Finite Group Databasebeta

← #469×D89 #26029844

Subgroups — #469×D89 #26029844

Order 11392.

596 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 135 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
2C2×M16×D89C211yesmaximal, characteristic, complemented
3#121×D89C212yesmaximal, complemented
4#19151852C211yesmaximal, characteristic, complemented
5#19151851C211yesmaximal, characteristic, complemented
6#19151850C212yesmaximal, complemented
7#19151849C212yesmaximal, complemented
8#19151848C211yesmaximal, characteristic, complemented
9#106×D89C211yesmaximal, characteristic, complemented
10#102×D89C212yesmaximal, complemented
11#469×C89C211yesmaximal, characteristic, complemented
12C2×D4×D89—22no—
13C2×D4×D89C2212yes—
14C22×C4×D89C2211yescharacteristic
15C2×D712C2211yescharacteristic, complemented
16C2×#13083559C2212yescomplemented
17D8×D89—24no—
18C2×#13083558C2211yescharacteristic, complemented
19C2×#13083557C2211yescharacteristic, complemented
20C2×#13083557C2211yescharacteristic, complemented
21M16×D89—24no—
22C2×C8×D89C2211yescharacteristic
23C2×C8×D89C2211yescharacteristic
24#15667987C2212yescomplemented
25#15667986C2212yescomplemented
26#15667985—22no—
27#15667984—22no—
28#15667983C2212yescomplemented
29C4⋊C4×D89C2212yes—
30C22⋊C4×D89—22no—
31#15667944C2211yescharacteristic, complemented
32#15667943C2212yescomplemented
33#15667934C2212yescomplemented
34#15667933C2212yescomplemented
35#15667932C2212yescomplemented
36C2×D8×C89C2211yescharacteristic, complemented
37C2×M16×C89C2211yescharacteristic, complemented
38#121×C89C2212yescomplemented
39#106×C89C2211yescharacteristic, complemented
40#102×C89C2212yescomplemented
41C23×D89—22no—
42C23×D89D411yescharacteristic
43C2×D356—22no—
44C2×D356C2312yes—
45C2×C22⋊D89—22no—
46C2×C22⋊D89—22no—
47C2×C22⋊D89—22no—
48D4×D89—24no—
49D4×D89—24no—
50D4×D89—48no—
51C22×Dic89D411yescharacteristic
52C2×C4×D89—22no—
53C2×C4×D89—22no—
54C2×C4×D89—22no—
55C2×C4×D89D411yescharacteristic
56C2×C4×D89D411yescharacteristic
57C2×C4×D89C2311yescharacteristic
58C2×C4×D89C2311yescharacteristic
59D712—22no—
60#13083559—24no—
61#13083558—22no—
62#13083557—22no—
63#13083557—22no—
64C2×#10623494C2311yescharacteristic
65C2×#10623494C2311yescharacteristic
66C8×D89—22no—
67C8×D89D414yescomplemented
68C4⋊Dic89C2312yes—
69#13083553—22no—
70C22⋊Dic89—22no—
71#13083551—22no—
72#13083551—22no—
73C2×D4×C89—22no—
74C2×D4×C89C2312yes—
75C22×C4×C89C2311yescharacteristic
76D8×C89—22no—
77M16×C89—22no—
78C2×C8×C89C2311yescharacteristic
79C2×C8×C89C2311yescharacteristic
80C4⋊C4×C89C2312yes—
81C22⋊C4×C89—22no—
82C23×C89—22no—
83C23×C89C2×D411yescharacteristic
84C22×D89—22no—
85C22×D89—24no—
86C22×D89—22no—
87C22×D89—44no—
88C22×D89—44no—
89C22×D89—44no—
90C22×D89C2×D411yescharacteristic
91C22×D89C2×D411yescharacteristic
92D4×C89—22no—
93D4×C89—22no—
94D4×C89—44no—
95C2×C4×C89—21no—
96C2×C4×C89—21no—
97C2×C4×C89—22no—
98C2×C4×C89C2×D411yescharacteristic
99C2×C4×C89C2411yescharacteristic
100C22⋊D89—44no—
101C22⋊D89—44no—
102C22⋊D89—44no—
103C2×Dic89—22no—
104C2×Dic89—22no—
105C2×Dic89C2×D411yescharacteristic
106C2×Dic89C2×D411yescharacteristic
107D356—22no—
108D356—22no—
109D356—44no—
110C4×D89—22no—
111C4×D89—21no—
112C4×D89—21no—
113C4×D89—22no—
114C4×D89—44no—
115C4×D89C2×D412yes—
116C4×D89#4112yes—
117C8×C89—21no—
118C8×C89C2×D412yescomplemented
119#10623494—21no—
120#10623494C2×D412yescomplemented
121C22×C89—21no—
122C22×C89—22no—
123C22×C89—42no—
124C22×C89—42no—
125C22×C89—42no—
126C22×C89C22×D411yescharacteristic
127C2×D89—21no—
128C2×D89—22no—
129C2×D89—44no—
130C2×D89—42no—
131C2×D89—42no—
132C2×D89—42no—
133C2×D89—88no—
134C2×D89#12112yes—
135C2×D89AGL(1,ℤ/8)14yes—
136C4×C89—21no—
137C4×C89—42no—
138C4×C89C22×D411yescharacteristic
139C4×C89C2×#4111yescharacteristic
140Dic89—21no—
141Dic89—42no—
142Dic89#12112yes—
143C2×C89—41no—
144C2×C89—82no—
145C2×C89C2×#12111yescharacteristic
146C2×C89C2×AGL(1,ℤ/8)12yes—
147D89—41no—
148D89—82no—
149D89#46914yesdirect product factor
150C2×#469—891nomaximal, Sylow
151C89C2×#46911yescharacteristic, complemented, Sylow
152C22×D8—891no—
153C22×M16—891no—
154C2×#121—892no—
155#469—891no—
156#469—891no—
157#469—892no—
158#469—891no—
159#469—892no—
160#469D8911yescharacteristic, direct product factor
161C2×#106—891no—
162C2×#102—892no—
163C22×D4—892no—
164C22×D4—1782no—
165C23×C4—891no—
166C2×D8—892no—
167C2×D8—891no—
168C2×D8—1784no—
169C2×D8C2×D8911yescharacteristic, complemented
170C2×M16—891no—
171C2×M16—891no—
172C2×M16—891no—
173C2×M16—1784no—
174C2×M16C2×D8911yescharacteristic, complemented
175C22×C8—891no—
176C22×C8—891no—
177#121—892no—
178#121—892no—
179#121—892no—
180#121—1782no—
181#121—1782no—
182#121C2×D8912yescomplemented
183C2×C4⋊C4—892no—
184C2×C22⋊C4—1782no—
185#106—891no—
186#106—892no—
187#106C2×D8911yescharacteristic, complemented
188#102—892no—
189#102—892no—
190#102—892no—
191#102C2×D8912yescomplemented
192C24—891no—
193C24—1782no—
194C2×D4—22no—
195C2×D4—892no—
196C2×D4—3568no—
197C2×D4—1782no—
198C2×D4—1784no—
199C2×D4—1784no—
200C2×D4—1782no—
201C2×D4—1782no—
202C2×D4—1782no—
203C2×D4C22×D8912yes—
204C22×C4—891no—
205C22×C4—891no—
206C22×C4—891no—
207C22×C4—891no—
208C22×C4—891no—
209C22×C4—1782no—
210C22×C4—1782no—
211C22×C4—1782no—
212C22×C4C22×D8911yescharacteristic
213D8—22no—
214D8—1784no—
215D8—1782no—
216M16—22no—
217M16—1782no—
218M16—1782no—
219M16—1782no—
220C2×C8—891no—
221C2×C8—894no—
222C2×C8—891no—
223C2×C8—1782no—
224C2×C8C22×D8911yescharacteristic
225C2×C8C22×D8911yescharacteristic
226C4⋊C4—892no—
227C4⋊C4—1782no—
228C4⋊C4C22×D8912yes—
229C22⋊C4—22no—
230C22⋊C4—1782no—
231C22⋊C4—1782no—
232C22⋊C4—1782no—
233C23—22no—
234C23—891no—
235C23—891no—
236C23—3564no—
237C23—3564no—
238C23—3564no—
239C23—1782no—
240C23—1784no—
241C23—1782no—
242C23D4×D8911yescharacteristic
243D4—22no—
244D4—22no—
245D4—44no—
246D4—3564no—
247D4—3564no—
248D4—3564no—
249D4—3564no—
250D4—1782no—
251D4—1782no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—891no—
256C2×C4—892no—
257C2×C4—892no—
258C2×C4—891no—
259C2×C4—3564no—
260C2×C4—1782no—
261C2×C4—1782no—
262C2×C4—1782no—
263C2×C4—1782no—
264C2×C4—1781no—
265C2×C4—1781no—
266C2×C4D4×D8911yescharacteristic
267C2×C4C23×D8911yescharacteristic
268C8—21no—
269C8—892no—
270C8—1781no—
271C8D4×D8912yescomplemented
272C22—21no—
273C22—22no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—892no—
278C22—894no—
279C22—3564no—
280C22—3562no—
281C22—3562no—
282C22—3562no—
283C22—1781no—
284C22—1782no—
285C22—7128no—
286C22C2×D4×D8911yescharacteristic
287C4—21no—
288C4—42no—
289C4—892no—
290C4—3562no—
291C4—1781no—
292C4C2×D4×D8911yescharacteristic
293C4#41×D8911yescharacteristic
294C2—41no—
295C2—82no—
296C2—894no—
297C2—3561no—
298C2—7122no—
299C2#121×D8911yescharacteristic
300C2AGL(1,ℤ/8)×D8912yes—
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#469×C89C2
socleC22×C89C22×D4
hypercenter#469D89
hypocenterC89C2×#469
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D8×D89C2semidirect
2. C2×M16×D89C2semidirect
3. #121×D89C2semidirect
4. #19151852C2semidirect
5. #19151851C2semidirect
6. #19151850C2semidirect
7. #19151849C2semidirect
8. #19151848C2semidirect
9. #106×D89C2semidirect
10. #102×D89C2semidirect
11. #469×C89C2semidirect
15. C2×D712C22semidirect
16. C2×#13083559C22semidirect
18. C2×#13083558C22semidirect
19. C2×#13083557C22semidirect
20. C2×#13083557C22semidirect
24. #15667987C22semidirect
25. #15667986C22semidirect
28. #15667983C22semidirect
31. #15667944C22semidirect
32. #15667943C22semidirect
33. #15667934C22semidirect
34. #15667933C22semidirect
35. #15667932C22semidirect
36. C2×D8×C89C22semidirect
37. C2×M16×C89C22semidirect
38. #121×C89C22semidirect
39. #106×C89C22semidirect
40. #102×C89C22semidirect
67. C8×D89D4semidirect
118. C8×C89C2×D4semidirect
120. #10623494C2×D4semidirect
149. D89#469direct (N × H)
151. C89C2×#469semidirect
160. #469D89direct (N × H)
169. C2×D8C2×D89semidirect
174. C2×M16C2×D89semidirect
182. #121C2×D89semidirect
187. #106C2×D89semidirect
191. #102C2×D89semidirect
271. C8D4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D892
C2×M16×D892
#121×D892
#191518522
#191518512
#191518502
#191518492
#191518482
#106×D892
#102×D892
#469×C892
C2×#46989