Finite Group Databasebeta

← #8429409

Subgroups — #8429409

Order 512.

4729 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59863C211yesmaximal, characteristic, complemented
2#59678C212yesmaximal, complemented
3#59078C212yesmaximal, complemented
4#59034C212yesmaximal, complemented
5#55241C218yesmaximal, complemented
6#53105C214yesmaximal, complemented
7#53062C214yesmaximal, complemented
8#53047C214yesmaximal, complemented
9#42860C214yesmaximal, complemented
10#42507C214yesmaximal, complemented
11#42459C214yesmaximal, complemented
12#39737C212yesmaximal, complemented
13#39507C212yesmaximal, complemented
14#39478C212yesmaximal, complemented
15#39139C212yesmaximal, complemented
16#38966C212yesmaximal, complemented
17#38920C212yesmaximal, complemented
18#37633C212yesmaximal, complemented
19#37627C212yesmaximal, complemented
20#37616C212yesmaximal, complemented
21#36560C211yesmaximal, characteristic, complemented
22#36134C211yesmaximal, characteristic, complemented
23#36127C211yesmaximal, characteristic, complemented
24#34941C211yesmaximal, characteristic, complemented
25#34934C211yesmaximal, characteristic, complemented
26#34932C211yesmaximal, characteristic, complemented
27C2×#557C2212yes—
28C2×#547C2212yes—
29C2×#533C2212yes—
30C2×#532C2212yes—
31C2×#529C2212yes—
32C2×#529C2212yes—
33#2868C2211yescharacteristic
34#2859C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2837C2218yes—
38#2837C2218yes—
39#2829C2218yes—
40#2829C2218yes—
41#2827C2218yes—
42#2814C2218yes—
43#2813C2218yes—
44#2808C2214yes—
45#2803C2218yes—
46#2803C2218yes—
47#2800C2218yes—
48#2796C2218yes—
49#2790C2218yes—
50#2790C2218yes—
51#2781C2218yes—
52#2772C2218yes—
53#2768C2218yes—
54#2767C2218yes—
55#2747C2218yes—
56#2741C2218yes—
57#2721C2218yes—
58#2718C2218yes—
59#2711C2218yes—
60#2706C2218yes—
61#2696C2218yes—
62#2694C2218yes—
63#2652C2218yes—
64#2651C2218yes—
65#2637C2218yes—
66#2636C2218yes—
67#2629C2214yes—
68#2629C2214yes—
69#2625C2214yes—
70#2624C2214yes—
71#2621C2214yes—
72#2620C2214yes—
73#2620C2214yes—
74#2620C2214yes—
75#2619C2214yes—
76#2597C2218yes—
77#2592C2214yes—
78#2574C2214yes—
79#2568C2212yes—
80#2567C2211yescharacteristic
81#2566C2214yes—
82#2565C2214yes—
83#2565C2214yes—
84#2563C2212yes—
85#2563C2211yescharacteristic
86#2562C2214yes—
87#2554C2214yes—
88#2553C2214yes—
89#2552C2212yes—
90#2552C2211yescharacteristic
91#2552C2214yes—
92#2552C2211yescharacteristic
93#2552C2211yescharacteristic
94#2548C2211yescharacteristic
95#2548C2212yes—
96#2547C2212yes—
97#2547C2211yescharacteristic
98#2547C2212yes—
99#2546C2212yes—
100#2546C2212yes—
101#2545C2214yes—
102#2544C2214yes—
103#2542C2214yes—
104#2542C2212yes—
105#2542C2211yescharacteristic
106#2541C2211yescharacteristic
107#2538C2211yescharacteristic
108#2538C2212yes—
109#2538C2211yescharacteristic
110#2537C2212yes—
111#2537C2212yes—
112#2537C2211yescharacteristic
113#2536C2214yes—
114#2513C2214yes—
115#2512C2212yes—
116#2511C2214yes—
117#2511C2214yes—
118#2508C2212yes—
119#2508C2214yes—
120#2506C2214yes—
121#2506C2214yes—
122#2497C2214yes—
123#2497C2212yes—
124#2496C2212yes—
125#2490C2214yes—
126#2490C2214yes—
127#2490C2214yes—
128#2490C2212yes—
129#2489C2214yes—
130#2489C2212yes—
131#2487C2214yes—
132#2485C2214yes—
133#2485C2214yes—
134#2485C2214yes—
135#2485C2214yes—
136#2460C2218yes—
137#2458C2218yes—
138#2454C2214yes—
139#2454C2212yes—
140#2448C2214yes—
141#2448C2214yes—
142#2445C2212yes—
143#2442C2214yes—
144#2441C2214yes—
145#2441C2214yes—
146#2432C2214yes—
147#2432C2214yes—
148#2429C2214yes—
149#2427C2212yes—
150#2426C2212yes—
151#2426C2214yes—
152#2423C2214yes—
153#2423C2212yes—
154#2423C2214yes—
155#2422C2214yes—
156#2422C2214yes—
157#2422C2212yes—
158#2421C2214yes—
159#2414C2214yes—
160#2414C2214yes—
161#2407C2214yes—
162#2407C2214yes—
163#2396C2214yes—
164#2395C2214yes—
165#2392C2214yes—
166#2367C2214yes—
167#2365C2212yes—
168#2365C2212yes—
169#2365C2212yes—
170#2355C2212yes—
171#2354C2212yes—
172#2354C2212yes—
173#2354C2212yes—
174#2352C2214yes—
175Q8×C4⋊C4C2212yes—
176D4×C4⋊C4C2212yes—
177D4×C4⋊C4C2212yes—
178#2341C2214yes—
179#2323C2214yes—
180#2317C2214yes—
181#2314C2214yes—
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2211yescharacteristic
185C4×#127C2212yes—
186C4×#127C2211yescharacteristic
187C4×#125C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×#121C2212yes—
191C4×#121C2212yes—
192#2293C2212yes—
193#2293C2212yes—
194#2285C2212yes—
195#2285C2212yes—
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C22×#41C2314yes—
200#557—48no—
201#547—48no—
202#533—48no—
203#532—48no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×#127C2311yescharacteristic
211C2×#127C2312yes—
212#529—48no—
213#529—48no—
214C2×#126C2314yes—
215C2×#126C2314yes—
216C2×#125C2312yes—
217C2×#125C2312yes—
218C2×#125C2314yes—
219C2×#125C2312yes—
220C2×#125C2314yes—
221C2×#125C2318yes—
222C2×#124C2314yes—
223C2×#124C2314yes—
224C2×#124C2312yes—
225C2×#124C2312yes—
226C2×#123C2314yes—
227C2×#123C2314yes—
228C2×#123C2318yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2312yes—
237C2×#121C2312yes—
238C2×#121C2314yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2314yes—
242C2×#121C2312yes—
243C2×#121C2314yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4C2312yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2312yes—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2314yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×#117C2314yes—
268C2×#117C2314yes—
269C2×#117C2314yes—
270C2×#117C2314yes—
271C2×#117C2314yes—
272C22×C4⋊C4C2314yes—
273C22×C42C2312yes—
274C22×C42C2312yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2314yes—
281#400C2314yes—
282#399C2318yes—
283#399C2314yes—
284#399C2318yes—
285#399C2318yes—
286#399C2314yes—
287#399C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2314yes—
293#398C2314yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2314yes—
298#398C2314yes—
299#398C2318yes—
300#397C2314yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2314yes—
307#397C2318yes—
308#397C2314yes—
309#397C2318yes—
310#397C2314yes—
311#397C2318yes—
312#396C2318yes—
313#396C2318yes—
314#396C2318yes—
315#396C2318yes—
316#396C2314yes—
317#396C2318yes—
318#396C2314yes—
319#396C2314yes—
320#396C2318yes—
321#396C2318yes—
322#396C2314yes—
323#395C2314yes—
324#394C2318yes—
325#394C2314yes—
326#394C2318yes—
327#394C2314yes—
328#394C2318yes—
329#394C2314yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2318yes—
339#394C2314yes—
340#394C2314yes—
341#393C2314yes—
342#393C2318yes—
343#392C2318yes—
344#392C2318yes—
345#392C2314yes—
346#391C2312yes—
347#391C2314yes—
348#391C2312yes—
349#391C2314yes—
350#391C2314yes—
351#391C2312yes—
352#391C2314yes—
353#391C2314yes—
354#391C2314yes—
355#391C2312yes—
356#390C2312yes—
357#390C2314yes—
358#390C2312yes—
359#390C2312yes—
360#390C2312yes—
361#390C2314yes—
362#390C2312yes—
363#390C2314yes—
364#390C2312yes—
365#390C2312yes—
366#390C2314yes—
367#390C2318yes—
368#390C2318yes—
369#390C2312yes—
370#390C2318yes—
371#390C2314yes—
372#390C2314yes—
373#390C2312yes—
374#390C2312yes—
375#390C2312yes—
376#389C2312yes—
377#389C2312yes—
378#389C2314yes—
379#389C2314yes—
380#389C2312yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#389C2314yes—
387#389C2314yes—
388#389C2312yes—
389#389C2318yes—
390#389C2318yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2312yes—
399#389C2312yes—
400#389C2312yes—
401#389C2312yes—
402#389C2312yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2314yes—
409#388C2314yes—
410#388C2318yes—
411#388C2314yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2314yes—
419#388C2318yes—
420#388C2318yes—
421#388C2314yes—
422#388C2314yes—
423#387C2314yes—
424#387C2314yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2314yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2314yes—
437#386C2318yes—
438#386C2318yes—
439#386C2314yes—
440#386C2314yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2318yes—
445#385C2314yes—
446#385C2318yes—
447#385C2318yes—
448#385C2314yes—
449#384C2312yes—
450#384C2311yescharacteristic
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#384C2312yes—
454#384C2312yes—
455#384C2312yes—
456#384C2314yes—
457#384C2318yes—
458#384C2312yes—
459#384C2312yes—
460#384C2312yes—
461#384C2312yes—
462#384C2312yes—
463#382C2312yes—
464#382C2314yes—
465#382C2314yes—
466#382C2318yes—
467#382C2314yes—
468#382C2314yes—
469#380C2312yes—
470#380C2314yes—
471#380C2314yes—
472#380C2314yes—
473#380C2312yes—
474#380C2314yes—
475#380C2314yes—
476#380C2312yes—
477#380C2312yes—
478#380C2314yes—
479#380C2314yes—
480#380C2312yes—
481#380C2318yes—
482#380C2314yes—
483#380C2314yes—
484#380C2314yes—
485#380C2312yes—
486#380C2312yes—
487#380C2314yes—
488#380C2312yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2311yescharacteristic
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2312yes—
523C43C2312yes—
524C43C2311yescharacteristic
525C2×#41—48no—
526C2×#41—48no—
527C2×#41—48no—
528C22×Q8C2411yescharacteristic
529C22×Q8C2412yes—
530C22×Q8C2414yes—
531C22×Q8C2412yes—
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2412yes—
535C22×D4C2412yes—
536C22×D4C2412yes—
537C22×D4C2414yes—
538C22×D4C2414yes—
539C22×D4C2414yes—
540C22×D4C2418yes—
541C23×C4C2414yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2418yes—
549C4⋊Q8—28no—
550C4⋊Q8—24no—
551C4⋊Q8—28no—
552C4⋊Q8—24no—
553C4⋊Q8—44no—
554C4⋊Q8—48no—
555#127—24no—
556#127—44no—
557#126—48no—
558#126—48no—
559#125—44no—
560#125—44no—
561#125—44no—
562#125—48no—
563#125—48no—
564#125—416no—
565#124—48no—
566#124—44no—
567#124—44no—
568#124—48no—
569#123—416no—
570#123—48no—
571#123—48no—
572C22⋊Q8—44no—
573C22⋊Q8—48no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576C22⋊Q8—44no—
577C22⋊Q8—48no—
578C22⋊Q8—48no—
579C22⋊Q8—48no—
580#121—44no—
581#121—44no—
582#121—44no—
583#121—44no—
584#121—48no—
585#121—48no—
586#121—48no—
587C4×Q8—24no—
588C4×Q8—28no—
589C4×Q8—24no—
590C4×Q8—44no—
591C4×Q8—42no—
592C4×Q8—48no—
593C4×Q8—48no—
594C4×Q8—48no—
595C4×Q8—48no—
596C4×D4—24no—
597C4×D4—28no—
598C4×D4—24no—
599C4×D4—28no—
600C4×D4—24no—
601C4×D4—24no—
602C4×D4—42no—
603C4×D4—42no—
604C4×D4—48no—
605C4×D4—48no—
606C4×D4—44no—
607C4×D4—48no—
608C4×D4—48no—
609C4×D4—48no—
610#117—48no—
611#117—48no—
612#117—48no—
613#117—48no—
614#117—48no—
615C2×C4⋊C4—48no—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2418yes—
707C2×C42—28no—
708C2×C42—28no—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2411yescharacteristic
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2411yescharacteristic
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2411yescharacteristic
724C2×C42C2418yes—
725C2×C42C2418yes—
726C2×C42C2418yes—
727C2×C42C2412yes—
728C2×C42C2411yescharacteristic
729C2×C42C2412yes—
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733#95C2414yes—
734#95C2414yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2412yes—
747#95C2412yes—
748#95C2412yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2414yes—
759#95C2418yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2418yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769C24C2512yes—
770C24C2512yes—
771C24C2514yes—
772#41—832no—
773C2×Q8—24no—
774C2×Q8—22no—
775C2×Q8—22no—
776C2×Q8—24no—
777C2×Q8—28no—
778C2×Q8—28no—
779C2×Q8—24no—
780C2×Q8—22no—
781C2×Q8—24no—
782C2×Q8—28no—
783C2×Q8—42no—
784C2×Q8—42no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—22no—
792C2×D4—24no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—44no—
801C2×D4—44no—
802C2×D4—44no—
803C2×D4—48no—
804C2×D4—48no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—44no—
810C2×D4—44no—
811C2×D4—48no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—28no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—28no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—28no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—48no—
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2514yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2511yescharacteristic
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2518yes—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2511yescharacteristic
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C4⋊C4—22no—
860C4⋊C4—28no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—22no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—22no—
867C4⋊C4—22no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—28no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—28no—
874C4⋊C4—22no—
875C4⋊C4—24no—
876C4⋊C4—22no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—24no—
885C4⋊C4—48no—
886C4⋊C4—42no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—42no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—42no—
900C4⋊C4—44no—
901C4⋊C4—42no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—48no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C22⋊C4—24no—
915C22⋊C4—28no—
916C22⋊C4—24no—
917C22⋊C4—24no—
918C22⋊C4—24no—
919C22⋊C4—28no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—48no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—42no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—42no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—48no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C42—24no—
951C42—24no—
952C42—24no—
953C42—24no—
954C42—24no—
955C42—24no—
956C42—24no—
957C42—28no—
958C42—24no—
959C42—24no—
960C42—28no—
961C42—22no—
962C42—24no—
963C42—22no—
964C42—22no—
965C42—41no—
966C42—42no—
967C42—48no—
968C42—48no—
969C42—42no—
970C42—48no—
971C42H(5,𝔽2)14yes—
972C42H(5,𝔽2)14yes—
973C422−1+414yes—
974C23—22no—
975C23—22no—
976C23—24no—
977C23—22no—
978C23—24no—
979C23—22no—
980C23—24no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—24no—
985C23—22no—
986C23—24no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—24no—
991C23—22no—
992C23—24no—
993C23—22no—
994C23—22no—
995C23C2611yescharacteristic
996Q8—48no—
997Q8—44no—
998Q8—416no—
999Q8—48no—
1000D4—48no—
1001D4—48no—
1002D4—44no—
1003D4—48no—
1004D4—44no—
1005D4—88no—
1006D4—88no—
1007D4—88no—
1008D4—816no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—28no—
1029C2×C4—28no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—28no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—48no—
1067C2×C4—48no—
1068C2×C4—48no—
1069C2×C4—48no—
1070C2×C4—416no—
1071C2×C4—84no—
1072C2×C4—84no—
1073C2×C4—816no—
1074C2×C4C2×H(5,𝔽2)12yes—
1075C2×C4C2×H(5,𝔽2)12yes—
1076C2×C4C2×H(5,𝔽2)12yes—
1077C2×C4C2×H(5,𝔽2)12yes—
1078C2×C4C2×H(5,𝔽2)12yes—
1079C2×C4C2×H(5,𝔽2)12yes—
1080C2×C4C2×2−1+412yes—
1081C2×C4C2×2−1+412yes—
1082C2×C4C2×2−1+412yes—
1083C2×C4#58512yes—
1084C2×C4#58512yes—
1085C2×C4#58512yes—
1086C22—44no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—44no—
1092C22—42no—
1093C22—42no—
1094C22—44no—
1095C22—42no—
1096C22—44no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—44no—
1101C22—42no—
1102C22—44no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—44no—
1107C22C22×H(5,𝔽2)11yescharacteristic
1108C22C22×H(5,𝔽2)11yescharacteristic
1109C22C22×2−1+411yescharacteristic
1110C22C2×#58511yescharacteristic
1111C22C2×#58511yescharacteristic
1112C22C2×#58511yescharacteristic
1113C222−1+611yescharacteristic
1114C4—22no—
1115C4—22no—
1116C4—22no—
1117C4—42no—
1118C4—44no—
1119C4—42no—
1120C4—42no—
1121C4—48no—
1122C4—42no—
1123C4—42no—
1124C4—44no—
1125C4—41no—
1126C4—44no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—44no—
1132C4—42no—
1133C4—44no—
1134C4#354614yes—
1135C4#354714yes—
1136C4#355414yes—
1137C2—82no—
1138C2—84no—
1139C2—82no—
1140C2C2×#355411yescharacteristic
1141C2C2×#354611yescharacteristic
1142C2C2×#354711yescharacteristic
1143C2#6292511yescharacteristic
1144C2#6292511yescharacteristic
1145C2#6295611yescharacteristic
1146C2#6303111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59863C2semidirect
2. #59678C2semidirect
3. #59078C2semidirect
4. #59034C2semidirect
5. #55241C2semidirect
6. #53105C2semidirect
7. #53062C2semidirect
8. #53047C2semidirect
9. #42860C2semidirect
10. #42507C2semidirect
11. #42459C2semidirect
12. #39737C2semidirect
13. #39507C2semidirect
14. #39478C2semidirect
15. #39139C2semidirect
16. #38966C2semidirect
17. #38920C2semidirect
18. #37633C2semidirect
19. #37627C2semidirect
20. #37616C2semidirect
21. #36560C2semidirect
22. #36134C2semidirect
23. #36127C2semidirect
24. #34941C2semidirect
25. #34934C2semidirect
26. #34932C2semidirect

Maximal subgroups

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

subgroupindex
#598632
#596782
#590782
#590342
#552412
#531052
#530622
#530472
#428602
#425072
#424592
#397372
#395072
#394782
#391392
#389662
#389202
#376332
#376272
#376162
#365602
#361342
#361272
#349412
#349342
#349322