Finite Group Databasebeta

← #26032065

Subgroups — #26032065

Order 11392.

494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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
1#19152252C211yesmaximal, characteristic, complemented
2#19151944C211yesmaximal, characteristic, complemented
3#19151909C212yesmaximal, complemented
4#19151878C211yesmaximal, characteristic, complemented
5#19151832C212yesmaximal, complemented
6#19151790C211yesmaximal, characteristic, complemented
7#19151732C212yesmaximal, complemented
8C4×#13083559C211yesmaximal, characteristic, complemented
9D4×#10623494C211yesmaximal, characteristic, complemented
10C2×#15667933C212yesmaximal, complemented
11D42×C89C211yesmaximal, characteristic, complemented
12C2×#13083573—21no—
13C2×#13083559C2211yescharacteristic
14C2×#13083559C2212yescomplemented
15C22×#10623494C2212yescomplemented
16#15668012C2211yescharacteristic, complemented
17#15667996—22no—
18#15667992—21no—
19#15667986C2212yescomplemented
20C4×D356C2211yescharacteristic, complemented
21C2×C4⋊Dic89C2212yescomplemented
22#15667945C2212yescomplemented
23#15667945C2211yescharacteristic, complemented
24C4⋊#10623494C2211yescharacteristic, complemented
25#15667933C2212yes—
26#15667933C2211yescharacteristic
27#15667933C2212yescomplemented
28#15667933C2212yescomplemented
29#15667933C2212yescomplemented
30#15667932C2211yescharacteristic, complemented
31C22⋊#10623494C2212yescomplemented
32C4×#10623494C2211yescharacteristic, complemented
33C22×D4×C89—21no—
34C22×D4×C89C2212yes—
35#127×C89C2211yescharacteristic
36#121×C89—21no—
37#121×C89C2212yes—
38#120×C89—22no—
39C4×D4×C89C2211yescharacteristic
40C4×D4×C89C2211yescharacteristic
41#13083573—44no—
42C2×Dic178—21no—
43C2×D356C2311yescharacteristic
44C2×C22⋊D89—22no—
45C22×Dic89—22no—
46C2×C4×D89—21no—
47#13083559—22no—
48#13083559—42no—
49C2×#10623494—42no—
50C2×#10623494C2311yescharacteristic
51C2×#10623494C2312yes—
52C2×#10623494C2311yescharacteristic
53C4⋊Dic89—22no—
54C4⋊Dic89—21no—
55C4⋊Dic89C2311yescharacteristic
56C4⋊Dic89C2312yes—
57#13083551—21no—
58#13083551—22no—
59C24×C89—22no—
60C2×D4×C89—24no—
61C2×D4×C89—22no—
62C2×D4×C89—22no—
63C2×D4×C89—21no—
64C2×D4×C89—21no—
65C2×D4×C89—42no—
66C2×D4×C89—44no—
67C2×D4×C89D411yescharacteristic
68C2×D4×C89C2312yes—
69C2×D4×C89C2311yescharacteristic
70C22×C4×C89—21no—
71C22×C4×C89C2312yes—
72C4⋊C4×C89D411yescharacteristic
73C4⋊C4×C89C2311yescharacteristic
74C22⋊C4×C89—21no—
75C22⋊C4×C89—22no—
76C22⋊C4×C89D412yes—
77C42×C89C2311yescharacteristic
78C23×C89—21no—
79C23×C89—22no—
80C23×C89—44no—
81C23×C89—44no—
82C23×C89—82no—
83C23×C89C2×D412yes—
84C22×D89—21no—
85D4×C89—22no—
86D4×C89—21no—
87D4×C89—22no—
88D4×C89—44no—
89D4×C89—44no—
90D4×C89—42no—
91D4×C89—81no—
92D4×C89D814yescomplemented
93D4×C89#4112yescomplemented
94C2×C4×C89—22no—
95C2×C4×C89—22no—
96C2×C4×C89—21no—
97C2×C4×C89—42no—
98C2×C4×C89C2×D411yescharacteristic
99C2×C4×C89C2×D412yes—
100C2×C4×C89C2×D411yescharacteristic
101C2×C4×C89C2411yescharacteristic
102C22⋊D89—44no—
103C2×Dic89—21no—
104C2×Dic89—22no—
105C2×Dic89—44no—
106D356—21no—
107D356—21no—
108C4×D89—42no—
109Dic178—42no—
110#10623494—21no—
111#10623494—21no—
112#10623494—22no—
113C22×C89—22no—
114C22×C89—22no—
115C22×C89—22no—
116C22×C89—41no—
117C22×C89—41no—
118C22×C89—42no—
119C22×C89—42no—
120C22×C89—42no—
121C22×C89—88no—
122C22×C89C2×D814yes—
123C22×C89C22×D411yescharacteristic
124C2×D89—41no—
125C2×D89—41no—
126C2×D89—41no—
127C4×C89—22no—
128C4×C89—21no—
129C4×C89—41no—
130C4×C89C2×D812yes—
131C4×C89C2×#4111yescharacteristic
132C4×C89H(5,𝔽2)11yescharacteristic
133Dic89—42no—
134Dic89—41no—
135C2×C89—24no—
136C2×C89—42no—
137C2×C89—82no—
138C2×C89#54611yescharacteristic
139C2×C89C22×D811yescharacteristic
140C2×C89#57711yescharacteristic
141D89—81no—
142#3294—891nomaximal, Sylow
143C89#329411yescharacteristic, complemented, Sylow
144#547—891no—
145D42D8911yescharacteristic, complemented
146#486—891no—
147#480—892no—
148#474—891no—
149#466—892no—
150#459—891no—
151#447—892no—
152C4×D8—891no—
153C8×D4—891no—
154C2×#102—892no—
155C2×#41—1781no—
156C22×D4—21no—
157C22×D4C2×D8912yes—
158C2×D8—892no—
159C2×D8—891no—
160C22×C8—892no—
161C4⋊Q8—891no—
162#127C2×D8911yescharacteristic
163#123—1782no—
164C22⋊Q8—1781no—
165#121—21no—
166#121—892no—
167#121C2×D8912yes—
168#120—22no—
169C4×D4—891no—
170C4×D4C2×D8911yescharacteristic
171C4×D4C2×D8911yescharacteristic
172C2×C4⋊C4—892no—
173#107—891no—
174#107—892no—
175C4⋊C8—891no—
176#102—891no—
177#102—892no—
178#102—892no—
179#102—892no—
180#102—892no—
181#102—891no—
182C22⋊C8—892no—
183C4×C8—891no—
184C24—22no—
185#41—3564no—
186C2×Q8—1781no—
187C2×D4—24no—
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—21no—
192C2×D4—42no—
193C2×D4—44no—
194C2×D4—891no—
195C2×D4—1782no—
196C2×D4C22⋊D8911yescharacteristic
197C2×D4C22×D8912yes—
198C2×D4C22×D8911yescharacteristic
199C22×C4—21no—
200C22×C4—1782no—
201C22×C4—1781no—
202C22×C4C22×D8912yes—
203D8—3562no—
204D8—1782no—
205C2×C8—891no—
206C2×C8—891no—
207C2×C8—892no—
208C2×C8—3562no—
209C4⋊C4—891no—
210C4⋊C4—892no—
211C4⋊C4—1782no—
212C4⋊C4—1781no—
213C4⋊C4C22⋊D8911yescharacteristic
214C4⋊C4C22×D8911yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—22no—
217C22⋊C4—1781no—
218C22⋊C4—1782no—
219C22⋊C4C22⋊D8912yes—
220C42C22×D8911yescharacteristic
221C23—21no—
222C23—22no—
223C23—44no—
224C23—44no—
225C23—82no—
226C23—1781no—
227C23C2×C22⋊D8912yes—
228Q8—3562no—
229D4—22no—
230D4—21no—
231D4—22no—
232D4—44no—
233D4—44no—
234D4—42no—
235D4—81no—
236D4—3564no—
237D4—1781no—
238D4—1781no—
239D4#1308355914yescomplemented
240D4#1308357312yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—42no—
245C2×C4—3564no—
246C2×C4—3562no—
247C2×C4—1781no—
248C2×C4—1782no—
249C2×C4C2×C22⋊D8911yescharacteristic
250C2×C4C2×C22⋊D8912yes—
251C2×C4C2×C22⋊D8911yescharacteristic
252C2×C4C23×D8911yescharacteristic
253C8—1781no—
254C8—1781no—
255C8—1782no—
256C22—22no—
257C22—22no—
258C22—22no—
259C22—41no—
260C22—41no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—88no—
265C22—3561no—
266C22—3561no—
267C22—3561no—
268C22C2×#1308355914yes—
269C22C22×C22⋊D8911yescharacteristic
270C4—21no—
271C4—22no—
272C4—41no—
273C4—3561no—
274C4—3562no—
275C4C2×#1308355912yes—
276C4C2×#1308357311yescharacteristic
277C4#1566805711yescharacteristic
278C2—24no—
279C2—42no—
280C2—82no—
281C2—7121no—
282C2#1915224211yescharacteristic
283C2C22×#1308355911yescharacteristic
284C2#1915240911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingD42×C89C2
socleC22×C89C22×D4
hypercenterD42D89
hypocenterC89#3294
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. #19152252C2semidirect
2. #19151944C2semidirect
3. #19151909C2semidirect
4. #19151878C2semidirect
5. #19151832C2semidirect
6. #19151790C2semidirect
7. #19151732C2semidirect
8. C4×#13083559C2semidirect
9. D4×#10623494C2semidirect
10. C2×#15667933C2semidirect
11. D42×C89C2semidirect
14. C2×#13083559C22semidirect
15. C22×#10623494C22semidirect
16. #15668012C22semidirect
19. #15667986C22semidirect
20. C4×D356C22semidirect
21. C2×C4⋊Dic89C22semidirect
22. #15667945C22semidirect
23. #15667945C22semidirect
24. C4⋊#10623494C22semidirect
27. #15667933C22semidirect
28. #15667933C22semidirect
29. #15667933C22semidirect
30. #15667932C22semidirect
31. C22⋊#10623494C22semidirect
32. C4×#10623494C22semidirect
92. D4×C89D8semidirect
93. D4×C89#41semidirect
143. C89#3294semidirect
145. D42D89semidirect
239. D4#13083559semidirect
240. D4#13083573semidirect

Maximal subgroups

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

subgroupindex
#191522522
#191519442
#191519092
#191518782
#191518322
#191517902
#191517322
C4×#130835592
D4×#106234942
C2×#156679332
D42×C892
#329489