Finite Group Databasebeta

← #36565041

Subgroups — #36565041

Order 22784.

762 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19151659C211yesmaximal, characteristic
2#26022861C211yesmaximal, characteristic
3#26021018C211yesmaximal, characteristic, complemented
4#26021018C211yesmaximal, characteristic, complemented
5#26021013C211yesmaximal, characteristic, complemented
6#26021008C211yesmaximal, characteristic, complemented
7#26020451C211yesmaximal, characteristic
8#26020451C211yesmaximal, characteristic
9#26020445C211yesmaximal, characteristic
10#26020440C211yesmaximal, characteristic
11#26020418C211yesmaximal, characteristic, complemented
12#26020414C211yesmaximal, characteristic, complemented
13#26020385C211yesmaximal, characteristic, complemented
14#26020379C211yesmaximal, characteristic, complemented
15C89×#2317C211yesmaximal, characteristic
16#19151659C418yescomplemented
17C2×#15667945C2211yescharacteristic
18C2×#15667945C2211yescharacteristic
19C2×#15667945C2211yescharacteristic
20C2×#15667945C2211yescharacteristic
21C2×#15667943C2211yescharacteristic
22C2×#15667943C2211yescharacteristic
23C2×#15667943C2211yescharacteristic
24C2×#15667943C2211yescharacteristic
25C2×C4⋊#10623494C2211yescharacteristic
26C2×C4⋊#10623494C2211yescharacteristic
27C2×C22⋊#10623494C2211yescharacteristic
28C2×C22⋊#10623494C2211yescharacteristic
29C2×#15667923C2211yescharacteristic
30C2×C4×#10623494C2211yescharacteristic
31#19151491—21no—
32#19151491—21no—
33#19151484—21no—
34#19151484—21no—
35#19151468C2211yescharacteristic
36#19151464C2211yescharacteristic
37#19151458C2211yescharacteristic
38#19151458C2211yescharacteristic
39C4×C4⋊Dic89C2211yescharacteristic
40C4×C4⋊Dic89C2211yescharacteristic
41#19151360C2211yescharacteristic
42#19151360C2211yescharacteristic
43#19151360C2211yescharacteristic
44#19151360C2211yescharacteristic
45#19151360C2211yescharacteristic
46#19151360C2211yescharacteristic
47#19151360C2211yescharacteristic
48#19151360C2211yescharacteristic
49C2×#117×C89C2211yescharacteristic
50C2×#117×C89C2211yescharacteristic
51C22×C4⋊C4×C89C2211yescharacteristic
52#389×C89—21no—
53#389×C89—21no—
54#385×C89—21no—
55#385×C89—21no—
56#384×C89C2211yescharacteristic
57#384×C89C2211yescharacteristic
58#382×C89C2211yescharacteristic
59#382×C89C2211yescharacteristic
60C22×#10623494C2311yescharacteristic
61C22×#10623494C2311yescharacteristic
62C22×#10623494C2311yescharacteristic
63C22×#10623494C2311yescharacteristic
64C2×C4⋊Dic89—21no—
65C2×C4⋊Dic89—21no—
66C2×C4⋊Dic89C2311yescharacteristic
67C2×C4⋊Dic89C2311yescharacteristic
68C2×C4⋊Dic89C2311yescharacteristic
69C2×C4⋊Dic89C2311yescharacteristic
70C2×C22⋊Dic89—21no—
71C2×C22⋊Dic89—21no—
72C2×C4×Dic89—21no—
73C2×C4×Dic89—21no—
74#15667945—41no—
75#15667945—41no—
76#15667945—41no—
77#15667945—41no—
78#15667943—41no—
79#15667943—41no—
80#15667943—41no—
81#15667943—41no—
82C4⋊#10623494C2×C414yescomplemented
83C4⋊#10623494C2×C414yescomplemented
84C22⋊#10623494C2×C414yes—
85C22⋊#10623494C2×C414yes—
86#15667923C2×C414yescomplemented
87C4×#10623494C2×C414yescomplemented
88#15667919—21no—
89#15667919—21no—
90#15667919—21no—
91#15667919—21no—
92#15667919—21no—
93#15667919—21no—
94C23×C4×C89—21no—
95C23×C4×C89C2311yescharacteristic
96#117×C89—41no—
97#117×C89—41no—
98#117×C89C2×C414yes—
99#117×C89Q814yes—
100C2×C4⋊C4×C89—21no—
101C2×C4⋊C4×C89—21no—
102C2×C4⋊C4×C89—21no—
103C2×C4⋊C4×C89—21no—
104C2×C4⋊C4×C89—21no—
105C2×C4⋊C4×C89—41no—
106C2×C4⋊C4×C89—41no—
107C2×C4⋊C4×C89D411yescharacteristic
108C2×C4⋊C4×C89D411yescharacteristic
109C2×C4⋊C4×C89C2311yescharacteristic
110C2×C4⋊C4×C89C2311yescharacteristic
111C2×C4⋊C4×C89C2311yescharacteristic
112C2×C4⋊C4×C89C2311yescharacteristic
113C2×C22⋊C4×C89—21no—
114C2×C22⋊C4×C89D411yescharacteristic
115C2×C22⋊C4×C89D411yescharacteristic
116C2×C42×C89—21no—
117C2×C42×C89C2311yescharacteristic
118C2×C42×C89C2311yescharacteristic
119#95×C89—21no—
120#95×C89—21no—
121#95×C89—21no—
122#95×C89—21no—
123C22×Dic89—21no—
124C22×Dic89—21no—
125C22×Dic89—21no—
126C22×Dic89—21no—
127C2×#10623494—21no—
128C2×#10623494—21no—
129C2×#10623494—21no—
130C2×#10623494—21no—
131C2×#10623494—21no—
132C2×#10623494—21no—
133C2×#10623494—21no—
134C2×#10623494—21no—
135C2×#10623494C22×C412yes—
136C2×#10623494C22×C412yes—
137C2×#10623494C22×C412yes—
138C2×#10623494C22×C412yes—
139C4⋊Dic89—21no—
140C4⋊Dic89—21no—
141C4⋊Dic89—21no—
142C4⋊Dic89—21no—
143C4⋊Dic89—21no—
144C4⋊Dic89—21no—
145C4⋊Dic89—21no—
146C4⋊Dic89—21no—
147C4⋊Dic89—81no—
148C4⋊Dic89—81no—
149C22⋊Dic89—81no—
150C22⋊Dic89—81no—
151C4×Dic89—81no—
152C4×Dic89—81no—
153C24×C89C2×D411yescharacteristic
154C22×C4×C89—21no—
155C22×C4×C89—21no—
156C22×C4×C89—21no—
157C22×C4×C89—21no—
158C22×C4×C89—21no—
159C22×C4×C89—21no—
160C22×C4×C89—21no—
161C22×C4×C89—21no—
162C22×C4×C89—42no—
163C22×C4×C89—81no—
164C22×C4×C89—81no—
165C22×C4×C89C22×C412yes—
166C22×C4×C89C2×D411yescharacteristic
167C22×C4×C89C2×D411yescharacteristic
168C22×C4×C89C2×D411yescharacteristic
169C22×C4×C89C2×D411yescharacteristic
170C22×C4×C89C2×D411yescharacteristic
171C22×C4×C89C2×Q812yes—
172C22×C4×C89C2411yescharacteristic
173C4⋊C4×C89—21no—
174C4⋊C4×C89—21no—
175C4⋊C4×C89—21no—
176C4⋊C4×C89—21no—
177C4⋊C4×C89—21no—
178C4⋊C4×C89—21no—
179C4⋊C4×C89—21no—
180C4⋊C4×C89—21no—
181C4⋊C4×C89—42no—
182C4⋊C4×C89—81no—
183C4⋊C4×C89—81no—
184C4⋊C4×C89—81no—
185C4⋊C4×C89—81no—
186C4⋊C4×C89C4⋊C414yes—
187C4⋊C4×C89C4⋊C414yes—
188C22⋊C4×C89—42no—
189C22⋊C4×C89C4⋊C414yes—
190C22⋊C4×C89C4⋊C414yes—
191C42×C89—42no—
192C42×C89C22×C412yes—
193C42×C89C22×C412yes—
194C42×C89C2×Q812yes—
195C42×C89C2×Q812yes—
196C23×C89—21no—
197C23×C89—21no—
198C23×C89—21no—
199C23×C89—21no—
200C23×C89—21no—
201C23×C89—21no—
202C23×C89C2×C4⋊C412yes—
203C23×C89C22×D411yescharacteristic
204C2×C4×C89—21no—
205C2×C4×C89—21no—
206C2×C4×C89—21no—
207C2×C4×C89—21no—
208C2×C4×C89—21no—
209C2×C4×C89—21no—
210C2×C4×C89—21no—
211C2×C4×C89—21no—
212C2×C4×C89—21no—
213C2×C4×C89—21no—
214C2×C4×C89—22no—
215C2×C4×C89—22no—
216C2×C4×C89—22no—
217C2×C4×C89—22no—
218C2×C4×C89—41no—
219C2×C4×C89—41no—
220C2×C4×C89—41no—
221C2×C4×C89—41no—
222C2×C4×C89—41no—
223C2×C4×C89—41no—
224C2×C4×C89—41no—
225C2×C4×C89—41no—
226C2×C4×C89—41no—
227C2×C4×C89—41no—
228C2×C4×C89—41no—
229C2×C4×C89—41no—
230C2×C4×C89—84no—
231C2×C4×C89C2×C4⋊C412yes—
232C2×C4×C89C2×C4⋊C412yes—
233C2×C4×C89C2×C4⋊C412yes—
234C2×C4×C89C2×C4⋊C412yes—
235C2×C4×C89C2×C4⋊C412yes—
236C2×C4×C89C23×C411yescharacteristic
237C2×C4×C89C22×Q811yescharacteristic
238C2×C4×C89H(5,𝔽2)11yescharacteristic
239C2×C4×C89H(5,𝔽2)11yescharacteristic
240C2×C4×C892−1+411yescharacteristic
241C2×C4×C892−1+411yescharacteristic
242C2×Dic89—41no—
243C2×Dic89—41no—
244C2×Dic89—41no—
245C2×Dic89—41no—
246C2×Dic89—41no—
247C2×Dic89—41no—
248C2×Dic89—41no—
249C2×Dic89—41no—
250C2×Dic89—41no—
251C2×Dic89—41no—
252C2×Dic89—41no—
253C2×Dic89—41no—
254#10623494—22no—
255#10623494—22no—
256#10623494—22no—
257#10623494—22no—
258C22×C89—22no—
259C22×C89—22no—
260C22×C89—22no—
261C22×C89—41no—
262C22×C89—41no—
263C22×C89—41no—
264C22×C89—41no—
265C22×C89C22×C4⋊C411yescharacteristic
266C22×C89#53511yescharacteristic
267C22×C89#53611yescharacteristic
268C22×C89#57611yescharacteristic
269C22×C89#57711yescharacteristic
270C22×C89#57711yescharacteristic
271C22×C89#57811yescharacteristic
272C4×C89—22no—
273C4×C89—22no—
274C4×C89—22no—
275C4×C89—22no—
276C4×C89—22no—
277C4×C89—81no—
278C4×C89—81no—
279C4×C89—81no—
280C4×C89—81no—
281C4×C89#52011yescharacteristic
282C4×C89#52011yescharacteristic
283C4×C89#54411yescharacteristic
284C4×C89#54411yescharacteristic
285Dic89—81no—
286Dic89—81no—
287Dic89—81no—
288Dic89—81no—
289#21992—891nomaximal, Sylow
290C2×C89—42no—
291C2×C89#231711yescharacteristic
292C2×C89#291211yescharacteristic
293C2×C89#291311yescharacteristic
294C2×C89#322411yescharacteristic
295C2×C89#322511yescharacteristic
296C2×C89#324111yescharacteristic
297C2×C89#324211yescharacteristic
298C2×#433—891no—
299#2317D8911yescharacteristic
300#2314—891no—
301#1949—891no—
302#1949—891no—
303#1948—891no—
304#1947—891no—
305#1854—891no—
306#1854—891no—
307#1853—891no—
308#1852—891no—
309#1847—891no—
310#1846—891no—
311#1836—891no—
312#1834—891no—
313C89#2199211yescharacteristic, complemented, Sylow
314C2×#117C2×D8911yescharacteristic
315C2×#117C2×D8911yescharacteristic
316C22×C4⋊C4C2×D8911yescharacteristic
317#433—898no—
318C2×#107—891no—
319C2×#107—891no—
320C2×#107—891no—
321C2×#107—891no—
322C2×#106—891no—
323C2×#106—891no—
324C2×#106—891no—
325C2×#106—891no—
326C2×C4⋊C8—891no—
327C2×C4⋊C8—891no—
328C2×C22⋊C8—891no—
329C2×C22⋊C8—891no—
330C2×#97—891no—
331C2×C4×C8—891no—
332#389—21no—
333#389—21no—
334#388—1781no—
335#388—1781no—
336#387—1781no—
337#387—1781no—
338#385—21no—
339#385—21no—
340#384—891no—
341#384C2×D8911yescharacteristic
342#384C2×D8911yescharacteristic
343#382—891no—
344#382C2×D8911yescharacteristic
345#382C2×D8911yescharacteristic
346#380—891no—
347#380—891no—
348C4×C4⋊C4—891no—
349C4×C4⋊C4—891no—
350#340—891no—
351#340—891no—
352#340—891no—
353#340—891no—
354#340—891no—
355#340—891no—
356#340—891no—
357#340—891no—
358C23×C4—21no—
359C23×C4C22×D8911yescharacteristic
360C22×C8—891no—
361C22×C8—891no—
362C22×C8—891no—
363C22×C8—891no—
364#117—41no—
365#117—41no—
366#117Dic17814yes—
367#117C4×D8914yes—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—41no—
374C2×C4⋊C4—41no—
375C2×C4⋊C4—891no—
376C2×C4⋊C4—891no—
377C2×C4⋊C4—891no—
378C2×C4⋊C4—891no—
379C2×C4⋊C4—1781no—
380C2×C4⋊C4—1781no—
381C2×C4⋊C4C22⋊D8911yescharacteristic
382C2×C4⋊C4C22⋊D8911yescharacteristic
383C2×C4⋊C4C22×D8911yescharacteristic
384C2×C4⋊C4C22×D8911yescharacteristic
385C2×C4⋊C4C22×D8911yescharacteristic
386C2×C4⋊C4C22×D8911yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—1781no—
389C2×C22⋊C4—1781no—
390C2×C22⋊C4C22⋊D8911yescharacteristic
391C2×C22⋊C4C22⋊D8911yescharacteristic
392C2×C42—21no—
393C2×C42—1781no—
394C2×C42—1781no—
395C2×C42C22×D8911yescharacteristic
396C2×C42C22×D8911yescharacteristic
397#107—3561no—
398#107—3561no—
399#107—3561no—
400#107—3561no—
401#106—3561no—
402#106—3561no—
403#106—3561no—
404#106—3561no—
405C4⋊C8—894no—
406C4⋊C8—894no—
407C22⋊C8—894no—
408C22⋊C8—894no—
409#97—894no—
410C4×C8—894no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—1781no—
416#95—1781no—
417#95—1781no—
418#95—1781no—
419#95—1781no—
420#95—1781no—
421C24C2×C22⋊D8911yescharacteristic
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—42no—
431C22×C4—81no—
432C22×C4—81no—
433C22×C4—1781no—
434C22×C4—1781no—
435C22×C4—1781no—
436C22×C4—1781no—
437C22×C4C2×C4×D8912yes—
438C22×C4C2×C22⋊D8911yescharacteristic
439C22×C4C2×C22⋊D8911yescharacteristic
440C22×C4C2×C22⋊D8911yescharacteristic
441C22×C4C2×C22⋊D8911yescharacteristic
442C22×C4C2×C22⋊D8911yescharacteristic
443C22×C4C2×Dic17812yes—
444C22×C4C23×D8911yescharacteristic
445C2×C8—892no—
446C2×C8—892no—
447C2×C8—892no—
448C2×C8—892no—
449C2×C8—1781no—
450C2×C8—1781no—
451C2×C8—1781no—
452C2×C8—1781no—
453C2×C8—1781no—
454C2×C8—1781no—
455C2×C8—1781no—
456C2×C8—1781no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—42no—
466C4⋊C4—81no—
467C4⋊C4—81no—
468C4⋊C4—81no—
469C4⋊C4—81no—
470C4⋊C4—1781no—
471C4⋊C4—1781no—
472C4⋊C4—1781no—
473C4⋊C4—1781no—
474C4⋊C4—1781no—
475C4⋊C4—1781no—
476C4⋊C4—1781no—
477C4⋊C4—1781no—
478C4⋊C4—7121no—
479C4⋊C4—7121no—
480C4⋊C4#1308355314yes—
481C4⋊C4#1308355314yes—
482C22⋊C4—42no—
483C22⋊C4—7121no—
484C22⋊C4—7121no—
485C22⋊C4#1308355314yes—
486C22⋊C4#1308355314yes—
487C42—42no—
488C42—7121no—
489C42—7121no—
490C42C2×C4×D8912yes—
491C42C2×C4×D8912yes—
492C42C2×Dic17812yes—
493C42C2×Dic17812yes—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23C2×#1308355312yes—
501C23C22×C22⋊D8911yescharacteristic
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—84no—
529C2×C4—3561no—
530C2×C4—3561no—
531C2×C4—3561no—
532C2×C4—3561no—
533C2×C4—3561no—
534C2×C4—3561no—
535C2×C4—3561no—
536C2×C4—3561no—
537C2×C4—3561no—
538C2×C4—3561no—
539C2×C4—3561no—
540C2×C4—3561no—
541C2×C4C2×#1308355312yes—
542C2×C4C2×#1308355312yes—
543C2×C4C2×#1308355312yes—
544C2×C4C2×#1308355312yes—
545C2×C4C2×#1308355312yes—
546C2×C4C22×C4×D8911yescharacteristic
547C2×C4C22×Dic17811yescharacteristic
548C2×C4#1566805711yescharacteristic
549C2×C4#1566805711yescharacteristic
550C2×C4#1566806011yescharacteristic
551C2×C4#1566806011yescharacteristic
552C8—1782no—
553C8—1782no—
554C8—1782no—
555C8—1782no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22C22×#1308355311yescharacteristic
564C22#1915216511yescharacteristic
565C22#1915217211yescharacteristic
566C22#1915240111yescharacteristic
567C22#1915240611yescharacteristic
568C22#1915240911yescharacteristic
569C22#1915241311yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—22no—
574C4—22no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4—7121no—
580C4—7121no—
581C4—7121no—
582C4—7121no—
583C4#1915207911yescharacteristic
584C4#1915207911yescharacteristic
585C4#1915222911yescharacteristic
586C4#1915222911yescharacteristic
587C2—42no—
588C2#2602287611yescharacteristic
589C2#2602884511yescharacteristic
590C2#2602885011yescharacteristic
591C2#2603134611yescharacteristic
592C2#2603136111yescharacteristic
593C2#2603150511yescharacteristic
594C2#2603152011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D89
commutatorC2×C4×C89C23×C4
FrattiniC22×C4C23×D89
FittingC89×#2317C2
socleC23×C89C22×D4
prime radicalC24×C89C2×D4
cosocleC22×C4×C89C24
hypercenter#2317D89
hypocenterC89#21992
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2317

Complements

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

NH ≅ G/Ntype
3. #26021018C2semidirect
4. #26021018C2semidirect
5. #26021013C2semidirect
6. #26021008C2semidirect
11. #26020418C2semidirect
12. #26020414C2semidirect
13. #26020385C2semidirect
14. #26020379C2semidirect
16. #19151659C4semidirect
82. C4⋊#10623494C2×C4semidirect
83. C4⋊#10623494C2×C4semidirect
86. #15667923C2×C4semidirect
87. C4×#10623494C2×C4semidirect
313. C89#21992semidirect

Maximal subgroups

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

subgroupindex
C2×#191516592
#260228612
#260210182
#260210132
#260210082
#260204512
#260204452
#260204402
#260204182
#260204142
#260203852
#260203792
C89×#23172
#2199289