Finite Group Databasebeta

← #26030731

Subgroups — #26030731

Order 11392.

564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15668040C211yesmaximal, characteristic, complemented
2C2×#15668032C211yesmaximal, characteristic, complemented
3C22×#13083561C211yesmaximal, characteristic, complemented
4#19152172C211yesmaximal, characteristic, complemented
5#19152162C211yesmaximal, characteristic, complemented
6#19151991C212yesmaximal, complemented
7#19151984C212yesmaximal, complemented
8#19151983C212yesmaximal, complemented
9#19151969C212yesmaximal, complemented
10#19151556C211yesmaximal, characteristic, complemented
11C2×#137×C89C211yesmaximal, characteristic, complemented
12C2×#13083574C2211yescharacteristic
13C22×D356C2211yescharacteristic
14#15668040—24no—
15#15668032—24no—
16C2×#13083564C2211yescharacteristic, complemented
17C2×#13083563C2212yes—
18C2×#13083562C2211yescharacteristic, complemented
19C2×#13083561—24no—
20C2×#13083561C2212yes—
21C2×#13083561C2212yes—
22C2×#13083561C2211yescharacteristic, complemented
23C2×D712C2212yes—
24C2×#13083559C2211yescharacteristic, complemented
25C22×#10623494C2211yescharacteristic
26#15668010C2212yescomplemented
27#15668008C2212yes—
28#15668001C2212yes—
29#15668001C2212yescomplemented
30#15667995—22no—
31#15667988—22no—
32#15667986—22no—
33#15667980—22no—
34#15667971C2211yescharacteristic
35#15667922C2212yescomplemented
36C8×Dic89C2212yescomplemented
37C2×#41×C89C2211yescharacteristic
38C22×Q8×C89C2211yescharacteristic
39#137×C89—24no—
40C2×Q16×C89C2212yescomplemented
41C2×SD16×C89C2212yescomplemented
42C2×M16×C89C2211yescharacteristic
43C23×D89—21no—
44#13083574—22no—
45#13083574—22no—
46C2×Dic178C2311yescharacteristic
47C2×D356—22no—
48C2×D356—22no—
49C2×D356—21no—
50C2×D356C2312yes—
51C2×D356C2311yescharacteristic
52C2×C22⋊D89—21no—
53C2×C22⋊D89—24no—
54C2×C4×D89—21no—
55#13083564—22no—
56#13083563—24no—
57#13083562—22no—
58#13083561—24no—
59#13083561—24no—
60#13083561—22no—
61D712—24no—
62#13083559—22no—
63C2×#10623494D414yescomplemented
64C2×#10623494C2311yescharacteristic
65C2×#10623494C2311yescharacteristic
66C4⋊Dic89D412yes—
67#13083553—24no—
68C22⋊Dic89D412yes—
69#13083551—24no—
70#13083551—24no—
71C4×Dic89C2312yes—
72#41×C89—22no—
73#41×C89—22no—
74C2×Q8×C89—21no—
75C2×Q8×C89—22no—
76C2×Q8×C89—22no—
77C2×Q8×C89C2311yescharacteristic
78C2×Q8×C89C2312yes—
79C2×D4×C89—21no—
80C2×D4×C89C2311yescharacteristic
81C22×C4×C89—21no—
82C22×C4×C89—21no—
83C22×C4×C89C2311yescharacteristic
84Q16×C89—24no—
85SD16×C89—24no—
86M16×C89D414yescomplemented
87C2×C8×C89C2312yes—
88C23×C89—21no—
89C23×C89C2×D411yescharacteristic
90C22×D89—21no—
91C22×D89—22no—
92C22×D89—42no—
93C22×D89—82no—
94Q8×C89—22no—
95Q8×C89—21no—
96Q8×C89—22no—
97Q8×C89—21no—
98Q8×C89—42no—
99D4×C89—21no—
100D4×C89—21no—
101D4×C89—42no—
102C2×C4×C89—21no—
103C2×C4×C89—22no—
104C2×C4×C89—42no—
105C2×C4×C89—42no—
106C2×C4×C89C2×D411yescharacteristic
107C2×C4×C89C2×D412yes—
108C2×C4×C89C2×D412yes—
109C2×C4×C89C2411yescharacteristic
110C22⋊D89—42no—
111C22⋊D89—84no—
112C2×Dic89—21no—
113C2×Dic89C2×D414yes—
114D356—21no—
115D356—21no—
116D356—22no—
117D356—22no—
118D356—42no—
119C4×D89—42no—
120Dic178—21no—
121Dic178—21no—
122C8×C89C2×D414yes—
123#10623494C2×D412yes—
124#10623494C2×D412yes—
125C22×C89—22no—
126C22×C89—41no—
127C22×C89—42no—
128C22×C89#12712yes—
129C22×C89C22×D411yescharacteristic
130C2×D89—41no—
131C2×D89—42no—
132C2×D89—44no—
133C2×D89—42no—
134C2×D89—84no—
135C4×C89—41no—
136C4×C89—42no—
137C4×C89#12712yes—
138C4×C89C22×D411yescharacteristic
139C4×C89C22×D411yescharacteristic
140Dic89—24no—
141Dic89—41no—
142C2×C89—22no—
143C2×C89—81no—
144C2×C89C2×#12711yescharacteristic
145C2×C89#57712yes—
146D89—81no—
147D89—82no—
148#3154—891nomaximal, Sylow
149C89#315411yescharacteristic, complemented, Sylow
150C2×#137D8911yescharacteristic, complemented
151C2×AGL(1,ℤ/8)—891no—
152C2×#135—891no—
153C22×SD16—891no—
154#536—891no—
155#535—891no—
156#497—892no—
157#496—892no—
158#495—892no—
159#492—892no—
160#405—891no—
161C2×#41—891no—
162C2×#41C2×D8911yescharacteristic
163C22×Q8C2×D8911yescharacteristic
164C22×D4—891no—
165#137—24no—
166AGL(1,ℤ/8)—1784no—
167#135—1784no—
168C2×Q16—891no—
169C2×Q16C2×D8912yescomplemented
170C2×SD16—892no—
171C2×SD16—892no—
172C2×SD16—891no—
173C2×SD16—891no—
174C2×SD16—892no—
175C2×SD16—1784no—
176C2×SD16C2×D8912yescomplemented
177C2×D8—891no—
178C2×D8—892no—
179C2×M16C2×D8911yescharacteristic
180C22×C8—891no—
181C4⋊Q8—892no—
182#127—892no—
183#124—892no—
184#124—892no—
185#123—1782no—
186C22⋊Q8—1782no—
187#121—1782no—
188#120—1782no—
189#117—891no—
190#97—892no—
191C4×C8—892no—
192C24—1781no—
193#41—22no—
194#41—22no—
195#41—1782no—
196#41—1782no—
197C2×Q8—21no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—891no—
201C2×Q8C22×D8911yescharacteristic
202C2×Q8C22×D8912yes—
203C2×D4—21no—
204C2×D4—891no—
205C2×D4—892no—
206C2×D4—1784no—
207C2×D4—1781no—
208C2×D4—1781no—
209C2×D4—1782no—
210C2×D4—1782no—
211C2×D4C22×D8911yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—1781no—
215C22×C4C22×D8911yescharacteristic
216Q16—24no—
217Q16—1782no—
218SD16—24no—
219SD16—1782no—
220SD16—1784no—
221SD16—1784no—
222SD16—1782no—
223SD16—1784no—
224D8—1782no—
225D8—1784no—
226M16C22⋊D8914yescomplemented
227C2×C8—894no—
228C2×C8—891no—
229C2×C8—891no—
230C2×C8C22×D8912yes—
231C4⋊C4—892no—
232C4⋊C4—1784no—
233C22⋊C4—892no—
234C22⋊C4—1784no—
235C22⋊C4—1784no—
236C42—892no—
237C23—21no—
238C23—3562no—
239C23—1781no—
240C23—1782no—
241C23—7122no—
242C23D4×D8911yescharacteristic
243Q8—22no—
244Q8—21no—
245Q8—22no—
246Q8—21no—
247Q8—42no—
248Q8—1781no—
249Q8—1781no—
250D4—21no—
251D4—21no—
252D4—42no—
253D4—3562no—
254D4—3562no—
255D4—1781no—
256D4—1782no—
257D4—1781no—
258D4—1782no—
259D4—7124no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—894no—
265C2×C4—3562no—
266C2×C4—1781no—
267C2×C4D4×D8911yescharacteristic
268C2×C4D4×D8912yes—
269C2×C4C2×C22⋊D8912yes—
270C2×C4C23×D8911yescharacteristic
271C8—892no—
272C8—892no—
273C8C2×C22⋊D8914yes—
274C22—22no—
275C22—41no—
276C22—42no—
277C22—3561no—
278C22—3562no—
279C22—3564no—
280C22—3562no—
281C22—7124no—
282C22#1566800812yes—
283C22C2×D4×D8911yescharacteristic
284C4—41no—
285C4—42no—
286C4—3561no—
287C4—1784no—
288C4#1566800812yes—
289C4C2×D4×D8911yescharacteristic
290C4C22×C22⋊D8911yescharacteristic
291C2—22no—
292C2—81no—
293C2—7121no—
294C2—7122no—
295C2C2×#1566800811yescharacteristic
296C2#1915240712yes—
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC2×#137×C89C2
socleC22×C89C22×D4
hypercenterC2×#137D89
hypocenterC89#3154
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#15668040C2semidirect
2. C2×#15668032C2semidirect
3. C22×#13083561C2semidirect
4. #19152172C2semidirect
5. #19152162C2semidirect
6. #19151991C2semidirect
7. #19151984C2semidirect
8. #19151983C2semidirect
9. #19151969C2semidirect
10. #19151556C2semidirect
11. C2×#137×C89C2semidirect
16. C2×#13083564C22semidirect
18. C2×#13083562C22semidirect
22. C2×#13083561C22semidirect
24. C2×#13083559C22semidirect
26. #15668010C22semidirect
29. #15668001C22semidirect
35. #15667922C22semidirect
36. C8×Dic89C22semidirect
40. C2×Q16×C89C22semidirect
41. C2×SD16×C89C22semidirect
63. C2×#10623494D4semidirect
86. M16×C89D4semidirect
149. C89#3154semidirect
150. C2×#137D89semidirect
169. C2×Q16C2×D89semidirect
176. C2×SD16C2×D89semidirect
226. M16C22⋊D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156680402
C2×#156680322
C22×#130835612
#191521722
#191521622
#191519912
#191519842
#191519832
#191519692
#191515562
C2×#137×C892
#315489