Finite Group Databasebeta

← #26032393

Subgroups — #26032393

Order 11392.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152294C211yesmaximal, characteristic, complemented
2#19151962C211yesmaximal, characteristic, complemented
3#19151919C211yesmaximal, characteristic, complemented
4#19151914C211yesmaximal, characteristic, complemented
5#19151898C211yesmaximal, characteristic, complemented
6#19151849C211yesmaximal, characteristic, complemented
7#19151832C211yesmaximal, characteristic, complemented
8#19151790C211yesmaximal, characteristic, complemented
9#19151732C211yesmaximal, characteristic, complemented
10#19151732C211yesmaximal, characteristic, complemented
11#19151708C211yesmaximal, characteristic, complemented
12#19151670C211yesmaximal, characteristic, complemented
13#19151603C211yesmaximal, characteristic, complemented
14C2×#15667933C211yesmaximal, characteristic, complemented
15D42×C89C211yesmaximal, characteristic, complemented
16C2×#13083559C2211yescharacteristic
17C2×#13083559C2211yescharacteristic, complemented
18C2×#13083559C2211yescharacteristic, complemented
19C2×#13083558C2211yescharacteristic, complemented
20C22×#10623494C2211yescharacteristic, complemented
21#15668007—21no—
22#15668004C2211yescharacteristic, complemented
23#15667994—21no—
24#15667986C2211yescharacteristic, complemented
25#15667986C2211yescharacteristic, complemented
26#15667984—21no—
27C4×D356C2211yescharacteristic, complemented
28#15667972—21no—
29#15667971C2211yescharacteristic, complemented
30C2×C4⋊Dic89C2211yescharacteristic, complemented
31#15667945C2211yescharacteristic, complemented
32#15667943C2211yescharacteristic, complemented
33#15667943C2211yescharacteristic, complemented
34C4⋊#10623494C2211yescharacteristic, complemented
35#15667933C2211yescharacteristic
36#15667933C2211yescharacteristic
37#15667933C2211yescharacteristic
38#15667933C2211yescharacteristic, complemented
39#15667933C2211yescharacteristic, complemented
40#15667933C2211yescharacteristic, complemented
41#15667933C2211yescharacteristic, complemented
42#15667933C2211yescharacteristic, complemented
43#15667933C2211yescharacteristic, complemented
44#15667932C2211yescharacteristic, 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×D356C2311yescharacteristic
60C2×C22⋊D89—21no—
61C2×C22⋊D89—21no—
62C22×Dic89—21no—
63C2×C4×D89—21no—
64#13083559—22no—
65#13083559—41no—
66#13083559—41no—
67#13083558—41no—
68C2×#10623494—41no—
69C2×#10623494C2311yescharacteristic
70C2×#10623494C2311yescharacteristic
71C2×#10623494C2311yescharacteristic
72C2×#10623494C2311yescharacteristic
73C4⋊Dic89—21no—
74C4⋊Dic89C2311yescharacteristic
75C4⋊Dic89C2311yescharacteristic
76C4⋊Dic89C2311yescharacteristic
77#13083553—21no—
78#13083553—21no—
79C22⋊Dic89—21no—
80#13083551—21no—
81#13083551—21no—
82#13083551—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
123C22×D89—21no—
124D4×C89—22no—
125D4×C89—21no—
126D4×C89—21no—
127D4×C89—21no—
128D4×C89—21no—
129D4×C89—21no—
130D4×C89—42no—
131D4×C89—42no—
132D4×C89—42no—
133D4×C89—42no—
134D4×C89—42no—
135D4×C89—81no—
136D4×C89#4112yes—
137C2×C4×C89—21no—
138C2×C4×C89—21no—
139C2×C4×C89—21no—
140C2×C4×C89—21no—
141C2×C4×C89—21no—
142C2×C4×C89—42no—
143C2×C4×C89C2×D411yescharacteristic
144C2×C4×C89C2×D411yescharacteristic
145C2×C4×C89C2×D411yescharacteristic
146C2×C4×C89C2×D411yescharacteristic
147C2×C4×C89C2411yescharacteristic
148C22⋊D89—42no—
149C22⋊D89—81no—
150C2×Dic89—21no—
151C2×Dic89—21no—
152C2×Dic89—21no—
153C2×Dic89—81no—
154D356—21no—
155D356—21no—
156C4×D89—81no—
157#10623494—21no—
158#10623494—21no—
159#10623494—21no—
160#10623494—21no—
161C22×C89—21no—
162C22×C89—21no—
163C22×C89—21no—
164C22×C89—22no—
165C22×C89—21no—
166C22×C89—21no—
167C22×C89—41no—
168C22×C89—41no—
169C22×C89—41no—
170C22×C89—41no—
171C22×C89—41no—
172C22×C89—41no—
173C22×C89—41no—
174C22×C89—41no—
175C22×C89—84no—
176C22×C89—84no—
177C22×C89AGL(1,ℤ/8)12yes—
178C22×C89C22×D411yescharacteristic
179C2×D89—41no—
180C2×D89—41no—
181C2×D89—41no—
182C4×C89—21no—
183C4×C89—21no—
184C4×C89—21no—
185C4×C89—21no—
186C4×C89—41no—
187C4×C89C2×#4111yescharacteristic
188C4×C89H(5,𝔽2)11yescharacteristic
189Dic89—41no—
190Dic89—41no—
191Dic89—41no—
192C2×C89—22no—
193C2×C89—41no—
194C2×C89—42no—
195C2×C89—81no—
196C2×C89—81no—
197C2×C89#54611yescharacteristic
198C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
199C2×C89#57611yescharacteristic
200D89—81no—
201#3318—891nomaximal, Sylow
202C89#331811yescharacteristic, complemented, Sylow
203#553—891no—
204D42D8911yescharacteristic, complemented
205#490—891no—
206#482—891no—
207#481—891no—
208#478—891no—
209#469—891no—
210#466—891no—
211#459—891no—
212#447—891no—
213#447—891no—
214#442—891no—
215#435—891no—
216#418—891no—
217C2×#102—891no—
218C22×D4—21no—
219C22×D4C2×D8911yescharacteristic
220C22×D4C2×D8911yescharacteristic
221C2×D8—891no—
222C2×D8—891no—
223C2×D8—891no—
224C2×M16—891no—
225C22×C8—891no—
226#127C2×D8911yescharacteristic
227#126—1781no—
228#125—891no—
229#123—1781no—
230#121—21no—
231#121—891no—
232#121—891no—
233#121—1781no—
234#121C2×D8911yescharacteristic
235#121C2×D8911yescharacteristic
236#120—21no—
237#120—21no—
238C4×D4—891no—
239C4×D4—1781no—
240C4×D4C2×D8911yescharacteristic
241C4×D4C2×D8911yescharacteristic
242#117—891no—
243C2×C4⋊C4—891no—
244#107—891no—
245#106—891no—
246#106—891no—
247C4⋊C8—891no—
248#102—891no—
249#102—891no—
250#102—891no—
251#102—891no—
252#102—891no—
253#102—891no—
254#102—891no—
255#102—891no—
256#102—891no—
257#102—891no—
258C22⋊C8—891no—
259C22⋊C8—891no—
260#97—891no—
261C24—21no—
262C24—21no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—44no—
274C2×D4—891no—
275C2×D4—1781no—
276C2×D4—1781no—
277C2×D4C22⋊D8911yescharacteristic
278C2×D4C22×D8911yescharacteristic
279C2×D4C22×D8911yescharacteristic
280C2×D4C22×D8911yescharacteristic
281C22×C4—21no—
282C22×C4—1781no—
283C22×C4—1781no—
284C22×C4C22×D8911yescharacteristic
285C22×C4C22×D8911yescharacteristic
286D8—3561no—
287D8—3561no—
288D8—1782no—
289M16—3561no—
290C2×C8—891no—
291C2×C8—891no—
292C2×C8—891no—
293C2×C8—891no—
294C2×C8—3561no—
295C4⋊C4—891no—
296C4⋊C4—891no—
297C4⋊C4—891no—
298C4⋊C4—1781no—
299C4⋊C4—1781no—
300C4⋊C4—1781no—
301C4⋊C4C22⋊D8911yescharacteristic
302C4⋊C4C22×D8911yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—1781no—
307C22⋊C4—1781no—
308C22⋊C4—1781no—
309C22⋊C4—1781no—
310C22⋊C4C22⋊D8911yescharacteristic
311C22⋊C4C22⋊D8911yescharacteristic
312C42—1781no—
313C42C22×D8911yescharacteristic
314C23—21no—
315C23—21no—
316C23—21no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—1781no—
324C23C2×C22⋊D8911yescharacteristic
325C23C2×C22⋊D8911yescharacteristic
326D4—22no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—42no—
334D4—42no—
335D4—42no—
336D4—42no—
337D4—81no—
338D4—3562no—
339D4—1781no—
340D4—1781no—
341D4—7121no—
342D4#1308357312yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—1781no—
350C2×C4—1781no—
351C2×C4—1781no—
352C2×C4—7121no—
353C2×C4—7121no—
354C2×C4C2×C22⋊D8911yescharacteristic
355C2×C4C2×C22⋊D8911yescharacteristic
356C2×C4C2×C22⋊D8911yescharacteristic
357C2×C4C2×C22⋊D8911yescharacteristic
358C2×C4C23×D8911yescharacteristic
359C8—1781no—
360C8—1781no—
361C8—1781no—
362C8—1781no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—22no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—84no—
378C22—84no—
379C22—3561no—
380C22—3561no—
381C22—3561no—
382C22#1566803812yes—
383C22C22×C22⋊D8911yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—3561no—
390C4—3561no—
391C4—3561no—
392C4C2×#1308357311yescharacteristic
393C4#1566805711yescharacteristic
394C2—22no—
395C2—41no—
396C2—42no—
397C2—81no—
398C2—81no—
399C2—7121no—
400C2#1915224211yescharacteristic
401C2C2×#1566803811yescharacteristic
402C2#1915240111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingD42×C89C2
socleC22×C89C22×D4
hypercenterD42D89
hypocenterC89#3318
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. #19152294C2semidirect
2. #19151962C2semidirect
3. #19151919C2semidirect
4. #19151914C2semidirect
5. #19151898C2semidirect
6. #19151849C2semidirect
7. #19151832C2semidirect
8. #19151790C2semidirect
9. #19151732C2semidirect
10. #19151732C2semidirect
11. #19151708C2semidirect
12. #19151670C2semidirect
13. #19151603C2semidirect
14. C2×#15667933C2semidirect
15. D42×C89C2semidirect
17. C2×#13083559C22semidirect
18. C2×#13083559C22semidirect
19. C2×#13083558C22semidirect
20. C22×#10623494C22semidirect
22. #15668004C22semidirect
24. #15667986C22semidirect
25. #15667986C22semidirect
27. C4×D356C22semidirect
29. #15667971C22semidirect
30. C2×C4⋊Dic89C22semidirect
31. #15667945C22semidirect
32. #15667943C22semidirect
33. #15667943C22semidirect
34. C4⋊#10623494C22semidirect
38. #15667933C22semidirect
39. #15667933C22semidirect
40. #15667933C22semidirect
41. #15667933C22semidirect
42. #15667933C22semidirect
43. #15667933C22semidirect
44. #15667932C22semidirect
45. C22⋊#10623494C22semidirect
46. C22⋊#10623494C22semidirect
47. #15667923C22semidirect
202. C89#3318semidirect
204. D42D89semidirect

Maximal subgroups

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

subgroupindex
#191522942
#191519622
#191519192
#191519142
#191518982
#191518492
#191518322
#191517902
#191517322
#191517082
#191516702
#191516032
C2×#156679332
D42×C892
#331889