Finite Group Databasebeta

← #7726750

Subgroups — #7726750

Order 512.

4540 conjugacy classes of subgroups.

The subgroup lattice has 1325 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48800C212yesmaximal, complemented
2#48799C212yesmaximal, complemented
3#47888C212yesmaximal, complemented
4#47885C212yesmaximal, complemented
5#47009C214yesmaximal, complemented
6#46403C214yesmaximal, complemented
7#43515C212yesmaximal, complemented
8#43514C212yesmaximal, complemented
9#43085C212yesmaximal, complemented
10#43082C212yesmaximal, complemented
11#39679C214yesmaximal, complemented
12#39549C212yesmaximal, complemented
13#39541C212yesmaximal, complemented
14#39512C212yesmaximal, complemented
15#39504C212yesmaximal, complemented
16#38234C214yesmaximal, complemented
17#38065C214yesmaximal, complemented
18#37442C211yesmaximal, characteristic
19#36782C214yesmaximal, complemented
20#36245C214yesmaximal, complemented
21#35399C214yesmaximal, complemented
22#35079C211yesmaximal, characteristic, complemented
23#35057C211yesmaximal, characteristic
24C2×#2583C211yesmaximal, characteristic, complemented
25#34380C211yesmaximal, characteristic, complemented
26#34233C211yesmaximal, characteristic
27C2×#2313C211yesmaximal, characteristic, complemented
28C2×#525C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31#2857C2212yes—
32#2852C2214yes—
33#2851C2212yes—
34#2851C2214yes—
35#2849C2212yes—
36#2849C2212yes—
37#2814C2212yes—
38#2814C2212yes—
39#2810C2214yescomplemented
40#2809C2214yescomplemented
41#2809C2214yescomplemented
42#2808C2214yescomplemented
43#2805C2214yescomplemented
44#2805C2214yescomplemented
45#2802C2214yescomplemented
46#2802C2214yescomplemented
47#2800C2214yescomplemented
48#2787C2214yescomplemented
49#2783C2214yescomplemented
50#2783C2214yescomplemented
51#2783C2214yescomplemented
52#2776C2214yescomplemented
53#2776C2214yescomplemented
54#2776C2214yescomplemented
55#2774C2214yescomplemented
56#2774C2214yescomplemented
57#2772C2214yescomplemented
58#2771C2214yes—
59#2769C2214yescomplemented
60#2766C2214yescomplemented
61#2766C2214yescomplemented
62#2765C2214yes—
63#2765C2214yes—
64#2764C2214yes—
65#2762C2214yescomplemented
66#2762C2214yescomplemented
67#2761C2214yes—
68#2759C2214yescomplemented
69#2751C2214yes—
70#2750C2214yes—
71#2747C2214yescomplemented
72#2745C2214yescomplemented
73#2744C2214yescomplemented
74#2743C2214yes—
75#2725C2214yescomplemented
76#2719C2214yescomplemented
77#2690C2214yescomplemented
78#2689C2214yescomplemented
79#2667C2212yes—
80#2665C2212yes—
81#2659C2212yes—
82#2646C2214yes—
83#2643C2214yes—
84#2639C2212yes—
85#2627C2212yes—
86#2627C2211yescharacteristic
87#2627C2211yescharacteristic
88#2625C2212yes—
89#2618C2212yes—
90#2618C2211yescharacteristic
91#2618C2211yescharacteristic
92#2616C2212yes—
93#2612C2214yescomplemented
94#2608C2214yescomplemented
95#2606C2214yescomplemented
96#2605C2214yescomplemented
97#2599C2214yescomplemented
98#2591C2212yes—
99#2590C2214yescomplemented
100#2590C2214yescomplemented
101#2590C2214yescomplemented
102#2587C2214yescomplemented
103#2585C2214yescomplemented
104#2583C2212yes—
105#2583C2212yes—
106#2583C2214yes—
107#2583C2212yes—
108#2583C2214yes—
109#2583C2212yes—
110#2583C2212yes—
111#2581C2214yescomplemented
112#2581C2214yescomplemented
113#2579C2214yes—
114#2577C2214yescomplemented
115#2575C2214yes—
116#2574C2214yescomplemented
117#2573C2214yes—
118#2570C2214yescomplemented
119#2569C2212yes—
120#2569C2214yescomplemented
121#2558C2214yes—
122#2553C2214yes—
123#2549C2212yes—
124#2533C2214yescomplemented
125#2532C2214yescomplemented
126#2527C2214yes—
127#2520C2214yescomplemented
128#2515C2214yes—
129#2514C2214yescomplemented
130#2510C2214yes—
131#2510C2214yes—
132#2508C2214yescomplemented
133#2508C2214yescomplemented
134#2505C2214yes—
135#2505C2214yes—
136#2505C2214yes—
137#2505C2214yes—
138#2503C2214yes—
139#2497C2214yescomplemented
140#2493C2214yes—
141#2493C2214yes—
142#2493C2214yes—
143#2488C2214yes—
144#2488C2214yes—
145#2486C2212yes—
146#2486C2214yes—
147#2485C2214yescomplemented
148#2484C2214yes—
149#2484C2212yes—
150#2481C2214yes—
151#2473C2214yes—
152#2470C2214yes—
153#2469C2214yescomplemented
154#2466C2214yescomplemented
155#2465C2214yescomplemented
156#2462C2214yescomplemented
157#2462C2214yescomplemented
158#2458C2214yes—
159#2450C2214yes—
160#2450C2214yes—
161#2446C2214yescomplemented
162#2442C2212yes—
163#2441C2212yes—
164#2440C2212yes—
165#2439C2212yes—
166#2439C2214yescomplemented
167#2438C2214yescomplemented
168#2437C2214yes—
169#2419C2214yes—
170#2417C2214yes—
171#2413C2214yes—
172#2413C2214yes—
173#2412C2214yes—
174#2409C2212yes—
175#2406C2212yes—
176C2×#398C2211yescharacteristic
177C2×#398C2211yescharacteristic
178C2×#395C2211yescharacteristic
179C2×#395C2211yescharacteristic
180#2378C2212yes—
181#2378C2212yes—
182#2361C2212yes—
183#2360C2214yes—
184#2360C2214yes—
185#2360C2212yes—
186#2359C2214yes—
187#2358C2214yes—
188#2353C2212yes—
189#2352C2214yes—
190#2349C2212yes—
191#2347C2211yescharacteristic
192#2346C2211yescharacteristic
193#2344C2212yes—
194#2343C2214yes—
195#2342C2214yes—
196#2341C2211yescharacteristic
197Q8×C22⋊C4C2212yes—
198#2339C2211yescharacteristic
199#2335C2214yes—
200#2329C2214yes—
201#2329C2214yes—
202#2329C2214yes—
203#2323C2214yes—
204#2322C2212yes—
205#2322C2212yes—
206#2318C2214yes—
207#2318C2212yes—
208#2316C2212yes—
209#2313C2212yes—
210#2313C2212yes—
211#2313C2212yes—
212#2313C2212yes—
213#2313C2212yes—
214#2313C2212yes—
215#2313C2212yes—
216#2313C2212yes—
217#2313C2212yes—
218C4×C22⋊Q8C2214yes—
219C4×C22⋊Q8C2212yes—
220C4×#121C2212yes—
221C2×#389C2212yes—
222C2×#389C2212yes—
223#2290C2214yes—
224C2×#387C2214yes—
225C2×#387C2214yes—
226C2×#385C2212yes—
227C2×#385C2212yes—
228#2280C2211yescharacteristic
229C2×#381C2212yes—
230C2×#380C2211yescharacteristic
231C2×#380C2211yescharacteristic
232#2275C2212yes—
233C2×C4×C22⋊C4C2211yescharacteristic
234C2×C4×C22⋊C4C2212yes—
235C22×#41C2311yescharacteristic
236C23×Q8C2311yescharacteristic
237C24×C4C2311yescharacteristic
238C24×C4C2311yescharacteristic
239C24×C4C2311yescharacteristic
240C2×C4⋊Q8C2312yes—
241C2×#126C2314yes—
242C2×#125C2314yes—
243C2×#125C2312yes—
244#525—28no—
245C2×#123C2312yes—
246C2×#123C2312yes—
247C2×#123C2312yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×C22⋊Q8—28no—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2311yescharacteristic
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2311yescharacteristic
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×#121C2311yescharacteristic
261C2×#121C2311yescharacteristic
262C2×#120C2312yes—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2314yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2312yes—
271C2×#117C2311yescharacteristic
272C2×#117C2314yes—
273C2×#117C2312yes—
274C2×#117C2314yes—
275C22×C4⋊C4—28no—
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2311yescharacteristic
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2312yes—
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2312yes—
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2312yes—
295C22×C22⋊C4C2312yes—
296C22×C42C2314yes—
297C22×C42C2312yes—
298#401C2314yes—
299#401C2314yes—
300#401C2314yes—
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#400C2312yes—
314#400C2312yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#399C2314yes—
329#398C2314yes—
330#398C2312yes—
331#398C2314yes—
332#398C2314yes—
333#398C2312yes—
334#398C2314yes—
335#398C2314yes—
336#398C2312yes—
337#398C2312yes—
338#398C2314yes—
339#398C2312yes—
340#398C2312yes—
341#398C2314yes—
342#398C2314yes—
343#398C2312yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2312yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#397C2314yes—
357#397C2312yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2312yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#395C2314yes—
377#395C2312yes—
378#395C2312yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2312yes—
383#395C2312yes—
384#395C2312yes—
385#395C2312yes—
386#395C2312yes—
387#395C2312yes—
388#394C2312yes—
389#394C2312yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#393C2314yes—
394#393C2312yes—
395#393C2312yes—
396#393C2314yes—
397#393C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2312yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#390C2314yes—
411#390C2312yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2312yes—
437#389C2312yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2314yes—
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#388C2314yes—
465#388C2314yes—
466#388C2314yes—
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#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
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#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2312yes—
530#386C2312yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2312yes—
548#385C2312yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#384C2312yes—
565#383C2314yes—
566#383C2312yes—
567#383C2314yes—
568#383C2314yes—
569#383C2314yes—
570#382C2314yes—
571#382C2314yes—
572#382C2312yes—
573#382C2314yes—
574#382C2314yes—
575#382C2312yes—
576#382C2314yes—
577#382C2314yes—
578#381C2314yes—
579#381C2314yes—
580#381C2312yes—
581#381C2312yes—
582#381C2312yes—
583#381C2312yes—
584#381C2314yes—
585#381C2314yes—
586#381C2312yes—
587#381C2314yes—
588#381C2312yes—
589#381C2312yes—
590#381C2314yes—
591#381C2312yes—
592#380C2312yes—
593#380C2312yes—
594#380C2312yes—
595#380C2311yescharacteristic
596#380C2312yes—
597#380C2312yes—
598#380C2311yescharacteristic
599#380C2311yescharacteristic
600#380C2312yes—
601#380C2311yescharacteristic
602#380C2311yescharacteristic
603#380C2314yes—
604#380C2314yes—
605#380C2314yes—
606#380C2314yes—
607#380C2311yescharacteristic
608#380C2314yes—
609#380C2312yes—
610#380C2312yes—
611#380C2314yes—
612#380C2314yes—
613#380C2314yes—
614#380C2314yes—
615#379C2312yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C22⋊C4C2312yes—
626C4×C22⋊C4C2312yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2312yes—
630C4×C22⋊C4C2312yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2312yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2311yescharacteristic
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2312yes—
637C4×C22⋊C4C2312yes—
638C4×C22⋊C4C2312yes—
639C4×C22⋊C4C2311yescharacteristic
640C4×C22⋊C4C2311yescharacteristic
641C4×C22⋊C4C2311yescharacteristic
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2314yes—
647#376C2314yes—
648#376C2312yes—
649C2×#95C2311yescharacteristic
650C2×#95C2312yes—
651C2×#95C2312yes—
652C2×#95C2314yes—
653C2×#95C2312yes—
654C2×#95C2312yes—
655C2×#95C2311yescharacteristic
656C2×#95C2312yes—
657C2×#95C2312yes—
658C2×#95C2312yes—
659C2×#95C2314yes—
660C2×#95C2314yes—
661C25C2411yescharacteristic
662C2×#41—24no—
663C2×#41—82no—
664C22×Q8—24no—
665C22×Q8—82no—
666C22×Q8C2412yes—
667C22×Q8C2411yescharacteristic
668C22×Q8C2414yes—
669C22×Q8C2412yes—
670C22×D4C2412yes—
671C22×D4C2412yes—
672C22×D4C2411yescharacteristic
673C22×D4C2412yes—
674C23×C4—24no—
675C23×C4—24no—
676C23×C4—42no—
677C23×C4—42no—
678C23×C4—82no—
679C23×C4—82no—
680C23×C4#4118yes—
681C23×C4C2412yes—
682C23×C4C2411yescharacteristic
683C23×C4C2411yescharacteristic
684C23×C4C2412yes—
685C23×C4C2412yes—
686C23×C4C2412yes—
687C23×C4C2414yes—
688C23×C4C2414yes—
689C23×C4C2411yescharacteristic
690C23×C4C2411yescharacteristic
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2414yes—
696C23×C4C2412yes—
697C23×C4C2411yescharacteristic
698C23×C4C2411yescharacteristic
699C23×C4C2411yescharacteristic
700C23×C4C2411yescharacteristic
701C23×C4C2411yescharacteristic
702C23×C4C2411yescharacteristic
703C4⋊Q8—82no—
704#126—84no—
705#125—82no—
706#125—84no—
707#123—28no—
708#123—48no—
709#123—44no—
710#123—44no—
711#123—84no—
712C22⋊Q8—28no—
713C22⋊Q8—28no—
714C22⋊Q8—28no—
715C22⋊Q8—28no—
716C22⋊Q8—24no—
717C22⋊Q8—24no—
718C22⋊Q8—216no—
719C22⋊Q8—48no—
720C22⋊Q8—84no—
721#121—24no—
722#121—24no—
723#120—28no—
724C4×Q8—84no—
725C4×Q8—82no—
726C4×Q8—84no—
727C4×D4—28no—
728C4×D4—28no—
729C4×D4—216no—
730C4×D4—48no—
731C4×D4—82no—
732#117—24no—
733#117—48no—
734#117—84no—
735#117—82no—
736C2×C4⋊C4—28no—
737C2×C4⋊C4—28no—
738C2×C4⋊C4—24no—
739C2×C4⋊C4—24no—
740C2×C4⋊C4—24no—
741C2×C4⋊C4—24no—
742C2×C4⋊C4—28no—
743C2×C4⋊C4—28no—
744C2×C4⋊C4—24no—
745C2×C4⋊C4—28no—
746C2×C4⋊C4—44no—
747C2×C4⋊C4—44no—
748C2×C4⋊C4—82no—
749C2×C4⋊C4—82no—
750C2×C4⋊C4—82no—
751C2×C4⋊C4—82no—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C22⋊C4—28no—
809C2×C22⋊C4—28no—
810C2×C22⋊C4—44no—
811C2×C22⋊C4—44no—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2412yes—
844C2×C42—84no—
845C2×C42—82no—
846C2×C42C2412yes—
847C2×C42C2414yes—
848C2×C42C2414yes—
849C2×C42C2414yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2412yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2412yes—
859C2×C42C2414yes—
860C2×C42C2412yes—
861C2×C42C2414yes—
862C2×C42C2412yes—
863#95C2411yescharacteristic
864#95C2412yes—
865#95C2411yescharacteristic
866#95C2414yes—
867#95C2411yescharacteristic
868#95C2414yes—
869#95C2411yescharacteristic
870#95C2414yes—
871#95C2412yes—
872#95C2414yes—
873#95C2414yes—
874#95C2412yes—
875#95C2412yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2412yes—
880#95C2414yes—
881#95C2412yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2412yes—
904#95C2412yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934C24—24no—
935C24—22no—
936C24—22no—
937C24—42no—
938C24C2×#4114yes—
939C24C2512yes—
940C24C2511yescharacteristic
941C24C2511yescharacteristic
942C24C2511yescharacteristic
943#41—88no—
944C2×Q8—24no—
945C2×Q8—22no—
946C2×Q8—24no—
947C2×Q8—28no—
948C2×Q8—44no—
949C2×Q8—42no—
950C2×Q8—44no—
951C2×Q8—44no—
952C2×Q8—44no—
953C2×Q8—88no—
954C2×D4—24no—
955C2×D4—24no—
956C2×D4—28no—
957C2×D4—24no—
958C2×D4—24no—
959C2×D4—24no—
960C2×D4—22no—
961C2×D4—42no—
962C2×D4—44no—
963C22×C4—24no—
964C22×C4—24no—
965C22×C4—24no—
966C22×C4—24no—
967C22×C4—22no—
968C22×C4—22no—
969C22×C4—22no—
970C22×C4—22no—
971C22×C4—24no—
972C22×C4—24no—
973C22×C4—24no—
974C22×C4—24no—
975C22×C4—22no—
976C22×C4—22no—
977C22×C4—24no—
978C22×C4—24no—
979C22×C4—22no—
980C22×C4—22no—
981C22×C4—28no—
982C22×C4—28no—
983C22×C4—24no—
984C22×C4—24no—
985C22×C4—24no—
986C22×C4—28no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—44no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—416no—
1013C22×C4—88no—
1014C22×C4—88no—
1015C22×C4C2×#4114yes—
1016C22×C4C2×#4114yes—
1017C22×C4C2×#4114yes—
1018C22×C4C2×#4114yes—
1019C22×C4C2×#4114yes—
1020C22×C4C2×#4114yes—
1021C22×C4C2512yes—
1022C22×C4C2514yes—
1023C22×C4C2514yes—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2514yes—
1027C22×C4C2514yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2514yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2514yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2511yescharacteristic
1039C22×C4C2511yescharacteristic
1040C22×C4C2511yescharacteristic
1041C22×C4C2511yescharacteristic
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—28no—
1055C4⋊C4—28no—
1056C4⋊C4—22no—
1057C4⋊C4—22no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—28no—
1061C4⋊C4—28no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—42no—
1070C4⋊C4—44no—
1071C4⋊C4—42no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—42no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—42no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C22⋊C4—28no—
1101C22⋊C4—28no—
1102C22⋊C4—24no—
1103C22⋊C4—24no—
1104C22⋊C4—24no—
1105C22⋊C4—24no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—24no—
1110C22⋊C4—24no—
1111C22⋊C4—24no—
1112C22⋊C4—24no—
1113C22⋊C4—24no—
1114C22⋊C4—24no—
1115C22⋊C4—28no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C42−1+418yes—
1132C42—24no—
1133C42—28no—
1134C42—44no—
1135C42—42no—
1136C42—42no—
1137C42—44no—
1138C42—42no—
1139C42—44no—
1140C42—44no—
1141C42—42no—
1142C42—44no—
1143C42—44no—
1144C42—44no—
1145C42—44no—
1146C42—44no—
1147C42—44no—
1148C42—44no—
1149C23—22no—
1150C23—21no—
1151C23—21no—
1152C23—22no—
1153C23—22no—
1154C23—22no—
1155C23—21no—
1156C23—21no—
1157C23—22no—
1158C23—28no—
1159C23—28no—
1160C23—22no—
1161C23—24no—
1162C23—22no—
1163C23—22no—
1164C23—24no—
1165C23—44no—
1166C23—48no—
1167C23—48no—
1168C23C22×#4112yes—
1169C23C22×#4112yes—
1170C23C22×#4112yes—
1171C23C2×2−1+414yes—
1172C23#58512yes—
1173C23#58512yes—
1174C23C2611yescharacteristic
1175Q8—48no—
1176Q8—44no—
1177Q8—88no—
1178Q8—84no—
1179D4—44no—
1180D4—48no—
1181D4—48no—
1182D4—84no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—44no—
1239C2×C4—44no—
1240C2×C4—44no—
1241C2×C4—44no—
1242C2×C4—44no—
1243C2×C4—44no—
1244C2×C4—48no—
1245C2×C4—48no—
1246C2×C4—48no—
1247C2×C4—48no—
1248C2×C4—48no—
1249C2×C4—48no—
1250C2×C4—44no—
1251C2×C4—44no—
1252C2×C4—88no—
1253C2×C4—84no—
1254C2×C4—88no—
1255C2×C4—88no—
1256C2×C4—82no—
1257C2×C4—82no—
1258C2×C4—84no—
1259C2×C4—84no—
1260C2×C4C22×#4112yes—
1261C2×C4C22×#4112yes—
1262C2×C4C22×#4112yes—
1263C2×C4C22×#4112yes—
1264C2×C4C2×2−1+414yes—
1265C2×C4C2×2−1+414yes—
1266C22—22no—
1267C22—22no—
1268C22—22no—
1269C22—22no—
1270C22—24no—
1271C22—24no—
1272C22—24no—
1273C22—24no—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—416no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—44no—
1284C22—44no—
1285C22#349314yes—
1286C22#350914yes—
1287C22C23×#4111yescharacteristic
1288C22C22×2−1+412yes—
1289C22C2×#58511yescharacteristic
1290C22C2×#58511yescharacteristic
1291C22H(7,𝔽2)12yes—
1292C4—22no—
1293C4—22no—
1294C4—22no—
1295C4—22no—
1296C4—24no—
1297C4—24no—
1298C4—44no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—44no—
1307C4—44no—
1308C4—42no—
1309C4—42no—
1310C4—44no—
1311C4—44no—
1312C4—44no—
1313C4—44no—
1314C4—44no—
1315C2—24no—
1316C2—24no—
1317C2—42no—
1318C2—82no—
1319C2C2×#349311yescharacteristic
1320C2C2×#350911yescharacteristic
1321C2#6284411yescharacteristic
1322C2#6294812yes—
1323C2#6294812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #48800C2semidirect
2. #48799C2semidirect
3. #47888C2semidirect
4. #47885C2semidirect
5. #47009C2semidirect
6. #46403C2semidirect
7. #43515C2semidirect
8. #43514C2semidirect
9. #43085C2semidirect
10. #43082C2semidirect
11. #39679C2semidirect
12. #39549C2semidirect
13. #39541C2semidirect
14. #39512C2semidirect
15. #39504C2semidirect
16. #38234C2semidirect
17. #38065C2semidirect
19. #36782C2semidirect
20. #36245C2semidirect
21. #35399C2semidirect
22. #35079C2semidirect
24. C2×#2583C2semidirect
25. #34380C2semidirect
27. C2×#2313C2semidirect
39. #2810C22semidirect
40. #2809C22semidirect
41. #2809C22semidirect
42. #2808C22semidirect
43. #2805C22semidirect
44. #2805C22semidirect
45. #2802C22semidirect
46. #2802C22semidirect
47. #2800C22semidirect
48. #2787C22semidirect
49. #2783C22semidirect
50. #2783C22semidirect
51. #2783C22semidirect
52. #2776C22semidirect
53. #2776C22semidirect
54. #2776C22semidirect
55. #2774C22semidirect
56. #2774C22semidirect
57. #2772C22semidirect
59. #2769C22semidirect
60. #2766C22semidirect
61. #2766C22semidirect
65. #2762C22semidirect
66. #2762C22semidirect
68. #2759C22semidirect
71. #2747C22semidirect
72. #2745C22semidirect
73. #2744C22semidirect
75. #2725C22semidirect
76. #2719C22semidirect
77. #2690C22semidirect
78. #2689C22semidirect
93. #2612C22semidirect
94. #2608C22semidirect
95. #2606C22semidirect
96. #2605C22semidirect
97. #2599C22semidirect
99. #2590C22semidirect
100. #2590C22semidirect
101. #2590C22semidirect
102. #2587C22semidirect
103. #2585C22semidirect
111. #2581C22semidirect
112. #2581C22semidirect
114. #2577C22semidirect
116. #2574C22semidirect
118. #2570C22semidirect
120. #2569C22semidirect
124. #2533C22semidirect
125. #2532C22semidirect
127. #2520C22semidirect
129. #2514C22semidirect
132. #2508C22semidirect
133. #2508C22semidirect
139. #2497C22semidirect
147. #2485C22semidirect
153. #2469C22semidirect
154. #2466C22semidirect
155. #2465C22semidirect
156. #2462C22semidirect
157. #2462C22semidirect
161. #2446C22semidirect
166. #2439C22semidirect
167. #2438C22semidirect

Maximal subgroups

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

subgroupindex
#488002
#487992
#478882
#478852
#470092
#464032
#435152
#435142
#430852
#430822
#396792
#395492
#395412
#395122
#395042
#382342
#380652
#374422
#367822
#362452
#353992
#350792
#350572
C2×#25832
#343802
#342332
C2×#23132