Finite Group Databasebeta

← #26030191

Subgroups — #26030191

Order 11392.

462 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D89C211yesmaximal, characteristic
2#117×D89C211yesmaximal, characteristic, complemented
3#19151923C211yesmaximal, characteristic, complemented
4#19151922C211yesmaximal, characteristic, complemented
5#19151919C211yesmaximal, characteristic, complemented
6#19151918C211yesmaximal, characteristic, complemented
7#19151915C211yesmaximal, characteristic, complemented
8#19151913C211yesmaximal, characteristic, complemented
9#19151910C211yesmaximal, characteristic, complemented
10#19151639C211yesmaximal, characteristic, complemented
11#19151637C211yesmaximal, characteristic, complemented
12#19151601C211yesmaximal, characteristic, complemented
13#19151601C211yesmaximal, characteristic, complemented
14#19151560C211yesmaximal, characteristic, complemented
15#482×C89C211yesmaximal, characteristic, complemented
16C2×D4×D89—21no—
17C2×D4×D89C2211yescharacteristic
18C22×C4×D89C2211yescharacteristic
19C2×#13083557C2211yescharacteristic
20C2×#13083557C2211yescharacteristic
21#15667987C2211yescharacteristic
22#15667986C2211yescharacteristic
23#15667985—21no—
24#15667984—21no—
25#15667983C2211yescharacteristic
26#15667971C2211yescharacteristic, complemented
27#15667970C2211yescharacteristic
28#15667970C2211yescharacteristic
29#15667969—21no—
30#15667968—21no—
31C4⋊C4×D89C2211yescharacteristic
32C4⋊C4×D89C2211yescharacteristic, complemented
33C4⋊C4×D89C2211yescharacteristic, complemented
34C22⋊C4×D89—21no—
35C22⋊C4×D89—21no—
36C42×D89—21no—
37#15667946C2211yescharacteristic, complemented
38#15667945C2211yescharacteristic, complemented
39#15667945C2211yescharacteristic, complemented
40#15667944C2211yescharacteristic, complemented
41#15667943C2211yescharacteristic, complemented
42#15667943C2211yescharacteristic, complemented
43#15667934C2211yescharacteristic, complemented
44#15667934C2211yescharacteristic, complemented
45#15667933C2211yescharacteristic, complemented
46#15667933C2211yescharacteristic, complemented
47#15667932C2211yescharacteristic, complemented
48#15667932C2211yescharacteristic, complemented
49C22⋊#10623494C2211yescharacteristic, complemented
50#15667924C2211yescharacteristic, complemented
51#15667924C2211yescharacteristic, complemented
52#121×C89C2211yescharacteristic
53#117×C89C2211yescharacteristic, complemented
54#107×C89C2211yescharacteristic, complemented
55#106×C89C2211yescharacteristic, complemented
56#102×C89C2211yescharacteristic, complemented
57#102×C89C2211yescharacteristic, complemented
58C22⋊C8×C89C2211yescharacteristic, complemented
59C23×D89—21no—
60C23×D89D411yescharacteristic
61C2×D356—21no—
62C2×D356C2311yescharacteristic
63C2×C22⋊D89—21no—
64C2×C22⋊D89—21no—
65C2×C22⋊D89—21no—
66D4×D89—22no—
67D4×D89—22no—
68D4×D89—44no—
69C22×Dic89D411yescharacteristic
70C2×C4×D89—22no—
71C2×C4×D89—22no—
72C2×C4×D89—21no—
73C2×C4×D89—21no—
74C2×C4×D89—21no—
75C2×C4×D89D411yescharacteristic
76C2×C4×D89D411yescharacteristic
77C2×C4×D89C2311yescharacteristic
78C2×C4×D89C2311yescharacteristic
79#13083557—22no—
80#13083557—22no—
81C2×#10623494C2311yescharacteristic
82C2×#10623494C2311yescharacteristic
83C4⋊Dic89C2311yescharacteristic
84C4⋊Dic89C2311yescharacteristic
85C4⋊Dic89C2311yescharacteristic
86#13083553—21no—
87#13083553—21no—
88#13083553—21no—
89C22⋊Dic89—21no—
90C22⋊Dic89—21no—
91#13083551—21no—
92#13083551—21no—
93#13083551—21no—
94#13083551—21no—
95C4×Dic89—21no—
96C4×Dic89—21no—
97C4×Dic89—21no—
98C2×D4×C89—21no—
99C2×D4×C89C2311yescharacteristic
100C22×C4×C89C2311yescharacteristic
101C2×C8×C89C2311yescharacteristic
102C2×C8×C89C2311yescharacteristic
103C4⋊C4×C89C2311yescharacteristic
104C4⋊C4×C89C2311yescharacteristic
105C4⋊C4×C89C2311yescharacteristic
106C22⋊C4×C89—21no—
107C22⋊C4×C89—21no—
108C42×C89—21no—
109C23×C89—21no—
110C23×C89C2×D411yescharacteristic
111C22×D89—22no—
112C22×D89—22no—
113C22×D89—21no—
114C22×D89—41no—
115C22×D89—42no—
116C22×D89—42no—
117C22×D89—42no—
118C22×D89C2×D411yescharacteristic
119C22×D89C2×D411yescharacteristic
120D4×C89—21no—
121D4×C89—21no—
122D4×C89—42no—
123C2×C4×C89—21no—
124C2×C4×C89—21no—
125C2×C4×C89—21no—
126C2×C4×C89—21no—
127C2×C4×C89—21no—
128C2×C4×C89C2×D411yescharacteristic
129C2×C4×C89C2411yescharacteristic
130C22⋊D89—42no—
131C22⋊D89—42no—
132C22⋊D89—42no—
133C2×Dic89—22no—
134C2×Dic89—21no—
135C2×Dic89—21no—
136C2×Dic89—21no—
137C2×Dic89C2×D411yescharacteristic
138C2×Dic89C2×D411yescharacteristic
139D356—21no—
140D356—21no—
141D356—42no—
142C4×D89—22no—
143C4×D89—21no—
144C4×D89—21no—
145C4×D89—22no—
146C4×D89—42no—
147C4×D89—42no—
148C4×D89—42no—
149C4×D89#4112yes—
150C4×D89#4112yes—
151C8×C89—21no—
152C8×C89—21no—
153#10623494—21no—
154#10623494—21no—
155C22×C89—21no—
156C22×C89—21no—
157C22×C89—21no—
158C22×C89—41no—
159C22×C89—41no—
160C22×C89—41no—
161C22×C89C22×D411yescharacteristic
162C2×D89—21no—
163C2×D89—21no—
164C2×D89—21no—
165C2×D89—21no—
166C2×D89—44no—
167C2×D89—41no—
168C2×D89—41no—
169C2×D89—41no—
170C2×D89—84no—
171C2×D89#12312yes—
172C2×D89AGL(1,ℤ/8)12yes—
173C4×C89—21no—
174C4×C89—41no—
175C4×C89—41no—
176C4×C89—41no—
177C4×C89C2×#4111yescharacteristic
178C4×C89C2×#4111yescharacteristic
179Dic89—21no—
180Dic89—41no—
181Dic89—41no—
182Dic89—41no—
183Dic89#12312yes—
184C2×C89—41no—
185C2×C89—81no—
186C2×C89C2×#12311yescharacteristic
187C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
188C2×C89#57511yescharacteristic
189D89—22no—
190D89—22no—
191D89—81no—
192#3094—891nomaximal, Sylow
193C89#309411yescharacteristic, complemented, Sylow
194C2×#121—891no—
195C2×#117—891no—
196#482—891no—
197#482—891no—
198#482—891no—
199#482D8911yescharacteristic, complemented
200#481—891no—
201#481—891no—
202#480—891no—
203#480—891no—
204#428—891no—
205#428—891no—
206#418—891no—
207#418—891no—
208#407—891no—
209C22×D4—891no—
210C22×D4—1781no—
211C23×C4—891no—
212C2×M16—891no—
213C2×M16—891no—
214#121—891no—
215#121—891no—
216#121—891no—
217#121—1781no—
218#121—1781no—
219#121C2×D8911yescharacteristic
220#117—891no—
221#117—891no—
222#117—891no—
223#117—1781no—
224#117—1781no—
225#117C2×D8911yescharacteristic, complemented
226C2×C4⋊C4—891no—
227C2×C4⋊C4—891no—
228C2×C4⋊C4—891no—
229C2×C22⋊C4—1781no—
230C2×C22⋊C4—1781no—
231C2×C42—1781no—
232#107—891no—
233#107—891no—
234#107—891no—
235#107C2×D8911yescharacteristic, complemented
236#106—891no—
237#106—891no—
238#106—891no—
239#106C2×D8911yescharacteristic, complemented
240#102—891no—
241#102—891no—
242#102—891no—
243#102—891no—
244#102—891no—
245#102—891no—
246#102C2×D8911yescharacteristic, complemented
247#102C2×D8911yescharacteristic, complemented
248C22⋊C8—891no—
249C22⋊C8—891no—
250C22⋊C8—891no—
251C22⋊C8C2×D8911yescharacteristic, complemented
252C24—891no—
253C24—1781no—
254C2×D4—21no—
255C2×D4—891no—
256C2×D4—3564no—
257C2×D4—1781no—
258C2×D4—1782no—
259C2×D4—1782no—
260C2×D4—1781no—
261C2×D4—1781no—
262C2×D4—1781no—
263C2×D4C22×D8911yescharacteristic
264C22×C4—891no—
265C22×C4—891no—
266C22×C4—891no—
267C22×C4—891no—
268C22×C4—891no—
269C22×C4—1782no—
270C22×C4—1782no—
271C22×C4—1781no—
272C22×C4—1781no—
273C22×C4—1781no—
274C22×C4C22×D8911yescharacteristic
275M16—1782no—
276M16—1782no—
277C2×C8—891no—
278C2×C8—891no—
279C2×C8C22×D8911yescharacteristic
280C2×C8C22×D8911yescharacteristic
281C4⋊C4—891no—
282C4⋊C4—891no—
283C4⋊C4—891no—
284C4⋊C4—1781no—
285C4⋊C4—1781no—
286C4⋊C4—1781no—
287C4⋊C4C22×D8911yescharacteristic
288C4⋊C4C22×D8911yescharacteristic
289C4⋊C4C22×D8911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—1781no—
293C22⋊C4—1781no—
294C22⋊C4—1781no—
295C22⋊C4—1781no—
296C22⋊C4—1781no—
297C22⋊C4—1781no—
298C42—21no—
299C42—1781no—
300C42—1781no—
301C42—1781no—
302C23—21no—
303C23—891no—
304C23—891no—
305C23—3561no—
306C23—3562no—
307C23—3562no—
308C23—3562no—
309C23—1782no—
310C23—1782no—
311C23—1781no—
312C23D4×D8911yescharacteristic
313D4—21no—
314D4—21no—
315D4—42no—
316D4—3562no—
317D4—3562no—
318D4—3562no—
319D4—3562no—
320D4—1781no—
321D4—1781no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—891no—
328C2×C4—892no—
329C2×C4—892no—
330C2×C4—891no—
331C2×C4—3562no—
332C2×C4—3562no—
333C2×C4—3562no—
334C2×C4—1782no—
335C2×C4—1782no—
336C2×C4—1782no—
337C2×C4—1781no—
338C2×C4—1781no—
339C2×C4—1781no—
340C2×C4—1781no—
341C2×C4—1781no—
342C2×C4D4×D8911yescharacteristic
343C2×C4C23×D8911yescharacteristic
344C8—21no—
345C8—21no—
346C8—1781no—
347C8—1781no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—892no—
355C22—892no—
356C22—3564no—
357C22—3561no—
358C22—3561no—
359C22—3561no—
360C22—1781no—
361C22—1781no—
362C22—1781no—
363C22—1781no—
364C22—7124no—
365C22C2×D4×D8911yescharacteristic
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—892no—
371C4—3561no—
372C4—3561no—
373C4—3561no—
374C4—1781no—
375C4#41×D8911yescharacteristic
376C4#41×D8911yescharacteristic
377C2—41no—
378C2—81no—
379C2—1782no—
380C2—1782no—
381C2—7121no—
382C2#123×D8911yescharacteristic
383C2AGL(1,ℤ/8)×D8911yescharacteristic
384C2#1915239511yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#482×C89C2
socleC22×C89C22×D4
prime radical#121×D89C2
hypercenter#482D89
hypocenterC89#3094
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #117×D89C2semidirect
3. #19151923C2semidirect
4. #19151922C2semidirect
5. #19151919C2semidirect
6. #19151918C2semidirect
7. #19151915C2semidirect
8. #19151913C2semidirect
9. #19151910C2semidirect
10. #19151639C2semidirect
11. #19151637C2semidirect
12. #19151601C2semidirect
13. #19151601C2semidirect
14. #19151560C2semidirect
15. #482×C89C2semidirect
26. #15667971C22semidirect
32. C4⋊C4×D89C22semidirect
33. C4⋊C4×D89C22semidirect
37. #15667946C22semidirect
38. #15667945C22semidirect
39. #15667945C22semidirect
40. #15667944C22semidirect
41. #15667943C22semidirect
42. #15667943C22semidirect
43. #15667934C22semidirect
44. #15667934C22semidirect
45. #15667933C22semidirect
46. #15667933C22semidirect
47. #15667932C22semidirect
48. #15667932C22semidirect
49. C22⋊#10623494C22semidirect
50. #15667924C22semidirect
51. #15667924C22semidirect
53. #117×C89C22semidirect
54. #107×C89C22semidirect
55. #106×C89C22semidirect
56. #102×C89C22semidirect
57. #102×C89C22semidirect
58. C22⋊C8×C89C22semidirect
193. C89#3094semidirect
199. #482D89semidirect
225. #117C2×D89semidirect
235. #107C2×D89semidirect
239. #106C2×D89semidirect
246. #102C2×D89semidirect
247. #102C2×D89semidirect
251. C22⋊C8C2×D89semidirect

Maximal subgroups

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

subgroupindex
#121×D892
#117×D892
#191519232
#191519222
#191519192
#191519182
#191519152
#191519132
#191519102
#191516392
#191516372
#191516012
#191515602
#482×C892
#309489