Finite Group Databasebeta

← D8×D452 #28402250

Subgroups — D8×D452 #28402250

Order 14464.

620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×D8×D113C212yesmaximal, complemented
2D4×D452C212yesmaximal, complemented
3#20298975C211yesmaximal, characteristic, complemented
4#20298835C212yesmaximal, complemented
5#20298793C212yesmaximal, complemented
6#20298733C214yesmaximal, complemented
7C8×D452C211yesmaximal, characteristic, complemented
8C4×D8×C113C211yesmaximal, characteristic, complemented
9C22×D452—22no—
10C2×D4×D113C2214yescomplemented
11C2×D904C2212yescomplemented
12C2×D904C2212yescomplemented
13C2×#14268632C2214yescomplemented
14D8×D113—28no—
15C2×C8×D113C2212yescomplemented
16#16813619C2212yescomplemented
17#16813597C2214yescomplemented
18#16813596—22no—
19#16813592—24no—
20C4×D452C2211yescharacteristic
21C4⋊#11744751C2211yescharacteristic, complemented
22#16813542C2214yescomplemented
23#16813534C2212yescomplemented
24C2×D8×C113C2211yescharacteristic
25C4×D4×C113C2212yescomplemented
26#107×C113C2211yescharacteristic, complemented
27#102×C113C2212yescomplemented
28C4×C8×C113C2211yescharacteristic, complemented
29C23×D113—24no—
30C2×D452—24no—
31C2×D452—22no—
32C2×D452—22no—
33C2×D452—48no—
34C2×D452D411yescharacteristic
35C2×D452C2314yes—
36C2×C22⋊D113—24no—
37D4×D113—28no—
38D4×D113—44no—
39C2×C4×D113C2312yes—
40D904—24no—
41D904—42no—
42#14268632—28no—
43C2×#11744751C2312yes—
44C8×D113—24no—
45C4⋊Dic113D411yescharacteristic
46#14268624—24no—
47#14268624D412yes—
48C2×D4×C113C2312yes—
49C22×C4×C113—22no—
50D8×C113D414yescomplemented
51C2×C8×C113C2311yescharacteristic
52C2×C8×C113C2311yescharacteristic
53C4⋊C4×C113C2312yes—
54C22⋊C4×C113—22no—
55C42×C113C2311yescharacteristic
56C23×C113—22no—
57C22×D113—24no—
58C22×D113—48no—
59C22×D113—48no—
60C22×D113—84no—
61C22×D113C2×D412yes—
62D4×C113—22no—
63D4×C113C2×D414yescomplemented
64C2×C4×C113—22no—
65C2×C4×C113—44no—
66C2×C4×C113C2×D411yescharacteristic
67C2×C4×C113C2×D411yescharacteristic
68C2×C4×C113C2411yescharacteristic
69C22⋊D113—48no—
70C2×Dic113C2×D412yes—
71D452—24no—
72D452—24no—
73D452—48no—
74D452—44no—
75D452—82no—
76D452D814yesdirect product factor
77C4×D113—22no—
78C4×D113—22no—
79C8×C113—21no—
80C8×C113C2×D412yescomplemented
81#11744751—22no—
82C22×C113—24no—
83C22×C113—42no—
84C22×C113—42no—
85C22×C113C22×D411yescharacteristic
86C2×D113—22no—
87C2×D113—22no—
88C2×D113—44no—
89C2×D113—44no—
90C2×D113—44no—
91C2×D113—816no—
92C2×D113C2×D814yescomplemented
93C4×C113—21no—
94C4×C113—42no—
95C4×C113C2×D812yescomplemented
96C4×C113C22×D411yescharacteristic
97C4×C113H(5,𝔽2)11yescharacteristic
98Dic113—22no—
99C2×C113—44no—
100C2×C113D4211yescharacteristic
101C2×C113C22×D811yescharacteristic
102C2×C113#57611yescharacteristic
103D113—24no—
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×D8D11311yescharacteristic, complemented
114C8×D4—1131no—
115C22×D4—1134no—
116C22×D4—2262no—
117C2×D8—1134no—
118C2×D8—1132no—
119C2×D8—1132no—
120C2×D8—2268no—
121C2×D8C2×D11311yescharacteristic
122C22×C8—1132no—
123#127—1132no—
124#121—1134no—
125#121—2262no—
126#120—2264no—
127C4×D4—1131no—
128C4×D4C2×D11312yescomplemented
129#107C2×D11311yescharacteristic, complemented
130C4⋊C8—1131no—
131#102—1134no—
132#102C2×D11312yescomplemented
133C22⋊C8—1132no—
134C4×C8C2×D11311yescharacteristic, complemented
135C24—2264no—
136C2×D4—1131no—
137C2×D4—1134no—
138C2×D4—4528no—
139C2×D4—4524no—
140C2×D4—2264no—
141C2×D4—2264no—
142C2×D4—2268no—
143C2×D4—2262no—
144C2×D4—2262no—
145C2×D4C22×D11312yes—
146C22×C4—22no—
147C22×C4—1132no—
148D8—4522no—
149D8—2268no—
150D8—2264no—
151D8D45214yesdirect product factor
152C2×C8—1132no—
153C2×C8—2264no—
154C2×C8C22×D11311yescharacteristic
155C2×C8C22×D11311yescharacteristic
156C4⋊C4—1131no—
157C4⋊C4C22×D11312yes—
158C22⋊C4—22no—
159C22⋊C4—1132no—
160C22⋊C4—2264no—
161C42C22×D11311yescharacteristic
162C23—22no—
163C23—1132no—
164C23—9044no—
165C23—4528no—
166C23—4528no—
167C23—2264no—
168D4—22no—
169D4—1134no—
170D4—9042no—
171D4—4528no—
172D4—4528no—
173D4—4524no—
174D4—2264no—
175D4—2264no—
176D4C2×D45214yescomplemented
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—1132no—
180C2×C4—2262no—
181C2×C4—2262no—
182C2×C4D4×D11311yescharacteristic
183C2×C4D4×D11311yescharacteristic
184C2×C4C23×D11311yescharacteristic
185C8—21no—
186C8—2262no—
187C8C2×D45212yescomplemented
188C22—24no—
189C22—42no—
190C22—42no—
191C22—1134no—
192C22—90416no—
193C22—4524no—
194C22—4524no—
195C22—4524no—
196C22—2262no—
197C22—2262no—
198C22C2×D4×D11311yescharacteristic
199C4—21no—
200C4—42no—
201C4—2262no—
202C4D8×D11312yescomplemented
203C4C22×D45211yescharacteristic
204C4#1681366811yescharacteristic
205C2—44no—
206C2—9044no—
207C2—2264no—
208C2D4×D45211yescharacteristic
209C2C2×D8×D11311yescharacteristic
210C2#2029940011yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC4×D8×C113C2
socleC22×C113C22×D4
hypercenterC4×D8D113
hypocenterC113D4×D8
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×D113C2semidirect
2. D4×D452C2semidirect
3. #20298975C2semidirect
4. #20298835C2semidirect
5. #20298793C2semidirect
6. #20298733C2semidirect
7. C8×D452C2semidirect
8. C4×D8×C113C2semidirect
10. C2×D4×D113C22semidirect
11. C2×D904C22semidirect
12. C2×D904C22semidirect
13. C2×#14268632C22semidirect
15. C2×C8×D113C22semidirect
16. #16813619C22semidirect
17. #16813597C22semidirect
21. C4⋊#11744751C22semidirect
22. #16813542C22semidirect
23. #16813534C22semidirect
25. C4×D4×C113C22semidirect
26. #107×C113C22semidirect
27. #102×C113C22semidirect
28. C4×C8×C113C22semidirect
50. D8×C113D4semidirect
63. D4×C113C2×D4semidirect
76. D452D8direct (N × H)
80. C8×C113C2×D4semidirect
92. C2×D113C2×D8semidirect
95. C4×C113C2×D8semidirect
106. C113D4×D8semidirect
113. C4×D8D113semidirect
128. C4×D4C2×D113semidirect
129. #107C2×D113semidirect
132. #102C2×D113semidirect
134. C4×C8C2×D113semidirect
151. D8D452direct (N × H)
176. D4C2×D452semidirect
187. C8C2×D452semidirect
202. C4D8×D113semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1132
D4×D4522
#202989752
#202988352
#202987932
#202987332
C8×D4522
C4×D8×C1132
D4×D8113