Finite Group Databasebeta

← #26032273

Subgroups — #26032273

Order 11392.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152288C211yesmaximal, characteristic, complemented
2#19151962C211yesmaximal, characteristic, complemented
3#19151919C211yesmaximal, characteristic, complemented
4#19151909C211yesmaximal, characteristic, complemented
5#19151898C211yesmaximal, characteristic, complemented
6#19151842C211yesmaximal, characteristic, complemented
7#19151825C211yesmaximal, characteristic, complemented
8#19151795C211yesmaximal, characteristic, complemented
9#19151749C211yesmaximal, characteristic, complemented
10#19151749C211yesmaximal, characteristic, complemented
11#19151698C211yesmaximal, characteristic, complemented
12#19151670C211yesmaximal, characteristic, complemented
13#19151603C211yesmaximal, characteristic, complemented
14C2×#15667933C211yesmaximal, characteristic, complemented
15D42×C89C211yesmaximal, characteristic
16C2×#13083562C2211yescharacteristic
17C2×#13083562C2211yescharacteristic, complemented
18C2×#13083562C2211yescharacteristic, complemented
19C2×#13083558C2211yescharacteristic, complemented
20C22×#10623494C2211yescharacteristic, complemented
21#15668005—21no—
22#15668004C2211yescharacteristic, complemented
23#15668002—21no—
24#15667993—21no—
25#15667991C2211yescharacteristic, complemented
26#15667991C2211yescharacteristic, complemented
27C4×Dic178C2211yescharacteristic, complemented
28#15667971C2211yescharacteristic, complemented
29#15667968—21no—
30C2×C4⋊Dic89C2211yescharacteristic, complemented
31#15667945C2211yescharacteristic, complemented
32#15667945C2211yescharacteristic, complemented
33#15667943C2211yescharacteristic, complemented
34C4⋊#10623494C2211yescharacteristic, complemented
35#15667935C2211yescharacteristic, complemented
36#15667933C2211yescharacteristic
37#15667933C2211yescharacteristic
38#15667933C2211yescharacteristic
39#15667933C2211yescharacteristic, complemented
40#15667933C2211yescharacteristic, complemented
41#15667933C2211yescharacteristic, complemented
42#15667933C2211yescharacteristic, complemented
43#15667933C2211yescharacteristic, complemented
44#15667933C2211yescharacteristic, complemented
45C22⋊#10623494C2211yescharacteristic, complemented
46C22⋊#10623494C2211yescharacteristic, complemented
47#15667923C2211yescharacteristic, complemented
48C22×D4×C89—21no—
49C22×D4×C89C2211yescharacteristic
50C22×D4×C89C2211yescharacteristic
51#127×C89C2211yescharacteristic
52#121×C89—21no—
53#121×C89C2211yescharacteristic
54#121×C89C2211yescharacteristic
55#120×C89—21no—
56#120×C89—21no—
57C4×D4×C89C2211yescharacteristic
58C4×D4×C89C2211yescharacteristic
59C2×Dic178C2311yescharacteristic
60C22×Dic89—21no—
61#13083562—22no—
62#13083562—41no—
63#13083562—41no—
64#13083558—41no—
65C2×#10623494—41no—
66C2×#10623494C2311yescharacteristic
67C2×#10623494C2311yescharacteristic
68C2×#10623494C2311yescharacteristic
69C2×#10623494C2311yescharacteristic
70C4⋊Dic89—21no—
71C4⋊Dic89C2311yescharacteristic
72C4⋊Dic89C2311yescharacteristic
73C4⋊Dic89C2311yescharacteristic
74#13083553—21no—
75#13083553—21no—
76#13083553—21no—
77#13083553—21no—
78#13083553—21no—
79C22⋊Dic89—21no—
80C22⋊Dic89—21no—
81C22⋊Dic89—21no—
82C4×Dic89—21no—
83C4×Dic89—21no—
84C24×C89—21no—
85C24×C89—21no—
86C2×D4×C89—22no—
87C2×D4×C89—22no—
88C2×D4×C89—21no—
89C2×D4×C89—21no—
90C2×D4×C89—21no—
91C2×D4×C89—21no—
92C2×D4×C89—21no—
93C2×D4×C89—21no—
94C2×D4×C89—41no—
95C2×D4×C89—41no—
96C2×D4×C89—44no—
97C2×D4×C89D411yescharacteristic
98C2×D4×C89C2311yescharacteristic
99C2×D4×C89C2311yescharacteristic
100C2×D4×C89C2311yescharacteristic
101C22×C4×C89—21no—
102C22×C4×C89C2311yescharacteristic
103C22×C4×C89C2311yescharacteristic
104C4⋊C4×C89D411yescharacteristic
105C4⋊C4×C89C2311yescharacteristic
106C22⋊C4×C89—21no—
107C22⋊C4×C89—21no—
108C22⋊C4×C89—21no—
109C22⋊C4×C89D411yescharacteristic
110C22⋊C4×C89D411yescharacteristic
111C42×C89C2311yescharacteristic
112C23×C89—21no—
113C23×C89—21no—
114C23×C89—21no—
115C23×C89—42no—
116C23×C89—42no—
117C23×C89—42no—
118C23×C89—42no—
119C23×C89—81no—
120C23×C89—81no—
121C23×C89C2×D411yescharacteristic
122C23×C89C2×D411yescharacteristic
123D4×C89—22no—
124D4×C89—21no—
125D4×C89—21no—
126D4×C89—21no—
127D4×C89—21no—
128D4×C89—21no—
129D4×C89—42no—
130D4×C89—42no—
131D4×C89—42no—
132D4×C89—42no—
133D4×C89—42no—
134D4×C89—81no—
135D4×C89#4112yes—
136C2×C4×C89—21no—
137C2×C4×C89—21no—
138C2×C4×C89—21no—
139C2×C4×C89—21no—
140C2×C4×C89—21no—
141C2×C4×C89—42no—
142C2×C4×C89C2×D411yescharacteristic
143C2×C4×C89C2×D411yescharacteristic
144C2×C4×C89C2×D411yescharacteristic
145C2×C4×C89C2×D411yescharacteristic
146C2×C4×C89C2411yescharacteristic
147C2×Dic89—21no—
148C2×Dic89—21no—
149C2×Dic89—21no—
150C2×Dic89—21no—
151C2×Dic89—42no—
152Dic178—21no—
153Dic178—21no—
154#10623494—21no—
155#10623494—21no—
156#10623494—21no—
157#10623494—21no—
158C22×C89—21no—
159C22×C89—21no—
160C22×C89—21no—
161C22×C89—22no—
162C22×C89—21no—
163C22×C89—21no—
164C22×C89—41no—
165C22×C89—41no—
166C22×C89—41no—
167C22×C89—41no—
168C22×C89—41no—
169C22×C89—41no—
170C22×C89—41no—
171C22×C89—41no—
172C22×C89—84no—
173C22×C89—84no—
174C22×C89AGL(1,ℤ/8)12yes—
175C22×C89C22×D411yescharacteristic
176C4×C89—21no—
177C4×C89—21no—
178C4×C89—21no—
179C4×C89—21no—
180C4×C89—41no—
181C4×C89C2×#4111yescharacteristic
182C4×C89H(5,𝔽2)11yescharacteristic
183Dic89—41no—
184Dic89—41no—
185Dic89—41no—
186Dic89—41no—
187C2×C89—22no—
188C2×C89—41no—
189C2×C89—42no—
190C2×C89—81no—
191C2×C89—81no—
192C2×C89#54611yescharacteristic
193C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
194C2×C89#57711yescharacteristic
195#3310—891nomaximal, Sylow
196C89#331011yescharacteristic, complemented, Sylow
197#552—891no—
198D42D8911yescharacteristic
199#490—891no—
200#482—891no—
201#480—891no—
202#478—891no—
203#468—891no—
204#465—891no—
205#460—891no—
206#450—891no—
207#450—891no—
208#440—891no—
209#435—891no—
210#418—891no—
211C2×#102—891no—
212C22×D4—21no—
213C22×D4C2×D8911yescharacteristic
214C22×D4C2×D8911yescharacteristic
215C2×SD16—891no—
216C2×SD16—891no—
217C2×SD16—891no—
218C2×M16—891no—
219C22×C8—891no—
220#127C2×D8911yescharacteristic
221#126—1781no—
222#125—891no—
223#125—1781no—
224#123—1781no—
225C22⋊Q8—891no—
226C22⋊Q8—891no—
227#121—21no—
228#121C2×D8911yescharacteristic
229#121C2×D8911yescharacteristic
230#120—21no—
231#120—21no—
232C4×Q8—891no—
233C4×D4C2×D8911yescharacteristic
234C4×D4C2×D8911yescharacteristic
235#117—891no—
236#117—1781no—
237C2×C4⋊C4—891no—
238#107—891no—
239#107—891no—
240#106—891no—
241C4⋊C8—891no—
242#103—891no—
243#102—891no—
244#102—891no—
245#102—891no—
246#102—891no—
247#102—891no—
248#102—891no—
249#102—891no—
250#102—891no—
251#102—891no—
252C22⋊C8—891no—
253C22⋊C8—891no—
254#97—891no—
255C24—21no—
256C24—21no—
257C2×Q8—891no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—44no—
269C2×D4C22⋊D8911yescharacteristic
270C2×D4C22×D8911yescharacteristic
271C2×D4C22×D8911yescharacteristic
272C2×D4C22×D8911yescharacteristic
273C22×C4—21no—
274C22×C4—1781no—
275C22×C4C22×D8911yescharacteristic
276C22×C4C22×D8911yescharacteristic
277SD16—3561no—
278SD16—3561no—
279SD16—1782no—
280M16—3561no—
281C2×C8—891no—
282C2×C8—891no—
283C2×C8—891no—
284C2×C8—891no—
285C2×C8—3561no—
286C4⋊C4—891no—
287C4⋊C4—891no—
288C4⋊C4—891no—
289C4⋊C4—1781no—
290C4⋊C4—1781no—
291C4⋊C4—1781no—
292C4⋊C4—1781no—
293C4⋊C4—1781no—
294C4⋊C4—1781no—
295C4⋊C4C22⋊D8911yescharacteristic
296C4⋊C4C22×D8911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—1781no—
301C22⋊C4—1781no—
302C22⋊C4—1781no—
303C22⋊C4C22⋊D8911yescharacteristic
304C22⋊C4C22⋊D8911yescharacteristic
305C42—1781no—
306C42—1781no—
307C42C22×D8911yescharacteristic
308C23—21no—
309C23—21no—
310C23—21no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23C2×C22⋊D8911yescharacteristic
318C23C2×C22⋊D8911yescharacteristic
319Q8—1781no—
320Q8—1781no—
321D4—22no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4#1308357312yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—3562no—
341C2×C4—1781no—
342C2×C4—1781no—
343C2×C4—1781no—
344C2×C4—1781no—
345C2×C4C2×C22⋊D8911yescharacteristic
346C2×C4C2×C22⋊D8911yescharacteristic
347C2×C4C2×C22⋊D8911yescharacteristic
348C2×C4C2×C22⋊D8911yescharacteristic
349C2×C4C23×D8911yescharacteristic
350C8—1781no—
351C8—1781no—
352C8—1781no—
353C8—1781no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—84no—
370C22#1566803812yes—
371C22C22×C22⋊D8911yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—3561no—
378C4—3561no—
379C4—3561no—
380C4—3561no—
381C4C2×#1308357311yescharacteristic
382C4#1566805711yescharacteristic
383C2—22no—
384C2—41no—
385C2—42no—
386C2—81no—
387C2—81no—
388C2#1915224211yescharacteristic
389C2C2×#1566803811yescharacteristic
390C2#1915240911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting, prime radicalD42×C89C2
socleC22×C89C22×D4
hypercenterD42D89
hypocenterC89#3310
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. #19152288C2semidirect
2. #19151962C2semidirect
3. #19151919C2semidirect
4. #19151909C2semidirect
5. #19151898C2semidirect
6. #19151842C2semidirect
7. #19151825C2semidirect
8. #19151795C2semidirect
9. #19151749C2semidirect
10. #19151749C2semidirect
11. #19151698C2semidirect
12. #19151670C2semidirect
13. #19151603C2semidirect
14. C2×#15667933C2semidirect
17. C2×#13083562C22semidirect
18. C2×#13083562C22semidirect
19. C2×#13083558C22semidirect
20. C22×#10623494C22semidirect
22. #15668004C22semidirect
25. #15667991C22semidirect
26. #15667991C22semidirect
27. C4×Dic178C22semidirect
28. #15667971C22semidirect
30. C2×C4⋊Dic89C22semidirect
31. #15667945C22semidirect
32. #15667945C22semidirect
33. #15667943C22semidirect
34. C4⋊#10623494C22semidirect
35. #15667935C22semidirect
39. #15667933C22semidirect
40. #15667933C22semidirect
41. #15667933C22semidirect
42. #15667933C22semidirect
43. #15667933C22semidirect
44. #15667933C22semidirect
45. C22⋊#10623494C22semidirect
46. C22⋊#10623494C22semidirect
47. #15667923C22semidirect
196. C89#3310semidirect

Maximal subgroups

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

subgroupindex
#191522882
#191519622
#191519192
#191519092
#191518982
#191518422
#191518252
#191517952
#191517492
#191516982
#191516702
#191516032
C2×#156679332
D42×C892
#331089