Finite Group Databasebeta

← #26032387

Subgroups — #26032387

Order 11392.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×D356C211yesmaximal, characteristic, complemented
2#19151964C211yesmaximal, characteristic, complemented
3#19151922C211yesmaximal, characteristic, complemented
4#19151916C211yesmaximal, characteristic, complemented
5#19151895C211yesmaximal, characteristic, complemented
6#19151849C211yesmaximal, characteristic, complemented
7#19151832C211yesmaximal, characteristic, complemented
8#19151793C211yesmaximal, characteristic, complemented
9#19151731C211yesmaximal, characteristic, complemented
10#19151731C211yesmaximal, characteristic, complemented
11#19151708C211yesmaximal, characteristic, complemented
12#19151670C211yesmaximal, characteristic, complemented
13#19151602C211yesmaximal, characteristic, complemented
14C2×#15667932C211yesmaximal, characteristic, complemented
15#553×C89C211yesmaximal, characteristic, complemented
16C22×D356C2211yescharacteristic
17C22×D356C2211yescharacteristic
18C2×D4×D89—21no—
19C2×#13083559C2211yescharacteristic
20C2×#13083559C2211yescharacteristic, complemented
21C2×#13083559C2211yescharacteristic, complemented
22C2×#13083558C2211yescharacteristic, complemented
23C22×#10623494C2211yescharacteristic, complemented
24#15668009C2211yescharacteristic
25#15667987—21no—
26#15667986C2211yescharacteristic
27#15667986C2211yescharacteristic
28#15667982—21no—
29#15667982—21no—
30C4×D356C2211yescharacteristic
31#15667945C2211yescharacteristic, complemented
32#15667943C2211yescharacteristic, complemented
33#15667943C2211yescharacteristic, complemented
34C4⋊#10623494C2211yescharacteristic, complemented
35#15667933C2211yescharacteristic, complemented
36#15667932C2211yescharacteristic
37#15667932C2211yescharacteristic
38#15667932C2211yescharacteristic
39#15667932C2211yescharacteristic, complemented
40#15667932C2211yescharacteristic, complemented
41#15667932C2211yescharacteristic, complemented
42#15667932C2211yescharacteristic, complemented
43#15667932C2211yescharacteristic, complemented
44#15667932C2211yescharacteristic, complemented
45C22⋊#10623494C2211yescharacteristic, complemented
46C22⋊#10623494C2211yescharacteristic, complemented
47#15667923C2211yescharacteristic, complemented
48#126×C89—21no—
49#125×C89C2211yescharacteristic, complemented
50#123×C89—21no—
51#121×C89—21no—
52#121×C89C2211yescharacteristic, complemented
53#121×C89C2211yescharacteristic, complemented
54C4×D4×C89—21no—
55C4×D4×C89C2211yescharacteristic
56C4×D4×C89C2211yescharacteristic, complemented
57#117×C89C2211yescharacteristic, complemented
58C2×C4⋊C4×C89C2211yescharacteristic, complemented
59C23×D89—21no—
60C23×D89—21no—
61C2×D356—22no—
62C2×D356—22no—
63C2×D356—21no—
64C2×D356—21no—
65C2×D356—21no—
66C2×D356—21no—
67C2×D356—41no—
68C2×D356—41no—
69C2×D356C2311yescharacteristic
70C2×D356C2311yescharacteristic
71C2×D356C2311yescharacteristic
72C2×C22⋊D89—21no—
73C2×C22⋊D89—21no—
74D4×D89—44no—
75C2×C4×D89—21no—
76#13083559—22no—
77#13083559—41no—
78#13083559—41no—
79#13083558—41no—
80C2×#10623494—41no—
81C2×#10623494C2311yescharacteristic
82C2×#10623494C2311yescharacteristic
83C2×#10623494C2311yescharacteristic
84C2×#10623494C2311yescharacteristic
85C4⋊Dic89C2311yescharacteristic
86#13083551—21no—
87#13083551—21no—
88#13083551—21no—
89C2×D4×C89—21no—
90C2×D4×C89—21no—
91C2×D4×C89D411yescharacteristic
92C2×D4×C89C2311yescharacteristic
93C22×C4×C89—21no—
94C22×C4×C89—21no—
95C22×C4×C89C2311yescharacteristic
96C22×C4×C89C2311yescharacteristic
97C4⋊C4×C89—21no—
98C4⋊C4×C89—21no—
99C4⋊C4×C89—21no—
100C4⋊C4×C89D411yescharacteristic
101C4⋊C4×C89C2311yescharacteristic
102C4⋊C4×C89C2311yescharacteristic
103C4⋊C4×C89C2311yescharacteristic
104C22⋊C4×C89—21no—
105C22⋊C4×C89—21no—
106C22⋊C4×C89—21no—
107C22⋊C4×C89—21no—
108C22⋊C4×C89D411yescharacteristic
109C22⋊C4×C89D411yescharacteristic
110C42×C89—21no—
111C42×C89C2311yescharacteristic
112C23×C89—21no—
113C23×C89C2×D411yescharacteristic
114C23×C89C2×D411yescharacteristic
115C22×D89—21no—
116C22×D89—21no—
117C22×D89—21no—
118C22×D89—42no—
119C22×D89—42no—
120C22×D89—42no—
121C22×D89—42no—
122C22×D89—81no—
123C22×D89—81no—
124D4×C89—22no—
125D4×C89—21no—
126D4×C89—21no—
127D4×C89—42no—
128D4×C89—81no—
129C2×C4×C89—21no—
130C2×C4×C89—21no—
131C2×C4×C89—21no—
132C2×C4×C89—21no—
133C2×C4×C89—21no—
134C2×C4×C89—21no—
135C2×C4×C89—21no—
136C2×C4×C89—81no—
137C2×C4×C89—81no—
138C2×C4×C89C2×D411yescharacteristic
139C2×C4×C89C2×D411yescharacteristic
140C2×C4×C89C2×D411yescharacteristic
141C2×C4×C89C2×D411yescharacteristic
142C2×C4×C89C2411yescharacteristic
143C22⋊D89—42no—
144C22⋊D89—42no—
145C2×Dic89—21no—
146D356—21no—
147D356—21no—
148D356—21no—
149D356—21no—
150D356—21no—
151D356—42no—
152D356—42no—
153D356—42no—
154D356—81no—
155D356#4112yes—
156C4×D89—42no—
157#10623494—21no—
158#10623494—21no—
159#10623494—21no—
160#10623494—21no—
161C22×C89—21no—
162C22×C89—21no—
163C22×C89—21no—
164C22×C89—21no—
165C22×C89—21no—
166C22×C89—41no—
167C22×C89—41no—
168C22×C89—41no—
169C22×C89AGL(1,ℤ/8)12yes—
170C22×C89C22×D411yescharacteristic
171C2×D89—22no—
172C2×D89—41no—
173C2×D89—41no—
174C2×D89—41no—
175C2×D89—41no—
176C2×D89—41no—
177C2×D89—41no—
178C2×D89—41no—
179C2×D89—41no—
180C2×D89—84no—
181C2×D89—84no—
182C4×C89—21no—
183C4×C89—21no—
184C4×C89—21no—
185C4×C89—21no—
186C4×C89—41no—
187C4×C89—41no—
188C4×C89—41no—
189C4×C89C2×#4111yescharacteristic
190C4×C89H(5,𝔽2)11yescharacteristic
191Dic89—41no—
192C2×C89—22no—
193C2×C89—41no—
194C2×C89—81no—
195C2×C89#54611yescharacteristic
196C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C89#57611yescharacteristic
198D89—42no—
199D89—81no—
200D89—81no—
201#3318—891nomaximal, Sylow
202C89#331811yescharacteristic, complemented, Sylow
203#553D8911yescharacteristic, complemented
204D42—891no—
205#490—891no—
206#482—891no—
207#481—891no—
208#478—891no—
209#469—891no—
210#466—891no—
211#459—891no—
212#447—891no—
213#447—891no—
214#442—891no—
215#435—891no—
216#418—891no—
217C2×#102—891no—
218C22×D4—891no—
219C22×D4—891no—
220C22×D4—1781no—
221C2×D8—891no—
222C2×D8—891no—
223C2×D8—891no—
224C2×M16—891no—
225C22×C8—891no—
226#127—891no—
227#126—21no—
228#125C2×D8911yescharacteristic, complemented
229#123—21no—
230#121—21no—
231#121—891no—
232#121—891no—
233#121—1781no—
234#121C2×D8911yescharacteristic, complemented
235#121C2×D8911yescharacteristic, complemented
236#120—1781no—
237#120—1781no—
238C4×D4—21no—
239C4×D4—891no—
240C4×D4C2×D8911yescharacteristic
241C4×D4C2×D8911yescharacteristic, complemented
242#117C2×D8911yescharacteristic, complemented
243C2×C4⋊C4C2×D8911yescharacteristic, complemented
244#107—891no—
245#106—891no—
246#106—891no—
247C4⋊C8—891no—
248#102—891no—
249#102—891no—
250#102—891no—
251#102—891no—
252#102—891no—
253#102—891no—
254#102—891no—
255#102—891no—
256#102—891no—
257#102—891no—
258C22⋊C8—891no—
259C22⋊C8—891no—
260#97—891no—
261C24—1781no—
262C24—1781no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—891no—
266C2×D4—891no—
267C2×D4—891no—
268C2×D4—3561no—
269C2×D4—3561no—
270C2×D4—3564no—
271C2×D4—1782no—
272C2×D4—1782no—
273C2×D4—1781no—
274C2×D4—1781no—
275C2×D4—1781no—
276C2×D4—1781no—
277C2×D4—1781no—
278C2×D4—1781no—
279C2×D4C22⋊D8911yescharacteristic
280C2×D4C22×D8911yescharacteristic
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—1781no—
284C22×C4C22×D8911yescharacteristic
285C22×C4C22×D8911yescharacteristic
286D8—3561no—
287D8—3561no—
288D8—1782no—
289M16—3561no—
290C2×C8—891no—
291C2×C8—891no—
292C2×C8—891no—
293C2×C8—891no—
294C2×C8—3561no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—891no—
299C4⋊C4C22⋊D8911yescharacteristic
300C4⋊C4C22×D8911yescharacteristic
301C4⋊C4C22×D8911yescharacteristic
302C4⋊C4C22×D8911yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—1781no—
308C22⋊C4—1781no—
309C22⋊C4—1781no—
310C22⋊C4C22⋊D8911yescharacteristic
311C22⋊C4C22⋊D8911yescharacteristic
312C42—21no—
313C42C22×D8911yescharacteristic
314C23—21no—
315C23—3562no—
316C23—3562no—
317C23—3562no—
318C23—3562no—
319C23—1781no—
320C23—1781no—
321C23—1781no—
322C23—7121no—
323C23—7121no—
324C23C2×C22⋊D8911yescharacteristic
325C23C2×C22⋊D8911yescharacteristic
326D4—22no—
327D4—21no—
328D4—21no—
329D4—42no—
330D4—81no—
331D4—892no—
332D4—3562no—
333D4—3562no—
334D4—3562no—
335D4—3562no—
336D4—3562no—
337D4—1781no—
338D4—1781no—
339D4—1781no—
340D4—1781no—
341D4—1781no—
342D4—7121no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—3562no—
353C2×C4—1781no—
354C2×C4C2×C22⋊D8911yescharacteristic
355C2×C4C2×C22⋊D8911yescharacteristic
356C2×C4C2×C22⋊D8911yescharacteristic
357C2×C4C2×C22⋊D8911yescharacteristic
358C2×C4C23×D8911yescharacteristic
359C8—1781no—
360C8—1781no—
361C8—1781no—
362C8—1781no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—3561no—
372C22—3561no—
373C22—3561no—
374C22—3561no—
375C22—3561no—
376C22—3561no—
377C22—3561no—
378C22—3561no—
379C22—1782no—
380C22—7124no—
381C22—7124no—
382C22#1566803712yes—
383C22C22×C22⋊D8911yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—3561no—
392C4#41×D8911yescharacteristic
393C4#1566805811yescharacteristic
394C2—22no—
395C2—41no—
396C2—81no—
397C2—3562no—
398C2—7121no—
399C2—7121no—
400C2#1915223611yescharacteristic
401C2C2×#1566803711yescharacteristic
402C2#1915240111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#553×C89C2
socleC22×C89C22×D4
hypercenter#553D89
hypocenterC89#3318
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. D4×D356C2semidirect
2. #19151964C2semidirect
3. #19151922C2semidirect
4. #19151916C2semidirect
5. #19151895C2semidirect
6. #19151849C2semidirect
7. #19151832C2semidirect
8. #19151793C2semidirect
9. #19151731C2semidirect
10. #19151731C2semidirect
11. #19151708C2semidirect
12. #19151670C2semidirect
13. #19151602C2semidirect
14. C2×#15667932C2semidirect
15. #553×C89C2semidirect
20. C2×#13083559C22semidirect
21. C2×#13083559C22semidirect
22. C2×#13083558C22semidirect
23. C22×#10623494C22semidirect
31. #15667945C22semidirect
32. #15667943C22semidirect
33. #15667943C22semidirect
34. C4⋊#10623494C22semidirect
35. #15667933C22semidirect
39. #15667932C22semidirect
40. #15667932C22semidirect
41. #15667932C22semidirect
42. #15667932C22semidirect
43. #15667932C22semidirect
44. #15667932C22semidirect
45. C22⋊#10623494C22semidirect
46. C22⋊#10623494C22semidirect
47. #15667923C22semidirect
49. #125×C89C22semidirect
52. #121×C89C22semidirect
53. #121×C89C22semidirect
56. C4×D4×C89C22semidirect
57. #117×C89C22semidirect
58. C2×C4⋊C4×C89C22semidirect
202. C89#3318semidirect
203. #553D89semidirect
228. #125C2×D89semidirect
234. #121C2×D89semidirect
235. #121C2×D89semidirect
241. C4×D4C2×D89semidirect
242. #117C2×D89semidirect
243. C2×C4⋊C4C2×D89semidirect

Maximal subgroups

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

subgroupindex
D4×D3562
#191519642
#191519222
#191519162
#191518952
#191518492
#191518322
#191517932
#191517312
#191517082
#191516702
#191516022
C2×#156679322
#553×C892
#331889