Finite Group Databasebeta

← C89×#25195 #36403043

Subgroups — C89×#25195 #36403043

Order 22784.

1014 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3063C211yesmaximal, characteristic, complemented
2C89×#3046C211yesmaximal, characteristic, complemented
3C2×#455×C89C211yesmaximal, characteristic, complemented
4C89×#3012C211yesmaximal, characteristic
5C2×#444×C89C211yesmaximal, characteristic, complemented
6C89×#2897C211yesmaximal, characteristic, complemented
7C89×#2063C211yesmaximal, characteristic, complemented
8C89×#2052C211yesmaximal, characteristic, complemented
9C89×#2039C211yesmaximal, characteristic, complemented
10C89×#2003C211yesmaximal, characteristic, complemented
11C89×#1959C211yesmaximal, characteristic, complemented
12C89×#1938C211yesmaximal, characteristic, complemented
13C89×#1908C211yesmaximal, characteristic, complemented
14C89×#1907C211yesmaximal, characteristic, complemented
15C89×#1859C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C89C2211yescharacteristic
17C2×#137×C89C2211yescharacteristic
18C2×#137×C89C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C89C2211yescharacteristic
20C2×#135×C89C2211yescharacteristic
21C2×#131×C89C2211yescharacteristic
22C2×#131×C89C2211yescharacteristic, complemented
23#537×C89C2211yescharacteristic
24#536×C89C2211yescharacteristic, complemented
25C2×#124×C89C2211yescharacteristic
26#520×C89C2211yescharacteristic
27#470×C89—21no—
28#468×C89—21no—
29#467×C89—21no—
30#465×C89—21no—
31#464×C89—21no—
32#463×C89—21no—
33#462×C89—21no—
34#461×C89—21no—
35#455×C89—24no—
36#452×C89—21no—
37#450×C89—21no—
38#449×C89—21no—
39#447×C89—21no—
40#444×C89—24no—
41C2×#108×C89C2211yescharacteristic, complemented
42#428×C89C2211yescharacteristic, complemented
43#424×C89C2211yescharacteristic, complemented
44C2×#104×C89C2211yescharacteristic
45C2×#104×C89C2211yescharacteristic
46C2×#104×C89C2211yescharacteristic, complemented
47#418×C89—21no—
48#418×C89C2211yescharacteristic
49#417×C89—21no—
50#417×C89C2211yescharacteristic
51#417×C89C2211yescharacteristic
52#417×C89C2211yescharacteristic, complemented
53#416×C89—21no—
54#416×C89C2211yescharacteristic
55C2×#103×C89C2211yescharacteristic, complemented
56C2×#103×C89C2211yescharacteristic, complemented
57C2×#102×C89—21no—
58C2×#102×C89C2211yescharacteristic
59C2×#102×C89C2211yescharacteristic
60C2×#101×C89C2211yescharacteristic, complemented
61C2×#100×C89C2211yescharacteristic
62#408×C89C2211yescharacteristic
63C2×#97×C89C2211yescharacteristic, complemented
64#384×C89C2211yescharacteristic, complemented
65#343×C89C2211yescharacteristic, complemented
66#343×C89C2211yescharacteristic, complemented
67#341×C89C2211yescharacteristic, complemented
68#339×C89C2211yescharacteristic, complemented
69H(5,𝔽2)×C89—22no—
70H(5,𝔽2)×C89—22no—
71H(5,𝔽2)×C89—22no—
72H(5,𝔽2)×C89—41no—
73C2×#41×C89—21no—
74C2×#41×C89—21no—
75C2×#41×C89C2311yescharacteristic
76C2×#41×C89C2311yescharacteristic
77C2×#41×C89C2311yescharacteristic
78C22×Q8×C89C2311yescharacteristic
79C22×D4×C89—21no—
80C22×D4×C89—21no—
81C22×D4×C89—41no—
82C22×D4×C89C2311yescharacteristic
83#137×C89—22no—
84#137×C89—22no—
85#137×C89—22no—
86#137×C89—41no—
87AGL(1,ℤ/8)×C89—22no—
88AGL(1,ℤ/8)×C89—41no—
89#135×C89—22no—
90#135×C89—22no—
91C2×Q16×C89—21no—
92C2×Q16×C89—21no—
93C2×Q16×C89D411yescharacteristic
94C2×SD16×C89—21no—
95C2×SD16×C89—21no—
96C2×SD16×C89—21no—
97C2×SD16×C89D411yescharacteristic
98C2×SD16×C89D411yescharacteristic
99C2×D8×C89—21no—
100C2×D8×C89D411yescharacteristic
101#131×C89—22no—
102#131×C89—22no—
103#131×C89—41no—
104#131×C89—41no—
105C2×M16×C89—21no—
106C2×M16×C89—21no—
107C2×M16×C89C2311yescharacteristic
108C2×M16×C89C2311yescharacteristic
109C2×M16×C89C2311yescharacteristic
110C2×M16×C89C2311yescharacteristic
111C22×C8×C89—21no—
112C22×C8×C89—21no—
113C22×C8×C89C2311yescharacteristic
114C22×C8×C89C2311yescharacteristic
115C4⋊Q8×C89—21no—
116#124×C89—21no—
117#124×C89—22no—
118#124×C89—22no—
119#123×C89—41no—
120C22⋊Q8×C89—21no—
121C22⋊Q8×C89—21no—
122C22⋊Q8×C89—21no—
123C22⋊Q8×C89—21no—
124#121×C89—21no—
125#121×C89—21no—
126#121×C89—41no—
127C4×Q8×C89—21no—
128C4×D4×C89—21no—
129C4×D4×C89—41no—
130#117×C89—21no—
131#117×C89C2311yescharacteristic
132C2×C4⋊C4×C89—21no—
133C2×C4⋊C4×C89—41no—
134C2×C4⋊C4×C89C2311yescharacteristic
135C2×C4⋊C4×C89C2311yescharacteristic
136C2×C22⋊C4×C89—41no—
137C2×C42×C89C2311yescharacteristic
138#108×C89—22no—
139#107×C89—21no—
140#106×C89—21no—
141C4⋊C8×C89—21no—
142C4⋊C8×C89—21no—
143#104×C89—22no—
144#104×C89—22no—
145#104×C89D414yescomplemented
146#103×C89—21no—
147#103×C89—21no—
148#103×C89—21no—
149#103×C89—21no—
150#103×C89—21no—
151#103×C89—21no—
152#103×C89—21no—
153#103×C89D411yescharacteristic
154#103×C89D411yescharacteristic
155#102×C89—21no—
156#102×C89—21no—
157#102×C89—21no—
158#102×C89—21no—
159#102×C89—21no—
160#102×C89—21no—
161#102×C89—21no—
162#102×C89—21no—
163#102×C89—21no—
164#102×C89D411yescharacteristic
165#102×C89D411yescharacteristic
166#101×C89—41no—
167#100×C89—22no—
168C22⋊C8×C89—21no—
169C22⋊C8×C89—21no—
170#97×C89—22no—
171C24×C89—21no—
172C24×C89—41no—
173#41×C89—21no—
174#41×C89—21no—
175#41×C89—24no—
176#41×C89—21no—
177#41×C89—21no—
178#41×C89—21no—
179#41×C89—21no—
180#41×C89—21no—
181#41×C89—21no—
182#41×C89—21no—
183#41×C89—21no—
184#41×C89—42no—
185#41×C89—42no—
186#41×C89—42no—
187#41×C89C2×D412yes—
188#41×C89#4112yes—
189C2×Q8×C89—21no—
190C2×Q8×C89—21no—
191C2×Q8×C89—21no—
192C2×Q8×C89—21no—
193C2×Q8×C89—21no—
194C2×Q8×C89—21no—
195C2×Q8×C89C2×D411yescharacteristic
196C2×Q8×C89C2×D411yescharacteristic
197C2×Q8×C89C2×D411yescharacteristic
198C2×D4×C89—21no—
199C2×D4×C89—24no—
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—42no—
208C2×D4×C89—41no—
209C2×D4×C89—41no—
210C2×D4×C89—42no—
211C2×D4×C89—44no—
212C2×D4×C89—44no—
213C2×D4×C89—42no—
214C2×D4×C89—41no—
215C2×D4×C89C2×D411yescharacteristic
216C2×D4×C89C2×D411yescharacteristic
217C2×D4×C89C2×D411yescharacteristic
218C2×D4×C89#4112yes—
219C22×C4×C89—21no—
220C22×C4×C89—21no—
221C22×C4×C89—21no—
222C22×C4×C89—21no—
223C22×C4×C89—21no—
224C22×C4×C89—21no—
225C22×C4×C89—21no—
226C22×C4×C89—41no—
227C22×C4×C89—41no—
228C22×C4×C89C2411yescharacteristic
229Q16×C89—22no—
230Q16×C89—42no—
231Q16×C89—42no—
232SD16×C89—22no—
233SD16×C89—22no—
234SD16×C89—42no—
235SD16×C89—42no—
236SD16×C89—42no—
237D8×C89—22no—
238D8×C89—42no—
239M16×C89—21no—
240M16×C89—21no—
241M16×C89—21no—
242M16×C89—21no—
243M16×C89—21no—
244M16×C89—21no—
245M16×C89—21no—
246M16×C89—42no—
247M16×C89—42no—
248M16×C89C2×D412yes—
249C2×C8×C89—21no—
250C2×C8×C89—21no—
251C2×C8×C89—21no—
252C2×C8×C89—21no—
253C2×C8×C89—21no—
254C2×C8×C89—21no—
255C2×C8×C89—21no—
256C2×C8×C89—21no—
257C2×C8×C89—42no—
258C2×C8×C89—42no—
259C2×C8×C89C2×D411yescharacteristic
260C2×C8×C89C2×D411yescharacteristic
261C2×C8×C89C2×D411yescharacteristic
262C2×C8×C89C2×D411yescharacteristic
263C4⋊C4×C89—21no—
264C4⋊C4×C89—21no—
265C4⋊C4×C89—21no—
266C4⋊C4×C89—21no—
267C4⋊C4×C89—41no—
268C4⋊C4×C89—41no—
269C4⋊C4×C89—41no—
270C4⋊C4×C89—41no—
271C4⋊C4×C89—82no—
272C4⋊C4×C89C2×D411yescharacteristic
273C4⋊C4×C89C2×D411yescharacteristic
274C22⋊C4×C89—21no—
275C22⋊C4×C89—44no—
276C22⋊C4×C89—41no—
277C22⋊C4×C89—41no—
278C22⋊C4×C89—41no—
279C22⋊C4×C89—41no—
280C22⋊C4×C89—41no—
281C42×C89—21no—
282C42×C89—21no—
283C42×C89—41no—
284C42×C89C2×D412yes—
285C23×C89—21no—
286C23×C89—21no—
287C23×C89—21no—
288C23×C89—22no—
289C23×C89—44no—
290C23×C89—41no—
291C23×C89—41no—
292C23×C89—81no—
293C23×C89—81no—
294C23×C89—161no—
295C23×C89—161no—
296C23×C89H(5,𝔽2)11yescharacteristic
297Q8×C89—21no—
298Q8×C89—21no—
299Q8×C89—21no—
300Q8×C89—21no—
301Q8×C89—21no—
302Q8×C89—41no—
303Q8×C89—41no—
304Q8×C89—41no—
305Q8×C89—41no—
306Q8×C89#12112yes—
307D4×C89—22no—
308D4×C89—22no—
309D4×C89—21no—
310D4×C89—21no—
311D4×C89—22no—
312D4×C89—21no—
313D4×C89—21no—
314D4×C89—21no—
315D4×C89—22no—
316D4×C89—44no—
317D4×C89—44no—
318D4×C89—41no—
319D4×C89—41no—
320D4×C89—41no—
321D4×C89—41no—
322D4×C89—41no—
323D4×C89—41no—
324D4×C89—161no—
325D4×C89#12112yes—
326C2×C4×C89—21no—
327C2×C4×C89—22no—
328C2×C4×C89—22no—
329C2×C4×C89—21no—
330C2×C4×C89—21no—
331C2×C4×C89—21no—
332C2×C4×C89—21no—
333C2×C4×C89—22no—
334C2×C4×C89—44no—
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—41no—
343C2×C4×C89—41no—
344C2×C4×C89—41no—
345C2×C4×C89—41no—
346C2×C4×C89—81no—
347C2×C4×C89—81no—
348C2×C4×C89—161no—
349C2×C4×C89C22×D411yescharacteristic
350C2×C4×C89C22×D411yescharacteristic
351C2×C4×C89C22×D411yescharacteristic
352C2×C4×C89C2×#4111yescharacteristic
353C2×C4×C89C2×#4111yescharacteristic
354C2×C4×C89H(5,𝔽2)11yescharacteristic
355C8×C89—21no—
356C8×C89—21no—
357C8×C89—21no—
358C8×C89—21no—
359C8×C89—22no—
360C8×C89—41no—
361C8×C89—41no—
362C8×C89—41no—
363C22×C89—21no—
364C22×C89—21no—
365C22×C89—22no—
366C22×C89—41no—
367C22×C89—41no—
368C22×C89—41no—
369C22×C89—42no—
370C22×C89—41no—
371C22×C89—41no—
372C22×C89—41no—
373C22×C89—41no—
374C22×C89—41no—
375C22×C89—82no—
376C22×C89—81no—
377C22×C89—81no—
378C22×C89—161no—
379C22×C89—164no—
380C22×C89#53811yescharacteristic
381C22×C89D4211yescharacteristic
382C22×C89#54611yescharacteristic
383C4×C89—22no—
384C4×C89—42no—
385C4×C89—41no—
386C4×C89—41no—
387C4×C89—41no—
388C4×C89—41no—
389C4×C89—81no—
390C4×C89—81no—
391C4×C89—81no—
392C4×C89C2×#12111yescharacteristic
393C4×C89#52511yescharacteristic
394C4×C89D4211yescharacteristic
395C4×C89#54611yescharacteristic
396#25195C8911yesmaximal, characteristic, direct product factor, Sylow
397C2×C89—21no—
398C2×C89—21no—
399C2×C89—42no—
400C2×C89—81no—
401C2×C89—81no—
402C2×C89—82no—
403C2×C89#242411yescharacteristic
404C2×C89#328811yescharacteristic
405C2×C89#328911yescharacteristic
406#3063C2×C8911yescharacteristic, complemented
407#3046C2×C8911yescharacteristic, complemented
408C2×#455C2×C8911yescharacteristic, complemented
409#3012C2×C8911yescharacteristic
410C2×#444C2×C8911yescharacteristic, complemented
411#2897C2×C8911yescharacteristic, complemented
412#2063C2×C8911yescharacteristic, complemented
413#2052C2×C8911yescharacteristic, complemented
414#2039C2×C8911yescharacteristic, complemented
415#2003C2×C8911yescharacteristic, complemented
416#1959C2×C8911yescharacteristic, complemented
417#1938C2×C8911yescharacteristic, complemented
418#1908C2×C8911yescharacteristic, complemented
419#1907C2×C8911yescharacteristic, complemented
420#1859C2×C8911yescharacteristic, complemented
421C89#2519511yescharacteristic, direct product factor, Sylow
422C2×H(5,𝔽2)C22×C8911yescharacteristic
423C2×#137C22×C8911yescharacteristic
424C2×#137C22×C8911yescharacteristic
425C2×AGL(1,ℤ/8)C22×C8911yescharacteristic
426C2×#135C22×C8911yescharacteristic
427C2×#131C22×C8911yescharacteristic
428C2×#131C22×C8911yescharacteristic, complemented
429#537C22×C8911yescharacteristic
430#536C22×C8911yescharacteristic, complemented
431C2×#124C22×C8911yescharacteristic
432#520C22×C8911yescharacteristic
433#470—21no—
434#468—21no—
435#467—21no—
436#465—21no—
437#464—21no—
438#463—21no—
439#462—21no—
440#461—21no—
441#455—24no—
442#452—21no—
443#450—21no—
444#449—21no—
445#447—21no—
446#444—24no—
447C2×#108C22×C8911yescharacteristic, complemented
448#428C22×C8911yescharacteristic, complemented
449#424C22×C8911yescharacteristic, complemented
450C2×#104C22×C8911yescharacteristic
451C2×#104C22×C8911yescharacteristic
452C2×#104C22×C8911yescharacteristic, complemented
453#418—21no—
454#418C22×C8911yescharacteristic
455#417—21no—
456#417C22×C8911yescharacteristic
457#417C22×C8911yescharacteristic
458#417C22×C8911yescharacteristic, complemented
459#416—21no—
460#416C22×C8911yescharacteristic
461C2×#103C22×C8911yescharacteristic, complemented
462C2×#103C22×C8911yescharacteristic, complemented
463C2×#102—21no—
464C2×#102C22×C8911yescharacteristic
465C2×#102C22×C8911yescharacteristic
466C2×#101C22×C8911yescharacteristic, complemented
467C2×#100C22×C8911yescharacteristic
468#408C22×C8911yescharacteristic
469C2×#97C22×C8911yescharacteristic, complemented
470#384C22×C8911yescharacteristic, complemented
471#343C22×C8911yescharacteristic, complemented
472#343C22×C8911yescharacteristic, complemented
473#341C22×C8911yescharacteristic, complemented
474#339C22×C8911yescharacteristic, complemented
475H(5,𝔽2)—22no—
476H(5,𝔽2)—22no—
477H(5,𝔽2)—22no—
478H(5,𝔽2)—41no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41C23×C8911yescharacteristic
482C2×#41C23×C8911yescharacteristic
483C2×#41C23×C8911yescharacteristic
484C22×Q8C23×C8911yescharacteristic
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—41no—
488C22×D4C23×C8911yescharacteristic
489#137—22no—
490#137—22no—
491#137—22no—
492#137—41no—
493AGL(1,ℤ/8)—22no—
494AGL(1,ℤ/8)—41no—
495#135—22no—
496#135—22no—
497C2×Q16—21no—
498C2×Q16—21no—
499C2×Q16D4×C8911yescharacteristic
500C2×SD16—21no—
501C2×SD16—21no—
502C2×SD16—21no—
503C2×SD16D4×C8911yescharacteristic
504C2×SD16D4×C8911yescharacteristic
505C2×D8—21no—
506C2×D8D4×C8911yescharacteristic
507#131—22no—
508#131—22no—
509#131—41no—
510#131—41no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16C23×C8911yescharacteristic
514C2×M16C23×C8911yescharacteristic
515C2×M16C23×C8911yescharacteristic
516C2×M16C23×C8911yescharacteristic
517C22×C8—21no—
518C22×C8—21no—
519C22×C8C23×C8911yescharacteristic
520C22×C8C23×C8911yescharacteristic
521C4⋊Q8—21no—
522#124—21no—
523#124—22no—
524#124—22no—
525#123—41no—
526C22⋊Q8—21no—
527C22⋊Q8—21no—
528C22⋊Q8—21no—
529C22⋊Q8—21no—
530#121—21no—
531#121—21no—
532#121—41no—
533C4×Q8—21no—
534C4×D4—21no—
535C4×D4—41no—
536#117—21no—
537#117C23×C8911yescharacteristic
538C2×C4⋊C4—21no—
539C2×C4⋊C4—41no—
540C2×C4⋊C4C23×C8911yescharacteristic
541C2×C4⋊C4C23×C8911yescharacteristic
542C2×C22⋊C4—41no—
543C2×C42C23×C8911yescharacteristic
544#108—22no—
545#107—21no—
546#106—21no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549#104—22no—
550#104—22no—
551#104D4×C8914yescomplemented
552#103—21no—
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#103—21no—
559#103D4×C8911yescharacteristic
560#103D4×C8911yescharacteristic
561#102—21no—
562#102—21no—
563#102—21no—
564#102—21no—
565#102—21no—
566#102—21no—
567#102—21no—
568#102—21no—
569#102—21no—
570#102D4×C8911yescharacteristic
571#102D4×C8911yescharacteristic
572#101—41no—
573#100—22no—
574C22⋊C8—21no—
575C22⋊C8—21no—
576#97—22no—
577C24—21no—
578C24—41no—
579#41—21no—
580#41—21no—
581#41—24no—
582#41—21no—
583#41—21no—
584#41—21no—
585#41—21no—
586#41—21no—
587#41—21no—
588#41—21no—
589#41—21no—
590#41—42no—
591#41—42no—
592#41—42no—
593#41C2×D4×C8912yes—
594#41#41×C8912yes—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C8911yescharacteristic
602C2×Q8C2×D4×C8911yescharacteristic
603C2×Q8C2×D4×C8911yescharacteristic
604C2×D4—21no—
605C2×D4—24no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—42no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—42no—
617C2×D4—44no—
618C2×D4—44no—
619C2×D4—42no—
620C2×D4—41no—
621C2×D4C2×D4×C8911yescharacteristic
622C2×D4C2×D4×C8911yescharacteristic
623C2×D4C2×D4×C8911yescharacteristic
624C2×D4#41×C8912yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4C24×C8911yescharacteristic
635Q16—22no—
636Q16—42no—
637Q16—42no—
638SD16—22no—
639SD16—22no—
640SD16—42no—
641SD16—42no—
642SD16—42no—
643D8—22no—
644D8—42no—
645M16—21no—
646M16—21no—
647M16—21no—
648M16—21no—
649M16—21no—
650M16—21no—
651M16—21no—
652M16—42no—
653M16—42no—
654M16C2×D4×C8912yes—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—42no—
664C2×C8—42no—
665C2×C8C2×D4×C8911yescharacteristic
666C2×C8C2×D4×C8911yescharacteristic
667C2×C8C2×D4×C8911yescharacteristic
668C2×C8C2×D4×C8911yescharacteristic
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—41no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C4⋊C4—41no—
677C4⋊C4—82no—
678C4⋊C4C2×D4×C8911yescharacteristic
679C4⋊C4C2×D4×C8911yescharacteristic
680C22⋊C4—21no—
681C22⋊C4—44no—
682C22⋊C4—41no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C42—21no—
688C42—21no—
689C42—41no—
690C42C2×D4×C8912yes—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—22no—
695C23—44no—
696C23—41no—
697C23—41no—
698C23—81no—
699C23—81no—
700C23—161no—
701C23—161no—
702C23H(5,𝔽2)×C8911yescharacteristic
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—21no—
707Q8—21no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711Q8—41no—
712Q8#121×C8912yes—
713D4—22no—
714D4—22no—
715D4—21no—
716D4—21no—
717D4—22no—
718D4—21no—
719D4—21no—
720D4—21no—
721D4—22no—
722D4—44no—
723D4—44no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—161no—
731D4#121×C8912yes—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—44no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—161no—
755C2×C4C22×D4×C8911yescharacteristic
756C2×C4C22×D4×C8911yescharacteristic
757C2×C4C22×D4×C8911yescharacteristic
758C2×C4C2×#41×C8911yescharacteristic
759C2×C4C2×#41×C8911yescharacteristic
760C2×C4H(5,𝔽2)×C8911yescharacteristic
761C8—21no—
762C8—21no—
763C8—21no—
764C8—21no—
765C8—22no—
766C8—41no—
767C8—41no—
768C8—41no—
769C22—21no—
770C22—21no—
771C22—22no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—82no—
782C22—81no—
783C22—81no—
784C22—161no—
785C22—164no—
786C22#538×C8911yescharacteristic
787C22D42×C8911yescharacteristic
788C22#546×C8911yescharacteristic
789C4—22no—
790C4—42no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—81no—
796C4—81no—
797C4—81no—
798C4C2×#121×C8911yescharacteristic
799C4#525×C8911yescharacteristic
800C4D42×C8911yescharacteristic
801C4#546×C8911yescharacteristic
802C2—21no—
803C2—21no—
804C2—42no—
805C2—81no—
806C2—81no—
807C2—82no—
808C2C89×#242411yescharacteristic
809C2C89×#328811yescharacteristic
810C2C89×#328911yescharacteristic
subgroupG/H
center, socleC22×C89D42
commutator, Frattini, cosocleC22×C4C24×C89
prime radicalC89×#3012C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C89 ◁ C22×C4×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C89×#3063C2semidirect
2. C89×#3046C2semidirect
3. C2×#455×C89C2semidirect
5. C2×#444×C89C2semidirect
6. C89×#2897C2semidirect
7. C89×#2063C2semidirect
8. C89×#2052C2semidirect
9. C89×#2039C2semidirect
10. C89×#2003C2semidirect
11. C89×#1959C2semidirect
12. C89×#1938C2semidirect
13. C89×#1908C2semidirect
14. C89×#1907C2semidirect
15. C89×#1859C2semidirect
22. C2×#131×C89C22semidirect
24. #536×C89C22semidirect
41. C2×#108×C89C22semidirect
42. #428×C89C22semidirect
43. #424×C89C22semidirect
46. C2×#104×C89C22semidirect
52. #417×C89C22semidirect
55. C2×#103×C89C22semidirect
56. C2×#103×C89C22semidirect
60. C2×#101×C89C22semidirect
63. C2×#97×C89C22semidirect
64. #384×C89C22semidirect
65. #343×C89C22semidirect
66. #343×C89C22semidirect
67. #341×C89C22semidirect
68. #339×C89C22semidirect
145. #104×C89D4semidirect
396. #25195C89direct (N × H)
406. #3063C2×C89semidirect
407. #3046C2×C89semidirect
408. C2×#455C2×C89semidirect
410. C2×#444C2×C89semidirect
411. #2897C2×C89semidirect
412. #2063C2×C89semidirect
413. #2052C2×C89semidirect
414. #2039C2×C89semidirect
415. #2003C2×C89semidirect
416. #1959C2×C89semidirect
417. #1938C2×C89semidirect
418. #1908C2×C89semidirect
419. #1907C2×C89semidirect
420. #1859C2×C89semidirect
421. C89#25195direct (N × H)
428. C2×#131C22×C89semidirect
430. #536C22×C89semidirect
447. C2×#108C22×C89semidirect
448. #428C22×C89semidirect
449. #424C22×C89semidirect
452. C2×#104C22×C89semidirect
458. #417C22×C89semidirect
461. C2×#103C22×C89semidirect
462. C2×#103C22×C89semidirect
466. C2×#101C22×C89semidirect
469. C2×#97C22×C89semidirect
470. #384C22×C89semidirect
471. #343C22×C89semidirect
472. #343C22×C89semidirect
473. #341C22×C89semidirect
474. #339C22×C89semidirect
551. #104D4×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#30632
C89×#30462
C2×#455×C892
C89×#30122
C2×#444×C892
C89×#28972
C89×#20632
C89×#20522
C89×#20392
C89×#20032
C89×#19592
C89×#19382
C89×#19082
C89×#19072
C89×#18592
#2519589