Finite Group Databasebeta

← C89×#18705 #36396553

Subgroups — C89×#18705 #36396553

Order 22784.

938 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3546C211yesmaximal, characteristic
2C89×#3252C211yesmaximal, characteristic, complemented
3C89×#3235C211yesmaximal, characteristic, complemented
4C89×#3167C211yesmaximal, characteristic, complemented
5C89×#1654C211yesmaximal, characteristic, complemented
6C89×#1652C211yesmaximal, characteristic, complemented
7C89×#1641C211yesmaximal, characteristic, complemented
8C89×#1639C211yesmaximal, characteristic, complemented
9C89×#1638C211yesmaximal, characteristic, complemented
10C89×#1635C211yesmaximal, characteristic, complemented
11C89×#1631C211yesmaximal, characteristic, complemented
12C89×#1629C211yesmaximal, 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#533×C89C2211yescharacteristic, complemented
31#532×C89C2211yescharacteristic
32#532×C89C2211yescharacteristic
33#529×C89C2211yescharacteristic
34#501×C89—21no—
35#498×C89C2211yescharacteristic, complemented
36#492×C89C2211yescharacteristic
37#490×C89—21no—
38#487×C89C2211yescharacteristic, complemented
39#486×C89C2211yescharacteristic
40#482×C89—21no—
41#482×C89—21no—
42#479×C89—21no—
43#477×C89C2211yescharacteristic, complemented
44#476×C89C2211yescharacteristic
45#476×C89C2211yescharacteristic
46#476×C89C2211yescharacteristic, complemented
47#474×C89C2211yescharacteristic
48#474×C89C2211yescharacteristic, complemented
49#470×C89—21no—
50#468×C89—21no—
51#465×C89—22no—
52#464×C89—21no—
53#462×C89C2211yescharacteristic, complemented
54#461×C89C2211yescharacteristic
55C4×SD16×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—
75C22×D4×C89—21no—
76C22×D4×C89—21no—
77C2×Q16×C89—21no—
78C2×SD16×C89—22no—
79C2×SD16×C89—21no—
80C2×M16×C89—21no—
81C22×C8×C89—21no—
82C4⋊Q8×C89D411yescharacteristic
83C4⋊Q8×C89C2311yescharacteristic
84C4⋊Q8×C89C2311yescharacteristic
85C4⋊Q8×C89C2311yescharacteristic
86#127×C89—22no—
87#127×C89—21no—
88#127×C89D411yescharacteristic
89#127×C89C2311yescharacteristic
90#126×C89—22no—
91#126×C89—22no—
92#126×C89—21no—
93#125×C89—21no—
94#125×C89D411yescharacteristic
95#124×C89—22no—
96#124×C89—21no—
97#124×C89—21no—
98#124×C89—21no—
99#124×C89D411yescharacteristic
100#123×C89—22no—
101#123×C89—22no—
102#123×C89—21no—
103#123×C89—22no—
104C22⋊Q8×C89—22no—
105C22⋊Q8×C89—21no—
106C22⋊Q8×C89—21no—
107C22⋊Q8×C89—21no—
108C22⋊Q8×C89—21no—
109C22⋊Q8×C89D411yescharacteristic
110#121×C89—22no—
111#121×C89—22no—
112#121×C89—22no—
113#121×C89—22no—
114#121×C89—22no—
115#121×C89—21no—
116#121×C89—22no—
117#121×C89—21no—
118#121×C89—21no—
119#121×C89—21no—
120#121×C89—21no—
121#121×C89—21no—
122#121×C89D412yes—
123#121×C89D411yescharacteristic
124#121×C89D411yescharacteristic
125#121×C89D411yescharacteristic
126#120×C89—22no—
127#120×C89—22no—
128#120×C89—22no—
129#120×C89—22no—
130C4×Q8×C89—21no—
131C4×Q8×C89—21no—
132C4×Q8×C89—21no—
133C4×Q8×C89C2311yescharacteristic
134C4×D4×C89—22no—
135C4×D4×C89—21no—
136C4×D4×C89—21no—
137C4×D4×C89—21no—
138C4×D4×C89—21no—
139C4×D4×C89D412yes—
140C4×D4×C89C2311yescharacteristic
141C4×D4×C89C2311yescharacteristic
142C4×D4×C89C2311yescharacteristic
143#117×C89—21no—
144#117×C89—21no—
145#117×C89—21no—
146C2×C4⋊C4×C89—21no—
147C2×C22⋊C4×C89—22no—
148C2×C42×C89C2311yescharacteristic
149#107×C89—21no—
150#107×C89—21no—
151#107×C89—21no—
152#106×C89—22no—
153#106×C89—21no—
154#106×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—22no—
163#103×C89—21no—
164#103×C89—21no—
165#102×C89—22no—
166#102×C89—21no—
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—
185C2×Q8×C89—21no—
186C2×Q8×C89—21no—
187C2×Q8×C89—21no—
188C2×Q8×C89—21no—
189C2×Q8×C89C2×D411yescharacteristic
190C2×D4×C89—22no—
191C2×D4×C89—22no—
192C2×D4×C89—22no—
193C2×D4×C89—22no—
194C2×D4×C89—22no—
195C2×D4×C89—21no—
196C2×D4×C89—21no—
197C2×D4×C89—22no—
198C2×D4×C89—21no—
199C2×D4×C89—21no—
200C2×D4×C89—21no—
201C2×D4×C89—21no—
202C2×D4×C89—21no—
203C2×D4×C89—81no—
204C2×D4×C89—81no—
205C2×D4×C89—81no—
206C2×D4×C89—81no—
207C2×D4×C89C2×D411yescharacteristic
208C2×D4×C89C2×D411yescharacteristic
209C2×D4×C89C2×D411yescharacteristic
210C2×D4×C89C2×D412yes—
211C22×C4×C89—22no—
212C22×C4×C89—22no—
213C22×C4×C89—21no—
214C22×C4×C89—21no—
215C22×C4×C89—21no—
216C22×C4×C89—22no—
217C22×C4×C89C2×D411yescharacteristic
218C22×C4×C89C2×D411yescharacteristic
219C22×C4×C89C2×D411yescharacteristic
220Q16×C89—81no—
221SD16×C89—44no—
222SD16×C89—81no—
223M16×C89—81no—
224C2×C8×C89—21no—
225C2×C8×C89—21no—
226C2×C8×C89—21no—
227C2×C8×C89—21no—
228C2×C8×C89—21no—
229C2×C8×C89—21no—
230C2×C8×C89—42no—
231C4⋊C4×C89—22no—
232C4⋊C4×C89—22no—
233C4⋊C4×C89—21no—
234C4⋊C4×C89—21no—
235C4⋊C4×C89—21no—
236C4⋊C4×C89—21no—
237C4⋊C4×C89—21no—
238C4⋊C4×C89—21no—
239C4⋊C4×C89—21no—
240C4⋊C4×C89—21no—
241C4⋊C4×C89—21no—
242C4⋊C4×C89—21no—
243C4⋊C4×C89—41no—
244C4⋊C4×C89—41no—
245C4⋊C4×C89C2×D411yescharacteristic
246C4⋊C4×C89C2×D412yes—
247C4⋊C4×C89C2×D411yescharacteristic
248C4⋊C4×C89C2×D411yescharacteristic
249C4⋊C4×C89C2×D411yescharacteristic
250C22⋊C4×C89—22no—
251C22⋊C4×C89—22no—
252C22⋊C4×C89—22no—
253C22⋊C4×C89—22no—
254C22⋊C4×C89—22no—
255C22⋊C4×C89—21no—
256C22⋊C4×C89—21no—
257C22⋊C4×C89—21no—
258C22⋊C4×C89—21no—
259C22⋊C4×C89—21no—
260C22⋊C4×C89—21no—
261C22⋊C4×C89—22no—
262C22⋊C4×C89—22no—
263C22⋊C4×C89—21no—
264C22⋊C4×C89—21no—
265C22⋊C4×C89—21no—
266C22⋊C4×C89—41no—
267C42×C89—22no—
268C42×C89—21no—
269C42×C89—41no—
270C42×C89C2×D411yescharacteristic
271C42×C89C2×D411yescharacteristic
272C42×C89C2×D411yescharacteristic
273C42×C89C2411yescharacteristic
274C23×C89—21no—
275C23×C89—21no—
276C23×C89—22no—
277C23×C89—21no—
278C23×C89—82no—
279C23×C89—82no—
280C23×C89—82no—
281C23×C89#12011yescharacteristic
282Q8×C89—21no—
283Q8×C89—21no—
284Q8×C89—42no—
285Q8×C89—41no—
286Q8×C89—41no—
287Q8×C89—41no—
288Q8×C89—41no—
289Q8×C89—81no—
290D4×C89—21no—
291D4×C89—21no—
292D4×C89—21no—
293D4×C89—21no—
294D4×C89—21no—
295D4×C89—21no—
296D4×C89—42no—
297D4×C89—41no—
298D4×C89—41no—
299D4×C89—41no—
300D4×C89—41no—
301D4×C89—81no—
302D4×C89—81no—
303D4×C89—81no—
304D4×C89—82no—
305D4×C89—81no—
306D4×C89—81no—
307D4×C89—82no—
308D4×C89—82no—
309D4×C89—82no—
310D4×C89—82no—
311D4×C89—82no—
312C2×C4×C89—21no—
313C2×C4×C89—21no—
314C2×C4×C89—21no—
315C2×C4×C89—21no—
316C2×C4×C89—21no—
317C2×C4×C89—21no—
318C2×C4×C89—21no—
319C2×C4×C89—22no—
320C2×C4×C89—21no—
321C2×C4×C89—21no—
322C2×C4×C89—41no—
323C2×C4×C89—41no—
324C2×C4×C89—41no—
325C2×C4×C89—41no—
326C2×C4×C89—41no—
327C2×C4×C89—41no—
328C2×C4×C89—41no—
329C2×C4×C89—41no—
330C2×C4×C89—41no—
331C2×C4×C89—82no—
332C2×C4×C89—82no—
333C2×C4×C89—82no—
334C2×C4×C89#12011yescharacteristic
335C2×C4×C89#12011yescharacteristic
336C2×C4×C89#12011yescharacteristic
337C2×C4×C89C22×D411yescharacteristic
338C2×C4×C89C22×D411yescharacteristic
339C2×C4×C89C22×D411yescharacteristic
340C8×C89—22no—
341C8×C89—41no—
342C8×C89—41no—
343C8×C89—41no—
344C8×C89—41no—
345C8×C89—41no—
346C22×C89—21no—
347C22×C89—21no—
348C22×C89—21no—
349C22×C89—41no—
350C22×C89—41no—
351C22×C89—42no—
352C22×C89—41no—
353C22×C89—41no—
354C22×C89—41no—
355C22×C89—42no—
356C22×C89—41no—
357C22×C89—42no—
358C22×C89—41no—
359C22×C89—41no—
360C22×C89—41no—
361C22×C89—164no—
362C22×C89C2×#12011yescharacteristic
363C4×C89—21no—
364C4×C89—21no—
365C4×C89—21no—
366C4×C89—21no—
367C4×C89—41no—
368C4×C89—42no—
369C4×C89—41no—
370C4×C89—41no—
371C4×C89—41no—
372C4×C89—41no—
373C4×C89—81no—
374C4×C89—81no—
375C4×C89#57611yescharacteristic
376C4×C89#57711yescharacteristic
377C4×C89#57711yescharacteristic
378C4×C89#57711yescharacteristic
379#18705C8911yesmaximal, characteristic, direct product factor, Sylow
380C2×C89—41no—
381C2×C89—81no—
382C2×C89—82no—
383C2×C89—81no—
384C2×C89—81no—
385C2×C89#300911yescharacteristic
386C2×C89#301211yescharacteristic
387C2×C89#301811yescharacteristic
388#3546C2×C8911yescharacteristic
389#3252C2×C8911yescharacteristic, complemented
390#3235C2×C8911yescharacteristic, complemented
391#3167C2×C8911yescharacteristic, complemented
392#1654C2×C8911yescharacteristic, complemented
393#1652C2×C8911yescharacteristic, complemented
394#1641C2×C8911yescharacteristic, complemented
395#1639C2×C8911yescharacteristic, complemented
396#1638C2×C8911yescharacteristic, complemented
397#1635C2×C8911yescharacteristic, complemented
398#1631C2×C8911yescharacteristic, complemented
399#1629C2×C8911yescharacteristic, complemented
400#1557C2×C8911yescharacteristic, complemented
401#1494C2×C8911yescharacteristic, complemented
402#1492C2×C8911yescharacteristic, complemented
403C89#1870511yescharacteristic, direct product factor, Sylow
404#560—22no—
405#556C22×C8911yescharacteristic
406#553—21no—
407#550—21no—
408#550C22×C8911yescharacteristic
409#547C22×C8911yescharacteristic
410#546—21no—
411#546—21no—
412D42C22×C8911yescharacteristic
413#542—21no—
414#538—22no—
415#537—21no—
416#535—21no—
417#535—21no—
418#533C22×C8911yescharacteristic, complemented
419#532C22×C8911yescharacteristic
420#532C22×C8911yescharacteristic
421#529C22×C8911yescharacteristic
422#501—21no—
423#498C22×C8911yescharacteristic, complemented
424#492C22×C8911yescharacteristic
425#490—21no—
426#487C22×C8911yescharacteristic, complemented
427#486C22×C8911yescharacteristic
428#482—21no—
429#482—21no—
430#479—21no—
431#477C22×C8911yescharacteristic, complemented
432#476C22×C8911yescharacteristic
433#476C22×C8911yescharacteristic
434#476C22×C8911yescharacteristic, complemented
435#474C22×C8911yescharacteristic
436#474C22×C8911yescharacteristic, complemented
437#470—21no—
438#468—21no—
439#465—22no—
440#464—21no—
441#462C22×C8911yescharacteristic, complemented
442#461C22×C8911yescharacteristic
443C4×SD16—22no—
444#432C22×C8911yescharacteristic, complemented
445#423C22×C8911yescharacteristic, complemented
446C2×C4×C8C22×C8911yescharacteristic, complemented
447#332C22×C8911yescharacteristic, complemented
448#332C22×C8911yescharacteristic, complemented
449#331C22×C8911yescharacteristic
450#331C22×C8911yescharacteristic
451Q8⋊C8C22×C8911yescharacteristic, complemented
452Q8⋊C8C22×C8911yescharacteristic, complemented
453D4⋊C8C22×C8911yescharacteristic
454D4⋊C8C22×C8911yescharacteristic
455D4⋊C8C22×C8911yescharacteristic
456D4⋊C8C22×C8911yescharacteristic
457D4⋊C8C22×C8911yescharacteristic, complemented
458D4⋊C8C22×C8911yescharacteristic, complemented
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C22×D4—21no—
464C22×D4—21no—
465C2×Q16—21no—
466C2×SD16—22no—
467C2×SD16—21no—
468C2×M16—21no—
469C22×C8—21no—
470C4⋊Q8D4×C8911yescharacteristic
471C4⋊Q8C23×C8911yescharacteristic
472C4⋊Q8C23×C8911yescharacteristic
473C4⋊Q8C23×C8911yescharacteristic
474#127—22no—
475#127—21no—
476#127D4×C8911yescharacteristic
477#127C23×C8911yescharacteristic
478#126—22no—
479#126—22no—
480#126—21no—
481#125—21no—
482#125D4×C8911yescharacteristic
483#124—22no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124D4×C8911yescharacteristic
488#123—22no—
489#123—22no—
490#123—21no—
491#123—22no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C8911yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—21no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C8911yescharacteristic
511#121D4×C8911yescharacteristic
512#121D4×C8911yescharacteristic
513#121D4×C8912yes—
514#120—22no—
515#120—22no—
516#120—22no—
517#120—22no—
518C4×Q8—21no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8C23×C8911yescharacteristic
522C4×D4—22no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4D4×C8912yes—
528C4×D4C23×C8911yescharacteristic
529C4×D4C23×C8911yescharacteristic
530C4×D4C23×C8911yescharacteristic
531#117—21no—
532#117—21no—
533#117—21no—
534C2×C4⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C42C23×C8911yescharacteristic
537#107—21no—
538#107—21no—
539#107—21no—
540#106—22no—
541#106—21no—
542#106—21no—
543#106—21no—
544C4⋊C8—21no—
545C4⋊C8C23×C8911yescharacteristic
546C4⋊C8C23×C8911yescharacteristic
547C4⋊C8C23×C8911yescharacteristic
548C4⋊C8C23×C8911yescharacteristic
549#103—21no—
550#103—22no—
551#103—21no—
552#103—21no—
553#102—22no—
554#102—21no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559C22⋊C8—21no—
560#97—21no—
561C4×C8—21no—
562C4×C8C23×C8911yescharacteristic
563C4×C8C23×C8911yescharacteristic
564C24—22no—
565#41—81no—
566#41—81no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C8911yescharacteristic
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4C2×D4×C8911yescharacteristic
596C2×D4C2×D4×C8911yescharacteristic
597C2×D4C2×D4×C8911yescharacteristic
598C2×D4C2×D4×C8912yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4C2×D4×C8911yescharacteristic
606C22×C4C2×D4×C8911yescharacteristic
607C22×C4C2×D4×C8911yescharacteristic
608Q16—81no—
609SD16—44no—
610SD16—81no—
611M16—81no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—42no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4C2×D4×C8911yescharacteristic
634C4⋊C4C2×D4×C8912yes—
635C4⋊C4C2×D4×C8911yescharacteristic
636C4⋊C4C2×D4×C8911yescharacteristic
637C4⋊C4C2×D4×C8911yescharacteristic
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C42—22no—
656C42—21no—
657C42—41no—
658C42C2×D4×C8911yescharacteristic
659C42C2×D4×C8911yescharacteristic
660C42C2×D4×C8911yescharacteristic
661C42C24×C8911yescharacteristic
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23#120×C8911yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—42no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—81no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—82no—
693D4—81no—
694D4—81no—
695D4—82no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4#120×C8911yescharacteristic
723C2×C4#120×C8911yescharacteristic
724C2×C4#120×C8911yescharacteristic
725C2×C4C22×D4×C8911yescharacteristic
726C2×C4C22×D4×C8911yescharacteristic
727C2×C4C22×D4×C8911yescharacteristic
728C8—22no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—164no—
750C22C2×#120×C8911yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—42no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4#576×C8911yescharacteristic
764C4#577×C8911yescharacteristic
765C4#577×C8911yescharacteristic
766C4#577×C8911yescharacteristic
767C2—41no—
768C2—81no—
769C2—82no—
770C2—81no—
771C2—81no—
772C2C89×#300911yescharacteristic
773C2C89×#301211yescharacteristic
774C2C89×#301811yescharacteristic
subgroupG/H
center, socleC22×C89C2×#120
commutator, Frattini, cosocleC42C24×C89
prime radicalC89×#3546C2
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
2. C89×#3252C2semidirect
3. C89×#3235C2semidirect
4. C89×#3167C2semidirect
5. C89×#1654C2semidirect
6. C89×#1652C2semidirect
7. C89×#1641C2semidirect
8. C89×#1639C2semidirect
9. C89×#1638C2semidirect
10. C89×#1635C2semidirect
11. C89×#1631C2semidirect
12. C89×#1629C2semidirect
13. C89×#1557C2semidirect
14. C89×#1494C2semidirect
15. C89×#1492C2semidirect
30. #533×C89C22semidirect
35. #498×C89C22semidirect
38. #487×C89C22semidirect
43. #477×C89C22semidirect
46. #476×C89C22semidirect
48. #474×C89C22semidirect
53. #462×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
379. #18705C89direct (N × H)
389. #3252C2×C89semidirect
390. #3235C2×C89semidirect
391. #3167C2×C89semidirect
392. #1654C2×C89semidirect
393. #1652C2×C89semidirect
394. #1641C2×C89semidirect
395. #1639C2×C89semidirect
396. #1638C2×C89semidirect
397. #1635C2×C89semidirect
398. #1631C2×C89semidirect
399. #1629C2×C89semidirect
400. #1557C2×C89semidirect
401. #1494C2×C89semidirect
402. #1492C2×C89semidirect
403. C89#18705direct (N × H)
418. #533C22×C89semidirect
423. #498C22×C89semidirect
426. #487C22×C89semidirect
431. #477C22×C89semidirect
434. #476C22×C89semidirect
436. #474C22×C89semidirect
441. #462C22×C89semidirect
444. #432C22×C89semidirect
445. #423C22×C89semidirect
446. C2×C4×C8C22×C89semidirect
447. #332C22×C89semidirect
448. #332C22×C89semidirect
451. Q8⋊C8C22×C89semidirect
452. Q8⋊C8C22×C89semidirect
457. D4⋊C8C22×C89semidirect
458. 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×#32522
C89×#32352
C89×#31672
C89×#16542
C89×#16522
C89×#16412
C89×#16392
C89×#16382
C89×#16352
C89×#16312
C89×#16292
C89×#15572
C89×#14942
C89×#14922
#1870589