Finite Group Databasebeta

← #26031048

Subgroups — #26031048

Order 11392.

514 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#121×D89C212yesmaximal, complemented
2#19151918C212yesmaximal, complemented
3#19151915C212yesmaximal, complemented
4#19151851C211yesmaximal, characteristic, complemented
5#19151849C212yesmaximal, complemented
6#19151733C212yesmaximal, complemented
7#19151730C212yesmaximal, complemented
8#19151561C211yesmaximal, characteristic, complemented
9#469×C89C211yesmaximal, characteristic, complemented
10C2×D4×D89—22no—
11C2×D4×D89C2212yescomplemented
12C22×C4×D89C2211yescharacteristic
13C2×D712C2211yescharacteristic, complemented
14C2×#13083559C2212yescomplemented
15C2×#13083558C2211yescharacteristic, complemented
16#15667987C2212yes—
17#15667986C2212yescomplemented
18#15667985—22no—
19#15667984—22no—
20#15667983C2212yes—
21C4⋊C4×D89C2212yescomplemented
22C22⋊C4×D89—22no—
23#15667944C2211yescharacteristic, complemented
24#15667943C2212yescomplemented
25#15667934C2212yescomplemented
26#15667933C2212yescomplemented
27#15667932C2212yescomplemented
28#15667924C2212yescomplemented
29#15667924C2212yescomplemented
30C2×D8×C89C2211yescharacteristic, complemented
31C2×M16×C89C2211yescharacteristic, complemented
32#121×C89C2212yescomplemented
33#106×C89C2211yescharacteristic, complemented
34#102×C89C2212yescomplemented
35C23×D89—22no—
36C23×D89D411yescharacteristic
37C2×D356—22no—
38C2×D356C2312yes—
39C2×C22⋊D89—22no—
40C2×C22⋊D89—22no—
41C2×C22⋊D89—22no—
42D4×D89—42no—
43D4×D89—42no—
44D4×D89—48no—
45C22×Dic89D411yescharacteristic
46C2×C4×D89—22no—
47C2×C4×D89—41no—
48C2×C4×D89—41no—
49C2×C4×D89D412yes—
50C2×C4×D89C2312yes—
51D712—41no—
52#13083559—42no—
53#13083558—41no—
54C2×#10623494C2312yes—
55C4⋊Dic89C2312yes—
56#13083553—22no—
57C22⋊Dic89—22no—
58#13083551—22no—
59#13083551—22no—
60C2×D4×C89—22no—
61C2×D4×C89C2312yes—
62C22×C4×C89C2311yescharacteristic
63D8×C89—41no—
64M16×C89—41no—
65C2×C8×C89C2311yescharacteristic
66C2×C8×C89C2311yescharacteristic
67C4⋊C4×C89C2312yes—
68C22⋊C4×C89—22no—
69C23×C89—22no—
70C23×C89C2×D411yescharacteristic
71C22×D89—24no—
72C22×D89—22no—
73C22×D89—41no—
74C22×D89—44no—
75C22×D89—44no—
76C22×D89—44no—
77C22×D89C2×D412yes—
78D4×C89—22no—
79D4×C89—22no—
80D4×C89—44no—
81C2×C4×C89—21no—
82C2×C4×C89—21no—
83C2×C4×C89—22no—
84C2×C4×C89C2×D411yescharacteristic
85C2×C4×C89C2411yescharacteristic
86C22⋊D89—44no—
87C22⋊D89—44no—
88C22⋊D89—44no—
89C2×Dic89—22no—
90C2×Dic89—41no—
91C2×Dic89C2×D412yes—
92D356—22no—
93D356—22no—
94D356—44no—
95C4×D89—22no—
96C4×D89—22no—
97C4×D89—42no—
98C4×D89—44no—
99C8×C89—21no—
100C8×C89—21no—
101#10623494—22no—
102C22×C89—21no—
103C22×C89—22no—
104C22×C89—42no—
105C22×C89—42no—
106C22×C89—42no—
107C22×C89C22×D411yescharacteristic
108C2×D89—22no—
109C2×D89—22no—
110C2×D89—44no—
111C2×D89—42no—
112C2×D89—42no—
113C2×D89—42no—
114C2×D89—88no—
115C2×D89AGL(1,ℤ/8)14yes—
116C4×C89—21no—
117C4×C89—42no—
118C4×C89H(5,𝔽2)11yescharacteristic
119C4×C89H(5,𝔽2)11yescharacteristic
120Dic89—22no—
121Dic89—42no—
122C2×C89—41no—
123C2×C89—82no—
124C2×C89#53411yescharacteristic
125C2×C89C2×AGL(1,ℤ/8)12yes—
126D89—24no—
127D89—82no—
128#3192—891nomaximal, Sylow
129C89#319211yescharacteristic, complemented, Sylow
130C2×#121—892no—
131#481—892no—
132#481—892no—
133#469—891no—
134#469—892no—
135#469D8911yescharacteristic, complemented
136#447—892no—
137#447—892no—
138#407—891no—
139C22×D4—892no—
140C22×D4—1782no—
141C23×C4—891no—
142C2×D8—892no—
143C2×D8—891no—
144C2×D8C2×D8911yescharacteristic, complemented
145C2×M16—891no—
146C2×M16C2×D8911yescharacteristic, complemented
147#121—892no—
148#121—892no—
149#121—892no—
150#121—1782no—
151#121—1782no—
152#121C2×D8912yescomplemented
153C2×C4⋊C4—892no—
154C2×C22⋊C4—1782no—
155#106—891no—
156#106—892no—
157#106C2×D8911yescharacteristic, complemented
158#102—892no—
159#102—892no—
160#102—892no—
161#102C2×D8912yescomplemented
162C22⋊C8—892no—
163C22⋊C8—892no—
164C24—891no—
165C24—1782no—
166C2×D4—22no—
167C2×D4—892no—
168C2×D4—3568no—
169C2×D4—3562no—
170C2×D4—3562no—
171C2×D4—1782no—
172C2×D4—1782no—
173C2×D4—1782no—
174C2×D4—1782no—
175C2×D4C22×D8912yes—
176C22×C4—891no—
177C22×C4—892no—
178C22×C4—892no—
179C22×C4—3561no—
180C22×C4—3561no—
181C22×C4—1782no—
182C22×C4C22×D8911yescharacteristic
183D8—41no—
184D8—3561no—
185D8—3562no—
186M16—41no—
187M16—3561no—
188C2×C8—892no—
189C2×C8C22×D8911yescharacteristic
190C2×C8C22×D8911yescharacteristic
191C4⋊C4—892no—
192C4⋊C4—1782no—
193C4⋊C4C22×D8912yes—
194C22⋊C4—22no—
195C22⋊C4—1782no—
196C22⋊C4—1782no—
197C22⋊C4—1782no—
198C23—22no—
199C23—892no—
200C23—3561no—
201C23—3564no—
202C23—3564no—
203C23—3564no—
204C23—1784no—
205C23—1782no—
206C23D4×D8911yescharacteristic
207D4—22no—
208D4—22no—
209D4—44no—
210D4—3564no—
211D4—3564no—
212D4—3564no—
213D4—3564no—
214D4—1782no—
215D4—1782no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—892no—
220C2×C4—3562no—
221C2×C4—3564no—
222C2×C4—3561no—
223C2×C4—1782no—
224C2×C4—1782no—
225C2×C4—1782no—
226C2×C4D4×D8911yescharacteristic
227C2×C4C23×D8911yescharacteristic
228C8—21no—
229C8—21no—
230C8—1782no—
231C22—21no—
232C22—22no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—894no—
237C22—3564no—
238C22—3562no—
239C22—3562no—
240C22—3562no—
241C22—1782no—
242C22—1782no—
243C22—7128no—
244C22C2×D4×D8911yescharacteristic
245C4—21no—
246C4—42no—
247C4—3562no—
248C4—1782no—
249C4#1566805711yescharacteristic
250C4#1566805811yescharacteristic
251C2—41no—
252C2—82no—
253C2—1784no—
254C2—7122no—
255C2#1915215611yescharacteristic
256C2AGL(1,ℤ/8)×D8912yes—
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#469×C89C2
socleC22×C89C22×D4
hypercenter#469D89
hypocenterC89#3192
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. #121×D89C2semidirect
2. #19151918C2semidirect
3. #19151915C2semidirect
4. #19151851C2semidirect
5. #19151849C2semidirect
6. #19151733C2semidirect
7. #19151730C2semidirect
8. #19151561C2semidirect
9. #469×C89C2semidirect
11. C2×D4×D89C22semidirect
13. C2×D712C22semidirect
14. C2×#13083559C22semidirect
15. C2×#13083558C22semidirect
17. #15667986C22semidirect
21. C4⋊C4×D89C22semidirect
23. #15667944C22semidirect
24. #15667943C22semidirect
25. #15667934C22semidirect
26. #15667933C22semidirect
27. #15667932C22semidirect
28. #15667924C22semidirect
29. #15667924C22semidirect
30. C2×D8×C89C22semidirect
31. C2×M16×C89C22semidirect
32. #121×C89C22semidirect
33. #106×C89C22semidirect
34. #102×C89C22semidirect
129. C89#3192semidirect
135. #469D89semidirect
144. C2×D8C2×D89semidirect
146. C2×M16C2×D89semidirect
152. #121C2×D89semidirect
157. #106C2×D89semidirect
161. #102C2×D89semidirect

Maximal subgroups

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

subgroupindex
#121×D892
#191519182
#191519152
#191518512
#191518492
#191517332
#191517302
#191515612
#469×C892
#319289