Finite Group Databasebeta

← C89×#18974 #36396822

Subgroups — C89×#18974 #36396822

Order 22784.

930 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3546C211yesmaximal, characteristic
2C89×#3254C211yesmaximal, characteristic, complemented
3C89×#3248C211yesmaximal, characteristic, complemented
4C89×#3228C211yesmaximal, characteristic, complemented
5C89×#1654C211yesmaximal, characteristic, complemented
6C89×#1652C211yesmaximal, characteristic, complemented
7C89×#1650C211yesmaximal, characteristic, complemented
8C89×#1647C211yesmaximal, characteristic, complemented
9C89×#1642C211yesmaximal, characteristic, complemented
10C89×#1641C211yesmaximal, characteristic, complemented
11C89×#1639C211yesmaximal, characteristic, complemented
12C89×#1639C211yesmaximal, characteristic, complemented
13C89×#1547C211yesmaximal, characteristic, complemented
14C89×#1495C211yesmaximal, characteristic, complemented
15C89×#1480C211yesmaximal, 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#500×C89C2211yescharacteristic, complemented
35#498×C89C2211yescharacteristic, complemented
36#486×C89C2211yescharacteristic
37#486×C89C2211yescharacteristic
38#482×C89—22no—
39#479×C89—21no—
40#478×C89—22no—
41#477×C89—21no—
42#475×C89C2211yescharacteristic, complemented
43#474×C89C2211yescharacteristic
44#474×C89C2211yescharacteristic
45#474×C89C2211yescharacteristic, complemented
46#468×C89—21no—
47#468×C89—21no—
48#467×C89—21no—
49#465×C89—21no—
50#464×C89—21no—
51#462×C89C2211yescharacteristic, complemented
52#461×C89C2211yescharacteristic
53#461×C89C2211yescharacteristic
54#461×C89C2211yescharacteristic, complemented
55#460×C89—21no—
56#431×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—21no—
79C2×SD16×C89—21no—
80C2×SD16×C89—21no—
81C2×M16×C89—21no—
82C22×C8×C89—21no—
83C4⋊Q8×C89D411yescharacteristic
84C4⋊Q8×C89C2311yescharacteristic
85C4⋊Q8×C89C2311yescharacteristic
86C4⋊Q8×C89C2311yescharacteristic
87#127×C89—22no—
88#127×C89—21no—
89#127×C89D411yescharacteristic
90#127×C89C2311yescharacteristic
91#126×C89—22no—
92#126×C89—22no—
93#126×C89—21no—
94#125×C89—21no—
95#125×C89D411yescharacteristic
96#124×C89—22no—
97#124×C89—21no—
98#124×C89—21no—
99#124×C89—21no—
100#124×C89D411yescharacteristic
101#123×C89—22no—
102#123×C89—22no—
103#123×C89—21no—
104#123×C89—22no—
105C22⋊Q8×C89—22no—
106C22⋊Q8×C89—21no—
107C22⋊Q8×C89—21no—
108C22⋊Q8×C89—21no—
109C22⋊Q8×C89—21no—
110C22⋊Q8×C89D411yescharacteristic
111#121×C89—22no—
112#121×C89—22no—
113#121×C89—22no—
114#121×C89—22no—
115#121×C89—22no—
116#121×C89—21no—
117#121×C89—22no—
118#121×C89—21no—
119#121×C89—21no—
120#121×C89—21no—
121#121×C89—21no—
122#121×C89—21no—
123#121×C89D411yescharacteristic
124#121×C89D411yescharacteristic
125#121×C89D411yescharacteristic
126#121×C89D412yes—
127#120×C89—22no—
128#120×C89—22no—
129#120×C89—22no—
130#120×C89—22no—
131C4×Q8×C89—21no—
132C4×Q8×C89—21no—
133C4×Q8×C89—21no—
134C4×Q8×C89C2311yescharacteristic
135C4×D4×C89—22no—
136C4×D4×C89—21no—
137C4×D4×C89—21no—
138C4×D4×C89—21no—
139C4×D4×C89—21no—
140C4×D4×C89D412yes—
141C4×D4×C89C2311yescharacteristic
142C4×D4×C89C2311yescharacteristic
143C4×D4×C89C2311yescharacteristic
144#117×C89—21no—
145#117×C89—21no—
146#117×C89—21no—
147C2×C4⋊C4×C89—21no—
148C2×C22⋊C4×C89—22no—
149C2×C42×C89C2311yescharacteristic
150#107×C89—21no—
151#107×C89—21no—
152#107×C89—21no—
153#107×C89—22no—
154#106×C89—21no—
155#106×C89—22no—
156C4⋊C8×C89—21no—
157C4⋊C8×C89—21no—
158C4⋊C8×C89—21no—
159C4⋊C8×C89C2311yescharacteristic
160C4⋊C8×C89C2311yescharacteristic
161C4⋊C8×C89C2311yescharacteristic
162C4⋊C8×C89C2311yescharacteristic
163#103×C89—21no—
164#103×C89—21no—
165#103×C89—21no—
166#103×C89—21no—
167#103×C89—21no—
168#102×C89—21no—
169#102×C89—21no—
170#102×C89—21no—
171#102×C89—22no—
172#102×C89—22no—
173C22⋊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—81no—
222SD16×C89—81no—
223SD16×C89—81no—
224M16×C89—81no—
225C2×C8×C89—21no—
226C2×C8×C89—21no—
227C2×C8×C89—21no—
228C2×C8×C89—21no—
229C2×C8×C89—21no—
230C2×C8×C89—21no—
231C2×C8×C89—81no—
232C4⋊C4×C89—22no—
233C4⋊C4×C89—22no—
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—21no—
244C4⋊C4×C89—41no—
245C4⋊C4×C89—41no—
246C4⋊C4×C89C2×D411yescharacteristic
247C4⋊C4×C89C2×D411yescharacteristic
248C4⋊C4×C89C2×D411yescharacteristic
249C4⋊C4×C89C2×D411yescharacteristic
250C4⋊C4×C89C2×D412yes—
251C22⋊C4×C89—22no—
252C22⋊C4×C89—22no—
253C22⋊C4×C89—22no—
254C22⋊C4×C89—22no—
255C22⋊C4×C89—22no—
256C22⋊C4×C89—21no—
257C22⋊C4×C89—21no—
258C22⋊C4×C89—21no—
259C22⋊C4×C89—21no—
260C22⋊C4×C89—21no—
261C22⋊C4×C89—21no—
262C22⋊C4×C89—22no—
263C22⋊C4×C89—22no—
264C22⋊C4×C89—21no—
265C22⋊C4×C89—21no—
266C22⋊C4×C89—21no—
267C22⋊C4×C89—41no—
268C42×C89—22no—
269C42×C89—21no—
270C42×C89—41no—
271C42×C89C2×D411yescharacteristic
272C42×C89C2×D411yescharacteristic
273C42×C89C2×D411yescharacteristic
274C42×C89C2411yescharacteristic
275C23×C89—21no—
276C23×C89—21no—
277C23×C89—22no—
278C23×C89—21no—
279C23×C89—82no—
280C23×C89—82no—
281C23×C89—82no—
282C23×C89#12011yescharacteristic
283Q8×C89—21no—
284Q8×C89—21no—
285Q8×C89—41no—
286Q8×C89—41no—
287Q8×C89—41no—
288Q8×C89—41no—
289Q8×C89—41no—
290Q8×C89—41no—
291Q8×C89—81no—
292D4×C89—21no—
293D4×C89—21no—
294D4×C89—21no—
295D4×C89—21no—
296D4×C89—21no—
297D4×C89—21no—
298D4×C89—42no—
299D4×C89—41no—
300D4×C89—41no—
301D4×C89—41no—
302D4×C89—41no—
303D4×C89—81no—
304D4×C89—81no—
305D4×C89—81no—
306D4×C89—81no—
307D4×C89—81no—
308D4×C89—82no—
309D4×C89—82no—
310D4×C89—82no—
311D4×C89—82no—
312D4×C89—82no—
313D4×C89—82no—
314C2×C4×C89—21no—
315C2×C4×C89—21no—
316C2×C4×C89—21no—
317C2×C4×C89—21no—
318C2×C4×C89—21no—
319C2×C4×C89—21no—
320C2×C4×C89—21no—
321C2×C4×C89—22no—
322C2×C4×C89—21no—
323C2×C4×C89—21no—
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—41no—
332C2×C4×C89—41no—
333C2×C4×C89—82no—
334C2×C4×C89—82no—
335C2×C4×C89—82no—
336C2×C4×C89#12011yescharacteristic
337C2×C4×C89#12011yescharacteristic
338C2×C4×C89#12011yescharacteristic
339C2×C4×C89C22×D411yescharacteristic
340C2×C4×C89C22×D411yescharacteristic
341C2×C4×C89C22×D411yescharacteristic
342C8×C89—41no—
343C8×C89—41no—
344C8×C89—41no—
345C8×C89—41no—
346C8×C89—41no—
347C8×C89—41no—
348C22×C89—21no—
349C22×C89—21no—
350C22×C89—21no—
351C22×C89—41no—
352C22×C89—41no—
353C22×C89—41no—
354C22×C89—41no—
355C22×C89—42no—
356C22×C89—42no—
357C22×C89—41no—
358C22×C89—41no—
359C22×C89—42no—
360C22×C89—41no—
361C22×C89—41no—
362C22×C89—41no—
363C22×C89—164no—
364C22×C89C2×#12011yescharacteristic
365C4×C89—21no—
366C4×C89—21no—
367C4×C89—21no—
368C4×C89—21no—
369C4×C89—41no—
370C4×C89—41no—
371C4×C89—41no—
372C4×C89—41no—
373C4×C89—42no—
374C4×C89—41no—
375C4×C89—81no—
376C4×C89—81no—
377C4×C89#57611yescharacteristic
378C4×C89#57611yescharacteristic
379C4×C89#57711yescharacteristic
380C4×C89#57711yescharacteristic
381#18974C8911yesmaximal, characteristic, direct product factor, Sylow
382C2×C89—41no—
383C2×C89—81no—
384C2×C89—82no—
385C2×C89—81no—
386C2×C89—81no—
387C2×C89#301211yescharacteristic
388C2×C89#301211yescharacteristic
389C2×C89#302211yescharacteristic
390#3546C2×C8911yescharacteristic
391#3254C2×C8911yescharacteristic, complemented
392#3248C2×C8911yescharacteristic, complemented
393#3228C2×C8911yescharacteristic, complemented
394#1654C2×C8911yescharacteristic, complemented
395#1652C2×C8911yescharacteristic, complemented
396#1650C2×C8911yescharacteristic, complemented
397#1647C2×C8911yescharacteristic, complemented
398#1642C2×C8911yescharacteristic, complemented
399#1641C2×C8911yescharacteristic, complemented
400#1639C2×C8911yescharacteristic, complemented
401#1639C2×C8911yescharacteristic, complemented
402#1547C2×C8911yescharacteristic, complemented
403#1495C2×C8911yescharacteristic, complemented
404#1480C2×C8911yescharacteristic, complemented
405C89#1897411yescharacteristic, direct product factor, Sylow
406#560—22no—
407#556C22×C8911yescharacteristic
408#553—21no—
409#550—21no—
410#550C22×C8911yescharacteristic
411#547C22×C8911yescharacteristic
412#546—21no—
413#546—21no—
414D42C22×C8911yescharacteristic
415#542—21no—
416#538—22no—
417#537—21no—
418#535—21no—
419#535—21no—
420#533C22×C8911yescharacteristic, complemented
421#532C22×C8911yescharacteristic
422#532C22×C8911yescharacteristic
423#529C22×C8911yescharacteristic
424#500C22×C8911yescharacteristic, complemented
425#498C22×C8911yescharacteristic, complemented
426#486C22×C8911yescharacteristic
427#486C22×C8911yescharacteristic
428#482—22no—
429#479—21no—
430#478—22no—
431#477—21no—
432#475C22×C8911yescharacteristic, complemented
433#474C22×C8911yescharacteristic
434#474C22×C8911yescharacteristic
435#474C22×C8911yescharacteristic, complemented
436#468—21no—
437#468—21no—
438#467—21no—
439#465—21no—
440#464—21no—
441#462C22×C8911yescharacteristic, complemented
442#461C22×C8911yescharacteristic
443#461C22×C8911yescharacteristic
444#461C22×C8911yescharacteristic, complemented
445#460—21no—
446#431C22×C8911yescharacteristic, complemented
447#423C22×C8911yescharacteristic, complemented
448C2×C4⋊C8C22×C8911yescharacteristic, complemented
449#332C22×C8911yescharacteristic, complemented
450#332C22×C8911yescharacteristic, complemented
451#331C22×C8911yescharacteristic
452#331C22×C8911yescharacteristic
453Q8⋊C8C22×C8911yescharacteristic, complemented
454Q8⋊C8C22×C8911yescharacteristic, complemented
455D4⋊C8C22×C8911yescharacteristic
456D4⋊C8C22×C8911yescharacteristic
457D4⋊C8C22×C8911yescharacteristic
458D4⋊C8C22×C8911yescharacteristic
459D4⋊C8C22×C8911yescharacteristic, complemented
460D4⋊C8C22×C8911yescharacteristic, complemented
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C22×D4—21no—
466C22×D4—21no—
467C2×Q16—21no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×M16—21no—
472C22×C8—21no—
473C4⋊Q8D4×C8911yescharacteristic
474C4⋊Q8C23×C8911yescharacteristic
475C4⋊Q8C23×C8911yescharacteristic
476C4⋊Q8C23×C8911yescharacteristic
477#127—22no—
478#127—21no—
479#127D4×C8911yescharacteristic
480#127C23×C8911yescharacteristic
481#126—22no—
482#126—22no—
483#126—21no—
484#125—21no—
485#125D4×C8911yescharacteristic
486#124—22no—
487#124—21no—
488#124—21no—
489#124—21no—
490#124D4×C8911yescharacteristic
491#123—22no—
492#123—22no—
493#123—21no—
494#123—22no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8D4×C8911yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—21no—
507#121—22no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121D4×C8911yescharacteristic
514#121D4×C8911yescharacteristic
515#121D4×C8911yescharacteristic
516#121D4×C8912yes—
517#120—22no—
518#120—22no—
519#120—22no—
520#120—22no—
521C4×Q8—21no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8C23×C8911yescharacteristic
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4D4×C8912yes—
531C4×D4C23×C8911yescharacteristic
532C4×D4C23×C8911yescharacteristic
533C4×D4C23×C8911yescharacteristic
534#117—21no—
535#117—21no—
536#117—21no—
537C2×C4⋊C4—21no—
538C2×C22⋊C4—22no—
539C2×C42C23×C8911yescharacteristic
540#107—21no—
541#107—21no—
542#107—21no—
543#107—22no—
544#106—21no—
545#106—22no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549C4⋊C8C23×C8911yescharacteristic
550C4⋊C8C23×C8911yescharacteristic
551C4⋊C8C23×C8911yescharacteristic
552C4⋊C8C23×C8911yescharacteristic
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—22no—
562#102—22no—
563C22⋊C8—21no—
564C4×C8C23×C8911yescharacteristic
565C4×C8C23×C8911yescharacteristic
566C24—22no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573#41—81no—
574#41—81no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C2×D4×C8911yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4C2×D4×C8911yescharacteristic
598C2×D4C2×D4×C8911yescharacteristic
599C2×D4C2×D4×C8911yescharacteristic
600C2×D4C2×D4×C8912yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4C2×D4×C8911yescharacteristic
608C22×C4C2×D4×C8911yescharacteristic
609C22×C4C2×D4×C8911yescharacteristic
610Q16—81no—
611SD16—81no—
612SD16—81no—
613SD16—81no—
614M16—81no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—81no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4C2×D4×C8911yescharacteristic
637C4⋊C4C2×D4×C8911yescharacteristic
638C4⋊C4C2×D4×C8911yescharacteristic
639C4⋊C4C2×D4×C8911yescharacteristic
640C4⋊C4C2×D4×C8912yes—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—41no—
658C42—22no—
659C42—21no—
660C42—41no—
661C42C2×D4×C8911yescharacteristic
662C42C2×D4×C8911yescharacteristic
663C42C2×D4×C8911yescharacteristic
664C42C24×C8911yescharacteristic
665C23—21no—
666C23—21no—
667C23—22no—
668C23—21no—
669C23—82no—
670C23—82no—
671C23—82no—
672C23#120×C8911yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—81no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—81no—
698D4—82no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4#120×C8911yescharacteristic
727C2×C4#120×C8911yescharacteristic
728C2×C4#120×C8911yescharacteristic
729C2×C4C22×D4×C8911yescharacteristic
730C2×C4C22×D4×C8911yescharacteristic
731C2×C4C22×D4×C8911yescharacteristic
732C8—41no—
733C8—41no—
734C8—41no—
735C8—41no—
736C8—41no—
737C8—41no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—164no—
754C22C2×#120×C8911yescharacteristic
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—41no—
765C4—81no—
766C4—81no—
767C4#576×C8911yescharacteristic
768C4#576×C8911yescharacteristic
769C4#577×C8911yescharacteristic
770C4#577×C8911yescharacteristic
771C2—41no—
772C2—81no—
773C2—82no—
774C2—81no—
775C2—81no—
776C2C89×#301211yescharacteristic
777C2C89×#301211yescharacteristic
778C2C89×#302211yescharacteristic
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×#3254C2semidirect
3. C89×#3248C2semidirect
4. C89×#3228C2semidirect
5. C89×#1654C2semidirect
6. C89×#1652C2semidirect
7. C89×#1650C2semidirect
8. C89×#1647C2semidirect
9. C89×#1642C2semidirect
10. C89×#1641C2semidirect
11. C89×#1639C2semidirect
12. C89×#1639C2semidirect
13. C89×#1547C2semidirect
14. C89×#1495C2semidirect
15. C89×#1480C2semidirect
30. #533×C89C22semidirect
34. #500×C89C22semidirect
35. #498×C89C22semidirect
42. #475×C89C22semidirect
45. #474×C89C22semidirect
51. #462×C89C22semidirect
54. #461×C89C22semidirect
56. #431×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
381. #18974C89direct (N × H)
391. #3254C2×C89semidirect
392. #3248C2×C89semidirect
393. #3228C2×C89semidirect
394. #1654C2×C89semidirect
395. #1652C2×C89semidirect
396. #1650C2×C89semidirect
397. #1647C2×C89semidirect
398. #1642C2×C89semidirect
399. #1641C2×C89semidirect
400. #1639C2×C89semidirect
401. #1639C2×C89semidirect
402. #1547C2×C89semidirect
403. #1495C2×C89semidirect
404. #1480C2×C89semidirect
405. C89#18974direct (N × H)
420. #533C22×C89semidirect
424. #500C22×C89semidirect
425. #498C22×C89semidirect
432. #475C22×C89semidirect
435. #474C22×C89semidirect
441. #462C22×C89semidirect
444. #461C22×C89semidirect
446. #431C22×C89semidirect
447. #423C22×C89semidirect
448. C2×C4⋊C8C22×C89semidirect
449. #332C22×C89semidirect
450. #332C22×C89semidirect
453. Q8⋊C8C22×C89semidirect
454. Q8⋊C8C22×C89semidirect
459. D4⋊C8C22×C89semidirect
460. 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×#32542
C89×#32482
C89×#32282
C89×#16542
C89×#16522
C89×#16502
C89×#16472
C89×#16422
C89×#16412
C89×#16392
C89×#15472
C89×#14952
C89×#14802
#1897489