Finite Group Databasebeta

← #26030719

Subgroups — #26030719

Order 11392.

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

normal subgroups only

This group has 572 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×#15668043C211yesmaximal, characteristic, complemented
2C2×#15668040C211yesmaximal, characteristic, complemented
3C2×#15668037C211yesmaximal, characteristic, complemented
4#19152144C211yesmaximal, characteristic, complemented
5C2×#15668001C211yesmaximal, characteristic, complemented
6#19151991C212yesmaximal, complemented
7#19151984C212yesmaximal, complemented
8#19151983C212yesmaximal, complemented
9#19151979C212yesmaximal, complemented
10M16×Dic89C211yesmaximal, characteristic, complemented
11C2×#137×C89C211yesmaximal, characteristic, complemented
12C2×#13083574C2211yescharacteristic
13C22×D356C2211yescharacteristic
14#15668043—24no—
15#15668040—24no—
16#15668037—24no—
17C2×#13083564C2212yescomplemented
18C2×#13083563C2212yes—
19C2×#13083561C2212yes—
20C2×#13083561C2212yescomplemented
21C2×D712C2212yes—
22C2×#13083559C2212yes—
23C2×#13083558C2211yescharacteristic
24#15668010C2211yescharacteristic, complemented
25#15668008C2211yescharacteristic, complemented
26#15668001—22no—
27#15668001C2212yes—
28#15668001C2212yes—
29#15668001C2211yescharacteristic, complemented
30#15667999C2211yescharacteristic, complemented
31#15667984—22no—
32C4×C22⋊D89—22no—
33C2×#13083551—22no—
34C2×C4×Dic89C2211yescharacteristic
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—22no—
54C22×Dic89D412yes—
55C2×C4×D89—21no—
56#13083564—24no—
57#13083563—24no—
58#13083561—24no—
59#13083561—24no—
60D712—24no—
61#13083559—24no—
62#13083558D414yescomplemented
63C2×#10623494C2312yes—
64#13083553—22no—
65C22⋊Dic89—22no—
66#13083551—22no—
67#13083551—24no—
68#13083551—24no—
69C4×Dic89D412yes—
70C4×Dic89C2311yescharacteristic
71C4×Dic89C2311yescharacteristic
72#41×C89—22no—
73#41×C89—22no—
74C2×Q8×C89—21no—
75C2×Q8×C89—22no—
76C2×Q8×C89—22no—
77C2×Q8×C89C2312yes—
78C2×Q8×C89C2311yescharacteristic
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—22no—
91C22×D89—21no—
92C22×D89—44no—
93C22×D89—42no—
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—44no—
111C22⋊D89—42no—
112C2×Dic89—21no—
113C2×Dic89—42no—
114C2×Dic89C2×D412yes—
115C2×Dic89C2×D412yes—
116D356—22no—
117D356—21no—
118D356—22no—
119D356—21no—
120D356—42no—
121C4×D89—42no—
122Dic178—21no—
123Dic178—21no—
124C8×C89C2×D414yes—
125#10623494C2×D414yes—
126C22×C89—22no—
127C22×C89—41no—
128C22×C89—42no—
129C22×C89#12712yes—
130C22×C89C22×D411yescharacteristic
131C2×D89—41no—
132C2×D89—42no—
133C2×D89—42no—
134C2×D89—44no—
135C2×D89—84no—
136C4×C89—41no—
137C4×C89—42no—
138C4×C89#12712yes—
139C4×C89C22×D411yescharacteristic
140C4×C89C22×D411yescharacteristic
141Dic89—22no—
142Dic89—22no—
143Dic89—41no—
144C2×C89—22no—
145C2×C89—81no—
146C2×C89C2×#12711yescharacteristic
147C2×C89#57512yes—
148D89—81no—
149D89—82no—
150#3153—891nomaximal, Sylow
151C89#315311yescharacteristic, complemented, Sylow
152C2×#137—891no—
153C2×#137D8911yescharacteristic, complemented
154C2×AGL(1,ℤ/8)—891no—
155C2×AGL(1,ℤ/8)—891no—
156#532—891no—
157C2×#124—891no—
158#497—892no—
159#496—892no—
160#495—892no—
161#495—892no—
162C4×M16—891no—
163C2×#41—891no—
164C2×#41C2×D8911yescharacteristic
165C22×Q8C2×D8911yescharacteristic
166C22×D4—891no—
167#137—24no—
168#137—1784no—
169AGL(1,ℤ/8)—1784no—
170AGL(1,ℤ/8)—1784no—
171C2×Q16—892no—
172C2×Q16C2×D8912yescomplemented
173C2×SD16—892no—
174C2×SD16—892no—
175C2×SD16—892no—
176C2×SD16C2×D8912yescomplemented
177C2×D8—892no—
178C2×D8—892no—
179C2×M16—891no—
180C2×M16C2×D8911yescharacteristic
181C4⋊Q8—891no—
182#127—891no—
183#124—892no—
184#124—892no—
185#124—891no—
186#124—891no—
187#124—1782no—
188#121—1782no—
189C4×D4—1782no—
190C2×C22⋊C4—1782no—
191C2×C42—891no—
192#97—892no—
193C4×C8—892no—
194C24—1781no—
195#41—22no—
196#41—22no—
197#41—1782no—
198#41—1782no—
199C2×Q8—21no—
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—891no—
203C2×Q8C22×D8912yes—
204C2×Q8C22×D8911yescharacteristic
205C2×D4—21no—
206C2×D4—892no—
207C2×D4—891no—
208C2×D4—1782no—
209C2×D4—1781no—
210C2×D4—1781no—
211C2×D4—1782no—
212C2×D4—1782no—
213C2×D4C22×D8911yescharacteristic
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—892no—
217C22×C4—1781no—
218C22×C4C22×D8911yescharacteristic
219Q16—24no—
220Q16—1784no—
221SD16—24no—
222SD16—1784no—
223SD16—1784no—
224SD16—1784no—
225D8—1784no—
226D8—1784no—
227M16—894no—
228M16C22⋊D8914yescomplemented
229C2×C8—892no—
230C2×C8C22×D8912yes—
231C4⋊C4—1782no—
232C22⋊C4—1784no—
233C22⋊C4—1784no—
234C22⋊C4—1782no—
235C22⋊C4—1782no—
236C42—892no—
237C42—891no—
238C42—891no—
239C23—21no—
240C23—3564no—
241C23—3562no—
242C23—1782no—
243C23—1781no—
244C23D4×D8911yescharacteristic
245Q8—21no—
246Q8—22no—
247Q8—22no—
248Q8—21no—
249Q8—42no—
250Q8—1781no—
251Q8—1781no—
252D4—21no—
253D4—21no—
254D4—42no—
255D4—3562no—
256D4—3564no—
257D4—3562no—
258D4—1782no—
259D4—1781no—
260D4—1781no—
261D4—1782no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—892no—
267C2×C4—892no—
268C2×C4—3562no—
269C2×C4—3562no—
270C2×C4—1781no—
271C2×C4D4×D8911yescharacteristic
272C2×C4D4×D8912yes—
273C2×C4C2×C22⋊D8912yes—
274C2×C4C23×D8911yescharacteristic
275C8—894no—
276C8C2×C22⋊D8914yes—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—3561no—
281C22—3562no—
282C22—3562no—
283C22—3564no—
284C22—7124no—
285C22#1566800812yes—
286C22C2×D4×D8911yescharacteristic
287C4—41no—
288C4—42no—
289C4—3561no—
290C4—1782no—
291C4—1782no—
292C4#1566800812yes—
293C4C2×D4×D8911yescharacteristic
294C4C22×C22⋊D8911yescharacteristic
295C2—22no—
296C2—81no—
297C2—7121no—
298C2—7122no—
299C2C2×#1566800811yescharacteristic
300C2#1915239712yes—
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC2×#137×C89C2
socleC22×C89C22×D4
hypercenterC2×#137D89
hypocenterC89#3153
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×#15668043C2semidirect
2. C2×#15668040C2semidirect
3. C2×#15668037C2semidirect
4. #19152144C2semidirect
5. C2×#15668001C2semidirect
6. #19151991C2semidirect
7. #19151984C2semidirect
8. #19151983C2semidirect
9. #19151979C2semidirect
10. M16×Dic89C2semidirect
11. C2×#137×C89C2semidirect
17. C2×#13083564C22semidirect
20. C2×#13083561C22semidirect
24. #15668010C22semidirect
25. #15668008C22semidirect
29. #15668001C22semidirect
30. #15667999C22semidirect
35. #15667922C22semidirect
36. C8×Dic89C22semidirect
40. C2×Q16×C89C22semidirect
41. C2×SD16×C89C22semidirect
62. #13083558D4semidirect
86. M16×C89D4semidirect
151. C89#3153semidirect
153. C2×#137D89semidirect
172. C2×Q16C2×D89semidirect
176. C2×SD16C2×D89semidirect
228. M16C22⋊D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156680432
C2×#156680402
C2×#156680372
#191521442
C2×#156680012
#191519912
#191519842
#191519832
#191519792
M16×Dic892
C2×#137×C892
#315389