Finite Group Databasebeta

← #26031080

Subgroups — #26031080

Order 11392.

414 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152105C211yesmaximal, characteristic
2C22⋊Q8×D89C211yesmaximal, characteristic, complemented
3#19151940C211yesmaximal, characteristic, complemented
4#19151936C211yesmaximal, characteristic, complemented
5#19151932C211yesmaximal, characteristic, complemented
6#19151915C211yesmaximal, characteristic, complemented
7#19151855C211yesmaximal, characteristic, complemented
8#19151853C211yesmaximal, characteristic, complemented
9#19151843C211yesmaximal, characteristic, complemented
10#19151841C211yesmaximal, characteristic, complemented
11#19151760C211yesmaximal, characteristic, complemented
12#19151752C211yesmaximal, characteristic, complemented
13#19151735C211yesmaximal, characteristic, complemented
14#19151560C211yesmaximal, characteristic, complemented
15#452×C89C211yesmaximal, characteristic, complemented
16C2×Q8×D89C2211yescharacteristic
17C22×C4×D89C2211yescharacteristic
18C2×#13083564C2211yescharacteristic, complemented
19C2×#13083562C2211yescharacteristic, complemented
20C2×#13083557C2211yescharacteristic
21C2×#13083557C2211yescharacteristic
22#15667993—21no—
23#15667992C2211yescharacteristic
24#15667991C2211yescharacteristic
25#15667990—21no—
26#15667989—21no—
27#15667988C2211yescharacteristic
28#15667988C2211yescharacteristic
29#15667988C2211yescharacteristic
30#15667983C2211yescharacteristic
31#15667983C2211yescharacteristic
32#15667980—21no—
33C4×C22⋊D89—21no—
34C4×C22⋊D89—21no—
35#15667971C2211yescharacteristic
36C4⋊C4×D89—21no—
37C4⋊C4×D89C2211yescharacteristic
38C22⋊C4×D89—21no—
39#15667946C2211yescharacteristic, complemented
40#15667945C2211yescharacteristic, complemented
41#15667944C2211yescharacteristic, complemented
42#15667943C2211yescharacteristic, complemented
43#15667937C2211yescharacteristic, complemented
44#15667937C2211yescharacteristic, complemented
45#15667936C2211yescharacteristic, complemented
46#15667936C2211yescharacteristic, complemented
47#15667936C2211yescharacteristic, complemented
48#15667933C2211yescharacteristic, complemented
49C22⋊#10623494C2211yescharacteristic
50#15667924C2211yescharacteristic
51#15667924C2211yescharacteristic
52C2×#41×C89C2211yescharacteristic
53C2×Q16×C89C2211yescharacteristic, complemented
54C2×SD16×C89C2211yescharacteristic, complemented
55C22⋊Q8×C89C2211yescharacteristic
56#103×C89C2211yescharacteristic, complemented
57#102×C89C2211yescharacteristic, complemented
58C22⋊C8×C89C2211yescharacteristic
59C23×D89D411yescharacteristic
60C2×Dic178—21no—
61C2×Dic178C2311yescharacteristic
62Q8×D89—41no—
63Q8×D89—41no—
64C2×C22⋊D89—21no—
65C2×C22⋊D89—21no—
66C22×Dic89D411yescharacteristic
67C2×C4×D89—21no—
68C2×C4×D89—21no—
69C2×C4×D89—41no—
70C2×C4×D89—41no—
71C2×C4×D89D411yescharacteristic
72C2×C4×D89D411yescharacteristic
73C2×C4×D89C2311yescharacteristic
74C2×C4×D89C2311yescharacteristic
75#13083564—41no—
76#13083562—41no—
77#13083557—41no—
78#13083557—41no—
79C2×#10623494C2311yescharacteristic
80C2×#10623494C2311yescharacteristic
81C4⋊Dic89—21no—
82C4⋊Dic89C2311yescharacteristic
83C4⋊Dic89C2311yescharacteristic
84C4⋊Dic89C2311yescharacteristic
85#13083553—21no—
86#13083553—21no—
87#13083553—21no—
88#13083553—21no—
89#13083553—21no—
90C22⋊Dic89—21no—
91C22⋊Dic89—21no—
92C22⋊Dic89—21no—
93C22⋊Dic89—21no—
94#13083551—21no—
95#13083551—21no—
96#13083551—21no—
97#13083551—21no—
98C4×Dic89—21no—
99#41×C89—41no—
100#41×C89—41no—
101C2×Q8×C89C2311yescharacteristic
102C2×Q8×C89C2311yescharacteristic
103C2×D4×C89—21no—
104C2×D4×C89C2311yescharacteristic
105C22×C4×C89—21no—
106C22×C4×C89C2311yescharacteristic
107Q16×C89—41no—
108SD16×C89—41no—
109C2×C8×C89C2311yescharacteristic
110C2×C8×C89C2311yescharacteristic
111C4⋊C4×C89—21no—
112C4⋊C4×C89C2311yescharacteristic
113C22⋊C4×C89—21no—
114C23×C89—21no—
115C23×C89C2×D411yescharacteristic
116C22×D89—22no—
117C22×D89—41no—
118C22×D89—41no—
119C22×D89C2×D411yescharacteristic
120C22×D89C2×D411yescharacteristic
121Q8×C89—21no—
122Q8×C89—21no—
123Q8×C89—21no—
124Q8×C89—21no—
125D4×C89—21no—
126D4×C89—21no—
127D4×C89—42no—
128C2×C4×C89—21no—
129C2×C4×C89—21no—
130C2×C4×C89—21no—
131C2×C4×C89—21no—
132C2×C4×C89—21no—
133C2×C4×C89—42no—
134C2×C4×C89C2×D411yescharacteristic
135C2×C4×C89C2411yescharacteristic
136C22⋊D89—42no—
137C22⋊D89—42no—
138C2×Dic89—21no—
139C2×Dic89—21no—
140C2×Dic89—21no—
141C2×Dic89—21no—
142C2×Dic89—41no—
143C2×Dic89C2×D411yescharacteristic
144C2×Dic89C2×D411yescharacteristic
145C4×D89—21no—
146C4×D89—21no—
147C4×D89—21no—
148C4×D89—21no—
149C4×D89—41no—
150C4×D89—41no—
151C4×D89—42no—
152C4×D89—42no—
153Dic178—21no—
154Dic178—21no—
155Dic178—42no—
156C8×C89—21no—
157C8×C89—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—21no—
168C2×D89—21no—
169C2×D89—21no—
170C2×D89—21no—
171C2×D89—21no—
172C2×D89—44no—
173C2×D89#13712yes—
174C4×C89—21no—
175C4×C89—41no—
176C4×C89—41no—
177C4×C89—41no—
178C4×C89H(5,𝔽2)11yescharacteristic
179C4×C89H(5,𝔽2)11yescharacteristic
180Dic89—21no—
181Dic89—21no—
182Dic89—41no—
183Dic89—41no—
184Dic89—41no—
185Dic89—41no—
186C2×C89—41no—
187C2×C89—81no—
188C2×C89#53411yescharacteristic
189C2×C89C2×#13711yescharacteristic
190C2×C89#57511yescharacteristic
191D89—22no—
192D89—41no—
193#3196—891nomaximal, Sylow
194C89#319611yescharacteristic, complemented, Sylow
195#525—891no—
196C2×C22⋊Q8—891no—
197#485—891no—
198#485—891no—
199#484—891no—
200#481—891no—
201#470—891no—
202#470—891no—
203#468—891no—
204#468—891no—
205#452—891no—
206#452D8911yescharacteristic, complemented
207#451—891no—
208#448—891no—
209#407—891no—
210C2×#41C2×D8911yescharacteristic
211C22×Q8—891no—
212C23×C4—891no—
213C2×Q16—891no—
214C2×Q16C2×D8911yescharacteristic, complemented
215C2×SD16—891no—
216C2×SD16C2×D8911yescharacteristic, complemented
217C2×M16—891no—
218C2×M16—891no—
219#123—1781no—
220C22⋊Q8—891no—
221C22⋊Q8—891no—
222C22⋊Q8—891no—
223C22⋊Q8—891no—
224C22⋊Q8—891no—
225C22⋊Q8—1781no—
226C22⋊Q8—1781no—
227C22⋊Q8C2×D8911yescharacteristic
228#121—891no—
229#121—891no—
230#120—1781no—
231C4×D4—1781no—
232C4×D4—1781no—
233#117—891no—
234C2×C4⋊C4—891no—
235C2×C4⋊C4—1781no—
236C2×C22⋊C4—1781no—
237#107—891no—
238#107—891no—
239#106—891no—
240#106—891no—
241#103—891no—
242#103—891no—
243#103—891no—
244#103—891no—
245#103—891no—
246#103C2×D8911yescharacteristic, complemented
247#102—891no—
248#102C2×D8911yescharacteristic, complemented
249C22⋊C8—891no—
250C22⋊C8—891no—
251C22⋊C8—891no—
252C22⋊C8C2×D8911yescharacteristic
253C24—891no—
254#41—41no—
255#41—41no—
256C2×Q8—891no—
257C2×Q8—3561no—
258C2×Q8—3561no—
259C2×Q8—1781no—
260C2×Q8C22×D8911yescharacteristic
261C2×Q8C22×D8911yescharacteristic
262C2×D4—21no—
263C2×D4—1781no—
264C2×D4—1781no—
265C2×D4C22×D8911yescharacteristic
266C22×C4—21no—
267C22×C4—891no—
268C22×C4—891no—
269C22×C4—891no—
270C22×C4—891no—
271C22×C4—891no—
272C22×C4—3561no—
273C22×C4—3561no—
274C22×C4—1781no—
275C22×C4—1781no—
276C22×C4C22×D8911yescharacteristic
277Q16—41no—
278Q16—3561no—
279SD16—41no—
280SD16—3561no—
281M16—3561no—
282M16—3561no—
283C2×C8—891no—
284C2×C8—891no—
285C2×C8C22×D8911yescharacteristic
286C2×C8C22×D8911yescharacteristic
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⋊C4—1781no—
296C4⋊C4—1781no—
297C4⋊C4C22×D8911yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—1781no—
300C22⋊C4—1781no—
301C22⋊C4—1781no—
302C22⋊C4—1781no—
303C22⋊C4—1781no—
304C22⋊C4—1781no—
305C22⋊C4—1781no—
306C22⋊C4—1781no—
307C42—1781no—
308C23—21no—
309C23—891no—
310C23—891no—
311C23—3561no—
312C23—3561no—
313C23—1782no—
314C23D4×D8911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—3562no—
320Q8—1781no—
321Q8—1781no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—3562no—
326D4—3562no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—891no—
334C2×C4—891no—
335C2×C4—3561no—
336C2×C4—3561no—
337C2×C4—3562no—
338C2×C4—3562no—
339C2×C4—3561no—
340C2×C4—1781no—
341C2×C4—1781no—
342C2×C4—1781no—
343C2×C4—1781no—
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—3564no—
362C22—1781no—
363C22—1781no—
364C22—1781no—
365C22—1781no—
366C22—1781no—
367C22C2×D4×D8911yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—3561no—
373C4—3561no—
374C4—3561no—
375C4—3561no—
376C4—1781no—
377C4—1781no—
378C4#1566805711yescharacteristic
379C4#1566805711yescharacteristic
380C2—41no—
381C2—81no—
382C2—3561no—
383C2—1782no—
384C2#1915215811yescharacteristic
385C2#137×D8911yescharacteristic
386C2#1915239511yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#452×C89C2
socleC22×C89C22×D4
prime radical#19152105C2
hypercenter#452D89
hypocenterC89#3196
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D89C2semidirect
3. #19151940C2semidirect
4. #19151936C2semidirect
5. #19151932C2semidirect
6. #19151915C2semidirect
7. #19151855C2semidirect
8. #19151853C2semidirect
9. #19151843C2semidirect
10. #19151841C2semidirect
11. #19151760C2semidirect
12. #19151752C2semidirect
13. #19151735C2semidirect
14. #19151560C2semidirect
15. #452×C89C2semidirect
18. C2×#13083564C22semidirect
19. C2×#13083562C22semidirect
39. #15667946C22semidirect
40. #15667945C22semidirect
41. #15667944C22semidirect
42. #15667943C22semidirect
43. #15667937C22semidirect
44. #15667937C22semidirect
45. #15667936C22semidirect
46. #15667936C22semidirect
47. #15667936C22semidirect
48. #15667933C22semidirect
53. C2×Q16×C89C22semidirect
54. C2×SD16×C89C22semidirect
56. #103×C89C22semidirect
57. #102×C89C22semidirect
194. C89#3196semidirect
206. #452D89semidirect
214. C2×Q16C2×D89semidirect
216. C2×SD16C2×D89semidirect
246. #103C2×D89semidirect
248. #102C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191521052
C22⋊Q8×D892
#191519402
#191519362
#191519322
#191519152
#191518552
#191518532
#191518432
#191518412
#191517602
#191517522
#191517352
#191515602
#452×C892
#319689