Finite Group Databasebeta

← #36576519

Subgroups — #36576519

Order 22784.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26030040C211yesmaximal, characteristic
2#26029195C211yesmaximal, characteristic, complemented
3#26021232C211yesmaximal, characteristic, complemented
4#26021025C211yesmaximal, characteristic, complemented
5#26021002C211yesmaximal, characteristic, complemented
6#26020997C211yesmaximal, characteristic, complemented
7#26020848C211yesmaximal, characteristic, complemented
8#26020848C211yesmaximal, characteristic, complemented
9#26020527C211yesmaximal, characteristic
10#26020527C211yesmaximal, characteristic
11#26020111C211yesmaximal, characteristic, complemented
12#26020094C211yesmaximal, characteristic
13#26020087C211yesmaximal, characteristic
14#26020062C211yesmaximal, characteristic
15C89×#2906C211yesmaximal, characteristic
16#19152155C2211yescharacteristic
17#19151905C411yescharacteristic, complemented
18#19151905C411yescharacteristic, complemented
19#19151898C411yescharacteristic, complemented
20#19151898C411yescharacteristic, complemented
21#19151893C411yescharacteristic, complemented
22#19151888C411yescharacteristic, complemented
23#19151883C411yescharacteristic, complemented
24#19151878C411yescharacteristic, complemented
25#19151727—21no—
26#19151727—21no—
27#19151725—21no—
28#19151722—21no—
29C2×#15667947C2211yescharacteristic
30C2×#15667947C2211yescharacteristic
31#19151634C2211yescharacteristic
32#19151634C2211yescharacteristic
33#19151624C2211yescharacteristic
34#19151624C2211yescharacteristic
35C2×C4⋊#10623494C2211yescharacteristic
36C2×#15667939C2211yescharacteristic
37C2×#15667939C2211yescharacteristic
38#19151594C2211yescharacteristic
39#19151594C2211yescharacteristic
40#19151553C2211yescharacteristic
41#19151553C2211yescharacteristic
42C4×#13083558C2211yescharacteristic
43C2×#15667922C2211yescharacteristic
44C2×C8×Dic89C2211yescharacteristic
45#19151444C2211yescharacteristic
46#19151362C2211yescharacteristic
47#19151362C2211yescharacteristic
48#19151359C2211yescharacteristic
49#19151359C2211yescharacteristic
50#19151359C2211yescharacteristic
51#19151359C2211yescharacteristic
52#19151357C2211yescharacteristic
53#19151357C2211yescharacteristic
54#19151352C2211yescharacteristic
55#19151352C2211yescharacteristic
56C2×#131×C89C2211yescharacteristic
57C2×#131×C89C2211yescharacteristic
58C4×#41×C89C2211yescharacteristic
59#424×C89—21no—
60#424×C89—21no—
61#424×C89C2211yescharacteristic
62#424×C89C2211yescharacteristic
63#423×C89—21no—
64#423×C89C2211yescharacteristic
65C2×C4⋊C8×C89—21no—
66C2×C4⋊C8×C89C2211yescharacteristic
67C2×#13083558C2311yescharacteristic
68C2×#13083558C2311yescharacteristic
69C22×#10623494C2311yescharacteristic
70C22×#10623494C2311yescharacteristic
71#15668012C2×C411yescharacteristic
72#15668012C2×C411yescharacteristic
73#15668004C2×C411yescharacteristic
74#15668004C2×C411yescharacteristic
75#15667991—21no—
76#15667991—21no—
77C4×Dic178—21no—
78C4×Dic178—21no—
79#15667971C2311yescharacteristic
80#15667971C2311yescharacteristic
81C2×C4×Dic89C2311yescharacteristic
82C2×C4×Dic89C2311yescharacteristic
83#15667947—41no—
84#15667947—41no—
85#15667945C2×C411yescharacteristic
86#15667945C2×C411yescharacteristic
87#15667945C2×C411yescharacteristic
88#15667945C2×C411yescharacteristic
89#15667943C2×C411yescharacteristic
90#15667943C2×C411yescharacteristic
91#15667943C2×C411yescharacteristic
92#15667943C2×C411yescharacteristic
93C4⋊#10623494C2×C411yescharacteristic
94C4⋊#10623494C2×C411yescharacteristic
95C4⋊#10623494C2×C411yescharacteristic
96C4⋊#10623494C2×C411yescharacteristic
97#15667941—21no—
98#15667941—21no—
99#15667941—21no—
100#15667941—21no—
101#15667939—22no—
102#15667939Q814yescomplemented
103#15667936C2×C411yescharacteristic
104#15667936C2×C411yescharacteristic
105#15667936C2×C411yescharacteristic
106#15667936C2×C411yescharacteristic
107#15667933C2×C411yescharacteristic
108#15667933C2×C411yescharacteristic
109#15667933C2×C411yescharacteristic
110#15667933C2×C411yescharacteristic
111#15667923—21no—
112#15667922—21no—
113#15667922—21no—
114#15667922—41no—
115C4×#10623494—21no—
116C8×Dic89—21no—
117C8×Dic89—21no—
118C8×Dic89—41no—
119#15667919—21no—
120#15667919—21no—
121C2×#41×C89C2311yescharacteristic
122#131×C89—22no—
123#131×C89—22no—
124#131×C89—41no—
125#131×C89—41no—
126C2×M16×C89—21no—
127C2×M16×C89—21no—
128C2×M16×C89C2311yescharacteristic
129C2×M16×C89C2311yescharacteristic
130C22×C8×C89—21no—
131C22×C8×C89—21no—
132C22×C8×C89C2311yescharacteristic
133C22×C8×C89C2311yescharacteristic
134C4×Q8×C89C2×C411yescharacteristic
135C4×Q8×C89C2×C411yescharacteristic
136C4×D4×C89—21no—
137C4×D4×C89—21no—
138C4×D4×C89C2×C411yescharacteristic
139C4×D4×C89C2×C411yescharacteristic
140#117×C89—21no—
141#117×C89C2311yescharacteristic
142C2×C42×C89—21no—
143C2×C42×C89C2311yescharacteristic
144C4⋊C8×C89—21no—
145C4⋊C8×C89—21no—
146C4⋊C8×C89—21no—
147C4⋊C8×C89—21no—
148C4⋊C8×C89—21no—
149C4⋊C8×C89—21no—
150C4⋊C8×C89D411yescharacteristic
151C4⋊C8×C89D411yescharacteristic
152C4⋊C8×C89D411yescharacteristic
153C4⋊C8×C89D411yescharacteristic
154C2×Dic178—21no—
155C2×Dic178—21no—
156C22×Dic89—21no—
157C22×Dic89—21no—
158#13083558—21no—
159#13083558—21no—
160#13083558—21no—
161#13083558C2×Q812yes—
162C2×#10623494—21no—
163C2×#10623494—21no—
164C2×#10623494—21no—
165C2×#10623494—21no—
166C2×#10623494—21no—
167C2×#10623494—21no—
168C2×#10623494C22×C411yescharacteristic
169C2×#10623494C22×C411yescharacteristic
170C2×#10623494C22×C411yescharacteristic
171C2×#10623494C22×C411yescharacteristic
172C4⋊Dic89—21no—
173C4⋊Dic89—21no—
174C4⋊Dic89C22×C411yescharacteristic
175C4⋊Dic89C22×C411yescharacteristic
176C4⋊Dic89C22×C411yescharacteristic
177C4⋊Dic89C22×C411yescharacteristic
178#13083553—21no—
179#13083553—21no—
180#13083553—21no—
181#13083553—21no—
182C22⋊Dic89—21no—
183C22⋊Dic89—21no—
184C4×Dic89—21no—
185C4×Dic89—21no—
186C4×Dic89—21no—
187C4×Dic89—21no—
188C4×Dic89—21no—
189C4×Dic89C2×Q812yes—
190#41×C89—21no—
191#41×C89—21no—
192#41×C89C2×Q812yes—
193#41×C89#4112yes—
194C2×Q8×C89C22×C411yescharacteristic
195C2×D4×C89—21no—
196C2×D4×C89C22×C411yescharacteristic
197C22×C4×C89—21no—
198C22×C4×C89—21no—
199C22×C4×C89—21no—
200C22×C4×C89#4111yescharacteristic
201C22×C4×C89#4111yescharacteristic
202C22×C4×C89C2411yescharacteristic
203M16×C89—21no—
204M16×C89—21no—
205M16×C89—21no—
206M16×C89—21no—
207M16×C89—42no—
208M16×C89—42no—
209C2×C8×C89—21no—
210C2×C8×C89—21no—
211C2×C8×C89—21no—
212C2×C8×C89—21no—
213C2×C8×C89—21no—
214C2×C8×C89—21no—
215C2×C8×C89—42no—
216C2×C8×C89—42no—
217C2×C8×C89C2×D411yescharacteristic
218C2×C8×C89C2×D411yescharacteristic
219C2×C8×C89C2×D411yescharacteristic
220C2×C8×C89C2×D411yescharacteristic
221C4⋊C4×C89—21no—
222C4⋊C4×C89—21no—
223C4⋊C4×C89C22×C411yescharacteristic
224C4⋊C4×C89C22×C411yescharacteristic
225C22⋊C4×C89—21no—
226C22⋊C4×C89—21no—
227C22⋊C4×C89—21no—
228C42×C89—21no—
229C42×C89—21no—
230C42×C89—21no—
231C42×C89C22×C411yescharacteristic
232C42×C89C22×C411yescharacteristic
233C42×C89C2×D411yescharacteristic
234C42×C89C2×D411yescharacteristic
235C23×C89—21no—
236C23×C89C2×#4111yescharacteristic
237Q8×C89—21no—
238Q8×C89C4×Q812yes—
239D4×C89—22no—
240D4×C89—22no—
241D4×C89—21no—
242D4×C89C4×Q812yes—
243C2×C4×C89—21no—
244C2×C4×C89—22no—
245C2×C4×C89—22no—
246C2×C4×C89—21no—
247C2×C4×C89—21no—
248C2×C4×C89—41no—
249C2×C4×C89—41no—
250C2×C4×C89—42no—
251C2×C4×C89—81no—
252C2×C4×C89C4×D411yescharacteristic
253C2×C4×C89C4×D411yescharacteristic
254C2×C4×C89C4×D411yescharacteristic
255C2×C4×C89C4×D411yescharacteristic
256C2×C4×C89C23×C411yescharacteristic
257C2×C4×C89C22×D411yescharacteristic
258C2×C4×C89C22×Q811yescharacteristic
259C2×C4×C89C2×#4111yescharacteristic
260C2×C4×C89H(5,𝔽2)11yescharacteristic
261C2×C4×C892−1+411yescharacteristic
262C2×Dic89—21no—
263C2×Dic89—21no—
264C2×Dic89—21no—
265C2×Dic89—21no—
266C2×Dic89—22no—
267C2×Dic89—41no—
268C2×Dic89—41no—
269C2×Dic89—41no—
270C2×Dic89—41no—
271C2×Dic89—41no—
272Dic178—42no—
273Dic178—81no—
274C8×C89—21no—
275C8×C89—21no—
276C8×C89—21no—
277C8×C89—21no—
278C8×C89—41no—
279C8×C89—41no—
280#10623494—21no—
281#10623494—21no—
282#10623494—21no—
283#10623494—21no—
284#10623494—22no—
285#10623494—41no—
286C22×C89—21no—
287C22×C89—21no—
288C22×C89—22no—
289C22×C89—41no—
290C22×C89—41no—
291C22×C89C2×C4×D411yescharacteristic
292C22×C89#55211yescharacteristic
293C22×C89#55411yescharacteristic
294C4×C89—22no—
295C4×C89—21no—
296C4×C89—21no—
297C4×C89—21no—
298C4×C89—21no—
299C4×C89—41no—
300C4×C89—41no—
301C4×C89C2×C4×Q811yescharacteristic
302C4×C89#52011yescharacteristic
303C4×C89#54611yescharacteristic
304C4×C89D4×Q811yescharacteristic
305Dic89—42no—
306Dic89—41no—
307Dic89—41no—
308Dic89—41no—
309Dic89—41no—
310Dic89—81no—
311#22984—891nomaximal, Sylow
312C2×C89—21no—
313C2×C89—21no—
314C2×C89—42no—
315C2×C89#236011yescharacteristic
316C2×C89#295511yescharacteristic
317C2×C89#295711yescharacteristic
318#3076—891no—
319#2962—891no—
320#2906D8911yescharacteristic
321#1995—891no—
322#1950—891no—
323#1946—891no—
324#1945—891no—
325#1922—891no—
326#1922—891no—
327#1866—891no—
328#1866—891no—
329#1768—891no—
330#1765—891no—
331#1764—891no—
332#1759—891no—
333C89#2298411yescharacteristic, complemented, Sylow
334C2×#131C2×D8911yescharacteristic
335C2×#131C2×D8911yescharacteristic
336#533—891no—
337C4×#41C2×D8911yescharacteristic
338#479—891no—
339#479—891no—
340#478—891no—
341#478—891no—
342#477—891no—
343#476—891no—
344#475—891no—
345#474—891no—
346#446—1781no—
347#446—1781no—
348#446—1781no—
349C8×Q8—1781no—
350C2×#108—891no—
351C2×#108—891no—
352#427—891no—
353#427—891no—
354#424—21no—
355#424—21no—
356#424—891no—
357#424—891no—
358#424C2×D8911yescharacteristic
359#424C2×D8911yescharacteristic
360#423—21no—
361#423C2×D8911yescharacteristic
362C2×C4⋊C8—21no—
363C2×C4⋊C8—891no—
364C2×C4⋊C8C2×D8911yescharacteristic
365C2×#104—891no—
366C2×#104—891no—
367#416—891no—
368#416—891no—
369#405—891no—
370#405—891no—
371C4×M16—891no—
372C2×#97—891no—
373C2×C4×C8—891no—
374#376—891no—
375#341—891no—
376#341—891no—
377#339—891no—
378#339—891no—
379#339—891no—
380#339—891no—
381#339—891no—
382#339—891no—
383#336—891no—
384#336—891no—
385C2×#41C22×D8911yescharacteristic
386#131—22no—
387#131—22no—
388#131—41no—
389#131—41no—
390C2×M16—21no—
391C2×M16—21no—
392C2×M16—891no—
393C2×M16—891no—
394C2×M16C22×D8911yescharacteristic
395C2×M16C22×D8911yescharacteristic
396C22×C8—21no—
397C22×C8—21no—
398C22×C8—891no—
399C22×C8—891no—
400C22×C8C22×D8911yescharacteristic
401C22×C8C22×D8911yescharacteristic
402C4⋊Q8—891no—
403C4⋊Q8—891no—
404#125—891no—
405#125—891no—
406C22⋊Q8—1781no—
407C22⋊Q8—1781no—
408C4×Q8—1781no—
409C4×Q8—1781no—
410C4×Q8C4×D8911yescharacteristic
411C4×Q8C4×D8911yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4C4×D8911yescharacteristic
415C4×D4C4×D8911yescharacteristic
416#117—21no—
417#117—891no—
418#117—891no—
419#117C22×D8911yescharacteristic
420C2×C42—21no—
421C2×C42—891no—
422C2×C42—891no—
423C2×C42C22×D8911yescharacteristic
424#108—3561no—
425#108—3561no—
426#107—891no—
427#107—891no—
428#107—891no—
429#107—891no—
430#106—891no—
431#106—891no—
432#106—891no—
433#106—891no—
434C4⋊C8—21no—
435C4⋊C8—21no—
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—21no—
439C4⋊C8—21no—
440C4⋊C8—891no—
441C4⋊C8—891no—
442C4⋊C8—891no—
443C4⋊C8—891no—
444C4⋊C8—1781no—
445C4⋊C8—1781no—
446C4⋊C8—1781no—
447C4⋊C8—1781no—
448C4⋊C8C22⋊D8911yescharacteristic
449C4⋊C8C22⋊D8911yescharacteristic
450C4⋊C8C22⋊D8911yescharacteristic
451C4⋊C8C22⋊D8911yescharacteristic
452#104—894no—
453#104—1782no—
454#103—891no—
455#103—891no—
456#103—891no—
457#103—891no—
458#102—891no—
459#102—891no—
460#102—891no—
461#102—891no—
462#97—3561no—
463#97—1781no—
464#97—1781no—
465#97—1781no—
466C4×C8—3561no—
467C4×C8—1781no—
468C4×C8—1781no—
469C4×C8—1781no—
470#95—1781no—
471#95—1781no—
472#41—21no—
473#41—21no—
474#41Q8×D8912yes—
475#41#1308357312yes—
476C2×Q8—1781no—
477C2×Q8—1781no—
478C2×Q8C2×C4×D8911yescharacteristic
479C2×D4—21no—
480C2×D4C2×C4×D8911yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—1781no—
485C22×C4—1781no—
486C22×C4#1308357411yescharacteristic
487C22×C4#1308357411yescharacteristic
488C22×C4C23×D8911yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—42no—
494M16—42no—
495M16—892no—
496M16—1781no—
497M16—1781no—
498M16—1781no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—42no—
506C2×C8—42no—
507C2×C8—891no—
508C2×C8—891no—
509C2×C8—891no—
510C2×C8—891no—
511C2×C8—1781no—
512C2×C8—1781no—
513C2×C8—1781no—
514C2×C8—1781no—
515C2×C8—1781no—
516C2×C8—1781no—
517C2×C8C2×C22⋊D8911yescharacteristic
518C2×C8C2×C22⋊D8911yescharacteristic
519C2×C8C2×C22⋊D8911yescharacteristic
520C2×C8C2×C22⋊D8911yescharacteristic
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—891no—
524C4⋊C4—891no—
525C4⋊C4—891no—
526C4⋊C4—891no—
527C4⋊C4—1781no—
528C4⋊C4—1781no—
529C4⋊C4—1781no—
530C4⋊C4—1781no—
531C4⋊C4—1781no—
532C4⋊C4—1781no—
533C4⋊C4C2×C4×D8911yescharacteristic
534C4⋊C4C2×C4×D8911yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—1781no—
539C22⋊C4—1781no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—892no—
544C42—1781no—
545C42—1781no—
546C42—1781no—
547C42—1781no—
548C42—1781no—
549C42C2×C4×D8911yescharacteristic
550C42C2×C4×D8911yescharacteristic
551C42C2×C22⋊D8911yescharacteristic
552C42C2×C22⋊D8911yescharacteristic
553C23—21no—
554C23C2×#1308357411yescharacteristic
555Q8—21no—
556Q8—3562no—
557Q8—7121no—
558Q8#1566797712yes—
559D4—22no—
560D4—22no—
561D4—21no—
562D4#1566797712yes—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—81no—
572C2×C4—3561no—
573C2×C4—3561no—
574C2×C4—3561no—
575C2×C4—3561no—
576C2×C4—3561no—
577C2×C4—1782no—
578C2×C4—1781no—
579C2×C4—1781no—
580C2×C4—1781no—
581C2×C4—1781no—
582C2×C4C4×C22⋊D8911yescharacteristic
583C2×C4C4×C22⋊D8911yescharacteristic
584C2×C4C4×C22⋊D8911yescharacteristic
585C2×C4C4×C22⋊D8911yescharacteristic
586C2×C4C22×C4×D8911yescharacteristic
587C2×C4C22×C22⋊D8911yescharacteristic
588C2×C4C2×Q8×D8911yescharacteristic
589C2×C4C2×#1308357311yescharacteristic
590C2×C4#1566805711yescharacteristic
591C2×C4#1566806011yescharacteristic
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—3561no—
599C8—1782no—
600C8—1781no—
601C8—1781no—
602C8—1781no—
603C8—1781no—
604C22—21no—
605C22—21no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22C2×C4×C22⋊D8911yescharacteristic
610C22#1915228311yescharacteristic
611C22#1915230311yescharacteristic
612C4—22no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—41no—
618C4—41no—
619C4—3562no—
620C4—3561no—
621C4—3561no—
622C4—3561no—
623C4—3561no—
624C4—7121no—
625C4C2×#1566797711yescharacteristic
626C4#1915207911yescharacteristic
627C4#1915224211yescharacteristic
628C4Q8×C22⋊D8911yescharacteristic
629C2—21no—
630C2—21no—
631C2—42no—
632C2#2602325711yescharacteristic
633C2#2602915311yescharacteristic
634C2#2602916711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D89
commutatorC2×C4×C89C23×C4
FrattiniC22×C4C23×D89
FittingC89×#2906C2
socleC22×C89C2×C4×D4
prime radicalC2×#41×C89C23
cosocleC22×C4×C89C24
hypercenter#2906D89
hypocenterC89#22984
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #26029195C2semidirect
3. #26021232C2semidirect
4. #26021025C2semidirect
5. #26021002C2semidirect
6. #26020997C2semidirect
7. #26020848C2semidirect
8. #26020848C2semidirect
11. #26020111C2semidirect
17. #19151905C4semidirect
18. #19151905C4semidirect
19. #19151898C4semidirect
20. #19151898C4semidirect
21. #19151893C4semidirect
22. #19151888C4semidirect
23. #19151883C4semidirect
24. #19151878C4semidirect
102. #15667939Q8semidirect
333. C89#22984semidirect

Maximal subgroups

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

subgroupindex
#260300402
#260291952
#260212322
#260210252
#260210022
#260209972
#260208482
#260205272
#260201112
#260200942
#260200872
#260200622
C89×#29062
#2298489