Finite Group Databasebeta

← #10069108

Subgroups — #10069108

Order 512.

4763 conjugacy classes of subgroups.

The subgroup lattice has 1274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59660C211yesmaximal, characteristic, complemented
2#56477C214yesmaximal, complemented
3#54961C214yesmaximal, complemented
4#54909C214yesmaximal, complemented
5#54851C212yesmaximal, complemented
6#53861C212yesmaximal, complemented
7#52327C214yesmaximal, complemented
8#48327C214yesmaximal, complemented
9#48317C214yesmaximal, complemented
10#47179C212yesmaximal, complemented
11#46969C212yesmaximal, complemented
12#46766C214yesmaximal, complemented
13#46017C212yesmaximal, complemented
14#45387C212yesmaximal, complemented
15#43289C212yesmaximal, complemented
16#43119C214yesmaximal, complemented
17#43117C214yesmaximal, complemented
18#42166C212yesmaximal, complemented
19#41406C212yesmaximal, complemented
20#41107C214yesmaximal, complemented
21#38952C211yesmaximal, characteristic, complemented
22#38810C212yesmaximal, complemented
23#37266C211yesmaximal, characteristic, complemented
24C2×#554C2212yes—
25C2×#554C2211yescharacteristic
26C2×#553C2212yes—
27C2×#550C2211yescharacteristic
28C2×#550C2212yes—
29C2×#547C2214yes—
30#2864C2212yes—
31#2858C2211yescharacteristic
32#2837C2214yes—
33#2832C2212yes—
34#2828C2212yes—
35#2828C2214yes—
36#2826C2214yes—
37#2826C2214yes—
38#2822C2212yes—
39#2819C2212yes—
40#2819C2212yes—
41#2816C2212yes—
42#2814C2214yes—
43#2813C2214yes—
44#2809C2211yescharacteristic
45#2809C2212yes—
46#2807C2214yes—
47#2805C2212yes—
48#2803C2214yes—
49#2795C2214yes—
50#2794C2212yes—
51#2790C2214yes—
52#2789C2212yes—
53#2785C2212yes—
54#2782C2214yes—
55#2780C2214yes—
56#2778C2214yes—
57#2774C2214yes—
58#2773C2214yes—
59#2767C2214yes—
60#2767C2214yes—
61#2765C2214yes—
62#2761C2214yes—
63#2761C2214yes—
64#2756C2214yes—
65#2754C2214yes—
66#2753C2214yes—
67#2752C2214yes—
68#2751C2214yes—
69#2747C2214yes—
70#2746C2214yes—
71#2745C2214yes—
72#2743C2214yes—
73#2743C2214yes—
74#2741C2214yes—
75#2741C2214yes—
76#2734C2212yes—
77#2734C2211yescharacteristic
78#2732C2212yes—
79#2730C2214yes—
80#2729C2214yes—
81#2728C2212yes—
82#2728C2212yes—
83#2727C2212yes—
84#2724C2212yes—
85#2721C2214yes—
86#2720C2214yes—
87#2718C2214yes—
88#2716C2214yes—
89#2714C2214yes—
90#2711C2214yes—
91#2709C2214yes—
92#2701C2214yes—
93#2699C2212yes—
94#2699C2214yes—
95#2693C2214yes—
96#2692C2214yes—
97#2687C2214yes—
98#2687C2214yes—
99#2682C2212yes—
100#2681C2214yes—
101#2680C2214yes—
102#2673C2214yes—
103#2673C2214yes—
104#2673C2214yes—
105#2673C2214yes—
106#2673C2214yes—
107#2673C2214yes—
108#2672C2214yes—
109#2672C2214yes—
110#2672C2214yes—
111#2667C2214yes—
112#2654C2214yes—
113#2639C2212yes—
114#2636C2214yes—
115#2635C2214yes—
116#2634C2212yes—
117#2633C2212yes—
118#2630C2214yes—
119#2630C2214yes—
120#2627C2214yes—
121#2625C2212yes—
122#2620C2212yes—
123#2618C2212yes—
124#2602C2214yes—
125#2600C2214yes—
126#2600C2214yes—
127#2594C2214yes—
128#2593C2212yes—
129#2591C2212yes—
130#2589C2214yes—
131#2586C2212yes—
132#2582C2211yescharacteristic
133#2579C2214yes—
134#2576C2214yes—
135#2574C2214yes—
136#2570C2214yes—
137#2567C2211yescharacteristic
138#2559C2214yes—
139#2558C2214yes—
140#2557C2214yes—
141#2553C2214yes—
142#2548C2211yescharacteristic
143#2537C2211yescharacteristic
144#2536C2212yes—
145#2536C2212yes—
146#2536C2212yes—
147#2535C2214yes—
148#2533C2214yes—
149#2529C2214yes—
150#2516C2214yes—
151#2502C2212yes—
152#2501C2212yes—
153#2489C2214yes—
154#2488C2214yes—
155#2488C2214yes—
156#2484C2212yes—
157#2479C2214yes—
158#2476C2214yes—
159#2473C2214yes—
160#2469C2214yes—
161#2468C2214yes—
162#2467C2214yes—
163#2466C2214yes—
164#2464C2214yes—
165#2463C2214yes—
166#2462C2214yes—
167#2461C2214yes—
168#2460C2214yes—
169#2459C2214yes—
170#2458C2214yes—
171#2457C2214yes—
172#2457C2214yes—
173#2456C2214yes—
174#2456C2214yes—
175#2455C2214yes—
176#2455C2214yes—
177#2454C2214yes—
178#2450C2214yes—
179#2449C2214yes—
180#2445C2214yes—
181#2445C2214yes—
182#2444C2214yes—
183#2444C2214yes—
184#2443C2214yes—
185#2443C2214yes—
186#2443C2214yes—
187#2443C2214yes—
188#2443C2214yes—
189#2442C2214yes—
190#2432C2212yes—
191#2430C2214yes—
192#2427C2214yes—
193#2419C2214yes—
194#2413C2214yes—
195#2407C2214yes—
196#2407C2214yes—
197#2406C2214yes—
198#2406C2214yes—
199#2397C2212yes—
200C2×#398C2212yes—
201#2388C2214yes—
202#2379C2212yes—
203#2379C2212yes—
204#2361C2214yes—
205#2360C2214yes—
206#2359C2214yes—
207D4×C4⋊C4C2214yes—
208#2333C2214yes—
209#2332C2214yes—
210#2328C2212yes—
211#2327C2212yes—
212#2322C2214yes—
213#2322C2214yes—
214#2318C2212yes—
215#2311C2212yes—
216C4×C4⋊Q8C2211yescharacteristic
217C4×#124C2212yes—
218#2293C2211yescharacteristic
219C22×#41C2312yes—
220C22×#41C2314yes—
221#554—44no—
222#554—48no—
223#553—48no—
224#550—44no—
225#550—48no—
226#547—416no—
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2311yescharacteristic
230C2×#127C2312yes—
231C2×#127C2311yescharacteristic
232C2×#127C2314yes—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#125C2312yes—
236C2×#125C2312yes—
237C2×#125C2314yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2312yes—
241C2×#124C2312yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×#121C2314yes—
261C2×#121C2312yes—
262C2×#121C2312yes—
263C2×#121C2314yes—
264C2×#121C2312yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2314yes—
288C2×#117C2312yes—
289C2×#117C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2314yes—
293C22×C4⋊C4C2314yes—
294C22×C4⋊C4C2314yes—
295#401C2314yes—
296#400C2312yes—
297#400C2312yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2312yes—
304#400C2314yes—
305#400C2312yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#399C2314yes—
314#399C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#398C2312yes—
322#398C2312yes—
323#398C2314yes—
324#398C2312yes—
325#398C2314yes—
326#398C2314yes—
327#398C2312yes—
328#398C2314yes—
329#398C2314yes—
330#398C2312yes—
331#398C2314yes—
332#398C2314yes—
333#398C2312yes—
334#398C2312yes—
335#398C2314yes—
336#398C2312yes—
337#398C2312yes—
338#398C2314yes—
339#398C2312yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
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#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#395C2312yes—
368#395C2312yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#394C2314yes—
374#394C2312yes—
375#394C2312yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2312yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2312yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2312yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2312yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#392C2314yes—
412#392C2314yes—
413#392C2314yes—
414#392C2314yes—
415#392C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#391C2311yescharacteristic
425#391C2311yescharacteristic
426#391C2312yes—
427#391C2314yes—
428#391C2312yes—
429#391C2314yes—
430#391C2312yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#390C2312yes—
435#390C2312yes—
436#390C2314yes—
437#390C2314yes—
438#390C2312yes—
439#390C2314yes—
440#390C2314yes—
441#390C2312yes—
442#390C2312yes—
443#390C2314yes—
444#390C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2312yes—
455#389C2314yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
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#388C2314yes—
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#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
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#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#384C2314yes—
578#383C2312yes—
579#382C2312yes—
580#382C2312yes—
581#382C2312yes—
582#382C2314yes—
583#382C2314yes—
584#382C2312yes—
585#382C2312yes—
586#382C2312yes—
587#381C2312yes—
588#381C2314yes—
589#381C2314yes—
590#381C2314yes—
591#381C2314yes—
592#381C2314yes—
593#381C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2312yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2311yescharacteristic
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2312yes—
616#376C2312yes—
617C2×#95C2312yes—
618C2×#95C2314yes—
619C43C2311yescharacteristic
620C2×#41—28no—
621C2×#41—44no—
622C2×#41—48no—
623C2×#41—48no—
624C2×#41—82no—
625C2×#41—84no—
626C22×Q8C2411yescharacteristic
627C22×Q8C2412yes—
628C22×Q8C2412yes—
629C22×Q8C2411yescharacteristic
630C22×Q8C2411yescharacteristic
631C22×Q8C2411yescharacteristic
632C22×D4C2414yes—
633C22×D4C2412yes—
634C22×D4C2414yes—
635C22×D4C2414yes—
636C22×D4C2412yes—
637C22×D4C2414yes—
638C22×D4C2412yes—
639C22×D4C2414yes—
640C22×D4C2412yes—
641C22×D4C2414yes—
642C22×D4C2412yes—
643C22×D4C2414yes—
644C22×D4C2412yes—
645C22×D4C2414yes—
646C22×D4C2411yescharacteristic
647C23×C4C2412yes—
648C23×C4C2414yes—
649C23×C4C2412yes—
650C23×C4C2412yes—
651C23×C4C2414yes—
652C23×C4C2414yes—
653C23×C4C2414yes—
654C23×C4C2414yes—
655C23×C4C2414yes—
656C23×C4C2414yes—
657C23×C4C2414yes—
658C4⋊Q8—28no—
659C4⋊Q8—24no—
660C4⋊Q8—42no—
661#127—28no—
662#127—42no—
663#127—48no—
664#126—48no—
665#126—84no—
666#125—44no—
667#125—44no—
668#125—48no—
669#124—44no—
670#124—44no—
671#124—44no—
672#124—82no—
673#123—48no—
674#123—48no—
675#123—48no—
676#123—48no—
677#123—48no—
678#123—48no—
679#123—48no—
680#123—48no—
681#123—84no—
682#123—84no—
683C22⋊Q8—216no—
684C22⋊Q8—44no—
685C22⋊Q8—44no—
686C22⋊Q8—44no—
687C22⋊Q8—48no—
688C22⋊Q8—48no—
689C22⋊Q8—48no—
690C22⋊Q8—48no—
691#121—216no—
692#121—48no—
693#121—48no—
694#121—48no—
695#121—48no—
696#121—48no—
697#121—48no—
698#121—44no—
699#121—44no—
700#121—44no—
701C4×Q8—42no—
702C4×Q8—42no—
703C4×Q8—44no—
704C4×Q8—44no—
705C4×D4—24no—
706C4×D4—28no—
707C4×D4—44no—
708C4×D4—44no—
709C4×D4—44no—
710C4×D4—48no—
711C4×D4—44no—
712C4×D4—48no—
713C4×D4—48no—
714C4×D4—48no—
715C4×D4—48no—
716C4×D4—48no—
717C4×D4—84no—
718C4×D4—84no—
719#117—44no—
720#117—82no—
721C2×C4⋊C4—48no—
722C2×C4⋊C4—48no—
723C2×C4⋊C4—48no—
724C2×C4⋊C4—44no—
725C2×C4⋊C4—44no—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C42C2412yes—
824C2×C42C2412yes—
825C2×C42C2411yescharacteristic
826C2×C42C2412yes—
827C2×C42C2411yescharacteristic
828C2×C42C2412yes—
829C2×C42C2411yescharacteristic
830C2×C42C2414yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2414yes—
836C2×C42C2414yes—
837C2×C42C2412yes—
838C2×C42C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2412yes—
842#95C2414yes—
843#95C2412yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2412yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2412yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2412yes—
870#95C2412yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2412yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889C24C2514yes—
890C24C2514yes—
891C24C2512yes—
892#41—816no—
893#41—832no—
894C2×Q8—24no—
895C2×Q8—22no—
896C2×Q8—24no—
897C2×Q8—41no—
898C2×Q8—42no—
899C2×Q8—41no—
900C2×Q8—42no—
901C2×Q8—42no—
902C2×Q8—41no—
903C2×Q8—41no—
904C2×Q8—42no—
905C2×Q8—41no—
906C2×Q8—41no—
907C2×Q8—42no—
908C2×Q8—42no—
909C2×Q8H(5,𝔽2)14yes—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—28no—
915C2×D4—24no—
916C2×D4—24no—
917C2×D4—24no—
918C2×D4—42no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—42no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4—44no—
938C2×D4—44no—
939C2×D4—42no—
940C2×D4—44no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—42no—
945C2×D4—44no—
946C2×D4—42no—
947C2×D4—42no—
948C2×D4—44no—
949C2×D4—44no—
950C2×D4H(5,𝔽2)14yes—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—28no—
955C22×C4—24no—
956C22×C4—28no—
957C22×C4—28no—
958C22×C4—28no—
959C22×C4—42no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4C2514yes—
983C22×C4C2511yescharacteristic
984C22×C4C2514yes—
985C22×C4C2514yes—
986C22×C4C2512yes—
987C22×C4C2514yes—
988C22×C4C2514yes—
989C22×C4C2512yes—
990C22×C4C2512yes—
991C22×C4C2514yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C22×C4C2514yes—
995C22×C4C2514yes—
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2511yescharacteristic
999C22×C4C2512yes—
1000C22×C4C2511yescharacteristic
1001C22×C4C2512yes—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—22no—
1008C4⋊C4—24no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—44no—
1014C4⋊C4—42no—
1015C4⋊C4—41no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—44no—
1023C4⋊C4—42no—
1024C4⋊C4—44no—
1025C4⋊C4—42no—
1026C4⋊C4—44no—
1027C4⋊C4—42no—
1028C4⋊C4—44no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—44no—
1032C4⋊C4—42no—
1033C4⋊C4—44no—
1034C4⋊C4—42no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—41no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C22⋊C4—28no—
1053C22⋊C4—24no—
1054C22⋊C4—24no—
1055C22⋊C4—24no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C42—24no—
1100C42—22no—
1101C42—24no—
1102C42—24no—
1103C42—22no—
1104C42—24no—
1105C42—42no—
1106C42—44no—
1107C42—44no—
1108C42—41no—
1109C42—42no—
1110C42—44no—
1111C42—44no—
1112C42—44no—
1113C42—42no—
1114C42—44no—
1115C23—22no—
1116C23—24no—
1117C23—22no—
1118C23—24no—
1119C23—24no—
1120C23—24no—
1121C23—24no—
1122C23—24no—
1123C23—24no—
1124C23—24no—
1125C23—24no—
1126C23—24no—
1127C23—24no—
1128C23—24no—
1129C23—24no—
1130C23—24no—
1131C23—24no—
1132C23—24no—
1133C23C2×H(5,𝔽2)14yes—
1134C23C2611yescharacteristic
1135Q8—44no—
1136Q8—48no—
1137Q8—82no—
1138Q8—84no—
1139Q8—161no—
1140Q8—161no—
1141D4—44no—
1142D4—416no—
1143D4—48no—
1144D4—416no—
1145D4—84no—
1146D4—84no—
1147D4—88no—
1148D4—88no—
1149D4—88no—
1150D4—84no—
1151D4—84no—
1152D4—88no—
1153D4—88no—
1154D4—162no—
1155D4—164no—
1156C2×C4—22no—
1157C2×C4—21no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—21no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—48no—
1207C2×C4—88no—
1208C2×C4—88no—
1209C2×C4—88no—
1210C2×C4—84no—
1211C2×C4—84no—
1212C2×C4—88no—
1213C2×C4—88no—
1214C2×C4—88no—
1215C2×C4—88no—
1216C2×C4—164no—
1217C2×C4C2×H(5,𝔽2)12yes—
1218C2×C4C2×H(5,𝔽2)12yes—
1219C2×C4C2×H(5,𝔽2)14yes—
1220C2×C4#58514yes—
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22C22×H(5,𝔽2)11yescharacteristic
1241C22C22×H(5,𝔽2)11yescharacteristic
1242C22C2×#58512yes—
1243C22H(7,𝔽2)11yescharacteristic
1244C222−1+612yes—
1245C4—22no—
1246C4—22no—
1247C4—24no—
1248C4—24no—
1249C4—42no—
1250C4—42no—
1251C4—42no—
1252C4—42no—
1253C4—41no—
1254C4—42no—
1255C4—44no—
1256C4—44no—
1257C4—44no—
1258C4—42no—
1259C4—44no—
1260C4—44no—
1261C4—42no—
1262C4—44no—
1263C4—44no—
1264C4—44no—
1265C2—44no—
1266C2—84no—
1267C2—84no—
1268C2#6287111yescharacteristic
1269C2#6289211yescharacteristic
1270C2#6289712yes—
1271C2#6302111yescharacteristic
1272C2#6304712yes—
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. #59660C2semidirect
2. #56477C2semidirect
3. #54961C2semidirect
4. #54909C2semidirect
5. #54851C2semidirect
6. #53861C2semidirect
7. #52327C2semidirect
8. #48327C2semidirect
9. #48317C2semidirect
10. #47179C2semidirect
11. #46969C2semidirect
12. #46766C2semidirect
13. #46017C2semidirect
14. #45387C2semidirect
15. #43289C2semidirect
16. #43119C2semidirect
17. #43117C2semidirect
18. #42166C2semidirect
19. #41406C2semidirect
20. #41107C2semidirect
21. #38952C2semidirect
22. #38810C2semidirect
23. #37266C2semidirect

Maximal subgroups

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

subgroupindex
#596602
#564772
#549612
#549092
#548512
#538612
#523272
#483272
#483172
#471792
#469692
#467662
#460172
#453872
#432892
#431192
#431172
#421662
#414062
#411072
#389522
#388102
#372662