Finite Group Databasebeta

← #8429477

Subgroups — #8429477

Order 512.

5159 conjugacy classes of subgroups.

The subgroup lattice has 1179 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C212yesmaximal, complemented
2#59815C211yesmaximal, characteristic, complemented
3#59680C212yesmaximal, complemented
4#59304C212yesmaximal, complemented
5#53716C218yesmaximal, complemented
6#53132C214yesmaximal, complemented
7#53095C214yesmaximal, complemented
8#52963C214yesmaximal, complemented
9#42928C214yesmaximal, complemented
10#42580C214yesmaximal, complemented
11#42504C214yesmaximal, complemented
12#39634C212yesmaximal, complemented
13#39169C212yesmaximal, complemented
14#38966C212yesmaximal, complemented
15#38952C212yesmaximal, complemented
16#38920C212yesmaximal, complemented
17#38908C212yesmaximal, complemented
18#37637C212yesmaximal, complemented
19#37625C212yesmaximal, complemented
20#37620C212yesmaximal, complemented
21#36594C211yesmaximal, characteristic, complemented
22#36559C211yesmaximal, characteristic, complemented
23#36180C211yesmaximal, characteristic, complemented
24#34951C211yesmaximal, characteristic, complemented
25#34934C211yesmaximal, characteristic, complemented
26#34934C211yesmaximal, characteristic, complemented
27C2×#556C2212yes—
28C2×#554C2212yes—
29C2×#554C2212yes—
30C2×#553C2214yes—
31C2×#550C2212yes—
32C2×#547C2212yes—
33C2×#529C2212yes—
34C2×#529C2212yes—
35#2868C2211yescharacteristic
36#2859C2212yes—
37#2858C2212yes—
38#2857C2212yes—
39#2831C2218yes—
40#2829C2218yes—
41#2827C2218yes—
42#2827C2218yes—
43#2826C2218yes—
44#2823C2218yes—
45#2823C2218yes—
46#2790C2218yes—
47#2780C2218yes—
48#2780C2218yes—
49#2768C2218yes—
50#2732C2218yes—
51#2718C2218yes—
52#2718C2218yes—
53#2714C2218yes—
54#2708C2218yes—
55#2706C2218yes—
56#2695C2218yes—
57#2695C2218yes—
58#2693C2218yes—
59#2691C2218yes—
60#2682C2214yes—
61#2676C2218yes—
62#2676C2218yes—
63#2672C2218yes—
64#2672C2218yes—
65#2647C2214yes—
66#2644C2214yes—
67#2641C2214yes—
68#2637C2218yes—
69#2636C2218yes—
70#2630C2218yes—
71#2629C2214yes—
72#2629C2214yes—
73#2625C2214yes—
74#2624C2214yes—
75#2620C2214yes—
76#2620C2214yes—
77#2618C2218yes—
78#2585C2214yes—
79#2582C2211yescharacteristic
80#2568C2211yescharacteristic
81#2567C2212yes—
82#2566C2214yes—
83#2566C2214yes—
84#2563C2212yes—
85#2554C2214yes—
86#2554C2214yes—
87#2552C2211yescharacteristic
88#2552C2211yescharacteristic
89#2552C2212yes—
90#2552C2214yes—
91#2552C2212yes—
92#2552C2211yescharacteristic
93#2548C2211yescharacteristic
94#2548C2211yescharacteristic
95#2547C2212yes—
96#2546C2211yescharacteristic
97#2545C2214yes—
98#2542C2214yes—
99#2541C2211yescharacteristic
100#2541C2214yes—
101#2541C2211yescharacteristic
102#2541C2212yes—
103#2538C2212yes—
104#2538C2212yes—
105#2538C2212yes—
106#2538C2211yescharacteristic
107#2538C2211yescharacteristic
108#2538C2218yes—
109#2538C2212yes—
110#2538C2212yes—
111#2537C2212yes—
112#2535C2214yes—
113#2512C2214yes—
114#2512C2214yes—
115#2512C2214yes—
116#2512C2212yes—
117#2512C2212yes—
118#2511C2212yes—
119#2509C2212yes—
120#2508C2214yes—
121#2502C2214yes—
122#2501C2214yes—
123#2496C2214yes—
124#2490C2212yes—
125#2490C2212yes—
126#2489C2214yes—
127#2487C2214yes—
128#2487C2214yes—
129#2456C2218yes—
130#2454C2214yes—
131#2454C2214yes—
132#2454C2214yes—
133#2454C2214yes—
134#2453C2212yes—
135#2452C2214yes—
136#2452C2214yes—
137#2446C2212yes—
138#2445C2214yes—
139#2445C2214yes—
140#2445C2212yes—
141#2445C2212yes—
142#2445C2214yes—
143#2443C2218yes—
144#2442C2214yes—
145#2441C2214yes—
146#2440C2214yes—
147#2440C2214yes—
148#2432C2214yes—
149#2427C2214yes—
150#2426C2212yes—
151#2426C2212yes—
152#2422C2214yes—
153#2417C2214yes—
154#2417C2214yes—
155#2417C2214yes—
156#2417C2214yes—
157#2416C2214yes—
158#2416C2214yes—
159#2416C2214yes—
160#2416C2214yes—
161#2414C2214yes—
162#2407C2214yes—
163#2407C2214yes—
164#2407C2214yes—
165#2402C2214yes—
166#2392C2214yes—
167#2392C2214yes—
168#2366C2214yes—
169#2354C2212yes—
170#2354C2212yes—
171D4×C4⋊C4C2212yes—
172D4×C4⋊C4C2214yes—
173D4×C4⋊C4C2212yes—
174D4×C4⋊C4C2212yes—
175D4×C4⋊C4C2212yes—
176D4×C4⋊C4C2212yes—
177#2328C2214yes—
178#2317C2214yes—
179#2311C2214yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×#127C2212yes—
184C4×#127C2212yes—
185C4×#127C2212yes—
186C4×#127C2211yescharacteristic
187C4×#127C2211yescharacteristic
188C4×#125C2212yes—
189C4×#121C2212yes—
190C4×#121C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193#2293C2212yes—
194#2293C2212yes—
195C2×#384C2212yes—
196C42×Q8C2211yescharacteristic
197C42×Q8C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C22×#41C2314yes—
200#556—48no—
201#554—48no—
202#554—48no—
203#553—416no—
204#550—48no—
205#547—48no—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×#127C2311yescharacteristic
212C2×#127C2312yes—
213C2×#127C2311yescharacteristic
214C2×#127C2312yes—
215C2×#127C2314yes—
216#529—48no—
217#529—48no—
218C2×#126C2314yes—
219C2×#126C2314yes—
220C2×#126C2318yes—
221C2×#126C2318yes—
222C2×#125C2312yes—
223C2×#125C2314yes—
224C2×#125C2314yes—
225C2×#125C2312yes—
226C2×#125C2312yes—
227C2×#124C2314yes—
228C2×#124C2312yes—
229C2×#124C2312yes—
230C2×#124C2314yes—
231C2×#123C2314yes—
232C2×#123C2314yes—
233C2×#123C2318yes—
234C2×#123C2318yes—
235C2×#123C2318yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2318yes—
243C2×C22⋊Q8C2318yes—
244C2×#121C2312yes—
245C2×#121C2314yes—
246C2×#121C2314yes—
247C2×#121C2314yes—
248C2×#121C2312yes—
249C2×#121C2312yes—
250C2×#121C2312yes—
251C2×#121C2318yes—
252C2×#121C2318yes—
253C2×#121C2318yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2314yes—
261C2×C4×Q8C2311yescharacteristic
262C2×C4×D4C2312yes—
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2312yes—
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2312yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2314yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2318yes—
280C2×C4×D4C2314yes—
281C2×#117C2314yes—
282C2×#117C2314yes—
283C2×#117C2314yes—
284C22×C4⋊C4C2314yes—
285C22×C4⋊C4C2314yes—
286C22×C4⋊C4C2314yes—
287C22×C4⋊C4C2314yes—
288C22×C4⋊C4C2314yes—
289C22×C42C2312yes—
290#400C2314yes—
291#400C2314yes—
292#400C2318yes—
293#400C2314yes—
294#400C2318yes—
295#400C2318yes—
296#400C2314yes—
297#399C2318yes—
298#399C2318yes—
299#399C2318yes—
300#399C2318yes—
301#398C2314yes—
302#398C2314yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2318yes—
307#398C2318yes—
308#398C2318yes—
309#398C2314yes—
310#398C2318yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#397C2318yes—
315#397C2318yes—
316#397C2314yes—
317#397C2314yes—
318#397C2318yes—
319#397C2318yes—
320#397C2318yes—
321#396C2318yes—
322#396C2318yes—
323#396C2318yes—
324#396C2318yes—
325#396C2314yes—
326#396C2318yes—
327#396C2318yes—
328#396C2314yes—
329#396C2318yes—
330#396C2318yes—
331#396C2318yes—
332#396C2318yes—
333#396C2318yes—
334#396C2318yes—
335#396C2318yes—
336#396C2314yes—
337#396C2314yes—
338#395C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2314yes—
346#394C2314yes—
347#394C2318yes—
348#394C2318yes—
349#394C2318yes—
350#394C2314yes—
351#394C2318yes—
352#394C2314yes—
353#394C2314yes—
354#394C2314yes—
355#393C2318yes—
356#392C2318yes—
357#392C2318yes—
358#392C2318yes—
359#392C2314yes—
360#392C2314yes—
361#391C2312yes—
362#391C2314yes—
363#391C2312yes—
364#391C2312yes—
365#391C2314yes—
366#391C2312yes—
367#391C2312yes—
368#391C2312yes—
369#391C2312yes—
370#390C2314yes—
371#390C2312yes—
372#390C2314yes—
373#390C2312yes—
374#390C2314yes—
375#390C2312yes—
376#390C2312yes—
377#390C2312yes—
378#390C2312yes—
379#390C2314yes—
380#390C2314yes—
381#390C2314yes—
382#390C2312yes—
383#390C2312yes—
384#390C2312yes—
385#390C2312yes—
386#390C2314yes—
387#390C2312yes—
388#390C2314yes—
389#390C2312yes—
390#390C2314yes—
391#390C2314yes—
392#390C2314yes—
393#390C2314yes—
394#390C2318yes—
395#390C2312yes—
396#390C2312yes—
397#390C2312yes—
398#390C2312yes—
399#389C2312yes—
400#389C2312yes—
401#389C2312yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2312yes—
407#389C2314yes—
408#389C2314yes—
409#389C2312yes—
410#389C2314yes—
411#389C2314yes—
412#389C2312yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2318yes—
419#389C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2312yes—
427#388C2314yes—
428#388C2314yes—
429#388C2318yes—
430#388C2318yes—
431#388C2314yes—
432#388C2314yes—
433#388C2318yes—
434#388C2314yes—
435#388C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2318yes—
443#386C2318yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#386C2318yes—
448#386C2318yes—
449#386C2318yes—
450#386C2318yes—
451#386C2318yes—
452#386C2314yes—
453#386C2314yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2318yes—
458#385C2318yes—
459#385C2318yes—
460#385C2318yes—
461#385C2318yes—
462#385C2318yes—
463#385C2318yes—
464#385C2318yes—
465#384C2311yescharacteristic
466#384C2312yes—
467#384C2311yescharacteristic
468#384C2312yes—
469#384C2312yes—
470#384C2311yescharacteristic
471#384C2312yes—
472#384C2312yes—
473#384C2314yes—
474#384C2314yes—
475#384C2318yes—
476#384C2312yes—
477#384C2312yes—
478#384C2314yes—
479#382C2312yes—
480#382C2314yes—
481#382C2318yes—
482#380C2314yes—
483#380C2314yes—
484#380C2318yes—
485#380C2318yes—
486#380C2314yes—
487#380C2314yes—
488#380C2312yes—
489#380C2314yes—
490#380C2314yes—
491#380C2314yes—
492#380C2314yes—
493#380C2318yes—
494#380C2318yes—
495#380C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2311yescharacteristic
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2311yescharacteristic
516C4×C4⋊C4C2311yescharacteristic
517C4×C4⋊C4C2311yescharacteristic
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2312yes—
523#376C2314yes—
524C43C2312yes—
525C43C2311yescharacteristic
526C43C2312yes—
527C2×#41—48no—
528C2×#41—48no—
529C2×#41—48no—
530C22×Q8C2411yescharacteristic
531C22×Q8C2411yescharacteristic
532C22×Q8C2412yes—
533C22×Q8C2414yes—
534C22×D4C2412yes—
535C22×D4C2412yes—
536C22×D4C2412yes—
537C22×D4C2412yes—
538C22×D4C2414yes—
539C22×D4C2411yescharacteristic
540C22×D4C2412yes—
541C22×D4C2412yes—
542C22×D4C2414yes—
543C22×D4C2414yes—
544C22×D4C2414yes—
545C22×D4C2418yes—
546C22×D4C2418yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2414yes—
550C23×C4C2414yes—
551C23×C4C2412yes—
552C23×C4C2418yes—
553C23×C4C2418yes—
554C23×C4C2418yes—
555C4⋊Q8—24no—
556C4⋊Q8—28no—
557C4⋊Q8—44no—
558C4⋊Q8—44no—
559C4⋊Q8—82no—
560#127—28no—
561#127—28no—
562#127—24no—
563#127—24no—
564#127—48no—
565#126—48no—
566#126—48no—
567#126—416no—
568#126—416no—
569#125—28no—
570#125—44no—
571#125—44no—
572#125—48no—
573#125—48no—
574#124—48no—
575#124—44no—
576#124—44no—
577#124—84no—
578#123—416no—
579#123—416no—
580#123—48no—
581#123—48no—
582#123—88no—
583C22⋊Q8—416no—
584C22⋊Q8—416no—
585C22⋊Q8—44no—
586C22⋊Q8—44no—
587C22⋊Q8—48no—
588C22⋊Q8—48no—
589C22⋊Q8—48no—
590C22⋊Q8—48no—
591#121—28no—
592#121—416no—
593#121—416no—
594#121—44no—
595#121—44no—
596#121—44no—
597#121—48no—
598#121—48no—
599#121—48no—
600#121—88no—
601C4×Q8—24no—
602C4×Q8—24no—
603C4×Q8—24no—
604C4×Q8—28no—
605C4×Q8—24no—
606C4×Q8—24no—
607C4×Q8—48no—
608C4×Q8—42no—
609C4×D4—24no—
610C4×D4—28no—
611C4×D4—28no—
612C4×D4—28no—
613C4×D4—24no—
614C4×D4—24no—
615C4×D4—28no—
616C4×D4—48no—
617C4×D4—416no—
618C4×D4—48no—
619C4×D4—48no—
620C4×D4—48no—
621C4×D4—44no—
622C4×D4—48no—
623C4×D4—48no—
624C4×D4—48no—
625C4×D4—48no—
626C4×D4—44no—
627C4×D4—84no—
628#117—216no—
629#117—48no—
630#117—48no—
631C2×C4⋊C4—48no—
632C2×C4⋊C4—48no—
633C2×C4⋊C4—48no—
634C2×C4⋊C4—48no—
635C2×C4⋊C4—84no—
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2418yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2418yes—
685C2×C4⋊C4C2418yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2411yescharacteristic
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2412yes—
697C2×C22⋊C4C2412yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2418yes—
727C2×C42—28no—
728C2×C42C2412yes—
729C2×C42C2412yes—
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2418yes—
733C2×C42C2412yes—
734C2×C42C2412yes—
735C2×C42C2414yes—
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2412yes—
739C2×C42C2411yescharacteristic
740C2×C42C2412yes—
741C2×C42C2412yes—
742C2×C42C2412yes—
743C2×C42C2412yes—
744C2×C42C2412yes—
745C2×C42C2412yes—
746C2×C42C2412yes—
747C2×C42C2412yes—
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2412yes—
757#95C2412yes—
758#95C2412yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2412yes—
764#95C2412yes—
765#95C2412yes—
766#95C2412yes—
767#95C2412yes—
768#95C2412yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2418yes—
773#95C2418yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2418yes—
780#95C2418yes—
781#95C2418yes—
782#95C2418yes—
783#95C2418yes—
784C24C2514yes—
785C24C2514yes—
786C24C2512yes—
787#41—832no—
788C2×Q8—22no—
789C2×Q8—22no—
790C2×Q8—22no—
791C2×Q8—22no—
792C2×Q8—24no—
793C2×Q8—24no—
794C2×Q8—28no—
795C2×Q8—22no—
796C2×Q8—22no—
797C2×Q8—24no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—22no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—28no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—22no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—42no—
822C2×D4—44no—
823C2×D4—42no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—42no—
828C2×D4—48no—
829C2×D4—48no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4—44no—
833C2×D4—42no—
834C2×D4—48no—
835C2×D4—48no—
836C2×D4—48no—
837C2×D4—48no—
838C2×D42−1+414yes—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—28no—
846C22×C4—28no—
847C22×C4—28no—
848C22×C4—28no—
849C22×C4—24no—
850C22×C4—28no—
851C22×C4—24no—
852C22×C4—28no—
853C22×C4—42no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2514yes—
868C22×C4C2511yescharacteristic
869C22×C4C2512yes—
870C22×C4C2512yes—
871C22×C4C2512yes—
872C22×C4C2512yes—
873C22×C4C2514yes—
874C22×C4C2514yes—
875C22×C4C2514yes—
876C22×C4C2518yes—
877C22×C4C2512yes—
878C22×C4C2512yes—
879C22×C4C2512yes—
880C22×C4C2511yescharacteristic
881C22×C4C2511yescharacteristic
882C22×C4C2511yescharacteristic
883C22×C4C2511yescharacteristic
884C22×C4C2511yescharacteristic
885C22×C4C2511yescharacteristic
886C4⋊C4—22no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—22no—
896C4⋊C4—28no—
897C4⋊C4—28no—
898C4⋊C4—28no—
899C4⋊C4—22no—
900C4⋊C4—22no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—28no—
906C4⋊C4—24no—
907C4⋊C4—22no—
908C4⋊C4—22no—
909C4⋊C4—24no—
910C4⋊C4—22no—
911C4⋊C4—24no—
912C4⋊C4—22no—
913C4⋊C4—48no—
914C4⋊C4—48no—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—42no—
918C4⋊C4—48no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—42no—
925C4⋊C4—44no—
926C4⋊C4—42no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—42no—
932C4⋊C4—48no—
933C4⋊C4—44no—
934C4⋊C4—48no—
935C4⋊C4—48no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4H(5,𝔽2)14yes—
941C22⋊C4—24no—
942C22⋊C4—216no—
943C22⋊C4—28no—
944C22⋊C4—24no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—24no—
949C22⋊C4—28no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—48no—
959C22⋊C4—48no—
960C22⋊C4—48no—
961C22⋊C4—48no—
962C22⋊C4—48no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—48no—
970C22⋊C4—44no—
971C22⋊C4—48no—
972C22⋊C4—48no—
973C22⋊C4—48no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—48no—
977C42—24no—
978C42—24no—
979C42—24no—
980C42—216no—
981C42—24no—
982C42—24no—
983C42—24no—
984C42—24no—
985C42—28no—
986C42—22no—
987C42—24no—
988C42—22no—
989C42—24no—
990C42—24no—
991C42—24no—
992C42—22no—
993C42—24no—
994C42—42no—
995C42—42no—
996C42—42no—
997C42—41no—
998C42H(5,𝔽2)14yes—
999C42H(5,𝔽2)14yes—
1000C422−1+414yes—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23C2×2−1+414yes—
1022C23C2611yescharacteristic
1023Q8—44no—
1024Q8—48no—
1025Q8—44no—
1026Q8—88no—
1027D4—28no—
1028D4—416no—
1029D4—48no—
1030D4—48no—
1031D4—48no—
1032D4—48no—
1033D4—48no—
1034D4—84no—
1035D4—88no—
1036D4—88no—
1037D4—88no—
1038D4—816no—
1039D4—168no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—28no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—28no—
1072C2×C4—24no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—28no—
1095C2×C4—24no—
1096C2×C4—48no—
1097C2×C4—48no—
1098C2×C4—416no—
1099C2×C4—48no—
1100C2×C4—416no—
1101C2×C4—816no—
1102C2×C4—168no—
1103C2×C4—168no—
1104C2×C4C2×H(5,𝔽2)14yes—
1105C2×C4C2×H(5,𝔽2)12yes—
1106C2×C4C2×H(5,𝔽2)12yes—
1107C2×C4C2×H(5,𝔽2)12yes—
1108C2×C4C2×H(5,𝔽2)12yes—
1109C2×C4C2×H(5,𝔽2)12yes—
1110C2×C4C2×H(5,𝔽2)12yes—
1111C2×C4C2×H(5,𝔽2)12yes—
1112C2×C4C2×2−1+412yes—
1113C2×C4C2×2−1+412yes—
1114C2×C4C2×2−1+412yes—
1115C2×C4C2×2−1+412yes—
1116C2×C4#58512yes—
1117C22—24no—
1118C22—24no—
1119C22—24no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—44no—
1125C22—44no—
1126C22—44no—
1127C22—44no—
1128C22—44no—
1129C22—44no—
1130C22—44no—
1131C22—44no—
1132C22—44no—
1133C22—44no—
1134C22—44no—
1135C22—44no—
1136C22—44no—
1137C22—44no—
1138C22C22×H(5,𝔽2)11yescharacteristic
1139C22C22×H(5,𝔽2)11yescharacteristic
1140C22C22×H(5,𝔽2)11yescharacteristic
1141C22C22×2−1+411yescharacteristic
1142C22C22×2−1+411yescharacteristic
1143C22C2×#58511yescharacteristic
1144C22H(7,𝔽2)11yescharacteristic
1145C4—24no—
1146C4—22no—
1147C4—22no—
1148C4—22no—
1149C4—42no—
1150C4—44no—
1151C4—44no—
1152C4—42no—
1153C4—42no—
1154C4—44no—
1155C4—42no—
1156C4—41no—
1157C4—42no—
1158C4—42no—
1159C4—44no—
1160C4—48no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4#354614yes—
1166C4#354814yes—
1167C4#355214yes—
1168C2—44no—
1169C2—84no—
1170C2—84no—
1171C2C2×#355211yescharacteristic
1172C2C2×#354611yescharacteristic
1173C2C2×#354811yescharacteristic
1174C2#6291611yescharacteristic
1175C2#6292611yescharacteristic
1176C2#6294411yescharacteristic
1177C2#6301311yescharacteristic
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. #59823C2semidirect
2. #59815C2semidirect
3. #59680C2semidirect
4. #59304C2semidirect
5. #53716C2semidirect
6. #53132C2semidirect
7. #53095C2semidirect
8. #52963C2semidirect
9. #42928C2semidirect
10. #42580C2semidirect
11. #42504C2semidirect
12. #39634C2semidirect
13. #39169C2semidirect
14. #38966C2semidirect
15. #38952C2semidirect
16. #38920C2semidirect
17. #38908C2semidirect
18. #37637C2semidirect
19. #37625C2semidirect
20. #37620C2semidirect
21. #36594C2semidirect
22. #36559C2semidirect
23. #36180C2semidirect
24. #34951C2semidirect
25. #34934C2semidirect
26. #34934C2semidirect

Maximal subgroups

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

subgroupindex
#598232
#598152
#596802
#593042
#537162
#531322
#530952
#529632
#429282
#425802
#425042
#396342
#391692
#389662
#389522
#389202
#389082
#376372
#376252
#376202
#365942
#365592
#361802
#349512
#349342