Finite Group Databasebeta

← #26031340

Subgroups — #26031340

Order 11392.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152167C211yesmaximal, characteristic, complemented
2#19151988C211yesmaximal, characteristic, complemented
3#19151980C211yesmaximal, characteristic, complemented
4#19151960C211yesmaximal, characteristic, complemented
5#19151946C211yesmaximal, characteristic, complemented
6#19151820C211yesmaximal, characteristic, complemented
7#19151813C211yesmaximal, characteristic, complemented
8#19151798C211yesmaximal, characteristic, complemented
9#19151793C211yesmaximal, characteristic, complemented
10#19151758C211yesmaximal, characteristic, complemented
11#19151748C211yesmaximal, characteristic, complemented
12#19151741C211yesmaximal, characteristic, complemented
13#19151731C211yesmaximal, characteristic, complemented
14#19151659C211yesmaximal, characteristic, complemented
15#542×C89C211yesmaximal, characteristic, complemented
16C2×#13083574C2211yescharacteristic
17C22×D356C2211yescharacteristic
18C2×#13083564C2211yescharacteristic, complemented
19C2×#13083562C2211yescharacteristic, complemented
20C2×#13083561C2211yescharacteristic
21C2×#13083561C2211yescharacteristic
22C2×#13083561C2211yescharacteristic, complemented
23C2×#13083559C2211yescharacteristic
24C2×#13083559C2211yescharacteristic
25C2×#13083559C2211yescharacteristic, complemented
26#15668009C2211yescharacteristic
27#15668009C2211yescharacteristic
28#15668000C2211yescharacteristic
29#15668000C2211yescharacteristic
30#15667987—21no—
31#15667987—21no—
32#15667982—21no—
33#15667982—21no—
34C4⋊#10623494C2211yescharacteristic, complemented
35C4⋊#10623494C2211yescharacteristic, complemented
36#15667935C2211yescharacteristic, complemented
37#15667935C2211yescharacteristic, complemented
38#15667932C2211yescharacteristic
39#15667932C2211yescharacteristic
40#15667932C2211yescharacteristic
41#15667932C2211yescharacteristic
42#15667932C2211yescharacteristic, complemented
43#15667932C2211yescharacteristic, complemented
44C22⋊#10623494C2211yescharacteristic
45C22⋊#10623494C2211yescharacteristic
46#15667923C2211yescharacteristic, complemented
47C4×#10623494C2211yescharacteristic, complemented
48C4⋊Q8×C89C2211yescharacteristic, complemented
49#126×C89—21no—
50#124×C89—21no—
51#124×C89C2211yescharacteristic, complemented
52#123×C89—21no—
53C22⋊Q8×C89—21no—
54C22⋊Q8×C89C2211yescharacteristic
55#121×C89C2211yescharacteristic
56C4×Q8×C89C2211yescharacteristic, complemented
57C4×D4×C89C2211yescharacteristic, complemented
58#117×C89C2211yescharacteristic
59C23×D89—21no—
60#13083574—41no—
61#13083574—41no—
62C2×Dic178C2311yescharacteristic
63C2×D356—21no—
64C2×D356—21no—
65C2×D356—21no—
66C2×D356—21no—
67C2×D356—21no—
68C2×D356—41no—
69C2×D356—41no—
70C2×D356C2311yescharacteristic
71C2×D356C2311yescharacteristic
72C2×D356C2311yescharacteristic
73C2×C22⋊D89—21no—
74C2×C4×D89—21no—
75#13083564—41no—
76#13083562—41no—
77#13083561—41no—
78#13083561—41no—
79#13083561—41no—
80#13083559—41no—
81#13083559—41no—
82#13083559—41no—
83C2×#10623494C2311yescharacteristic
84C2×#10623494C2311yescharacteristic
85C2×#10623494C2311yescharacteristic
86C2×#10623494C2311yescharacteristic
87#13083551—21no—
88#13083551—21no—
89#13083551—21no—
90#13083551—21no—
91C2×Q8×C89—21no—
92C2×Q8×C89C2311yescharacteristic
93C2×D4×C89—21no—
94C2×D4×C89C2311yescharacteristic
95C22×C4×C89—21no—
96C22×C4×C89C2311yescharacteristic
97C4⋊C4×C89—21no—
98C4⋊C4×C89—21no—
99C4⋊C4×C89—21no—
100C4⋊C4×C89D411yescharacteristic
101C4⋊C4×C89D411yescharacteristic
102C4⋊C4×C89C2311yescharacteristic
103C4⋊C4×C89C2311yescharacteristic
104C22⋊C4×C89—21no—
105C22⋊C4×C89—21no—
106C22⋊C4×C89—21no—
107C22⋊C4×C89—21no—
108C22⋊C4×C89—21no—
109C22⋊C4×C89D411yescharacteristic
110C22⋊C4×C89D411yescharacteristic
111C42×C89—21no—
112C42×C89C2311yescharacteristic
113C42×C89C2311yescharacteristic
114C23×C89—21no—
115C23×C89C2×D411yescharacteristic
116C22×D89—21no—
117C22×D89—21no—
118C22×D89—21no—
119C22×D89—42no—
120C22×D89—81no—
121C22×D89—81no—
122Q8×C89—21no—
123Q8×C89—21no—
124Q8×C89—81no—
125D4×C89—21no—
126D4×C89—21no—
127D4×C89—81no—
128C2×C4×C89—21no—
129C2×C4×C89—21no—
130C2×C4×C89—21no—
131C2×C4×C89—21no—
132C2×C4×C89—21no—
133C2×C4×C89—81no—
134C2×C4×C89C2×D411yescharacteristic
135C2×C4×C89C2×D411yescharacteristic
136C2×C4×C89C2×D411yescharacteristic
137C2×C4×C89C2×D411yescharacteristic
138C2×C4×C89C2×D411yescharacteristic
139C2×C4×C89C2411yescharacteristic
140C22⋊D89—42no—
141C2×Dic89—21no—
142D356—21no—
143D356—21no—
144D356—21no—
145D356—21no—
146D356—21no—
147D356—21no—
148D356—42no—
149D356—81no—
150D356—81no—
151D356—81no—
152D356—81no—
153C4×D89—42no—
154Dic178—21no—
155Dic178—21no—
156#10623494—21no—
157#10623494—21no—
158#10623494—21no—
159#10623494—21no—
160C22×C89—21no—
161C22×C89—21no—
162C22×C89—21no—
163C22×C89—41no—
164C22×C89—41no—
165C22×C89—41no—
166C22×C89C22×D411yescharacteristic
167C2×D89—41no—
168C2×D89—41no—
169C2×D89—41no—
170C2×D89—41no—
171C2×D89—41no—
172C2×D89—41no—
173C2×D89—41no—
174C2×D89—41no—
175C2×D89—41no—
176C2×D89—84no—
177C4×C89—21no—
178C4×C89—21no—
179C4×C89—21no—
180C4×C89—21no—
181C4×C89—21no—
182C4×C89—41no—
183C4×C89—41no—
184C4×C89—41no—
185C4×C89H(5,𝔽2)11yescharacteristic
186C4×C89H(5,𝔽2)11yescharacteristic
187Dic89—41no—
188C2×C89—41no—
189C2×C89—81no—
190C2×C89#53511yescharacteristic
191C2×C89#57611yescharacteristic
192C2×C89#57711yescharacteristic
193D89—81no—
194D89—81no—
195D89—81no—
196#3224—891nomaximal, Sylow
197C89#322411yescharacteristic, complemented, Sylow
198#542D8911yescharacteristic, complemented
199#535—891no—
200#496—891no—
201#495—891no—
202#489—891no—
203#486—891no—
204#464—891no—
205#463—891no—
206#460—891no—
207#459—891no—
208#452—891no—
209#450—891no—
210#449—891no—
211#447—891no—
212#433—891no—
213C2×#41—891no—
214C22×D4—891no—
215C2×Q16—891no—
216C2×SD16—891no—
217C2×SD16—891no—
218C2×SD16—891no—
219C2×SD16—891no—
220C2×D8—891no—
221C2×D8—891no—
222C2×D8—891no—
223C4⋊Q8C2×D8911yescharacteristic, complemented
224#127—891no—
225#127—891no—
226#126—21no—
227#124—21no—
228#124—891no—
229#124—891no—
230#124C2×D8911yescharacteristic, complemented
231#123—21no—
232C22⋊Q8—21no—
233C22⋊Q8C2×D8911yescharacteristic
234#121—1781no—
235#121—1781no—
236#121C2×D8911yescharacteristic
237#120—1781no—
238#120—1781no—
239C4×Q8C2×D8911yescharacteristic, complemented
240C4×D4C2×D8911yescharacteristic, complemented
241#117C2×D8911yescharacteristic
242C4⋊C8—891no—
243C4⋊C8—891no—
244#103—891no—
245#103—891no—
246#102—891no—
247#102—891no—
248#102—891no—
249#102—891no—
250#102—891no—
251#102—891no—
252C22⋊C8—891no—
253C22⋊C8—891no—
254#97—891no—
255C4×C8—891no—
256C24—1781no—
257#41—3561no—
258#41—3561no—
259C2×Q8—21no—
260C2×Q8—891no—
261C2×Q8C22×D8911yescharacteristic
262C2×D4—21no—
263C2×D4—891no—
264C2×D4—891no—
265C2×D4—891no—
266C2×D4—3561no—
267C2×D4—3561no—
268C2×D4—1781no—
269C2×D4—1781no—
270C2×D4—1781no—
271C2×D4—1781no—
272C2×D4—1781no—
273C2×D4—1781no—
274C2×D4C22×D8911yescharacteristic
275C22×C4—21no—
276C22×C4—1781no—
277C22×C4C22×D8911yescharacteristic
278Q16—3561no—
279SD16—3561no—
280SD16—3561no—
281SD16—3561no—
282SD16—3561no—
283D8—3561no—
284D8—3561no—
285D8—3561no—
286C2×C8—891no—
287C2×C8—891no—
288C2×C8—891no—
289C2×C8—891no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4C22⋊D8911yescharacteristic
294C4⋊C4C22⋊D8911yescharacteristic
295C4⋊C4C22×D8911yescharacteristic
296C4⋊C4C22×D8911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—1781no—
303C22⋊C4—1781no—
304C22⋊C4—1781no—
305C22⋊C4—1781no—
306C22⋊C4C22⋊D8911yescharacteristic
307C22⋊C4C22⋊D8911yescharacteristic
308C42—21no—
309C42C22×D8911yescharacteristic
310C42C22×D8911yescharacteristic
311C23—21no—
312C23—3562no—
313C23—1781no—
314C23—1781no—
315C23—1781no—
316C23—7121no—
317C23—7121no—
318C23C2×C22⋊D8911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—81no—
322Q8—1781no—
323Q8—1781no—
324D4—21no—
325D4—21no—
326D4—81no—
327D4—3562no—
328D4—3562no—
329D4—1781no—
330D4—1781no—
331D4—1781no—
332D4—1781no—
333D4—1781no—
334D4—1781no—
335D4—7121no—
336D4—7121no—
337D4—7121no—
338D4—7121no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—3562no—
346C2×C4—1781no—
347C2×C4C2×C22⋊D8911yescharacteristic
348C2×C4C2×C22⋊D8911yescharacteristic
349C2×C4C2×C22⋊D8911yescharacteristic
350C2×C4C2×C22⋊D8911yescharacteristic
351C2×C4C2×C22⋊D8911yescharacteristic
352C2×C4C23×D8911yescharacteristic
353C8—1781no—
354C8—1781no—
355C8—1781no—
356C8—1781no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—3561no—
364C22—3561no—
365C22—3561no—
366C22—3561no—
367C22—3561no—
368C22—3561no—
369C22—3561no—
370C22—3561no—
371C22—3561no—
372C22—7124no—
373C22C22×C22⋊D8911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—3561no—
383C4#1566805811yescharacteristic
384C4#1566805811yescharacteristic
385C2—41no—
386C2—81no—
387C2—7121no—
388C2—7121no—
389C2—7121no—
390C2#1915216211yescharacteristic
391C2#1915240111yescharacteristic
392C2#1915240611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#542×C89C2
socleC22×C89C22×D4
hypercenter#542D89
hypocenterC89#3224
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #19152167C2semidirect
2. #19151988C2semidirect
3. #19151980C2semidirect
4. #19151960C2semidirect
5. #19151946C2semidirect
6. #19151820C2semidirect
7. #19151813C2semidirect
8. #19151798C2semidirect
9. #19151793C2semidirect
10. #19151758C2semidirect
11. #19151748C2semidirect
12. #19151741C2semidirect
13. #19151731C2semidirect
14. #19151659C2semidirect
15. #542×C89C2semidirect
18. C2×#13083564C22semidirect
19. C2×#13083562C22semidirect
22. C2×#13083561C22semidirect
25. C2×#13083559C22semidirect
34. C4⋊#10623494C22semidirect
35. C4⋊#10623494C22semidirect
36. #15667935C22semidirect
37. #15667935C22semidirect
42. #15667932C22semidirect
43. #15667932C22semidirect
46. #15667923C22semidirect
47. C4×#10623494C22semidirect
48. C4⋊Q8×C89C22semidirect
51. #124×C89C22semidirect
56. C4×Q8×C89C22semidirect
57. C4×D4×C89C22semidirect
197. C89#3224semidirect
198. #542D89semidirect
223. C4⋊Q8C2×D89semidirect
230. #124C2×D89semidirect
239. C4×Q8C2×D89semidirect
240. C4×D4C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191521672
#191519882
#191519802
#191519602
#191519462
#191518202
#191518132
#191517982
#191517932
#191517582
#191517482
#191517412
#191517312
#191516592
#542×C892
#322489