Finite Group Databasebeta

← #26031848

Subgroups — #26031848

Order 11392.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15668038C212yesmaximal, complemented
2#19152253C211yesmaximal, characteristic, complemented
3#19151970C211yesmaximal, characteristic, complemented
4#19151842C212yesmaximal, complemented
5#19151803C211yesmaximal, characteristic, complemented
6#19151790C211yesmaximal, characteristic, complemented
7#19151749C212yesmaximal, complemented
8#19151741C212yesmaximal, complemented
9C4×#13083559C211yesmaximal, characteristic, complemented
10#19151676C211yesmaximal, characteristic, complemented
11D42×C89C211yesmaximal, characteristic, complemented
12C2×#13083574C2212yescomplemented
13#15668038—28no—
14C2×#13083562C2212yes—
15C2×#13083562C2212yescomplemented
16C2×#13083562C2212yescomplemented
17C2×#13083559C2211yescharacteristic
18C2×#13083559C2212yescomplemented
19C2×#13083558C2212yescomplemented
20#15668012C2211yescharacteristic, complemented
21#15667994—22no—
22#15667991C2212yescomplemented
23#15667983—21no—
24C4×D356C2211yescharacteristic, complemented
25C4⋊C4×D89—21no—
26#15667945C2211yescharacteristic, complemented
27C4⋊#10623494C2211yescharacteristic, complemented
28#15667935C2212yescomplemented
29#15667933C2211yescharacteristic
30#15667933C2212yescomplemented
31#15667932C2211yescharacteristic, complemented
32C22⋊#10623494C2212yescomplemented
33C4×#10623494C2211yescharacteristic, complemented
34C22×D4×C89—21no—
35C22×D4×C89C2212yes—
36#127×C89C2211yescharacteristic
37#121×C89—21no—
38#121×C89C2212yes—
39#120×C89—22no—
40C4×D4×C89C2211yescharacteristic
41C4×D4×C89C2211yescharacteristic
42#13083574—24no—
43#13083574—42no—
44C2×Dic178C2312yes—
45C2×D356C2311yescharacteristic
46C2×C22⋊D89—22no—
47C2×C4×D89—21no—
48C2×C4×D89—22no—
49#13083562—24no—
50#13083562—24no—
51#13083562—42no—
52#13083559—24no—
53#13083559D414yescomplemented
54#13083558—24no—
55C2×#10623494C2312yes—
56C2×#10623494C2311yescharacteristic
57C2×#10623494C2311yescharacteristic
58C4⋊Dic89—21no—
59C4⋊Dic89—21no—
60C4⋊Dic89C2311yescharacteristic
61#13083553—22no—
62C22⋊Dic89—22no—
63#13083551—21no—
64C24×C89—22no—
65C2×D4×C89—24no—
66C2×D4×C89—22no—
67C2×D4×C89—22no—
68C2×D4×C89—21no—
69C2×D4×C89—21no—
70C2×D4×C89—42no—
71C2×D4×C89—44no—
72C2×D4×C89D411yescharacteristic
73C2×D4×C89C2312yes—
74C2×D4×C89C2311yescharacteristic
75C22×C4×C89—21no—
76C22×C4×C89C2312yes—
77C4⋊C4×C89D411yescharacteristic
78C4⋊C4×C89C2311yescharacteristic
79C22⋊C4×C89—21no—
80C22⋊C4×C89—22no—
81C22⋊C4×C89D412yes—
82C42×C89C2311yescharacteristic
83C23×C89—21no—
84C23×C89—22no—
85C23×C89—44no—
86C23×C89—44no—
87C23×C89—82no—
88C23×C89C2×D412yes—
89C22×D89—21no—
90D4×C89—22no—
91D4×C89—22no—
92D4×C89—21no—
93D4×C89—22no—
94D4×C89—44no—
95D4×C89—44no—
96D4×C89—42no—
97D4×C89—81no—
98D4×C89C2×D412yes—
99C2×C4×C89—22no—
100C2×C4×C89—22no—
101C2×C4×C89—21no—
102C2×C4×C89—42no—
103C2×C4×C89C2×D411yescharacteristic
104C2×C4×C89C2×D412yes—
105C2×C4×C89C2×D411yescharacteristic
106C2×C4×C89C2411yescharacteristic
107C22⋊D89—44no—
108C2×Dic89—21no—
109C2×Dic89—22no—
110D356—21no—
111D356C2×D412yescomplemented
112C4×D89—44no—
113C4×D89—42no—
114Dic178—22no—
115Dic178—22no—
116#10623494—22no—
117#10623494—21no—
118#10623494C2×D412yescomplemented
119C22×C89—22no—
120C22×C89—22no—
121C22×C89—22no—
122C22×C89—22no—
123C22×C89—41no—
124C22×C89—41no—
125C22×C89—42no—
126C22×C89—42no—
127C22×C89—42no—
128C22×C89—88no—
129C22×C89C22×D411yescharacteristic
130C2×D89—22no—
131C2×D89—41no—
132C2×D89—41no—
133C4×C89—22no—
134C4×C89—21no—
135C4×C89—41no—
136C4×C89AGL(1,ℤ/8)12yescomplemented
137C4×C89C22×D411yescharacteristic
138C4×C89H(5,𝔽2)11yescharacteristic
139Dic89—42no—
140Dic89—41no—
141C2×C89—42no—
142C2×C89—42no—
143C2×C89—82no—
144C2×C89D4211yescharacteristic
145C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
146C2×C89#57711yescharacteristic
147D89—42no—
148#3272—891nomaximal, Sylow
149C89#327211yescharacteristic, complemented, Sylow
150C2×AGL(1,ℤ/8)—892no—
151#547—891no—
152D42D8911yescharacteristic, complemented
153#492—891no—
154#468—892no—
155#461—891no—
156#459—891no—
157#450—892no—
158#449—892no—
159C4×D8—891no—
160#436—891no—
161C2×#41—892no—
162C22×D4—21no—
163C22×D4C2×D8912yes—
164AGL(1,ℤ/8)—1788no—
165C2×SD16—892no—
166C2×SD16—892no—
167C2×SD16—892no—
168C2×D8—891no—
169C2×D8—892no—
170C2×M16—892no—
171C4⋊Q8—891no—
172#127C2×D8911yescharacteristic
173#123—1782no—
174C22⋊Q8—892no—
175#121—21no—
176#121—1781no—
177#121C2×D8912yes—
178#120—22no—
179C4×D4—891no—
180C4×D4C2×D8911yescharacteristic
181C4×D4C2×D8911yescharacteristic
182C2×C4⋊C4—1781no—
183#107—891no—
184C4⋊C8—891no—
185#103—892no—
186#102—891no—
187#102—892no—
188#102—891no—
189C22⋊C8—892no—
190C4×C8—891no—
191C24—22no—
192#41—3562no—
193#41—1784no—
194C2×Q8—892no—
195C2×D4—24no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—42no—
201C2×D4—44no—
202C2×D4—891no—
203C2×D4—1782no—
204C2×D4C22⋊D8911yescharacteristic
205C2×D4C22×D8912yes—
206C2×D4C22×D8911yescharacteristic
207C22×C4—21no—
208C22×C4—1781no—
209C22×C4—1782no—
210C22×C4C22×D8912yes—
211SD16—3562no—
212SD16—1784no—
213SD16—1784no—
214D8—894no—
215D8—1784no—
216M16—1784no—
217C2×C8—891no—
218C2×C8—891no—
219C2×C8—892no—
220C4⋊C4—891no—
221C4⋊C4—1781no—
222C4⋊C4—1782no—
223C4⋊C4—1781no—
224C4⋊C4C22⋊D8911yescharacteristic
225C4⋊C4C22×D8911yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—22no—
228C22⋊C4—1782no—
229C22⋊C4—1781no—
230C22⋊C4C22⋊D8912yes—
231C42C22×D8911yescharacteristic
232C23—21no—
233C23—22no—
234C23—44no—
235C23—44no—
236C23—82no—
237C23—1781no—
238C23C2×C22⋊D8912yes—
239Q8—1782no—
240Q8—1782no—
241D4—22no—
242D4—22no—
243D4—21no—
244D4—22no—
245D4—44no—
246D4—44no—
247D4—42no—
248D4—81no—
249D4—892no—
250D4—3564no—
251D4—1781no—
252D4D4×D8912yes—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—3564no—
258C2×C4—3562no—
259C2×C4—1781no—
260C2×C4—1782no—
261C2×C4C2×C22⋊D8911yescharacteristic
262C2×C4C2×C22⋊D8912yes—
263C2×C4C2×C22⋊D8911yescharacteristic
264C2×C4C23×D8911yescharacteristic
265C8—892no—
266C8—1782no—
267C8—1781no—
268C22—22no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—41no—
273C22—41no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—88no—
278C22—3561no—
279C22—3561no—
280C22—1782no—
281C22C22×C22⋊D8911yescharacteristic
282C4—21no—
283C4—22no—
284C4—41no—
285C4—3561no—
286C4—3562no—
287C4#1566803812yescomplemented
288C4C2×D4×D8911yescharacteristic
289C4#1566805711yescharacteristic
290C2—42no—
291C2—42no—
292C2—82no—
293C2—3562no—
294C2D4×C22⋊D8911yescharacteristic
295C2C2×#1566803811yescharacteristic
296C2#1915240911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingD42×C89C2
socleC22×C89C22×D4
hypercenterD42D89
hypocenterC89#3272
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#15668038C2semidirect
2. #19152253C2semidirect
3. #19151970C2semidirect
4. #19151842C2semidirect
5. #19151803C2semidirect
6. #19151790C2semidirect
7. #19151749C2semidirect
8. #19151741C2semidirect
9. C4×#13083559C2semidirect
10. #19151676C2semidirect
11. D42×C89C2semidirect
12. C2×#13083574C22semidirect
15. C2×#13083562C22semidirect
16. C2×#13083562C22semidirect
18. C2×#13083559C22semidirect
19. C2×#13083558C22semidirect
20. #15668012C22semidirect
22. #15667991C22semidirect
24. C4×D356C22semidirect
26. #15667945C22semidirect
27. C4⋊#10623494C22semidirect
28. #15667935C22semidirect
30. #15667933C22semidirect
31. #15667932C22semidirect
32. C22⋊#10623494C22semidirect
33. C4×#10623494C22semidirect
53. #13083559D4semidirect
111. D356C2×D4semidirect
118. #10623494C2×D4semidirect
136. C4×C89AGL(1,ℤ/8)semidirect
149. C89#3272semidirect
152. D42D89semidirect
287. C4#15668038semidirect

Maximal subgroups

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

subgroupindex
C2×#156680382
#191522532
#191519702
#191518422
#191518032
#191517902
#191517492
#191517412
C4×#130835592
#191516762
D42×C892
#327289