Finite Group Databasebeta

← #26032288

Subgroups — #26032288

Order 11392.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152318C211yesmaximal, characteristic, complemented
2#19151957C211yesmaximal, characteristic, complemented
3#19151936C211yesmaximal, characteristic, complemented
4#19151919C211yesmaximal, characteristic, complemented
5#19151888C211yesmaximal, characteristic, complemented
6#19151854C211yesmaximal, characteristic, complemented
7#19151825C211yesmaximal, characteristic, complemented
8#19151817C211yesmaximal, characteristic, complemented
9#19151760C211yesmaximal, characteristic, complemented
10#19151749C211yesmaximal, characteristic, complemented
11#19151698C211yesmaximal, characteristic, complemented
12#19151670C211yesmaximal, characteristic, complemented
13#19151603C211yesmaximal, characteristic, complemented
14#19151594C211yesmaximal, characteristic, complemented
15#546×C89C211yesmaximal, characteristic
16C2×#13083564C2211yescharacteristic, complemented
17C2×#13083562C2211yescharacteristic
18C2×#13083562C2211yescharacteristic
19C2×#13083558C2211yescharacteristic
20C22×#10623494C2211yescharacteristic, complemented
21#15668012C2211yescharacteristic, complemented
22#15668005—21no—
23#15668005—21no—
24#15667999—21no—
25#15667991C2211yescharacteristic
26#15667991C2211yescharacteristic, complemented
27C4×Dic178C2211yescharacteristic, complemented
28#15667977—21no—
29#15667971C2211yescharacteristic
30#15667971C2211yescharacteristic, complemented
31#15667945C2211yescharacteristic, complemented
32#15667943C2211yescharacteristic, complemented
33#15667943C2211yescharacteristic, complemented
34C4⋊#10623494C2211yescharacteristic, complemented
35#15667936C2211yescharacteristic, complemented
36#15667936C2211yescharacteristic, complemented
37#15667936C2211yescharacteristic, complemented
38#15667935C2211yescharacteristic, complemented
39#15667933C2211yescharacteristic
40#15667933C2211yescharacteristic
41#15667933C2211yescharacteristic
42#15667933C2211yescharacteristic
43#15667933C2211yescharacteristic
44#15667933C2211yescharacteristic
45C22⋊#10623494C2211yescharacteristic
46C22⋊#10623494C2211yescharacteristic, complemented
47#15667923C2211yescharacteristic, complemented
48C2×#41×C89C2211yescharacteristic
49C22×D4×C89C2211yescharacteristic
50#124×C89C2211yescharacteristic
51#123×C89—21no—
52C22⋊Q8×C89C2211yescharacteristic
53#121×C89—21no—
54#121×C89C2211yescharacteristic
55#120×C89—21no—
56C4×D4×C89C2211yescharacteristic
57C4×D4×C89C2211yescharacteristic
58C2×C22⋊C4×C89—21no—
59C2×Dic178—21no—
60C2×Dic178C2311yescharacteristic
61#13083564—41no—
62#13083562—22no—
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—
77C22⋊Dic89—21no—
78C22⋊Dic89—21no—
79C22⋊Dic89—21no—
80C22⋊Dic89—21no—
81C4×Dic89—21no—
82C4×Dic89—21no—
83C4×Dic89—21no—
84C24×C89—21no—
85#41×C89—22no—
86#41×C89—41no—
87C2×Q8×C89C2311yescharacteristic
88C2×D4×C89—22no—
89C2×D4×C89—21no—
90C2×D4×C89—21no—
91C2×D4×C89—21no—
92C2×D4×C89—41no—
93C2×D4×C89D411yescharacteristic
94C2×D4×C89C2311yescharacteristic
95C2×D4×C89C2311yescharacteristic
96C22×C4×C89—21no—
97C22×C4×C89—21no—
98C22×C4×C89C2311yescharacteristic
99C22×C4×C89C2311yescharacteristic
100C4⋊C4×C89—21no—
101C4⋊C4×C89D411yescharacteristic
102C4⋊C4×C89C2311yescharacteristic
103C22⋊C4×C89—21no—
104C22⋊C4×C89—21no—
105C22⋊C4×C89—21no—
106C22⋊C4×C89—21no—
107C22⋊C4×C89—21no—
108C22⋊C4×C89D411yescharacteristic
109C22⋊C4×C89D411yescharacteristic
110C42×C89C2311yescharacteristic
111C23×C89—21no—
112C23×C89—21no—
113C23×C89—42no—
114C23×C89—42no—
115C23×C89—81no—
116C23×C89C2×D411yescharacteristic
117C23×C89C2×D411yescharacteristic
118Q8×C89—21no—
119Q8×C89—21no—
120D4×C89—21no—
121D4×C89—21no—
122D4×C89—21no—
123D4×C89—41no—
124D4×C89—42no—
125D4×C89—42no—
126D4×C89—81no—
127D4×C89#4112yes—
128C2×C4×C89—21no—
129C2×C4×C89—21no—
130C2×C4×C89—21no—
131C2×C4×C89—21no—
132C2×C4×C89—21no—
133C2×C4×C89—21no—
134C2×C4×C89—42no—
135C2×C4×C89—81no—
136C2×C4×C89C2×D411yescharacteristic
137C2×C4×C89C2×D411yescharacteristic
138C2×C4×C89C2×D411yescharacteristic
139C2×C4×C89C2×D411yescharacteristic
140C2×C4×C89C2411yescharacteristic
141C2×Dic89—21no—
142C2×Dic89—21no—
143C2×Dic89—21no—
144C2×Dic89—21no—
145Dic178—21no—
146Dic178—21no—
147Dic178—42no—
148#10623494—21no—
149#10623494—21no—
150#10623494—21no—
151#10623494—21no—
152C22×C89—21no—
153C22×C89—21no—
154C22×C89—22no—
155C22×C89—21no—
156C22×C89—21no—
157C22×C89—21no—
158C22×C89—21no—
159C22×C89—41no—
160C22×C89—41no—
161C22×C89—41no—
162C22×C89—41no—
163C22×C89—41no—
164C22×C89—84no—
165C22×C89C22×D411yescharacteristic
166C4×C89—21no—
167C4×C89—21no—
168C4×C89—21no—
169C4×C89—21no—
170C4×C89—41no—
171C4×C89—41no—
172C4×C89C2×#4111yescharacteristic
173C4×C89H(5,𝔽2)11yescharacteristic
174Dic89—41no—
175Dic89—41no—
176Dic89—41no—
177Dic89—41no—
178C2×C89—41no—
179C2×C89—41no—
180C2×C89—42no—
181C2×C89—81no—
182C2×C89#54611yescharacteristic
183C2×C89#57511yescharacteristic
184C2×C89#57711yescharacteristic
185#3311—891nomaximal, Sylow
186C89#331111yescharacteristic, complemented, Sylow
187#556—891no—
188#546D8911yescharacteristic
189#489—891no—
190#485—891no—
191#482—891no—
192#476—891no—
193#470—891no—
194#465—891no—
195#464—891no—
196#452—891no—
197#450—891no—
198#440—891no—
199#435—891no—
200#418—891no—
201#416—891no—
202C2×#41C2×D8911yescharacteristic
203C22×D4C2×D8911yescharacteristic
204C2×Q16—891no—
205C2×SD16—891no—
206C2×SD16—891no—
207C2×M16—891no—
208C22×C8—891no—
209C4⋊Q8—891no—
210#126—1781no—
211#126—1781no—
212#124—1781no—
213#124C2×D8911yescharacteristic
214#123—21no—
215C22⋊Q8—891no—
216C22⋊Q8—891no—
217C22⋊Q8C2×D8911yescharacteristic
218#121—21no—
219#121C2×D8911yescharacteristic
220#120—21no—
221C4×Q8—891no—
222C4×Q8—1781no—
223C4×D4C2×D8911yescharacteristic
224C4×D4C2×D8911yescharacteristic
225#117—891no—
226#117—891no—
227C2×C22⋊C4—21no—
228#107—891no—
229#106—891no—
230#106—891no—
231C4⋊C8—891no—
232#103—891no—
233#103—891no—
234#103—891no—
235#103—891no—
236#102—891no—
237#102—891no—
238#102—891no—
239#102—891no—
240#102—891no—
241#102—891no—
242C22⋊C8—891no—
243C22⋊C8—891no—
244#97—891no—
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—891no—
249C2×Q8—1781no—
250C2×Q8C22×D8911yescharacteristic
251C2×D4—22no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4C22⋊D8911yescharacteristic
257C2×D4C22×D8911yescharacteristic
258C2×D4C22×D8911yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4C22×D8911yescharacteristic
262C22×C4C22×D8911yescharacteristic
263Q16—3561no—
264SD16—3561no—
265SD16—1782no—
266M16—3561no—
267C2×C8—891no—
268C2×C8—891no—
269C2×C8—891no—
270C2×C8—891no—
271C2×C8—3561no—
272C4⋊C4—21no—
273C4⋊C4—891no—
274C4⋊C4—891no—
275C4⋊C4—891no—
276C4⋊C4—1781no—
277C4⋊C4—1781no—
278C4⋊C4—1781no—
279C4⋊C4—1781no—
280C4⋊C4C22⋊D8911yescharacteristic
281C4⋊C4C22×D8911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1781no—
288C22⋊C4—1781no—
289C22⋊C4—1781no—
290C22⋊C4—1781no—
291C22⋊C4C22⋊D8911yescharacteristic
292C22⋊C4C22⋊D8911yescharacteristic
293C42—1781no—
294C42—1781no—
295C42—1781no—
296C42C22×D8911yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×C22⋊D8911yescharacteristic
303C23C2×C22⋊D8911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—3562no—
307Q8—1781no—
308Q8—1781no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—42no—
314D4—42no—
315D4—81no—
316D4#1308357312yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—81no—
325C2×C4—1781no—
326C2×C4—1781no—
327C2×C4—1781no—
328C2×C4—1781no—
329C2×C4C2×C22⋊D8911yescharacteristic
330C2×C4C2×C22⋊D8911yescharacteristic
331C2×C4C2×C22⋊D8911yescharacteristic
332C2×C4C2×C22⋊D8911yescharacteristic
333C2×C4C23×D8911yescharacteristic
334C8—1781no—
335C8—1781no—
336C8—1781no—
337C8—1781no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—84no—
351C22C22×C22⋊D8911yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—3561no—
359C4—3561no—
360C4—3561no—
361C4—3561no—
362C4C2×#1308357311yescharacteristic
363C4#1566805711yescharacteristic
364C2—41no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2#1915224211yescharacteristic
369C2#1915239611yescharacteristic
370C2#1915240911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting, prime radical#546×C89C2
socleC22×C89C22×D4
hypercenter#546D89
hypocenterC89#3311
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #19152318C2semidirect
2. #19151957C2semidirect
3. #19151936C2semidirect
4. #19151919C2semidirect
5. #19151888C2semidirect
6. #19151854C2semidirect
7. #19151825C2semidirect
8. #19151817C2semidirect
9. #19151760C2semidirect
10. #19151749C2semidirect
11. #19151698C2semidirect
12. #19151670C2semidirect
13. #19151603C2semidirect
14. #19151594C2semidirect
16. C2×#13083564C22semidirect
20. C22×#10623494C22semidirect
21. #15668012C22semidirect
26. #15667991C22semidirect
27. C4×Dic178C22semidirect
30. #15667971C22semidirect
31. #15667945C22semidirect
32. #15667943C22semidirect
33. #15667943C22semidirect
34. C4⋊#10623494C22semidirect
35. #15667936C22semidirect
36. #15667936C22semidirect
37. #15667936C22semidirect
38. #15667935C22semidirect
46. C22⋊#10623494C22semidirect
47. #15667923C22semidirect
186. C89#3311semidirect

Maximal subgroups

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

subgroupindex
#191523182
#191519572
#191519362
#191519192
#191518882
#191518542
#191518252
#191518172
#191517602
#191517492
#191516982
#191516702
#191516032
#191515942
#546×C892
#331189