Finite Group Databasebeta

← #7715069

Subgroups — #7715069

Order 512.

4384 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51772C214yesmaximal, complemented
2#51771C214yesmaximal, complemented
3#51570C214yesmaximal, complemented
4#51569C214yesmaximal, complemented
5#47462C214yesmaximal, complemented
6#46841C214yesmaximal, complemented
7#46459C214yesmaximal, complemented
8#46399C214yesmaximal, complemented
9#39083C212yesmaximal, complemented
10#39082C212yesmaximal, complemented
11#39079C212yesmaximal, complemented
12#39078C212yesmaximal, complemented
13#39069C212yesmaximal, complemented
14#39068C212yesmaximal, complemented
15#39065C212yesmaximal, complemented
16#39064C212yesmaximal, complemented
17#37477C211yesmaximal, characteristic, complemented
18#37455C211yesmaximal, characteristic
19#37382C211yesmaximal, characteristic, complemented
20#37287C212yesmaximal, complemented
21#37286C211yesmaximal, characteristic, complemented
22#35321C211yesmaximal, characteristic, complemented
23#35290C212yesmaximal, complemented
24#35287C211yesmaximal, characteristic, complemented
25#35263C212yesmaximal, complemented
26#34404C212yesmaximal, complemented
27#34048C211yesmaximal, characteristic, complemented
28C2×#525C2212yes—
29C22×#117C2211yescharacteristic
30#2863C2212yescomplemented
31#2863C2212yescomplemented
32#2860C2212yescomplemented
33#2860C2212yescomplemented
34#2855C2212yes—
35#2855C2212yes—
36#2854C2212yes—
37#2854C2212yes—
38#2841C2214yes—
39#2812C2214yes—
40#2793C2214yescomplemented
41#2791C2214yescomplemented
42#2787C2214yes—
43#2781C2214yes—
44#2781C2214yescomplemented
45#2779C2214yes—
46#2775C2214yescomplemented
47#2770C2214yes—
48#2770C2214yescomplemented
49#2769C2214yescomplemented
50#2768C2214yescomplemented
51#2767C2214yescomplemented
52#2767C2214yescomplemented
53#2766C2214yescomplemented
54#2765C2214yescomplemented
55#2758C2214yescomplemented
56#2757C2214yes—
57#2756C2214yes—
58#2753C2214yes—
59#2750C2214yes—
60#2749C2214yes—
61#2747C2214yes—
62#2746C2214yes—
63#2746C2214yes—
64#2744C2214yes—
65#2742C2214yescomplemented
66#2741C2214yes—
67#2741C2214yescomplemented
68#2741C2214yescomplemented
69#2740C2214yescomplemented
70#2739C2214yes—
71#2739C2214yescomplemented
72#2738C2214yescomplemented
73#2738C2214yescomplemented
74#2737C2214yes—
75#2737C2214yescomplemented
76#2723C2214yes—
77#2722C2214yescomplemented
78#2720C2214yescomplemented
79#2718C2214yescomplemented
80#2705C2214yes—
81#2702C2214yes—
82#2698C2214yescomplemented
83#2696C2214yes—
84#2694C2214yes—
85#2693C2214yes—
86#2690C2214yes—
87#2687C2214yes—
88#2659C2214yes—
89#2647C2211yescharacteristic, complemented
90#2647C2211yescharacteristic, complemented
91#2647C2212yescomplemented
92#2646C2214yes—
93#2642C2211yescharacteristic, complemented
94#2641C2211yescharacteristic, complemented
95#2640C2212yescomplemented
96#2630C2214yes—
97#2630C2214yes—
98#2629C2211yescharacteristic
99#2629C2211yescharacteristic
100#2628C2212yes—
101#2625C2212yes—
102#2625C2212yes—
103#2624C2212yes—
104#2624C2212yes—
105#2621C2211yescharacteristic
106#2620C2212yes—
107#2619C2211yescharacteristic
108#2606C2214yescomplemented
109#2604C2214yescomplemented
110#2602C2214yes—
111#2600C2214yes—
112#2600C2214yes—
113#2596C2214yescomplemented
114#2595C2214yes—
115#2593C2214yescomplemented
116#2590C2214yescomplemented
117#2585C2214yescomplemented
118#2578C2214yes—
119#2578C2214yes—
120#2578C2214yescomplemented
121#2577C2214yes—
122#2577C2214yes—
123#2577C2214yescomplemented
124#2574C2214yescomplemented
125#2574C2214yescomplemented
126#2573C2214yes—
127#2573C2214yescomplemented
128#2572C2214yes—
129#2569C2214yescomplemented
130#2564C2214yescomplemented
131#2562C2214yes—
132#2560C2214yes—
133#2554C2214yes—
134#2553C2214yes—
135#2553C2214yescomplemented
136#2536C2214yes—
137#2533C2214yescomplemented
138#2529C2214yescomplemented
139#2525C2214yescomplemented
140#2524C2214yescomplemented
141#2519C2214yescomplemented
142#2516C2214yes—
143#2515C2214yes—
144#2514C2212yescomplemented
145#2513C2212yescomplemented
146#2512C2212yescomplemented
147#2511C2212yescomplemented
148#2509C2212yescomplemented
149#2508C2212yescomplemented
150#2507C2212yescomplemented
151#2506C2212yescomplemented
152#2500C2212yes—
153#2499C2212yes—
154#2498C2214yes—
155#2498C2214yes—
156#2495C2214yes—
157#2493C2214yescomplemented
158#2487C2214yes—
159#2486C2214yes—
160#2485C2214yes—
161#2485C2214yes—
162#2469C2214yescomplemented
163#2468C2214yes—
164#2468C2214yes—
165#2468C2214yescomplemented
166#2467C2214yes—
167#2463C2214yes—
168#2462C2214yescomplemented
169#2458C2214yes—
170#2457C2214yes—
171#2454C2212yescomplemented
172#2453C2212yescomplemented
173#2452C2212yescomplemented
174#2451C2212yescomplemented
175#2448C2212yescomplemented
176#2447C2212yescomplemented
177#2446C2212yescomplemented
178#2445C2212yescomplemented
179#2442C2212yes—
180#2442C2212yes—
181#2440C2212yes—
182#2440C2212yes—
183#2437C2214yes—
184#2432C2212yes—
185#2431C2212yes—
186#2421C2214yes—
187#2419C2214yescomplemented
188#2412C2214yes—
189#2412C2214yes—
190#2376C2214yes—
191#2376C2214yes—
192#2361C2212yes—
193#2361C2212yes—
194#2360C2212yes—
195#2360C2212yes—
196#2353C2214yes—
197#2349C2214yes—
198#2347C2212yes—
199#2346C2212yes—
200#2341C2212yes—
201#2339C2212yes—
202#2324C2212yes—
203#2324C2212yes—
204#2323C2212yes—
205#2323C2212yes—
206#2321C2214yes—
207#2321C2214yes—
208#2320C2212yescomplemented
209#2320C2212yescomplemented
210#2319C2214yes—
211#2319C2212yescomplemented
212#2319C2212yescomplemented
213#2318C2214yes—
214#2316C2212yes—
215#2316C2212yes—
216#2314C2212yes—
217#2314C2212yes—
218#2314C2212yes—
219#2314C2212yes—
220#2313C2212yes—
221#2313C2212yes—
222#2312C2212yes—
223#2312C2212yes—
224#2311C2212yes—
225#2311C2212yes—
226C4×C4⋊Q8C2211yescharacteristic, complemented
227C4×C4⋊Q8C2212yescomplemented
228C4×#127C2211yescharacteristic, complemented
229C4×#125C2211yescharacteristic, complemented
230C4×#125C2211yescharacteristic, complemented
231C4×#124C2212yescomplemented
232#2298C2212yes—
233#2298C2212yes—
234#2298C2212yes—
235#2298C2212yes—
236#2285C2211yescharacteristic
237#2285C2211yescharacteristic
238#2280C2211yescharacteristic
239#2280C2211yescharacteristic
240C2×#380C2212yes—
241C4×#117C2211yescharacteristic
242C4×#117C2211yescharacteristic
243C22×#41C2312yes—
244C24×C4C2311yescharacteristic
245C2×C4⋊Q8C2311yescharacteristic
246C2×C4⋊Q8C2312yes—
247C2×#127C2311yescharacteristic
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#125C2311yescharacteristic
252C2×#125C2311yescharacteristic
253C2×#125C2314yes—
254C2×#124C2312yes—
255#525—216no—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×#121C2312yes—
266C2×#121C2312yes—
267C2×#120C2314yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×#117—28no—
279C2×#117C2312yes—
280C2×#117C2312yes—
281C2×#117C2312yes—
282C2×#117C2312yes—
283C2×#117C2312yes—
284C2×#117C2311yescharacteristic
285C2×#117C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C2×#117C2311yescharacteristic
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C22⋊C4C2312yes—
292C22×C22⋊C4C2314yes—
293C22×C42C2311yescharacteristic
294C22×C42C2311yescharacteristic
295#401C2314yes—
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#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#393C2314yes—
385#393C2314yes—
386#393C2314yes—
387#393C2314yes—
388#392C2314yes—
389#392C2314yes—
390#392C2314yes—
391#391C2314yes—
392#391C2312yes—
393#391C2314yes—
394#391C2312yes—
395#391C2312yes—
396#391C2312yes—
397#391C2312yes—
398#391C2312yes—
399#391C2312yes—
400#391C2312yes—
401#390C2314yes—
402#390C2312yes—
403#390C2314yes—
404#390C2312yes—
405#390C2312yes—
406#390C2312yes—
407#390C2314yes—
408#390C2314yes—
409#390C2312yes—
410#390C2312yes—
411#390C2314yes—
412#390C2312yes—
413#390C2312yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2312yes—
431#389C2312yes—
432#389C2312yes—
433#389C2312yes—
434#389C2314yes—
435#389C2312yes—
436#389C2312yes—
437#389C2314yes—
438#389C2312yes—
439#389C2312yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#388C2312yes—
444#388C2314yes—
445#388C2314yes—
446#388C2312yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2312yes—
451#388C2312yes—
452#388C2312yes—
453#388C2312yes—
454#388C2312yes—
455#388C2312yes—
456#388C2312yes—
457#388C2312yes—
458#388C2312yes—
459#388C2312yes—
460#388C2312yes—
461#388C2312yes—
462#388C2312yes—
463#388C2312yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2312yes—
498#387C2314yes—
499#387C2312yes—
500#387C2312yes—
501#387C2312yes—
502#387C2312yes—
503#387C2312yes—
504#387C2312yes—
505#387C2312yes—
506#387C2312yes—
507#387C2312yes—
508#387C2312yes—
509#387C2312yes—
510#387C2312yes—
511#387C2312yes—
512#387C2312yes—
513#387C2312yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#384C2311yescharacteristic
576#384C2312yes—
577#384C2311yescharacteristic
578#384C2312yes—
579#384C2311yescharacteristic
580#384C2311yescharacteristic
581#383C2314yes—
582#383C2314yes—
583#383C2314yes—
584#383C2314yes—
585#383C2314yes—
586#383C2314yes—
587#382C2311yescharacteristic
588#382C2311yescharacteristic
589#382C2311yescharacteristic
590#382C2312yes—
591#382C2311yescharacteristic
592#382C2314yes—
593#382C2314yes—
594#382C2314yes—
595#382C2312yes—
596#382C2314yes—
597#381C2311yescharacteristic
598#381C2311yescharacteristic
599#381C2312yes—
600#381C2314yes—
601#381C2314yes—
602#381C2314yes—
603#381C2314yes—
604#381C2314yes—
605#381C2314yes—
606#380C2314yes—
607#380C2314yes—
608#380C2314yes—
609#380C2314yes—
610#380C2314yes—
611#380C2314yes—
612#380C2314yes—
613#380C2314yes—
614#380C2312yes—
615#380C2312yes—
616#380C2312yes—
617#380C2312yes—
618#380C2314yes—
619#380C2312yes—
620#380C2312yes—
621#380C2312yes—
622#380C2312yes—
623#380C2314yes—
624#380C2314yes—
625#380C2314yes—
626#380C2314yes—
627#380C2314yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2312yes—
632#380C2314yes—
633#380C2314yes—
634#379C2311yescharacteristic
635#379C2311yescharacteristic
636#379C2312yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667#376C2314yes—
668#376C2311yescharacteristic
669#376C2312yes—
670#376C2311yescharacteristic
671C2×#95C2314yes—
672C2×#95C2314yes—
673C43C2311yescharacteristic
674C43C2311yescharacteristic
675C43C2312yes—
676C25C2411yescharacteristic
677C2×#41—28no—
678C2×#41—44no—
679C2×#41—44no—
680C22×Q8C2412yes—
681C22×Q8C2414yes—
682C22×D4C2412yes—
683C22×D4C2414yes—
684C22×D4C2414yes—
685C22×D4C2414yes—
686C22×D4C2414yes—
687C23×C4—42no—
688C23×C4—42no—
689C23×C4#4118yes—
690C23×C4C2412yes—
691C23×C4C2411yescharacteristic
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2414yes—
695C23×C4C2414yes—
696C23×C4C2414yes—
697C23×C4C2414yes—
698C23×C4C2414yes—
699C23×C4C2411yescharacteristic
700C23×C4C2412yes—
701C4⋊Q8—44no—
702C4⋊Q8—42no—
703#127—42no—
704#126—84no—
705#126—84no—
706#126—84no—
707#125—42no—
708#125—42no—
709#125—84no—
710#124—44no—
711#123—216no—
712#123—84no—
713#123—84no—
714#123—84no—
715C22⋊Q8—28no—
716C22⋊Q8—28no—
717C22⋊Q8—84no—
718C22⋊Q8—84no—
719C22⋊Q8—84no—
720#121—28no—
721#121—28no—
722#120—216no—
723C4×Q8—44no—
724C4×Q8—44no—
725C4×Q8—84no—
726C4×D4—216no—
727C4×D4—216no—
728C4×D4—44no—
729C4×D4—44no—
730C4×D4—84no—
731C4×D4—84no—
732C4×D4—84no—
733#117—28no—
734#117—28no—
735#117—28no—
736#117—28no—
737#117—28no—
738#117—42no—
739#117—42no—
740#117—42no—
741#117—42no—
742C2×C4⋊C4—28no—
743C2×C4⋊C4—44no—
744C2×C4⋊C4—44no—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2411yescharacteristic
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C22⋊C4—28no—
800C2×C22⋊C4—84no—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
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×C22⋊C4C2411yescharacteristic
815C2×C22⋊C4C2411yescharacteristic
816C2×C22⋊C4C2411yescharacteristic
817C2×C22⋊C4C2411yescharacteristic
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C42—24no—
849C2×C42—24no—
850C2×C42C2411yescharacteristic
851C2×C42C2411yescharacteristic
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2411yescharacteristic
855C2×C42C2411yescharacteristic
856C2×C42C2411yescharacteristic
857C2×C42C2414yes—
858C2×C42C2412yes—
859C2×C42C2411yescharacteristic
860C2×C42C2412yes—
861C2×C42C2411yescharacteristic
862C2×C42C2411yescharacteristic
863C2×C42C2412yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2412yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2414yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2414yes—
877#95C2412yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2412yes—
893#95C2414yes—
894#95C2414yes—
895#95C2412yes—
896#95C2412yes—
897#95C2414yes—
898#95C2414yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2412yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2412yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2412yes—
918#95C2412yes—
919#95C2414yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945C24—42no—
946C24—41no—
947C24—41no—
948C24—42no—
949C24C2×#4114yes—
950C24C2514yes—
951C24C2511yescharacteristic
952C24C2512yes—
953#41—816no—
954C2×Q8—24no—
955C2×Q8—24no—
956C2×Q8—24no—
957C2×Q8—44no—
958C2×Q8—44no—
959C2×Q8—44no—
960C2×D4—28no—
961C2×D4—28no—
962C2×D4—28no—
963C2×D4—24no—
964C2×D4—24no—
965C2×D4—24no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C22×C4—24no—
976C22×C4—24no—
977C22×C4—22no—
978C22×C4—22no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—28no—
982C22×C4—416no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—41no—
986C22×C4—41no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4C2×#4114yes—
1006C22×C4C2×#4118yes—
1007C22×C4C2×#4114yes—
1008C22×C4C2×#4118yes—
1009C22×C4C2514yes—
1010C22×C4C2511yescharacteristic
1011C22×C4C2511yescharacteristic
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2511yescharacteristic
1016C22×C4C2514yes—
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C22×C4C2514yes—
1020C22×C4C2514yes—
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2514yes—
1024C22×C4C2514yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2512yes—
1028C22×C4C2514yes—
1029C22×C4C2511yescharacteristic
1030C22×C4C2512yes—
1031C22×C4C2511yescharacteristic
1032C22×C4C2511yescharacteristic
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—24no—
1038C4⋊C4—24no—
1039C4⋊C4—28no—
1040C4⋊C4—28no—
1041C4⋊C4—24no—
1042C4⋊C4—24no—
1043C4⋊C4—24no—
1044C4⋊C4—24no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—42no—
1048C4⋊C4—44no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—42no—
1055C4⋊C4—41no—
1056C4⋊C4—42no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
1059C4⋊C4—42no—
1060C4⋊C4—41no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—42no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—42no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—42no—
1083C4⋊C4—44no—
1084C4⋊C4—42no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C22⋊C4—24no—
1088C22⋊C4—24no—
1089C22⋊C4—24no—
1090C22⋊C4—24no—
1091C22⋊C4—28no—
1092C22⋊C4—28no—
1093C22⋊C4—28no—
1094C22⋊C4—28no—
1095C22⋊C4—28no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—42no—
1101C22⋊C4—44no—
1102C22⋊C4—42no—
1103C22⋊C4—44no—
1104C22⋊C4—42no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—42no—
1108C22⋊C4—44no—
1109C22⋊C4—41no—
1110C22⋊C4—41no—
1111C22⋊C4—41no—
1112C22⋊C4—41no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—42no—
1124C22⋊C4—42no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C42—24no—
1135C42—22no—
1136C42—22no—
1137C42—22no—
1138C42—22no—
1139C42—24no—
1140C42—28no—
1141C42—22no—
1142C42—24no—
1143C42—22no—
1144C42—24no—
1145C42—22no—
1146C42—22no—
1147C42—42no—
1148C42—44no—
1149C42—42no—
1150C42—42no—
1151C42—42no—
1152C42—42no—
1153C42—44no—
1154C42—44no—
1155C42—44no—
1156C42—44no—
1157C42—42no—
1158C42—44no—
1159C42—42no—
1160C42—42no—
1161C23—21no—
1162C23—21no—
1163C23—22no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—24no—
1172C23—24no—
1173C23—24no—
1174C23—24no—
1175C23—24no—
1176C23—24no—
1177C23—24no—
1178C23—44no—
1179C23—48no—
1180C23—84no—
1181C23—82no—
1182C23—82no—
1183C23C22×#4114yes—
1184C23C22×#4112yes—
1185C23C2611yescharacteristic
1186Q8—48no—
1187Q8—88no—
1188D4—416no—
1189D4—48no—
1190D4—88no—
1191D4—88no—
1192D4—88no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—28no—
1198C2×C4—216no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—21no—
1207C2×C4—22no—
1208C2×C4—21no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—21no—
1214C2×C4—22no—
1215C2×C4—21no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—44no—
1259C2×C4—48no—
1260C2×C4—88no—
1261C2×C4—84no—
1262C2×C4—84no—
1263C2×C4—164no—
1264C2×C4—164no—
1265C2×C4—164no—
1266C2×C4—164no—
1267C2×C4C22×#4112yes—
1268C2×C4C22×#4114yes—
1269C2×C4C22×#4112yes—
1270C2×C4#58512yes—
1271C2×C4#58512yes—
1272C22—24no—
1273C22—22no—
1274C22—24no—
1275C22—24no—
1276C22—24no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—41no—
1282C22—41no—
1283C22—42no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22—44no—
1288C22—44no—
1289C22—44no—
1290C22—44no—
1291C22—88no—
1292C22C23×#4111yescharacteristic
1293C22C2×#58511yescharacteristic
1294C22C2×#58511yescharacteristic
1295C22H(7,𝔽2)12yes—
1296C222−1+612yes—
1297C4—24no—
1298C4—22no—
1299C4—44no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—42no—
1304C4—44no—
1305C4—44no—
1306C4—42no—
1307C4—42no—
1308C4—44no—
1309C4—42no—
1310C4—44no—
1311C4—42no—
1312C4—41no—
1313C4—41no—
1314C4—44no—
1315C4—44no—
1316C4—42no—
1317C4—41no—
1318C4—41no—
1319C4—42no—
1320C4#349114yes—
1321C2—44no—
1322C2—42no—
1323C2—84no—
1324C2C2×#349111yescharacteristic
1325C2#6285612yes—
1326C2#6288212yes—
1327C2#6288311yescharacteristic
1328C2#6289011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37455C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51772C2semidirect
2. #51771C2semidirect
3. #51570C2semidirect
4. #51569C2semidirect
5. #47462C2semidirect
6. #46841C2semidirect
7. #46459C2semidirect
8. #46399C2semidirect
9. #39083C2semidirect
10. #39082C2semidirect
11. #39079C2semidirect
12. #39078C2semidirect
13. #39069C2semidirect
14. #39068C2semidirect
15. #39065C2semidirect
16. #39064C2semidirect
17. #37477C2semidirect
19. #37382C2semidirect
20. #37287C2semidirect
21. #37286C2semidirect
22. #35321C2semidirect
23. #35290C2semidirect
24. #35287C2semidirect
25. #35263C2semidirect
26. #34404C2semidirect
27. #34048C2semidirect
30. #2863C22semidirect
31. #2863C22semidirect
32. #2860C22semidirect
33. #2860C22semidirect
40. #2793C22semidirect
41. #2791C22semidirect
44. #2781C22semidirect
46. #2775C22semidirect
48. #2770C22semidirect
49. #2769C22semidirect
50. #2768C22semidirect
51. #2767C22semidirect
52. #2767C22semidirect
53. #2766C22semidirect
54. #2765C22semidirect
55. #2758C22semidirect
65. #2742C22semidirect
67. #2741C22semidirect
68. #2741C22semidirect
69. #2740C22semidirect
71. #2739C22semidirect
72. #2738C22semidirect
73. #2738C22semidirect
75. #2737C22semidirect
77. #2722C22semidirect
78. #2720C22semidirect
79. #2718C22semidirect
82. #2698C22semidirect
89. #2647C22semidirect
90. #2647C22semidirect
91. #2647C22semidirect
93. #2642C22semidirect
94. #2641C22semidirect
95. #2640C22semidirect
108. #2606C22semidirect
109. #2604C22semidirect
113. #2596C22semidirect
115. #2593C22semidirect
116. #2590C22semidirect
117. #2585C22semidirect
120. #2578C22semidirect
123. #2577C22semidirect
124. #2574C22semidirect
125. #2574C22semidirect
127. #2573C22semidirect
129. #2569C22semidirect
130. #2564C22semidirect
135. #2553C22semidirect
137. #2533C22semidirect
138. #2529C22semidirect
139. #2525C22semidirect
140. #2524C22semidirect
141. #2519C22semidirect
144. #2514C22semidirect
145. #2513C22semidirect
146. #2512C22semidirect
147. #2511C22semidirect
148. #2509C22semidirect
149. #2508C22semidirect
150. #2507C22semidirect
151. #2506C22semidirect
157. #2493C22semidirect
162. #2469C22semidirect
165. #2468C22semidirect
168. #2462C22semidirect
171. #2454C22semidirect
172. #2453C22semidirect
173. #2452C22semidirect
174. #2451C22semidirect
175. #2448C22semidirect
176. #2447C22semidirect
177. #2446C22semidirect
178. #2445C22semidirect
187. #2419C22semidirect
208. #2320C22semidirect
209. #2320C22semidirect
211. #2319C22semidirect
212. #2319C22semidirect
226. C4×C4⋊Q8C22semidirect
227. C4×C4⋊Q8C22semidirect
228. C4×#127C22semidirect
229. C4×#125C22semidirect
230. C4×#125C22semidirect
231. C4×#124C22semidirect

Maximal subgroups

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

subgroupindex
#517722
#517712
#515702
#515692
#474622
#468412
#464592
#463992
#390832
#390822
#390792
#390782
#390692
#390682
#390652
#390642
#374772
#374552
#373822
#372872
#372862
#353212
#352902
#352872
#352632
#344042
#340482