Finite Group Databasebeta

← #26032329

Subgroups — #26032329

Order 11392.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152303C211yesmaximal, characteristic, complemented
2#19152242C211yesmaximal, characteristic
3#19151956C211yesmaximal, characteristic, complemented
4#19151933C211yesmaximal, characteristic, complemented
5#19151910C211yesmaximal, characteristic, complemented
6#19151876C211yesmaximal, characteristic, complemented
7#19151843C211yesmaximal, characteristic, complemented
8#19151839C211yesmaximal, characteristic, complemented
9#19151819C211yesmaximal, characteristic, complemented
10#19151761C211yesmaximal, characteristic, complemented
11#19151749C211yesmaximal, characteristic, complemented
12#19151695C211yesmaximal, characteristic, complemented
13#19151669C211yesmaximal, characteristic, complemented
14#19151596C211yesmaximal, characteristic, complemented
15C2×#102×C89C211yesmaximal, characteristic, complemented
16C2×#13083573C2211yescharacteristic
17C2×Dic356C2211yescharacteristic, complemented
18C2×#13083562C2211yescharacteristic
19C2×#13083562C2211yescharacteristic
20C2×#13083557C2211yescharacteristic, complemented
21#15668011C2211yescharacteristic, complemented
22#15668002—21no—
23#15667999C2211yescharacteristic
24#15667993—21no—
25#15667992C2211yescharacteristic, complemented
26#15667991—21no—
27#15667991C2211yescharacteristic
28#15667991C2211yescharacteristic
29#15667990—21no—
30#15667984—21no—
31#15667983C2211yescharacteristic
32#15667981—21no—
33#15667977C2211yescharacteristic, complemented
34D4×Dic89C2211yescharacteristic
35C4×C22⋊D89—21no—
36C4×C22⋊D89C2211yescharacteristic
37C4⋊C4×D89C2211yescharacteristic, complemented
38C2×C22⋊Dic89—21no—
39#15667946C2211yescharacteristic, complemented
40#15667945C2211yescharacteristic, complemented
41#15667945C2211yescharacteristic, complemented
42#15667941C2211yescharacteristic, complemented
43#15667937C2211yescharacteristic, complemented
44#15667937C2211yescharacteristic, complemented
45#15667935C2211yescharacteristic, complemented
46#15667935C2211yescharacteristic, complemented
47#15667933C2211yescharacteristic
48#15667933C2211yescharacteristic
49C22⋊#10623494C2211yescharacteristic
50#15667924C2211yescharacteristic, complemented
51#15667922C2211yescharacteristic, complemented
52C22×D4×C89C2211yescharacteristic
53C22×C8×C89C2211yescharacteristic
54C2×C4⋊C4×C89C2211yescharacteristic
55#102×C89C2211yescharacteristic
56#102×C89C2211yescharacteristic
57#102×C89C2211yescharacteristic
58#102×C89C2211yescharacteristic
59#13083573—22no—
60#13083573—41no—
61C2×Dic178—21no—
62C2×Dic178C2311yescharacteristic
63C2×Dic178C2311yescharacteristic
64C2×C22⋊D89—21no—
65C2×C22⋊D89—21no—
66C2×C22⋊D89D411yescharacteristic
67C22×Dic89—21no—
68C22×Dic89—21no—
69C2×C4×D89—21no—
70C2×C4×D89C2311yescharacteristic
71Dic356—41no—
72#13083562—22no—
73#13083562—41no—
74#13083557—41no—
75C2×#10623494C2311yescharacteristic
76C2×#10623494C2311yescharacteristic
77C4⋊Dic89—21no—
78C4⋊Dic89C2311yescharacteristic
79C4⋊Dic89C2311yescharacteristic
80#13083553—21no—
81#13083553—21no—
82#13083553—21no—
83#13083553—21no—
84#13083553—21no—
85#13083553D411yescharacteristic
86C22⋊Dic89—21no—
87C22⋊Dic89—21no—
88C22⋊Dic89—21no—
89C22⋊Dic89—21no—
90C22⋊Dic89—21no—
91C22⋊Dic89—21no—
92C22⋊Dic89D411yescharacteristic
93#13083551—21no—
94#13083551D411yescharacteristic
95C4×Dic89—21no—
96C4×Dic89C2311yescharacteristic
97C24×C89—21no—
98C2×D4×C89—22no—
99C2×D4×C89—21no—
100C2×D4×C89—41no—
101C2×D4×C89C2311yescharacteristic
102C2×D4×C89C2311yescharacteristic
103C22×C4×C89—21no—
104C22×C4×C89C2311yescharacteristic
105C2×C8×C89—41no—
106C2×C8×C89C2311yescharacteristic
107C2×C8×C89C2311yescharacteristic
108C4⋊C4×C89—21no—
109C4⋊C4×C89C2311yescharacteristic
110C4⋊C4×C89C2311yescharacteristic
111C23×C89—21no—
112C23×C89—21no—
113C23×C89—42no—
114C23×C89—42no—
115C23×C89—81no—
116C23×C89C2×D411yescharacteristic
117C22×D89C2×D411yescharacteristic
118D4×C89—21no—
119D4×C89—21no—
120D4×C89—21no—
121D4×C89—42no—
122D4×C89#4112yes—
123C2×C4×C89—21no—
124C2×C4×C89—21no—
125C2×C4×C89—21no—
126C2×C4×C89—21no—
127C2×C4×C89—81no—
128C2×C4×C89C2×D411yescharacteristic
129C2×C4×C89C2411yescharacteristic
130C22⋊D89—22no—
131C22⋊D89—42no—
132C22⋊D89—81no—
133C2×Dic89—21no—
134C2×Dic89—21no—
135C2×Dic89—21no—
136C2×Dic89—21no—
137C2×Dic89—42no—
138C2×Dic89—81no—
139C2×Dic89C2×D411yescharacteristic
140C2×Dic89C2×D411yescharacteristic
141C2×Dic89C2×D411yescharacteristic
142C4×D89—21no—
143C4×D89—21no—
144C4×D89—81no—
145Dic178—21no—
146Dic178—21no—
147Dic178—21no—
148Dic178—21no—
149Dic178—81no—
150C8×C89—21no—
151C8×C89—21no—
152#10623494—21no—
153#10623494—21no—
154C22×C89—21no—
155C22×C89—21no—
156C22×C89—22no—
157C22×C89—41no—
158C22×C89—41no—
159C22×C89—41no—
160C22×C89—41no—
161C22×C89—41no—
162C22×C89—84no—
163C22×C89#13712yes—
164C22×C89C22×D411yescharacteristic
165C2×D89—21no—
166C2×D89—21no—
167C2×D89—21no—
168C4×C89—21no—
169C4×C89—41no—
170C4×C89—41no—
171C4×C89C2×#4111yescharacteristic
172C4×C89H(5,𝔽2)11yescharacteristic
173Dic89—21no—
174Dic89—21no—
175Dic89—21no—
176Dic89—41no—
177Dic89—41no—
178Dic89—41no—
179Dic89—41no—
180C2×C89—22no—
181C2×C89—42no—
182C2×C89—81no—
183C2×C89#54611yescharacteristic
184C2×C89C2×#13711yescharacteristic
185C2×C89#57611yescharacteristic
186D89—41no—
187#3314—891nomaximal, Sylow
188C89#331411yescharacteristic, complemented, Sylow
189#554—891no—
190#546—891no—
191#489—891no—
192#484—891no—
193#480—891no—
194#474—891no—
195#468—891no—
196#467—891no—
197#464—891no—
198#452—891no—
199#450—891no—
200#440—891no—
201#435—891no—
202#417—891no—
203C2×#102D8911yescharacteristic, complemented
204C2×#41—891no—
205C22×D4C2×D8911yescharacteristic
206C2×Q16—891no—
207C2×SD16—891no—
208C2×SD16—891no—
209C2×M16—891no—
210C22×C8C2×D8911yescharacteristic
211C4⋊Q8—891no—
212#125—1781no—
213#124—891no—
214#123—1781no—
215C22⋊Q8—891no—
216C22⋊Q8—891no—
217C22⋊Q8—891no—
218C22⋊Q8—1781no—
219C22⋊Q8—1781no—
220#121—891no—
221#121—1781no—
222#120—1781no—
223C4×Q8—891no—
224C4×D4—891no—
225C4×D4—891no—
226C4×D4—1781no—
227C2×C4⋊C4—891no—
228C2×C4⋊C4C2×D8911yescharacteristic
229C2×C22⋊C4—1781no—
230#107—891no—
231#107—891no—
232#107—891no—
233C4⋊C8—891no—
234#103—891no—
235#103—891no—
236#103—891no—
237#103—891no—
238#102—891no—
239#102—891no—
240#102C2×D8911yescharacteristic
241#102C2×D8911yescharacteristic
242#102C2×D8911yescharacteristic
243#102C2×D8911yescharacteristic
244C22⋊C8—891no—
245C22⋊C8—891no—
246#97—891no—
247C24—21no—
248#41—3561no—
249#41—1782no—
250C2×Q8—891no—
251C2×Q8—891no—
252C2×Q8—1781no—
253C2×D4—22no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4—891no—
257C2×D4—1781no—
258C2×D4—1781no—
259C2×D4C22×D8911yescharacteristic
260C2×D4C22×D8911yescharacteristic
261C22×C4—21no—
262C22×C4—891no—
263C22×C4—1781no—
264C22×C4—1781no—
265C22×C4—1781no—
266C22×C4C22×D8911yescharacteristic
267Q16—3561no—
268SD16—3561no—
269SD16—1782no—
270M16—3561no—
271C2×C8—41no—
272C2×C8—891no—
273C2×C8—891no—
274C2×C8C22×D8911yescharacteristic
275C2×C8C22×D8911yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—891no—
278C4⋊C4—891no—
279C4⋊C4—891no—
280C4⋊C4—1781no—
281C4⋊C4—1781no—
282C4⋊C4—1781no—
283C4⋊C4—1781no—
284C4⋊C4—1781no—
285C4⋊C4—1781no—
286C4⋊C4C22×D8911yescharacteristic
287C4⋊C4C22×D8911yescharacteristic
288C22⋊C4—891no—
289C22⋊C4—891no—
290C22⋊C4—1781no—
291C22⋊C4—1781no—
292C22⋊C4—1781no—
293C22⋊C4—1781no—
294C22⋊C4—1781no—
295C22⋊C4—1781no—
296C22⋊C4—1781no—
297C42—891no—
298C42—1781no—
299C23—21no—
300C23—21no—
301C23—42no—
302C23—42no—
303C23—81no—
304C23—891no—
305C23D4×D8911yescharacteristic
306Q8—1781no—
307Q8—1781no—
308Q8—1781no—
309Q8—1781no—
310Q8—7121no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—3562no—
316D4—1782no—
317D4—7121no—
318D4#1308357412yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—81no—
324C2×C4—891no—
325C2×C4—891no—
326C2×C4—891no—
327C2×C4—3562no—
328C2×C4—1781no—
329C2×C4—1781no—
330C2×C4—1781no—
331C2×C4—1781no—
332C2×C4—1781no—
333C2×C4—1781no—
334C2×C4—7121no—
335C2×C4—7121no—
336C2×C4D4×D8911yescharacteristic
337C2×C4C23×D8911yescharacteristic
338C8—21no—
339C8—21no—
340C8—1781no—
341C8—1781no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—84no—
351C22—1781no—
352C22—1781no—
353C22—1781no—
354C22#1566804112yes—
355C22C2×D4×D8911yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—3561no—
360C4—3561no—
361C4—3561no—
362C4—3561no—
363C4—1781no—
364C4—1781no—
365C4—1781no—
366C4C2×#1308357411yescharacteristic
367C4#1566805711yescharacteristic
368C2—22no—
369C2—42no—
370C2—81no—
371C2—3561no—
372C2#1915223811yescharacteristic
373C2C2×#1566804111yescharacteristic
374C2#1915239911yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC2×#102×C89C2
socleC22×C89C22×D4
prime radical#19152242C2
hypercenterC2×#102D89
hypocenterC89#3314
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #19152303C2semidirect
3. #19151956C2semidirect
4. #19151933C2semidirect
5. #19151910C2semidirect
6. #19151876C2semidirect
7. #19151843C2semidirect
8. #19151839C2semidirect
9. #19151819C2semidirect
10. #19151761C2semidirect
11. #19151749C2semidirect
12. #19151695C2semidirect
13. #19151669C2semidirect
14. #19151596C2semidirect
15. C2×#102×C89C2semidirect
17. C2×Dic356C22semidirect
20. C2×#13083557C22semidirect
21. #15668011C22semidirect
25. #15667992C22semidirect
33. #15667977C22semidirect
37. C4⋊C4×D89C22semidirect
39. #15667946C22semidirect
40. #15667945C22semidirect
41. #15667945C22semidirect
42. #15667941C22semidirect
43. #15667937C22semidirect
44. #15667937C22semidirect
45. #15667935C22semidirect
46. #15667935C22semidirect
50. #15667924C22semidirect
51. #15667922C22semidirect
188. C89#3314semidirect
203. C2×#102D89semidirect

Maximal subgroups

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

subgroupindex
#191523032
#191522422
#191519562
#191519332
#191519102
#191518762
#191518432
#191518392
#191518192
#191517612
#191517492
#191516952
#191516692
#191515962
C2×#102×C892
#331489