Finite Group Databasebeta

← #8750652

Subgroups — #8750652

Order 512.

4621 conjugacy classes of subgroups.

The subgroup lattice has 1496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59864C211yesmaximal, characteristic, complemented
2#59712C212yesmaximal, complemented
3#58304C214yesmaximal, complemented
4#58014C214yesmaximal, complemented
5#57783C212yesmaximal, complemented
6#56766C214yesmaximal, complemented
7#56504C214yesmaximal, complemented
8#53080C212yesmaximal, complemented
9#53046C212yesmaximal, complemented
10#52957C211yesmaximal, characteristic, complemented
11#52403C214yesmaximal, complemented
12#47773C212yesmaximal, complemented
13#45208C212yesmaximal, complemented
14#45176C212yesmaximal, complemented
15#45047C211yesmaximal, characteristic, complemented
16#44930C212yesmaximal, complemented
17#44878C212yesmaximal, complemented
18#42915C211yesmaximal, characteristic, complemented
19#42731C212yesmaximal, complemented
20#42712C212yesmaximal, complemented
21#42671C212yesmaximal, complemented
22#42503C212yesmaximal, complemented
23#42403C212yesmaximal, complemented
24#41009C214yesmaximal, complemented
25#39789C212yesmaximal, complemented
26#39747C211yesmaximal, characteristic, complemented
27#36696C211yesmaximal, characteristic, complemented
28#35759C211yesmaximal, characteristic, complemented
29#35682C212yesmaximal, complemented
30C2×#556C2211yescharacteristic
31C2×#550C2211yescharacteristic
32C2×#547C2212yes—
33C2×#544C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2858C2211yescharacteristic
36#2843C2211yescharacteristic
37#2837C2214yes—
38#2832C2214yes—
39#2832C2214yes—
40#2830C2211yescharacteristic
41#2830C2212yes—
42#2829C2212yes—
43#2829C2212yes—
44#2829C2212yes—
45#2828C2214yes—
46#2828C2211yescharacteristic
47#2828C2212yes—
48#2828C2212yes—
49#2824C2214yes—
50#2824C2214yes—
51#2824C2214yes—
52#2824C2212yes—
53#2823C2211yescharacteristic
54#2821C2212yes—
55#2819C2214yes—
56#2818C2212yes—
57#2813C2214yes—
58#2805C2214yes—
59#2804C2212yes—
60#2804C2212yes—
61#2804C2212yes—
62#2803C2214yes—
63#2800C2214yes—
64#2799C2214yes—
65#2798C2214yes—
66#2788C2214yes—
67#2788C2214yes—
68#2784C2212yes—
69#2782C2214yes—
70#2779C2214yes—
71#2763C2214yes—
72#2763C2214yes—
73#2761C2214yes—
74#2753C2214yes—
75#2751C2214yes—
76#2750C2214yes—
77#2750C2214yes—
78#2743C2214yes—
79#2739C2214yes—
80#2737C2214yes—
81#2733C2214yes—
82#2731C2214yes—
83#2729C2214yes—
84#2728C2214yes—
85#2723C2214yes—
86#2715C2214yes—
87#2714C2214yes—
88#2714C2214yes—
89#2714C2214yes—
90#2712C2214yes—
91#2712C2214yes—
92#2712C2214yes—
93#2712C2212yes—
94#2710C2214yes—
95#2710C2214yes—
96#2709C2214yes—
97#2707C2214yes—
98#2702C2214yes—
99#2701C2214yes—
100#2701C2214yes—
101#2700C2214yes—
102#2700C2214yes—
103#2698C2214yes—
104#2686C2214yes—
105#2686C2214yes—
106#2681C2214yes—
107#2675C2212yes—
108#2674C2214yes—
109#2673C2214yes—
110#2672C2214yes—
111#2671C2214yes—
112#2664C2212yes—
113#2662C2214yes—
114#2662C2214yes—
115#2657C2212yes—
116#2652C2214yes—
117#2650C2214yes—
118#2649C2214yes—
119#2648C2214yes—
120#2640C2214yes—
121#2639C2214yes—
122#2636C2212yes—
123#2635C2214yes—
124#2634C2212yes—
125#2630C2214yes—
126#2628C2212yes—
127#2625C2211yescharacteristic
128#2616C2211yescharacteristic
129#2615C2212yes—
130#2605C2214yes—
131#2604C2212yes—
132#2602C2214yes—
133#2600C2214yes—
134#2593C2212yes—
135#2588C2214yes—
136#2581C2212yes—
137#2580C2214yes—
138#2580C2214yes—
139#2574C2214yes—
140#2571C2212yes—
141#2568C2212yes—
142#2566C2212yes—
143#2563C2212yes—
144#2563C2212yes—
145#2562C2212yes—
146#2558C2214yes—
147#2555C2214yes—
148#2551C2212yes—
149#2550C2212yes—
150#2548C2212yes—
151#2547C2212yes—
152#2547C2211yescharacteristic
153#2544C2214yes—
154#2544C2212yes—
155#2541C2211yescharacteristic
156#2537C2212yes—
157#2529C2214yes—
158#2521C2214yes—
159#2518C2214yes—
160#2513C2212yes—
161#2511C2212yes—
162#2511C2212yes—
163#2505C2214yes—
164#2505C2214yes—
165#2503C2211yescharacteristic
166#2503C2211yescharacteristic
167#2500C2212yes—
168#2497C2212yes—
169#2496C2212yes—
170#2492C2212yes—
171#2492C2212yes—
172#2492C2214yes—
173#2491C2212yes—
174#2491C2212yes—
175#2491C2212yes—
176#2491C2212yes—
177#2491C2214yes—
178#2490C2212yes—
179#2489C2212yes—
180#2487C2212yes—
181#2487C2211yescharacteristic
182#2487C2211yescharacteristic
183#2485C2212yes—
184#2466C2214yes—
185#2465C2214yes—
186#2465C2214yes—
187#2463C2214yes—
188#2461C2214yes—
189#2459C2214yes—
190#2459C2214yes—
191#2458C2214yes—
192#2458C2214yes—
193#2457C2214yes—
194#2457C2214yes—
195#2456C2214yes—
196#2455C2212yes—
197#2452C2212yes—
198#2451C2212yes—
199#2450C2214yes—
200#2446C2214yes—
201#2445C2212yes—
202#2442C2212yes—
203#2440C2212yes—
204#2439C2212yes—
205#2439C2212yes—
206#2432C2214yes—
207#2431C2214yes—
208#2430C2214yes—
209#2428C2212yes—
210#2426C2214yes—
211#2422C2212yes—
212#2419C2214yes—
213#2416C2212yes—
214#2416C2212yes—
215#2415C2212yes—
216#2414C2212yes—
217#2414C2212yes—
218#2407C2212yes—
219#2407C2212yes—
220#2407C2214yes—
221#2407C2212yes—
222#2407C2212yes—
223#2407C2214yes—
224#2398C2212yes—
225#2395C2212yes—
226#2395C2211yescharacteristic
227#2392C2212yes—
228#2392C2212yes—
229#2392C2212yes—
230#2388C2214yes—
231#2388C2212yes—
232#2388C2211yescharacteristic
233#2373C2214yes—
234#2369C2212yes—
235#2369C2212yes—
236#2366C2212yes—
237#2363C2212yes—
238#2361C2212yes—
239#2360C2212yes—
240#2357C2212yes—
241#2352C2212yes—
242#2352C2212yes—
243D4×C4⋊C4C2212yes—
244D4×C4⋊C4C2212yes—
245#2347C2211yescharacteristic
246#2346C2211yescharacteristic
247#2345C2212yes—
248#2339C2212yes—
249#2337C2214yes—
250#2326C2212yes—
251#2324C2212yes—
252#2324C2212yes—
253#2314C2212yes—
254#2311C2212yes—
255C4×C4⋊Q8C2212yes—
256C4×#127C2211yescharacteristic
257C4×#126C2212yes—
258#2295C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2311yescharacteristic
261C22×#41C2314yes—
262#556—44no—
263#550—44no—
264#547—48no—
265#544—44no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×#127C2311yescharacteristic
273C2×#127C2311yescharacteristic
274C2×#127C2312yes—
275C2×#127C2312yes—
276C2×#126C2312yes—
277C2×#126C2312yes—
278C2×#126C2312yes—
279C2×#126C2314yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2314yes—
285C2×#124C2314yes—
286C2×#124C2312yes—
287C2×#124C2314yes—
288C2×#124C2312yes—
289C2×#124C2314yes—
290C2×#124C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2311yescharacteristic
297C2×C22⋊Q8C2311yescharacteristic
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2314yes—
308C2×#121C2314yes—
309C2×#121C2314yes—
310C2×#121C2314yes—
311C2×#121C2314yes—
312#520—44no—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2314yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×#117C2311yescharacteristic
333C2×#117C2311yescharacteristic
334C2×#117C2312yes—
335C2×#117C2311yescharacteristic
336C2×#117C2312yes—
337C22×C4⋊C4C2312yes—
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2311yescharacteristic
340C22×C4⋊C4C2311yescharacteristic
341#400C2314yes—
342#400C2312yes—
343#400C2312yes—
344#400C2311yescharacteristic
345#400C2312yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2314yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2312yes—
359#400C2314yes—
360#400C2312yes—
361#400C2314yes—
362#400C2314yes—
363#399C2311yescharacteristic
364#399C2312yes—
365#399C2312yes—
366#399C2314yes—
367#399C2312yes—
368#399C2314yes—
369#398C2314yes—
370#398C2311yescharacteristic
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2312yes—
386#397C2312yes—
387#397C2312yes—
388#397C2314yes—
389#397C2312yes—
390#397C2311yescharacteristic
391#397C2312yes—
392#397C2312yes—
393#397C2312yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2312yes—
402#396C2312yes—
403#396C2312yes—
404#396C2312yes—
405#396C2312yes—
406#396C2312yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2311yescharacteristic
416#395C2312yes—
417#395C2312yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#394C2314yes—
423#394C2312yes—
424#394C2312yes—
425#394C2312yes—
426#394C2312yes—
427#394C2312yes—
428#394C2312yes—
429#394C2312yes—
430#394C2314yes—
431#394C2314yes—
432#394C2311yescharacteristic
433#394C2312yes—
434#394C2312yes—
435#394C2312yes—
436#394C2312yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2312yes—
447#394C2312yes—
448#394C2312yes—
449#394C2312yes—
450#394C2314yes—
451#394C2314yes—
452#394C2312yes—
453#394C2312yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#393C2314yes—
466#393C2314yes—
467#393C2314yes—
468#393C2314yes—
469#393C2314yes—
470#393C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2311yescharacteristic
474#393C2314yes—
475#393C2314yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#393C2312yes—
480#393C2314yes—
481#393C2314yes—
482#392C2312yes—
483#392C2312yes—
484#392C2312yes—
485#392C2312yes—
486#392C2312yes—
487#392C2312yes—
488#392C2312yes—
489#392C2314yes—
490#392C2314yes—
491#392C2314yes—
492#392C2314yes—
493#392C2312yes—
494#392C2311yescharacteristic
495#392C2314yes—
496#392C2314yes—
497#392C2314yes—
498#392C2314yes—
499#392C2314yes—
500#392C2314yes—
501#392C2312yes—
502#391C2314yes—
503#391C2312yes—
504#391C2312yes—
505#391C2314yes—
506#391C2314yes—
507#391C2314yes—
508#391C2314yes—
509#391C2314yes—
510#391C2314yes—
511#391C2314yes—
512#391C2312yes—
513#391C2312yes—
514#391C2314yes—
515#391C2314yes—
516#391C2314yes—
517#391C2314yes—
518#391C2312yes—
519#390C2312yes—
520#390C2311yescharacteristic
521#390C2312yes—
522#390C2311yescharacteristic
523#390C2314yes—
524#390C2314yes—
525#390C2312yes—
526#390C2312yes—
527#390C2312yes—
528#390C2312yes—
529#390C2314yes—
530#390C2312yes—
531#390C2312yes—
532#390C2314yes—
533#390C2314yes—
534#390C2312yes—
535#390C2314yes—
536#390C2314yes—
537#390C2314yes—
538#390C2314yes—
539#389C2314yes—
540#389C2312yes—
541#389C2312yes—
542#389C2314yes—
543#389C2314yes—
544#389C2312yes—
545#389C2312yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2312yes—
550#389C2312yes—
551#389C2314yes—
552#389C2312yes—
553#389C2312yes—
554#389C2314yes—
555#389C2314yes—
556#388C2312yes—
557#388C2312yes—
558#388C2312yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2312yes—
628#386C2314yes—
629#386C2312yes—
630#386C2314yes—
631#386C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2312yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2312yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#384C2311yescharacteristic
654#384C2312yes—
655#384C2312yes—
656#383C2312yes—
657#383C2312yes—
658#382C2314yes—
659#382C2314yes—
660#382C2314yes—
661#382C2312yes—
662#382C2312yes—
663#382C2312yes—
664#381C2314yes—
665#381C2314yes—
666#381C2314yes—
667#381C2314yes—
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2312yes—
673#380C2311yescharacteristic
674#380C2311yescharacteristic
675#380C2312yes—
676#380C2312yes—
677#380C2312yes—
678#380C2314yes—
679#380C2314yes—
680#380C2314yes—
681#380C2312yes—
682#380C2314yes—
683#380C2312yes—
684#380C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2311yescharacteristic
708C4×C22⋊C4C2311yescharacteristic
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2312yes—
713#376C2312yes—
714#376C2312yes—
715C2×#95C2314yes—
716C43C2311yescharacteristic
717C2×#41—42no—
718C2×#41—44no—
719C2×#41—48no—
720C2×#41—44no—
721C2×#41—44no—
722C2×#41—44no—
723C2×#41—84no—
724C2×#41—84no—
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2414yes—
728C22×Q8C2411yescharacteristic
729C22×Q8C2414yes—
730C22×Q8C2414yes—
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2412yes—
735C22×D4C2411yescharacteristic
736C22×D4C2411yescharacteristic
737C22×D4C2414yes—
738C22×D4C2411yescharacteristic
739C22×D4C2412yes—
740C22×D4C2412yes—
741C22×D4C2412yes—
742C22×D4C2414yes—
743C22×D4C2412yes—
744C22×D4C2412yes—
745C22×D4C2414yes—
746C22×D4C2414yes—
747C22×D4C2414yes—
748C22×D4C2414yes—
749C23×C4C2411yescharacteristic
750C23×C4C2412yes—
751C23×C4C2412yes—
752C23×C4C2411yescharacteristic
753C23×C4C2414yes—
754C23×C4C2412yes—
755C23×C4C2412yes—
756C23×C4C2414yes—
757C23×C4C2414yes—
758C23×C4C2414yes—
759C23×C4C2414yes—
760C4⋊Q8—28no—
761C4⋊Q8—44no—
762C4⋊Q8—44no—
763C4⋊Q8—42no—
764C4⋊Q8—44no—
765C4⋊Q8—84no—
766#127—24no—
767#127—42no—
768#127—44no—
769#127—82no—
770#126—28no—
771#126—44no—
772#126—44no—
773#126—84no—
774#125—44no—
775#125—44no—
776#124—28no—
777#124—44no—
778#124—84no—
779#124—84no—
780#124—82no—
781#124—84no—
782#124—84no—
783#124—82no—
784#124—84no—
785#123—48no—
786#123—48no—
787#123—84no—
788#123—84no—
789C22⋊Q8—48no—
790C22⋊Q8—48no—
791C22⋊Q8—44no—
792C22⋊Q8—42no—
793C22⋊Q8—42no—
794C22⋊Q8—84no—
795C22⋊Q8—84no—
796#121—28no—
797#121—48no—
798#121—44no—
799#121—44no—
800#121—44no—
801#121—44no—
802#121—84no—
803#121—84no—
804#121—84no—
805#121—84no—
806C4×Q8—24no—
807C4×Q8—44no—
808C4×Q8—44no—
809C4×Q8—84no—
810C4×D4—44no—
811C4×D4—44no—
812C4×D4—44no—
813C4×D4—44no—
814C4×D4—44no—
815C4×D4—44no—
816C4×D4—44no—
817C4×D4—44no—
818C4×D4—44no—
819C4×D4—42no—
820C4×D4—42no—
821C4×D4—48no—
822C4×D4—84no—
823C4×D4—84no—
824C4×D4—84no—
825#117—24no—
826#117—24no—
827#117—44no—
828#117—42no—
829#117—44no—
830C2×C4⋊C4—28no—
831C2×C4⋊C4—42no—
832C2×C4⋊C4—42no—
833C2×C4⋊C4—44no—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2411yescharacteristic
908C2×C22⋊C4C2411yescharacteristic
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2412yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2411yescharacteristic
956C2×C42C2412yes—
957C2×C42C2412yes—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2414yes—
961C2×C42C2414yes—
962C2×C42C2412yes—
963C2×C42C2411yescharacteristic
964C2×C42C2414yes—
965C2×C42C2414yes—
966C2×C42C2412yes—
967C2×C42C2414yes—
968C2×C42C2411yescharacteristic
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2411yescharacteristic
974#95C2414yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2411yescharacteristic
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2411yescharacteristic
990#95C2412yes—
991#95C2411yescharacteristic
992#95C2412yes—
993#95C2414yes—
994#95C2412yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028C24C2511yescharacteristic
1029C24C2511yescharacteristic
1030C24C2514yes—
1031C24C2512yes—
1032C24C2512yes—
1033#41—416no—
1034#41—816no—
1035#41—832no—
1036C2×Q8—22no—
1037C2×Q8—28no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—41no—
1041C2×Q8—42no—
1042C2×Q8—42no—
1043C2×Q8—44no—
1044C2×Q8—44no—
1045C2×Q8—44no—
1046C2×Q8—42no—
1047C2×Q8—44no—
1048C2×Q8—44no—
1049C2×Q8—44no—
1050C2×Q8—44no—
1051C2×Q8—44no—
1052C2×D4—24no—
1053C2×D4—28no—
1054C2×D4—24no—
1055C2×D4—24no—
1056C2×D4—24no—
1057C2×D4—22no—
1058C2×D4—22no—
1059C2×D4—24no—
1060C2×D4—24no—
1061C2×D4—41no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C2×D4—42no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—42no—
1072C2×D4—42no—
1073C2×D4—41no—
1074C2×D4—42no—
1075C2×D4—41no—
1076C2×D4—42no—
1077C2×D4—42no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C2×D4—42no—
1083C2×D4—42no—
1084C2×D4—42no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—44no—
1088C2×D4—41no—
1089C2×D4—42no—
1090C2×D4—42no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4—41no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—42no—
1097C2×D4—44no—
1098C2×D4—44no—
1099C2×D4—44no—
1100C2×D4—44no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C22×C4—24no—
1105C22×C4—22no—
1106C22×C4—22no—
1107C22×C4—24no—
1108C22×C4—24no—
1109C22×C4—24no—
1110C22×C4—24no—
1111C22×C4—24no—
1112C22×C4—24no—
1113C22×C4—24no—
1114C22×C4—28no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—44no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—42no—
1127C22×C4—42no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2514yes—
1138C22×C4C2511yescharacteristic
1139C22×C4C2512yes—
1140C22×C4C2514yes—
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2512yes—
1147C22×C4C2514yes—
1148C22×C4C2514yes—
1149C22×C4C2514yes—
1150C22×C4C2512yes—
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C22×C4C2512yes—
1154C22×C4C2511yescharacteristic
1155C22×C4C2512yes—
1156C22×C4C2511yescharacteristic
1157C4⋊C4—24no—
1158C4⋊C4—28no—
1159C4⋊C4—24no—
1160C4⋊C4—22no—
1161C4⋊C4—22no—
1162C4⋊C4—24no—
1163C4⋊C4—28no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—41no—
1176C4⋊C4—41no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—41no—
1182C4⋊C4—41no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—42no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—42no—
1202C4⋊C4—44no—
1203C4⋊C4—42no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—42no—
1207C4⋊C4H(5,𝔽2)14yes—
1208C22⋊C4—24no—
1209C22⋊C4—24no—
1210C22⋊C4—28no—
1211C22⋊C4—28no—
1212C22⋊C4—28no—
1213C22⋊C4—24no—
1214C22⋊C4—24no—
1215C22⋊C4—24no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—44no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—44no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—41no—
1234C22⋊C4—41no—
1235C22⋊C4—42no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—42no—
1246C22⋊C4—44no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—42no—
1253C22⋊C4—42no—
1254C22⋊C4—42no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—42no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—42no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—42no—
1266C22⋊C4—42no—
1267C22⋊C4—42no—
1268C22⋊C4—44no—
1269C22⋊C4—42no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—42no—
1273C42—24no—
1274C42—24no—
1275C42—24no—
1276C42—22no—
1277C42—24no—
1278C42—24no—
1279C42—24no—
1280C42—24no—
1281C42—44no—
1282C42—44no—
1283C42—44no—
1284C42—44no—
1285C42—42no—
1286C42—41no—
1287C42—44no—
1288C42—44no—
1289C42—42no—
1290C42—44no—
1291C422−1+414yes—
1292C23—21no—
1293C23—21no—
1294C23—24no—
1295C23—22no—
1296C23—22no—
1297C23—22no—
1298C23—24no—
1299C23—21no—
1300C23—21no—
1301C23—22no—
1302C23—22no—
1303C23—22no—
1304C23—22no—
1305C23—22no—
1306C23—24no—
1307C23—24no—
1308C23—22no—
1309C23—22no—
1310C23—22no—
1311C23—22no—
1312C23—22no—
1313C23—24no—
1314C23—21no—
1315C23—22no—
1316C23—22no—
1317C23—24no—
1318C23—22no—
1319C23—24no—
1320C23—22no—
1321C23—21no—
1322C23—22no—
1323C23C2611yescharacteristic
1324Q8—44no—
1325Q8—44no—
1326Q8—84no—
1327Q8—88no—
1328Q8—88no—
1329Q8—164no—
1330D4—48no—
1331D4—48no—
1332D4—44no—
1333D4—48no—
1334D4—48no—
1335D4—48no—
1336D4—84no—
1337D4—82no—
1338D4—82no—
1339D4—88no—
1340D4—84no—
1341D4—88no—
1342D4—84no—
1343D4—88no—
1344D4—88no—
1345D4—162no—
1346D4—164no—
1347D4—164no—
1348C2×C4—21no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—21no—
1352C2×C4—24no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—21no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—22no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—24no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—24no—
1390C2×C4—22no—
1391C2×C4—24no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—24no—
1395C2×C4—24no—
1396C2×C4—24no—
1397C2×C4—24no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—24no—
1401C2×C4—24no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—24no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—44no—
1410C2×C4—48no—
1411C2×C4—44no—
1412C2×C4—48no—
1413C2×C4—88no—
1414C2×C4—88no—
1415C2×C4—88no—
1416C2×C4—88no—
1417C2×C4—162no—
1418C2×C4—162no—
1419C2×C4—164no—
1420C2×C4C2×H(5,𝔽2)14yes—
1421C2×C4C2×H(5,𝔽2)12yes—
1422C2×C4C2×2−1+414yes—
1423C2×C4C2×2−1+412yes—
1424C2×C4#58514yes—
1425C22—41no—
1426C22—42no—
1427C22—42no—
1428C22—41no—
1429C22—44no—
1430C22—42no—
1431C22—42no—
1432C22—44no—
1433C22—41no—
1434C22—41no—
1435C22—44no—
1436C22—42no—
1437C22—42no—
1438C22—42no—
1439C22—42no—
1440C22—42no—
1441C22—44no—
1442C22—42no—
1443C22—41no—
1444C22—41no—
1445C22—44no—
1446C22—42no—
1447C22—42no—
1448C22—42no—
1449C22—42no—
1450C22—42no—
1451C22—42no—
1452C22—42no—
1453C22—42no—
1454C22—44no—
1455C22—44no—
1456C22C22×H(5,𝔽2)11yescharacteristic
1457C22C22×2−1+411yescharacteristic
1458C22C2×#58512yes—
1459C22H(7,𝔽2)12yes—
1460C22H(7,𝔽2)11yescharacteristic
1461C4—24no—
1462C4—22no—
1463C4—24no—
1464C4—41no—
1465C4—42no—
1466C4—41no—
1467C4—42no—
1468C4—42no—
1469C4—44no—
1470C4—42no—
1471C4—44no—
1472C4—41no—
1473C4—42no—
1474C4—44no—
1475C4—44no—
1476C4—42no—
1477C4—42no—
1478C4—44no—
1479C4—42no—
1480C4—42no—
1481C4—42no—
1482C4—42no—
1483C4—42no—
1484C4#354014yes—
1485C2—82no—
1486C2—81no—
1487C2—82no—
1488C2—81no—
1489C2—84no—
1490C2C2×#354011yescharacteristic
1491C2#6291711yescharacteristic
1492C2#6292612yes—
1493C2#6304511yescharacteristic
1494C2#6305112yes—
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. #59864C2semidirect
2. #59712C2semidirect
3. #58304C2semidirect
4. #58014C2semidirect
5. #57783C2semidirect
6. #56766C2semidirect
7. #56504C2semidirect
8. #53080C2semidirect
9. #53046C2semidirect
10. #52957C2semidirect
11. #52403C2semidirect
12. #47773C2semidirect
13. #45208C2semidirect
14. #45176C2semidirect
15. #45047C2semidirect
16. #44930C2semidirect
17. #44878C2semidirect
18. #42915C2semidirect
19. #42731C2semidirect
20. #42712C2semidirect
21. #42671C2semidirect
22. #42503C2semidirect
23. #42403C2semidirect
24. #41009C2semidirect
25. #39789C2semidirect
26. #39747C2semidirect
27. #36696C2semidirect
28. #35759C2semidirect
29. #35682C2semidirect

Maximal subgroups

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

subgroupindex
#598642
#597122
#583042
#580142
#577832
#567662
#565042
#530802
#530462
#529572
#524032
#477732
#452082
#451762
#450472
#449302
#448782
#429152
#427312
#427122
#426712
#425032
#424032
#410092
#397892
#397472
#366962
#357592
#356822