Finite Group Databasebeta

← #8095545

Subgroups — #8095545

Order 512.

4599 conjugacy classes of subgroups.

The subgroup lattice has 1391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53154C211yesmaximal, characteristic, complemented
2#53128C212yesmaximal, complemented
3#53125C211yesmaximal, characteristic, complemented
4#53074C211yesmaximal, characteristic, complemented
5#52985C211yesmaximal, characteristic, complemented
6#52984C212yesmaximal, complemented
7#52691C214yesmaximal, complemented
8#52656C214yesmaximal, complemented
9#52539C214yesmaximal, complemented
10#52536C214yesmaximal, complemented
11#46103C214yesmaximal, complemented
12#46069C212yesmaximal, complemented
13#46036C214yesmaximal, complemented
14#46010C212yesmaximal, complemented
15#45937C214yesmaximal, complemented
16#45865C214yesmaximal, complemented
17#45602C212yesmaximal, complemented
18#45522C212yesmaximal, complemented
19#35623C212yesmaximal, complemented
20#35601C212yesmaximal, complemented
21#35539C212yesmaximal, complemented
22#35323C211yesmaximal, characteristic, complemented
23#35278C211yesmaximal, characteristic, complemented
24#35215C212yesmaximal, complemented
25#35169C212yesmaximal, complemented
26#34918C212yesmaximal, complemented
27#34881C211yesmaximal, characteristic, complemented
28C2×#542C2212yes—
29C2×#540C2211yescharacteristic
30C2×#540C2211yescharacteristic
31C2×#520C2212yes—
32#2867C2211yescharacteristic
33#2863C2212yes—
34#2859C2211yescharacteristic
35#2857C2211yescharacteristic
36#2856C2212yes—
37#2854C2214yes—
38#2854C2214yes—
39#2852C2214yes—
40#2851C2211yescharacteristic
41#2850C2214yes—
42#2839C2214yes—
43#2837C2214yes—
44#2837C2214yes—
45#2832C2214yes—
46#2832C2214yes—
47#2830C2214yes—
48#2828C2214yes—
49#2828C2214yes—
50#2827C2214yes—
51#2827C2214yes—
52#2827C2214yes—
53#2826C2214yes—
54#2826C2214yes—
55#2824C2214yes—
56#2824C2214yes—
57#2824C2214yes—
58#2818C2214yes—
59#2815C2214yes—
60#2814C2214yes—
61#2813C2214yes—
62#2803C2214yes—
63#2796C2214yes—
64#2782C2214yes—
65#2780C2214yes—
66#2779C2214yes—
67#2774C2214yes—
68#2771C2214yes—
69#2769C2214yes—
70#2758C2214yes—
71#2753C2214yes—
72#2750C2214yes—
73#2749C2214yes—
74#2749C2214yes—
75#2743C2214yes—
76#2740C2214yes—
77#2738C2214yes—
78#2730C2214yes—
79#2710C2214yes—
80#2709C2214yes—
81#2709C2214yes—
82#2709C2214yes—
83#2708C2214yes—
84#2708C2214yes—
85#2705C2214yes—
86#2703C2214yes—
87#2702C2214yes—
88#2699C2214yes—
89#2696C2214yes—
90#2695C2214yes—
91#2691C2214yes—
92#2689C2214yes—
93#2688C2214yes—
94#2687C2214yes—
95#2686C2214yes—
96#2676C2214yes—
97#2673C2214yes—
98#2673C2214yes—
99#2673C2214yes—
100#2671C2214yes—
101#2671C2214yes—
102#2663C2214yes—
103#2661C2214yes—
104#2649C2214yes—
105#2648C2214yes—
106#2647C2211yescharacteristic
107#2642C2211yescharacteristic
108#2641C2211yescharacteristic
109#2641C2211yescharacteristic
110#2625C2212yes—
111#2619C2212yes—
112#2610C2214yes—
113#2603C2214yes—
114#2602C2214yes—
115#2601C2214yes—
116#2597C2214yes—
117#2595C2214yes—
118#2593C2212yes—
119#2592C2212yes—
120#2591C2214yes—
121#2590C2214yes—
122#2585C2212yes—
123#2580C2212yes—
124#2578C2214yes—
125#2577C2214yes—
126#2573C2212yes—
127#2570C2212yes—
128#2568C2212yes—
129#2563C2212yes—
130#2559C2214yes—
131#2559C2214yes—
132#2557C2214yes—
133#2555C2214yes—
134#2554C2212yes—
135#2553C2214yes—
136#2550C2212yes—
137#2545C2212yes—
138#2544C2212yes—
139#2544C2212yes—
140#2544C2212yes—
141#2540C2214yes—
142#2540C2212yes—
143#2535C2212yes—
144#2533C2214yes—
145#2530C2214yes—
146#2525C2212yes—
147#2516C2214yes—
148#2516C2212yes—
149#2513C2212yes—
150#2512C2212yes—
151#2511C2212yes—
152#2509C2212yes—
153#2504C2212yes—
154#2503C2212yes—
155#2495C2212yes—
156#2491C2212yes—
157#2490C2212yes—
158#2489C2212yes—
159#2481C2214yes—
160#2481C2214yes—
161#2477C2214yes—
162#2477C2214yes—
163#2476C2214yes—
164#2471C2214yes—
165#2470C2214yes—
166#2470C2214yes—
167#2469C2212yes—
168#2464C2214yes—
169#2463C2214yes—
170#2459C2214yes—
171#2459C2214yes—
172#2458C2212yes—
173#2458C2214yes—
174#2457C2214yes—
175#2457C2214yes—
176#2457C2214yes—
177#2456C2214yes—
178#2454C2212yes—
179#2453C2212yes—
180#2452C2212yes—
181#2449C2214yes—
182#2448C2212yes—
183#2447C2212yes—
184#2445C2212yes—
185#2445C2214yes—
186#2445C2212yes—
187#2445C2214yes—
188#2445C2212yes—
189#2443C2214yes—
190#2442C2212yes—
191#2440C2212yes—
192#2432C2212yes—
193#2431C2212yes—
194#2431C2212yes—
195#2431C2212yes—
196#2428C2212yes—
197#2428C2214yes—
198#2428C2212yes—
199#2428C2212yes—
200#2428C2214yes—
201#2427C2212yes—
202#2426C2212yes—
203#2423C2212yes—
204#2422C2212yes—
205#2420C2212yes—
206#2416C2212yes—
207#2416C2212yes—
208#2414C2214yes—
209#2413C2214yes—
210#2407C2212yes—
211#2407C2212yes—
212#2402C2211yescharacteristic
213#2398C2211yescharacteristic
214#2398C2214yes—
215#2396C2211yescharacteristic
216#2395C2214yes—
217#2392C2211yescharacteristic
218#2380C2214yes—
219#2378C2214yes—
220#2377C2214yes—
221#2377C2214yes—
222#2330C2211yescharacteristic
223#2328C2212yes—
224#2327C2211yescharacteristic
225#2324C2212yes—
226#2324C2212yes—
227#2323C2212yes—
228C4×#127C2212yes—
229C4×#126C2212yes—
230C4×#124C2212yes—
231C4×#124C2212yes—
232C4×#123C2214yes—
233C4×#123C2212yes—
234#2298C2212yes—
235#2295C2212yes—
236#2293C2212yes—
237#2293C2212yes—
238#2293C2211yescharacteristic
239#2290C2214yes—
240C42×Q8C2211yescharacteristic
241C42×D4C2212yes—
242C4×#117C2211yescharacteristic
243C22×#41C2312yes—
244#542—48no—
245#540—44no—
246#540—44no—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2311yescharacteristic
249C2×#127C2312yes—
250C2×#127C2314yes—
251C2×#127C2312yes—
252C2×#127C2311yescharacteristic
253C2×#127C2311yescharacteristic
254C2×#127C2314yes—
255C2×#126C2312yes—
256C2×#126C2314yes—
257C2×#126C2314yes—
258C2×#125C2311yescharacteristic
259C2×#125C2311yescharacteristic
260C2×#125C2311yescharacteristic
261C2×#124C2312yes—
262C2×#124C2314yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2312yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2314yes—
279C2×#121C2312yes—
280C2×#121C2312yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#121C2312yes—
284C2×#121C2312yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2312yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×#121C2314yes—
291C2×#121C2314yes—
292C2×#121C2314yes—
293#520—48no—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2314yes—
309C2×#117C2311yescharacteristic
310C2×#117C2312yes—
311C2×#117C2314yes—
312C2×#117C2311yescharacteristic
313C2×#117C2314yes—
314C22×C4⋊C4C2314yes—
315C22×C4⋊C4C2312yes—
316C22×C42C2311yescharacteristic
317C22×C42C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2312yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2312yes—
336#400C2314yes—
337#400C2314yes—
338#400C2311yescharacteristic
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2311yescharacteristic
344#399C2314yes—
345#398C2314yes—
346#398C2311yescharacteristic
347#398C2312yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2312yes—
353#398C2312yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2311yescharacteristic
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2312yes—
377#396C2312yes—
378#396C2312yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#395C2314yes—
388#395C2311yescharacteristic
389#395C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2312yes—
416#394C2312yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2311yescharacteristic
424#394C2314yes—
425#394C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2311yescharacteristic
429#393C2312yes—
430#393C2314yes—
431#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#392C2314yes—
435#392C2314yes—
436#392C2314yes—
437#392C2314yes—
438#392C2314yes—
439#392C2314yes—
440#392C2314yes—
441#392C2314yes—
442#392C2314yes—
443#392C2314yes—
444#392C2314yes—
445#392C2314yes—
446#392C2314yes—
447#392C2314yes—
448#392C2311yescharacteristic
449#392C2314yes—
450#391C2314yes—
451#391C2312yes—
452#391C2312yes—
453#391C2314yes—
454#391C2314yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2314yes—
462#390C2314yes—
463#390C2312yes—
464#390C2312yes—
465#390C2314yes—
466#390C2314yes—
467#390C2314yes—
468#390C2314yes—
469#390C2314yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2312yes—
476#390C2314yes—
477#390C2314yes—
478#390C2314yes—
479#390C2312yes—
480#390C2312yes—
481#390C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2312yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#388C2312yes—
502#388C2312yes—
503#388C2312yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2312yes—
509#388C2312yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2312yes—
523#388C2312yes—
524#388C2312yes—
525#388C2312yes—
526#388C2312yes—
527#388C2312yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2312yes—
535#388C2312yes—
536#388C2314yes—
537#388C2314yes—
538#388C2312yes—
539#388C2314yes—
540#388C2312yes—
541#387C2312yes—
542#387C2312yes—
543#387C2312yes—
544#387C2314yes—
545#387C2314yes—
546#387C2312yes—
547#387C2312yes—
548#387C2312yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2312yes—
558#387C2312yes—
559#387C2312yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
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#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2312yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2312yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#384C2312yes—
619#384C2311yescharacteristic
620#383C2312yes—
621#383C2314yes—
622#383C2314yes—
623#382C2311yescharacteristic
624#382C2312yes—
625#382C2312yes—
626#382C2312yes—
627#382C2314yes—
628#381C2312yes—
629#381C2314yes—
630#381C2314yes—
631#381C2314yes—
632#381C2314yes—
633#380C2314yes—
634#380C2314yes—
635#380C2314yes—
636#380C2314yes—
637#380C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2314yes—
641#380C2314yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2311yescharacteristic
654C4×C4⋊C4C2311yescharacteristic
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2312yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2314yes—
672#376C2311yescharacteristic
673#376C2314yes—
674#376C2311yescharacteristic
675C43C2311yescharacteristic
676C43C2311yescharacteristic
677C43C2312yes—
678C2×#41—44no—
679C2×#41—44no—
680C2×#41—44no—
681C22×Q8C2412yes—
682C22×Q8C2411yescharacteristic
683C22×Q8C2414yes—
684C22×D4C2412yes—
685C22×D4C2412yes—
686C22×D4C2414yes—
687C22×D4C2414yes—
688C22×D4C2414yes—
689C22×D4C2411yescharacteristic
690C22×D4C2412yes—
691C22×D4C2414yes—
692C22×D4C2414yes—
693C22×D4C2414yes—
694C22×D4C2414yes—
695C22×D4C2414yes—
696C22×D4C2414yes—
697C22×D4C2414yes—
698C22×D4C2414yes—
699C22×D4C2414yes—
700C23×C4C2412yes—
701C23×C4C2411yescharacteristic
702C23×C4C2414yes—
703C23×C4C2414yes—
704C23×C4C2412yes—
705C23×C4C2414yes—
706C23×C4C2414yes—
707C23×C4C2414yes—
708C23×C4C2414yes—
709C23×C4C2414yes—
710C4⋊Q8—44no—
711C4⋊Q8—42no—
712#127—44no—
713#127—44no—
714#127—48no—
715#127—42no—
716#127—42no—
717#127—84no—
718#126—44no—
719#126—48no—
720#126—84no—
721#125—42no—
722#125—42no—
723#125—42no—
724#124—48no—
725#124—44no—
726#124—44no—
727#124—44no—
728#124—84no—
729#123—44no—
730#123—48no—
731#123—48no—
732#123—48no—
733#123—48no—
734#123—84no—
735#123—84no—
736#123—84no—
737C22⋊Q8—48no—
738C22⋊Q8—48no—
739C22⋊Q8—44no—
740C22⋊Q8—44no—
741C22⋊Q8—84no—
742#121—48no—
743#121—48no—
744#121—48no—
745#121—44no—
746#121—48no—
747#121—44no—
748#121—44no—
749#121—44no—
750#121—44no—
751#121—84no—
752#121—84no—
753#121—84no—
754#121—84no—
755#121—84no—
756C4×Q8—28no—
757C4×Q8—42no—
758C4×Q8—44no—
759C4×Q8—44no—
760C4×D4—28no—
761C4×D4—28no—
762C4×D4—48no—
763C4×D4—48no—
764C4×D4—44no—
765C4×D4—44no—
766C4×D4—44no—
767C4×D4—42no—
768C4×D4—44no—
769C4×D4—48no—
770C4×D4—84no—
771#117—28no—
772#117—24no—
773#117—42no—
774#117—48no—
775#117—84no—
776C2×C4⋊C4—48no—
777C2×C4⋊C4—44no—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2411yescharacteristic
834C2×C22⋊C4C2411yescharacteristic
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C42—42no—
883C2×C42—84no—
884C2×C42C2414yes—
885C2×C42C2412yes—
886C2×C42C2411yescharacteristic
887C2×C42C2411yescharacteristic
888C2×C42C2411yescharacteristic
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2411yescharacteristic
893C2×C42C2412yes—
894C2×C42C2411yescharacteristic
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2411yescharacteristic
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2412yes—
926#95C2414yes—
927#95C2412yes—
928#95C2412yes—
929#95C2414yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2414yes—
934#95C2414yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2411yescharacteristic
939#95C2412yes—
940#95C2412yes—
941#95C2411yescharacteristic
942#95C2412yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2411yescharacteristic
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2411yescharacteristic
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966C24C2512yes—
967C24C2511yescharacteristic
968C24C2514yes—
969C24C2514yes—
970#41—432no—
971C2×Q8—24no—
972C2×Q8—24no—
973C2×Q8—24no—
974C2×Q8—41no—
975C2×Q8—42no—
976C2×Q8—44no—
977C2×Q8—44no—
978C2×Q8—44no—
979C2×D4—24no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—28no—
986C2×D4—28no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—42no—
991C2×D4—41no—
992C2×D4—44no—
993C2×D4—42no—
994C2×D4—42no—
995C2×D4—44no—
996C2×D4—42no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C22×C4—24no—
1027C22×C4—22no—
1028C22×C4—22no—
1029C22×C4—22no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—28no—
1033C22×C4—28no—
1034C22×C4—24no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—42no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—42no—
1048C22×C4—44no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4C2511yescharacteristic
1057C22×C4C2511yescharacteristic
1058C22×C4C2512yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2514yes—
1064C22×C4C2514yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2514yes—
1072C22×C4C2512yes—
1073C22×C4C2511yescharacteristic
1074C22×C4C2511yescharacteristic
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—28no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—28no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—28no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—41no—
1095C4⋊C4—41no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—42no—
1099C4⋊C4—41no—
1100C4⋊C4—44no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—41no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C22⋊C4—24no—
1125C22⋊C4—24no—
1126C22⋊C4—24no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—24no—
1130C22⋊C4—24no—
1131C22⋊C4—41no—
1132C22⋊C4—41no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—42no—
1141C22⋊C4—42no—
1142C22⋊C4—42no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—42no—
1154C22⋊C4—42no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—42no—
1170C22⋊C4—42no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—42no—
1181C22⋊C4—42no—
1182C22⋊C4—42no—
1183C42—24no—
1184C42—22no—
1185C42—28no—
1186C42—22no—
1187C42—22no—
1188C42—22no—
1189C42—22no—
1190C42—24no—
1191C42—24no—
1192C42—24no—
1193C42—24no—
1194C42—42no—
1195C42—42no—
1196C42—44no—
1197C42—44no—
1198C42—44no—
1199C42—44no—
1200C42—42no—
1201C42—42no—
1202C42—42no—
1203C42—42no—
1204C42—42no—
1205C42H(5,𝔽2)14yes—
1206C23—22no—
1207C23—21no—
1208C23—24no—
1209C23—24no—
1210C23—22no—
1211C23—22no—
1212C23—21no—
1213C23—24no—
1214C23—24no—
1215C23—21no—
1216C23—24no—
1217C23—24no—
1218C23—24no—
1219C23—24no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—24no—
1224C23—24no—
1225C23—24no—
1226C23—22no—
1227C23—24no—
1228C23—24no—
1229C23—22no—
1230C23—24no—
1231C23—22no—
1232C23C2611yescharacteristic
1233Q8—44no—
1234Q8—48no—
1235Q8—164no—
1236D4—416no—
1237D4—48no—
1238D4—48no—
1239D4—88no—
1240D4—88no—
1241D4—82no—
1242D4—84no—
1243D4—164no—
1244D4—164no—
1245D4—164no—
1246D4—164no—
1247D4—164no—
1248D4—164no—
1249D4—164no—
1250D4—164no—
1251D4—164no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—21no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—21no—
1271C2×C4—22no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—22no—
1275C2×C4—21no—
1276C2×C4—22no—
1277C2×C4—21no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—21no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—416no—
1313C2×C4—44no—
1314C2×C4—48no—
1315C2×C4—84no—
1316C2×C4—88no—
1317C2×C4—88no—
1318C2×C4—88no—
1319C2×C4—88no—
1320C2×C4—164no—
1321C2×C4—164no—
1322C2×C4C2×H(5,𝔽2)14yes—
1323C2×C4C2×H(5,𝔽2)12yes—
1324C2×C4#58514yes—
1325C2×C4#58512yes—
1326C2×C4#58512yes—
1327C22—44no—
1328C22—44no—
1329C22—42no—
1330C22—41no—
1331C22—44no—
1332C22—42no—
1333C22—44no—
1334C22—41no—
1335C22—42no—
1336C22—44no—
1337C22—42no—
1338C22—44no—
1339C22—44no—
1340C22—44no—
1341C22—42no—
1342C22—44no—
1343C22—42no—
1344C22—41no—
1345C22—44no—
1346C22—44no—
1347C22—44no—
1348C22—42no—
1349C22—42no—
1350C22—42no—
1351C22—44no—
1352C22—44no—
1353C22C22×H(5,𝔽2)11yescharacteristic
1354C22C2×#58511yescharacteristic
1355C22C2×#58512yes—
1356C22C2×#58511yescharacteristic
1357C22H(7,𝔽2)12yes—
1358C4—24no—
1359C4—24no—
1360C4—41no—
1361C4—41no—
1362C4—42no—
1363C4—42no—
1364C4—44no—
1365C4—41no—
1366C4—41no—
1367C4—42no—
1368C4—42no—
1369C4—44no—
1370C4—42no—
1371C4—41no—
1372C4—42no—
1373C4—44no—
1374C4—44no—
1375C4—44no—
1376C4—42no—
1377C4—44no—
1378C4—42no—
1379C4—42no—
1380C4#352914yes—
1381C2—84no—
1382C2—84no—
1383C2—82no—
1384C2—81no—
1385C2C2×#352911yescharacteristic
1386C2#6283911yescharacteristic
1387C2#6288311yescharacteristic
1388C2#6294112yes—
1389C2#6296112yes—
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. #53154C2semidirect
2. #53128C2semidirect
3. #53125C2semidirect
4. #53074C2semidirect
5. #52985C2semidirect
6. #52984C2semidirect
7. #52691C2semidirect
8. #52656C2semidirect
9. #52539C2semidirect
10. #52536C2semidirect
11. #46103C2semidirect
12. #46069C2semidirect
13. #46036C2semidirect
14. #46010C2semidirect
15. #45937C2semidirect
16. #45865C2semidirect
17. #45602C2semidirect
18. #45522C2semidirect
19. #35623C2semidirect
20. #35601C2semidirect
21. #35539C2semidirect
22. #35323C2semidirect
23. #35278C2semidirect
24. #35215C2semidirect
25. #35169C2semidirect
26. #34918C2semidirect
27. #34881C2semidirect

Maximal subgroups

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

subgroupindex
#531542
#531282
#531252
#530742
#529852
#529842
#526912
#526562
#525392
#525362
#461032
#460692
#460362
#460102
#459372
#458652
#456022
#455222
#356232
#356012
#355392
#353232
#352782
#352152
#351692
#349182
#348812