Finite Group Databasebeta

← D8×C22⋊D43 #19146266

Subgroups — D8×C22⋊D43 #19146266

Order 5504.

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×D43C211yesmaximal, characteristic, complemented
2D4×C22⋊D43C212yesmaximal, complemented
3#14583274C211yesmaximal, characteristic, complemented
4#14583135C211yesmaximal, characteristic, complemented
5#14583132C211yesmaximal, characteristic, complemented
6#14583092C212yesmaximal, complemented
7#14583033C212yesmaximal, complemented
8#14583031C212yesmaximal, complemented
9D8×Dic43C211yesmaximal, characteristic, complemented
10C8×C22⋊D43C211yesmaximal, characteristic, complemented
11C22×D8×C43C211yesmaximal, characteristic, complemented
12C22×C22⋊D43—22no—
13C2×D4×D43C2212yescomplemented
14C2×D344C2211yescharacteristic, complemented
15C2×#10621882C2212yescomplemented
16C2×#10621882C2212yescomplemented
17D8×D43—24no—
18C2×C8×D43C2211yescharacteristic, complemented
19#13063321C2212yescomplemented
20#13063299C2212yescomplemented
21#13063297—22no—
22#13063296C2212yescomplemented
23#13063294—22no—
24#13063293—22no—
25D4×Dic43C2212yescomplemented
26C4×C22⋊D43C2211yescharacteristic
27#13063259C2211yescharacteristic, complemented
28Dic43⋊C8C2211yescharacteristic, complemented
29#13063247C2212yescomplemented
30#13063246C2212yescomplemented
31#13063246C2212yescomplemented
32C22⋊(C43⋊C8)C2211yescharacteristic, complemented
33(C2×D43)⋊C8C2211yescharacteristic, complemented
34C8×Dic43C2211yescharacteristic, complemented
35C22×D4×C43C2212yescomplemented
36C2×D8×C43—24no—
37C2×D8×C43C2211yescharacteristic
38C2×D8×C43C2212yescomplemented
39C2×D8×C43C2211yescharacteristic, complemented
40C22×C8×C43C2211yescharacteristic, complemented
41C24×C43—22no—
42C23×D43—22no—
43C2×D4×C43—22no—
44C2×D4×C43—24no—
45C2×D4×C43—42no—
46C2×D4×C43C2312yes—
47C2×D4×C43C2312yes—
48C22×C4×C43C2311yescharacteristic
49C2×C22⋊D43—22no—
50C2×C22⋊D43—22no—
51C2×C22⋊D43—22no—
52C2×C22⋊D43—22no—
53C2×C22⋊D43—22no—
54C2×C22⋊D43—48no—
55C2×C22⋊D43D411yescharacteristic
56C22×Dic43—22no—
57D4×D43—24no—
58D4×D43—42no—
59C2×D172C2312yes—
60C2×C4×D43C2311yescharacteristic
61D8×C43—24no—
62D8×C43—22no—
63D8×C43D414yescomplemented
64C2×C8×C43—22no—
65C2×C8×C43C2311yescharacteristic
66C2×C8×C43C2311yescharacteristic
67C22⋊Dic43—22no—
68C22⋊Dic43—22no—
69C22⋊Dic43D411yescharacteristic
70#10621882—24no—
71#10621882—42no—
72(C2×D43)⋊C4—22no—
73(C2×D43)⋊C4D411yescharacteristic
74C4⋊Dic43C2312yes—
75Dic43⋊C4D411yescharacteristic
76C4×Dic43C2311yescharacteristic
77C2×C43⋊C8C2311yescharacteristic
78C2×C43⋊C8C2311yescharacteristic
79D344—22no—
80C8×D43—22no—
81C23×C43—22no—
82C23×C43—22no—
83C23×C43—44no—
84C23×C43—44no—
85C23×C43—82no—
86C23×C43C2×D411yescharacteristic
87C22×D43—22no—
88C22×D43—44no—
89C22×D43—44no—
90C22×D43—82no—
91C22×D43C2×D411yescharacteristic
92D4×C43—22no—
93D4×C43—22no—
94D4×C43—22no—
95D4×C43—44no—
96D4×C43C2×D414yescomplemented
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43C2×D411yescharacteristic
100C2×C4×C43C2411yescharacteristic
101C22⋊D43—44no—
102C22⋊D43—44no—
103C22⋊D43—44no—
104C22⋊D43—44no—
105C22⋊D43—82no—
106C22⋊D43D814yesdirect product factor
107C2×Dic43—22no—
108C2×Dic43—44no—
109C2×Dic43C2×D411yescharacteristic
110C2×Dic43C2×D411yescharacteristic
111C2×Dic43C2×D411yescharacteristic
112D172—22no—
113D172—22no—
114C4×D43—21no—
115C4×D43—21no—
116C8×C43—21no—
117C8×C43C2×D412yescomplemented
118C43⋊C8—21no—
119C43⋊C8—21no—
120C22×C43—21no—
121C22×C43—21no—
122C22×C43—24no—
123C22×C43—42no—
124C22×C43—42no—
125C22×C43—42no—
126C22×C43—42no—
127C22×C43—42no—
128C22×C43—88no—
129C22×C43C2×D812yescomplemented
130C22×C43C22×D411yescharacteristic
131C2×D43—21no—
132C2×D43—21no—
133C2×D43—42no—
134C2×D43—42no—
135C2×D43—42no—
136C2×D43—88no—
137C2×D43C2×D812yescomplemented
138C4×C43—21no—
139C4×C43C22×D411yescharacteristic
140C4×C43H(5,𝔽2)11yescharacteristic
141Dic43—21no—
142Dic43—21no—
143Dic43—42no—
144Dic43C2×D812yescomplemented
145D4×D8—431nomaximal, Sylow
146C2×C43—22no—
147C2×C43—44no—
148C2×C43—82no—
149C2×C43D4211yescharacteristic
150C2×C43C22×D811yescharacteristic
151C2×C43#57611yescharacteristic
152D43—22no—
153D43—82no—
154C22×D8—431no—
155C22×D8D4311yescharacteristic, complemented
156D42—432no—
157#493—431no—
158#466—431no—
159#466—431no—
160#459—432no—
161#447—432no—
162#447—432no—
163C4×D8—431no—
164C8×D4—431no—
165C43D4×D811yescharacteristic, complemented, Sylow
166C22×D4—432no—
167C22×D4—862no—
168C22×D4C2×D4312yescomplemented
169C2×D8—24no—
170C2×D8—432no—
171C2×D8—432no—
172C2×D8—431no—
173C2×D8—864no—
174C2×D8C2×D4311yescharacteristic
175C2×D8C2×D4312yescomplemented
176C2×D8C2×D4311yescharacteristic, complemented
177C22×C8—431no—
178C22×C8C2×D4311yescharacteristic, complemented
179#127—432no—
180#121—432no—
181#121—432no—
182#121—862no—
183#120—862no—
184#120—862no—
185C4×D4—431no—
186C4×D4—432no—
187#107—431no—
188C4⋊C8—431no—
189#102—432no—
190#102—432no—
191#102—432no—
192C22⋊C8—431no—
193C22⋊C8—431no—
194C4×C8—431no—
195C24—22no—
196C24—862no—
197C2×D4—24no—
198C2×D4—22no—
199C2×D4—42no—
200C2×D4—431no—
201C2×D4—432no—
202C2×D4—862no—
203C2×D4—862no—
204C2×D4—862no—
205C2×D4—864no—
206C2×D4—862no—
207C2×D4—862no—
208C2×D4—1722no—
209C2×D4—1728no—
210C2×D4C22×D4312yes—
211C2×D4C22×D4312yes—
212C22×C4—431no—
213C22×C4—862no—
214C22×C4C22×D4311yescharacteristic
215D8—24no—
216D8—22no—
217D8—864no—
218D8—862no—
219D8—1722no—
220D8C22⋊D4314yesdirect product factor
221C2×C8—22no—
222C2×C8—431no—
223C2×C8—431no—
224C2×C8—862no—
225C2×C8C22×D4311yescharacteristic
226C2×C8C22×D4311yescharacteristic
227C4⋊C4—431no—
228C4⋊C4—432no—
229C22⋊C4—431no—
230C22⋊C4—431no—
231C22⋊C4—862no—
232C22⋊C4—862no—
233C22⋊C4—862no—
234C42—431no—
235C23—22no—
236C23—22no—
237C23—44no—
238C23—44no—
239C23—82no—
240C23—431no—
241C23—862no—
242C23—3442no—
243C23—1724no—
244C23—1724no—
245C23D4×D4311yescharacteristic
246D4—22no—
247D4—22no—
248D4—22no—
249D4—44no—
250D4—434no—
251D4—862no—
252D4—862no—
253D4—3442no—
254D4—1724no—
255D4—1724no—
256D4—1724no—
257D4—1724no—
258D4C2×C22⋊D4314yescomplemented
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—431no—
262C2×C4—431no—
263C2×C4—431no—
264C2×C4—861no—
265C2×C4—861no—
266C2×C4—862no—
267C2×C4—1724no—
268C2×C4D4×D4311yescharacteristic
269C2×C4C23×D4311yescharacteristic
270C8—21no—
271C8—861no—
272C8—861no—
273C8C2×C22⋊D4312yescomplemented
274C22—21no—
275C22—21no—
276C22—24no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—88no—
283C22—432no—
284C22—861no—
285C22—861no—
286C22—3448no—
287C22—1722no—
288C22—1722no—
289C22—1722no—
290C22D8×D4312yescomplemented
291C22C2×D4×D4311yescharacteristic
292C4—21no—
293C4—432no—
294C4—861no—
295C4—861no—
296C4—1722no—
297C4C22×C22⋊D4311yescharacteristic
298C4#1306337011yescharacteristic
299C2—22no—
300C2—44no—
301C2—82no—
302C2—862no—
303C2—3442no—
304C2D4×C22⋊D4311yescharacteristic
305C2C2×D8×D4311yescharacteristic
306C2#1458370011yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC22×D8×C43C2
socleC22×C43C22×D4
hypercenterC22×D8D43
hypocenterC43D4×D8
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×D43C2semidirect
2. D4×C22⋊D43C2semidirect
3. #14583274C2semidirect
4. #14583135C2semidirect
5. #14583132C2semidirect
6. #14583092C2semidirect
7. #14583033C2semidirect
8. #14583031C2semidirect
9. D8×Dic43C2semidirect
10. C8×C22⋊D43C2semidirect
11. C22×D8×C43C2semidirect
13. C2×D4×D43C22semidirect
14. C2×D344C22semidirect
15. C2×#10621882C22semidirect
16. C2×#10621882C22semidirect
18. C2×C8×D43C22semidirect
19. #13063321C22semidirect
20. #13063299C22semidirect
22. #13063296C22semidirect
25. D4×Dic43C22semidirect
27. #13063259C22semidirect
28. Dic43⋊C8C22semidirect
29. #13063247C22semidirect
30. #13063246C22semidirect
31. #13063246C22semidirect
32. C22⋊(C43⋊C8)C22semidirect
33. (C2×D43)⋊C8C22semidirect
34. C8×Dic43C22semidirect
35. C22×D4×C43C22semidirect
38. C2×D8×C43C22semidirect
39. C2×D8×C43C22semidirect
40. C22×C8×C43C22semidirect
63. D8×C43D4semidirect
96. D4×C43C2×D4semidirect
106. C22⋊D43D8direct (N × H)
117. C8×C43C2×D4semidirect
129. C22×C43C2×D8semidirect
137. C2×D43C2×D8semidirect
144. Dic43C2×D8semidirect
155. C22×D8D43semidirect
165. C43D4×D8semidirect
168. C22×D4C2×D43semidirect
175. C2×D8C2×D43semidirect
176. C2×D8C2×D43semidirect
178. C22×C8C2×D43semidirect
220. D8C22⋊D43direct (N × H)
258. D4C2×C22⋊D43semidirect
273. C8C2×C22⋊D43semidirect
290. C22D8×D43semidirect