Finite Group Databasebeta

← #26031873

Subgroups — #26031873

Order 11392.

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

normal subgroups only

This group has 556 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×#15668039C212yesmaximal, complemented
2#19152270C211yesmaximal, characteristic, complemented
3D4×D356C211yesmaximal, characteristic, complemented
4#19151975C211yesmaximal, characteristic, complemented
5#19151852C212yesmaximal, complemented
6#19151798C211yesmaximal, characteristic, complemented
7#19151793C211yesmaximal, characteristic, complemented
8#19151746C212yesmaximal, complemented
9#19151733C212yesmaximal, complemented
10#19151677C211yesmaximal, characteristic, complemented
11C4×SD16×C89C211yesmaximal, characteristic, complemented
12C2×#13083575C2212yescomplemented
13C22×D356—21no—
14C2×D4×D89C2212yes—
15#15668039—28no—
16C2×#13083561C2212yescomplemented
17C2×D712C2212yescomplemented
18C2×D712C2212yescomplemented
19C2×#13083559C2212yes—
20C2×#13083557C2212yescomplemented
21#15668009—21no—
22#15668009C2211yescharacteristic
23#15668009C2211yescharacteristic, complemented
24#15667987—22no—
25#15667987C2212yes—
26#15667987C2212yescomplemented
27#15667986—21no—
28#15667982—22no—
29C4×D356—21no—
30C4×D356C2211yescharacteristic
31C4⋊#10623494C2211yescharacteristic, complemented
32#15667932C2212yescomplemented
33#15667932C2212yescomplemented
34#15667924C2212yescomplemented
35C2×SD16×C89C2211yescharacteristic
36C4×Q8×C89C2211yescharacteristic, complemented
37C4×D4×C89C2211yescharacteristic
38#106×C89C2211yescharacteristic, complemented
39#103×C89C2211yescharacteristic, complemented
40#102×C89C2211yescharacteristic
41C4×C8×C89C2211yescharacteristic, complemented
42C23×D89—22no—
43#13083575—24no—
44#13083575—42no—
45C2×D356—22no—
46C2×D356—22no—
47C2×D356—21no—
48C2×D356—21no—
49C2×D356—22no—
50C2×D356—21no—
51C2×D356—21no—
52C2×D356—44no—
53C2×D356D411yescharacteristic
54C2×D356C2312yes—
55C2×D356C2312yes—
56C2×C22⋊D89—22no—
57D4×D89—24no—
58D4×D89—42no—
59C2×C4×D89—22no—
60C2×C4×D89C2312yes—
61#13083561—24no—
62D712—24no—
63D712—42no—
64#13083559—24no—
65#13083557—24no—
66C2×#10623494C2312yes—
67C4⋊Dic89D411yescharacteristic
68#13083551—22no—
69#13083551—22no—
70#13083551D412yes—
71C2×Q8×C89C2311yescharacteristic
72C2×D4×C89C2311yescharacteristic
73C22×C4×C89—21no—
74SD16×C89D414yescomplemented
75C2×C8×C89C2311yescharacteristic
76C2×C8×C89C2311yescharacteristic
77C4⋊C4×C89—21no—
78C4⋊C4×C89C2311yescharacteristic
79C4⋊C4×C89C2311yescharacteristic
80C22⋊C4×C89—21no—
81C42×C89—21no—
82C42×C89C2311yescharacteristic
83C23×C89—21no—
84C22×D89—22no—
85C22×D89—22no—
86C22×D89—44no—
87C22×D89—44no—
88C22×D89—82no—
89C22×D89C2×D412yes—
90Q8×C89—21no—
91Q8×C89C2×D412yescomplemented
92D4×C89—21no—
93D4×C89C2×D412yes—
94C2×C4×C89—21no—
95C2×C4×C89—21no—
96C2×C4×C89—21no—
97C2×C4×C89—42no—
98C2×C4×C89C2×D411yescharacteristic
99C2×C4×C89C2×D411yescharacteristic
100C2×C4×C89C2411yescharacteristic
101C22⋊D89—44no—
102C2×Dic89C2×D412yes—
103D356—22no—
104D356—22no—
105D356—22no—
106D356—22no—
107D356—22no—
108D356—44no—
109D356—44no—
110D356—42no—
111D356—42no—
112D356—81no—
113D356—81no—
114D356—82no—
115C4×D89—22no—
116C4×D89—22no—
117C4×D89—44no—
118C8×C89—21no—
119C8×C89C2×D412yescomplemented
120#10623494—22no—
121C22×C89—22no—
122C22×C89—41no—
123C22×C89—41no—
124C22×C89C22×D411yescharacteristic
125C2×D89—22no—
126C2×D89—22no—
127C2×D89—22no—
128C2×D89—42no—
129C2×D89—42no—
130C2×D89—42no—
131C2×D89—42no—
132C2×D89—42no—
133C2×D89—42no—
134C2×D89—88no—
135C4×C89—22no—
136C4×C89—21no—
137C4×C89—41no—
138C4×C89—41no—
139C4×C89AGL(1,ℤ/8)12yescomplemented
140C4×C89C22×D411yescharacteristic
141C4×C89H(5,𝔽2)11yescharacteristic
142Dic89—22no—
143C2×C89—42no—
144C2×C89D4211yescharacteristic
145C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
146C2×C89#57611yescharacteristic
147D89—42no—
148D89—82no—
149D89—82no—
150#3274—891nomaximal, Sylow
151C89#327411yescharacteristic, complemented, Sylow
152C2×AGL(1,ℤ/8)—892no—
153#550—891no—
154D42—891no—
155#493—891no—
156#469—892no—
157#460—891no—
158#459—891no—
159#449—892no—
160#447—892no—
161C4×SD16D8911yescharacteristic, complemented
162#436—891no—
163C2×#41—892no—
164C22×D4—892no—
165C22×D4—1781no—
166AGL(1,ℤ/8)—1788no—
167C2×SD16—892no—
168C2×SD16C2×D8911yescharacteristic
169C2×D8—892no—
170C2×D8—892no—
171C2×D8—892no—
172C2×M16—892no—
173#127—891no—
174#127—891no—
175#127—1781no—
176#121—892no—
177#121—892no—
178#121—1782no—
179#121—1781no—
180#120—1782no—
181C4×Q8C2×D8911yescharacteristic, complemented
182C4×D4—891no—
183C4×D4—1781no—
184C4×D4C2×D8911yescharacteristic
185#106C2×D8911yescharacteristic, complemented
186C4⋊C8—891no—
187#103C2×D8911yescharacteristic, complemented
188#102—892no—
189#102—892no—
190#102C2×D8911yescharacteristic
191C22⋊C8—892no—
192C4×C8C2×D8911yescharacteristic, complemented
193C24—1782no—
194#41—3562no—
195#41—1784no—
196C2×Q8C22×D8911yescharacteristic
197C2×D4—891no—
198C2×D4—892no—
199C2×D4—892no—
200C2×D4—3564no—
201C2×D4—3562no—
202C2×D4—1782no—
203C2×D4—1782no—
204C2×D4—1782no—
205C2×D4—1782no—
206C2×D4—1784no—
207C2×D4—1781no—
208C2×D4—1781no—
209C2×D4—1781no—
210C2×D4—1781no—
211C2×D4C22×D8911yescharacteristic
212C22×C4—21no—
213C22×C4—892no—
214C22×C4—1782no—
215SD16—1784no—
216SD16D35614yescomplemented
217D8—3562no—
218D8—1784no—
219D8—1784no—
220M16—1784no—
221C2×C8—892no—
222C2×C8C22×D8911yescharacteristic
223C2×C8C22×D8911yescharacteristic
224C4⋊C4—21no—
225C4⋊C4—891no—
226C4⋊C4C22×D8911yescharacteristic
227C4⋊C4C22×D8911yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—892no—
230C22⋊C4—1782no—
231C22⋊C4—1782no—
232C42—21no—
233C42C22×D8911yescharacteristic
234C23—21no—
235C23—892no—
236C23—3564no—
237C23—3564no—
238C23—1782no—
239C23—1782no—
240C23—7122no—
241Q8—21no—
242Q8C2×D35612yescomplemented
243D4—21no—
244D4—3564no—
245D4—3564no—
246D4—3564no—
247D4—3562no—
248D4—3562no—
249D4—1782no—
250D4—1782no—
251D4—1782no—
252D4—1782no—
253D4—1782no—
254D4—7121no—
255D4—7121no—
256D4—7122no—
257D4C2×D35612yes—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—892no—
263C2×C4—3564no—
264C2×C4—1782no—
265C2×C4—1782no—
266C2×C4D4×D8911yescharacteristic
267C2×C4D4×D8911yescharacteristic
268C2×C4C23×D8911yescharacteristic
269C8—21no—
270C8—1782no—
271C8C2×D35612yescomplemented
272C22—22no—
273C22—41no—
274C22—41no—
275C22—3562no—
276C22—3562no—
277C22—3562no—
278C22—3562no—
279C22—3562no—
280C22—3562no—
281C22—1782no—
282C22—1782no—
283C22—1782no—
284C22—7128no—
285C22C2×D4×D8911yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—41no—
290C4—1782no—
291C4#1566803912yescomplemented
292C4C22×D35611yescharacteristic
293C4#1566805811yescharacteristic
294C2—42no—
295C2—3562no—
296C2—7122no—
297C2—7122no—
298C2D4×D35611yescharacteristic
299C2C2×#1566803911yescharacteristic
300C2#1915240011yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC4×SD16×C89C2
socleC22×C89C22×D4
hypercenterC4×SD16D89
hypocenterC89#3274
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#15668039C2semidirect
2. #19152270C2semidirect
3. D4×D356C2semidirect
4. #19151975C2semidirect
5. #19151852C2semidirect
6. #19151798C2semidirect
7. #19151793C2semidirect
8. #19151746C2semidirect
9. #19151733C2semidirect
10. #19151677C2semidirect
11. C4×SD16×C89C2semidirect
12. C2×#13083575C22semidirect
16. C2×#13083561C22semidirect
17. C2×D712C22semidirect
18. C2×D712C22semidirect
20. C2×#13083557C22semidirect
23. #15668009C22semidirect
26. #15667987C22semidirect
31. C4⋊#10623494C22semidirect
32. #15667932C22semidirect
33. #15667932C22semidirect
34. #15667924C22semidirect
36. C4×Q8×C89C22semidirect
38. #106×C89C22semidirect
39. #103×C89C22semidirect
41. C4×C8×C89C22semidirect
74. SD16×C89D4semidirect
91. Q8×C89C2×D4semidirect
119. C8×C89C2×D4semidirect
139. C4×C89AGL(1,ℤ/8)semidirect
151. C89#3274semidirect
161. C4×SD16D89semidirect
181. C4×Q8C2×D89semidirect
185. #106C2×D89semidirect
187. #103C2×D89semidirect
192. C4×C8C2×D89semidirect
216. SD16D356semidirect
242. Q8C2×D356semidirect
271. C8C2×D356semidirect
291. C4#15668039semidirect

Maximal subgroups

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

subgroupindex
C2×#156680392
#191522702
D4×D3562
#191519752
#191518522
#191517982
#191517932
#191517462
#191517332
#191516772
C4×SD16×C892
#327489