Finite Group Databasebeta

← #26031089

Subgroups — #26031089

Order 11392.

418 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152109C211yesmaximal, characteristic, complemented
2#19151939C211yesmaximal, characteristic, complemented
3#19151936C211yesmaximal, characteristic, complemented
4#19151922C211yesmaximal, characteristic, complemented
5#19151919C211yesmaximal, characteristic, complemented
6#19151854C211yesmaximal, characteristic, complemented
7#19151849C211yesmaximal, characteristic, complemented
8#19151846C211yesmaximal, characteristic, complemented
9#19151842C211yesmaximal, characteristic, complemented
10#19151760C211yesmaximal, characteristic, complemented
11#19151758C211yesmaximal, characteristic, complemented
12#19151743C211yesmaximal, characteristic, complemented
13#19151741C211yesmaximal, characteristic, complemented
14#19151562C211yesmaximal, characteristic, complemented
15#525×C89C211yesmaximal, characteristic, complemented
16C2×#13083574C2211yescharacteristic
17C2×#13083564C2211yescharacteristic, complemented
18C2×#13083562C2211yescharacteristic, complemented
19C2×#13083561C2211yescharacteristic, complemented
20C2×#13083559C2211yescharacteristic, complemented
21C2×#13083558C2211yescharacteristic
22C2×#13083558C2211yescharacteristic
23#15667995—21no—
24#15667991C2211yescharacteristic
25#15667991C2211yescharacteristic
26#15667986C2211yescharacteristic
27#15667986C2211yescharacteristic
28#15667981—21no—
29C4×C22⋊D89—21no—
30C4×C22⋊D89—21no—
31#15667971C2211yescharacteristic
32#15667945C2211yescharacteristic, complemented
33#15667945C2211yescharacteristic, complemented
34#15667943C2211yescharacteristic, complemented
35#15667943C2211yescharacteristic, complemented
36#15667936C2211yescharacteristic, complemented
37#15667936C2211yescharacteristic, complemented
38#15667935C2211yescharacteristic, complemented
39#15667935C2211yescharacteristic, complemented
40#15667933C2211yescharacteristic, complemented
41#15667933C2211yescharacteristic, complemented
42#15667932C2211yescharacteristic, complemented
43#15667932C2211yescharacteristic, complemented
44C22⋊#10623494C2211yescharacteristic
45C22⋊#10623494C2211yescharacteristic
46C22⋊#10623494C2211yescharacteristic
47C22⋊#10623494C2211yescharacteristic
48C2×#41×C89C2211yescharacteristic
49C23×C4×C89C2211yescharacteristic
50#123×C89—21no—
51C22⋊Q8×C89C2211yescharacteristic
52C22⋊Q8×C89C2211yescharacteristic
53#121×C89C2211yescharacteristic
54#121×C89C2211yescharacteristic
55#120×C89—21no—
56C4×D4×C89—21no—
57C4×D4×C89—21no—
58#117×C89C2211yescharacteristic
59#13083574—41no—
60#13083574—41no—
61C2×Dic178C2311yescharacteristic
62C2×D356C2311yescharacteristic
63C2×C22⋊D89—21no—
64C2×C22⋊D89—21no—
65C2×C22⋊D89—21no—
66C2×C4×D89—21no—
67#13083564—41no—
68#13083562—41no—
69#13083561—41no—
70#13083559—41no—
71#13083558—41no—
72#13083558—41no—
73C2×#10623494C2311yescharacteristic
74C2×#10623494C2311yescharacteristic
75C2×#10623494C2311yescharacteristic
76C2×#10623494C2311yescharacteristic
77C4⋊Dic89C2311yescharacteristic
78C4⋊Dic89C2311yescharacteristic
79#13083553—21no—
80#13083553—21no—
81C22⋊Dic89—21no—
82C22⋊Dic89—21no—
83C22⋊Dic89—21no—
84#13083551—21no—
85#13083551—21no—
86C4×Dic89—21no—
87C24×C89D411yescharacteristic
88#41×C89—41no—
89#41×C89—41no—
90C2×Q8×C89C2311yescharacteristic
91C2×D4×C89—21no—
92C2×D4×C89—21no—
93C2×D4×C89—21no—
94C2×D4×C89C2311yescharacteristic
95C22×C4×C89—21no—
96C22×C4×C89—41no—
97C22×C4×C89—41no—
98C22×C4×C89D411yescharacteristic
99C22×C4×C89D411yescharacteristic
100C22×C4×C89D411yescharacteristic
101C22×C4×C89C2311yescharacteristic
102C22×C4×C89C2311yescharacteristic
103C22×C4×C89C2311yescharacteristic
104C4⋊C4×C89—21no—
105C4⋊C4×C89—21no—
106C4⋊C4×C89C2311yescharacteristic
107C4⋊C4×C89C2311yescharacteristic
108C22⋊C4×C89—21no—
109C22⋊C4×C89—21no—
110C22⋊C4×C89—21no—
111C22⋊C4×C89—21no—
112C22⋊C4×C89—21no—
113C42×C89—21no—
114C23×C89—21no—
115C23×C89—41no—
116C23×C89—41no—
117C23×C89—41no—
118C23×C89C2×D411yescharacteristic
119C23×C89C2×D411yescharacteristic
120C23×C89C2×D411yescharacteristic
121C22×D89—21no—
122Q8×C89—21no—
123Q8×C89—21no—
124D4×C89—21no—
125D4×C89—21no—
126D4×C89—42no—
127D4×C89—42no—
128D4×C89—42no—
129C2×C4×C89—21no—
130C2×C4×C89—21no—
131C2×C4×C89—21no—
132C2×C4×C89—21no—
133C2×C4×C89—21no—
134C2×C4×C89—21no—
135C2×C4×C89—21no—
136C2×C4×C89—21no—
137C2×C4×C89—21no—
138C2×C4×C89—41no—
139C2×C4×C89—41no—
140C2×C4×C89—41no—
141C2×C4×C89—42no—
142C2×C4×C89C2×D411yescharacteristic
143C2×C4×C89C2×D411yescharacteristic
144C2×C4×C89C2×D411yescharacteristic
145C2×C4×C89C2411yescharacteristic
146C22⋊D89—42no—
147C22⋊D89—42no—
148C22⋊D89—42no—
149C2×Dic89—21no—
150C2×Dic89—21no—
151C2×Dic89—21no—
152D356—21no—
153D356—21no—
154C4×D89—42no—
155Dic178—21no—
156Dic178—21no—
157#10623494—21no—
158#10623494—21no—
159#10623494—21no—
160#10623494—21no—
161C22×C89—21no—
162C22×C89—21no—
163C22×C89—21no—
164C22×C89—21no—
165C22×C89—21no—
166C22×C89—21no—
167C22×C89—21no—
168C22×C89—21no—
169C22×C89—21no—
170C22×C89—44no—
171C22×C89—41no—
172C22×C89—41no—
173C22×C89—41no—
174C22×C89C22×D411yescharacteristic
175C2×D89—41no—
176C2×D89—41no—
177C2×D89—41no—
178C4×C89—21no—
179C4×C89—21no—
180C4×C89—21no—
181C4×C89—41no—
182C4×C89—41no—
183C4×C89—41no—
184C4×C89H(5,𝔽2)11yescharacteristic
185C4×C89H(5,𝔽2)11yescharacteristic
186Dic89—41no—
187Dic89—41no—
188Dic89—41no—
189C2×C89—41no—
190C2×C89—41no—
191C2×C89—41no—
192C2×C89—81no—
193C2×C89#53411yescharacteristic
194C2×C89#57511yescharacteristic
195C2×C89#57511yescharacteristic
196D89—81no—
197#3197—891nomaximal, Sylow
198C89#319711yescharacteristic, complemented, Sylow
199#525—891no—
200#525D8911yescharacteristic, complemented
201#485—891no—
202#485—891no—
203#482—891no—
204#482—891no—
205#470—891no—
206#469—891no—
207#468—891no—
208#468—891no—
209#452—891no—
210#452—891no—
211#449—891no—
212#449—891no—
213#407—891no—
214C2×#41—891no—
215C2×#41C2×D8911yescharacteristic
216C23×C4C2×D8911yescharacteristic
217C2×Q16—891no—
218C2×SD16—891no—
219C2×SD16—891no—
220C2×D8—891no—
221C2×M16—891no—
222C2×M16—891no—
223#123—21no—
224#123—1781no—
225C22⋊Q8—891no—
226C22⋊Q8—891no—
227C22⋊Q8C2×D8911yescharacteristic
228C22⋊Q8C2×D8911yescharacteristic
229#121—891no—
230#121—891no—
231#121C2×D8911yescharacteristic
232#121C2×D8911yescharacteristic
233#120—21no—
234#120—1781no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—1781no—
238C4×D4—1781no—
239#117—891no—
240#117C2×D8911yescharacteristic
241#107—891no—
242#107—891no—
243#106—891no—
244#106—891no—
245#103—891no—
246#103—891no—
247#103—891no—
248#103—891no—
249#102—891no—
250#102—891no—
251#102—891no—
252#102—891no—
253C22⋊C8—891no—
254C22⋊C8—891no—
255C22⋊C8—891no—
256C22⋊C8—891no—
257C24C22⋊D8911yescharacteristic
258#41—41no—
259#41—41no—
260#41—3561no—
261#41—3561no—
262C2×Q8—891no—
263C2×Q8C22×D8911yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—891no—
268C2×D4—1781no—
269C2×D4—1781no—
270C2×D4—1781no—
271C2×D4C22×D8911yescharacteristic
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—1781no—
276C22×C4C22⋊D8911yescharacteristic
277C22×C4C22⋊D8911yescharacteristic
278C22×C4C22⋊D8911yescharacteristic
279C22×C4C22×D8911yescharacteristic
280C22×C4C22×D8911yescharacteristic
281C22×C4C22×D8911yescharacteristic
282Q16—3561no—
283SD16—3561no—
284SD16—3561no—
285D8—3561no—
286M16—3561no—
287M16—3561no—
288C2×C8—891no—
289C2×C8—891no—
290C2×C8—891no—
291C2×C8—891no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—891no—
295C4⋊C4—891no—
296C4⋊C4—1781no—
297C4⋊C4—1781no—
298C4⋊C4C22×D8911yescharacteristic
299C4⋊C4C22×D8911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—1781no—
306C22⋊C4—1781no—
307C22⋊C4—1781no—
308C22⋊C4—1781no—
309C22⋊C4—1781no—
310C42—21no—
311C42—1781no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—1781no—
317C23C2×C22⋊D8911yescharacteristic
318C23C2×C22⋊D8911yescharacteristic
319C23C2×C22⋊D8911yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—1781no—
323Q8—1781no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—3562no—
330D4—3562no—
331D4—3562no—
332D4—1781no—
333D4—1781no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—3562no—
348C2×C4—1781no—
349C2×C4—1781no—
350C2×C4—1781no—
351C2×C4C2×C22⋊D8911yescharacteristic
352C2×C4C2×C22⋊D8911yescharacteristic
353C2×C4C2×C22⋊D8911yescharacteristic
354C2×C4C23×D8911yescharacteristic
355C8—1781no—
356C8—1781no—
357C8—1781no—
358C8—1781no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—44no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—3561no—
373C22—3561no—
374C22—3561no—
375C22C22×C22⋊D8911yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—3561no—
383C4—3561no—
384C4—3561no—
385C4#1566805711yescharacteristic
386C4#1566805711yescharacteristic
387C2—41no—
388C2—41no—
389C2—41no—
390C2—81no—
391C2—7121no—
392C2#1915215711yescharacteristic
393C2#1915239611yescharacteristic
394C2#1915239611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#525×C89C2
socleC22×C89C22×D4
hypercenter#525D89
hypocenterC89#3197
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #19152109C2semidirect
2. #19151939C2semidirect
3. #19151936C2semidirect
4. #19151922C2semidirect
5. #19151919C2semidirect
6. #19151854C2semidirect
7. #19151849C2semidirect
8. #19151846C2semidirect
9. #19151842C2semidirect
10. #19151760C2semidirect
11. #19151758C2semidirect
12. #19151743C2semidirect
13. #19151741C2semidirect
14. #19151562C2semidirect
15. #525×C89C2semidirect
17. C2×#13083564C22semidirect
18. C2×#13083562C22semidirect
19. C2×#13083561C22semidirect
20. C2×#13083559C22semidirect
32. #15667945C22semidirect
33. #15667945C22semidirect
34. #15667943C22semidirect
35. #15667943C22semidirect
36. #15667936C22semidirect
37. #15667936C22semidirect
38. #15667935C22semidirect
39. #15667935C22semidirect
40. #15667933C22semidirect
41. #15667933C22semidirect
42. #15667932C22semidirect
43. #15667932C22semidirect
198. C89#3197semidirect
200. #525D89semidirect

Maximal subgroups

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

subgroupindex
#191521092
#191519392
#191519362
#191519222
#191519192
#191518542
#191518492
#191518462
#191518422
#191517602
#191517582
#191517432
#191517412
#191515622
#525×C892
#319789