Finite Group Databasebeta

← #26032462

Subgroups — #26032462

Order 11392.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152244C211yesmaximal, characteristic
2#19151955C211yesmaximal, characteristic, complemented
3#19151939C211yesmaximal, characteristic, complemented
4#19151916C211yesmaximal, characteristic, complemented
5#19151895C211yesmaximal, characteristic, complemented
6#19151854C211yesmaximal, characteristic, complemented
7#19151846C211yesmaximal, characteristic, complemented
8#19151820C211yesmaximal, characteristic, complemented
9#19151758C211yesmaximal, characteristic, complemented
10#19151748C211yesmaximal, characteristic, complemented
11C4×#13083561C211yesmaximal, characteristic, complemented
12#19151676C211yesmaximal, characteristic, complemented
13#19151602C211yesmaximal, characteristic, complemented
14#19151597C211yesmaximal, characteristic, complemented
15#552×C89C211yesmaximal, characteristic, complemented
16C2×#13083574C2211yescharacteristic
17C22×D356C2211yescharacteristic
18C2×#13083564C2211yescharacteristic, complemented
19C2×#13083561C2211yescharacteristic
20C2×#13083561C2211yescharacteristic
21C2×#13083558C2211yescharacteristic
22C2×#13083558C2211yescharacteristic, 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#15667943C2211yescharacteristic, complemented
33#15667943C2211yescharacteristic, complemented
34C4⋊#10623494C2211yescharacteristic, complemented
35#15667936C2211yescharacteristic, complemented
36#15667935C2211yescharacteristic, complemented
37#15667935C2211yescharacteristic, complemented
38#15667935C2211yescharacteristic, 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×C89—21no—
50#125×C89C2211yescharacteristic, complemented
51#123×C89—21no—
52C22⋊Q8×C89C2211yescharacteristic
53C22⋊Q8×C89C2211yescharacteristic, complemented
54C4×Q8×C89C2211yescharacteristic, complemented
55C4×D4×C89C2211yescharacteristic
56#117×C89—21no—
57#117×C89C2211yescharacteristic
58C2×C4⋊C4×C89C2211yescharacteristic, complemented
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#13083564—41no—
73#13083561—22no—
74#13083561—41no—
75#13083558—41no—
76#13083558—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×Q8×C89C2311yescharacteristic
89C2×D4×C89D411yescharacteristic
90C22×C4×C89—21no—
91C22×C4×C89C2311yescharacteristic
92C22×C4×C89C2311yescharacteristic
93C4⋊C4×C89—21no—
94C4⋊C4×C89—21no—
95C4⋊C4×C89—21no—
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×C89D411yescharacteristic
107C22⋊C4×C89D411yescharacteristic
108C42×C89—21no—
109C42×C89—21no—
110C42×C89C2311yescharacteristic
111C23×C89C2×D411yescharacteristic
112C23×C89C2×D411yescharacteristic
113C22×D89—21no—
114C22×D89—21no—
115C22×D89—42no—
116C22×D89—42no—
117C22×D89—81no—
118Q8×C89—21no—
119Q8×C89—21no—
120D4×C89—41no—
121C2×C4×C89—21no—
122C2×C4×C89—21no—
123C2×C4×C89—21no—
124C2×C4×C89—21no—
125C2×C4×C89—21no—
126C2×C4×C89—21no—
127C2×C4×C89—21no—
128C2×C4×C89—21no—
129C2×C4×C89—42no—
130C2×C4×C89C2×D411yescharacteristic
131C2×C4×C89C2×D411yescharacteristic
132C2×C4×C89C2×D411yescharacteristic
133C2×C4×C89C2×D411yescharacteristic
134C2×C4×C89C2411yescharacteristic
135C22⋊D89—42no—
136C22⋊D89—81no—
137C2×Dic89—21no—
138C2×Dic89—21no—
139D356—21no—
140D356—21no—
141D356—21no—
142D356—42no—
143D356#4112yes—
144C4×D89—42no—
145C4×D89—81no—
146Dic178—21no—
147Dic178—21no—
148#10623494—21no—
149#10623494—21no—
150#10623494—21no—
151#10623494—21no—
152C22×C89—21no—
153C22×C89—21no—
154C22×C89—21no—
155C22×C89—21no—
156C22×C89—21no—
157C22×C89—21no—
158C22×C89C22×D411yescharacteristic
159C2×D89—22no—
160C2×D89—41no—
161C2×D89—41no—
162C2×D89—41no—
163C2×D89—41no—
164C2×D89—41no—
165C2×D89—84no—
166C4×C89—21no—
167C4×C89—21no—
168C4×C89—21no—
169C4×C89—21no—
170C4×C89—41no—
171C4×C89—41no—
172C4×C89—41no—
173C4×C89—41no—
174C4×C89C2×#4111yescharacteristic
175C4×C89H(5,𝔽2)11yescharacteristic
176Dic89—41no—
177Dic89—41no—
178C2×C89—41no—
179C2×C89—41no—
180C2×C89#54611yescharacteristic
181C2×C89#57511yescharacteristic
182C2×C89#57711yescharacteristic
183D89—42no—
184D89—81no—
185#3323—891nomaximal, Sylow
186C89#332311yescharacteristic, complemented, Sylow
187#552D8911yescharacteristic, complemented
188#546—891no—
189#488—891no—
190#485—891no—
191#481—891no—
192#478—891no—
193#470—891no—
194#468—891no—
195#464—891no—
196#452—891no—
197#450—891no—
198C4×SD16—891no—
199#436—891no—
200#418—891no—
201#417—891no—
202C2×#41—891no—
203C22×D4—891no—
204C2×Q16—891no—
205C2×SD16—891no—
206C2×SD16—891no—
207C2×M16—891no—
208C2×M16—891no—
209#126—21no—
210#125—21no—
211#125C2×D8911yescharacteristic, complemented
212#124—891no—
213#123—21no—
214#123—1781no—
215C22⋊Q8—891no—
216C22⋊Q8C2×D8911yescharacteristic
217C22⋊Q8C2×D8911yescharacteristic, complemented
218#121—891no—
219#121—1781no—
220#120—1781no—
221C4×Q8C2×D8911yescharacteristic, complemented
222C4×D4—891no—
223C4×D4C2×D8911yescharacteristic
224#117—21no—
225#117C2×D8911yescharacteristic
226C2×C4⋊C4C2×D8911yescharacteristic, complemented
227C2×C22⋊C4—1781no—
228#107—891no—
229#106—891no—
230#106—891no—
231C4⋊C8—891no—
232#103—891no—
233#103—891no—
234#103—891no—
235#103—891no—
236#102—891no—
237#102—891no—
238#102—891no—
239#102—891no—
240#102—891no—
241#102—891no—
242C22⋊C8—891no—
243C22⋊C8—891no—
244C4×C8—891no—
245C24—1781no—
246#41—3561no—
247#41—1782no—
248C2×Q8—891no—
249C2×Q8C22×D8911yescharacteristic
250C2×D4—891no—
251C2×D4—891no—
252C2×D4—3561no—
253C2×D4—1782no—
254C2×D4—1781no—
255C2×D4—1781no—
256C2×D4—1781no—
257C2×D4C22⋊D8911yescharacteristic
258C22×C4—21no—
259C22×C4—1781no—
260C22×C4—1781no—
261C22×C4C22×D8911yescharacteristic
262C22×C4C22×D8911yescharacteristic
263Q16—3561no—
264SD16—3561no—
265SD16—1782no—
266M16—3561no—
267M16—3561no—
268C2×C8—891no—
269C2×C8—891no—
270C2×C8—891no—
271C2×C8—891no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—891no—
279C4⋊C4—1781no—
280C4⋊C4C22⋊D8911yescharacteristic
281C4⋊C4C22×D8911yescharacteristic
282C4⋊C4C22×D8911yescharacteristic
283C4⋊C4C22×D8911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1781no—
288C22⋊C4—1781no—
289C22⋊C4—1781no—
290C22⋊C4—1781no—
291C22⋊C4—1781no—
292C22⋊C4C22⋊D8911yescharacteristic
293C22⋊C4C22⋊D8911yescharacteristic
294C42—21no—
295C42—21no—
296C42C22×D8911yescharacteristic
297C23—3562no—
298C23—3562no—
299C23—1781no—
300C23—1781no—
301C23—7121no—
302C23C2×C22⋊D8911yescharacteristic
303C23C2×C22⋊D8911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1781no—
307Q8—1781no—
308D4—41no—
309D4—892no—
310D4—3562no—
311D4—3562no—
312D4—1781no—
313D4—1781no—
314D4—1781no—
315D4—7121no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—3562no—
326C2×C4—1781no—
327C2×C4—1781no—
328C2×C4—7121no—
329C2×C4C2×C22⋊D8911yescharacteristic
330C2×C4C2×C22⋊D8911yescharacteristic
331C2×C4C2×C22⋊D8911yescharacteristic
332C2×C4C2×C22⋊D8911yescharacteristic
333C2×C4C23×D8911yescharacteristic
334C8—1781no—
335C8—1781no—
336C8—1781no—
337C8—1781no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—3561no—
345C22—3561no—
346C22—3561no—
347C22—3561no—
348C22—3561no—
349C22—1782no—
350C22—7124no—
351C22C22×C22⋊D8911yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—3561no—
361C4—3561no—
362C4#41×D8911yescharacteristic
363C4#1566805811yescharacteristic
364C2—41no—
365C2—41no—
366C2—3562no—
367C2—7121no—
368C2#1915223611yescharacteristic
369C2#1915239611yescharacteristic
370C2#1915240611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#552×C89C2
socleC22×C89C22×D4
prime radical#19152244C2
hypercenter#552D89
hypocenterC89#3323
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #19151955C2semidirect
3. #19151939C2semidirect
4. #19151916C2semidirect
5. #19151895C2semidirect
6. #19151854C2semidirect
7. #19151846C2semidirect
8. #19151820C2semidirect
9. #19151758C2semidirect
10. #19151748C2semidirect
11. C4×#13083561C2semidirect
12. #19151676C2semidirect
13. #19151602C2semidirect
14. #19151597C2semidirect
15. #552×C89C2semidirect
18. C2×#13083564C22semidirect
22. C2×#13083558C22semidirect
31. #15667945C22semidirect
32. #15667943C22semidirect
33. #15667943C22semidirect
34. C4⋊#10623494C22semidirect
35. #15667936C22semidirect
36. #15667935C22semidirect
37. #15667935C22semidirect
38. #15667935C22semidirect
46. C22⋊#10623494C22semidirect
47. C4×#10623494C22semidirect
50. #125×C89C22semidirect
53. C22⋊Q8×C89C22semidirect
54. C4×Q8×C89C22semidirect
58. C2×C4⋊C4×C89C22semidirect
186. C89#3323semidirect
187. #552D89semidirect
211. #125C2×D89semidirect
217. C22⋊Q8C2×D89semidirect
221. C4×Q8C2×D89semidirect
226. C2×C4⋊C4C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191522442
#191519552
#191519392
#191519162
#191518952
#191518542
#191518462
#191518202
#191517582
#191517482
C4×#130835612
#191516762
#191516022
#191515972
#552×C892
#332389