Finite Group Databasebeta

← #26032276

Subgroups — #26032276

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#19152287C211yesmaximal, characteristic, complemented
2#19152232C211yesmaximal, characteristic
3#19151961C211yesmaximal, characteristic, complemented
4#19151913C211yesmaximal, characteristic, complemented
5#19151897C211yesmaximal, characteristic, complemented
6#19151842C211yesmaximal, characteristic, complemented
7#19151828C211yesmaximal, characteristic, complemented
8#19151797C211yesmaximal, characteristic, complemented
9#19151751C211yesmaximal, characteristic, complemented
10#19151750C211yesmaximal, characteristic, complemented
11#19151697C211yesmaximal, characteristic, complemented
12#19151672C211yesmaximal, characteristic, complemented
13#19151602C211yesmaximal, characteristic, complemented
14#102×D89C211yesmaximal, characteristic, complemented
15#482×C89C211yesmaximal, characteristic, complemented
16C22×D356C2211yescharacteristic
17C2×D4×D89—21no—
18C2×D4×D89C2211yescharacteristic
19C2×#13083563C2211yescharacteristic
20C2×#13083563C2211yescharacteristic, complemented
21C2×#13083562C2211yescharacteristic, complemented
22C2×#13083558C2211yescharacteristic, complemented
23C2×C8×D89C2211yescharacteristic, complemented
24#15668008C2211yescharacteristic
25#15668005—21no—
26#15668004—21no—
27#15668003C2211yescharacteristic, complemented
28#15667994—21no—
29#15667992C2211yescharacteristic, complemented
30#15667991C2211yescharacteristic, complemented
31#15667987C2211yescharacteristic
32#15667985—21no—
33#15667982—21no—
34#15667980—21no—
35#15667977C2211yescharacteristic, complemented
36#15667974C2211yescharacteristic
37C4×C22⋊D89C2211yescharacteristic
38#15667969—21no—
39C4⋊C4×D89C2211yescharacteristic, complemented
40#15667945C2211yescharacteristic, complemented
41#15667941C2211yescharacteristic, complemented
42#15667935C2211yescharacteristic, complemented
43#15667934C2211yescharacteristic
44#15667934C2211yescharacteristic, complemented
45#15667933C2211yescharacteristic, complemented
46#15667932C2211yescharacteristic
47#15667932C2211yescharacteristic
48#15667932C2211yescharacteristic, complemented
49#15667932C2211yescharacteristic, complemented
50#15667924C2211yescharacteristic, complemented
51#15667922C2211yescharacteristic, 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×D89—21no—
61C2×Dic178C2311yescharacteristic
62C2×D356—22no—
63C2×D356—21no—
64C2×D356—21no—
65C2×D356—41no—
66C2×D356C2311yescharacteristic
67C2×D356C2311yescharacteristic
68C2×C22⋊D89—21no—
69C2×C22⋊D89—21no—
70C2×C22⋊D89—21no—
71C2×C22⋊D89D411yescharacteristic
72D4×D89—22no—
73D4×D89—41no—
74D4×D89—44no—
75C2×C4×D89—21no—
76C2×C4×D89—21no—
77C2×C4×D89C2311yescharacteristic
78#13083563—22no—
79#13083563—41no—
80#13083562—41no—
81#13083558—41no—
82C2×#10623494C2311yescharacteristic
83C2×#10623494C2311yescharacteristic
84C8×D89—41no—
85C4⋊Dic89—21no—
86C4⋊Dic89—21no—
87C4⋊Dic89C2311yescharacteristic
88#13083553—21no—
89#13083553—21no—
90#13083553—21no—
91#13083553—21no—
92#13083553D411yescharacteristic
93C22⋊Dic89—21no—
94C22⋊Dic89D411yescharacteristic
95#13083551—21no—
96#13083551—21no—
97#13083551—21no—
98#13083551D411yescharacteristic
99C4×Dic89—21no—
100C4×Dic89C2311yescharacteristic
101C2×D4×C89—21no—
102C2×D4×C89C2311yescharacteristic
103C22×C4×C89C2311yescharacteristic
104C2×C8×C89C2311yescharacteristic
105C2×C8×C89C2311yescharacteristic
106C4⋊C4×C89C2311yescharacteristic
107C4⋊C4×C89C2311yescharacteristic
108C4⋊C4×C89C2311yescharacteristic
109C22⋊C4×C89—21no—
110C22⋊C4×C89—21no—
111C42×C89—21no—
112C23×C89—21no—
113C23×C89C2×D411yescharacteristic
114C22×D89—21no—
115C22×D89—21no—
116C22×D89—42no—
117C22×D89—42no—
118C22×D89—42no—
119C22×D89—42no—
120C22×D89—81no—
121C22×D89—81no—
122C22×D89C2×D411yescharacteristic
123D4×C89—21no—
124D4×C89—21no—
125D4×C89—42no—
126C2×C4×C89—21no—
127C2×C4×C89—21no—
128C2×C4×C89—21no—
129C2×C4×C89—21no—
130C2×C4×C89—21no—
131C2×C4×C89C2×D411yescharacteristic
132C2×C4×C89C2411yescharacteristic
133C22⋊D89—22no—
134C22⋊D89—42no—
135C22⋊D89—42no—
136C22⋊D89—81no—
137C2×Dic89—21no—
138C2×Dic89—21no—
139C2×Dic89C2×D411yescharacteristic
140C2×Dic89C2×D411yescharacteristic
141C2×Dic89C2×D411yescharacteristic
142D356—21no—
143D356—21no—
144D356—21no—
145D356—42no—
146D356—42no—
147D356#4112yes—
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—21no—
159C22×C89—21no—
160C22×C89—21no—
161C22×C89—41no—
162C22×C89—41no—
163C22×C89—41no—
164C22×C89C22×D411yescharacteristic
165C2×D89—21no—
166C2×D89—21no—
167C2×D89—22no—
168C2×D89—41no—
169C2×D89—41no—
170C2×D89—41no—
171C2×D89—41no—
172C2×D89—41no—
173C2×D89—84no—
174C2×D89—84no—
175C2×D89AGL(1,ℤ/8)12yes—
176C4×C89—21no—
177C4×C89—41no—
178C4×C89—41no—
179C4×C89—41no—
180C4×C89C2×#4111yescharacteristic
181C4×C89H(5,𝔽2)11yescharacteristic
182Dic89—21no—
183Dic89—21no—
184Dic89—21no—
185Dic89—41no—
186Dic89—41no—
187C2×C89—41no—
188C2×C89—81no—
189C2×C89#54611yescharacteristic
190C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C89#57711yescharacteristic
192D89—22no—
193D89—42no—
194D89—81no—
195#3310—891nomaximal, Sylow
196C89#331011yescharacteristic, complemented, Sylow
197#552—891no—
198D42—891no—
199#490—891no—
200#482D8911yescharacteristic, complemented
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#127—891no—
221#126—1781no—
222#125—891no—
223#125—1781no—
224#123—1781no—
225C22⋊Q8—891no—
226C22⋊Q8—891no—
227#121—891no—
228#121—1781no—
229#121C2×D8911yescharacteristic
230#120—1781no—
231#120—1781no—
232C4×Q8—891no—
233C4×D4—891no—
234C4×D4—891no—
235#117—1781no—
236#117C2×D8911yescharacteristic, complemented
237C2×C4⋊C4—891no—
238#107—891no—
239#107C2×D8911yescharacteristic, complemented
240#106C2×D8911yescharacteristic, complemented
241C4⋊C8—891no—
242#103—891no—
243#102—891no—
244#102—891no—
245#102—891no—
246#102—891no—
247#102—891no—
248#102—891no—
249#102—891no—
250#102C2×D8911yescharacteristic, complemented
251#102C2×D8911yescharacteristic, complemented
252C22⋊C8—891no—
253C22⋊C8C2×D8911yescharacteristic, complemented
254#97—891no—
255C24—1781no—
256C24—1781no—
257C2×Q8—891no—
258C2×D4—21no—
259C2×D4—891no—
260C2×D4—891no—
261C2×D4—891no—
262C2×D4—3561no—
263C2×D4—3564no—
264C2×D4—3561no—
265C2×D4—1782no—
266C2×D4—1781no—
267C2×D4—1781no—
268C2×D4—1781no—
269C2×D4—1781no—
270C2×D4—1782no—
271C2×D4—1781no—
272C2×D4C22×D8911yescharacteristic
273C22×C4—891no—
274C22×C4—1781no—
275C22×C4—1781no—
276C22×C4C22×D8911yescharacteristic
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—891no—
287C4⋊C4—891no—
288C4⋊C4—1781no—
289C4⋊C4—1781no—
290C4⋊C4—1781no—
291C4⋊C4—1781no—
292C4⋊C4—1781no—
293C4⋊C4—1781no—
294C4⋊C4C22×D8911yescharacteristic
295C4⋊C4C22×D8911yescharacteristic
296C4⋊C4C22×D8911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—891no—
300C22⋊C4—891no—
301C22⋊C4—1781no—
302C22⋊C4—1781no—
303C22⋊C4—1781no—
304C22⋊C4—1781no—
305C42—21no—
306C42—891no—
307C42—1781no—
308C23—21no—
309C23—891no—
310C23—3562no—
311C23—3562no—
312C23—3562no—
313C23—3562no—
314C23—1781no—
315C23—1781no—
316C23—7121no—
317C23—7121no—
318C23D4×D8911yescharacteristic
319Q8—1781no—
320Q8—1781no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—892no—
325D4—3562no—
326D4—3562no—
327D4—3562no—
328D4—3562no—
329D4—1782no—
330D4—1781no—
331D4—1781no—
332D4—1781no—
333D4—7121no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—891no—
340C2×C4—891no—
341C2×C4—891no—
342C2×C4—3562no—
343C2×C4—3562no—
344C2×C4—1781no—
345C2×C4—1781no—
346C2×C4—1781no—
347C2×C4—1781no—
348C2×C4D4×D8911yescharacteristic
349C2×C4C23×D8911yescharacteristic
350C8—21no—
351C8—21no—
352C8—1781no—
353C8—1781no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—892no—
361C22—3561no—
362C22—3561no—
363C22—3561no—
364C22—3561no—
365C22—3561no—
366C22—1782no—
367C22—1781no—
368C22—1781no—
369C22—7124no—
370C22—7124no—
371C22C2×D4×D8911yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—3561no—
377C4—3561no—
378C4—1781no—
379C4—1781no—
380C4—1781no—
381C4#41×D8911yescharacteristic
382C4#1566805811yescharacteristic
383C2—41no—
384C2—81no—
385C2—3562no—
386C2—1782no—
387C2—7121no—
388C2#1915224011yescharacteristic
389C2AGL(1,ℤ/8)×D8911yescharacteristic
390C2#1915240511yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#482×C89C2
socleC22×C89C22×D4
prime radical#19152232C2
hypercenter#482D89
hypocenterC89#3310
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
1. #19152287C2semidirect
3. #19151961C2semidirect
4. #19151913C2semidirect
5. #19151897C2semidirect
6. #19151842C2semidirect
7. #19151828C2semidirect
8. #19151797C2semidirect
9. #19151751C2semidirect
10. #19151750C2semidirect
11. #19151697C2semidirect
12. #19151672C2semidirect
13. #19151602C2semidirect
14. #102×D89C2semidirect
15. #482×C89C2semidirect
20. C2×#13083563C22semidirect
21. C2×#13083562C22semidirect
22. C2×#13083558C22semidirect
23. C2×C8×D89C22semidirect
27. #15668003C22semidirect
29. #15667992C22semidirect
30. #15667991C22semidirect
35. #15667977C22semidirect
39. C4⋊C4×D89C22semidirect
40. #15667945C22semidirect
41. #15667941C22semidirect
42. #15667935C22semidirect
44. #15667934C22semidirect
45. #15667933C22semidirect
48. #15667932C22semidirect
49. #15667932C22semidirect
50. #15667924C22semidirect
51. #15667922C22semidirect
53. #117×C89C22semidirect
54. #107×C89C22semidirect
55. #106×C89C22semidirect
56. #102×C89C22semidirect
57. #102×C89C22semidirect
58. C22⋊C8×C89C22semidirect
196. C89#3310semidirect
200. #482D89semidirect
236. #117C2×D89semidirect
239. #107C2×D89semidirect
240. #106C2×D89semidirect
250. #102C2×D89semidirect
251. #102C2×D89semidirect
253. C22⋊C8C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191522872
#191522322
#191519612
#191519132
#191518972
#191518422
#191518282
#191517972
#191517512
#191517502
#191516972
#191516722
#191516022
#102×D892
#482×C892
#331089