Finite Group Databasebeta

← C89×#18704 #36396552

Subgroups — C89×#18704 #36396552

Order 22784.

972 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3546C211yesmaximal, characteristic, complemented
2C89×#3251C211yesmaximal, characteristic, complemented
3C89×#3214C211yesmaximal, characteristic, complemented
4C89×#3169C211yesmaximal, characteristic, complemented
5C89×#1650C211yesmaximal, characteristic, complemented
6C89×#1647C211yesmaximal, characteristic, complemented
7C89×#1642C211yesmaximal, characteristic, complemented
8C89×#1639C211yesmaximal, characteristic, complemented
9C89×#1628C211yesmaximal, characteristic, complemented
10C89×#1625C211yesmaximal, characteristic, complemented
11C89×#1621C211yesmaximal, characteristic, complemented
12C89×#1619C211yesmaximal, characteristic, complemented
13C89×#1557C211yesmaximal, characteristic, complemented
14C89×#1494C211yesmaximal, characteristic, complemented
15C89×#1492C211yesmaximal, characteristic, complemented
16#560×C89—22no—
17#556×C89C2211yescharacteristic
18#553×C89—21no—
19#550×C89—21no—
20#550×C89C2211yescharacteristic
21#547×C89C2211yescharacteristic
22#546×C89—21no—
23#546×C89—21no—
24D42×C89C2211yescharacteristic
25#542×C89—21no—
26#538×C89—22no—
27#537×C89—21no—
28#535×C89—21no—
29#535×C89—21no—
30#532×C89C2211yescharacteristic
31#532×C89C2211yescharacteristic
32#532×C89C2211yescharacteristic, complemented
33#529×C89C2211yescharacteristic
34#500×C89C2211yescharacteristic, complemented
35#496×C89—21no—
36#493×C89C2211yescharacteristic
37#489×C89—21no—
38#486×C89C2211yescharacteristic
39#486×C89C2211yescharacteristic, complemented
40#478×C89—21no—
41#475×C89C2211yescharacteristic, complemented
42#474×C89C2211yescharacteristic
43#469×C89—21no—
44#468×C89—21no—
45#466×C89—22no—
46#463×C89—21no—
47#461×C89C2211yescharacteristic
48#461×C89C2211yescharacteristic, complemented
49#460×C89C2211yescharacteristic, complemented
50#459×C89C2211yescharacteristic
51#459×C89C2211yescharacteristic
52#459×C89C2211yescharacteristic, complemented
53#449×C89—21no—
54#449×C89—21no—
55C4×D8×C89—22no—
56#432×C89C2211yescharacteristic, complemented
57#423×C89C2211yescharacteristic, complemented
58C2×C4×C8×C89C2211yescharacteristic, complemented
59#332×C89C2211yescharacteristic, complemented
60#332×C89C2211yescharacteristic, complemented
61#331×C89C2211yescharacteristic
62#331×C89C2211yescharacteristic
63Q8⋊C8×C89C2211yescharacteristic, complemented
64Q8⋊C8×C89C2211yescharacteristic, complemented
65D4⋊C8×C89C2211yescharacteristic
66D4⋊C8×C89C2211yescharacteristic
67D4⋊C8×C89C2211yescharacteristic
68D4⋊C8×C89C2211yescharacteristic
69D4⋊C8×C89C2211yescharacteristic, complemented
70D4⋊C8×C89C2211yescharacteristic, complemented
71C2×#41×C89—21no—
72C2×#41×C89—21no—
73C2×#41×C89—21no—
74C2×#41×C89—21no—
75C2×#41×C89—21no—
76C22×D4×C89—21no—
77C22×D4×C89—21no—
78C2×SD16×C89—21no—
79C2×SD16×C89—21no—
80C2×SD16×C89—21no—
81C2×D8×C89—22no—
82C2×D8×C89—21no—
83C2×D8×C89—21no—
84C2×D8×C89—21no—
85C2×M16×C89—21no—
86C22×C8×C89—21no—
87C4⋊Q8×C89D411yescharacteristic
88C4⋊Q8×C89C2311yescharacteristic
89C4⋊Q8×C89C2311yescharacteristic
90#127×C89—22no—
91#127×C89—21no—
92#127×C89D411yescharacteristic
93#127×C89C2311yescharacteristic
94#127×C89C2311yescharacteristic
95#126×C89—22no—
96#126×C89—22no—
97#126×C89—21no—
98#125×C89D411yescharacteristic
99#124×C89—22no—
100#124×C89—21no—
101#124×C89—21no—
102#124×C89—21no—
103#124×C89—21no—
104#124×C89D411yescharacteristic
105#123×C89—22no—
106#123×C89—22no—
107#123×C89—21no—
108#123×C89—22no—
109C22⋊Q8×C89—22no—
110C22⋊Q8×C89—21no—
111C22⋊Q8×C89—21no—
112C22⋊Q8×C89D411yescharacteristic
113#121×C89—22no—
114#121×C89—22no—
115#121×C89—22no—
116#121×C89—22no—
117#121×C89—22no—
118#121×C89—21no—
119#121×C89—22no—
120#121×C89—21no—
121#121×C89—21no—
122#121×C89—21no—
123#121×C89—21no—
124#121×C89—21no—
125#121×C89—21no—
126#121×C89—21no—
127#121×C89D411yescharacteristic
128#121×C89D411yescharacteristic
129#121×C89D412yes—
130#121×C89D411yescharacteristic
131#120×C89—22no—
132#120×C89—22no—
133#120×C89—22no—
134#120×C89—22no—
135C4×Q8×C89—21no—
136C4×Q8×C89C2311yescharacteristic
137C4×D4×C89—22no—
138C4×D4×C89—21no—
139C4×D4×C89—21no—
140C4×D4×C89—21no—
141C4×D4×C89—21no—
142C4×D4×C89—21no—
143C4×D4×C89—21no—
144C4×D4×C89D412yes—
145C4×D4×C89C2311yescharacteristic
146C4×D4×C89C2311yescharacteristic
147C4×D4×C89C2311yescharacteristic
148#117×C89—21no—
149#117×C89—21no—
150C2×C4⋊C4×C89—21no—
151C2×C22⋊C4×C89—22no—
152C2×C42×C89C2311yescharacteristic
153#107×C89—22no—
154#107×C89—21no—
155#106×C89—21no—
156C4⋊C8×C89—21no—
157C4⋊C8×C89C2311yescharacteristic
158C4⋊C8×C89C2311yescharacteristic
159C4⋊C8×C89C2311yescharacteristic
160C4⋊C8×C89C2311yescharacteristic
161#103×C89—21no—
162#103×C89—21no—
163#103×C89—21no—
164#102×C89—22no—
165#102×C89—21no—
166#102×C89—22no—
167#102×C89—21no—
168#102×C89—21no—
169#102×C89—21no—
170#102×C89—21no—
171C22⋊C8×C89—21no—
172#97×C89—21no—
173C4×C8×C89—21no—
174C4×C8×C89C2311yescharacteristic
175C4×C8×C89C2311yescharacteristic
176C24×C89—22no—
177#41×C89—81no—
178#41×C89—81no—
179#41×C89—81no—
180#41×C89—81no—
181#41×C89—81no—
182#41×C89—81no—
183#41×C89—81no—
184#41×C89—81no—
185#41×C89—81no—
186#41×C89—81no—
187C2×Q8×C89—21no—
188C2×Q8×C89—21no—
189C2×Q8×C89—21no—
190C2×Q8×C89C2×D411yescharacteristic
191C2×D4×C89—22no—
192C2×D4×C89—22no—
193C2×D4×C89—22no—
194C2×D4×C89—22no—
195C2×D4×C89—22no—
196C2×D4×C89—21no—
197C2×D4×C89—21no—
198C2×D4×C89—22no—
199C2×D4×C89—21no—
200C2×D4×C89—21no—
201C2×D4×C89—21no—
202C2×D4×C89—21no—
203C2×D4×C89—21no—
204C2×D4×C89—21no—
205C2×D4×C89—21no—
206C2×D4×C89—21no—
207C2×D4×C89—41no—
208C2×D4×C89—81no—
209C2×D4×C89—81no—
210C2×D4×C89—81no—
211C2×D4×C89—81no—
212C2×D4×C89C2×D411yescharacteristic
213C2×D4×C89C2×D411yescharacteristic
214C2×D4×C89C2×D411yescharacteristic
215C2×D4×C89C2×D412yes—
216C22×C4×C89—22no—
217C22×C4×C89—22no—
218C22×C4×C89—21no—
219C22×C4×C89—21no—
220C22×C4×C89—21no—
221C22×C4×C89—22no—
222C22×C4×C89—41no—
223C22×C4×C89C2×D411yescharacteristic
224C22×C4×C89C2×D411yescharacteristic
225C22×C4×C89C2×D411yescharacteristic
226SD16×C89—81no—
227SD16×C89—81no—
228SD16×C89—81no—
229D8×C89—44no—
230D8×C89—81no—
231D8×C89—81no—
232D8×C89—81no—
233M16×C89—81no—
234C2×C8×C89—21no—
235C2×C8×C89—21no—
236C2×C8×C89—21no—
237C2×C8×C89—21no—
238C2×C8×C89—21no—
239C2×C8×C89—21no—
240C2×C8×C89—42no—
241C4⋊C4×C89—22no—
242C4⋊C4×C89—22no—
243C4⋊C4×C89—21no—
244C4⋊C4×C89—21no—
245C4⋊C4×C89—21no—
246C4⋊C4×C89—21no—
247C4⋊C4×C89—21no—
248C4⋊C4×C89—21no—
249C4⋊C4×C89—21no—
250C4⋊C4×C89—21no—
251C4⋊C4×C89C2×D411yescharacteristic
252C4⋊C4×C89C2×D411yescharacteristic
253C4⋊C4×C89C2×D411yescharacteristic
254C4⋊C4×C89C2×D411yescharacteristic
255C4⋊C4×C89C2×D412yes—
256C22⋊C4×C89—22no—
257C22⋊C4×C89—22no—
258C22⋊C4×C89—22no—
259C22⋊C4×C89—22no—
260C22⋊C4×C89—22no—
261C22⋊C4×C89—21no—
262C22⋊C4×C89—21no—
263C22⋊C4×C89—21no—
264C22⋊C4×C89—21no—
265C22⋊C4×C89—21no—
266C22⋊C4×C89—21no—
267C22⋊C4×C89—22no—
268C22⋊C4×C89—22no—
269C22⋊C4×C89—21no—
270C22⋊C4×C89—21no—
271C22⋊C4×C89—21no—
272C22⋊C4×C89—41no—
273C22⋊C4×C89—41no—
274C42×C89—22no—
275C42×C89—21no—
276C42×C89C2×D411yescharacteristic
277C42×C89C2×D411yescharacteristic
278C42×C89C2×D411yescharacteristic
279C42×C89C2411yescharacteristic
280C23×C89—21no—
281C23×C89—21no—
282C23×C89—22no—
283C23×C89—21no—
284C23×C89—41no—
285C23×C89—82no—
286C23×C89—82no—
287C23×C89—82no—
288C23×C89#12011yescharacteristic
289Q8×C89—21no—
290Q8×C89—21no—
291Q8×C89—41no—
292Q8×C89—41no—
293Q8×C89—41no—
294Q8×C89—41no—
295Q8×C89—81no—
296D4×C89—21no—
297D4×C89—21no—
298D4×C89—21no—
299D4×C89—21no—
300D4×C89—21no—
301D4×C89—21no—
302D4×C89—42no—
303D4×C89—42no—
304D4×C89—41no—
305D4×C89—41no—
306D4×C89—41no—
307D4×C89—41no—
308D4×C89—41no—
309D4×C89—41no—
310D4×C89—41no—
311D4×C89—41no—
312D4×C89—81no—
313D4×C89—81no—
314D4×C89—81no—
315D4×C89—82no—
316D4×C89—81no—
317D4×C89—81no—
318D4×C89—82no—
319D4×C89—82no—
320D4×C89—82no—
321D4×C89—82no—
322D4×C89—82no—
323D4×C89—82no—
324C2×C4×C89—21no—
325C2×C4×C89—21no—
326C2×C4×C89—21no—
327C2×C4×C89—21no—
328C2×C4×C89—21no—
329C2×C4×C89—21no—
330C2×C4×C89—21no—
331C2×C4×C89—22no—
332C2×C4×C89—21no—
333C2×C4×C89—21no—
334C2×C4×C89—41no—
335C2×C4×C89—41no—
336C2×C4×C89—41no—
337C2×C4×C89—41no—
338C2×C4×C89—41no—
339C2×C4×C89—41no—
340C2×C4×C89—41no—
341C2×C4×C89—41no—
342C2×C4×C89—82no—
343C2×C4×C89—82no—
344C2×C4×C89—82no—
345C2×C4×C89—82no—
346C2×C4×C89#12011yescharacteristic
347C2×C4×C89#12011yescharacteristic
348C2×C4×C89#12011yescharacteristic
349C2×C4×C89C22×D411yescharacteristic
350C2×C4×C89C22×D411yescharacteristic
351C2×C4×C89C22×D411yescharacteristic
352C8×C89—22no—
353C8×C89—41no—
354C8×C89—41no—
355C8×C89—41no—
356C8×C89—41no—
357C8×C89—41no—
358C22×C89—21no—
359C22×C89—21no—
360C22×C89—21no—
361C22×C89—41no—
362C22×C89—41no—
363C22×C89—42no—
364C22×C89—41no—
365C22×C89—41no—
366C22×C89—41no—
367C22×C89—42no—
368C22×C89—41no—
369C22×C89—42no—
370C22×C89—41no—
371C22×C89—41no—
372C22×C89—41no—
373C22×C89—81no—
374C22×C89—81no—
375C22×C89—81no—
376C22×C89—164no—
377C22×C89C2×#12011yescharacteristic
378C4×C89—21no—
379C4×C89—21no—
380C4×C89—21no—
381C4×C89—21no—
382C4×C89—41no—
383C4×C89—42no—
384C4×C89—41no—
385C4×C89—41no—
386C4×C89—41no—
387C4×C89—41no—
388C4×C89—81no—
389C4×C89#57611yescharacteristic
390C4×C89#57611yescharacteristic
391C4×C89#57611yescharacteristic
392C4×C89#57711yescharacteristic
393#18704C8911yesmaximal, characteristic, direct product factor, Sylow
394C2×C89—41no—
395C2×C89—81no—
396C2×C89—82no—
397C2×C89—81no—
398C2×C89—81no—
399C2×C89—161no—
400C2×C89#300811yescharacteristic
401C2×C89#301211yescharacteristic
402C2×C89#301811yescharacteristic
403#3546C2×C8911yescharacteristic, complemented
404#3251C2×C8911yescharacteristic, complemented
405#3214C2×C8911yescharacteristic, complemented
406#3169C2×C8911yescharacteristic, complemented
407#1650C2×C8911yescharacteristic, complemented
408#1647C2×C8911yescharacteristic, complemented
409#1642C2×C8911yescharacteristic, complemented
410#1639C2×C8911yescharacteristic, complemented
411#1628C2×C8911yescharacteristic, complemented
412#1625C2×C8911yescharacteristic, complemented
413#1621C2×C8911yescharacteristic, complemented
414#1619C2×C8911yescharacteristic, complemented
415#1557C2×C8911yescharacteristic, complemented
416#1494C2×C8911yescharacteristic, complemented
417#1492C2×C8911yescharacteristic, complemented
418C89#1870411yescharacteristic, direct product factor, Sylow
419#560—22no—
420#556C22×C8911yescharacteristic
421#553—21no—
422#550—21no—
423#550C22×C8911yescharacteristic
424#547C22×C8911yescharacteristic
425#546—21no—
426#546—21no—
427D42C22×C8911yescharacteristic
428#542—21no—
429#538—22no—
430#537—21no—
431#535—21no—
432#535—21no—
433#532C22×C8911yescharacteristic
434#532C22×C8911yescharacteristic
435#532C22×C8911yescharacteristic, complemented
436#529C22×C8911yescharacteristic
437#500C22×C8911yescharacteristic, complemented
438#496—21no—
439#493C22×C8911yescharacteristic
440#489—21no—
441#486C22×C8911yescharacteristic
442#486C22×C8911yescharacteristic, complemented
443#478—21no—
444#475C22×C8911yescharacteristic, complemented
445#474C22×C8911yescharacteristic
446#469—21no—
447#468—21no—
448#466—22no—
449#463—21no—
450#461C22×C8911yescharacteristic
451#461C22×C8911yescharacteristic, complemented
452#460C22×C8911yescharacteristic, complemented
453#459C22×C8911yescharacteristic
454#459C22×C8911yescharacteristic
455#459C22×C8911yescharacteristic, complemented
456#449—21no—
457#449—21no—
458C4×D8—22no—
459#432C22×C8911yescharacteristic, complemented
460#423C22×C8911yescharacteristic, complemented
461C2×C4×C8C22×C8911yescharacteristic, complemented
462#332C22×C8911yescharacteristic, complemented
463#332C22×C8911yescharacteristic, complemented
464#331C22×C8911yescharacteristic
465#331C22×C8911yescharacteristic
466Q8⋊C8C22×C8911yescharacteristic, complemented
467Q8⋊C8C22×C8911yescharacteristic, complemented
468D4⋊C8C22×C8911yescharacteristic
469D4⋊C8C22×C8911yescharacteristic
470D4⋊C8C22×C8911yescharacteristic
471D4⋊C8C22×C8911yescharacteristic
472D4⋊C8C22×C8911yescharacteristic, complemented
473D4⋊C8C22×C8911yescharacteristic, complemented
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C22×D4—21no—
480C22×D4—21no—
481C2×SD16—21no—
482C2×SD16—21no—
483C2×SD16—21no—
484C2×D8—22no—
485C2×D8—21no—
486C2×D8—21no—
487C2×D8—21no—
488C2×M16—21no—
489C22×C8—21no—
490C4⋊Q8D4×C8911yescharacteristic
491C4⋊Q8C23×C8911yescharacteristic
492C4⋊Q8C23×C8911yescharacteristic
493#127—22no—
494#127—21no—
495#127D4×C8911yescharacteristic
496#127C23×C8911yescharacteristic
497#127C23×C8911yescharacteristic
498#126—22no—
499#126—22no—
500#126—21no—
501#125D4×C8911yescharacteristic
502#124—22no—
503#124—21no—
504#124—21no—
505#124—21no—
506#124—21no—
507#124D4×C8911yescharacteristic
508#123—22no—
509#123—22no—
510#123—21no—
511#123—22no—
512C22⋊Q8—22no—
513C22⋊Q8—21no—
514C22⋊Q8—21no—
515C22⋊Q8D4×C8911yescharacteristic
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—21no—
522#121—22no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121D4×C8911yescharacteristic
531#121D4×C8911yescharacteristic
532#121D4×C8911yescharacteristic
533#121D4×C8912yes—
534#120—22no—
535#120—22no—
536#120—22no—
537#120—22no—
538C4×Q8—21no—
539C4×Q8C23×C8911yescharacteristic
540C4×D4—22no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4D4×C8912yes—
548C4×D4C23×C8911yescharacteristic
549C4×D4C23×C8911yescharacteristic
550C4×D4C23×C8911yescharacteristic
551#117—21no—
552#117—21no—
553C2×C4⋊C4—21no—
554C2×C22⋊C4—22no—
555C2×C42C23×C8911yescharacteristic
556#107—22no—
557#107—21no—
558#106—21no—
559C4⋊C8—21no—
560C4⋊C8C23×C8911yescharacteristic
561C4⋊C8C23×C8911yescharacteristic
562C4⋊C8C23×C8911yescharacteristic
563C4⋊C8C23×C8911yescharacteristic
564#103—21no—
565#103—21no—
566#103—21no—
567#102—22no—
568#102—21no—
569#102—22no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574C22⋊C8—21no—
575#97—21no—
576C4×C8—21no—
577C4×C8C23×C8911yescharacteristic
578C4×C8C23×C8911yescharacteristic
579C24—22no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—81no—
586#41—81no—
587#41—81no—
588#41—81no—
589#41—81no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8C2×D4×C8911yescharacteristic
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C2×D4×C8911yescharacteristic
616C2×D4C2×D4×C8911yescharacteristic
617C2×D4C2×D4×C8911yescharacteristic
618C2×D4C2×D4×C8912yes—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—41no—
626C22×C4C2×D4×C8911yescharacteristic
627C22×C4C2×D4×C8911yescharacteristic
628C22×C4C2×D4×C8911yescharacteristic
629SD16—81no—
630SD16—81no—
631SD16—81no—
632D8—44no—
633D8—81no—
634D8—81no—
635D8—81no—
636M16—81no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—42no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4C2×D4×C8911yescharacteristic
655C4⋊C4C2×D4×C8911yescharacteristic
656C4⋊C4C2×D4×C8911yescharacteristic
657C4⋊C4C2×D4×C8911yescharacteristic
658C4⋊C4C2×D4×C8912yes—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C42—22no—
678C42—21no—
679C42C2×D4×C8911yescharacteristic
680C42C2×D4×C8911yescharacteristic
681C42C2×D4×C8911yescharacteristic
682C42C24×C8911yescharacteristic
683C23—21no—
684C23—21no—
685C23—22no—
686C23—21no—
687C23—41no—
688C23—82no—
689C23—82no—
690C23—82no—
691C23#120×C8911yescharacteristic
692Q8—21no—
693Q8—21no—
694Q8—41no—
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—81no—
699D4—21no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—42no—
706D4—42no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—81no—
716D4—81no—
717D4—81no—
718D4—82no—
719D4—81no—
720D4—81no—
721D4—82no—
722D4—82no—
723D4—82no—
724D4—82no—
725D4—82no—
726D4—82no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—82no—
746C2×C4—82no—
747C2×C4—82no—
748C2×C4—82no—
749C2×C4#120×C8911yescharacteristic
750C2×C4#120×C8911yescharacteristic
751C2×C4#120×C8911yescharacteristic
752C2×C4C22×D4×C8911yescharacteristic
753C2×C4C22×D4×C8911yescharacteristic
754C2×C4C22×D4×C8911yescharacteristic
755C8—22no—
756C8—41no—
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—164no—
780C22C2×#120×C8911yescharacteristic
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—41no—
786C4—42no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4#576×C8911yescharacteristic
793C4#576×C8911yescharacteristic
794C4#576×C8911yescharacteristic
795C4#577×C8911yescharacteristic
796C2—41no—
797C2—81no—
798C2—82no—
799C2—81no—
800C2—81no—
801C2—161no—
802C2C89×#300811yescharacteristic
803C2C89×#301211yescharacteristic
804C2C89×#301811yescharacteristic
subgroupG/H
center, socleC22×C89C2×#120
commutator, Frattini, cosocleC42C24×C89
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C89 ◁ C2×C42×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C89×#3546C2semidirect
2. C89×#3251C2semidirect
3. C89×#3214C2semidirect
4. C89×#3169C2semidirect
5. C89×#1650C2semidirect
6. C89×#1647C2semidirect
7. C89×#1642C2semidirect
8. C89×#1639C2semidirect
9. C89×#1628C2semidirect
10. C89×#1625C2semidirect
11. C89×#1621C2semidirect
12. C89×#1619C2semidirect
13. C89×#1557C2semidirect
14. C89×#1494C2semidirect
15. C89×#1492C2semidirect
32. #532×C89C22semidirect
34. #500×C89C22semidirect
39. #486×C89C22semidirect
41. #475×C89C22semidirect
48. #461×C89C22semidirect
49. #460×C89C22semidirect
52. #459×C89C22semidirect
56. #432×C89C22semidirect
57. #423×C89C22semidirect
58. C2×C4×C8×C89C22semidirect
59. #332×C89C22semidirect
60. #332×C89C22semidirect
63. Q8⋊C8×C89C22semidirect
64. Q8⋊C8×C89C22semidirect
69. D4⋊C8×C89C22semidirect
70. D4⋊C8×C89C22semidirect
393. #18704C89direct (N × H)
403. #3546C2×C89semidirect
404. #3251C2×C89semidirect
405. #3214C2×C89semidirect
406. #3169C2×C89semidirect
407. #1650C2×C89semidirect
408. #1647C2×C89semidirect
409. #1642C2×C89semidirect
410. #1639C2×C89semidirect
411. #1628C2×C89semidirect
412. #1625C2×C89semidirect
413. #1621C2×C89semidirect
414. #1619C2×C89semidirect
415. #1557C2×C89semidirect
416. #1494C2×C89semidirect
417. #1492C2×C89semidirect
418. C89#18704direct (N × H)
435. #532C22×C89semidirect
437. #500C22×C89semidirect
442. #486C22×C89semidirect
444. #475C22×C89semidirect
451. #461C22×C89semidirect
452. #460C22×C89semidirect
455. #459C22×C89semidirect
459. #432C22×C89semidirect
460. #423C22×C89semidirect
461. C2×C4×C8C22×C89semidirect
462. #332C22×C89semidirect
463. #332C22×C89semidirect
466. Q8⋊C8C22×C89semidirect
467. Q8⋊C8C22×C89semidirect
472. D4⋊C8C22×C89semidirect
473. D4⋊C8C22×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#35462
C89×#32512
C89×#32142
C89×#31692
C89×#16502
C89×#16472
C89×#16422
C89×#16392
C89×#16282
C89×#16252
C89×#16212
C89×#16192
C89×#15572
C89×#14942
C89×#14922
#1870489