Finite Group Databasebeta

← D8×C22⋊D89 #26031923

Subgroups — D8×C22⋊D89 #26031923

Order 11392.

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×D89C211yesmaximal, characteristic, complemented
2D4×C22⋊D89C212yesmaximal, complemented
3#19151973C211yesmaximal, characteristic, complemented
4#19151834C211yesmaximal, characteristic, complemented
5#19151831C211yesmaximal, characteristic, complemented
6#19151791C212yesmaximal, complemented
7#19151732C212yesmaximal, complemented
8#19151730C212yesmaximal, complemented
9D8×Dic89C211yesmaximal, characteristic, complemented
10C8×C22⋊D89C211yesmaximal, characteristic, complemented
11C22×D8×C89C211yesmaximal, characteristic, complemented
12C22×C22⋊D89—22no—
13C2×D4×D89C2212yescomplemented
14C2×D712C2211yescharacteristic, complemented
15C2×#13083559C2212yescomplemented
16C2×#13083559C2212yescomplemented
17D8×D89—24no—
18C2×C8×D89C2211yescharacteristic, complemented
19#15668008C2212yescomplemented
20#15667986C2212yescomplemented
21#15667984—22no—
22#15667983C2212yescomplemented
23#15667981—22no—
24#15667980—22no—
25D4×Dic89C2212yescomplemented
26C4×C22⋊D89C2211yescharacteristic
27#15667946C2211yescharacteristic, complemented
28#15667941C2211yescharacteristic, complemented
29#15667934C2212yescomplemented
30#15667933C2212yescomplemented
31#15667933C2212yescomplemented
32C22⋊#10623494C2211yescharacteristic, complemented
33#15667924C2211yescharacteristic, complemented
34C8×Dic89C2211yescharacteristic, complemented
35C22×D4×C89C2212yescomplemented
36C2×D8×C89—24no—
37C2×D8×C89C2211yescharacteristic
38C2×D8×C89C2211yescharacteristic, complemented
39C2×D8×C89C2212yescomplemented
40C22×C8×C89C2211yescharacteristic, complemented
41C23×D89—22no—
42C2×D356C2312yes—
43C2×C22⋊D89—22no—
44C2×C22⋊D89—22no—
45C2×C22⋊D89—22no—
46C2×C22⋊D89—22no—
47C2×C22⋊D89—22no—
48C2×C22⋊D89—48no—
49C2×C22⋊D89D411yescharacteristic
50D4×D89—24no—
51D4×D89—42no—
52C22×Dic89—22no—
53C2×C4×D89C2311yescharacteristic
54D712—22no—
55#13083559—24no—
56#13083559—42no—
57C2×#10623494C2311yescharacteristic
58C2×#10623494C2311yescharacteristic
59C8×D89—22no—
60C4⋊Dic89C2312yes—
61#13083553D411yescharacteristic
62C22⋊Dic89—22no—
63C22⋊Dic89—22no—
64C22⋊Dic89D411yescharacteristic
65#13083551—22no—
66#13083551D411yescharacteristic
67C4×Dic89C2311yescharacteristic
68C24×C89—22no—
69C2×D4×C89—24no—
70C2×D4×C89—22no—
71C2×D4×C89—42no—
72C2×D4×C89C2312yes—
73C2×D4×C89C2312yes—
74C22×C4×C89C2311yescharacteristic
75D8×C89—24no—
76D8×C89—22no—
77D8×C89D414yescomplemented
78C2×C8×C89—22no—
79C2×C8×C89C2311yescharacteristic
80C2×C8×C89C2311yescharacteristic
81C23×C89—22no—
82C23×C89—22no—
83C23×C89—44no—
84C23×C89—44no—
85C23×C89—82no—
86C23×C89C2×D411yescharacteristic
87C22×D89—22no—
88C22×D89—44no—
89C22×D89—44no—
90C22×D89—82no—
91C22×D89C2×D411yescharacteristic
92D4×C89—22no—
93D4×C89—22no—
94D4×C89—22no—
95D4×C89—44no—
96D4×C89C2×D414yescomplemented
97C2×C4×C89—21no—
98C2×C4×C89—21no—
99C2×C4×C89C2×D411yescharacteristic
100C2×C4×C89C2411yescharacteristic
101C22⋊D89—44no—
102C22⋊D89—44no—
103C22⋊D89—44no—
104C22⋊D89—44no—
105C22⋊D89—82no—
106C22⋊D89D814yesdirect product factor
107C2×Dic89—22no—
108C2×Dic89—44no—
109C2×Dic89C2×D411yescharacteristic
110C2×Dic89C2×D411yescharacteristic
111C2×Dic89C2×D411yescharacteristic
112D356—22no—
113D356—22no—
114C4×D89—21no—
115C4×D89—21no—
116C8×C89—21no—
117C8×C89C2×D412yescomplemented
118#10623494—21no—
119#10623494—21no—
120C22×C89—21no—
121C22×C89—21no—
122C22×C89—24no—
123C22×C89—42no—
124C22×C89—42no—
125C22×C89—42no—
126C22×C89—42no—
127C22×C89—42no—
128C22×C89—88no—
129C22×C89C2×D812yescomplemented
130C22×C89C22×D411yescharacteristic
131C2×D89—21no—
132C2×D89—21no—
133C2×D89—42no—
134C2×D89—42no—
135C2×D89—42no—
136C2×D89—88no—
137C2×D89C2×D812yescomplemented
138C4×C89—21no—
139C4×C89C22×D411yescharacteristic
140C4×C89H(5,𝔽2)11yescharacteristic
141Dic89—21no—
142Dic89—21no—
143Dic89—42no—
144Dic89C2×D812yescomplemented
145C2×C89—22no—
146C2×C89—44no—
147C2×C89—82no—
148C2×C89D4211yescharacteristic
149C2×C89C22×D811yescharacteristic
150C2×C89#57611yescharacteristic
151D89—22no—
152D89—82no—
153D4×D8—891nomaximal, Sylow
154C89D4×D811yescharacteristic, complemented, Sylow
155C22×D8—891no—
156C22×D8D8911yescharacteristic, complemented
157D42—892no—
158#493—891no—
159#466—891no—
160#466—891no—
161#459—892no—
162#447—892no—
163#447—892no—
164C4×D8—891no—
165C8×D4—891no—
166C22×D4—892no—
167C22×D4—1782no—
168C22×D4C2×D8912yescomplemented
169C2×D8—24no—
170C2×D8—892no—
171C2×D8—892no—
172C2×D8—891no—
173C2×D8—1784no—
174C2×D8C2×D8911yescharacteristic
175C2×D8C2×D8912yescomplemented
176C2×D8C2×D8911yescharacteristic, complemented
177C22×C8—891no—
178C22×C8C2×D8911yescharacteristic, complemented
179#127—892no—
180#121—892no—
181#121—892no—
182#121—1782no—
183#120—1782no—
184#120—1782no—
185C4×D4—891no—
186C4×D4—892no—
187#107—891no—
188C4⋊C8—891no—
189#102—892no—
190#102—892no—
191#102—892no—
192C22⋊C8—891no—
193C22⋊C8—891no—
194C4×C8—891no—
195C24—22no—
196C24—1782no—
197C2×D4—24no—
198C2×D4—22no—
199C2×D4—42no—
200C2×D4—891no—
201C2×D4—892no—
202C2×D4—3568no—
203C2×D4—3562no—
204C2×D4—1782no—
205C2×D4—1782no—
206C2×D4—1782no—
207C2×D4—1782no—
208C2×D4—1782no—
209C2×D4—1784no—
210C2×D4C22×D8912yes—
211C2×D4C22×D8912yes—
212C22×C4—891no—
213C22×C4—1782no—
214C22×C4C22×D8911yescharacteristic
215D8—24no—
216D8—22no—
217D8—3562no—
218D8—1784no—
219D8—1782no—
220D8C22⋊D8914yesdirect product factor
221C2×C8—22no—
222C2×C8—891no—
223C2×C8—891no—
224C2×C8—1782no—
225C2×C8C22×D8911yescharacteristic
226C2×C8C22×D8911yescharacteristic
227C4⋊C4—891no—
228C4⋊C4—892no—
229C22⋊C4—891no—
230C22⋊C4—891no—
231C22⋊C4—1782no—
232C22⋊C4—1782no—
233C22⋊C4—1782no—
234C42—891no—
235C23—22no—
236C23—22no—
237C23—44no—
238C23—44no—
239C23—82no—
240C23—891no—
241C23—3564no—
242C23—3564no—
243C23—1782no—
244C23—7122no—
245C23D4×D8911yescharacteristic
246D4—22no—
247D4—22no—
248D4—22no—
249D4—44no—
250D4—894no—
251D4—3564no—
252D4—3564no—
253D4—3564no—
254D4—3564no—
255D4—1782no—
256D4—1782no—
257D4—7122no—
258D4C2×C22⋊D8914yescomplemented
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—891no—
262C2×C4—891no—
263C2×C4—891no—
264C2×C4—3564no—
265C2×C4—1782no—
266C2×C4—1781no—
267C2×C4—1781no—
268C2×C4D4×D8911yescharacteristic
269C2×C4C23×D8911yescharacteristic
270C8—21no—
271C8—1781no—
272C8—1781no—
273C8C2×C22⋊D8912yescomplemented
274C22—21no—
275C22—21no—
276C22—24no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—88no—
283C22—892no—
284C22—3562no—
285C22—3562no—
286C22—3562no—
287C22—1781no—
288C22—1781no—
289C22—7128no—
290C22D8×D8912yescomplemented
291C22C2×D4×D8911yescharacteristic
292C4—21no—
293C4—892no—
294C4—3562no—
295C4—1781no—
296C4—1781no—
297C4C22×C22⋊D8911yescharacteristic
298C4#1566805711yescharacteristic
299C2—22no—
300C2—44no—
301C2—82no—
302C2—1782no—
303C2—7122no—
304C2D4×C22⋊D8911yescharacteristic
305C2C2×D8×D8911yescharacteristic
306C2#1915239911yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC22×D8×C89C2
socleC22×C89C22×D4
hypercenterC22×D8D89
hypocenterC89D4×D8
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×D89C2semidirect
2. D4×C22⋊D89C2semidirect
3. #19151973C2semidirect
4. #19151834C2semidirect
5. #19151831C2semidirect
6. #19151791C2semidirect
7. #19151732C2semidirect
8. #19151730C2semidirect
9. D8×Dic89C2semidirect
10. C8×C22⋊D89C2semidirect
11. C22×D8×C89C2semidirect
13. C2×D4×D89C22semidirect
14. C2×D712C22semidirect
15. C2×#13083559C22semidirect
16. C2×#13083559C22semidirect
18. C2×C8×D89C22semidirect
19. #15668008C22semidirect
20. #15667986C22semidirect
22. #15667983C22semidirect
25. D4×Dic89C22semidirect
27. #15667946C22semidirect
28. #15667941C22semidirect
29. #15667934C22semidirect
30. #15667933C22semidirect
31. #15667933C22semidirect
32. C22⋊#10623494C22semidirect
33. #15667924C22semidirect
34. C8×Dic89C22semidirect
35. C22×D4×C89C22semidirect
38. C2×D8×C89C22semidirect
39. C2×D8×C89C22semidirect
40. C22×C8×C89C22semidirect
77. D8×C89D4semidirect
96. D4×C89C2×D4semidirect
106. C22⋊D89D8direct (N × H)
117. C8×C89C2×D4semidirect
129. C22×C89C2×D8semidirect
137. C2×D89C2×D8semidirect
144. Dic89C2×D8semidirect
154. C89D4×D8semidirect
156. C22×D8D89semidirect
168. C22×D4C2×D89semidirect
175. C2×D8C2×D89semidirect
176. C2×D8C2×D89semidirect
178. C22×C8C2×D89semidirect
220. D8C22⋊D89direct (N × H)
258. D4C2×C22⋊D89semidirect
273. C8C2×C22⋊D89semidirect
290. C22D8×D89semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D892
D4×C22⋊D892
#191519732
#191518342
#191518312
#191517912
#191517322
#191517302
D8×Dic892
C8×C22⋊D892
C22×D8×C892
D4×D889