Finite Group Databasebeta

← #8943770

Subgroups — #8943770

Order 512.

4646 conjugacy classes of subgroups.

The subgroup lattice has 1295 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57630C214yesmaximal, complemented
2#56407C214yesmaximal, complemented
3#54748C214yesmaximal, complemented
4#51828C214yesmaximal, complemented
5#50880C212yesmaximal, complemented
6#49549C212yesmaximal, complemented
7#49199C214yesmaximal, complemented
8#48743C214yesmaximal, complemented
9#47883C212yesmaximal, complemented
10#46858C212yesmaximal, complemented
11#46398C212yesmaximal, complemented
12#43657C214yesmaximal, complemented
13#43550C214yesmaximal, complemented
14#42908C212yesmaximal, complemented
15#40944C214yesmaximal, complemented
16#40803C214yesmaximal, complemented
17#37948C212yesmaximal, complemented
18#37940C212yesmaximal, complemented
19#36707C211yesmaximal, characteristic, complemented
20#35925C212yesmaximal, complemented
21#35703C212yesmaximal, complemented
22#35644C211yesmaximal, characteristic, complemented
23#35349C211yesmaximal, characteristic, complemented
24C2×#548C2212yes—
25C2×#544C2211yescharacteristic, complemented
26C2×#537C2211yescharacteristic, complemented
27C22×C22⋊Q8C2211yescharacteristic
28C2×#518C2211yescharacteristic
29#2847C2212yes—
30#2836C2214yescomplemented
31#2833C2214yescomplemented
32#2827C2214yescomplemented
33#2824C2212yescomplemented
34#2817C2214yescomplemented
35#2812C2212yes—
36#2804C2214yescomplemented
37#2799C2214yescomplemented
38#2789C2214yescomplemented
39#2788C2214yes—
40#2786C2214yes—
41#2784C2214yes—
42#2784C2214yescomplemented
43#2781C2214yes—
44#2778C2214yes—
45#2772C2214yescomplemented
46#2771C2212yes—
47#2767C2214yescomplemented
48#2767C2214yescomplemented
49#2766C2214yescomplemented
50#2763C2214yescomplemented
51#2762C2214yescomplemented
52#2761C2214yes—
53#2760C2212yes—
54#2759C2214yescomplemented
55#2754C2214yescomplemented
56#2753C2214yescomplemented
57#2747C2214yescomplemented
58#2746C2214yes—
59#2746C2214yes—
60#2746C2214yes—
61#2746C2214yescomplemented
62#2745C2214yescomplemented
63#2745C2214yescomplemented
64#2744C2214yescomplemented
65#2744C2214yescomplemented
66#2743C2214yescomplemented
67#2743C2214yescomplemented
68#2742C2214yes—
69#2731C2214yescomplemented
70#2730C2214yescomplemented
71#2729C2214yescomplemented
72#2723C2214yescomplemented
73#2716C2214yescomplemented
74#2711C2214yescomplemented
75#2708C2214yes—
76#2704C2214yescomplemented
77#2696C2214yes—
78#2693C2212yescomplemented
79#2692C2214yes—
80#2692C2214yescomplemented
81#2688C2214yes—
82#2688C2214yes—
83#2687C2214yescomplemented
84#2686C2214yescomplemented
85#2686C2214yescomplemented
86#2681C2214yes—
87#2677C2212yescomplemented
88#2677C2214yescomplemented
89#2676C2214yes—
90#2676C2214yescomplemented
91#2674C2214yescomplemented
92#2667C2212yescomplemented
93#2666C2214yescomplemented
94#2659C2212yescomplemented
95#2653C2214yescomplemented
96#2653C2214yescomplemented
97#2650C2214yescomplemented
98#2646C2212yes—
99#2639C2214yescomplemented
100#2638C2212yes—
101#2636C2214yescomplemented
102#2635C2214yescomplemented
103#2631C2212yes—
104#2618C2212yescomplemented
105#2618C2212yescomplemented
106#2617C2212yes—
107#2617C2212yes—
108#2616C2212yescomplemented
109#2610C2212yes—
110#2609C2214yescomplemented
111#2600C2214yes—
112#2599C2212yes—
113#2598C2214yes—
114#2589C2214yescomplemented
115#2579C2212yes—
116#2579C2212yes—
117#2578C2214yes—
118#2576C2214yes—
119#2576C2214yescomplemented
120#2575C2214yescomplemented
121#2574C2214yes—
122#2574C2214yescomplemented
123#2573C2214yescomplemented
124#2564C2214yescomplemented
125#2563C2214yes—
126#2561C2212yes—
127#2561C2212yes—
128#2553C2214yescomplemented
129#2543C2212yes—
130#2539C2212yes—
131#2535C2214yescomplemented
132#2534C2214yes—
133#2528C2214yescomplemented
134#2517C2212yescomplemented
135#2517C2214yescomplemented
136#2510C2214yes—
137#2505C2214yescomplemented
138#2505C2214yescomplemented
139#2503C2212yescomplemented
140#2503C2212yescomplemented
141#2492C2214yes—
142#2492C2214yescomplemented
143#2489C2214yes—
144#2489C2214yescomplemented
145#2488C2214yescomplemented
146#2487C2212yes—
147#2477C2214yes—
148#2477C2214yescomplemented
149#2476C2214yes—
150#2476C2214yes—
151#2474C2214yescomplemented
152#2474C2214yescomplemented
153#2472C2214yes—
154#2468C2214yescomplemented
155#2468C2214yescomplemented
156#2467C2214yes—
157#2464C2214yes—
158#2463C2214yes—
159#2462C2214yescomplemented
160#2460C2214yescomplemented
161#2459C2214yes—
162#2459C2214yescomplemented
163#2457C2214yes—
164#2456C2214yes—
165#2455C2214yescomplemented
166#2452C2214yescomplemented
167#2450C2214yes—
168#2450C2214yes—
169#2450C2214yescomplemented
170#2450C2214yescomplemented
171#2449C2214yes—
172#2444C2214yes—
173#2438C2214yes—
174#2437C2214yes—
175#2437C2212yes—
176#2436C2212yescomplemented
177#2434C2214yescomplemented
178#2427C2214yescomplemented
179#2421C2214yescomplemented
180#2420C2214yes—
181#2419C2214yescomplemented
182#2418C2214yes—
183#2410C2214yes—
184#2409C2212yes—
185#2409C2212yes—
186#2409C2214yescomplemented
187#2406C2212yescomplemented
188#2404C2212yes—
189#2398C2212yes—
190#2392C2214yescomplemented
191#2388C2212yes—
192C2×#393C2212yes—
193#2379C2214yescomplemented
194#2378C2212yescomplemented
195#2368C2214yescomplemented
196#2364C2214yes—
197#2358C2214yes—
198#2358C2214yes—
199#2353C2212yes—
200#2352C2214yescomplemented
201#2349C2214yescomplemented
202#2343C2214yescomplemented
203#2339C2212yescomplemented
204#2335C2214yescomplemented
205#2325C2212yes—
206#2325C2212yescomplemented
207#2321C2214yes—
208#2315C2211yescharacteristic
209#2315C2211yescharacteristic
210#2315C2212yes—
211#2313C2212yescomplemented
212#2313C2211yescharacteristic, complemented
213#2310C2212yescomplemented
214#2308C2211yescharacteristic
215C2×#386C2211yescharacteristic
216C2×#385C2211yescharacteristic
217#2280C2212yes—
218#2274C2211yescharacteristic, complemented
219C22×#41C2312yes—
220C23×Q8C2311yescharacteristic
221C23×Q8C2312yes—
222C23×D4C2311yescharacteristic
223C24×C4C2311yescharacteristic
224#548—48no—
225#544—44no—
226#537—44no—
227C2×C4⋊Q8C2314yes—
228C2×C4⋊Q8C2314yes—
229C2×#126C2314yes—
230C2×#125C2314yes—
231C2×#124C2312yes—
232C2×#124C2314yes—
233C2×#124C2314yes—
234C2×#123C2314yes—
235C2×#123C2314yes—
236C2×#123C2314yes—
237C2×C22⋊Q8—44no—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×#121C2312yes—
249C2×#121C2312yes—
250C2×#121C2312yes—
251C2×#121C2312yes—
252C2×#121C2314yes—
253C2×#121C2314yes—
254C2×#121C2314yes—
255C2×#121C2312yes—
256C2×#120C2314yes—
257C2×#120C2314yes—
258#518—44no—
259C2×C4×Q8C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×#117C2312yes—
272C2×#117C2312yes—
273C2×#117C2314yes—
274C2×#117C2312yes—
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2312yes—
278C22×C4⋊C4C2311yescharacteristic
279C22×C22⋊C4C2311yescharacteristic
280C22×C22⋊C4C2311yescharacteristic
281C22×C22⋊C4C2311yescharacteristic
282C22×C22⋊C4C2311yescharacteristic
283C22×C22⋊C4C2312yes—
284C22×C22⋊C4C2311yescharacteristic
285C22×C22⋊C4C2312yes—
286C22×C22⋊C4C2314yes—
287#401C2314yes—
288#401C2314yes—
289#401C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#399C2314yes—
310#399C2314yes—
311#399C2314yes—
312#399C2314yes—
313#399C2312yes—
314#399C2312yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2312yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#397C2312yes—
330#397C2312yes—
331#397C2312yes—
332#397C2312yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2312yes—
345#397C2314yes—
346#397C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#395C2312yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2312yes—
364#395C2314yes—
365#395C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2312yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#393C2312yes—
386#393C2312yes—
387#393C2312yes—
388#393C2312yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2312yes—
393#393C2312yes—
394#393C2312yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#393C2312yes—
402#392C2312yes—
403#392C2314yes—
404#392C2312yes—
405#392C2312yes—
406#392C2314yes—
407#392C2312yes—
408#392C2314yes—
409#392C2314yes—
410#392C2312yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#390C2314yes—
424#390C2314yes—
425#390C2314yes—
426#390C2314yes—
427#390C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#386C2312yes—
497#386C2312yes—
498#386C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2312yes—
510#386C2312yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2312yes—
531#385C2314yes—
532#385C2312yes—
533#385C2312yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2312yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2312yes—
547#385C2312yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#383C2312yes—
559#383C2314yes—
560#382C2314yes—
561#382C2314yes—
562#382C2314yes—
563#382C2314yes—
564#382C2314yes—
565#382C2314yes—
566#382C2314yes—
567#381C2314yes—
568#381C2314yes—
569#381C2314yes—
570#381C2312yes—
571#381C2312yes—
572#381C2314yes—
573#381C2314yes—
574#381C2314yes—
575#381C2314yes—
576#380C2314yes—
577#380C2314yes—
578#380C2314yes—
579#380C2314yes—
580#380C2314yes—
581#380C2312yes—
582#380C2312yes—
583#380C2312yes—
584#380C2312yes—
585#380C2312yes—
586#380C2312yes—
587#380C2312yes—
588#380C2314yes—
589#380C2314yes—
590#380C2312yes—
591#380C2314yes—
592#380C2312yes—
593#380C2312yes—
594#380C2314yes—
595#379C2314yes—
596#379C2312yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2312yes—
603C4×C22⋊C4C2312yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613#376C2312yes—
614C2×#95C2314yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C2×#95C2314yes—
619C25C2411yescharacteristic
620C25C2411yescharacteristic
621C2×#41—28no—
622C2×#41—84no—
623C22×Q8—42no—
624C22×Q8—44no—
625C22×Q8—44no—
626C22×Q8—84no—
627C22×Q8C2412yes—
628C22×Q8C2412yes—
629C22×Q8C2414yes—
630C22×Q8C2412yes—
631C22×Q8C2414yes—
632C22×D4—24no—
633C22×D4—42no—
634C22×D4—42no—
635C22×D4C2412yes—
636C22×D4C2412yes—
637C22×D4C2414yes—
638C22×D4C2412yes—
639C22×D4C2414yes—
640C22×D4C2414yes—
641C22×D4C2414yes—
642C22×D4C2414yes—
643C22×D4C2412yes—
644C22×D4C2412yes—
645C23×C4—44no—
646C23×C4—42no—
647C23×C4C2411yescharacteristic
648C23×C4C2411yescharacteristic
649C23×C4C2412yes—
650C23×C4C2411yescharacteristic
651C23×C4C2411yescharacteristic
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2411yescharacteristic
655C23×C4C2412yes—
656C23×C4C2411yescharacteristic
657C23×C4C2414yes—
658C23×C4C2412yes—
659C23×C4C2411yescharacteristic
660C23×C4C2414yes—
661C23×C4C2411yescharacteristic
662C23×C4C2412yes—
663C23×C4C2414yes—
664C23×C4C2414yes—
665C23×C4C2414yes—
666C23×C4C2411yescharacteristic
667C4⋊Q8—48no—
668C4⋊Q8—84no—
669#126—84no—
670#125—48no—
671#124—44no—
672#124—48no—
673#124—48no—
674#123—48no—
675#123—84no—
676#123—84no—
677C22⋊Q8—28no—
678C22⋊Q8—44no—
679C22⋊Q8—48no—
680C22⋊Q8—48no—
681C22⋊Q8—48no—
682C22⋊Q8—48no—
683C22⋊Q8—48no—
684C22⋊Q8—84no—
685C22⋊Q8—84no—
686C22⋊Q8—84no—
687#121—44no—
688#121—44no—
689#121—48no—
690#121—48no—
691#121—48no—
692#121—44no—
693#121—44no—
694#121—44no—
695#120—216no—
696#120—84no—
697C4×Q8—44no—
698C4×D4—28no—
699C4×D4—48no—
700C4×D4—44no—
701C4×D4—44no—
702C4×D4—48no—
703C4×D4—48no—
704C4×D4—44no—
705C4×D4—84no—
706C4×D4—84no—
707C4×D4—84no—
708C4×D4—84no—
709#117—44no—
710#117—48no—
711#117—44no—
712#117—44no—
713C2×C4⋊C4—24no—
714C2×C4⋊C4—24no—
715C2×C4⋊C4—44no—
716C2×C4⋊C4—42no—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C22⋊C4—24no—
758C2×C22⋊C4—44no—
759C2×C22⋊C4—44no—
760C2×C22⋊C4—42no—
761C2×C22⋊C4—42no—
762C2×C22⋊C4—42no—
763C2×C22⋊C4—42no—
764C2×C22⋊C4—84no—
765C2×C22⋊C4C2412yes—
766C2×C22⋊C4C2412yes—
767C2×C22⋊C4C2412yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C42C2414yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825#95C2412yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2412yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2412yes—
840#95C2414yes—
841#95C2412yes—
842#95C2412yes—
843#95C2412yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2412yes—
860#95C2414yes—
861#95C2412yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883C24—22no—
884C24—22no—
885C24—22no—
886C24—41no—
887C24—42no—
888C24—42no—
889C24—41no—
890C24—42no—
891C24—42no—
892C242−1+414yes—
893C24C2514yes—
894C24C2511yescharacteristic
895C24C2511yescharacteristic
896C24C2512yes—
897C24C2511yescharacteristic
898#41—816no—
899C2×Q8—24no—
900C2×Q8—24no—
901C2×Q8—28no—
902C2×Q8—44no—
903C2×Q8—44no—
904C2×Q8—44no—
905C2×Q8—44no—
906C2×Q8—44no—
907C2×Q8—44no—
908C2×Q8—44no—
909C2×Q8—42no—
910C2×Q8—44no—
911C2×Q8—88no—
912C2×Q8—816no—
913C2×D4—24no—
914C2×D4—28no—
915C2×D4—24no—
916C2×D4—24no—
917C2×D4—24no—
918C2×D4—28no—
919C2×D4—28no—
920C2×D4—28no—
921C2×D4—28no—
922C2×D4—24no—
923C2×D4—42no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—42no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—44no—
941C2×D4—416no—
942C22×C4—22no—
943C22×C4—24no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—28no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—41no—
955C22×C4—41no—
956C22×C4—42no—
957C22×C4—44no—
958C22×C4—42no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—41no—
977C22×C4—42no—
978C22×C4—41no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—44no—
982C22×C4—42no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—42no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—42no—
990C22×C4—44no—
991C22×C4—88no—
992C22×C4H(5,𝔽2)14yes—
993C22×C4C2512yes—
994C22×C4C2514yes—
995C22×C4C2514yes—
996C22×C4C2514yes—
997C22×C4C2512yes—
998C22×C4C2512yes—
999C22×C4C2512yes—
1000C22×C4C2514yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2514yes—
1004C22×C4C2514yes—
1005C22×C4C2512yes—
1006C22×C4C2514yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—24no—
1014C4⋊C4—28no—
1015C4⋊C4—24no—
1016C4⋊C4—28no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—44no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—42no—
1033C4⋊C4—44no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—42no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C22⋊C4—24no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—24no—
1057C22⋊C4—28no—
1058C22⋊C4—24no—
1059C22⋊C4—24no—
1060C22⋊C4—24no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—44no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C42—24no—
1101C42—28no—
1102C42—44no—
1103C42—42no—
1104C42—44no—
1105C42—44no—
1106C42—44no—
1107C42—44no—
1108C42—44no—
1109C42—44no—
1110C42—44no—
1111C23—28no—
1112C23—21no—
1113C23—21no—
1114C23—22no—
1115C23—21no—
1116C23—21no—
1117C23—24no—
1118C23—21no—
1119C23—22no—
1120C23—21no—
1121C23—22no—
1122C23—22no—
1123C23—22no—
1124C23—22no—
1125C23—22no—
1126C23—24no—
1127C23—22no—
1128C23—24no—
1129C23—24no—
1130C23—24no—
1131C23—24no—
1132C23—24no—
1133C23—24no—
1134C23—24no—
1135C23—44no—
1136C23—48no—
1137C23—82no—
1138C23—82no—
1139C23—84no—
1140C23—84no—
1141C23—161no—
1142C23—161no—
1143C23—162no—
1144C23C2×H(5,𝔽2)12yes—
1145C23C2×2−1+412yes—
1146C23C2×2−1+414yes—
1147C23#58512yes—
1148C23C2611yescharacteristic
1149Q8—48no—
1150Q8—88no—
1151Q8—84no—
1152Q8—88no—
1153Q8—162no—
1154D4—48no—
1155D4—48no—
1156D4—48no—
1157D4—416no—
1158D4—88no—
1159D4—88no—
1160D4—88no—
1161D4—88no—
1162D4—162no—
1163D4—162no—
1164C2×C4—28no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—24no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—44no—
1212C2×C4—44no—
1213C2×C4—84no—
1214C2×C4—84no—
1215C2×C4—84no—
1216C2×C4—88no—
1217C2×C4—82no—
1218C2×C4—84no—
1219C2×C4—82no—
1220C2×C4—82no—
1221C2×C4—82no—
1222C2×C4—88no—
1223C2×C4—88no—
1224C2×C4—162no—
1225C2×C4—161no—
1226C2×C4—161no—
1227C2×C4—164no—
1228C2×C4—164no—
1229C2×C4—162no—
1230C2×C4C2×H(5,𝔽2)14yes—
1231C2×C4#58514yes—
1232C22—22no—
1233C22—24no—
1234C22—22no—
1235C22—22no—
1236C22—22no—
1237C22—22no—
1238C22—28no—
1239C22—24no—
1240C22—24no—
1241C22—41no—
1242C22—41no—
1243C22—42no—
1244C22—42no—
1245C22—41no—
1246C22—41no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—44no—
1251C22—42no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—88no—
1260C22—164no—
1261C22C22×H(5,𝔽2)11yescharacteristic
1262C22C22×2−1+411yescharacteristic
1263C22C2×#58511yescharacteristic
1264C22C2×#58512yes—
1265C22H(7,𝔽2)12yes—
1266C4—24no—
1267C4—24no—
1268C4—42no—
1269C4—44no—
1270C4—42no—
1271C4—42no—
1272C4—42no—
1273C4—42no—
1274C4—44no—
1275C4—42no—
1276C4—44no—
1277C4—42no—
1278C4—44no—
1279C4—44no—
1280C4—44no—
1281C4—44no—
1282C4—44no—
1283C4—44no—
1284C2—42no—
1285C2—42no—
1286C2—42no—
1287C2—44no—
1288C2—84no—
1289C2#6281911yescharacteristic
1290C2#6282411yescharacteristic
1291C2#6286211yescharacteristic
1292C2#6290212yes—
1293C2#6291012yes—
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. #57630C2semidirect
2. #56407C2semidirect
3. #54748C2semidirect
4. #51828C2semidirect
5. #50880C2semidirect
6. #49549C2semidirect
7. #49199C2semidirect
8. #48743C2semidirect
9. #47883C2semidirect
10. #46858C2semidirect
11. #46398C2semidirect
12. #43657C2semidirect
13. #43550C2semidirect
14. #42908C2semidirect
15. #40944C2semidirect
16. #40803C2semidirect
17. #37948C2semidirect
18. #37940C2semidirect
19. #36707C2semidirect
20. #35925C2semidirect
21. #35703C2semidirect
22. #35644C2semidirect
23. #35349C2semidirect
25. C2×#544C22semidirect
26. C2×#537C22semidirect
30. #2836C22semidirect
31. #2833C22semidirect
32. #2827C22semidirect
33. #2824C22semidirect
34. #2817C22semidirect
36. #2804C22semidirect
37. #2799C22semidirect
38. #2789C22semidirect
42. #2784C22semidirect
45. #2772C22semidirect
47. #2767C22semidirect
48. #2767C22semidirect
49. #2766C22semidirect
50. #2763C22semidirect
51. #2762C22semidirect
54. #2759C22semidirect
55. #2754C22semidirect
56. #2753C22semidirect
57. #2747C22semidirect
61. #2746C22semidirect
62. #2745C22semidirect
63. #2745C22semidirect
64. #2744C22semidirect
65. #2744C22semidirect
66. #2743C22semidirect
67. #2743C22semidirect
69. #2731C22semidirect
70. #2730C22semidirect
71. #2729C22semidirect
72. #2723C22semidirect
73. #2716C22semidirect
74. #2711C22semidirect
76. #2704C22semidirect
78. #2693C22semidirect
80. #2692C22semidirect
83. #2687C22semidirect
84. #2686C22semidirect
85. #2686C22semidirect
87. #2677C22semidirect
88. #2677C22semidirect
90. #2676C22semidirect
91. #2674C22semidirect
92. #2667C22semidirect
93. #2666C22semidirect
94. #2659C22semidirect
95. #2653C22semidirect
96. #2653C22semidirect
97. #2650C22semidirect
99. #2639C22semidirect
101. #2636C22semidirect
102. #2635C22semidirect
104. #2618C22semidirect
105. #2618C22semidirect
108. #2616C22semidirect
110. #2609C22semidirect
114. #2589C22semidirect
119. #2576C22semidirect
120. #2575C22semidirect
122. #2574C22semidirect
123. #2573C22semidirect
124. #2564C22semidirect
128. #2553C22semidirect
131. #2535C22semidirect
133. #2528C22semidirect
134. #2517C22semidirect
135. #2517C22semidirect
137. #2505C22semidirect
138. #2505C22semidirect
139. #2503C22semidirect
140. #2503C22semidirect
142. #2492C22semidirect
144. #2489C22semidirect
145. #2488C22semidirect
148. #2477C22semidirect
151. #2474C22semidirect
152. #2474C22semidirect
154. #2468C22semidirect
155. #2468C22semidirect
159. #2462C22semidirect
160. #2460C22semidirect
162. #2459C22semidirect
165. #2455C22semidirect
166. #2452C22semidirect
169. #2450C22semidirect
170. #2450C22semidirect
176. #2436C22semidirect
177. #2434C22semidirect
178. #2427C22semidirect
179. #2421C22semidirect
181. #2419C22semidirect
186. #2409C22semidirect
187. #2406C22semidirect
190. #2392C22semidirect
193. #2379C22semidirect
194. #2378C22semidirect
195. #2368C22semidirect
200. #2352C22semidirect
201. #2349C22semidirect
202. #2343C22semidirect
203. #2339C22semidirect
204. #2335C22semidirect
206. #2325C22semidirect
211. #2313C22semidirect
212. #2313C22semidirect
213. #2310C22semidirect
218. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#576302
#564072
#547482
#518282
#508802
#495492
#491992
#487432
#478832
#468582
#463982
#436572
#435502
#429082
#409442
#408032
#379482
#379402
#367072
#359252
#357032
#356442
#353492