Finite Group Databasebeta

← #26032213

Subgroups — #26032213

Order 11392.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152252C211yesmaximal, characteristic, complemented
2#19151957C211yesmaximal, characteristic, complemented
3#19151926C211yesmaximal, characteristic, complemented
4#19151914C211yesmaximal, characteristic, complemented
5#19151888C211yesmaximal, characteristic, complemented
6#19151849C211yesmaximal, characteristic, complemented
7#19151829C211yesmaximal, characteristic, complemented
8#19151810C211yesmaximal, characteristic, complemented
9#19151743C211yesmaximal, characteristic, complemented
10#19151732C211yesmaximal, characteristic, complemented
11#19151708C211yesmaximal, characteristic, complemented
12#19151670C211yesmaximal, characteristic, complemented
13#19151599C211yesmaximal, characteristic, complemented
14C2×#15667933C211yesmaximal, characteristic, complemented
15#546×C89C211yesmaximal, characteristic, complemented
16C2×#13083573—21no—
17C2×#13083561C2211yescharacteristic, complemented
18C2×#13083559C2211yescharacteristic
19C2×#13083559C2211yescharacteristic
20C2×#13083558C2211yescharacteristic, complemented
21C22×#10623494C2211yescharacteristic
22#15668012C2211yescharacteristic, complemented
23#15667996—21no—
24#15667996—21no—
25#15667992—21no—
26#15667986C2211yescharacteristic
27#15667986C2211yescharacteristic, complemented
28C4×D356C2211yescharacteristic, complemented
29C2×C4⋊Dic89C2211yescharacteristic
30C2×C4⋊Dic89C2211yescharacteristic, complemented
31#15667943C2211yescharacteristic, complemented
32#15667943C2211yescharacteristic, complemented
33#15667943C2211yescharacteristic, complemented
34C4⋊#10623494C2211yescharacteristic, complemented
35#15667936C2211yescharacteristic, complemented
36#15667936C2211yescharacteristic, complemented
37#15667936C2211yescharacteristic, complemented
38#15667933C2211yescharacteristic
39#15667933C2211yescharacteristic
40#15667933C2211yescharacteristic
41#15667933C2211yescharacteristic
42#15667933C2211yescharacteristic
43#15667933C2211yescharacteristic
44#15667932C2211yescharacteristic, complemented
45C22⋊#10623494C2211yescharacteristic
46C22⋊#10623494C2211yescharacteristic, complemented
47#15667923C2211yescharacteristic, complemented
48C2×#41×C89C2211yescharacteristic
49C22×D4×C89C2211yescharacteristic
50#124×C89C2211yescharacteristic
51#123×C89—21no—
52C22⋊Q8×C89C2211yescharacteristic
53#121×C89—21no—
54#121×C89C2211yescharacteristic
55#120×C89—21no—
56C4×D4×C89C2211yescharacteristic
57C4×D4×C89C2211yescharacteristic
58C2×C22⋊C4×C89—21no—
59#13083573—44no—
60C2×Dic178—21no—
61C2×D356C2311yescharacteristic
62C2×C22⋊D89—21no—
63C2×C22⋊D89—21no—
64C22×Dic89—21no—
65C22×Dic89—21no—
66C2×C4×D89—21no—
67#13083561—41no—
68#13083559—22no—
69#13083559—41no—
70#13083558—41no—
71C2×#10623494—41no—
72C2×#10623494C2311yescharacteristic
73C2×#10623494C2311yescharacteristic
74C2×#10623494C2311yescharacteristic
75C2×#10623494C2311yescharacteristic
76C4⋊Dic89—21no—
77C4⋊Dic89—21no—
78C4⋊Dic89—21no—
79C4⋊Dic89C2311yescharacteristic
80C4⋊Dic89C2311yescharacteristic
81C4⋊Dic89C2311yescharacteristic
82#13083551—21no—
83#13083551—21no—
84#13083551—21no—
85C24×C89—21no—
86#41×C89—22no—
87#41×C89—41no—
88C2×Q8×C89C2311yescharacteristic
89C2×D4×C89—22no—
90C2×D4×C89—21no—
91C2×D4×C89—21no—
92C2×D4×C89—21no—
93C2×D4×C89—41no—
94C2×D4×C89D411yescharacteristic
95C2×D4×C89C2311yescharacteristic
96C2×D4×C89C2311yescharacteristic
97C22×C4×C89—21no—
98C22×C4×C89—21no—
99C22×C4×C89C2311yescharacteristic
100C22×C4×C89C2311yescharacteristic
101C4⋊C4×C89—21no—
102C4⋊C4×C89D411yescharacteristic
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×C89C2311yescharacteristic
112C23×C89—21no—
113C23×C89—21no—
114C23×C89—42no—
115C23×C89—42no—
116C23×C89—81no—
117C23×C89C2×D411yescharacteristic
118C23×C89C2×D411yescharacteristic
119C22×D89—21no—
120Q8×C89—21no—
121Q8×C89—21no—
122D4×C89—22no—
123D4×C89—21no—
124D4×C89—21no—
125D4×C89—21no—
126D4×C89—42no—
127D4×C89—42no—
128D4×C89—81no—
129D4×C89#4112yescomplemented
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—42no—
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—
146C2×Dic89—21no—
147C2×Dic89—21no—
148C2×Dic89—42no—
149C2×Dic89—42no—
150D356—21no—
151D356—21no—
152C4×D89—42no—
153Dic178—42no—
154#10623494—21no—
155#10623494—21no—
156#10623494—21no—
157#10623494—21no—
158C22×C89—21no—
159C22×C89—21no—
160C22×C89—21no—
161C22×C89—22no—
162C22×C89—21no—
163C22×C89—21no—
164C22×C89—41no—
165C22×C89—41no—
166C22×C89—41no—
167C22×C89—41no—
168C22×C89—41no—
169C22×C89—84no—
170C22×C89AGL(1,ℤ/8)12yes—
171C22×C89C22×D411yescharacteristic
172C2×D89—41no—
173C2×D89—41no—
174C2×D89—41no—
175C4×C89—21no—
176C4×C89—21no—
177C4×C89—21no—
178C4×C89—21no—
179C4×C89—41no—
180C4×C89—41no—
181C4×C89C2×#4111yescharacteristic
182C4×C89H(5,𝔽2)11yescharacteristic
183Dic89—41no—
184Dic89—41no—
185Dic89—41no—
186C2×C89—22no—
187C2×C89—41no—
188C2×C89—42no—
189C2×C89—81no—
190C2×C89#54611yescharacteristic
191C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C89#57711yescharacteristic
193D89—81no—
194#3306—891nomaximal, Sylow
195C89#330611yescharacteristic, complemented, Sylow
196#547—891no—
197#546D8911yescharacteristic, complemented
198#489—891no—
199#483—891no—
200#481—891no—
201#476—891no—
202#469—891no—
203#465—891no—
204#463—891no—
205#449—891no—
206#447—891no—
207#442—891no—
208#435—891no—
209#417—891no—
210C2×#102—891no—
211C2×#41—1781no—
212C2×#41C2×D8911yescharacteristic
213C22×D4C2×D8911yescharacteristic
214C2×SD16—891no—
215C2×D8—891no—
216C2×D8—891no—
217C2×M16—891no—
218C22×C8—891no—
219C4⋊Q8—891no—
220#124C2×D8911yescharacteristic
221#123—21no—
222#123—1781no—
223#123—1781no—
224C22⋊Q8—1781no—
225C22⋊Q8C2×D8911yescharacteristic
226#121—21no—
227#121—891no—
228#121—891no—
229#121C2×D8911yescharacteristic
230#120—21no—
231C4×D4—891no—
232C4×D4C2×D8911yescharacteristic
233C4×D4C2×D8911yescharacteristic
234C2×C4⋊C4—891no—
235C2×C4⋊C4—891no—
236C2×C22⋊C4—21no—
237#106—891no—
238#106—891no—
239#106—891no—
240C4⋊C8—891no—
241#103—891no—
242#103—891no—
243#103—891no—
244#102—891no—
245#102—891no—
246#102—891no—
247#102—891no—
248#102—891no—
249#102—891no—
250#102—891no—
251C22⋊C8—891no—
252C22⋊C8—891no—
253#97—891no—
254C24—21no—
255#41—22no—
256#41—41no—
257#41—3564no—
258C2×Q8—1781no—
259C2×Q8C22×D8911yescharacteristic
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—891no—
266C2×D4—1781no—
267C2×D4—1781no—
268C2×D4C22⋊D8911yescharacteristic
269C2×D4C22×D8911yescharacteristic
270C2×D4C22×D8911yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—1781no—
274C22×C4—1781no—
275C22×C4—1781no—
276C22×C4C22×D8911yescharacteristic
277C22×C4C22×D8911yescharacteristic
278SD16—3561no—
279D8—3561no—
280D8—1782no—
281M16—3561no—
282C2×C8—891no—
283C2×C8—891no—
284C2×C8—891no—
285C2×C8—891no—
286C2×C8—3561no—
287C4⋊C4—21no—
288C4⋊C4—891no—
289C4⋊C4—891no—
290C4⋊C4—891no—
291C4⋊C4—1781no—
292C4⋊C4—1781no—
293C4⋊C4—1781no—
294C4⋊C4C22⋊D8911yescharacteristic
295C4⋊C4C22×D8911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—1781no—
302C22⋊C4—1781no—
303C22⋊C4—1781no—
304C22⋊C4C22⋊D8911yescharacteristic
305C22⋊C4C22⋊D8911yescharacteristic
306C42C22×D8911yescharacteristic
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—1781no—
313C23C2×C22⋊D8911yescharacteristic
314C23C2×C22⋊D8911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—3562no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—3562no—
326D4—3562no—
327D4—1781no—
328D4—1781no—
329D4#1308357312yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—3562no—
339C2×C4—3562no—
340C2×C4—3562no—
341C2×C4—1781no—
342C2×C4—1781no—
343C2×C4—1781no—
344C2×C4C2×C22⋊D8911yescharacteristic
345C2×C4C2×C22⋊D8911yescharacteristic
346C2×C4C2×C22⋊D8911yescharacteristic
347C2×C4C2×C22⋊D8911yescharacteristic
348C2×C4C23×D8911yescharacteristic
349C8—1781no—
350C8—1781no—
351C8—1781no—
352C8—1781no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—3561no—
366C22—3561no—
367C22—3561no—
368C22#1566803712yes—
369C22C22×C22⋊D8911yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—3561no—
377C4—3561no—
378C4—3561no—
379C4C2×#1308357311yescharacteristic
380C4#1566805711yescharacteristic
381C2—22no—
382C2—41no—
383C2—42no—
384C2—81no—
385C2—7121no—
386C2#1915224211yescharacteristic
387C2C2×#1566803711yescharacteristic
388C2#1915240911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#546×C89C2
socleC22×C89C22×D4
hypercenter#546D89
hypocenterC89#3306
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #19152252C2semidirect
2. #19151957C2semidirect
3. #19151926C2semidirect
4. #19151914C2semidirect
5. #19151888C2semidirect
6. #19151849C2semidirect
7. #19151829C2semidirect
8. #19151810C2semidirect
9. #19151743C2semidirect
10. #19151732C2semidirect
11. #19151708C2semidirect
12. #19151670C2semidirect
13. #19151599C2semidirect
14. C2×#15667933C2semidirect
15. #546×C89C2semidirect
17. C2×#13083561C22semidirect
20. C2×#13083558C22semidirect
22. #15668012C22semidirect
27. #15667986C22semidirect
28. C4×D356C22semidirect
30. C2×C4⋊Dic89C22semidirect
31. #15667943C22semidirect
32. #15667943C22semidirect
33. #15667943C22semidirect
34. C4⋊#10623494C22semidirect
35. #15667936C22semidirect
36. #15667936C22semidirect
37. #15667936C22semidirect
44. #15667932C22semidirect
46. C22⋊#10623494C22semidirect
47. #15667923C22semidirect
129. D4×C89#41semidirect
195. C89#3306semidirect
197. #546D89semidirect
329. D4#13083573semidirect

Maximal subgroups

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

subgroupindex
#191522522
#191519572
#191519262
#191519142
#191518882
#191518492
#191518292
#191518102
#191517432
#191517322
#191517082
#191516702
#191515992
C2×#156679332
#546×C892
#330689