Finite Group Databasebeta

← D8×C22⋊D47 #20255059

Subgroups — D8×C22⋊D47 #20255059

Order 6016.

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×D47C211yesmaximal, characteristic, complemented
2D4×C22⋊D47C212yesmaximal, complemented
3#15689498C211yesmaximal, characteristic, complemented
4#15689359C211yesmaximal, characteristic, complemented
5#15689356C211yesmaximal, characteristic, complemented
6#15689316C212yesmaximal, complemented
7#15689257C212yesmaximal, complemented
8#15689255C212yesmaximal, complemented
9D8×Dic47C211yesmaximal, characteristic, complemented
10C8×C22⋊D47C211yesmaximal, characteristic, complemented
11C22×D8×C47C211yesmaximal, characteristic, complemented
12C22×C22⋊D47—22no—
13C2×D4×D47C2212yescomplemented
14C2×D376C2211yescharacteristic, complemented
15C2×#10625334C2212yescomplemented
16C2×#10625334C2212yescomplemented
17D8×D47—24no—
18C2×C8×D47C2211yescharacteristic, complemented
19#13094020C2212yescomplemented
20#13093998C2212yescomplemented
21#13093996—22no—
22#13093995C2212yescomplemented
23#13093993—22no—
24#13093992—22no—
25D4×Dic47C2212yescomplemented
26C4×C22⋊D47C2211yescharacteristic
27#13093958C2211yescharacteristic, complemented
28Dic47⋊C8C2211yescharacteristic, complemented
29#13093946C2212yescomplemented
30#13093945C2212yescomplemented
31#13093945C2212yescomplemented
32C22⋊(C47⋊C8)C2211yescharacteristic, complemented
33(C2×D47)⋊C8C2211yescharacteristic, complemented
34C8×Dic47C2211yescharacteristic, complemented
35C22×D4×C47C2212yescomplemented
36C2×D8×C47—24no—
37C2×D8×C47C2211yescharacteristic
38C2×D8×C47C2211yescharacteristic, complemented
39C2×D8×C47C2212yescomplemented
40C22×C8×C47C2211yescharacteristic, complemented
41C24×C47—22no—
42C23×D47—22no—
43C2×D4×C47—24no—
44C2×D4×C47—22no—
45C2×D4×C47—42no—
46C2×D4×C47C2312yes—
47C2×D4×C47C2312yes—
48C22×C4×C47C2311yescharacteristic
49C2×C22⋊D47—22no—
50C2×C22⋊D47—22no—
51C2×C22⋊D47—22no—
52C2×C22⋊D47—22no—
53C2×C22⋊D47—22no—
54C2×C22⋊D47—48no—
55C2×C22⋊D47D411yescharacteristic
56C22×Dic47—22no—
57D4×D47—24no—
58D4×D47—42no—
59C2×D188C2312yes—
60C2×C4×D47C2311yescharacteristic
61D8×C47—24no—
62D8×C47—22no—
63D8×C47D414yescomplemented
64C2×C8×C47—22no—
65C2×C8×C47C2311yescharacteristic
66C2×C8×C47C2311yescharacteristic
67C22⋊Dic47—22no—
68C22⋊Dic47—22no—
69C22⋊Dic47D411yescharacteristic
70#10625334—24no—
71#10625334—42no—
72(C2×D47)⋊C4—22no—
73(C2×D47)⋊C4D411yescharacteristic
74C4⋊Dic47C2312yes—
75Dic47⋊C4D411yescharacteristic
76C4×Dic47C2311yescharacteristic
77C2×C47⋊C8C2311yescharacteristic
78C2×C47⋊C8C2311yescharacteristic
79D376—22no—
80C8×D47—22no—
81C23×C47—22no—
82C23×C47—22no—
83C23×C47—44no—
84C23×C47—44no—
85C23×C47—82no—
86C23×C47C2×D411yescharacteristic
87C22×D47—22no—
88C22×D47—44no—
89C22×D47—44no—
90C22×D47—82no—
91C22×D47C2×D411yescharacteristic
92D4×C47—22no—
93D4×C47—22no—
94D4×C47—22no—
95D4×C47—44no—
96D4×C47C2×D414yescomplemented
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47C2×D411yescharacteristic
100C2×C4×C47C2411yescharacteristic
101C22⋊D47—44no—
102C22⋊D47—44no—
103C22⋊D47—44no—
104C22⋊D47—44no—
105C22⋊D47—82no—
106C22⋊D47D814yesdirect product factor
107C2×Dic47—22no—
108C2×Dic47—44no—
109C2×Dic47C2×D411yescharacteristic
110C2×Dic47C2×D411yescharacteristic
111C2×Dic47C2×D411yescharacteristic
112D188—22no—
113D188—22no—
114C4×D47—21no—
115C4×D47—21no—
116C8×C47—21no—
117C8×C47C2×D412yescomplemented
118C47⋊C8—21no—
119C47⋊C8—21no—
120C22×C47—21no—
121C22×C47—21no—
122C22×C47—24no—
123C22×C47—42no—
124C22×C47—42no—
125C22×C47—42no—
126C22×C47—42no—
127C22×C47—42no—
128C22×C47—88no—
129C22×C47C2×D812yescomplemented
130C22×C47C22×D411yescharacteristic
131C2×D47—21no—
132C2×D47—21no—
133C2×D47—42no—
134C2×D47—42no—
135C2×D47—42no—
136C2×D47—88no—
137C2×D47C2×D812yescomplemented
138C4×C47—21no—
139C4×C47C22×D411yescharacteristic
140C4×C47H(5,𝔽2)11yescharacteristic
141Dic47—21no—
142Dic47—21no—
143Dic47—42no—
144Dic47C2×D812yescomplemented
145D4×D8—471nomaximal, Sylow
146C2×C47—22no—
147C2×C47—44no—
148C2×C47—82no—
149C2×C47D4211yescharacteristic
150C2×C47C22×D811yescharacteristic
151C2×C47#57611yescharacteristic
152D47—22no—
153D47—82no—
154C22×D8—471no—
155C22×D8D4711yescharacteristic, complemented
156D42—472no—
157#493—471no—
158#466—471no—
159#466—471no—
160#459—472no—
161#447—472no—
162#447—472no—
163C4×D8—471no—
164C8×D4—471no—
165C47D4×D811yescharacteristic, complemented, Sylow
166C22×D4—472no—
167C22×D4—942no—
168C22×D4C2×D4712yescomplemented
169C2×D8—24no—
170C2×D8—472no—
171C2×D8—472no—
172C2×D8—471no—
173C2×D8—944no—
174C2×D8C2×D4711yescharacteristic
175C2×D8C2×D4712yescomplemented
176C2×D8C2×D4711yescharacteristic, complemented
177C22×C8—471no—
178C22×C8C2×D4711yescharacteristic, complemented
179#127—472no—
180#121—472no—
181#121—472no—
182#121—942no—
183#120—942no—
184#120—942no—
185C4×D4—471no—
186C4×D4—472no—
187#107—471no—
188C4⋊C8—471no—
189#102—472no—
190#102—472no—
191#102—472no—
192C22⋊C8—471no—
193C22⋊C8—471no—
194C4×C8—471no—
195C24—22no—
196C24—942no—
197C2×D4—24no—
198C2×D4—22no—
199C2×D4—42no—
200C2×D4—471no—
201C2×D4—472no—
202C2×D4—942no—
203C2×D4—942no—
204C2×D4—942no—
205C2×D4—944no—
206C2×D4—942no—
207C2×D4—942no—
208C2×D4—1882no—
209C2×D4—1888no—
210C2×D4C22×D4712yes—
211C2×D4C22×D4712yes—
212C22×C4—471no—
213C22×C4—942no—
214C22×C4C22×D4711yescharacteristic
215D8—24no—
216D8—22no—
217D8—944no—
218D8—942no—
219D8—1882no—
220D8C22⋊D4714yesdirect product factor
221C2×C8—22no—
222C2×C8—471no—
223C2×C8—471no—
224C2×C8—942no—
225C2×C8C22×D4711yescharacteristic
226C2×C8C22×D4711yescharacteristic
227C4⋊C4—471no—
228C4⋊C4—472no—
229C22⋊C4—471no—
230C22⋊C4—471no—
231C22⋊C4—942no—
232C22⋊C4—942no—
233C22⋊C4—942no—
234C42—471no—
235C23—22no—
236C23—22no—
237C23—44no—
238C23—44no—
239C23—82no—
240C23—471no—
241C23—942no—
242C23—3762no—
243C23—1884no—
244C23—1884no—
245C23D4×D4711yescharacteristic
246D4—22no—
247D4—22no—
248D4—22no—
249D4—44no—
250D4—474no—
251D4—942no—
252D4—942no—
253D4—3762no—
254D4—1884no—
255D4—1884no—
256D4—1884no—
257D4—1884no—
258D4C2×C22⋊D4714yescomplemented
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—471no—
262C2×C4—471no—
263C2×C4—471no—
264C2×C4—941no—
265C2×C4—941no—
266C2×C4—942no—
267C2×C4—1884no—
268C2×C4D4×D4711yescharacteristic
269C2×C4C23×D4711yescharacteristic
270C8—21no—
271C8—941no—
272C8—941no—
273C8C2×C22⋊D4712yescomplemented
274C22—21no—
275C22—21no—
276C22—24no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—88no—
283C22—472no—
284C22—941no—
285C22—941no—
286C22—3768no—
287C22—1882no—
288C22—1882no—
289C22—1882no—
290C22D8×D4712yescomplemented
291C22C2×D4×D4711yescharacteristic
292C4—21no—
293C4—472no—
294C4—941no—
295C4—941no—
296C4—1882no—
297C4C22×C22⋊D4711yescharacteristic
298C4#1309406911yescharacteristic
299C2—22no—
300C2—44no—
301C2—82no—
302C2—942no—
303C2—3762no—
304C2D4×C22⋊D4711yescharacteristic
305C2C2×D8×D4711yescharacteristic
306C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC22×D8×C47C2
socleC22×C47C22×D4
hypercenterC22×D8D47
hypocenterC47D4×D8
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×D47C2semidirect
2. D4×C22⋊D47C2semidirect
3. #15689498C2semidirect
4. #15689359C2semidirect
5. #15689356C2semidirect
6. #15689316C2semidirect
7. #15689257C2semidirect
8. #15689255C2semidirect
9. D8×Dic47C2semidirect
10. C8×C22⋊D47C2semidirect
11. C22×D8×C47C2semidirect
13. C2×D4×D47C22semidirect
14. C2×D376C22semidirect
15. C2×#10625334C22semidirect
16. C2×#10625334C22semidirect
18. C2×C8×D47C22semidirect
19. #13094020C22semidirect
20. #13093998C22semidirect
22. #13093995C22semidirect
25. D4×Dic47C22semidirect
27. #13093958C22semidirect
28. Dic47⋊C8C22semidirect
29. #13093946C22semidirect
30. #13093945C22semidirect
31. #13093945C22semidirect
32. C22⋊(C47⋊C8)C22semidirect
33. (C2×D47)⋊C8C22semidirect
34. C8×Dic47C22semidirect
35. C22×D4×C47C22semidirect
38. C2×D8×C47C22semidirect
39. C2×D8×C47C22semidirect
40. C22×C8×C47C22semidirect
63. D8×C47D4semidirect
96. D4×C47C2×D4semidirect
106. C22⋊D47D8direct (N × H)
117. C8×C47C2×D4semidirect
129. C22×C47C2×D8semidirect
137. C2×D47C2×D8semidirect
144. Dic47C2×D8semidirect
155. C22×D8D47semidirect
165. C47D4×D8semidirect
168. C22×D4C2×D47semidirect
175. C2×D8C2×D47semidirect
176. C2×D8C2×D47semidirect
178. C22×C8C2×D47semidirect
220. D8C22⋊D47direct (N × H)
258. D4C2×C22⋊D47semidirect
273. C8C2×C22⋊D47semidirect
290. C22D8×D47semidirect