Finite Group Databasebeta

← #26029079

Subgroups — #26029079

Order 11392.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15668039C211yesmaximal, characteristic
2#19152080C211yesmaximal, characteristic, complemented
3#19152070C211yesmaximal, characteristic, complemented
4#19151709C211yesmaximal, characteristic, complemented
5#19151708C211yesmaximal, characteristic, complemented
6#19151699C211yesmaximal, characteristic, complemented
7#19151696C211yesmaximal, characteristic, complemented
8#19151683C211yesmaximal, characteristic, complemented
9C4×D712C211yesmaximal, characteristic, complemented
10#19151678C211yesmaximal, characteristic, complemented
11#19151637C211yesmaximal, characteristic, complemented
12#19151593C211yesmaximal, characteristic, complemented
13#102×D89C211yesmaximal, characteristic, complemented
14#19151552C211yesmaximal, characteristic, complemented
15C4×SD16×C89C211yesmaximal, characteristic, complemented
16C2×#13083575C2211yescharacteristic
17C2×D4×D89C2211yescharacteristic
18#15668039C418yescomplemented
19C2×#13083561C2211yescharacteristic
20C2×D712C2211yescharacteristic
21C2×#13083559C2211yescharacteristic
22C2×#13083557C2211yescharacteristic
23C2×C8×D89C2211yescharacteristic
24Q8×Dic89C2211yescharacteristic, complemented
25C4×D356—21no—
26C4×D356C2211yescharacteristic
27C4×D356C2211yescharacteristic, complemented
28D4×Dic89C2211yescharacteristic
29#15667974—21no—
30#15667974C2211yescharacteristic
31#15667974C2211yescharacteristic, complemented
32C4×C22⋊D89—21no—
33#15667972—21no—
34#15667970C2211yescharacteristic
35#15667969—21no—
36#15667969C2211yescharacteristic
37C4⋊C4×D89—21no—
38C4⋊C4×D89C2211yescharacteristic
39C2×#13083551—21no—
40C22⋊C4×D89—21no—
41#15667946C2211yescharacteristic, complemented
42#15667945C2211yescharacteristic, complemented
43#15667943C2211yescharacteristic, complemented
44#15667936C2211yescharacteristic, complemented
45#15667934C2211yescharacteristic
46#15667934C2211yescharacteristic, complemented
47#15667933C2211yescharacteristic
48#15667932C2211yescharacteristic
49#15667932C2211yescharacteristic, complemented
50#15667923C2211yescharacteristic, complemented
51#15667922C2211yescharacteristic, complemented
52C8×Dic89C2211yescharacteristic, complemented
53C2×SD16×C89C2211yescharacteristic
54C4×Q8×C89C2211yescharacteristic, complemented
55C4×D4×C89C2211yescharacteristic
56#106×C89C2211yescharacteristic, complemented
57#103×C89C2211yescharacteristic, complemented
58#102×C89C2211yescharacteristic
59C4×C8×C89C2211yescharacteristic, complemented
60C23×D89—21no—
61#13083575—22no—
62#13083575C2×C414yescomplemented
63C2×D356—21no—
64C2×D356C2311yescharacteristic
65C2×D356C2311yescharacteristic
66C2×C22⋊D89—21no—
67D4×D89—22no—
68D4×D89C2×C414yescomplemented
69C22×Dic89—21no—
70C2×C4×D89—21no—
71C2×C4×D89—21no—
72C2×C4×D89—21no—
73C2×C4×D89—21no—
74C2×C4×D89—21no—
75C2×C4×D89—21no—
76C2×C4×D89C2311yescharacteristic
77#13083561C2×C414yescomplemented
78D712C2×C414yescomplemented
79#13083559C2×C414yescomplemented
80#13083557C2×C414yescomplemented
81C2×#10623494C2311yescharacteristic
82C2×#10623494C2311yescharacteristic
83C8×D89—22no—
84C4⋊Dic89—21no—
85C4⋊Dic89C2311yescharacteristic
86C4⋊Dic89C2311yescharacteristic
87#13083553—21no—
88#13083553D411yescharacteristic
89#13083553D411yescharacteristic
90C22⋊Dic89—21no—
91#13083551—21no—
92#13083551—21no—
93#13083551—21no—
94#13083551—21no—
95#13083551—21no—
96#13083551D411yescharacteristic
97#13083551D411yescharacteristic
98C4×Dic89—21no—
99C4×Dic89—21no—
100C4×Dic89C2311yescharacteristic
101C2×Q8×C89C2311yescharacteristic
102C2×D4×C89C2311yescharacteristic
103C22×C4×C89—21no—
104SD16×C89C2×C414yescomplemented
105C2×C8×C89C2311yescharacteristic
106C2×C8×C89C2311yescharacteristic
107C4⋊C4×C89—21no—
108C4⋊C4×C89C2311yescharacteristic
109C4⋊C4×C89C2311yescharacteristic
110C22⋊C4×C89—21no—
111C42×C89—21no—
112C42×C89C2311yescharacteristic
113C23×C89—21no—
114C22×D89—21no—
115C22×D89—21no—
116C22×D89—24no—
117C22×D89—81no—
118C22×D89—81no—
119C22×D89C2×D411yescharacteristic
120Q8×C89—21no—
121Q8×C89C22×C412yes—
122D4×C89—21no—
123D4×C89C22×C412yes—
124C2×C4×C89—21no—
125C2×C4×C89—21no—
126C2×C4×C89—21no—
127C2×C4×C89—81no—
128C2×C4×C89C2×D411yescharacteristic
129C2×C4×C89C2×D411yescharacteristic
130C2×C4×C89C2411yescharacteristic
131C22⋊D89—24no—
132C2×Dic89—21no—
133C2×Dic89—21no—
134C2×Dic89—81no—
135C2×Dic89C2×D411yescharacteristic
136C2×Dic89C2×D411yescharacteristic
137C2×Dic89C2×D411yescharacteristic
138D356—24no—
139D356—21no—
140D356—21no—
141D356C22×C412yes—
142D356C22×C412yes—
143C4×D89—24no—
144C4×D89—81no—
145C4×D89—81no—
146C4×D89—81no—
147C4×D89—81no—
148C4×D89—81no—
149C4×D89C22×C412yes—
150C4×D89#4112yes—
151C8×C89—21no—
152C8×C89C22×C412yes—
153#10623494—21no—
154#10623494C22×C412yes—
155C22×C89—22no—
156C22×C89—41no—
157C22×C89—41no—
158C22×C89C22×D411yescharacteristic
159C2×D89—21no—
160C2×D89—21no—
161C2×D89—22no—
162C2×D89—22no—
163C2×D89—41no—
164C2×D89—41no—
165C2×D89—41no—
166C2×D89—41no—
167C2×D89—84no—
168C2×D89C4×D412yes—
169C4×C89—22no—
170C4×C89—21no—
171C4×C89—21no—
172C4×C89—41no—
173C4×C89—41no—
174C4×C89C23×C411yescharacteristic
175C4×C89C2×#4111yescharacteristic
176Dic89—21no—
177Dic89—21no—
178Dic89—41no—
179Dic89—41no—
180Dic89C4×D412yes—
181C2×C89—42no—
182C2×C89C2×C4×D411yescharacteristic
183C2×C89#57611yescharacteristic
184C2×C89#57711yescharacteristic
185D89—22no—
186D89—42no—
187D89—42no—
188#2946—891nomaximal, Sylow
189C89#294611yescharacteristic, complemented, Sylow
190C2×AGL(1,ℤ/8)—891no—
191#520—891no—
192#518—891no—
193#442—891no—
194#442—891no—
195#440—891no—
196#440—891no—
197C4×SD16—891no—
198C4×SD16D8911yescharacteristic, complemented
199C4×D8—891no—
200C4×D8—891no—
201#428—891no—
202#416—891no—
203C2×#102—891no—
204#405—891no—
205C2×#41—891no—
206C22×D4—891no—
207AGL(1,ℤ/8)—898no—
208C2×SD16—891no—
209C2×SD16C2×D8911yescharacteristic
210C2×D8—891no—
211C2×D8—891no—
212C2×M16—891no—
213C22×C8—891no—
214C4×Q8—891no—
215C4×Q8C2×D8911yescharacteristic, complemented
216C4×D4—891no—
217C4×D4—891no—
218C4×D4—891no—
219C4×D4—891no—
220C4×D4—891no—
221C4×D4—1781no—
222C4×D4—1781no—
223C4×D4—1781no—
224C4×D4—1781no—
225C4×D4C2×D8911yescharacteristic
226#117—891no—
227#117—891no—
228#117—1781no—
229C2×C4⋊C4—891no—
230C2×C4⋊C4—1781no—
231C2×C22⋊C4—1781no—
232C2×C22⋊C4—1781no—
233#107—891no—
234#107—891no—
235#106—891no—
236#106C2×D8911yescharacteristic, complemented
237#103—891no—
238#103C2×D8911yescharacteristic, complemented
239#102—891no—
240#102—891no—
241#102—891no—
242#102—891no—
243#102—891no—
244#102C2×D8911yescharacteristic
245#97—891no—
246#97—891no—
247C4×C8—891no—
248C4×C8C2×D8911yescharacteristic, complemented
249C24—1781no—
250#41—894no—
251#41—1782no—
252C2×Q8C22×D8911yescharacteristic
253C2×D4—894no—
254C2×D4—891no—
255C2×D4—891no—
256C2×D4—1781no—
257C2×D4—1782no—
258C2×D4—1781no—
259C2×D4C22×D8911yescharacteristic
260C22×C4—21no—
261C22×C4—891no—
262C22×C4—1781no—
263C22×C4—1781no—
264C22×C4—1781no—
265C22×C4—1781no—
266C22×C4—1781no—
267C22×C4—1781no—
268C22×C4—1781no—
269SD16—894no—
270SD16C4×D8914yescomplemented
271D8—894no—
272D8—894no—
273M16—894no—
274C2×C8—891no—
275C2×C8—891no—
276C2×C8—1782no—
277C2×C8C22×D8911yescharacteristic
278C2×C8C22×D8911yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—891no—
281C4⋊C4—891no—
282C4⋊C4—891no—
283C4⋊C4—891no—
284C4⋊C4—1781no—
285C4⋊C4—1781no—
286C4⋊C4C22×D8911yescharacteristic
287C4⋊C4C22×D8911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—891no—
290C22⋊C4—891no—
291C22⋊C4—1781no—
292C22⋊C4—1781no—
293C22⋊C4—1781no—
294C22⋊C4—1781no—
295C22⋊C4—1781no—
296C22⋊C4—1781no—
297C42—21no—
298C42—891no—
299C42—1781no—
300C42—1781no—
301C42C22×D8911yescharacteristic
302C23—21no—
303C23—891no—
304C23—1784no—
305C23—1781no—
306C23—1781no—
307C23—7121no—
308C23—7121no—
309Q8—21no—
310Q8C2×C4×D8912yes—
311D4—21no—
312D4—892no—
313D4—892no—
314D4—1784no—
315D4—1784no—
316D4—1781no—
317D4—1781no—
318D4C2×C4×D8912yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—891no—
324C2×C4—892no—
325C2×C4—892no—
326C2×C4—891no—
327C2×C4—891no—
328C2×C4—1784no—
329C2×C4—1781no—
330C2×C4—1781no—
331C2×C4—7121no—
332C2×C4—7121no—
333C2×C4—7121no—
334C2×C4—7121no—
335C2×C4—7121no—
336C2×C4—7121no—
337C2×C4D4×D8911yescharacteristic
338C2×C4D4×D8911yescharacteristic
339C2×C4C23×D8911yescharacteristic
340C8—21no—
341C8—892no—
342C8—1781no—
343C8C2×C4×D8912yes—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—892no—
348C22—3561no—
349C22—3561no—
350C22—3561no—
351C22—3561no—
352C22—1782no—
353C22—1782no—
354C22—1781no—
355C22—1781no—
356C22—7124no—
357C22C2×D4×D8911yescharacteristic
358C4—21no—
359C4—21no—
360C4—22no—
361C4—41no—
362C4—41no—
363C4—892no—
364C4—3561no—
365C4—3561no—
366C4—1781no—
367C4—1781no—
368C4C22×C4×D8911yescharacteristic
369C4#41×D8911yescharacteristic
370C2—42no—
371C2—3562no—
372C2—3562no—
373C2—1782no—
374C2C4×D4×D8911yescharacteristic
375C2#1915240011yescharacteristic
376C2#1915240411yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutatorC4×C89C23×C4
FrattiniC2×C4C23×D89
FittingC4×SD16×C89C2
socleC22×C89C22×D4
prime radicalC2×#15668039C2
cosocleC2×C4×C89C24
hypercenterC4×SD16D89
hypocenterC89#2946
LCSG ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #19152080C2semidirect
3. #19152070C2semidirect
4. #19151709C2semidirect
5. #19151708C2semidirect
6. #19151699C2semidirect
7. #19151696C2semidirect
8. #19151683C2semidirect
9. C4×D712C2semidirect
10. #19151678C2semidirect
11. #19151637C2semidirect
12. #19151593C2semidirect
13. #102×D89C2semidirect
14. #19151552C2semidirect
15. C4×SD16×C89C2semidirect
18. #15668039C4semidirect
24. Q8×Dic89C22semidirect
27. C4×D356C22semidirect
31. #15667974C22semidirect
41. #15667946C22semidirect
42. #15667945C22semidirect
43. #15667943C22semidirect
44. #15667936C22semidirect
46. #15667934C22semidirect
49. #15667932C22semidirect
50. #15667923C22semidirect
51. #15667922C22semidirect
52. C8×Dic89C22semidirect
54. C4×Q8×C89C22semidirect
56. #106×C89C22semidirect
57. #103×C89C22semidirect
59. C4×C8×C89C22semidirect
62. #13083575C2×C4semidirect
68. D4×D89C2×C4semidirect
77. #13083561C2×C4semidirect
78. D712C2×C4semidirect
79. #13083559C2×C4semidirect
80. #13083557C2×C4semidirect
104. SD16×C89C2×C4semidirect
189. C89#2946semidirect
198. C4×SD16D89semidirect
215. C4×Q8C2×D89semidirect
236. #106C2×D89semidirect
238. #103C2×D89semidirect
248. C4×C8C2×D89semidirect
270. SD16C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156680392
#191520802
#191520702
#191517092
#191517082
#191516992
#191516962
#191516832
C4×D7122
#191516782
#191516372
#191515932
#102×D892
#191515522
C4×SD16×C892
#294689