Finite Group Databasebeta

← #26029101

Subgroups — #26029101

Order 11392.

528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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
2#19152070C212yesmaximal, complemented
3#19151711C211yesmaximal, characteristic, complemented
4#19151710C211yesmaximal, characteristic, complemented
5#19151709C211yesmaximal, characteristic, complemented
6C4×#13083559C212yesmaximal, complemented
7#19151678C212yesmaximal, complemented
8#19151633C211yesmaximal, characteristic, complemented
9#19151601C212yesmaximal, complemented
10#19151555C211yesmaximal, characteristic, complemented
11#442×C89C211yesmaximal, characteristic, complemented
12C2×D4×D89C2212yes—
13C2×D712C2211yescharacteristic
14C2×#13083559C2212yes—
15D8×D89C418yescomplemented
16C2×#13083557C2211yescharacteristic
17C2×C8×D89C2211yescharacteristic
18C4×D356C2212yescomplemented
19D4×Dic89C2212yescomplemented
20#15667974C2212yescomplemented
21C4×C22⋊D89—22no—
22#15667972—22no—
23#15667970C2212yes—
24#15667969C2211yescharacteristic
25C2×#13083551—22no—
26C22⋊C4×D89—22no—
27#15667945C2212yescomplemented
28#15667944C2211yescharacteristic, complemented
29#15667934C2212yescomplemented
30#15667933C2212yescomplemented
31#15667932C2212yescomplemented
32#15667922C2211yescharacteristic, complemented
33C4×#10623494C2211yescharacteristic, complemented
34C8×Dic89C2211yescharacteristic, 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×D89C2311yescharacteristic
49D712C2×C414yescomplemented
50#13083559C2×C418yescomplemented
51#13083557—22no—
52C2×#10623494C2311yescharacteristic
53C2×#10623494C2311yescharacteristic
54C8×D89C2×C414yescomplemented
55C4⋊Dic89C2312yes—
56#13083553D412yes—
57C22⋊Dic89—22no—
58#13083551—22no—
59#13083551—22no—
60#13083551—22no—
61#13083551D412yes—
62C4×Dic89—22no—
63C4×Dic89C2311yescharacteristic
64C2×D4×C89C2312yes—
65C22×C4×C89—22no—
66D8×C89C2×C414yescomplemented
67C2×C8×C89C2311yescharacteristic
68C2×C8×C89C2311yescharacteristic
69C4⋊C4×C89C2312yes—
70C22⋊C4×C89—22no—
71C42×C89C2311yescharacteristic
72C23×C89—22no—
73C22×D89—22no—
74C22×D89—28no—
75C22×D89—82no—
76C22×D89—82no—
77C22×D89C2×D411yescharacteristic
78D4×C89—22no—
79D4×C89C22×C414yes—
80C2×C4×C89—22no—
81C2×C4×C89—82no—
82C2×C4×C89C2×D412yes—
83C2×C4×C89C2411yescharacteristic
84C22⋊D89—28no—
85C2×Dic89—22no—
86C2×Dic89—82no—
87C2×Dic89C2×D412yes—
88C2×Dic89C2×D411yescharacteristic
89D356—22no—
90D356C22×C414yes—
91C4×D89—82no—
92C4×D89—82no—
93C4×D89C22×C412yes—
94C4×D89#4112yes—
95C8×C89—21no—
96C8×C89C22×C412yes—
97#10623494—21no—
98#10623494C22×C412yes—
99C22×C89—24no—
100C22×C89—42no—
101C22×C89—42no—
102C22×C89C22×D411yescharacteristic
103C2×D89—22no—
104C2×D89—24no—
105C2×D89—42no—
106C2×D89—42no—
107C2×D89—88no—
108C2×D89C4×D412yes—
109C4×C89—22no—
110C4×C89—42no—
111C4×C89C23×C411yescharacteristic
112C4×C89C2×#4111yescharacteristic
113Dic89—22no—
114Dic89—42no—
115Dic89C4×D412yes—
116C2×C89—44no—
117C2×C89C2×C4×D411yescharacteristic
118C2×C89#57612yes—
119D89—22no—
120D89—44no—
121#2948—891nomaximal, Sylow
122C89#294811yescharacteristic, complemented, Sylow
123C22×D8—891no—
124#518—892no—
125#442—891no—
126#442—891no—
127#442—891no—
128#442D8911yescharacteristic, complemented
129C4×D8—892no—
130C4×D8—892no—
131#427—891no—
132#418—892no—
133#405—891no—
134C22×D4—892no—
135C2×D8—892no—
136C2×D8—898no—
137C2×D8—891no—
138C2×D8C2×D8911yescharacteristic
139C2×M16—891no—
140C22×C8—891no—
141C4×D4—892no—
142C4×D4—892no—
143C4×D4—892no—
144C4×D4—1782no—
145C4×D4—1782no—
146C4×D4C2×D8912yescomplemented
147#117—891no—
148#117—892no—
149C2×C22⋊C4—1782no—
150C2×C22⋊C4—1782no—
151#107—892no—
152#106—891no—
153#106C2×D8911yescharacteristic, complemented
154#102—892no—
155#102—892no—
156#102—892no—
157#102C2×D8912yescomplemented
158#97—891no—
159#97C2×D8911yescharacteristic, complemented
160C4×C8—891no—
161C4×C8—891no—
162C24—1782no—
163C2×D4—898no—
164C2×D4—892no—
165C2×D4—1784no—
166C2×D4—1782no—
167C2×D4C22×D8912yes—
168C22×C4—22no—
169C22×C4—891no—
170C22×C4—1782no—
171C22×C4—1782no—
172C22×C4—1782no—
173D8—898no—
174D8—894no—
175D8C4×D8914yescomplemented
176M16—1782no—
177C2×C8—891no—
178C2×C8—894no—
179C2×C8—891no—
180C2×C8C22×D8911yescharacteristic
181C2×C8C22×D8911yescharacteristic
182C4⋊C4—892no—
183C4⋊C4—892no—
184C4⋊C4C22×D8912yes—
185C22⋊C4—22no—
186C22⋊C4—892no—
187C22⋊C4—1782no—
188C22⋊C4—1782no—
189C22⋊C4—1782no—
190C22⋊C4—1782no—
191C42—891no—
192C42—1782no—
193C42C22×D8911yescharacteristic
194C23—22no—
195C23—891no—
196C23—1788no—
197C23—1782no—
198C23—7122no—
199C23—7122no—
200D4—22no—
201D4—894no—
202D4—1788no—
203D4—1782no—
204D4C2×C4×D8914yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—891no—
208C2×C4—892no—
209C2×C4—892no—
210C2×C4—892no—
211C2×C4—1782no—
212C2×C4—7122no—
213C2×C4—7122no—
214C2×C4—7122no—
215C2×C4D4×D8912yes—
216C2×C4C23×D8911yescharacteristic
217C8—21no—
218C8—892no—
219C8—1781no—
220C8C2×C4×D8912yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—892no—
225C22—3562no—
226C22—3562no—
227C22—1784no—
228C22—1782no—
229C22—7128no—
230C22C2×D4×D8911yescharacteristic
231C4—22no—
232C4—42no—
233C4—892no—
234C4—3562no—
235C4—1782no—
236C4C22×C4×D8911yescharacteristic
237C4#41×D8911yescharacteristic
238C2—44no—
239C2—3564no—
240C2—1782no—
241C2C4×D4×D8911yescharacteristic
242C2#1915240212yes—
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
hypocenterC89#2948
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. #19152070C2semidirect
3. #19151711C2semidirect
4. #19151710C2semidirect
5. #19151709C2semidirect
6. C4×#13083559C2semidirect
7. #19151678C2semidirect
8. #19151633C2semidirect
9. #19151601C2semidirect
10. #19151555C2semidirect
11. #442×C89C2semidirect
15. D8×D89C4semidirect
18. C4×D356C22semidirect
19. D4×Dic89C22semidirect
20. #15667974C22semidirect
27. #15667945C22semidirect
28. #15667944C22semidirect
29. #15667934C22semidirect
30. #15667933C22semidirect
31. #15667932C22semidirect
32. #15667922C22semidirect
33. C4×#10623494C22semidirect
34. C8×Dic89C22semidirect
36. C4×D4×C89C22semidirect
37. #106×C89C22semidirect
38. #102×C89C22semidirect
39. #97×C89C22semidirect
44. D4×D89C2×C4semidirect
49. D712C2×C4semidirect
50. #13083559C2×C4semidirect
54. C8×D89C2×C4semidirect
66. D8×C89C2×C4semidirect
122. C89#2948semidirect
128. #442D89semidirect
146. C4×D4C2×D89semidirect
153. #106C2×D89semidirect
157. #102C2×D89semidirect
159. #97C2×D89semidirect
175. D8C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D892
#191520702
#191517112
#191517102
#191517092
C4×#130835592
#191516782
#191516332
#191516012
#191515552
#442×C892
#294889