2D4×D452C212yesmaximal, complemented
3#20298975C211yesmaximal, characteristic, complemented
4#20298834C212yesmaximal, complemented
5#20298794C212yesmaximal, complemented
6#20298734C214yesmaximal, complemented
7C4×D904C211yesmaximal, characteristic, complemented
8C8×D4×C113C211yesmaximal, characteristic, complemented
9C22×D452C2214yescomplemented
10C2×D4×D113—22no—
11C2×D904—28no—
12C2×D904C2211yescharacteristic
13C2×D904C2214yescomplemented
14C2×D904C2212yescomplemented
15C2×D904C2212yescomplemented
16#16813619C2212yescomplemented
17#16813597—22no—
18#16813596C2214yescomplemented
19#16813592—24no—
20C4×D452C2212yescomplemented
21#16813556C2211yescharacteristic, complemented
22#16813544C2214yescomplemented
23#16813544C2212yescomplemented
24C22×C8×C113C2212yescomplemented
25C4×D4×C113C2211yescharacteristic
26C4⋊C8×C113C2211yescharacteristic, complemented
27C22⋊C8×C113C2212yescomplemented
28C4×C8×C113C2211yescharacteristic, complemented
29C23×D113—24no—
30C2×D452—28no—
31C2×D452—24no—
32C2×D452—22no—
33C2×D452—22no—
34C2×D452—44no—
35C2×D452C2314yes—
36C2×D452C2312yes—
37C2×C22⋊D113—24no—
38D4×D113—48no—
39C2×C4×D113—22no—
40D904—28no—
41D904—24no—
42D904—42no—
43D904D414yesdirect product factor
44C4⋊Dic113C2312yes—
45#14268624—22no—
46#14268624—24no—
47C2×D4×C113D411yescharacteristic
48C22×C4×C113C2312yes—
49C2×C8×C113—24no—
50C2×C8×C113C2311yescharacteristic
51C2×C8×C113C2312yes—
52C2×C8×C113C2311yescharacteristic
53C4⋊C4×C113D411yescharacteristic
54C22⋊C4×C113D412yes—
55C42×C113C2311yescharacteristic
56C23×C113C2×D412yes—
57C22×D113—22no—
58C22×D113—24no—
59C22×D113—48no—
60C22×D113—48no—
61C22×D113—84no—
62D4×C113D814yescomplemented
63C2×C4×C113—22no—
64C2×C4×C113—22no—
65C2×C4×C113C2×D411yescharacteristic
66C2×C4×C113C2×D412yes—
67C2×C4×C113C2×D411yescharacteristic
68C2×C4×C113C2411yescharacteristic
69C22⋊D113—48no—
70C2×Dic113—22no—
71D452—24no—
72D452—22no—
73D452—24no—
74D452—48no—
75D452—44no—
76D452—82no—
77D452C2×D414yescomplemented
78C4×D113—44no—
79C8×C113—22no—
80C8×C113—21no—
81C8×C113C2×D412yescomplemented
82C22×C113—22no—
83C22×C113—22no—
84C22×C113C2×D814yescomplemented
85C22×C113C22×D411yescharacteristic
86C2×D113—24no—
87C2×D113—42no—
88C2×D113—42no—
89C2×D113—44no—
90C2×D113—44no—
91C2×D113—44no—
92C2×D113—816no—
93C4×C113—22no—
94C4×C113—21no—
95C4×C113C2×D812yescomplemented
96C4×C113C22×D411yescharacteristic
97C4×C113H(5,𝔽2)11yescharacteristic
98Dic113—42no—
99C2×C113—24no—
100C2×C113D4211yescharacteristic
101C2×C113C22×D811yescharacteristic
102C2×C113#57611yescharacteristic
103D113—44no—
104D113—84no—
105D4×D8—1131nomaximal, Sylow
106C113D4×D811yescharacteristic, complemented, Sylow
107C22×D8—1132no—
108D42—1132no—
109#493—1131no—
110#466—1132no—
111#459—1132no—
112#447—1134no—
113C4×D8—1131no—
114C8×D4D11311yescharacteristic, complemented
115C22×D4—1134no—
116C22×D4—2262no—
117C2×D8—1131no—
118C2×D8—1132no—
119C2×D8—1134no—
120C2×D8—1132no—
121C2×D8—2268no—
122C22×C8C2×D11312yescomplemented
123#127—1132no—
124#121—1134no—
125#121—2262no—
126#120—2264no—
127C4×D4—1132no—
128C4×D4C2×D11311yescharacteristic
129#107—1131no—
130C4⋊C8C2×D11311yescharacteristic, complemented
131#102—1132no—
132#102—1134no—
133C22⋊C8C2×D11312yescomplemented
134C4×C8C2×D11311yescharacteristic, complemented
135C24—2264no—
136C2×D4—1132no—
137C2×D4—1134no—
138C2×D4—4524no—
139C2×D4—4528no—
140C2×D4—2268no—
141C2×D4—2264no—
142C2×D4—2262no—
143C2×D4—2264no—
144C2×D4—2262no—
145C2×D4D45211yescharacteristic
146C22×C4—2262no—
147C22×C4C22×D11312yes—
148D8—1134no—
149D8—4522no—
150D8—2268no—
151D8—2264no—
152C2×C8—24no—
153C2×C8C22×D11311yescharacteristic
154C2×C8C22×D11312yes—
155C2×C8C22×D11311yescharacteristic
156C4⋊C4—1132no—
157C4⋊C4D45211yescharacteristic
158C22⋊C4—2262no—
159C22⋊C4—2264no—
160C22⋊C4D45212yes—
161C42C22×D11311yescharacteristic
162C23—9044no—
163C23—4528no—
164C23—4528no—
165C23—2264no—
166C23—2262no—
167C23C2×D45212yes—
168D4—1134no—
169D4—9042no—
170D4—4528no—
171D4—4528no—
172D4—4524no—
173D4—2264no—
174D4—2264no—
175D4—2262no—
176D4D90414yesdirect product factor
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—4524no—
180C2×C4—2262no—
181C2×C4C2×D45211yescharacteristic
182C2×C4C2×D45212yes—
183C2×C4C2×D45211yescharacteristic
184C2×C4C23×D11311yescharacteristic
185C8—22no—
186C8—21no—
187C8D4×D11312yescomplemented
188C22—22no—
189C22—22no—
190C22—90416no—
191C22—4524no—
192C22—4524no—
193C22—4524no—
194C22—4522no—
195C22—4522no—
196C22—2264no—
197C22C2×D90414yescomplemented
198C22C22×D45211yescharacteristic
199C4—21no—
200C4—22no—
201C4—4522no—
202C4C2×D90412yescomplemented
203C4C2×D4×D11311yescharacteristic
204C4#1681366811yescharacteristic
205C2—24no—
206C2—9044no—
207C2—4524no—
208C2D4×D45211yescharacteristic
209C2C22×D90411yescharacteristic
210C2#2029940311yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC8×D4×C113C2
socleC22×C113C22×D4
hypercenterC8×D4D113
hypocenterC113D4×D8
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×D904C2semidirect
2. D4×D452C2semidirect
3. #20298975C2semidirect
4. #20298834C2semidirect
5. #20298794C2semidirect
6. #20298734C2semidirect
7. C4×D904C2semidirect
8. C8×D4×C113C2semidirect
9. C22×D452C22semidirect
13. C2×D904C22semidirect
14. C2×D904C22semidirect
15. C2×D904C22semidirect
16. #16813619C22semidirect
18. #16813596C22semidirect
20. C4×D452C22semidirect
21. #16813556C22semidirect
22. #16813544C22semidirect
23. #16813544C22semidirect
24. C22×C8×C113C22semidirect
26. C4⋊C8×C113C22semidirect
27. C22⋊C8×C113C22semidirect
28. C4×C8×C113C22semidirect
43. D904D4direct (N × H)
62. D4×C113D8semidirect
77. D452C2×D4semidirect
81. C8×C113C2×D4semidirect
84. C22×C113C2×D8semidirect
95. C4×C113C2×D8semidirect
106. C113D4×D8semidirect
114. C8×D4D113semidirect
122. C22×C8C2×D113semidirect
130. C4⋊C8C2×D113semidirect
133. C22⋊C8C2×D113semidirect
134. C4×C8C2×D113semidirect
176. D4D904direct (N × H)
187. C8D4×D113semidirect
197. C22C2×D904semidirect
202. C4C2×D904semidirect

Maximal subgroups

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

subgroupindex
C22×D9042
D4×D4522
#202989752
#202988342
#202987942
#202987342
C4×D9042
C8×D4×C1132
D4×D8113