Finite Group Databasebeta

← #2383×D89 #36717085

Subgroups — #2383×D89 #36717085

Order 22784.

2502 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126×D89C211yesmaximal, characteristic
2#26023445C211yesmaximal, characteristic, complemented
3#26023444C211yesmaximal, characteristic, complemented
4#26023443C213yesmaximal, complemented
5#26023442C213yesmaximal, complemented
6#26023441C211yesmaximal, characteristic, complemented
7#26023440C213yesmaximal, complemented
8#26023439C213yesmaximal, complemented
9#389×D89C213yesmaximal, complemented
10#388×D89C213yesmaximal
11#387×D89C213yesmaximal, complemented
12#385×D89C213yesmaximal
13#384×D89C211yesmaximal, characteristic, complemented
14#383×D89C211yesmaximal, characteristic, complemented
15C89×#2383C211yesmaximal, characteristic, complemented
16C23×C4×D89C2211yescharacteristic
17C2×#15668007C2213yes—
18C2×#15668006C2211yescharacteristic
19C2×#15668005C2213yes—
20#126×D89C4116yescomplemented
21C2×C4⋊C4×D89C2213yes—
22C2×C4⋊C4×D89C2213yes—
23C2×C4⋊C4×D89C2213yes—
24C2×C4⋊C4×D89C2213yes—
25C2×C22⋊C4×D89C2213yes—
26C2×C22⋊C4×D89C2213yes—
27C2×C42×D89C2213yes—
28C2×C42×D89C2211yescharacteristic
29#19151497C2213yescomplemented
30#19151496C2213yescomplemented
31#19151495C2213yescomplemented
32#19151495C2213yescomplemented
33#19151494C2213yescomplemented
34#19151493C2213yescomplemented
35#19151493C2213yescomplemented
36#19151492C2213yes—
37#19151491C2213yes—
38#19151490C2213yes—
39#19151489C2213yes—
40#19151488C2213yes—
41#19151487C2213yes—
42#19151486C2213yes—
43#19151485C2213yescomplemented
44#19151484C2213yescomplemented
45#19151483C2213yescomplemented
46#19151482C2213yescomplemented
47#19151481C2213yescomplemented
48#19151480C2213yescomplemented
49#19151479C2213yescomplemented
50#19151473C2213yes—
51#19151472C2213yes—
52#19151472C2213yes—
53#19151471C2213yes—
54#19151470C2213yes—
55#19151469C2213yes—
56#19151469C2213yes—
57#19151468C2211yescharacteristic, complemented
58#19151467C2213yescomplemented
59#19151467C2213yescomplemented
60#19151466C2211yescharacteristic, complemented
61#19151465C2213yescomplemented
62#19151465C2213yescomplemented
63#95×D89C2213yes—
64#95×D89C2213yes—
65#95×D89C2213yes—
66#95×D89C2213yes—
67C2×#126×C89C2211yescharacteristic
68#389×C89C2213yescomplemented
69#388×C89C2213yes—
70#387×C89C2213yescomplemented
71#385×C89C2213yes—
72#384×C89C2211yescharacteristic, complemented
73#383×C89C2211yescharacteristic, complemented
74C24×D89C2311yescharacteristic
75C23×Dic89C2311yescharacteristic
76C22×C4×D89—46no—
77C22×C4×D89C2311yescharacteristic
78C22×C4×D89C2311yescharacteristic
79C22×C4×D89C2313yes—
80C22×C4×D89C2313yes—
81C22×C4×D89C2313yes—
82C22×C4×D89C2313yes—
83C22×C4×D89C2311yescharacteristic
84C22×C4×D89C2311yescharacteristic
85#15668007C2×C4124yescomplemented
86#15668006C2×C418yescomplemented
87#15668005C2×C4124yescomplemented
88C2×C4⋊Dic89C2313yes—
89C2×C4⋊Dic89C2313yes—
90C2×C4⋊Dic89C2313yes—
91C2×C4⋊Dic89C2313yes—
92C2×#13083553C2313yes—
93C2×#13083553C2313yes—
94C2×#13083553C2313yes—
95C2×#13083553C2313yes—
96C2×#13083553C2313yes—
97C2×#13083553C2313yes—
98C2×#13083553C2313yes—
99C2×#13083553C2313yes—
100C4⋊C4×D89—46no—
101C4⋊C4×D89—46no—
102C4⋊C4×D89—46no—
103C4⋊C4×D89C2×C4124yescomplemented
104C2×C22⋊Dic89C2313yes—
105C2×C22⋊Dic89C2313yes—
106C2×#13083551C2313yes—
107C2×#13083551C2313yes—
108C2×#13083551C2313yes—
109C2×#13083551C2313yes—
110C22⋊C4×D89—46no—
111C22⋊C4×D89C2×C4124yes—
112C2×C4×Dic89C2313yes—
113C2×C4×Dic89C2313yes—
114C2×C4×Dic89C2313yes—
115C2×C4×Dic89C2313yes—
116C42×D89—46no—
117C42×D89C2×C418yescomplemented
118#15667919C2313yes—
119#15667919C2313yes—
120#15667919C2313yes—
121#15667919C2313yes—
122#15667919C2313yes—
123#15667919C2313yes—
124#15667919C2313yes—
125#15667919C2313yes—
126#15667919C2313yes—
127#15667919C2313yes—
128#15667919C2313yes—
129#15667919C2313yes—
130C23×C4×C89C2311yescharacteristic
131#126×C89C2×C418yescomplemented
132C2×C4⋊C4×C89C2313yes—
133C2×C4⋊C4×C89C2313yes—
134C2×C4⋊C4×C89C2313yes—
135C2×C4⋊C4×C89C2313yes—
136C2×C22⋊C4×C89C2313yes—
137C2×C22⋊C4×C89C2313yes—
138C2×C42×C89C2313yes—
139C2×C42×C89C2311yescharacteristic
140#95×C89C2313yes—
141#95×C89C2313yes—
142#95×C89C2313yes—
143#95×C89C2313yes—
144C23×D89—26no—
145C23×D89—26no—
146C23×D89C22×C414yes—
147C23×D89C2411yescharacteristic
148C23×D89C2411yescharacteristic
149C22×Dic89—43no—
150C22×Dic89C2411yescharacteristic
151C22×Dic89C2411yescharacteristic
152C22×Dic89C2413yes—
153C22×Dic89C2413yes—
154C22×Dic89C2413yes—
155C22×Dic89C2413yes—
156C2×C4×D89—26no—
157C2×C4×D89—26no—
158C2×C4×D89—26no—
159C2×C4×D89—26no—
160C2×C4×D89—26no—
161C2×C4×D89—26no—
162C2×C4×D89—26no—
163C2×C4×D89—26no—
164C2×C4×D89—26no—
165C2×C4×D89—26no—
166C2×C4×D89—212no—
167C2×C4×D89—43no—
168C2×C4×D89—43no—
169C2×C4×D89—416no—
170C2×C4×D89C22×C4112yes—
171C2×C4×D89C22×C4112yes—
172C4⋊Dic89—43no—
173C4⋊Dic89—43no—
174C4⋊Dic89—43no—
175C4⋊Dic89C22×C4112yescomplemented
176#13083553—43no—
177#13083553—43no—
178#13083553—43no—
179#13083553—43no—
180#13083553—43no—
181#13083553—43no—
182#13083553C22×C4112yescomplemented
183#13083553C22×C4112yescomplemented
184C22⋊Dic89—43no—
185C22⋊Dic89C22×C4112yes—
186#13083551—43no—
187#13083551—43no—
188#13083551C22×C4112yes—
189#13083551C22×C4112yes—
190C4×Dic89—43no—
191C4×Dic89—43no—
192C4×Dic89—43no—
193C4×Dic89C22×C4112yescomplemented
194C24×C89C2411yescharacteristic
195C22×C4×C89—43no—
196C22×C4×C89C2411yescharacteristic
197C22×C4×C89C2411yescharacteristic
198C22×C4×C89C2413yes—
199C22×C4×C89C2413yes—
200C22×C4×C89C2413yes—
201C22×C4×C89C2413yes—
202C4⋊C4×C89—43no—
203C4⋊C4×C89—43no—
204C4⋊C4×C89—43no—
205C4⋊C4×C89C22×C4112yescomplemented
206C22⋊C4×C89—43no—
207C22⋊C4×C89C22×C4112yes—
208C42×C89—43no—
209C42×C89C22×C414yescomplemented
210C23×C89—23no—
211C23×C89—23no—
212C23×C89C23×C412yes—
213C23×C89C2511yescharacteristic
214C22×D89—23no—
215C22×D89—23no—
216C22×D89—224no—
217C22×D89—44no—
218C22×D89—412no—
219C22×D89C23×C412yes—
220C22×D89C23×C412yes—
221C22×D89H(5,𝔽2)16yes—
222C22×D892−1+416yes—
223C2×C4×C89—23no—
224C2×C4×C89—23no—
225C2×C4×C89—23no—
226C2×C4×C89—23no—
227C2×C4×C89—23no—
228C2×C4×C89—23no—
229C2×C4×C89—23no—
230C2×C4×C89—23no—
231C2×C4×C89—23no—
232C2×C4×C89—23no—
233C2×C4×C89—26no—
234C2×C4×C89—44no—
235C2×C4×C89C23×C416yes—
236C2×C4×C89C23×C416yes—
237C2×Dic89—23no—
238C2×Dic89—23no—
239C2×Dic89—23no—
240C2×Dic89—23no—
241C2×Dic89—23no—
242C2×Dic89—23no—
243C2×Dic89—23no—
244C2×Dic89—23no—
245C2×Dic89—23no—
246C2×Dic89—23no—
247C2×Dic89—26no—
248C2×Dic89—44no—
249C2×Dic89C23×C416yes—
250C2×Dic89C23×C416yes—
251C4×D89—224no—
252C4×D89—224no—
253C4×D89—44no—
254C4×D89—44no—
255C4×D89—412no—
256C4×D89—44no—
257C4×D89—44no—
258C4×D89—412no—
259C22×C89—26no—
260C22×C89—41no—
261C22×C89—43no—
262C22×C89C24×C411yescharacteristic
263C22×C89C2×H(5,𝔽2)13yes—
264C22×C89C2×2−1+413yes—
265C2×D89—26no—
266C2×D89—41no—
267C2×D89—43no—
268C2×D89—416no—
269C2×D89#520112yes—
270C2×D89#56014yes—
271C2×D89#563112yes—
272C4×C89—26no—
273C4×C89—26no—
274C4×C89—41no—
275C4×C89—41no—
276C4×C89—43no—
277C4×C89—43no—
278Dic89—26no—
279Dic89—26no—
280Dic89—41no—
281Dic89—41no—
282Dic89—43no—
283Dic89—43no—
284C2×#2383—891nomaximal, Sylow
285C2×C89—42no—
286C2×C89C2×#52013yes—
287C2×C89C2×#56011yescharacteristic
288C2×C89C2×#56313yes—
289D89—42no—
290D89#238318yesdirect product factor
291C22×#126—891no—
292#2383—893no—
293#2383—893no—
294#2383—893no—
295#2383—893no—
296#2383—891no—
297#2383—891no—
298#2383—891no—
299#2383D8911yescharacteristic, direct product factor
300C2×#389—893no—
301C2×#388—893no—
302C2×#387—893no—
303C2×#385—893no—
304C2×#384—891no—
305C2×#383—891no—
306C89C2×#238311yescharacteristic, complemented, Sylow
307C24×C4—891no—
308C2×#126—8916no—
309C2×#126—893no—
310C2×#126—893no—
311C2×#126—891no—
312C2×#126C2×D8911yescharacteristic
313C22×C4⋊C4—893no—
314C22×C4⋊C4—893no—
315C22×C4⋊C4—893no—
316C22×C4⋊C4—893no—
317C22×C22⋊C4—893no—
318C22×C22⋊C4—893no—
319C22×C42—891no—
320C22×C42—893no—
321#389—893no—
322#389—893no—
323#389—893no—
324#389—893no—
325#389—893no—
326#389—893no—
327#389—893no—
328#389C2×D8913yescomplemented
329#388—893no—
330#388—893no—
331#388—893no—
332#388—893no—
333#388—893no—
334#388—893no—
335#388—893no—
336#388C2×D8913yes—
337#387—893no—
338#387—893no—
339#387—893no—
340#387—893no—
341#387—893no—
342#387—893no—
343#387—893no—
344#387C2×D8913yescomplemented
345#385—893no—
346#385—893no—
347#385—893no—
348#385—893no—
349#385—893no—
350#385—893no—
351#385—893no—
352#385C2×D8913yes—
353#384—893no—
354#384—893no—
355#384—891no—
356#384C2×D8911yescharacteristic, complemented
357#383—891no—
358#383—893no—
359#383—893no—
360#383C2×D8911yescharacteristic, complemented
361C2×#95—893no—
362C2×#95—893no—
363C2×#95—893no—
364C2×#95—893no—
365C25—891no—
366C23×C4—893no—
367C23×C4—893no—
368C23×C4—891no—
369C23×C4—891no—
370C23×C4—891no—
371C23×C4—893no—
372C23×C4—893no—
373C23×C4—891no—
374C23×C4—891no—
375C23×C4—3566no—
376C23×C4C22×D8911yescharacteristic
377#126—8924no—
378#126—8924no—
379#126—898no—
380#126C4×D8918yescomplemented
381C2×C4⋊C4—893no—
382C2×C4⋊C4—893no—
383C2×C4⋊C4—893no—
384C2×C4⋊C4—8924no—
385C2×C4⋊C4—893no—
386C2×C4⋊C4—893no—
387C2×C4⋊C4—893no—
388C2×C4⋊C4—893no—
389C2×C4⋊C4—893no—
390C2×C4⋊C4—893no—
391C2×C4⋊C4—893no—
392C2×C4⋊C4—893no—
393C2×C4⋊C4—893no—
394C2×C4⋊C4—3566no—
395C2×C4⋊C4—3566no—
396C2×C4⋊C4—3566no—
397C2×C4⋊C4C22×D8913yes—
398C2×C4⋊C4C22×D8913yes—
399C2×C4⋊C4C22×D8913yes—
400C2×C4⋊C4C22×D8913yes—
401C2×C22⋊C4—893no—
402C2×C22⋊C4—893no—
403C2×C22⋊C4—893no—
404C2×C22⋊C4—8924no—
405C2×C22⋊C4—893no—
406C2×C22⋊C4—893no—
407C2×C22⋊C4—893no—
408C2×C22⋊C4—3566no—
409C2×C22⋊C4C22×D8913yes—
410C2×C22⋊C4C22×D8913yes—
411C2×C42—893no—
412C2×C42—898no—
413C2×C42—893no—
414C2×C42—893no—
415C2×C42—893no—
416C2×C42—3566no—
417C2×C42C22×D8913yes—
418C2×C42C22×D8911yescharacteristic
419#95—893no—
420#95—893no—
421#95—893no—
422#95—893no—
423#95—893no—
424#95—893no—
425#95—893no—
426#95—893no—
427#95—893no—
428#95—893no—
429#95—893no—
430#95—893no—
431#95C22×D8913yes—
432#95C22×D8913yes—
433#95C22×D8913yes—
434#95C22×D8913yes—
435C24—891no—
436C24—894no—
437C24—891no—
438C24—1786no—
439C24—1786no—
440C24C23×D8911yescharacteristic
441C22×C4—43no—
442C22×C4—893no—
443C22×C4—893no—
444C22×C4—8912no—
445C22×C4—8912no—
446C22×C4—893no—
447C22×C4—891no—
448C22×C4—891no—
449C22×C4—893no—
450C22×C4—3563no—
451C22×C4—3563no—
452C22×C4—35616no—
453C22×C4—3563no—
454C22×C4—1786no—
455C22×C4—1786no—
456C22×C4—1786no—
457C22×C4—1786no—
458C22×C4—1786no—
459C22×C4—1786no—
460C22×C4—17812no—
461C22×C4—1786no—
462C22×C4—1786no—
463C22×C4—1786no—
464C22×C4—1786no—
465C22×C4C23×D8913yes—
466C22×C4C23×D8911yescharacteristic
467C22×C4C23×D8911yescharacteristic
468C22×C4C23×D8913yes—
469C22×C4C23×D8913yes—
470C22×C4C23×D8913yes—
471C4⋊C4—43no—
472C4⋊C4—43no—
473C4⋊C4—43no—
474C4⋊C4—8912no—
475C4⋊C4—8912no—
476C4⋊C4—8912no—
477C4⋊C4—3563no—
478C4⋊C4—3563no—
479C4⋊C4—3563no—
480C4⋊C4—3563no—
481C4⋊C4—3563no—
482C4⋊C4—3563no—
483C4⋊C4—3563no—
484C4⋊C4—3563no—
485C4⋊C4—3563no—
486C4⋊C4C2×C4×D89112yescomplemented
487C22⋊C4—43no—
488C22⋊C4—8912no—
489C22⋊C4—8912no—
490C22⋊C4—8912no—
491C22⋊C4—3563no—
492C22⋊C4—3563no—
493C22⋊C4—3563no—
494C22⋊C4C2×C4×D89112yes—
495C42—43no—
496C42—8912no—
497C42—3563no—
498C42—3563no—
499C42—3563no—
500C42C2×C4×D8914yescomplemented
501C23—23no—
502C23—23no—
503C23—892no—
504C23—896no—
505C23—896no—
506C23—892no—
507C23—3564no—
508C23—35612no—
509C23—17824no—
510C23—1783no—
511C23—1783no—
512C23C22×C4×D8912yes—
513C23C24×D8911yescharacteristic
514C2×C4—23no—
515C2×C4—23no—
516C2×C4—23no—
517C2×C4—23no—
518C2×C4—23no—
519C2×C4—23no—
520C2×C4—23no—
521C2×C4—23no—
522C2×C4—23no—
523C2×C4—23no—
524C2×C4—26no—
525C2×C4—44no—
526C2×C4—896no—
527C2×C4—896no—
528C2×C4—3564no—
529C2×C4—3564no—
530C2×C4—35612no—
531C2×C4—35612no—
532C2×C4—3564no—
533C2×C4—3564no—
534C2×C4—3564no—
535C2×C4—17824no—
536C2×C4—17824no—
537C2×C4—1783no—
538C2×C4—1783no—
539C2×C4—1783no—
540C2×C4—1783no—
541C2×C4—1783no—
542C2×C4—1783no—
543C2×C4—1786no—
544C2×C4—1783no—
545C2×C4—1783no—
546C2×C4—1783no—
547C2×C4—1783no—
548C2×C4C22×C4×D8916yes—
549C2×C4C22×C4×D8916yes—
550C22—26no—
551C22—41no—
552C22—43no—
553C22—8912no—
554C22—894no—
555C22—8912no—
556C22—35616no—
557C22—3561no—
558C22—3563no—
559C22—1786no—
560C22C23×C4×D8911yescharacteristic
561C22H(5,𝔽2)×D8913yes—
562C222−1+4×D8913yes—
563C4—26no—
564C4—26no—
565C4—41no—
566C4—41no—
567C4—43no—
568C4—43no—
569C4—3561no—
570C4—3561no—
571C4—3563no—
572C4—3563no—
573C4—1786no—
574C4—1786no—
575C2—42no—
576C2—898no—
577C2—3562no—
578C2#520×D8913yes—
579C2#560×D8911yescharacteristic
580C2#563×D8913yes—
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingC89×#2383C2
socle, cosocleC23×C89C25
prime radicalC24×D89C23
hypercenter#2383D89
hypocenterC89C2×#2383
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2383

Complements

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

NH ≅ G/Ntype
2. #26023445C2semidirect
3. #26023444C2semidirect
4. #26023443C2semidirect
5. #26023442C2semidirect
6. #26023441C2semidirect
7. #26023440C2semidirect
8. #26023439C2semidirect
9. #389×D89C2semidirect
11. #387×D89C2semidirect
13. #384×D89C2semidirect
14. #383×D89C2semidirect
15. C89×#2383C2semidirect
20. #126×D89C4semidirect
29. #19151497C22semidirect
30. #19151496C22semidirect
31. #19151495C22semidirect
32. #19151495C22semidirect
33. #19151494C22semidirect
34. #19151493C22semidirect
35. #19151493C22semidirect
43. #19151485C22semidirect
44. #19151484C22semidirect
45. #19151483C22semidirect
46. #19151482C22semidirect
47. #19151481C22semidirect
48. #19151480C22semidirect
49. #19151479C22semidirect
57. #19151468C22semidirect
58. #19151467C22semidirect
59. #19151467C22semidirect
60. #19151466C22semidirect
61. #19151465C22semidirect
62. #19151465C22semidirect
68. #389×C89C22semidirect
70. #387×C89C22semidirect
72. #384×C89C22semidirect
73. #383×C89C22semidirect
85. #15668007C2×C4semidirect
86. #15668006C2×C4semidirect
87. #15668005C2×C4semidirect
103. C4⋊C4×D89C2×C4semidirect
117. C42×D89C2×C4semidirect
131. #126×C89C2×C4semidirect
175. C4⋊Dic89C22×C4semidirect
182. #13083553C22×C4semidirect
183. #13083553C22×C4semidirect
193. C4×Dic89C22×C4semidirect
205. C4⋊C4×C89C22×C4semidirect
209. C42×C89C22×C4semidirect
290. D89#2383direct (N × H)
299. #2383D89direct (N × H)
306. C89C2×#2383semidirect
328. #389C2×D89semidirect
344. #387C2×D89semidirect
356. #384C2×D89semidirect
360. #383C2×D89semidirect
380. #126C4×D89semidirect
486. C4⋊C4C2×C4×D89semidirect
500. C42C2×C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#126×D892
#260234452
#260234442
#260234432
#260234422
#260234412
#260234402
#260234392
#389×D892
#388×D892
#387×D892
#385×D892
#384×D892
#383×D892
C89×#23832
C2×#238389