Finite Group Databasebeta

← #26030607

Subgroups — #26030607

Order 11392.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152228C211yesmaximal, characteristic, complemented
2#19152161C211yesmaximal, characteristic
3#19151961C211yesmaximal, characteristic, complemented
4#19151958C211yesmaximal, characteristic, complemented
5#19151956C211yesmaximal, characteristic, complemented
6#19151955C211yesmaximal, characteristic, complemented
7#19151951C211yesmaximal, characteristic, complemented
8#19151944C211yesmaximal, characteristic, complemented
9#19151943C211yesmaximal, characteristic, complemented
10#19151601C211yesmaximal, characteristic, complemented
11#19151596C211yesmaximal, characteristic, complemented
12#19151591C211yesmaximal, characteristic, complemented
13#102×D89C211yesmaximal, characteristic, complemented
14#19151555C211yesmaximal, characteristic, complemented
15#490×C89C211yesmaximal, characteristic, complemented
16C2×#13083573C2211yescharacteristic
17C2×D4×D89C2211yescharacteristic
18C2×#13083557C2211yescharacteristic
19C2×C8×D89C2211yescharacteristic
20#15668012C2211yescharacteristic, complemented
21#15668011—21no—
22#15668011C2211yescharacteristic, complemented
23#15668008C2211yescharacteristic
24#15668003C2211yescharacteristic, complemented
25#15668002—21no—
26#15668000C2211yescharacteristic
27#15667999C2211yescharacteristic
28#15667992—21no—
29#15667990—21no—
30#15667984—21no—
31#15667984—21no—
32#15667980—21no—
33#15667980—21no—
34#15667970C2211yescharacteristic
35#15667969C2211yescharacteristic
36C4⋊C4×D89C2211yescharacteristic
37#15667937C2211yescharacteristic, complemented
38#15667937C2211yescharacteristic, complemented
39#15667935C2211yescharacteristic, complemented
40#15667935C2211yescharacteristic, complemented
41#15667934C2211yescharacteristic
42#15667934C2211yescharacteristic
43#15667933C2211yescharacteristic
44#15667933C2211yescharacteristic
45#15667933C2211yescharacteristic, complemented
46#15667933C2211yescharacteristic, complemented
47#15667932C2211yescharacteristic
48#15667932C2211yescharacteristic
49#15667922C2211yescharacteristic, complemented
50C4×#10623494C2211yescharacteristic, complemented
51C8×Dic89C2211yescharacteristic, complemented
52#127×C89C2211yescharacteristic
53#125×C89C2211yescharacteristic, complemented
54#102×C89C2211yescharacteristic
55#102×C89C2211yescharacteristic
56#102×C89C2211yescharacteristic, complemented
57#102×C89C2211yescharacteristic, complemented
58#97×C89C2211yescharacteristic, complemented
59C23×D89—21no—
60#13083573—22no—
61#13083573—22no—
62C2×Dic178—21no—
63C2×Dic178—21no—
64C2×Dic178C2311yescharacteristic
65C2×D356C2311yescharacteristic
66C2×C22⋊D89—21no—
67C2×C22⋊D89—21no—
68C2×C22⋊D89—21no—
69C2×C22⋊D89—21no—
70D4×D89—22no—
71D4×D89—22no—
72C22×Dic89—21no—
73C2×C4×D89—21no—
74C2×C4×D89C2311yescharacteristic
75#13083557—22no—
76C2×#10623494C2311yescharacteristic
77C2×#10623494C2311yescharacteristic
78C8×D89—22no—
79C4⋊Dic89—21no—
80C4⋊Dic89—21no—
81C4⋊Dic89C2311yescharacteristic
82C4⋊Dic89C2311yescharacteristic
83#13083553—21no—
84#13083553—21no—
85#13083553—21no—
86#13083553D411yescharacteristic
87#13083553D411yescharacteristic
88C22⋊Dic89—21no—
89C22⋊Dic89—21no—
90#13083551—21no—
91#13083551—21no—
92#13083551—21no—
93#13083551D411yescharacteristic
94#13083551D411yescharacteristic
95C4×Dic89—21no—
96C4×Dic89C2311yescharacteristic
97C2×D4×C89—21no—
98C2×D4×C89—21no—
99C2×D4×C89C2311yescharacteristic
100C2×D4×C89C2311yescharacteristic
101C2×C8×C89C2311yescharacteristic
102C2×C8×C89C2311yescharacteristic
103C4⋊C4×C89—21no—
104C4⋊C4×C89—21no—
105C4⋊C4×C89C2311yescharacteristic
106C4⋊C4×C89C2311yescharacteristic
107C42×C89C2311yescharacteristic
108C23×C89—21no—
109C23×C89—21no—
110C22×D89—21no—
111C22×D89—42no—
112C22×D89—81no—
113C22×D89—81no—
114C22×D89C2×D411yescharacteristic
115D4×C89—21no—
116D4×C89—21no—
117D4×C89—21no—
118D4×C89—21no—
119D4×C89—81no—
120D4×C89—81no—
121C2×C4×C89—21no—
122C2×C4×C89—21no—
123C2×C4×C89C2×D411yescharacteristic
124C2×C4×C89C2×D411yescharacteristic
125C2×C4×C89C2411yescharacteristic
126C22⋊D89—42no—
127C22⋊D89—42no—
128C22⋊D89—81no—
129C22⋊D89—81no—
130C2×Dic89—21no—
131C2×Dic89—21no—
132C2×Dic89—21no—
133C2×Dic89—42no—
134C2×Dic89C2×D411yescharacteristic
135C2×Dic89C2×D411yescharacteristic
136C2×Dic89C2×D411yescharacteristic
137D356—21no—
138D356—21no—
139C4×D89—81no—
140C4×D89#4112yes—
141C4×D89#4112yes—
142Dic178—21no—
143Dic178—21no—
144Dic178—81no—
145Dic178—81no—
146C8×C89—21no—
147C8×C89—21no—
148#10623494—21no—
149#10623494—21no—
150C22×C89—41no—
151C22×C89—41no—
152C22×C89—41no—
153C22×C89—41no—
154C22×C89—41no—
155C22×C89—41no—
156C22×C89C22×D411yescharacteristic
157C2×D89—21no—
158C2×D89—21no—
159C2×D89—41no—
160C2×D89—41no—
161C2×D89—41no—
162C2×D89—84no—
163C2×D89#12412yes—
164C4×C89—21no—
165C4×C89—21no—
166C4×C89—41no—
167C4×C89—41no—
168C4×C89C2×#4111yescharacteristic
169C4×C89C2×#4111yescharacteristic
170Dic89—21no—
171Dic89—21no—
172Dic89—41no—
173Dic89—41no—
174Dic89—41no—
175Dic89#12412yes—
176C2×C89—81no—
177C2×C89—81no—
178C2×C89C2×#12411yescharacteristic
179C2×C89#57611yescharacteristic
180C2×C89#57711yescharacteristic
181D89—22no—
182D89—81no—
183#3136—891nomaximal, Sylow
184C89#313611yescharacteristic, complemented, Sylow
185#544—891no—
186#535—891no—
187#490—891no—
188#490D8911yescharacteristic, complemented
189#489—891no—
190#489—891no—
191#488—891no—
192#488—891no—
193#486—891no—
194#486—891no—
195#418—891no—
196#417—891no—
197#416—891no—
198C2×#102—891no—
199#405—891no—
200C2×#41—891no—
201C22×D4—891no—
202C2×M16—891no—
203C22×C8—891no—
204C4⋊Q8—891no—
205C4⋊Q8—891no—
206C4⋊Q8—1781no—
207#127—891no—
208#127C2×D8911yescharacteristic
209#125—891no—
210#125—1781no—
211#125C2×D8911yescharacteristic, complemented
212#124—891no—
213#124—891no—
214C22⋊Q8—1781no—
215C22⋊Q8—1781no—
216#121—1781no—
217#121—1781no—
218#120—1781no—
219#120—1781no—
220#117—891no—
221#117—891no—
222C2×C4⋊C4—891no—
223#103—891no—
224#103—891no—
225#103—891no—
226#103—891no—
227#102—891no—
228#102—891no—
229#102—891no—
230#102—891no—
231#102—891no—
232#102—891no—
233#102—891no—
234#102—891no—
235#102C2×D8911yescharacteristic
236#102C2×D8911yescharacteristic
237#102C2×D8911yescharacteristic, complemented
238#102C2×D8911yescharacteristic, complemented
239#97—891no—
240#97C2×D8911yescharacteristic, complemented
241C4×C8—891no—
242C4×C8—891no—
243C24—1781no—
244#41—1782no—
245#41—1782no—
246C2×Q8—891no—
247C2×Q8—1781no—
248C2×Q8—1781no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—891no—
252C2×D4—1782no—
253C2×D4—1782no—
254C2×D4—1781no—
255C2×D4—1781no—
256C2×D4—1781no—
257C2×D4—1781no—
258C2×D4C22×D8911yescharacteristic
259C2×D4C22×D8911yescharacteristic
260C22×C4—891no—
261C22×C4—1781no—
262C22×C4—1781no—
263M16—1782no—
264C2×C8—891no—
265C2×C8—891no—
266C2×C8—1782no—
267C2×C8C22×D8911yescharacteristic
268C2×C8C22×D8911yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—891no—
272C4⋊C4—891no—
273C4⋊C4—891no—
274C4⋊C4—891no—
275C4⋊C4—1781no—
276C4⋊C4—1781no—
277C4⋊C4—1781no—
278C4⋊C4—1781no—
279C4⋊C4—1781no—
280C4⋊C4C22×D8911yescharacteristic
281C4⋊C4C22×D8911yescharacteristic
282C22⋊C4—891no—
283C22⋊C4—891no—
284C22⋊C4—1781no—
285C22⋊C4—1781no—
286C22⋊C4—1781no—
287C22⋊C4—1781no—
288C22⋊C4—1781no—
289C42—891no—
290C42—1781no—
291C42C22×D8911yescharacteristic
292C23—21no—
293C23—21no—
294C23—891no—
295C23—3562no—
296C23—1781no—
297C23—7121no—
298C23—7121no—
299Q8—1781no—
300Q8—1781no—
301Q8—7121no—
302Q8—7121no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—81no—
309D4—3562no—
310D4—3562no—
311D4—1781no—
312D4—1781no—
313D4—7121no—
314D4—7121no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—891no—
318C2×C4—892no—
319C2×C4—892no—
320C2×C4—891no—
321C2×C4—891no—
322C2×C4—3562no—
323C2×C4—1781no—
324C2×C4—1781no—
325C2×C4—1781no—
326C2×C4—7121no—
327C2×C4D4×D8911yescharacteristic
328C2×C4D4×D8911yescharacteristic
329C2×C4C23×D8911yescharacteristic
330C8—21no—
331C8—21no—
332C8—1781no—
333C8—1781no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—892no—
341C22—3561no—
342C22—3561no—
343C22—3561no—
344C22—1781no—
345C22—1781no—
346C22—7124no—
347C22C2×D4×D8911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—892no—
353C4—3561no—
354C4—3561no—
355C4—3561no—
356C4—1781no—
357C4—1781no—
358C4#41×D8911yescharacteristic
359C4#41×D8911yescharacteristic
360C2—81no—
361C2—81no—
362C2—1782no—
363C2—7121no—
364C2#124×D8911yescharacteristic
365C2#1915240211yescharacteristic
366C2#1915240811yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#490×C89C2
socleC22×C89C22×D4
prime radical#19152161C2
hypercenter#490D89
hypocenterC89#3136
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #19152228C2semidirect
3. #19151961C2semidirect
4. #19151958C2semidirect
5. #19151956C2semidirect
6. #19151955C2semidirect
7. #19151951C2semidirect
8. #19151944C2semidirect
9. #19151943C2semidirect
10. #19151601C2semidirect
11. #19151596C2semidirect
12. #19151591C2semidirect
13. #102×D89C2semidirect
14. #19151555C2semidirect
15. #490×C89C2semidirect
20. #15668012C22semidirect
22. #15668011C22semidirect
24. #15668003C22semidirect
37. #15667937C22semidirect
38. #15667937C22semidirect
39. #15667935C22semidirect
40. #15667935C22semidirect
45. #15667933C22semidirect
46. #15667933C22semidirect
49. #15667922C22semidirect
50. C4×#10623494C22semidirect
51. C8×Dic89C22semidirect
53. #125×C89C22semidirect
56. #102×C89C22semidirect
57. #102×C89C22semidirect
58. #97×C89C22semidirect
184. C89#3136semidirect
188. #490D89semidirect
211. #125C2×D89semidirect
237. #102C2×D89semidirect
238. #102C2×D89semidirect
240. #97C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191522282
#191521612
#191519612
#191519582
#191519562
#191519552
#191519512
#191519442
#191519432
#191516012
#191515962
#191515912
#102×D892
#191515552
#490×C892
#313689