Finite Group Databasebeta

← C89×#19871 #36397719

Subgroups — C89×#19871 #36397719

Order 22784.

632 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3399C211yesmaximal, characteristic, complemented
2C89×#3396C211yesmaximal, characteristic, complemented
3C89×#3394C211yesmaximal, characteristic, complemented
4C89×#3304C211yesmaximal, characteristic, complemented
5C89×#1721C211yesmaximal, characteristic, complemented
6C89×#1686C211yesmaximal, characteristic, complemented
7C89×#1682C211yesmaximal, characteristic, complemented
8C89×#1668C211yesmaximal, characteristic, complemented
9C89×#1667C211yesmaximal, characteristic, complemented
10C89×#1640C211yesmaximal, characteristic, complemented
11C89×#1628C211yesmaximal, characteristic, complemented
12C89×#1621C211yesmaximal, characteristic, complemented
13C89×#1620C211yesmaximal, characteristic, complemented
14C89×#1584C211yesmaximal, characteristic, complemented
15C89×SD16⋊C8C211yesmaximal, characteristic, complemented
16#559×C89C2211yescharacteristic
17#559×C89C2211yescharacteristic
18#556×C89C2211yescharacteristic
19#550×C89C2211yescharacteristic
20#496×C89—21no—
21#495×C89—21no—
22#495×C89—21no—
23#493×C89C2211yescharacteristic
24#493×C89C2211yescharacteristic
25#493×C89C2211yescharacteristic
26#492×C89C2211yescharacteristic
27#486×C89C2211yescharacteristic
28#486×C89C2211yescharacteristic
29#482×C89—21no—
30#475×C89C2211yescharacteristic
31#465×C89—21no—
32#464×C89—21no—
33#463×C89—21no—
34#463×C89—21no—
35#463×C89—21no—
36#463×C89—21no—
37#462×C89C2211yescharacteristic
38#460×C89C2211yescharacteristic
39#460×C89C2211yescharacteristic
40#460×C89C2211yescharacteristic
41#460×C89C2211yescharacteristic
42#459×C89—21no—
43#459×C89C2211yescharacteristic
44#459×C89C2211yescharacteristic
45#452×C89—21no—
46#446×C89C2211yescharacteristic
47C8×Q8×C89C2211yescharacteristic
48C8×Q8×C89C2211yescharacteristic
49#442×C89—21no—
50C4×Q16×C89C2211yescharacteristic
51C4×SD16×C89—21no—
52C4×SD16×C89C2211yescharacteristic
53C4×D8×C89—21no—
54C8×D4×C89C2211yescharacteristic
55#416×C89—21no—
56#335×C89C2211yescharacteristic
57#335×C89C2211yescharacteristic
58#332×C89C2211yescharacteristic
59#331×C89C2211yescharacteristic
60#331×C89C2211yescharacteristic
61#331×C89C2211yescharacteristic
62Q8⋊C8×C89C2211yescharacteristic
63Q8⋊C8×C89C2211yescharacteristic
64Q8⋊C8×C89C2211yescharacteristic
65D4⋊C8×C89C2211yescharacteristic
66#322×C89C2211yescharacteristic
67C2×#41×C89—21no—
68C2×Q16×C89—21no—
69C2×Q16×C89D411yescharacteristic
70C2×SD16×C89—21no—
71C2×SD16×C89—21no—
72C2×SD16×C89—21no—
73C2×SD16×C89—21no—
74C2×SD16×C89—21no—
75C2×SD16×C89—21no—
76C2×SD16×C89D411yescharacteristic
77C2×D8×C89—21no—
78C2×D8×C89—21no—
79C2×D8×C89—21no—
80C2×D8×C89—21no—
81C2×D8×C89—21no—
82C2×D8×C89—21no—
83C2×D8×C89—41no—
84C22×C8×C89—21no—
85C4⋊Q8×C89C2311yescharacteristic
86#127×C89—21no—
87#127×C89C2311yescharacteristic
88#127×C89C2311yescharacteristic
89#127×C89C2311yescharacteristic
90#126×C89—41no—
91#124×C89—21no—
92#124×C89—21no—
93#124×C89—21no—
94#124×C89—21no—
95#124×C89—21no—
96#123×C89—41no—
97#123×C89—41no—
98C22⋊Q8×C89—21no—
99#121×C89—21no—
100#121×C89—41no—
101C4×Q8×C89—21no—
102C4×Q8×C89C2311yescharacteristic
103C4×Q8×C89C2311yescharacteristic
104C4×Q8×C89C2311yescharacteristic
105C4×D4×C89—21no—
106C4×D4×C89—21no—
107C4×D4×C89—21no—
108C4×D4×C89—21no—
109C4×D4×C89—21no—
110C4×D4×C89C2311yescharacteristic
111#117×C89—21no—
112#107×C89D411yescharacteristic
113#106×C89—21no—
114#106×C89D411yescharacteristic
115C4⋊C8×C89—21no—
116C4⋊C8×C89—21no—
117C4⋊C8×C89—21no—
118C4⋊C8×C89C2311yescharacteristic
119C4⋊C8×C89C2311yescharacteristic
120C4⋊C8×C89C2311yescharacteristic
121C4⋊C8×C89C2311yescharacteristic
122#103×C89—21no—
123#103×C89—21no—
124#103×C89D411yescharacteristic
125#103×C89D411yescharacteristic
126#103×C89D411yescharacteristic
127#102×C89—21no—
128#102×C89—21no—
129#102×C89—21no—
130#102×C89—21no—
131#102×C89—21no—
132#102×C89—21no—
133#102×C89—21no—
134#102×C89—21no—
135#102×C89—41no—
136#102×C89D411yescharacteristic
137C22⋊C8×C89—21no—
138#97×C89—21no—
139C4×C8×C89—21no—
140C4×C8×C89—21no—
141C4×C8×C89C2311yescharacteristic
142C4×C8×C89C2311yescharacteristic
143C4×C8×C89C2311yescharacteristic
144#41×C89—42no—
145#41×C89—81no—
146C2×Q8×C89—21no—
147C2×Q8×C89C2×D411yescharacteristic
148C2×Q8×C89C2×D411yescharacteristic
149C2×Q8×C89C2×D411yescharacteristic
150C2×D4×C89—21no—
151C2×D4×C89—21no—
152C2×D4×C89—21no—
153C2×D4×C89—21no—
154C2×D4×C89—21no—
155C2×D4×C89—21no—
156C2×D4×C89—21no—
157C2×D4×C89—21no—
158C2×D4×C89—21no—
159C2×D4×C89—41no—
160C2×D4×C89—41no—
161C2×D4×C89C2×D411yescharacteristic
162C22×C4×C89—21no—
163C22×C4×C89—41no—
164C22×C4×C89—41no—
165C22×C4×C89—41no—
166Q16×C89—41no—
167Q16×C89—81no—
168SD16×C89—22no—
169SD16×C89—42no—
170SD16×C89—81no—
171SD16×C89—81no—
172SD16×C89—81no—
173SD16×C89—81no—
174SD16×C89—81no—
175D8×C89—42no—
176D8×C89—42no—
177D8×C89—81no—
178D8×C89—81no—
179D8×C89—81no—
180D8×C89—81no—
181D8×C89—82no—
182C2×C8×C89—21no—
183C2×C8×C89—21no—
184C2×C8×C89—21no—
185C2×C8×C89—21no—
186C2×C8×C89—21no—
187C2×C8×C89—81no—
188C2×C8×C89C2×D411yescharacteristic
189C2×C8×C89C2×D411yescharacteristic
190C2×C8×C89C2×D411yescharacteristic
191C2×C8×C89C2×D411yescharacteristic
192C4⋊C4×C89—21no—
193C4⋊C4×C89—21no—
194C4⋊C4×C89—21no—
195C4⋊C4×C89—21no—
196C4⋊C4×C89—21no—
197C4⋊C4×C89—41no—
198C4⋊C4×C89C2×D411yescharacteristic
199C4⋊C4×C89C2×D411yescharacteristic
200C4⋊C4×C89C2×D411yescharacteristic
201C4⋊C4×C89C2×D411yescharacteristic
202C22⋊C4×C89—21no—
203C22⋊C4×C89—41no—
204C22⋊C4×C89—41no—
205C22⋊C4×C89—41no—
206C22⋊C4×C89—41no—
207C22⋊C4×C89—41no—
208C22⋊C4×C89—41no—
209C22⋊C4×C89—41no—
210C22⋊C4×C89—41no—
211C22⋊C4×C89—41no—
212C42×C89—21no—
213C42×C89—21no—
214C42×C89—21no—
215C42×C89—41no—
216C42×C89C2411yescharacteristic
217C23×C89—21no—
218C23×C89—41no—
219C23×C89—41no—
220C23×C89—41no—
221Q8×C89—21no—
222Q8×C89—21no—
223Q8×C89—21no—
224Q8×C89—21no—
225Q8×C89—21no—
226Q8×C89—21no—
227Q8×C89—41no—
228Q8×C89—41no—
229D4×C89—21no—
230D4×C89—21no—
231D4×C89—41no—
232D4×C89—41no—
233D4×C89—41no—
234D4×C89—41no—
235D4×C89—41no—
236D4×C89—41no—
237D4×C89—41no—
238D4×C89—41no—
239D4×C89—41no—
240D4×C89—41no—
241D4×C89—41no—
242D4×C89—41no—
243D4×C89—81no—
244D4×C89—81no—
245D4×C89—81no—
246D4×C89—82no—
247D4×C89—161no—
248C2×C4×C89—21no—
249C2×C4×C89—21no—
250C2×C4×C89—21no—
251C2×C4×C89—21no—
252C2×C4×C89—21no—
253C2×C4×C89—21no—
254C2×C4×C89—21no—
255C2×C4×C89—41no—
256C2×C4×C89—41no—
257C2×C4×C89—41no—
258C2×C4×C89—82no—
259C2×C4×C89—161no—
260C2×C4×C89—161no—
261C2×C4×C89C22×D411yescharacteristic
262C2×C4×C89C22×D411yescharacteristic
263C2×C4×C89H(5,𝔽2)11yescharacteristic
264C8×C89—21no—
265C8×C89—21no—
266C8×C89—21no—
267C8×C89—41no—
268C8×C89—41no—
269C8×C89—41no—
270C8×C89—41no—
271C8×C89—41no—
272C8×C89#13512yes—
273C22×C89—41no—
274C22×C89—41no—
275C22×C89—41no—
276C22×C89—81no—
277C22×C89—81no—
278C22×C89—81no—
279C22×C89—81no—
280C22×C89—81no—
281C22×C89—81no—
282C22×C89—81no—
283C22×C89—81no—
284C22×C89—81no—
285C22×C89D4211yescharacteristic
286C4×C89—21no—
287C4×C89—41no—
288C4×C89—41no—
289C4×C89—41no—
290C4×C89—41no—
291C4×C89—41no—
292C4×C89—41no—
293C4×C89—41no—
294C4×C89—81no—
295C4×C89C2×#13511yescharacteristic
296C4×C89#57511yescharacteristic
297C4×C89#57611yescharacteristic
298C4×C89#57611yescharacteristic
299#19871C8911yesmaximal, characteristic, direct product factor, Sylow
300C2×C89—81no—
301C2×C89—161no—
302C2×C89—161no—
303C2×C89—161no—
304C2×C89#326811yescharacteristic
305C2×C89#328711yescharacteristic
306C2×C89#328811yescharacteristic
307#3399C2×C8911yescharacteristic, complemented
308#3396C2×C8911yescharacteristic, complemented
309#3394C2×C8911yescharacteristic, complemented
310#3304C2×C8911yescharacteristic, complemented
311#1721C2×C8911yescharacteristic, complemented
312#1686C2×C8911yescharacteristic, complemented
313#1682C2×C8911yescharacteristic, complemented
314#1668C2×C8911yescharacteristic, complemented
315#1667C2×C8911yescharacteristic, complemented
316#1640C2×C8911yescharacteristic, complemented
317#1628C2×C8911yescharacteristic, complemented
318#1621C2×C8911yescharacteristic, complemented
319#1620C2×C8911yescharacteristic, complemented
320#1584C2×C8911yescharacteristic, complemented
321SD16⋊C8C2×C8911yescharacteristic, complemented
322C89#1987111yescharacteristic, direct product factor, Sylow
323#559C22×C8911yescharacteristic
324#559C22×C8911yescharacteristic
325#556C22×C8911yescharacteristic
326#550C22×C8911yescharacteristic
327#496—21no—
328#495—21no—
329#495—21no—
330#493C22×C8911yescharacteristic
331#493C22×C8911yescharacteristic
332#493C22×C8911yescharacteristic
333#492C22×C8911yescharacteristic
334#486C22×C8911yescharacteristic
335#486C22×C8911yescharacteristic
336#482—21no—
337#475C22×C8911yescharacteristic
338#465—21no—
339#464—21no—
340#463—21no—
341#463—21no—
342#463—21no—
343#463—21no—
344#462C22×C8911yescharacteristic
345#460C22×C8911yescharacteristic
346#460C22×C8911yescharacteristic
347#460C22×C8911yescharacteristic
348#460C22×C8911yescharacteristic
349#459—21no—
350#459C22×C8911yescharacteristic
351#459C22×C8911yescharacteristic
352#452—21no—
353#446C22×C8911yescharacteristic
354C8×Q8C22×C8911yescharacteristic
355C8×Q8C22×C8911yescharacteristic
356#442—21no—
357C4×Q16C22×C8911yescharacteristic
358C4×SD16—21no—
359C4×SD16C22×C8911yescharacteristic
360C4×D8—21no—
361C8×D4C22×C8911yescharacteristic
362#416—21no—
363#335C22×C8911yescharacteristic
364#335C22×C8911yescharacteristic
365#332C22×C8911yescharacteristic
366#331C22×C8911yescharacteristic
367#331C22×C8911yescharacteristic
368#331C22×C8911yescharacteristic
369Q8⋊C8C22×C8911yescharacteristic
370Q8⋊C8C22×C8911yescharacteristic
371Q8⋊C8C22×C8911yescharacteristic
372D4⋊C8C22×C8911yescharacteristic
373#322C22×C8911yescharacteristic
374C2×#41—21no—
375C2×Q16—21no—
376C2×Q16D4×C8911yescharacteristic
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16D4×C8911yescharacteristic
384C2×D8—21no—
385C2×D8—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—41no—
391C22×C8—21no—
392C4⋊Q8C23×C8911yescharacteristic
393#127—21no—
394#127C23×C8911yescharacteristic
395#127C23×C8911yescharacteristic
396#127C23×C8911yescharacteristic
397#126—41no—
398#124—21no—
399#124—21no—
400#124—21no—
401#124—21no—
402#124—21no—
403#123—41no—
404#123—41no—
405C22⋊Q8—21no—
406#121—21no—
407#121—41no—
408C4×Q8—21no—
409C4×Q8C23×C8911yescharacteristic
410C4×Q8C23×C8911yescharacteristic
411C4×Q8C23×C8911yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4C23×C8911yescharacteristic
418#117—21no—
419#107D4×C8911yescharacteristic
420#106—21no—
421#106D4×C8911yescharacteristic
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8C23×C8911yescharacteristic
426C4⋊C8C23×C8911yescharacteristic
427C4⋊C8C23×C8911yescharacteristic
428C4⋊C8C23×C8911yescharacteristic
429#103—21no—
430#103—21no—
431#103D4×C8911yescharacteristic
432#103D4×C8911yescharacteristic
433#103D4×C8911yescharacteristic
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—41no—
443#102D4×C8911yescharacteristic
444C22⋊C8—21no—
445#97—21no—
446C4×C8—21no—
447C4×C8—21no—
448C4×C8C23×C8911yescharacteristic
449C4×C8C23×C8911yescharacteristic
450C4×C8C23×C8911yescharacteristic
451#41—42no—
452#41—81no—
453C2×Q8—21no—
454C2×Q8C2×D4×C8911yescharacteristic
455C2×Q8C2×D4×C8911yescharacteristic
456C2×Q8C2×D4×C8911yescharacteristic
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4C2×D4×C8911yescharacteristic
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473Q16—41no—
474Q16—81no—
475SD16—22no—
476SD16—42no—
477SD16—81no—
478SD16—81no—
479SD16—81no—
480SD16—81no—
481SD16—81no—
482D8—42no—
483D8—42no—
484D8—81no—
485D8—81no—
486D8—81no—
487D8—81no—
488D8—82no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—81no—
495C2×C8C2×D4×C8911yescharacteristic
496C2×C8C2×D4×C8911yescharacteristic
497C2×C8C2×D4×C8911yescharacteristic
498C2×C8C2×D4×C8911yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4C2×D4×C8911yescharacteristic
506C4⋊C4C2×D4×C8911yescharacteristic
507C4⋊C4C2×D4×C8911yescharacteristic
508C4⋊C4C2×D4×C8911yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—41no—
523C42C24×C8911yescharacteristic
524C23—21no—
525C23—41no—
526C23—41no—
527C23—41no—
528Q8—21no—
529Q8—21no—
530Q8—21no—
531Q8—21no—
532Q8—21no—
533Q8—21no—
534Q8—41no—
535Q8—41no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—81no—
551D4—81no—
552D4—81no—
553D4—82no—
554D4—161no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—82no—
566C2×C4—161no—
567C2×C4—161no—
568C2×C4C22×D4×C8911yescharacteristic
569C2×C4C22×D4×C8911yescharacteristic
570C2×C4H(5,𝔽2)×C8911yescharacteristic
571C8—21no—
572C8—21no—
573C8—21no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8#135×C8912yes—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22D42×C8911yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4C2×#135×C8911yescharacteristic
603C4#575×C8911yescharacteristic
604C4#576×C8911yescharacteristic
605C4#576×C8911yescharacteristic
606C2—81no—
607C2—161no—
608C2—161no—
609C2—161no—
610C2C89×#326811yescharacteristic
611C2C89×#328711yescharacteristic
612C2C89×#328811yescharacteristic
subgroupG/H
center, socleC22×C89D42
commutator, Frattini, cosocleC42C24×C89
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C89 ◁ C42×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C89×#3399C2semidirect
2. C89×#3396C2semidirect
3. C89×#3394C2semidirect
4. C89×#3304C2semidirect
5. C89×#1721C2semidirect
6. C89×#1686C2semidirect
7. C89×#1682C2semidirect
8. C89×#1668C2semidirect
9. C89×#1667C2semidirect
10. C89×#1640C2semidirect
11. C89×#1628C2semidirect
12. C89×#1621C2semidirect
13. C89×#1620C2semidirect
14. C89×#1584C2semidirect
15. C89×SD16⋊C8C2semidirect
299. #19871C89direct (N × H)
307. #3399C2×C89semidirect
308. #3396C2×C89semidirect
309. #3394C2×C89semidirect
310. #3304C2×C89semidirect
311. #1721C2×C89semidirect
312. #1686C2×C89semidirect
313. #1682C2×C89semidirect
314. #1668C2×C89semidirect
315. #1667C2×C89semidirect
316. #1640C2×C89semidirect
317. #1628C2×C89semidirect
318. #1621C2×C89semidirect
319. #1620C2×C89semidirect
320. #1584C2×C89semidirect
321. SD16⋊C8C2×C89semidirect
322. C89#19871direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#33992
C89×#33962
C89×#33942
C89×#33042
C89×#17212
C89×#16862
C89×#16822
C89×#16682
C89×#16672
C89×#16402
C89×#16282
C89×#16212
C89×#16202
C89×#15842
C89×SD16⋊C82
#1987189