Finite Group Databasebeta

← #26032096

Subgroups — #26032096

Order 11392.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152244C211yesmaximal, characteristic, complemented
2#19151955C211yesmaximal, characteristic, complemented
3#19151933C211yesmaximal, characteristic, complemented
4#19151922C211yesmaximal, characteristic, complemented
5#19151895C211yesmaximal, characteristic, complemented
6#19151832C211yesmaximal, characteristic, complemented
7#19151825C211yesmaximal, characteristic, complemented
8#19151813C211yesmaximal, characteristic, complemented
9#19151741C211yesmaximal, characteristic, complemented
10#19151731C211yesmaximal, characteristic, complemented
11C4×#13083559C211yesmaximal, characteristic, complemented
12D4×#10623494C211yesmaximal, characteristic, complemented
13#19151592C211yesmaximal, characteristic, complemented
14C2×#15667932C211yesmaximal, characteristic, complemented
15#553×C89C211yesmaximal, characteristic, complemented
16C2×#13083574C2211yescharacteristic
17C22×D356C2211yescharacteristic
18C2×#13083562C2211yescharacteristic, complemented
19C2×#13083559C2211yescharacteristic
20C2×#13083559C2211yescharacteristic
21C22×#10623494C2211yescharacteristic
22C22×#10623494C2211yescharacteristic, complemented
23#15668000C2211yescharacteristic
24#15667997—21no—
25#15667991C2211yescharacteristic
26#15667986C2211yescharacteristic
27#15667985—21no—
28#15667980—21no—
29C4×D356C2211yescharacteristic
30C22⋊C4×D89—21no—
31#15667945C2211yescharacteristic, complemented
32#15667945C2211yescharacteristic, complemented
33#15667943C2211yescharacteristic, complemented
34C4⋊#10623494C2211yescharacteristic, complemented
35#15667935C2211yescharacteristic, complemented
36#15667935C2211yescharacteristic, complemented
37#15667935C2211yescharacteristic, complemented
38#15667933C2211yescharacteristic, complemented
39#15667932C2211yescharacteristic
40#15667932C2211yescharacteristic
41#15667932C2211yescharacteristic
42#15667932C2211yescharacteristic
43#15667932C2211yescharacteristic
44#15667932C2211yescharacteristic
45C22⋊#10623494C2211yescharacteristic
46C22⋊#10623494C2211yescharacteristic, complemented
47C4×#10623494C2211yescharacteristic, complemented
48#126×C89—21no—
49#125×C89C2211yescharacteristic, complemented
50#123×C89—21no—
51#121×C89—21no—
52#121×C89C2211yescharacteristic
53#121×C89C2211yescharacteristic, complemented
54C4×D4×C89—21no—
55C4×D4×C89C2211yescharacteristic
56C4×D4×C89C2211yescharacteristic, complemented
57#117×C89C2211yescharacteristic, complemented
58C2×C4⋊C4×C89C2211yescharacteristic
59C23×D89—21no—
60#13083574—22no—
61#13083574—41no—
62C2×Dic178C2311yescharacteristic
63C2×D356—22no—
64C2×D356—21no—
65C2×D356—41no—
66C2×D356C2311yescharacteristic
67C2×D356C2311yescharacteristic
68C2×C22⋊D89—21no—
69C2×C22⋊D89—21no—
70C2×C4×D89—21no—
71C2×C4×D89—21no—
72#13083562—41no—
73#13083559—22no—
74#13083559—41no—
75C2×#10623494—41no—
76C2×#10623494—41no—
77C2×#10623494C2311yescharacteristic
78C2×#10623494C2311yescharacteristic
79C2×#10623494C2311yescharacteristic
80C2×#10623494C2311yescharacteristic
81C4⋊Dic89C2311yescharacteristic
82#13083553—21no—
83C22⋊Dic89—21no—
84#13083551—21no—
85#13083551—21no—
86#13083551—21no—
87#13083551—21no—
88C2×D4×C89—21no—
89C2×D4×C89—21no—
90C2×D4×C89D411yescharacteristic
91C2×D4×C89C2311yescharacteristic
92C22×C4×C89—21no—
93C22×C4×C89—21no—
94C22×C4×C89C2311yescharacteristic
95C22×C4×C89C2311yescharacteristic
96C4⋊C4×C89—21no—
97C4⋊C4×C89—21no—
98C4⋊C4×C89—21no—
99C4⋊C4×C89D411yescharacteristic
100C4⋊C4×C89C2311yescharacteristic
101C4⋊C4×C89C2311yescharacteristic
102C4⋊C4×C89C2311yescharacteristic
103C22⋊C4×C89—21no—
104C22⋊C4×C89—21no—
105C22⋊C4×C89—21no—
106C22⋊C4×C89—21no—
107C22⋊C4×C89D411yescharacteristic
108C22⋊C4×C89D411yescharacteristic
109C42×C89—21no—
110C42×C89C2311yescharacteristic
111C23×C89—21no—
112C23×C89C2×D411yescharacteristic
113C23×C89C2×D411yescharacteristic
114C22×D89—21no—
115C22×D89—21no—
116C22×D89—42no—
117C22×D89—42no—
118C22×D89—81no—
119D4×C89—22no—
120D4×C89—21no—
121D4×C89—21no—
122D4×C89—42no—
123D4×C89—81no—
124C2×C4×C89—21no—
125C2×C4×C89—21no—
126C2×C4×C89—21no—
127C2×C4×C89—21no—
128C2×C4×C89—21no—
129C2×C4×C89—21no—
130C2×C4×C89—21no—
131C2×C4×C89—81no—
132C2×C4×C89—81no—
133C2×C4×C89C2×D411yescharacteristic
134C2×C4×C89C2×D411yescharacteristic
135C2×C4×C89C2×D411yescharacteristic
136C2×C4×C89C2×D411yescharacteristic
137C2×C4×C89C2411yescharacteristic
138C22⋊D89—42no—
139C22⋊D89—81no—
140C2×Dic89—21no—
141C2×Dic89—21no—
142D356—21no—
143D356—21no—
144D356—21no—
145D356—42no—
146D356#4112yes—
147C4×D89—42no—
148C4×D89—81no—
149Dic178—21no—
150Dic178—21no—
151#10623494—21no—
152#10623494—21no—
153#10623494—21no—
154#10623494—21no—
155C22×C89—21no—
156C22×C89—21no—
157C22×C89—21no—
158C22×C89—21no—
159C22×C89—21no—
160C22×C89—41no—
161C22×C89—41no—
162C22×C89—41no—
163C22×C89#13512yes—
164C22×C89C22×D411yescharacteristic
165C2×D89—22no—
166C2×D89—41no—
167C2×D89—41no—
168C2×D89—41no—
169C2×D89—41no—
170C2×D89—41no—
171C2×D89—84no—
172C4×C89—21no—
173C4×C89—21no—
174C4×C89—21no—
175C4×C89—21no—
176C4×C89—41no—
177C4×C89—41no—
178C4×C89—41no—
179C4×C89C2×#4111yescharacteristic
180C4×C89H(5,𝔽2)11yescharacteristic
181Dic89—41no—
182Dic89—41no—
183C2×C89—22no—
184C2×C89—41no—
185C2×C89—81no—
186C2×C89#54611yescharacteristic
187C2×C89C2×#13511yescharacteristic
188C2×C89#57611yescharacteristic
189D89—42no—
190D89—81no—
191#3297—891nomaximal, Sylow
192C89#329711yescharacteristic, complemented, Sylow
193#553D8911yescharacteristic, complemented
194#546—891no—
195#488—891no—
196#484—891no—
197#482—891no—
198#478—891no—
199#466—891no—
200#465—891no—
201#463—891no—
202#449—891no—
203#447—891no—
204C4×D8—891no—
205C8×D4—891no—
206#416—891no—
207C2×#102—891no—
208C2×#41—891no—
209C22×D4—891no—
210C2×SD16—891no—
211C2×D8—891no—
212C2×D8—891no—
213C22×C8—891no—
214C22×C8—891no—
215#126—21no—
216#125C2×D8911yescharacteristic, complemented
217#124—891no—
218#123—21no—
219#123—1781no—
220C22⋊Q8—891no—
221#121—21no—
222#121—891no—
223#121—1781no—
224#121C2×D8911yescharacteristic
225#121C2×D8911yescharacteristic, complemented
226#120—1781no—
227C4×D4—21no—
228C4×D4—891no—
229C4×D4C2×D8911yescharacteristic
230C4×D4C2×D8911yescharacteristic, complemented
231#117C2×D8911yescharacteristic, complemented
232C2×C4⋊C4C2×D8911yescharacteristic
233C2×C22⋊C4—1781no—
234#107—891no—
235#107—891no—
236#106—891no—
237C4⋊C8—891no—
238#103—891no—
239#103—891no—
240#103—891no—
241#102—891no—
242#102—891no—
243#102—891no—
244#102—891no—
245#102—891no—
246#102—891no—
247#102—891no—
248C22⋊C8—891no—
249C22⋊C8—891no—
250C4×C8—891no—
251C24—1781no—
252#41—3561no—
253#41—1782no—
254C2×Q8—891no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—891no—
258C2×D4—891no—
259C2×D4—3561no—
260C2×D4—1782no—
261C2×D4—1781no—
262C2×D4—1781no—
263C2×D4—1781no—
264C2×D4C22⋊D8911yescharacteristic
265C2×D4C22×D8911yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—1781no—
269C22×C4—1781no—
270C22×C4C22×D8911yescharacteristic
271C22×C4C22×D8911yescharacteristic
272SD16—3561no—
273D8—3561no—
274D8—1782no—
275C2×C8—891no—
276C2×C8—891no—
277C2×C8—891no—
278C2×C8—891no—
279C2×C8—3561no—
280C2×C8—3561no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—891no—
285C4⋊C4—1781no—
286C4⋊C4C22⋊D8911yescharacteristic
287C4⋊C4C22×D8911yescharacteristic
288C4⋊C4C22×D8911yescharacteristic
289C4⋊C4C22×D8911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—1781no—
295C22⋊C4—1781no—
296C22⋊C4—1781no—
297C22⋊C4—1781no—
298C22⋊C4—1781no—
299C22⋊C4C22⋊D8911yescharacteristic
300C22⋊C4C22⋊D8911yescharacteristic
301C42—21no—
302C42C22×D8911yescharacteristic
303C23—21no—
304C23—3562no—
305C23—3562no—
306C23—1781no—
307C23—1781no—
308C23—7121no—
309C23C2×C22⋊D8911yescharacteristic
310C23C2×C22⋊D8911yescharacteristic
311Q8—1781no—
312Q8—1781no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—81no—
318D4—892no—
319D4—3562no—
320D4—3562no—
321D4—1781no—
322D4—1781no—
323D4—1781no—
324D4—7121no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—3562no—
335C2×C4—1781no—
336C2×C4—1781no—
337C2×C4—7121no—
338C2×C4C2×C22⋊D8911yescharacteristic
339C2×C4C2×C22⋊D8911yescharacteristic
340C2×C4C2×C22⋊D8911yescharacteristic
341C2×C4C2×C22⋊D8911yescharacteristic
342C2×C4C23×D8911yescharacteristic
343C8—1781no—
344C8—1781no—
345C8—1781no—
346C8—1781no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—3561no—
356C22—3561no—
357C22—3561no—
358C22—3561no—
359C22—3561no—
360C22—1782no—
361C22—7124no—
362C22#1566803212yes—
363C22C22×C22⋊D8911yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—3561no—
372C4—3561no—
373C4#41×D8911yescharacteristic
374C4#1566805811yescharacteristic
375C2—22no—
376C2—41no—
377C2—81no—
378C2—3562no—
379C2—7121no—
380C2#1915223611yescharacteristic
381C2C2×#1566803211yescharacteristic
382C2#1915240111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#553×C89C2
socleC22×C89C22×D4
hypercenter#553D89
hypocenterC89#3297
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. #19152244C2semidirect
2. #19151955C2semidirect
3. #19151933C2semidirect
4. #19151922C2semidirect
5. #19151895C2semidirect
6. #19151832C2semidirect
7. #19151825C2semidirect
8. #19151813C2semidirect
9. #19151741C2semidirect
10. #19151731C2semidirect
11. C4×#13083559C2semidirect
12. D4×#10623494C2semidirect
13. #19151592C2semidirect
14. C2×#15667932C2semidirect
15. #553×C89C2semidirect
18. C2×#13083562C22semidirect
22. C22×#10623494C22semidirect
31. #15667945C22semidirect
32. #15667945C22semidirect
33. #15667943C22semidirect
34. C4⋊#10623494C22semidirect
35. #15667935C22semidirect
36. #15667935C22semidirect
37. #15667935C22semidirect
38. #15667933C22semidirect
46. C22⋊#10623494C22semidirect
47. C4×#10623494C22semidirect
49. #125×C89C22semidirect
53. #121×C89C22semidirect
56. C4×D4×C89C22semidirect
57. #117×C89C22semidirect
192. C89#3297semidirect
193. #553D89semidirect
216. #125C2×D89semidirect
225. #121C2×D89semidirect
230. C4×D4C2×D89semidirect
231. #117C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191522442
#191519552
#191519332
#191519222
#191518952
#191518322
#191518252
#191518132
#191517412
#191517312
C4×#130835592
D4×#106234942
#191515922
C2×#156679322
#553×C892
#329789