Finite Group Databasebeta

← #26031847

Subgroups — #26031847

Order 11392.

546 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 125 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×#15668036C212yesmaximal, complemented
2#19152252C211yesmaximal, characteristic, complemented
3#19152233C211yesmaximal, characteristic, complemented
4#19151970C211yesmaximal, characteristic, complemented
5#19151843C212yesmaximal, complemented
6#19151804C211yesmaximal, characteristic, complemented
7#19151750C212yesmaximal, complemented
8#19151740C212yesmaximal, complemented
9C4×#13083559C211yesmaximal, characteristic, complemented
10#19151675C211yesmaximal, characteristic, complemented
11#459×C89C211yesmaximal, characteristic, complemented
12C2×#13083573C2212yescomplemented
13C2×D4×D89—21no—
14C2×D4×D89C2212yes—
15#15668036—28no—
16C2×#13083563C2212yes—
17C2×#13083562C2212yescomplemented
18C2×#13083562C2212yescomplemented
19C2×#13083559C2211yescharacteristic
20C2×#13083557C2212yescomplemented
21#15668012C2211yescharacteristic, complemented
22#15667996—22no—
23#15667992C2212yescomplemented
24#15667986—21no—
25#15667983—21no—
26#15667983C2212yes—
27#15667980—22no—
28C4×D356C2211yescharacteristic
29C4×D356C2211yescharacteristic
30C2×C4⋊Dic89—21no—
31#15667945C2211yescharacteristic, complemented
32#15667937C2212yescomplemented
33#15667933C2211yescharacteristic, complemented
34#15667932C2211yescharacteristic
35#15667924C2212yescomplemented
36C4×#10623494C2211yescharacteristic, complemented
37C2×D8×C89C2212yescomplemented
38#127×C89C2211yescharacteristic
39C4×D4×C89C2211yescharacteristic, complemented
40C4⋊C8×C89C2211yescharacteristic, complemented
41#102×C89C2212yescomplemented
42C23×D89—22no—
43#13083573—24no—
44#13083573—42no—
45C2×Dic178C2312yes—
46C2×D356D411yescharacteristic
47C2×D356C2311yescharacteristic
48C2×C22⋊D89—22no—
49C2×C22⋊D89—22no—
50C2×C22⋊D89—22no—
51D4×D89—24no—
52D4×D89—42no—
53D4×D89—44no—
54C22×Dic89—22no—
55C2×C4×D89—21no—
56C2×C4×D89C2312yes—
57#13083563—24no—
58#13083562—24no—
59#13083562—42no—
60#13083559D414yescomplemented
61#13083557—24no—
62C2×#10623494C2311yescharacteristic
63C2×#10623494C2311yescharacteristic
64C4⋊Dic89—21no—
65C4⋊Dic89—21no—
66C4⋊Dic89—22no—
67C4⋊Dic89D411yescharacteristic
68C4⋊Dic89C2311yescharacteristic
69C22⋊Dic89—22no—
70#13083551—22no—
71#13083551—21no—
72#13083551D412yes—
73C2×D4×C89—21no—
74C2×D4×C89—21no—
75C2×D4×C89C2312yes—
76C2×D4×C89C2311yescharacteristic
77C22×C4×C89—21no—
78D8×C89—24no—
79C2×C8×C89C2312yes—
80C4⋊C4×C89C2311yescharacteristic
81C22⋊C4×C89—21no—
82C42×C89C2311yescharacteristic
83C23×C89—21no—
84C23×C89—22no—
85C22×D89—21no—
86C22×D89—44no—
87C22×D89—44no—
88C22×D89—82no—
89C22×D89C2×D412yes—
90D4×C89—22no—
91D4×C89—21no—
92D4×C89—22no—
93D4×C89—42no—
94D4×C89—81no—
95D4×C89C2×D412yescomplemented
96C2×C4×C89—21no—
97C2×C4×C89—42no—
98C2×C4×C89C2×D411yescharacteristic
99C2×C4×C89C2×D411yescharacteristic
100C2×C4×C89C2411yescharacteristic
101C22⋊D89—44no—
102C22⋊D89—44no—
103C22⋊D89—44no—
104C2×Dic89—21no—
105C2×Dic89—22no—
106C2×Dic89—44no—
107C2×Dic89C2×D412yes—
108D356—22no—
109D356—21no—
110D356C2×D412yes—
111C4×D89—22no—
112C4×D89—22no—
113C4×D89—42no—
114Dic178—22no—
115Dic178—22no—
116C8×C89—22no—
117#10623494—21no—
118#10623494C2×D412yescomplemented
119C22×C89—22no—
120C22×C89—41no—
121C22×C89—41no—
122C22×C89—42no—
123C22×C89—42no—
124C22×C89—42no—
125C22×C89C22×D411yescharacteristic
126C2×D89—22no—
127C2×D89—22no—
128C2×D89—22no—
129C2×D89—22no—
130C2×D89—41no—
131C2×D89—41no—
132C2×D89—88no—
133C4×C89—21no—
134C4×C89—41no—
135C4×C89AGL(1,ℤ/8)12yescomplemented
136C4×C89C22×D411yescharacteristic
137C4×C89H(5,𝔽2)11yescharacteristic
138Dic89—22no—
139Dic89—42no—
140Dic89—41no—
141C2×C89—42no—
142C2×C89—82no—
143C2×C89D4211yescharacteristic
144C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
145C2×C89#57711yescharacteristic
146D89—42no—
147D89—42no—
148#3272—891nomaximal, Sylow
149C89#327211yescharacteristic, complemented, Sylow
150C2×AGL(1,ℤ/8)—892no—
151#547—891no—
152D42—891no—
153#492—891no—
154#468—892no—
155#461—891no—
156#459D8911yescharacteristic, complemented
157#450—892no—
158#449—892no—
159C4×D8—891no—
160#436—891no—
161C2×#41—892no—
162C22×D4—892no—
163C22×D4—1781no—
164AGL(1,ℤ/8)—1788no—
165C2×SD16—892no—
166C2×SD16—892no—
167C2×SD16—892no—
168C2×D8—891no—
169C2×D8C2×D8912yescomplemented
170C2×M16—892no—
171C4⋊Q8—891no—
172#127C2×D8911yescharacteristic
173#123—1782no—
174C22⋊Q8—892no—
175#121—892no—
176#121—1781no—
177#121—1781no—
178#120—1782no—
179C4×D4—891no—
180C4×D4—891no—
181C4×D4C2×D8911yescharacteristic, complemented
182C2×C4⋊C4—1781no—
183#107—891no—
184C4⋊C8C2×D8911yescharacteristic, complemented
185#103—892no—
186#102—891no—
187#102—891no—
188#102C2×D8912yescomplemented
189C22⋊C8—892no—
190C4×C8—891no—
191C24—1782no—
192#41—3562no—
193#41—1784no—
194C2×Q8—892no—
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—891no—
198C2×D4—891no—
199C2×D4—3564no—
200C2×D4—3562no—
201C2×D4—1782no—
202C2×D4—1784no—
203C2×D4—1782no—
204C2×D4—1782no—
205C2×D4C22×D8912yes—
206C2×D4C22×D8911yescharacteristic
207C22×C4—21no—
208C22×C4—892no—
209C22×C4—1782no—
210C22×C4—1781no—
211SD16—3562no—
212SD16—1784no—
213SD16—1784no—
214D8—24no—
215D8—894no—
216M16—1784no—
217C2×C8—891no—
218C2×C8—891no—
219C2×C8C22×D8912yes—
220C4⋊C4—891no—
221C4⋊C4—891no—
222C4⋊C4—1782no—
223C4⋊C4—1781no—
224C4⋊C4—1781no—
225C4⋊C4C22×D8911yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—892no—
228C22⋊C4—1782no—
229C22⋊C4—1782no—
230C22⋊C4—1781no—
231C42C22×D8911yescharacteristic
232C23—21no—
233C23—22no—
234C23—892no—
235C23—3564no—
236C23—3564no—
237C23—1781no—
238C23—7122no—
239Q8—1782no—
240Q8—1782no—
241D4—22no—
242D4—21no—
243D4—22no—
244D4—42no—
245D4—81no—
246D4—892no—
247D4—3564no—
248D4—3564no—
249D4—3564no—
250D4—1782no—
251D4—1781no—
252D4D4×D8912yescomplemented
253C2×C4—21no—
254C2×C4—42no—
255C2×C4—892no—
256C2×C4—3564no—
257C2×C4—3562no—
258C2×C4—1781no—
259C2×C4—1782no—
260C2×C4—1782no—
261C2×C4—1782no—
262C2×C4D4×D8911yescharacteristic
263C2×C4D4×D8911yescharacteristic
264C2×C4C23×D8911yescharacteristic
265C8—22no—
266C8—892no—
267C8—1781no—
268C22—22no—
269C22—41no—
270C22—41no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—3561no—
275C22—3561no—
276C22—1782no—
277C22—1782no—
278C22—1782no—
279C22—1782no—
280C22—7128no—
281C22C2×D4×D8911yescharacteristic
282C4—21no—
283C4—41no—
284C4—3562no—
285C4—3561no—
286C4—1782no—
287C4#1566803612yescomplemented
288C4C2×D4×D8911yescharacteristic
289C4#1566805811yescharacteristic
290C2—42no—
291C2—82no—
292C2—3562no—
293C2—3562no—
294C2#1915223211yescharacteristic
295C2C2×#1566803611yescharacteristic
296C2#1915240811yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#459×C89C2
socleC22×C89C22×D4
hypercenter#459D89
hypocenterC89#3272
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#15668036C2semidirect
2. #19152252C2semidirect
3. #19152233C2semidirect
4. #19151970C2semidirect
5. #19151843C2semidirect
6. #19151804C2semidirect
7. #19151750C2semidirect
8. #19151740C2semidirect
9. C4×#13083559C2semidirect
10. #19151675C2semidirect
11. #459×C89C2semidirect
12. C2×#13083573C22semidirect
17. C2×#13083562C22semidirect
18. C2×#13083562C22semidirect
20. C2×#13083557C22semidirect
21. #15668012C22semidirect
23. #15667992C22semidirect
31. #15667945C22semidirect
32. #15667937C22semidirect
33. #15667933C22semidirect
35. #15667924C22semidirect
36. C4×#10623494C22semidirect
37. C2×D8×C89C22semidirect
39. C4×D4×C89C22semidirect
40. C4⋊C8×C89C22semidirect
41. #102×C89C22semidirect
60. #13083559D4semidirect
95. D4×C89C2×D4semidirect
118. #10623494C2×D4semidirect
135. C4×C89AGL(1,ℤ/8)semidirect
149. C89#3272semidirect
156. #459D89semidirect
169. C2×D8C2×D89semidirect
181. C4×D4C2×D89semidirect
184. C4⋊C8C2×D89semidirect
188. #102C2×D89semidirect
252. D4D4×D89semidirect
287. C4#15668036semidirect

Maximal subgroups

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

subgroupindex
C2×#156680362
#191522522
#191522332
#191519702
#191518432
#191518042
#191517502
#191517402
C4×#130835592
#191516752
#459×C892
#327289