Finite Group Databasebeta

← #26030999

Subgroups — #26030999

Order 11392.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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#19151913C212yesmaximal, complemented
3#19151910C212yesmaximal, complemented
4#19151834C211yesmaximal, characteristic, complemented
5#19151832C212yesmaximal, complemented
6#19151733C212yesmaximal, complemented
7#19151730C212yesmaximal, complemented
8C2×#15667924C211yesmaximal, characteristic, complemented
9#466×C89C211yesmaximal, characteristic, complemented
10C2×D4×D89—22no—
11C2×D4×D89C2212yescomplemented
12C22×C4×D89C2211yescharacteristic
13C2×D712C2211yescharacteristic, complemented
14C2×#13083559C2212yescomplemented
15C22×#10623494C2211yescharacteristic, complemented
16#15667987C2212yes—
17#15667986C2212yescomplemented
18#15667985—22no—
19#15667984—22no—
20#15667983C2212yes—
21C4⋊C4×D89C2212yescomplemented
22C22⋊C4×D89—22no—
23#15667946C2211yescharacteristic, complemented
24#15667945C2212yescomplemented
25#15667934C2212yescomplemented
26#15667933C2212yescomplemented
27#15667932C2212yescomplemented
28#15667924C2212yescomplemented
29#15667924C2212yescomplemented
30C2×D8×C89C2211yescharacteristic, complemented
31C22×C8×C89C2211yescharacteristic, complemented
32#121×C89C2212yescomplemented
33#107×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—
53C2×#10623494—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—
64C2×C8×C89—41no—
65C2×C8×C89C2311yescharacteristic
66C2×C8×C89C2311yescharacteristic
67C4⋊C4×C89C2312yes—
68C22⋊C4×C89—22no—
69C23×C89—22no—
70C23×C89C2×D411yescharacteristic
71C22×D89—22no—
72C22×D89—41no—
73C22×D89—41no—
74C22×D89—44no—
75C22×D89—44no—
76C22×D89—44no—
77C22×D89D814yescomplemented
78C22×D89C2×D412yes—
79D4×C89—22no—
80D4×C89—22no—
81D4×C89—44no—
82C2×C4×C89—21no—
83C2×C4×C89—21no—
84C2×C4×C89—22no—
85C2×C4×C89C2×D411yescharacteristic
86C2×C4×C89C2411yescharacteristic
87C22⋊D89—44no—
88C22⋊D89—44no—
89C22⋊D89—44no—
90C2×Dic89—22no—
91C2×Dic89—41no—
92C2×Dic89C2×D412yes—
93D356—22no—
94D356—22no—
95D356—44no—
96C4×D89—22no—
97C4×D89—22no—
98C4×D89—42no—
99C4×D89—44no—
100C8×C89—21no—
101C8×C89—21no—
102#10623494—22no—
103C22×C89—21no—
104C22×C89—21no—
105C22×C89—42no—
106C22×C89—42no—
107C22×C89—42no—
108C22×C89C2×D812yes—
109C22×C89C22×D411yescharacteristic
110C2×D89—22no—
111C2×D89—22no—
112C2×D89—44no—
113C2×D89—42no—
114C2×D89—42no—
115C2×D89—42no—
116C2×D89—88no—
117C2×D89C2×D814yes—
118C4×C89—21no—
119C4×C89—42no—
120C4×C89H(5,𝔽2)11yescharacteristic
121C4×C89H(5,𝔽2)11yescharacteristic
122Dic89—22no—
123Dic89—42no—
124C2×C89—22no—
125C2×C89—82no—
126C2×C89#53411yescharacteristic
127C2×C89C22×D811yescharacteristic
128C2×C89#57511yescharacteristic
129D89—24no—
130D89—82no—
131#3186—891nomaximal, Sylow
132C89#318611yescharacteristic, complemented, Sylow
133C2×#121—892no—
134#480—892no—
135#480—892no—
136#466—891no—
137#466—892no—
138#466D8911yescharacteristic, complemented
139#447—892no—
140#447—892no—
141C2×C22⋊C8—891no—
142C22×D4—892no—
143C22×D4—1782no—
144C23×C4—891no—
145C2×D8—892no—
146C2×D8—891no—
147C2×D8C2×D8911yescharacteristic, complemented
148C22×C8—891no—
149C22×C8C2×D8911yescharacteristic, complemented
150#121—892no—
151#121—892no—
152#121—892no—
153#121—1782no—
154#121—1782no—
155#121C2×D8912yescomplemented
156C2×C4⋊C4—892no—
157C2×C22⋊C4—1782no—
158#107—891no—
159#107—892no—
160#107C2×D8911yescharacteristic, complemented
161#102—892no—
162#102—892no—
163#102—892no—
164#102C2×D8912yescomplemented
165C22⋊C8—892no—
166C22⋊C8—892no—
167C24—891no—
168C24—1782no—
169C2×D4—22no—
170C2×D4—892no—
171C2×D4—3568no—
172C2×D4—3562no—
173C2×D4—3562no—
174C2×D4—1782no—
175C2×D4—1782no—
176C2×D4—1782no—
177C2×D4—1782no—
178C2×D4C22×D8912yes—
179C22×C4—891no—
180C22×C4—892no—
181C22×C4—892no—
182C22×C4—3561no—
183C22×C4—3561no—
184C22×C4—1782no—
185C22×C4C22×D8911yescharacteristic
186D8—41no—
187D8—3561no—
188D8—3562no—
189C2×C8—41no—
190C2×C8—892no—
191C2×C8—3561no—
192C2×C8C22×D8911yescharacteristic
193C2×C8C22×D8911yescharacteristic
194C4⋊C4—892no—
195C4⋊C4—1782no—
196C4⋊C4C22×D8912yes—
197C22⋊C4—22no—
198C22⋊C4—1782no—
199C22⋊C4—1782no—
200C22⋊C4—1782no—
201C23—22no—
202C23—894no—
203C23—892no—
204C23—3561no—
205C23—3561no—
206C23—3564no—
207C23—3564no—
208C23—3564no—
209C23—1782no—
210C23D4×D8911yescharacteristic
211D4—22no—
212D4—22no—
213D4—44no—
214D4—3564no—
215D4—3564no—
216D4—3564no—
217D4—3564no—
218D4—1782no—
219D4—1782no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—892no—
224C2×C4—3562no—
225C2×C4—3564no—
226C2×C4—3561no—
227C2×C4—1782no—
228C2×C4—1782no—
229C2×C4—1782no—
230C2×C4D4×D8911yescharacteristic
231C2×C4C23×D8911yescharacteristic
232C8—21no—
233C8—21no—
234C8—1782no—
235C22—21no—
236C22—21no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—894no—
241C22—3564no—
242C22—3562no—
243C22—3562no—
244C22—3562no—
245C22—1782no—
246C22—1782no—
247C22—7128no—
248C22D8×D8912yes—
249C22C2×D4×D8911yescharacteristic
250C4—21no—
251C4—42no—
252C4—3562no—
253C4—1782no—
254C4#1566805711yescharacteristic
255C4#1566805811yescharacteristic
256C2—22no—
257C2—82no—
258C2—1784no—
259C2—7122no—
260C2#1915215611yescharacteristic
261C2C2×D8×D8911yescharacteristic
262C2#1915239511yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#466×C89C2
socleC22×C89C22×D4
hypercenter#466D89
hypocenterC89#3186
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #121×D89C2semidirect
2. #19151913C2semidirect
3. #19151910C2semidirect
4. #19151834C2semidirect
5. #19151832C2semidirect
6. #19151733C2semidirect
7. #19151730C2semidirect
8. C2×#15667924C2semidirect
9. #466×C89C2semidirect
11. C2×D4×D89C22semidirect
13. C2×D712C22semidirect
14. C2×#13083559C22semidirect
15. C22×#10623494C22semidirect
17. #15667986C22semidirect
21. C4⋊C4×D89C22semidirect
23. #15667946C22semidirect
24. #15667945C22semidirect
25. #15667934C22semidirect
26. #15667933C22semidirect
27. #15667932C22semidirect
28. #15667924C22semidirect
29. #15667924C22semidirect
30. C2×D8×C89C22semidirect
31. C22×C8×C89C22semidirect
32. #121×C89C22semidirect
33. #107×C89C22semidirect
34. #102×C89C22semidirect
77. C22×D89D8semidirect
132. C89#3186semidirect
138. #466D89semidirect
147. C2×D8C2×D89semidirect
149. C22×C8C2×D89semidirect
155. #121C2×D89semidirect
160. #107C2×D89semidirect
164. #102C2×D89semidirect

Maximal subgroups

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

subgroupindex
#121×D892
#191519132
#191519102
#191518342
#191518322
#191517332
#191517302
C2×#156679242
#466×C892
#318689