Finite Group Databasebeta

← #8757637

Subgroups — #8757637

Order 512.

4322 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58952C212yesmaximal, complemented
2#58582C214yesmaximal, complemented
3#57382C212yesmaximal, complemented
4#56731C214yesmaximal, complemented
5#56261C214yesmaximal, complemented
6#56033C214yesmaximal, complemented
7#53899C212yesmaximal, complemented
8#53748C212yesmaximal, complemented
9#52082C212yesmaximal, complemented
10#51999C212yesmaximal, complemented
11#51984C212yesmaximal, complemented
12#51923C212yesmaximal, complemented
13#51873C212yesmaximal, complemented
14#51601C212yesmaximal, complemented
15#47152C212yesmaximal, complemented
16#47133C214yesmaximal, complemented
17#47121C214yesmaximal, complemented
18#46758C212yesmaximal, complemented
19#46230C212yesmaximal, complemented
20#46228C212yesmaximal, complemented
21#46227C212yesmaximal, complemented
22#46143C212yesmaximal, complemented
23#46141C212yesmaximal, complemented
24#45979C212yesmaximal, complemented
25#35333C211yesmaximal, characteristic, complemented
26#35200C211yesmaximal, characteristic, complemented
27#35190C211yesmaximal, characteristic
28C2×#563C2212yes—
29C2×#533C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C22×#125C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33#2851C2212yes—
34#2851C2212yes—
35#2851C2212yes—
36#2851C2212yes—
37#2850C2212yes—
38#2850C2212yes—
39#2844C2212yes—
40#2838C2214yes—
41#2837C2214yes—
42#2834C2212yes—
43#2830C2214yes—
44#2827C2214yes—
45#2826C2214yes—
46#2824C2212yes—
47#2822C2212yes—
48#2820C2212yes—
49#2820C2212yes—
50#2814C2214yes—
51#2811C2212yes—
52#2809C2212yes—
53#2803C2214yes—
54#2799C2214yes—
55#2795C2214yes—
56#2795C2214yes—
57#2793C2214yes—
58#2791C2214yes—
59#2790C2214yes—
60#2788C2214yes—
61#2781C2214yes—
62#2781C2214yes—
63#2776C2214yes—
64#2775C2214yes—
65#2774C2214yes—
66#2770C2214yes—
67#2764C2214yes—
68#2763C2214yes—
69#2761C2214yes—
70#2758C2214yes—
71#2757C2214yes—
72#2756C2214yes—
73#2755C2214yes—
74#2750C2214yes—
75#2750C2214yes—
76#2745C2214yes—
77#2742C2212yes—
78#2741C2214yes—
79#2739C2214yes—
80#2738C2214yes—
81#2734C2214yes—
82#2731C2212yes—
83#2731C2212yes—
84#2731C2214yes—
85#2730C2214yes—
86#2728C2214yes—
87#2725C2214yes—
88#2723C2214yes—
89#2721C2214yes—
90#2721C2214yes—
91#2720C2214yes—
92#2720C2214yes—
93#2720C2214yes—
94#2717C2214yes—
95#2716C2214yes—
96#2715C2214yes—
97#2713C2214yes—
98#2712C2214yes—
99#2712C2212yes—
100#2710C2214yes—
101#2709C2214yes—
102#2709C2214yes—
103#2707C2214yes—
104#2702C2214yes—
105#2700C2214yes—
106#2700C2214yes—
107#2698C2214yes—
108#2693C2212yes—
109#2692C2214yes—
110#2692C2214yes—
111#2691C2214yes—
112#2691C2214yes—
113#2690C2214yes—
114#2690C2214yes—
115#2686C2214yes—
116#2681C2214yes—
117#2677C2212yes—
118#2677C2214yes—
119#2677C2214yes—
120#2672C2214yes—
121#2672C2214yes—
122#2672C2214yes—
123#2666C2214yes—
124#2662C2214yes—
125#2660C2214yes—
126#2653C2214yes—
127#2651C2214yes—
128#2648C2214yes—
129#2638C2212yes—
130#2638C2212yes—
131#2635C2212yes—
132#2635C2212yes—
133#2629C2212yes—
134#2629C2212yes—
135#2612C2214yes—
136#2605C2214yes—
137#2599C2212yes—
138#2599C2212yes—
139#2598C2212yes—
140#2598C2212yes—
141#2597C2214yes—
142#2596C2214yes—
143#2589C2214yes—
144#2588C2214yes—
145#2586C2214yes—
146#2579C2212yes—
147#2579C2212yes—
148#2579C2212yes—
149#2579C2212yes—
150#2578C2214yes—
151#2576C2214yes—
152#2574C2214yes—
153#2574C2214yes—
154#2568C2211yescharacteristic
155#2567C2211yescharacteristic
156#2566C2212yes—
157#2566C2212yes—
158#2565C2212yes—
159#2565C2212yes—
160#2563C2211yescharacteristic
161#2558C2214yes—
162#2557C2214yes—
163#2556C2214yes—
164#2548C2211yescharacteristic
165#2547C2211yescharacteristic
166#2546C2211yescharacteristic
167#2544C2214yes—
168#2542C2211yescharacteristic
169#2541C2211yescharacteristic
170#2533C2214yes—
171#2531C2214yes—
172#2531C2214yes—
173#2530C2214yes—
174#2528C2214yes—
175#2526C2214yes—
176#2525C2214yes—
177#2521C2214yes—
178#2520C2214yes—
179#2517C2212yes—
180#2515C2214yes—
181#2511C2214yes—
182#2502C2214yes—
183#2500C2212yes—
184#2499C2212yes—
185#2485C2212yes—
186#2485C2212yes—
187#2481C2214yes—
188#2481C2214yes—
189#2481C2214yes—
190#2479C2214yes—
191#2477C2214yes—
192#2474C2214yes—
193#2470C2214yes—
194#2469C2214yes—
195#2466C2214yes—
196#2466C2214yes—
197#2463C2212yes—
198#2461C2214yes—
199#2458C2214yes—
200#2451C2214yes—
201#2449C2214yes—
202#2449C2214yes—
203#2449C2214yes—
204#2443C2214yes—
205#2440C2214yes—
206#2440C2214yes—
207#2432C2212yes—
208#2432C2214yes—
209#2431C2212yes—
210#2429C2214yes—
211#2417C2214yes—
212#2407C2212yes—
213#2407C2212yes—
214#2406C2214yes—
215#2382C2212yes—
216#2382C2212yes—
217#2381C2212yes—
218#2379C2212yes—
219#2379C2212yes—
220#2372C2212yes—
221#2369C2212yes—
222#2337C2214yes—
223#2328C2212yes—
224#2327C2212yes—
225#2326C2212yes—
226#2326C2212yes—
227#2322C2214yes—
228#2317C2211yescharacteristic
229#2317C2211yescharacteristic
230#2311C2211yescharacteristic
231#2311C2211yescharacteristic
232#2285C2211yescharacteristic
233#2283C2211yescharacteristic
234#2283C2211yescharacteristic
235C22×#41C2311yescharacteristic
236C22×#41C2312yes—
237#563—48no—
238#533—44no—
239#532—44no—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2311yescharacteristic
242C2×C4⋊Q8C2311yescharacteristic
243C2×C4⋊Q8C2311yescharacteristic
244C2×C4⋊Q8C2314yes—
245C2×C4⋊Q8C2314yes—
246C2×#127C2312yes—
247C2×#127C2311yescharacteristic
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#125—44no—
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#125C2312yes—
257C2×#125C2314yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2314yes—
262C2×#124C2314yes—
263C2×#124C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×#121C2312yes—
278C2×#121C2312yes—
279C2×#121C2312yes—
280C2×#121C2312yes—
281C4×#41—44no—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×D4C2311yescharacteristic
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2311yescharacteristic
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2311yescharacteristic
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2314yes—
295C2×#117C2311yescharacteristic
296C2×#117C2311yescharacteristic
297C2×#117C2311yescharacteristic
298C2×#117C2311yescharacteristic
299C2×#117C2311yescharacteristic
300C2×#117C2312yes—
301C22×C4⋊C4C2311yescharacteristic
302C22×C4⋊C4C2311yescharacteristic
303C22×C4⋊C4C2312yes—
304C22×C4⋊C4C2312yes—
305C22×C4⋊C4C2314yes—
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309#401C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2312yes—
313#400C2312yes—
314#400C2314yes—
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#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2312yes—
333#399C2314yes—
334#399C2312yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2312yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2312yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2312yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2312yes—
392#395C2312yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2312yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2312yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#393C2312yes—
426#393C2312yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#393C2314yes—
432#393C2314yes—
433#392C2312yes—
434#392C2312yes—
435#392C2314yes—
436#392C2314yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2314yes—
444#391C2314yes—
445#391C2312yes—
446#391C2312yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#390C2312yes—
457#390C2312yes—
458#390C2312yes—
459#390C2314yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2312yes—
465#390C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
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#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#386C2312yes—
560#386C2312yes—
561#386C2312yes—
562#386C2312yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2312yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2312yes—
589#385C2312yes—
590#385C2312yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#384C2312yes—
606#384C2312yes—
607#384C2312yes—
608#384C2312yes—
609#384C2312yes—
610#384C2314yes—
611#383C2314yes—
612#383C2314yes—
613#383C2312yes—
614#383C2312yes—
615#382C2312yes—
616#382C2312yes—
617#382C2312yes—
618#382C2312yes—
619#382C2312yes—
620#382C2312yes—
621#382C2312yes—
622#382C2314yes—
623#382C2314yes—
624#381C2314yes—
625#381C2312yes—
626#381C2312yes—
627#381C2314yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2314yes—
635#380C2312yes—
636#380C2312yes—
637#380C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2314yes—
641#380C2314yes—
642#380C2312yes—
643C4×C4⋊C4C2311yescharacteristic
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2311yescharacteristic
647C4×C4⋊C4C2311yescharacteristic
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2311yescharacteristic
653C4×C22⋊C4C2312yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660#376C2312yes—
661#376C2312yes—
662#376C2314yes—
663C2×#41—24no—
664C2×#41—42no—
665C2×#41—42no—
666C2×#41—44no—
667C2×#41—82no—
668C2×#41—82no—
669C22×Q8C2412yes—
670C22×Q8C2412yes—
671C22×Q8C2412yes—
672C22×Q8C2414yes—
673C22×Q8C2414yes—
674C22×Q8C2411yescharacteristic
675C22×D4C2411yescharacteristic
676C22×D4C2411yescharacteristic
677C22×D4C2411yescharacteristic
678C22×D4C2414yes—
679C22×D4C2412yes—
680C22×D4C2412yes—
681C22×D4C2412yes—
682C22×D4C2414yes—
683C22×D4C2414yes—
684C23×C4C2411yescharacteristic
685C23×C4C2411yescharacteristic
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2411yescharacteristic
689C23×C4C2411yescharacteristic
690C23×C4C2411yescharacteristic
691C23×C4C2411yescharacteristic
692C23×C4C2411yescharacteristic
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2414yes—
696C23×C4C2414yes—
697C23×C4C2414yes—
698C4⋊Q8—28no—
699C4⋊Q8—42no—
700C4⋊Q8—42no—
701C4⋊Q8—42no—
702C4⋊Q8—48no—
703C4⋊Q8—84no—
704#127—42no—
705#127—44no—
706#126—48no—
707#126—48no—
708#126—84no—
709#125—28no—
710#125—28no—
711#125—44no—
712#125—44no—
713#125—44no—
714#125—84no—
715#124—28no—
716#124—28no—
717#124—48no—
718#124—44no—
719#124—84no—
720#124—84no—
721#123—48no—
722#123—48no—
723#123—84no—
724C22⋊Q8—48no—
725C22⋊Q8—48no—
726C22⋊Q8—44no—
727C22⋊Q8—44no—
728C22⋊Q8—84no—
729C22⋊Q8—84no—
730C22⋊Q8—84no—
731C22⋊Q8—82no—
732C22⋊Q8—84no—
733C22⋊Q8—82no—
734#121—44no—
735#121—44no—
736#121—82no—
737#121—82no—
738C4×Q8—42no—
739C4×Q8—42no—
740C4×Q8—44no—
741C4×Q8—44no—
742C4×D4—44no—
743C4×D4—44no—
744C4×D4—42no—
745C4×D4—42no—
746C4×D4—42no—
747C4×D4—42no—
748C4×D4—42no—
749C4×D4—42no—
750C4×D4—84no—
751#117—42no—
752#117—42no—
753#117—42no—
754#117—42no—
755#117—42no—
756#117—44no—
757C2×C4⋊C4—42no—
758C2×C4⋊C4—44no—
759C2×C4⋊C4—44no—
760C2×C4⋊C4—42no—
761C2×C4⋊C4—84no—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2411yescharacteristic
826C2×C22⋊C4C2411yescharacteristic
827C2×C22⋊C4C2411yescharacteristic
828C2×C22⋊C4C2411yescharacteristic
829C2×C22⋊C4C2411yescharacteristic
830C2×C22⋊C4C2411yescharacteristic
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⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C42—24no—
862C2×C42—24no—
863C2×C42—24no—
864C2×C42C2411yescharacteristic
865C2×C42C2411yescharacteristic
866C2×C42C2411yescharacteristic
867C2×C42C2411yescharacteristic
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2411yescharacteristic
871C2×C42C2411yescharacteristic
872C2×C42C2411yescharacteristic
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2414yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2412yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2412yes—
885C2×C42C2414yes—
886C2×C42C2411yescharacteristic
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#95C2414yes—
904#95C2414yes—
905#95C2412yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
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—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943C24C2514yes—
944C24C2511yescharacteristic
945C24C2511yescharacteristic
946C24C2511yescharacteristic
947#41—416no—
948#41—816no—
949C2×Q8—24no—
950C2×Q8—24no—
951C2×Q8—41no—
952C2×Q8—41no—
953C2×Q8—42no—
954C2×Q8—42no—
955C2×Q8—44no—
956C2×Q8—42no—
957C2×Q8—42no—
958C2×Q8—42no—
959C2×Q8—44no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—44no—
963C2×Q8—44no—
964C2×Q8—44no—
965C2×Q82−1+414yes—
966C2×D4—22no—
967C2×D4—22no—
968C2×D4—28no—
969C2×D4—24no—
970C2×D4—22no—
971C2×D4—22no—
972C2×D4—22no—
973C2×D4—24no—
974C2×D4—41no—
975C2×D4—41no—
976C2×D4—41no—
977C2×D4—41no—
978C2×D4—42no—
979C2×D4—42no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—42no—
983C2×D4—42no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—42no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—44no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—22no—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—22no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—22no—
1004C22×C4—22no—
1005C22×C4—42no—
1006C22×C4—41no—
1007C22×C4—41no—
1008C22×C4—42no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4C2514yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2514yes—
1029C22×C4C2514yes—
1030C22×C4C2514yes—
1031C22×C4C2511yescharacteristic
1032C22×C4C2514yes—
1033C22×C4C2514yes—
1034C22×C4C2511yescharacteristic
1035C22×C4C2514yes—
1036C22×C4C2514yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2514yes—
1039C22×C4C2511yescharacteristic
1040C22×C4C2514yes—
1041C22×C4C2514yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C22×C4C2511yescharacteristic
1047C22×C4C2511yescharacteristic
1048C22×C4C2511yescharacteristic
1049C4⋊C4—24no—
1050C4⋊C4—28no—
1051C4⋊C4—28no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—28no—
1056C4⋊C4—28no—
1057C4⋊C4—28no—
1058C4⋊C4—28no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—44no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—42no—
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—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C22⋊C4—24no—
1106C22⋊C4—24no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—28no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—41no—
1121C22⋊C4—41no—
1122C22⋊C4—41no—
1123C22⋊C4—41no—
1124C22⋊C4—41no—
1125C22⋊C4—41no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C42—22no—
1149C42—22no—
1150C42—22no—
1151C42—22no—
1152C42—22no—
1153C42—22no—
1154C42—22no—
1155C42—22no—
1156C42—22no—
1157C42—24no—
1158C42—24no—
1159C42—44no—
1160C42—42no—
1161C42—42no—
1162C42—44no—
1163C42—44no—
1164C42—42no—
1165C42—44no—
1166C42—44no—
1167C42—44no—
1168C42—44no—
1169C42—42no—
1170C42H(5,𝔽2)14yes—
1171C23—21no—
1172C23—21no—
1173C23—22no—
1174C23—22no—
1175C23—24no—
1176C23—21no—
1177C23—21no—
1178C23—24no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—24no—
1183C23—21no—
1184C23—22no—
1185C23—24no—
1186C23—22no—
1187C23—24no—
1188C23—22no—
1189C23—24no—
1190C23—24no—
1191C23—22no—
1192C23#58512yes—
1193C23C2611yescharacteristic
1194Q8—44no—
1195Q8—84no—
1196Q8—84no—
1197Q8—84no—
1198Q8—164no—
1199Q8—164no—
1200D4—44no—
1201D4—44no—
1202D4—44no—
1203D4—84no—
1204D4—84no—
1205D4—88no—
1206D4—84no—
1207D4—88no—
1208D4—164no—
1209C2×C4—28no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—44no—
1266C2×C4—44no—
1267C2×C4—44no—
1268C2×C4—44no—
1269C2×C4—82no—
1270C2×C4—82no—
1271C2×C4—82no—
1272C2×C4—82no—
1273C2×C4—88no—
1274C2×C4—84no—
1275C2×C4—84no—
1276C2×C4—88no—
1277C2×C4—164no—
1278C2×C4C2×H(5,𝔽2)12yes—
1279C2×C4C2×H(5,𝔽2)12yes—
1280C2×C4C2×H(5,𝔽2)12yes—
1281C2×C4C2×2−1+412yes—
1282C2×C4C2×2−1+412yes—
1283C2×C4C2×2−1+412yes—
1284C22—24no—
1285C22—22no—
1286C22—42no—
1287C22—41no—
1288C22—41no—
1289C22—44no—
1290C22—42no—
1291C22—44no—
1292C22—42no—
1293C22—44no—
1294C22—44no—
1295C22—42no—
1296C22—42no—
1297C22—41no—
1298C22—41no—
1299C22—44no—
1300C22—41no—
1301C22—44no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—44no—
1306C22C22×H(5,𝔽2)11yescharacteristic
1307C22C22×2−1+411yescharacteristic
1308C22C2×#58511yescharacteristic
1309C22H(7,𝔽2)12yes—
1310C222−1+612yes—
1311C4—22no—
1312C4—22no—
1313C4—22no—
1314C4—22no—
1315C4—22no—
1316C4—22no—
1317C4—44no—
1318C4—44no—
1319C4—44no—
1320C4—44no—
1321C4—44no—
1322C4—44no—
1323C4—44no—
1324C4—41no—
1325C4—41no—
1326C4—44no—
1327C4—44no—
1328C4—41no—
1329C4—44no—
1330C4—41no—
1331C4—41no—
1332C4—44no—
1333C4—41no—
1334C2—42no—
1335C2—84no—
1336C2—81no—
1337C2—81no—
1338C2#6281911yescharacteristic
1339C2#6287411yescharacteristic
1340C2#6288611yescharacteristic
1341C2#6305912yes—
1342C2#6306112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35190C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58952C2semidirect
2. #58582C2semidirect
3. #57382C2semidirect
4. #56731C2semidirect
5. #56261C2semidirect
6. #56033C2semidirect
7. #53899C2semidirect
8. #53748C2semidirect
9. #52082C2semidirect
10. #51999C2semidirect
11. #51984C2semidirect
12. #51923C2semidirect
13. #51873C2semidirect
14. #51601C2semidirect
15. #47152C2semidirect
16. #47133C2semidirect
17. #47121C2semidirect
18. #46758C2semidirect
19. #46230C2semidirect
20. #46228C2semidirect
21. #46227C2semidirect
22. #46143C2semidirect
23. #46141C2semidirect
24. #45979C2semidirect
25. #35333C2semidirect
26. #35200C2semidirect

Maximal subgroups

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

subgroupindex
#589522
#585822
#573822
#567312
#562612
#560332
#538992
#537482
#520822
#519992
#519842
#519232
#518732
#516012
#471522
#471332
#471212
#467582
#462302
#462282
#462272
#461432
#461412
#459792
#353332
#352002
#351902