Finite Group Databasebeta

← #36526014

Subgroups — #36526014

Order 22784.

676 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26029378C211yesmaximal, characteristic, complemented
2#26029287C211yesmaximal, characteristic, complemented
3C4×#15668038C211yesmaximal, characteristic
4#26019151C211yesmaximal, characteristic, complemented
5#26019145C211yesmaximal, characteristic, complemented
6#26019119C211yesmaximal, characteristic, complemented
7#26019106C211yesmaximal, characteristic, complemented
8#26019085C211yesmaximal, characteristic, complemented
9#26019084C211yesmaximal, characteristic, complemented
10#26019073C211yesmaximal, characteristic, complemented
11#26019044C211yesmaximal, characteristic, complemented
12#26019017C211yesmaximal, characteristic, complemented
13#26018687C211yesmaximal, characteristic, complemented
14#26018547C211yesmaximal, characteristic, complemented
15C89×#1486C211yesmaximal, characteristic, complemented
16C2×#15668038C411yescharacteristic
17C4×#13083574C2211yescharacteristic
18#19151725C2211yescharacteristic, complemented
19#19151725C2211yescharacteristic, complemented
20#19151708C411yescharacteristic
21#19151708C411yescharacteristic
22#19151698C411yescharacteristic
23#19151698C411yescharacteristic
24C4×#13083562C2211yescharacteristic
25C4×#13083562C2211yescharacteristic
26C4×#13083559C2211yescharacteristic
27C4×#13083559C2211yescharacteristic
28#19151676C2211yescharacteristic
29#19151676C2211yescharacteristic
30#19151670—21no—
31#19151670—21no—
32#19151667—21no—
33#19151667—21no—
34D4×#10623494C2211yescharacteristic
35D4×#10623494C2211yescharacteristic
36#19151663C2211yescharacteristic, complemented
37#19151663C2211yescharacteristic, complemented
38#19151655C2211yescharacteristic
39#19151654—21no—
40#19151651C2211yescharacteristic
41#19151638C411yescharacteristic
42C4⋊C8×D89—21no—
43#19151603C411yescharacteristic
44#19151597C411yescharacteristic
45#19151562—21no—
46C2×C22⋊#10623494—21no—
47C4×#13083558C2211yescharacteristic
48#19151350C2211yescharacteristic, complemented
49#19151350C2211yescharacteristic, complemented
50#19151348C2211yescharacteristic, complemented
51#19151348C2211yescharacteristic, complemented
52#19151330C2211yescharacteristic, complemented
53#19151330C2211yescharacteristic, complemented
54#19151327C2211yescharacteristic, complemented
55#19151327C2211yescharacteristic, complemented
56#19151320C2211yescharacteristic, complemented
57#19151320C2211yescharacteristic, complemented
58#19151319C2211yescharacteristic, complemented
59C8×#10623494C2211yescharacteristic, complemented
60C2×C4×D4×C89C2211yescharacteristic
61#431×C89C2211yescharacteristic
62#423×C89C2211yescharacteristic
63D4⋊C8×C89C2211yescharacteristic
64D4⋊C8×C89C2211yescharacteristic
65D4⋊C8×C89C2211yescharacteristic
66D4⋊C8×C89C2211yescharacteristic
67C2×#13083574C2×C411yescharacteristic
68#15668038—24no—
69C2×#13083562C2×C411yescharacteristic
70C2×#13083562C2×C411yescharacteristic
71C2×#13083559C2×C411yescharacteristic
72C2×#13083559C2×C411yescharacteristic
73C2×#13083558—21no—
74C2×#13083558—21no—
75C2×#13083558C2×C411yescharacteristic
76C2×#13083558C2×C411yescharacteristic
77C22×#10623494—21no—
78C22×#10623494—21no—
79C2×C8×D89—21no—
80C2×C8×D89—21no—
81C4×Dic178C2×C411yescharacteristic
82C4×Dic178C2311yescharacteristic
83C4×D356C2×C411yescharacteristic
84C4×D356C2311yescharacteristic
85C4×C22⋊D89—21no—
86C4×C22⋊D89—21no—
87#15667971C2×C411yescharacteristic
88#15667969—21no—
89C42×D89—21no—
90#15667945C2×C411yescharacteristic
91#15667945C2×C411yescharacteristic
92#15667943C2×C411yescharacteristic
93#15667943C2×C411yescharacteristic
94C4⋊#10623494D411yescharacteristic
95C4⋊#10623494D411yescharacteristic
96C4⋊#10623494C2311yescharacteristic
97C4⋊#10623494C2311yescharacteristic
98#15667941—21no—
99#15667941—21no—
100#15667935C2×C411yescharacteristic
101#15667935C2×C411yescharacteristic
102#15667933C2×C411yescharacteristic
103#15667933C2×C411yescharacteristic
104#15667933C2×C411yescharacteristic
105#15667933C2×C411yescharacteristic
106#15667932C2×C411yescharacteristic
107#15667932C2×C411yescharacteristic
108C22⋊#10623494—21no—
109C22⋊#10623494—21no—
110C22⋊#10623494—21no—
111C22⋊#10623494—21no—
112C22⋊#10623494—21no—
113C22⋊#10623494D411yescharacteristic
114C22⋊#10623494D411yescharacteristic
115#15667924—21no—
116#15667924—21no—
117#15667923—21no—
118#15667923C2×C411yescharacteristic
119#15667923C2×C411yescharacteristic
120#15667922—21no—
121#15667922—21no—
122C4×#10623494C2311yescharacteristic
123C4×#10623494C2311yescharacteristic
124C4×#10623494C2311yescharacteristic
125C4×#10623494C2311yescharacteristic
126C22×D4×C89C2×C411yescharacteristic
127C23×C4×C89—21no—
128C2×M16×C89—21no—
129C4×D4×C89—21no—
130C4×D4×C89—21no—
131C4×D4×C89C2×C411yescharacteristic
132C4×D4×C89C2×C411yescharacteristic
133C4×D4×C89C2311yescharacteristic
134C4×D4×C89C2311yescharacteristic
135C2×C4⋊C4×C89C2×C411yescharacteristic
136C2×C22⋊C4×C89—21no—
137C2×C42×C89C2311yescharacteristic
138C4⋊C8×C89—21no—
139C4⋊C8×C89—21no—
140C4⋊C8×C89C2311yescharacteristic
141C4⋊C8×C89C2311yescharacteristic
142C22⋊C8×C89—21no—
143C4×C8×C89C2311yescharacteristic
144C4×C8×C89C2311yescharacteristic
145#13083574—22no—
146#13083574—41no—
147C2×Dic178C22×C411yescharacteristic
148C2×D356C22×C411yescharacteristic
149C2×C22⋊D89—21no—
150C2×C4×D89—21no—
151C2×C4×D89—21no—
152C2×C4×D89—21no—
153#13083562—22no—
154#13083562—22no—
155#13083559—22no—
156#13083559M1614yescomplemented
157#13083558—22no—
158#13083558—41no—
159#13083558—81no—
160#13083558—81no—
161C2×#10623494—21no—
162C2×#10623494—21no—
163C2×#10623494—81no—
164C2×#10623494—81no—
165C2×#10623494C22×C411yescharacteristic
166C2×#10623494C22×C411yescharacteristic
167C2×#10623494C22×C411yescharacteristic
168C2×#10623494C22×C411yescharacteristic
169C2×#10623494C2×D411yescharacteristic
170C2×#10623494C2×D411yescharacteristic
171C2×#10623494C2×D411yescharacteristic
172C2×#10623494C2×D411yescharacteristic
173C8×D89—81no—
174C8×D89—81no—
175C4⋊Dic89C22×C411yescharacteristic
176C4⋊Dic89C22×C411yescharacteristic
177#13083553—21no—
178#13083553—21no—
179C22⋊Dic89—21no—
180#13083551—21no—
181#13083551—21no—
182C4×Dic89—21no—
183C4×Dic89—21no—
184C4×Dic89—21no—
185C24×C89—21no—
186C2×D4×C89—22no—
187C2×D4×C89—21no—
188C2×D4×C89—41no—
189C2×D4×C89C22×C411yescharacteristic
190C2×D4×C89C22×C411yescharacteristic
191C22×C4×C89—21no—
192C22×C4×C89—21no—
193C22×C4×C89—21no—
194C22×C4×C89—21no—
195C22×C4×C89—21no—
196C22×C4×C89—81no—
197C22×C4×C89—81no—
198C22×C4×C89C22×C411yescharacteristic
199C22×C4×C89C2×D411yescharacteristic
200C22×C4×C89#4111yescharacteristic
201M16×C89—81no—
202C2×C8×C89—21no—
203C2×C8×C89—21no—
204C2×C8×C89—21no—
205C2×C8×C89—21no—
206C4⋊C4×C89—21no—
207C4⋊C4×C89C22×C411yescharacteristic
208C4⋊C4×C89C22×C411yescharacteristic
209C22⋊C4×C89—21no—
210C22⋊C4×C89—21no—
211C22⋊C4×C89—21no—
212C22⋊C4×C89—21no—
213C42×C89C22×C411yescharacteristic
214C42×C89C2×D411yescharacteristic
215C42×C89#4111yescharacteristic
216C42×C89C2411yescharacteristic
217C23×C89—21no—
218C23×C89—21no—
219C23×C89—42no—
220C23×C89—42no—
221C23×C89—81no—
222C23×C89C4×D411yescharacteristic
223C22×D89—21no—
224D4×C89—21no—
225D4×C89—21no—
226D4×C89—21no—
227D4×C89—42no—
228D4×C89C2×M1612yes—
229C2×C4×C89—21no—
230C2×C4×C89—21no—
231C2×C4×C89—21no—
232C2×C4×C89—21no—
233C2×C4×C89—21no—
234C2×C4×C89—21no—
235C2×C4×C89—41no—
236C2×C4×C89—41no—
237C2×C4×C89—41no—
238C2×C4×C89—41no—
239C2×C4×C89—41no—
240C2×C4×C89—81no—
241C2×C4×C89—81no—
242C2×C4×C89—81no—
243C2×C4×C89C4×D411yescharacteristic
244C2×C4×C89C4×D411yescharacteristic
245C2×C4×C89C4×D411yescharacteristic
246C2×C4×C89C23×C411yescharacteristic
247C2×C4×C89C22×D411yescharacteristic
248C2×C4×C89C2×#4111yescharacteristic
249C22⋊D89—42no—
250C2×Dic89—21no—
251C2×Dic89—21no—
252C2×Dic89—21no—
253D356—21no—
254D356C2×M1612yes—
255C4×D89—42no—
256C4×D89—42no—
257C4×D89—41no—
258C4×D89—41no—
259Dic178—21no—
260Dic178—21no—
261C8×C89—41no—
262C8×C89—41no—
263C8×C89—41no—
264C8×C89—41no—
265#10623494—21no—
266#10623494—21no—
267#10623494—21no—
268#10623494—21no—
269#10623494—21no—
270#10623494—21no—
271#10623494—21no—
272#10623494—41no—
273#10623494—41no—
274#10623494C2×M1612yes—
275C22×C89—21no—
276C22×C89—22no—
277C22×C89—21no—
278C22×C89—21no—
279C22×C89—41no—
280C22×C89—41no—
281C22×C89—41no—
282C22×C89—41no—
283C22×C89—41no—
284C22×C89—84no—
285C22×C89C2×C4×D411yescharacteristic
286C2×D89—22no—
287C2×D89—41no—
288C2×D89—41no—
289C4×C89—21no—
290C4×C89—21no—
291C4×C89—21no—
292C4×C89—21no—
293C4×C89—41no—
294C4×C89—41no—
295C4×C89C22×M1611yescharacteristic
296C4×C89#56811yescharacteristic
297C4×C89#57611yescharacteristic
298C4×C89#57711yescharacteristic
299Dic89—41no—
300Dic89—41no—
301Dic89—41no—
302#18050—891nomaximal, Sylow
303C2×C89—41no—
304C2×C89—42no—
305C2×C89—81no—
306C2×C89D4×M1611yescharacteristic
307C2×C89#294611yescharacteristic
308C2×C89#295511yescharacteristic
309D89—42no—
310#2990—891no—
311#2974—891no—
312C4×AGL(1,ℤ/8)—891no—
313#1592—891no—
314#1590—891no—
315#1586—891no—
316#1585—891no—
317#1582—891no—
318#1581—891no—
319#1580—891no—
320C8×D8—891no—
321#1569—891no—
322#1488—891no—
323#1486D8911yescharacteristic, complemented
324#1453—891no—
325C89#1805011yescharacteristic, complemented, Sylow
326C2×AGL(1,ℤ/8)—891no—
327C4×#41—891no—
328C2×C4×D4C2×D8911yescharacteristic
329#446—891no—
330#446—891no—
331#442—891no—
332#442—891no—
333#440—891no—
334#440—891no—
335C4×SD16—891no—
336C4×SD16—891no—
337C4×D8—891no—
338C4×D8—891no—
339#436—891no—
340#436—891no—
341#435—1781no—
342#435—1781no—
343#435—1781no—
344#435—1781no—
345C8×D4—891no—
346C8×D4—891no—
347C8×D4—891no—
348C8×D4—891no—
349#432—891no—
350#432—1781no—
351#431—891no—
352#431C2×D8911yescharacteristic
353#428—891no—
354#423C2×D8911yescharacteristic
355C2×C4⋊C8—1781no—
356#418—891no—
357#417—891no—
358#407—1781no—
359C2×C22⋊C8—1781no—
360C4×M16—891no—
361#335—891no—
362#335—891no—
363#334—891no—
364#334—891no—
365Q8⋊C8—891no—
366Q8⋊C8—891no—
367D4⋊C8—891no—
368D4⋊C8—891no—
369D4⋊C8C2×D8911yescharacteristic
370D4⋊C8C2×D8911yescharacteristic
371D4⋊C8C2×D8911yescharacteristic
372D4⋊C8C2×D8911yescharacteristic
373#322—891no—
374#322—891no—
375#322—891no—
376C82—891no—
377C2×#41—891no—
378C22×D4C4×D8911yescharacteristic
379C23×C4—21no—
380AGL(1,ℤ/8)—1784no—
381C2×SD16—891no—
382C2×SD16—891no—
383C2×D8—891no—
384C2×D8—891no—
385C2×M16—21no—
386C2×M16—891no—
387C2×M16—891no—
388C2×M16—1781no—
389C2×M16—1781no—
390C22×C8—1781no—
391C22×C8—1781no—
392C22×C8—1781no—
393C22×C8—1781no—
394C4×Q8—891no—
395C4×Q8—891no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—891no—
399C4×D4—891no—
400C4×D4—1781no—
401C4×D4—1781no—
402C4×D4C4×D8911yescharacteristic
403C4×D4C4×D8911yescharacteristic
404C4×D4C22×D8911yescharacteristic
405C4×D4C22×D8911yescharacteristic
406#117—891no—
407#117—1781no—
408C2×C4⋊C4C4×D8911yescharacteristic
409C2×C22⋊C4—21no—
410C2×C42—1781no—
411C2×C42C22×D8911yescharacteristic
412#107—891no—
413#107—891no—
414#106—891no—
415#106—891no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8—891no—
419C4⋊C8—891no—
420C4⋊C8—891no—
421C4⋊C8—891no—
422C4⋊C8—1781no—
423C4⋊C8—1781no—
424C4⋊C8C22×D8911yescharacteristic
425C4⋊C8C22×D8911yescharacteristic
426#103—891no—
427#103—891no—
428#102—891no—
429#102—891no—
430#102—891no—
431#102—891no—
432#102—891no—
433#102—891no—
434C22⋊C8—21no—
435C22⋊C8—891no—
436C22⋊C8—891no—
437C22⋊C8—1781no—
438C22⋊C8—1781no—
439C22⋊C8—1781no—
440C22⋊C8—1781no—
441C22⋊C8—1781no—
442C22⋊C8—1781no—
443C22⋊C8—1781no—
444#97—891no—
445#97—891no—
446#97—1781no—
447#97—1781no—
448#97—1781no—
449C4×C8—891no—
450C4×C8—891no—
451C4×C8—891no—
452C4×C8—891no—
453C4×C8C22×D8911yescharacteristic
454C4×C8C22×D8911yescharacteristic
455C24—21no—
456#41—3561no—
457#41—1782no—
458C2×Q8—891no—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—891no—
463C2×D4—1781no—
464C2×D4C2×C4×D8911yescharacteristic
465C2×D4C2×C4×D8911yescharacteristic
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—81no—
472C22×C4—81no—
473C22×C4—1781no—
474C22×C4—1781no—
475C22×C4—1781no—
476C22×C4C2×C4×D8911yescharacteristic
477C22×C4D4×D8911yescharacteristic
478C22×C4#1308357311yescharacteristic
479SD16—1782no—
480SD16—1782no—
481D8—894no—
482D8—1782no—
483M16—81no—
484M16—3561no—
485M16—1782no—
486M16—7121no—
487M16—7121no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—891no—
493C2×C8—891no—
494C2×C8—891no—
495C2×C8—891no—
496C2×C8—891no—
497C2×C8—891no—
498C2×C8—891no—
499C2×C8—891no—
500C2×C8—1781no—
501C2×C8—1781no—
502C2×C8—7121no—
503C2×C8—7121no—
504C2×C8—7121no—
505C2×C8—7121no—
506C4⋊C4—21no—
507C4⋊C4—891no—
508C4⋊C4—891no—
509C4⋊C4—1781no—
510C4⋊C4—1781no—
511C4⋊C4C2×C4×D8911yescharacteristic
512C4⋊C4C2×C4×D8911yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—1781no—
518C22⋊C4—1781no—
519C22⋊C4—1781no—
520C42—1781no—
521C42—1781no—
522C42—1781no—
523C42C2×C4×D8911yescharacteristic
524C42D4×D8911yescharacteristic
525C42#1308357311yescharacteristic
526C42C23×D8911yescharacteristic
527C23—21no—
528C23—21no—
529C23—42no—
530C23—42no—
531C23—81no—
532C23—1781no—
533C23#1566797211yescharacteristic
534Q8—1781no—
535Q8—1781no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—42no—
540D4—892no—
541D4—3562no—
542D4—1781no—
543D4M16×D8912yes—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—81no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4—3562no—
559C2×C4—3562no—
560C2×C4—3561no—
561C2×C4—3561no—
562C2×C4—1781no—
563C2×C4—1781no—
564C2×C4—1781no—
565C2×C4#1566797211yescharacteristic
566C2×C4#1566797211yescharacteristic
567C2×C4#1566797211yescharacteristic
568C2×C4C22×C4×D8911yescharacteristic
569C2×C4C2×D4×D8911yescharacteristic
570C2×C4C2×#1308357311yescharacteristic
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C8—892no—
576C8—3561no—
577C8—3561no—
578C8—1781no—
579C8—1781no—
580C8—1781no—
581C8—1781no—
582C8—1781no—
583C8—1781no—
584C8—1781no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—84no—
595C22—3561no—
596C22—3561no—
597C22—1782no—
598C22C2×#1566797211yescharacteristic
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—41no—
604C4—41no—
605C4—3561no—
606C4—3561no—
607C4—3561no—
608C4C2×M16×D8911yescharacteristic
609C4#1915236411yescharacteristic
610C4#1915239911yescharacteristic
611C4#1915240411yescharacteristic
612C2—41no—
613C2—42no—
614C2—81no—
615C2—3562no—
616C2#2602898411yescharacteristic
617C2#2602907811yescharacteristic
618C2#2602915111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
FittingC89×#1486C2
socleC22×C89C2×C4×D4
prime radicalC2×#15668038C4
cosocleC42×C89C24
hypercenter#1486D89
hypocenterC89#18050
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
1. #26029378C2semidirect
2. #26029287C2semidirect
4. #26019151C2semidirect
5. #26019145C2semidirect
6. #26019119C2semidirect
7. #26019106C2semidirect
8. #26019085C2semidirect
9. #26019084C2semidirect
10. #26019073C2semidirect
11. #26019044C2semidirect
12. #26019017C2semidirect
13. #26018687C2semidirect
14. #26018547C2semidirect
15. C89×#1486C2semidirect
18. #19151725C22semidirect
19. #19151725C22semidirect
36. #19151663C22semidirect
37. #19151663C22semidirect
48. #19151350C22semidirect
49. #19151350C22semidirect
50. #19151348C22semidirect
51. #19151348C22semidirect
52. #19151330C22semidirect
53. #19151330C22semidirect
54. #19151327C22semidirect
55. #19151327C22semidirect
56. #19151320C22semidirect
57. #19151320C22semidirect
58. #19151319C22semidirect
59. C8×#10623494C22semidirect
156. #13083559M16semidirect
323. #1486D89semidirect
325. C89#18050semidirect

Maximal subgroups

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

subgroupindex
#260293782
#260292872
C4×#156680382
#260191512
#260191452
#260191192
#260191062
#260190852
#260190842
#260190732
#260190442
#260190172
#260186872
#260185472
C89×#14862
#1805089