Finite Group Databasebeta

← #26032272

Subgroups — #26032272

Order 11392.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152286C211yesmaximal, characteristic, complemented
2#19152233C211yesmaximal, characteristic
3#19151920C211yesmaximal, characteristic, complemented
4#19151910C211yesmaximal, characteristic, complemented
5#19151895C211yesmaximal, characteristic, complemented
6#19151843C211yesmaximal, characteristic, complemented
7#19151826C211yesmaximal, characteristic, complemented
8#19151795C211yesmaximal, characteristic, complemented
9#19151750C211yesmaximal, characteristic, complemented
10#19151750C211yesmaximal, characteristic, complemented
11#19151700C211yesmaximal, characteristic, complemented
12#19151671C211yesmaximal, characteristic, complemented
13#19151601C211yesmaximal, characteristic, complemented
14#102×D89C211yesmaximal, characteristic, complemented
15#490×C89C211yesmaximal, characteristic, complemented
16C2×D4×D89—21no—
17C2×D4×D89C2211yescharacteristic
18C2×D4×D89C2211yescharacteristic
19C2×#13083563C2211yescharacteristic
20C2×#13083562C2211yescharacteristic, complemented
21C2×#13083562C2211yescharacteristic, complemented
22C2×#13083557C2211yescharacteristic, complemented
23C2×C8×D89C2211yescharacteristic, complemented
24#15668007—21no—
25#15668003—21no—
26#15667997—21no—
27#15667992C2211yescharacteristic, complemented
28#15667992C2211yescharacteristic, complemented
29#15667983—21no—
30#15667983C2211yescharacteristic
31#15667983C2211yescharacteristic
32#15667980—21no—
33#15667980—21no—
34C4×Dic178C2211yescharacteristic, complemented
35C4×D356C2211yescharacteristic
36C4×D356C2211yescharacteristic
37#15667970—21no—
38#15667970C2211yescharacteristic, complemented
39C4⋊C4×D89C2211yescharacteristic, complemented
40#15667946C2211yescharacteristic, complemented
41#15667945C2211yescharacteristic, complemented
42#15667943C2211yescharacteristic, complemented
43C4⋊#10623494C2211yescharacteristic, complemented
44#15667937C2211yescharacteristic, complemented
45#15667934C2211yescharacteristic
46#15667933C2211yescharacteristic, complemented
47#15667933C2211yescharacteristic, complemented
48#15667932C2211yescharacteristic
49#15667932C2211yescharacteristic
50#15667924C2211yescharacteristic, complemented
51#15667924C2211yescharacteristic, complemented
52#127×C89C2211yescharacteristic
53#125×C89C2211yescharacteristic, complemented
54#102×C89C2211yescharacteristic, complemented
55#102×C89C2211yescharacteristic, complemented
56#102×C89C2211yescharacteristic, complemented
57#102×C89C2211yescharacteristic, complemented
58#97×C89C2211yescharacteristic, complemented
59C23×D89—21no—
60C23×D89—21no—
61C2×Dic178C2311yescharacteristic
62C2×D356D411yescharacteristic
63C2×D356C2311yescharacteristic
64C2×C22⋊D89—21no—
65C2×C22⋊D89—21no—
66C2×C22⋊D89—21no—
67C2×C22⋊D89—21no—
68D4×D89—22no—
69D4×D89—22no—
70D4×D89—41no—
71D4×D89—41no—
72D4×D89—44no—
73C2×C4×D89—21no—
74C2×C4×D89—21no—
75C2×C4×D89C2311yescharacteristic
76C2×C4×D89C2311yescharacteristic
77#13083563—22no—
78#13083562—41no—
79#13083562—41no—
80#13083557—41no—
81C2×#10623494C2311yescharacteristic
82C2×#10623494C2311yescharacteristic
83C8×D89—41no—
84C4⋊Dic89—21no—
85C4⋊Dic89—21no—
86C4⋊Dic89D411yescharacteristic
87C4⋊Dic89C2311yescharacteristic
88C4⋊Dic89C2311yescharacteristic
89#13083553—21no—
90#13083553—21no—
91C22⋊Dic89—21no—
92C22⋊Dic89—21no—
93#13083551—21no—
94#13083551—21no—
95#13083551—21no—
96#13083551—21no—
97#13083551D411yescharacteristic
98#13083551D411yescharacteristic
99C4×Dic89—21no—
100C4×Dic89—21no—
101C2×D4×C89—21no—
102C2×D4×C89—21no—
103C2×D4×C89C2311yescharacteristic
104C2×D4×C89C2311yescharacteristic
105C2×C8×C89C2311yescharacteristic
106C2×C8×C89C2311yescharacteristic
107C4⋊C4×C89—21no—
108C4⋊C4×C89—21no—
109C4⋊C4×C89C2311yescharacteristic
110C4⋊C4×C89C2311yescharacteristic
111C42×C89C2311yescharacteristic
112C23×C89—21no—
113C23×C89—21no—
114C22×D89—21no—
115C22×D89—42no—
116C22×D89—42no—
117C22×D89—42no—
118C22×D89—42no—
119C22×D89—81no—
120C22×D89—81no—
121C22×D89C2×D411yescharacteristic
122C22×D89C2×D411yescharacteristic
123D4×C89—21no—
124D4×C89—21no—
125D4×C89—21no—
126D4×C89—21no—
127D4×C89—42no—
128D4×C89—81no—
129C2×C4×C89—21no—
130C2×C4×C89—21no—
131C2×C4×C89C2×D411yescharacteristic
132C2×C4×C89C2×D411yescharacteristic
133C2×C4×C89C2411yescharacteristic
134C22⋊D89—42no—
135C22⋊D89—42no—
136C22⋊D89—42no—
137C22⋊D89—42no—
138C2×Dic89—21no—
139C2×Dic89—21no—
140C2×Dic89—21no—
141C2×Dic89C2×D411yescharacteristic
142C2×Dic89C2×D411yescharacteristic
143D356—22no—
144D356—21no—
145D356#4112yes—
146C4×D89—21no—
147C4×D89—21no—
148C4×D89—21no—
149C4×D89—21no—
150C4×D89—42no—
151C4×D89—42no—
152Dic178—21no—
153Dic178—21no—
154C8×C89—21no—
155C8×C89—21no—
156#10623494—21no—
157#10623494—21no—
158C22×C89—41no—
159C22×C89—41no—
160C22×C89—41no—
161C22×C89—41no—
162C22×C89—41no—
163C22×C89—41no—
164C22×C89C22×D411yescharacteristic
165C2×D89—21no—
166C2×D89—21no—
167C2×D89—21no—
168C2×D89—22no—
169C2×D89—21no—
170C2×D89—21no—
171C2×D89—41no—
172C2×D89—41no—
173C2×D89—84no—
174C2×D89—84no—
175C2×D89AGL(1,ℤ/8)12yes—
176C4×C89—21no—
177C4×C89—21no—
178C4×C89—41no—
179C4×C89—41no—
180C4×C89C2×#4111yescharacteristic
181C4×C89H(5,𝔽2)11yescharacteristic
182Dic89—21no—
183Dic89—21no—
184Dic89—41no—
185Dic89—41no—
186Dic89—41no—
187C2×C89—81no—
188C2×C89—81no—
189C2×C89#54611yescharacteristic
190C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C89#57711yescharacteristic
192D89—22no—
193D89—41no—
194D89—42no—
195#3310—891nomaximal, Sylow
196C89#331011yescharacteristic, complemented, Sylow
197#552—891no—
198D42—891no—
199#490D8911yescharacteristic, complemented
200#482—891no—
201#480—891no—
202#478—891no—
203#468—891no—
204#465—891no—
205#460—891no—
206#450—891no—
207#450—891no—
208#440—891no—
209#435—891no—
210#418—891no—
211C2×#102—891no—
212C22×D4—891no—
213C22×D4—891no—
214C22×D4—1781no—
215C2×SD16—891no—
216C2×SD16—891no—
217C2×SD16—891no—
218C2×M16—891no—
219C22×C8—891no—
220#127C2×D8911yescharacteristic
221#126—1781no—
222#125—1781no—
223#125C2×D8911yescharacteristic, complemented
224#123—1781no—
225C22⋊Q8—891no—
226C22⋊Q8—891no—
227#121—891no—
228#121—891no—
229#121—1781no—
230#120—1781no—
231#120—1781no—
232C4×Q8—891no—
233C4×D4—891no—
234C4×D4—891no—
235#117—891no—
236#117—1781no—
237C2×C4⋊C4—891no—
238#107—891no—
239#107—891no—
240#106—891no—
241C4⋊C8—891no—
242#103—891no—
243#102—891no—
244#102—891no—
245#102—891no—
246#102—891no—
247#102—891no—
248#102C2×D8911yescharacteristic, complemented
249#102C2×D8911yescharacteristic, complemented
250#102C2×D8911yescharacteristic, complemented
251#102C2×D8911yescharacteristic, complemented
252C22⋊C8—891no—
253C22⋊C8—891no—
254#97C2×D8911yescharacteristic, complemented
255C24—1781no—
256C24—1781no—
257C2×Q8—891no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—891no—
261C2×D4—891no—
262C2×D4—3564no—
263C2×D4—3561no—
264C2×D4—3561no—
265C2×D4—1781no—
266C2×D4—1781no—
267C2×D4—1782no—
268C2×D4—1782no—
269C2×D4—1781no—
270C2×D4—1781no—
271C2×D4C22×D8911yescharacteristic
272C2×D4C22×D8911yescharacteristic
273C22×C4—891no—
274C22×C4—891no—
275C22×C4—1781no—
276C22×C4—1781no—
277SD16—3561no—
278SD16—3561no—
279SD16—1782no—
280M16—3561no—
281C2×C8—891no—
282C2×C8—891no—
283C2×C8—3561no—
284C2×C8C22×D8911yescharacteristic
285C2×C8C22×D8911yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—891no—
289C4⋊C4—891no—
290C4⋊C4—891no—
291C4⋊C4—1781no—
292C4⋊C4—1781no—
293C4⋊C4—1781no—
294C4⋊C4—1781no—
295C4⋊C4C22×D8911yescharacteristic
296C4⋊C4C22×D8911yescharacteristic
297C22⋊C4—891no—
298C22⋊C4—891no—
299C22⋊C4—1781no—
300C22⋊C4—1781no—
301C22⋊C4—1781no—
302C22⋊C4—1781no—
303C22⋊C4—1781no—
304C22⋊C4—1781no—
305C42—1781no—
306C42—1781no—
307C42C22×D8911yescharacteristic
308C23—21no—
309C23—21no—
310C23—891no—
311C23—891no—
312C23—3562no—
313C23—3562no—
314C23—3562no—
315C23—3562no—
316C23—1781no—
317C23—7121no—
318C23—7121no—
319Q8—1781no—
320Q8—1781no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—81no—
327D4—892no—
328D4—3562no—
329D4—3562no—
330D4—3562no—
331D4—3562no—
332D4—1782no—
333D4—1781no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—891no—
337C2×C4—891no—
338C2×C4—3562no—
339C2×C4—3562no—
340C2×C4—1781no—
341C2×C4—1781no—
342C2×C4—1781no—
343C2×C4—1781no—
344C2×C4—1781no—
345C2×C4—1781no—
346C2×C4—1781no—
347C2×C4D4×D8911yescharacteristic
348C2×C4D4×D8911yescharacteristic
349C2×C4C23×D8911yescharacteristic
350C8—21no—
351C8—21no—
352C8—1781no—
353C8—1781no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—892no—
361C22—3561no—
362C22—3561no—
363C22—1781no—
364C22—1781no—
365C22—1782no—
366C22—1781no—
367C22—1781no—
368C22—1781no—
369C22—7124no—
370C22—7124no—
371C22C2×D4×D8911yescharacteristic
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—3561no—
377C4—3561no—
378C4—3561no—
379C4—1781no—
380C4—1781no—
381C4#41×D8911yescharacteristic
382C4#1566805811yescharacteristic
383C2—81no—
384C2—81no—
385C2—3562no—
386C2—3561no—
387C2—1782no—
388C2#1915224111yescharacteristic
389C2AGL(1,ℤ/8)×D8911yescharacteristic
390C2#1915240811yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#490×C89C2
socleC22×C89C22×D4
prime radical#19152233C2
hypercenter#490D89
hypocenterC89#3310
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #19152286C2semidirect
3. #19151920C2semidirect
4. #19151910C2semidirect
5. #19151895C2semidirect
6. #19151843C2semidirect
7. #19151826C2semidirect
8. #19151795C2semidirect
9. #19151750C2semidirect
10. #19151750C2semidirect
11. #19151700C2semidirect
12. #19151671C2semidirect
13. #19151601C2semidirect
14. #102×D89C2semidirect
15. #490×C89C2semidirect
20. C2×#13083562C22semidirect
21. C2×#13083562C22semidirect
22. C2×#13083557C22semidirect
23. C2×C8×D89C22semidirect
27. #15667992C22semidirect
28. #15667992C22semidirect
34. C4×Dic178C22semidirect
38. #15667970C22semidirect
39. C4⋊C4×D89C22semidirect
40. #15667946C22semidirect
41. #15667945C22semidirect
42. #15667943C22semidirect
43. C4⋊#10623494C22semidirect
44. #15667937C22semidirect
46. #15667933C22semidirect
47. #15667933C22semidirect
50. #15667924C22semidirect
51. #15667924C22semidirect
53. #125×C89C22semidirect
54. #102×C89C22semidirect
55. #102×C89C22semidirect
56. #102×C89C22semidirect
57. #102×C89C22semidirect
58. #97×C89C22semidirect
196. C89#3310semidirect
199. #490D89semidirect
223. #125C2×D89semidirect
248. #102C2×D89semidirect
249. #102C2×D89semidirect
250. #102C2×D89semidirect
251. #102C2×D89semidirect
254. #97C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191522862
#191522332
#191519202
#191519102
#191518952
#191518432
#191518262
#191517952
#191517502
#191517002
#191516712
#191516012
#102×D892
#490×C892
#331089