Finite Group Databasebeta

← #26032070

Subgroups — #26032070

Order 11392.

462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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
1D4×D356C211yesmaximal, characteristic
2#19151946C211yesmaximal, characteristic, complemented
3#19151916C212yesmaximal, complemented
4#19151885C211yesmaximal, characteristic, complemented
5#19151829C212yesmaximal, complemented
6#19151798C211yesmaximal, characteristic, complemented
7#19151748C212yesmaximal, complemented
8C4×#13083561C211yesmaximal, characteristic, complemented
9D4×#10623494C211yesmaximal, characteristic, complemented
10C2×#15667932C212yesmaximal, complemented
11#554×C89C211yesmaximal, characteristic, complemented
12C22×D356C2212yes—
13C2×D4×D89—21no—
14C2×#13083561C2211yescharacteristic
15C2×#13083561C2212yescomplemented
16C22×#10623494C2212yescomplemented
17#15668009C2211yescharacteristic
18#15667987—21no—
19#15667986C2212yes—
20#15667982—22no—
21C4×D356C2211yescharacteristic
22#15667943C2212yescomplemented
23#15667943C2211yescharacteristic, complemented
24C4⋊#10623494C2211yescharacteristic, complemented
25#15667936C2211yescharacteristic, complemented
26#15667932C2212yes—
27#15667932C2211yescharacteristic
28#15667932C2212yescomplemented
29#15667932C2212yescomplemented
30#15667932C2212yescomplemented
31C22⋊#10623494C2212yescomplemented
32C4×#10623494C2211yescharacteristic, complemented
33C4⋊Q8×C89C2211yescharacteristic, complemented
34#125×C89—21no—
35C22⋊Q8×C89—22no—
36C22⋊Q8×C89C2212yescomplemented
37C4×Q8×C89C2211yescharacteristic, complemented
38C4×D4×C89—21no—
39C4×D4×C89C2211yescharacteristic
40C2×C4⋊C4×C89C2212yescomplemented
41C23×D89—22no—
42C2×D356—24no—
43C2×D356—22no—
44C2×D356—21no—
45C2×D356—21no—
46C2×D356—42no—
47C2×D356C2312yes—
48C2×D356C2311yescharacteristic
49C2×C22⋊D89—22no—
50D4×D89—44no—
51C2×C4×D89—21no—
52#13083561—22no—
53#13083561—42no—
54C2×#10623494—42no—
55C2×#10623494C2311yescharacteristic
56C2×#10623494C2312yes—
57C2×#10623494C2311yescharacteristic
58C4⋊Dic89C2311yescharacteristic
59#13083551—21no—
60#13083551—22no—
61C2×Q8×C89—21no—
62C2×Q8×C89C2311yescharacteristic
63C2×D4×C89D411yescharacteristic
64C22×C4×C89—22no—
65C22×C4×C89C2312yes—
66C4⋊C4×C89—22no—
67C4⋊C4×C89—21no—
68C4⋊C4×C89—21no—
69C4⋊C4×C89—22no—
70C4⋊C4×C89D411yescharacteristic
71C4⋊C4×C89C2311yescharacteristic
72C4⋊C4×C89C2312yes—
73C22⋊C4×C89—22no—
74C22⋊C4×C89D412yes—
75C42×C89—21no—
76C42×C89C2311yescharacteristic
77C23×C89C2×D412yes—
78C22×D89—21no—
79C22×D89—22no—
80C22×D89—44no—
81C22×D89—44no—
82C22×D89—82no—
83Q8×C89—21no—
84Q8×C89—21no—
85Q8×C89—81no—
86D4×C89SD1614yescomplemented
87C2×C4×C89—22no—
88C2×C4×C89—22no—
89C2×C4×C89—21no—
90C2×C4×C89—21no—
91C2×C4×C89—22no—
92C2×C4×C89—82no—
93C2×C4×C89C2×D411yescharacteristic
94C2×C4×C89C2×D412yes—
95C2×C4×C89C2×D411yescharacteristic
96C2×C4×C89C2411yescharacteristic
97C22⋊D89—44no—
98C2×Dic89—21no—
99D356—22no—
100D356—21no—
101D356—22no—
102D356—44no—
103D356—42no—
104D356—81no—
105D356#4112yes—
106C4×D89—42no—
107#10623494—21no—
108#10623494—21no—
109#10623494—22no—
110C22×C89—22no—
111C22×C89—22no—
112C22×C89C2×SD1614yes—
113C22×C89C22×D411yescharacteristic
114C2×D89—22no—
115C2×D89—41no—
116C2×D89—41no—
117C2×D89—42no—
118C2×D89—42no—
119C2×D89—42no—
120C2×D89—88no—
121C4×C89—22no—
122C4×C89—21no—
123C4×C89—41no—
124C4×C89—41no—
125C4×C89—42no—
126C4×C89C2×SD1612yes—
127C4×C89C2×#4111yescharacteristic
128C4×C89H(5,𝔽2)11yescharacteristic
129Dic89—41no—
130C2×C89—24no—
131C2×C89#54611yescharacteristic
132C2×C89C22×SD1611yescharacteristic
133C2×C89#57611yescharacteristic
134D89—42no—
135D89—82no—
136#3295—891nomaximal, Sylow
137C89#329511yescharacteristic, complemented, Sylow
138#554D8911yescharacteristic, complemented
139D42—891no—
140#486—891no—
141#481—892no—
142#476—891no—
143#465—892no—
144#460—891no—
145#450—892no—
146C4×SD16—891no—
147C8×D4—891no—
148C2×#102—892no—
149C22×D4—892no—
150C22×D4—1781no—
151C2×SD16—892no—
152C2×SD16—891no—
153C22×C8—892no—
154C4⋊Q8C2×D8911yescharacteristic, complemented
155#127—891no—
156#125—21no—
157C22⋊Q8—22no—
158C22⋊Q8C2×D8912yescomplemented
159#121—892no—
160#121—1781no—
161#120—1782no—
162C4×Q8C2×D8911yescharacteristic, complemented
163C4×D4—21no—
164C4×D4—891no—
165C4×D4C2×D8911yescharacteristic
166C2×C4⋊C4C2×D8912yescomplemented
167#106—891no—
168#106—892no—
169C4⋊C8—891no—
170#103—891no—
171#102—891no—
172#102—892no—
173#102—892no—
174#102—892no—
175#102—892no—
176C22⋊C8—892no—
177C4×C8—891no—
178C24—1782no—
179C2×Q8—21no—
180C2×Q8C22×D8911yescharacteristic
181C2×D4—891no—
182C2×D4—892no—
183C2×D4—3562no—
184C2×D4—3564no—
185C2×D4—1784no—
186C2×D4—1782no—
187C2×D4—1782no—
188C2×D4—1781no—
189C2×D4—1781no—
190C2×D4C22⋊D8911yescharacteristic
191C22×C4—22no—
192C22×C4—1781no—
193C22×C4C22×D8912yes—
194SD16—3562no—
195SD16—1782no—
196C2×C8—891no—
197C2×C8—891no—
198C2×C8—892no—
199C2×C8—3562no—
200C4⋊C4—22no—
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—22no—
204C4⋊C4—891no—
205C4⋊C4C22⋊D8911yescharacteristic
206C4⋊C4C22×D8911yescharacteristic
207C4⋊C4C22×D8912yes—
208C22⋊C4—22no—
209C22⋊C4—1781no—
210C22⋊C4—1782no—
211C22⋊C4C22⋊D8912yes—
212C42—21no—
213C42C22×D8911yescharacteristic
214C23—3564no—
215C23—3564no—
216C23—1782no—
217C23—1781no—
218C23—7122no—
219C23C2×C22⋊D8912yes—
220Q8—21no—
221Q8—21no—
222Q8—81no—
223D4—892no—
224D4—3564no—
225D4—3564no—
226D4—3562no—
227D4—1782no—
228D4—1782no—
229D4—1781no—
230D4—7121no—
231D4#1308356114yescomplemented
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—82no—
238C2×C4—3562no—
239C2×C4—1781no—
240C2×C4C2×C22⋊D8911yescharacteristic
241C2×C4C2×C22⋊D8912yes—
242C2×C4C2×C22⋊D8911yescharacteristic
243C2×C4C23×D8911yescharacteristic
244C8—1781no—
245C8—1781no—
246C8—1782no—
247C22—22no—
248C22—22no—
249C22—3561no—
250C22—3561no—
251C22—3562no—
252C22—3562no—
253C22—3562no—
254C22—1782no—
255C22—7128no—
256C22C2×#1308356114yes—
257C22C22×C22⋊D8911yescharacteristic
258C4—21no—
259C4—22no—
260C4—41no—
261C4—42no—
262C4—41no—
263C4—3561no—
264C4C2×#1308356112yes—
265C4#41×D8911yescharacteristic
266C4#1566805811yescharacteristic
267C2—24no—
268C2—3562no—
269C2—7122no—
270C2#1915223611yescharacteristic
271C2C22×#1308356111yescharacteristic
272C2#1915240111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#554×C89C2
socleC22×C89C22×D4
prime radicalD4×D356C2
hypercenter#554D89
hypocenterC89#3295
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #19151946C2semidirect
3. #19151916C2semidirect
4. #19151885C2semidirect
5. #19151829C2semidirect
6. #19151798C2semidirect
7. #19151748C2semidirect
8. C4×#13083561C2semidirect
9. D4×#10623494C2semidirect
10. C2×#15667932C2semidirect
11. #554×C89C2semidirect
15. C2×#13083561C22semidirect
16. C22×#10623494C22semidirect
22. #15667943C22semidirect
23. #15667943C22semidirect
24. C4⋊#10623494C22semidirect
25. #15667936C22semidirect
28. #15667932C22semidirect
29. #15667932C22semidirect
30. #15667932C22semidirect
31. C22⋊#10623494C22semidirect
32. C4×#10623494C22semidirect
33. C4⋊Q8×C89C22semidirect
36. C22⋊Q8×C89C22semidirect
37. C4×Q8×C89C22semidirect
40. C2×C4⋊C4×C89C22semidirect
86. D4×C89SD16semidirect
137. C89#3295semidirect
138. #554D89semidirect
154. C4⋊Q8C2×D89semidirect
158. C22⋊Q8C2×D89semidirect
162. C4×Q8C2×D89semidirect
166. C2×C4⋊C4C2×D89semidirect
231. D4#13083561semidirect

Maximal subgroups

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

subgroupindex
D4×D3562
#191519462
#191519162
#191518852
#191518292
#191517982
#191517482
C4×#130835612
D4×#106234942
C2×#156679322
#554×C892
#329589