Finite Group Databasebeta

← #442×D89 #26029041

Subgroups — #442×D89 #26029041

Order 11392.

608 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 183 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
2C4×D4×D89C212yesmaximal, complemented
3#19151711C211yesmaximal, characteristic, complemented
4#19151710C211yesmaximal, characteristic, complemented
5#19151709C211yesmaximal, characteristic, complemented
6#19151708C212yesmaximal, complemented
7#19151707C212yesmaximal, complemented
8#106×D89C211yesmaximal, characteristic, complemented
9#102×D89C212yesmaximal, complemented
10#97×D89C211yesmaximal, characteristic, complemented
11#442×C89C211yesmaximal, characteristic, complemented
12C2×D4×D89C2212yes—
13C22×C4×D89—22no—
14C2×D712C2211yescharacteristic
15C2×#13083559C2212yes—
16D8×D89C418yescomplemented
17C2×C8×D89C2211yescharacteristic
18C2×C8×D89C2211yescharacteristic
19C4×D356C2212yescomplemented
20D4×Dic89C2212yescomplemented
21#15667974C2212yescomplemented
22C4×C22⋊D89—22no—
23#15667972—22no—
24C4⋊C4×D89C2212yes—
25C22⋊C4×D89—22no—
26C42×D89C2211yescharacteristic
27#15667944C2211yescharacteristic, complemented
28#15667943C2212yescomplemented
29#15667934C2212yescomplemented
30#15667933C2212yescomplemented
31#15667932C2212yescomplemented
32#15667923C2211yescharacteristic, complemented
33#15667922C2211yescharacteristic, complemented
34#15667922C2211yescharacteristic, complemented
35C2×D8×C89C2211yescharacteristic
36C4×D4×C89C2212yescomplemented
37#106×C89C2211yescharacteristic, complemented
38#102×C89C2212yescomplemented
39#97×C89C2211yescharacteristic, complemented
40C23×D89—22no—
41C2×D356C2312yes—
42C2×C22⋊D89—22no—
43D4×D89—24no—
44D4×D89C2×C418yescomplemented
45C22×Dic89—22no—
46C2×C4×D89—22no—
47C2×C4×D89—22no—
48C2×C4×D89—22no—
49C2×C4×D89—48no—
50C2×C4×D89D412yes—
51C2×C4×D89C2311yescharacteristic
52D712C2×C414yescomplemented
53#13083559C2×C418yescomplemented
54C2×#10623494C2311yescharacteristic
55C2×#10623494C2311yescharacteristic
56C8×D89—22no—
57C8×D89C2×C414yescomplemented
58C4⋊Dic89C2312yes—
59#13083553—22no—
60C22⋊Dic89—22no—
61#13083551—22no—
62#13083551—22no—
63C4×Dic89D412yes—
64C4×Dic89C2311yescharacteristic
65C2×D4×C89C2312yes—
66C22×C4×C89—22no—
67D8×C89C2×C414yescomplemented
68C2×C8×C89C2311yescharacteristic
69C2×C8×C89C2311yescharacteristic
70C4⋊C4×C89C2312yes—
71C22⋊C4×C89—22no—
72C42×C89C2311yescharacteristic
73C23×C89—22no—
74C22×D89—22no—
75C22×D89—28no—
76C22×D89—44no—
77C22×D89—44no—
78C22×D89C2×D411yescharacteristic
79D4×C89—22no—
80D4×C89C22×C414yescomplemented
81C2×C4×C89—22no—
82C2×C4×C89—44no—
83C2×C4×C89C2×D412yes—
84C2×C4×C89C2411yescharacteristic
85C22⋊D89—28no—
86C2×Dic89—22no—
87C2×Dic89—44no—
88C2×Dic89C2×D412yes—
89C2×Dic89C2×D411yescharacteristic
90D356—22no—
91D356C22×C414yescomplemented
92C4×D89—24no—
93C4×D89—44no—
94C4×D89—44no—
95C4×D89—44no—
96C4×D89C22×C412yes—
97C4×D89#4112yes—
98C8×C89—21no—
99C8×C89C22×C412yescomplemented
100#10623494—21no—
101#10623494C22×C412yescomplemented
102C22×C89—24no—
103C22×C89—42no—
104C22×C89—42no—
105C22×C89C22×D411yescharacteristic
106C2×D89—24no—
107C2×D89—42no—
108C2×D89—42no—
109C2×D89—416no—
110C2×D89C4×D412yes—
111C2×D89AGL(1,ℤ/8)14yes—
112C4×C89—22no—
113C4×C89—42no—
114C4×C89C23×C411yescharacteristic
115C4×C89C2×#4111yescharacteristic
116Dic89—22no—
117Dic89—42no—
118Dic89C4×D412yes—
119C2×C89—44no—
120C2×C89C2×C4×D411yescharacteristic
121C2×C89C2×AGL(1,ℤ/8)12yes—
122D89—44no—
123D89#44214yesdirect product factor
124C2×#442—891nomaximal, Sylow
125C89C2×#44211yescharacteristic, complemented, Sylow
126C22×D8—891no—
127C2×C4×D4—892no—
128#442—891no—
129#442—892no—
130#442—891no—
131#442—892no—
132#442—891no—
133#442D8911yescharacteristic, direct product factor
134C2×#106—891no—
135C2×#102—892no—
136C2×#97—891no—
137C22×D4—892no—
138C23×C4—1782no—
139C2×D8—892no—
140C2×D8—898no—
141C2×D8—891no—
142C2×D8C2×D8911yescharacteristic
143C22×C8—891no—
144C22×C8—891no—
145C4×D4—892no—
146C4×D4—892no—
147C4×D4—892no—
148C4×D4—1782no—
149C4×D4—1782no—
150C4×D4C2×D8912yescomplemented
151C2×C4⋊C4—892no—
152C2×C22⋊C4—1782no—
153C2×C42—891no—
154#106—891no—
155#106—892no—
156#106C2×D8911yescharacteristic, complemented
157#102—892no—
158#102—892no—
159#102—892no—
160#102C2×D8912yescomplemented
161#97—891no—
162#97—891no—
163#97—891no—
164#97C2×D8911yescharacteristic, complemented
165C24—1782no—
166C2×D4—898no—
167C2×D4—892no—
168C2×D4—1784no—
169C2×D4—1782no—
170C2×D4C22×D8912yes—
171C22×C4—22no—
172C22×C4—891no—
173C22×C4—892no—
174C22×C4—3568no—
175C22×C4—1782no—
176C22×C4—1782no—
177C22×C4—1782no—
178C22×C4—1782no—
179D8—898no—
180D8—894no—
181D8C4×D8914yescomplemented
182C2×C8—891no—
183C2×C8—894no—
184C2×C8—891no—
185C2×C8—1782no—
186C2×C8C22×D8911yescharacteristic
187C2×C8C22×D8911yescharacteristic
188C4⋊C4—892no—
189C4⋊C4—1782no—
190C4⋊C4C22×D8912yes—
191C22⋊C4—22no—
192C22⋊C4—1782no—
193C22⋊C4—1782no—
194C22⋊C4—1782no—
195C42—892no—
196C42—891no—
197C42C22×D8911yescharacteristic
198C23—22no—
199C23—891no—
200C23—3564no—
201C23—3564no—
202C23—1788no—
203C23—1782no—
204D4—22no—
205D4—894no—
206D4—1788no—
207D4—1782no—
208D4C2×C4×D8914yescomplemented
209C2×C4—22no—
210C2×C4—44no—
211C2×C4—891no—
212C2×C4—892no—
213C2×C4—892no—
214C2×C4—892no—
215C2×C4—3564no—
216C2×C4—3564no—
217C2×C4—3564no—
218C2×C4—3564no—
219C2×C4—1784no—
220C2×C4—1782no—
221C2×C4D4×D8912yes—
222C2×C4C23×D8911yescharacteristic
223C8—21no—
224C8—892no—
225C8—1781no—
226C8C2×C4×D8912yescomplemented
227C22—24no—
228C22—42no—
229C22—42no—
230C22—892no—
231C22—894no—
232C22—35616no—
233C22—3562no—
234C22—3562no—
235C22—1784no—
236C22C2×D4×D8911yescharacteristic
237C4—22no—
238C4—42no—
239C4—892no—
240C4—3562no—
241C4—1782no—
242C4C22×C4×D8911yescharacteristic
243C4#41×D8911yescharacteristic
244C2—44no—
245C2—894no—
246C2—3564no—
247C2C4×D4×D8911yescharacteristic
248C2AGL(1,ℤ/8)×D8912yes—
subgroupG/H
centerC22C2×D4×D89
commutatorC4×C89C23×C4
FrattiniC2×C4C23×D89
Fitting#442×C89C2
socleC22×C89C22×D4
prime radicalC2×D8×D89C2
cosocleC2×C4×C89C24
hypercenter#442D89
hypocenterC89C2×#442
LCSG ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×D4×D89C2semidirect
3. #19151711C2semidirect
4. #19151710C2semidirect
5. #19151709C2semidirect
6. #19151708C2semidirect
7. #19151707C2semidirect
8. #106×D89C2semidirect
9. #102×D89C2semidirect
10. #97×D89C2semidirect
11. #442×C89C2semidirect
16. D8×D89C4semidirect
19. C4×D356C22semidirect
20. D4×Dic89C22semidirect
21. #15667974C22semidirect
27. #15667944C22semidirect
28. #15667943C22semidirect
29. #15667934C22semidirect
30. #15667933C22semidirect
31. #15667932C22semidirect
32. #15667923C22semidirect
33. #15667922C22semidirect
34. #15667922C22semidirect
36. C4×D4×C89C22semidirect
37. #106×C89C22semidirect
38. #102×C89C22semidirect
39. #97×C89C22semidirect
44. D4×D89C2×C4semidirect
52. D712C2×C4semidirect
53. #13083559C2×C4semidirect
57. C8×D89C2×C4semidirect
67. D8×C89C2×C4semidirect
80. D4×C89C22×C4semidirect
91. D356C22×C4semidirect
99. C8×C89C22×C4semidirect
101. #10623494C22×C4semidirect
123. D89#442direct (N × H)
125. C89C2×#442semidirect
133. #442D89direct (N × H)
150. C4×D4C2×D89semidirect
156. #106C2×D89semidirect
160. #102C2×D89semidirect
164. #97C2×D89semidirect
181. D8C4×D89semidirect
208. D4C2×C4×D89semidirect
226. C8C2×C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D892
C4×D4×D892
#191517112
#191517102
#191517092
#191517082
#191517072
#106×D892
#102×D892
#97×D892
#442×C892
C2×#44289