Finite Group Databasebeta

← D8×C22⋊D269 #46822556

Subgroups — D8×C22⋊D269 #46822556

Order 34432.

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×D269C211yesmaximal, characteristic, complemented
2D4×C22⋊D269C212yesmaximal, complemented
3#31770980C211yesmaximal, characteristic, complemented
4#31770841C211yesmaximal, characteristic, complemented
5#31770838C211yesmaximal, characteristic, complemented
6#31770798C212yesmaximal, complemented
7#31770739C212yesmaximal, complemented
8#31770737C212yesmaximal, complemented
9D8×Dic269C211yesmaximal, characteristic, complemented
10C8×C22⋊D269C211yesmaximal, characteristic, complemented
11C22×D8×C269C211yesmaximal, characteristic, complemented
12C22×C22⋊D269—22no—
13C2×D4×D269C2212yescomplemented
14C2×D2152C2211yescharacteristic, complemented
15C2×#16864387C2212yescomplemented
16C2×#16864387C2212yescomplemented
17D8×D269—24no—
18C2×C8×D269C2211yescharacteristic, complemented
19#22575449C2212yescomplemented
20#22575427C2212yescomplemented
21#22575425—22no—
22#22575424C2212yescomplemented
23#22575422—22no—
24#22575421—22no—
25D4×Dic269C2212yescomplemented
26C4×C22⋊D269C2211yescharacteristic
27#22575387C2211yescharacteristic, complemented
28#22575382C2211yescharacteristic, complemented
29#22575375C2212yescomplemented
30#22575374C2212yescomplemented
31#22575374C2212yescomplemented
32C22⋊#14524130C2211yescharacteristic, complemented
33#22575365C2211yescharacteristic, complemented
34C8×Dic269C2211yescharacteristic, complemented
35C22×D4×C269C2212yescomplemented
36C2×D8×C269—24no—
37C2×D8×C269C2211yescharacteristic
38C2×D8×C269C2211yescharacteristic, complemented
39C2×D8×C269C2212yescomplemented
40C22×C8×C269C2211yescharacteristic, complemented
41C23×D269—22no—
42C2×D1076C2312yes—
43C2×C22⋊D269—22no—
44C2×C22⋊D269—22no—
45C2×C22⋊D269—22no—
46C2×C22⋊D269—22no—
47C2×C22⋊D269—22no—
48C2×C22⋊D269—48no—
49C2×C22⋊D269D411yescharacteristic
50D4×D269—24no—
51D4×D269—42no—
52C22×Dic269—22no—
53C2×C4×D269C2311yescharacteristic
54D2152—22no—
55#16864387—24no—
56#16864387—42no—
57C2×#14524130C2311yescharacteristic
58C2×#14524130C2311yescharacteristic
59C8×D269—22no—
60C4⋊Dic269C2312yes—
61#16864381D411yescharacteristic
62C22⋊Dic269—22no—
63C22⋊Dic269—22no—
64C22⋊Dic269D411yescharacteristic
65#16864379—22no—
66#16864379D411yescharacteristic
67C4×Dic269C2311yescharacteristic
68C24×C269—22no—
69C2×D4×C269—24no—
70C2×D4×C269—22no—
71C2×D4×C269—42no—
72C2×D4×C269C2312yes—
73C2×D4×C269C2312yes—
74C22×C4×C269C2311yescharacteristic
75D8×C269—24no—
76D8×C269—22no—
77D8×C269D414yescomplemented
78C2×C8×C269—22no—
79C2×C8×C269C2311yescharacteristic
80C2×C8×C269C2311yescharacteristic
81C22×D269—22no—
82C22×D269—44no—
83C22×D269—44no—
84C22×D269—82no—
85C22×D269C2×D411yescharacteristic
86D1076—22no—
87D1076—22no—
88C22⋊D269—44no—
89C22⋊D269—44no—
90C22⋊D269—44no—
91C22⋊D269—44no—
92C22⋊D269—82no—
93C22⋊D269D814yesdirect product factor
94C2×Dic269—22no—
95C2×Dic269—44no—
96C2×Dic269C2×D411yescharacteristic
97C2×Dic269C2×D411yescharacteristic
98C2×Dic269C2×D411yescharacteristic
99C4×D269—21no—
100C4×D269—21no—
101#14524130—21no—
102#14524130—21no—
103C23×C269—22no—
104C23×C269—22no—
105C23×C269—44no—
106C23×C269—44no—
107C23×C269—82no—
108C23×C269C2×D411yescharacteristic
109D4×C269—22no—
110D4×C269—22no—
111D4×C269—22no—
112D4×C269—44no—
113D4×C269C2×D414yescomplemented
114C2×C4×C269—21no—
115C2×C4×C269—21no—
116C2×C4×C269C2×D411yescharacteristic
117C2×C4×C269C2411yescharacteristic
118C8×C269—21no—
119C8×C269C2×D412yescomplemented
120C22×C269—21no—
121C22×C269—21no—
122C22×C269—24no—
123C22×C269—42no—
124C22×C269—42no—
125C22×C269—42no—
126C22×C269—42no—
127C22×C269—42no—
128C22×C269—88no—
129C22×C269C2×D812yescomplemented
130C22×C269C22×D411yescharacteristic
131C2×D269—21no—
132C2×D269—21no—
133C2×D269—42no—
134C2×D269—42no—
135C2×D269—42no—
136C2×D269—88no—
137C2×D269C2×D812yescomplemented
138C4×C269—21no—
139C4×C269C22×D411yescharacteristic
140C4×C269H(5,𝔽2)11yescharacteristic
141Dic269—21no—
142Dic269—21no—
143Dic269—42no—
144Dic269C2×D812yescomplemented
145C2×C269—22no—
146C2×C269—44no—
147C2×C269—82no—
148C2×C269D4211yescharacteristic
149C2×C269C22×D811yescharacteristic
150C2×C269#57611yescharacteristic
151D269—22no—
152D269—82no—
153C269D4×D811yescharacteristic, complemented, Sylow
154D4×D8—2691nomaximal, Sylow
155C22×D8—2691no—
156C22×D8D26911yescharacteristic, complemented
157D42—2692no—
158#493—2691no—
159#466—2691no—
160#466—2691no—
161#459—2692no—
162#447—2692no—
163#447—2692no—
164C4×D8—2691no—
165C8×D4—2691no—
166C22×D4—2692no—
167C22×D4—5382no—
168C22×D4C2×D26912yescomplemented
169C2×D8—24no—
170C2×D8—2692no—
171C2×D8—2692no—
172C2×D8—2691no—
173C2×D8—5384no—
174C2×D8C2×D26911yescharacteristic
175C2×D8C2×D26912yescomplemented
176C2×D8C2×D26911yescharacteristic, complemented
177C22×C8—2691no—
178C22×C8C2×D26911yescharacteristic, complemented
179#127—2692no—
180#121—2692no—
181#121—2692no—
182#121—5382no—
183#120—5382no—
184#120—5382no—
185C4×D4—2691no—
186C4×D4—2692no—
187#107—2691no—
188C4⋊C8—2691no—
189#102—2692no—
190#102—2692no—
191#102—2692no—
192C22⋊C8—2691no—
193C22⋊C8—2691no—
194C4×C8—2691no—
195C24—22no—
196C24—5382no—
197C2×D4—24no—
198C2×D4—22no—
199C2×D4—42no—
200C2×D4—2691no—
201C2×D4—2692no—
202C2×D4—5382no—
203C2×D4—5382no—
204C2×D4—5382no—
205C2×D4—5384no—
206C2×D4—5382no—
207C2×D4—5382no—
208C2×D4—10762no—
209C2×D4—10768no—
210C2×D4C22×D26912yes—
211C2×D4C22×D26912yes—
212C22×C4—2691no—
213C22×C4—5382no—
214C22×C4C22×D26911yescharacteristic
215D8—24no—
216D8—22no—
217D8—5384no—
218D8—5382no—
219D8—10762no—
220D8C22⋊D26914yesdirect product factor
221C2×C8—22no—
222C2×C8—2691no—
223C2×C8—2691no—
224C2×C8—5382no—
225C2×C8C22×D26911yescharacteristic
226C2×C8C22×D26911yescharacteristic
227C4⋊C4—2691no—
228C4⋊C4—2692no—
229C22⋊C4—2691no—
230C22⋊C4—2691no—
231C22⋊C4—5382no—
232C22⋊C4—5382no—
233C22⋊C4—5382no—
234C42—2691no—
235C23—22no—
236C23—22no—
237C23—44no—
238C23—44no—
239C23—82no—
240C23—2691no—
241C23—5382no—
242C23—10764no—
243C23—10764no—
244C23—21522no—
245C23D4×D26911yescharacteristic
246D4—22no—
247D4—22no—
248D4—22no—
249D4—44no—
250D4—2694no—
251D4—5382no—
252D4—5382no—
253D4—10764no—
254D4—10764no—
255D4—10764no—
256D4—10764no—
257D4—21522no—
258D4C2×C22⋊D26914yescomplemented
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—2691no—
262C2×C4—2691no—
263C2×C4—2691no—
264C2×C4—5381no—
265C2×C4—5381no—
266C2×C4—5382no—
267C2×C4—10764no—
268C2×C4D4×D26911yescharacteristic
269C2×C4C23×D26911yescharacteristic
270C8—21no—
271C8—5381no—
272C8—5381no—
273C8C2×C22⋊D26912yescomplemented
274C22—21no—
275C22—21no—
276C22—24no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—88no—
283C22—2692no—
284C22—5381no—
285C22—5381no—
286C22—10762no—
287C22—10762no—
288C22—10762no—
289C22—21528no—
290C22D8×D26912yescomplemented
291C22C2×D4×D26911yescharacteristic
292C4—21no—
293C4—2692no—
294C4—5381no—
295C4—5381no—
296C4—10762no—
297C4C22×C22⋊D26911yescharacteristic
298C4#2257549811yescharacteristic
299C2—22no—
300C2—44no—
301C2—82no—
302C2—5382no—
303C2—21522no—
304C2D4×C22⋊D26911yescharacteristic
305C2C2×D8×D26911yescharacteristic
306C2#3177140611yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC22×D8×C269C2
socleC22×C269C22×D4
hypercenterC22×D8D269
hypocenterC269D4×D8
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×D269C2semidirect
2. D4×C22⋊D269C2semidirect
3. #31770980C2semidirect
4. #31770841C2semidirect
5. #31770838C2semidirect
6. #31770798C2semidirect
7. #31770739C2semidirect
8. #31770737C2semidirect
9. D8×Dic269C2semidirect
10. C8×C22⋊D269C2semidirect
11. C22×D8×C269C2semidirect
13. C2×D4×D269C22semidirect
14. C2×D2152C22semidirect
15. C2×#16864387C22semidirect
16. C2×#16864387C22semidirect
18. C2×C8×D269C22semidirect
19. #22575449C22semidirect
20. #22575427C22semidirect
22. #22575424C22semidirect
25. D4×Dic269C22semidirect
27. #22575387C22semidirect
28. #22575382C22semidirect
29. #22575375C22semidirect
30. #22575374C22semidirect
31. #22575374C22semidirect
32. C22⋊#14524130C22semidirect
33. #22575365C22semidirect
34. C8×Dic269C22semidirect
35. C22×D4×C269C22semidirect
38. C2×D8×C269C22semidirect
39. C2×D8×C269C22semidirect
40. C22×C8×C269C22semidirect
77. D8×C269D4semidirect
93. C22⋊D269D8direct (N × H)
113. D4×C269C2×D4semidirect
119. C8×C269C2×D4semidirect
129. C22×C269C2×D8semidirect
137. C2×D269C2×D8semidirect
144. Dic269C2×D8semidirect
153. C269D4×D8semidirect
156. C22×D8D269semidirect
168. C22×D4C2×D269semidirect
175. C2×D8C2×D269semidirect
176. C2×D8C2×D269semidirect
178. C22×C8C2×D269semidirect
220. D8C22⋊D269direct (N × H)
258. D4C2×C22⋊D269semidirect
273. C8C2×C22⋊D269semidirect
290. C22D8×D269semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D2692
D4×C22⋊D2692
#317709802
#317708412
#317708382
#317707982
#317707392
#317707372
D8×Dic2692
C8×C22⋊D2692
C22×D8×C2692
D4×D8269