Finite Group Databasebeta

← #8095621

Subgroups — #8095621

Order 512.

4607 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#53132C211yesmaximal, characteristic, complemented
3#53105C212yesmaximal, complemented
4#53076C211yesmaximal, characteristic, complemented
5#53074C211yesmaximal, characteristic, complemented
6#53060C212yesmaximal, complemented
7#52683C214yesmaximal, complemented
8#52682C214yesmaximal, complemented
9#52632C214yesmaximal, complemented
10#52622C214yesmaximal, complemented
11#46079C212yesmaximal, complemented
12#46010C212yesmaximal, complemented
13#45722C214yesmaximal, complemented
14#45649C212yesmaximal, complemented
15#45596C214yesmaximal, complemented
16#45546C214yesmaximal, complemented
17#45533C214yesmaximal, complemented
18#45522C212yesmaximal, complemented
19#35570C212yesmaximal, complemented
20#35561C212yesmaximal, complemented
21#35549C212yesmaximal, complemented
22#35323C211yesmaximal, characteristic, complemented
23#35278C211yesmaximal, characteristic, complemented
24#35211C212yesmaximal, complemented
25#35156C212yesmaximal, complemented
26#34879C211yesmaximal, characteristic, complemented
27#34727C212yesmaximal, complemented
28C2×#540C2211yescharacteristic
29C2×#540C2211yescharacteristic
30C2×#529C2212yes—
31C2×C4×#41C2212yes—
32#2867C2211yescharacteristic
33#2863C2212yes—
34#2859C2211yescharacteristic
35#2857C2211yescharacteristic
36#2856C2212yes—
37#2854C2214yes—
38#2853C2214yes—
39#2852C2214yes—
40#2852C2214yes—
41#2851C2211yescharacteristic
42#2837C2214yes—
43#2836C2214yes—
44#2829C2214yes—
45#2829C2214yes—
46#2829C2214yes—
47#2829C2214yes—
48#2829C2214yes—
49#2828C2214yes—
50#2828C2214yes—
51#2827C2214yes—
52#2827C2214yes—
53#2827C2214yes—
54#2825C2214yes—
55#2824C2214yes—
56#2823C2214yes—
57#2818C2214yes—
58#2815C2214yes—
59#2814C2214yes—
60#2813C2214yes—
61#2813C2214yes—
62#2803C2214yes—
63#2797C2214yes—
64#2796C2214yes—
65#2791C2214yes—
66#2786C2214yes—
67#2782C2214yes—
68#2781C2214yes—
69#2780C2214yes—
70#2779C2214yes—
71#2779C2214yes—
72#2777C2214yes—
73#2776C2214yes—
74#2773C2214yes—
75#2766C2214yes—
76#2753C2214yes—
77#2746C2214yes—
78#2743C2214yes—
79#2741C2214yes—
80#2721C2214yes—
81#2718C2214yes—
82#2714C2214yes—
83#2711C2214yes—
84#2711C2214yes—
85#2709C2214yes—
86#2709C2214yes—
87#2709C2214yes—
88#2706C2214yes—
89#2705C2214yes—
90#2703C2214yes—
91#2701C2214yes—
92#2696C2214yes—
93#2695C2214yes—
94#2691C2214yes—
95#2691C2214yes—
96#2682C2214yes—
97#2681C2214yes—
98#2673C2214yes—
99#2673C2214yes—
100#2673C2214yes—
101#2671C2214yes—
102#2647C2211yescharacteristic
103#2642C2211yescharacteristic
104#2641C2211yescharacteristic
105#2641C2211yescharacteristic
106#2635C2214yes—
107#2630C2214yes—
108#2630C2214yes—
109#2630C2214yes—
110#2625C2212yes—
111#2619C2212yes—
112#2609C2214yes—
113#2609C2214yes—
114#2602C2214yes—
115#2600C2214yes—
116#2600C2214yes—
117#2592C2212yes—
118#2590C2214yes—
119#2577C2214yes—
120#2576C2214yes—
121#2574C2212yes—
122#2573C2212yes—
123#2572C2212yes—
124#2566C2212yes—
125#2565C2212yes—
126#2560C2214yes—
127#2559C2214yes—
128#2558C2214yes—
129#2553C2212yes—
130#2553C2214yes—
131#2553C2214yes—
132#2552C2212yes—
133#2552C2212yes—
134#2545C2212yes—
135#2544C2212yes—
136#2544C2212yes—
137#2544C2212yes—
138#2543C2214yes—
139#2540C2212yes—
140#2538C2212yes—
141#2537C2212yes—
142#2533C2214yes—
143#2531C2214yes—
144#2530C2214yes—
145#2526C2214yes—
146#2524C2212yes—
147#2518C2214yes—
148#2515C2212yes—
149#2512C2212yes—
150#2512C2212yes—
151#2511C2212yes—
152#2510C2214yes—
153#2508C2212yes—
154#2500C2212yes—
155#2500C2214yes—
156#2499C2212yes—
157#2498C2214yes—
158#2494C2212yes—
159#2490C2212yes—
160#2490C2212yes—
161#2489C2212yes—
162#2479C2214yes—
163#2476C2214yes—
164#2471C2214yes—
165#2470C2214yes—
166#2468C2212yes—
167#2467C2214yes—
168#2467C2214yes—
169#2466C2214yes—
170#2464C2214yes—
171#2460C2214yes—
172#2457C2214yes—
173#2457C2212yes—
174#2456C2214yes—
175#2456C2214yes—
176#2455C2214yes—
177#2454C2212yes—
178#2454C2212yes—
179#2453C2212yes—
180#2450C2214yes—
181#2448C2212yes—
182#2447C2212yes—
183#2445C2212yes—
184#2445C2212yes—
185#2445C2212yes—
186#2445C2214yes—
187#2445C2214yes—
188#2441C2212yes—
189#2441C2212yes—
190#2432C2212yes—
191#2431C2212yes—
192#2431C2212yes—
193#2431C2212yes—
194#2428C2214yes—
195#2428C2212yes—
196#2428C2212yes—
197#2428C2212yes—
198#2428C2214yes—
199#2427C2212yes—
200#2426C2212yes—
201#2425C2214yes—
202#2423C2212yes—
203#2422C2212yes—
204#2422C2212yes—
205#2422C2214yes—
206#2420C2214yes—
207#2419C2214yes—
208#2414C2212yes—
209#2414C2212yes—
210#2407C2212yes—
211#2407C2212yes—
212#2402C2211yescharacteristic
213#2398C2211yescharacteristic
214#2397C2214yes—
215#2396C2211yescharacteristic
216#2392C2211yescharacteristic
217#2392C2214yes—
218#2382C2214yes—
219#2380C2214yes—
220#2377C2214yes—
221#2376C2214yes—
222#2330C2211yescharacteristic
223#2328C2212yes—
224#2327C2211yescharacteristic
225#2326C2212yes—
226#2326C2212yes—
227#2323C2212yes—
228#2319C2212yes—
229C4×#127C2212yes—
230C4×#126C2212yes—
231C4×#123C2212yes—
232C4×#121C2214yes—
233C4×#121C2212yes—
234C4×#121C2212yes—
235#2295C2211yescharacteristic
236#2295C2212yes—
237#2290C2212yes—
238#2290C2214yes—
239#2283C2212yes—
240#2275C2212yes—
241C42×D4C2211yescharacteristic
242C4×#117C2211yescharacteristic
243C22×#41C2312yes—
244#540—44no—
245#540—44no—
246C2×C4⋊Q8C2311yescharacteristic
247C2×#127C2312yes—
248C2×#127C2314yes—
249C2×#127C2312yes—
250C2×#127C2311yescharacteristic
251C2×#127C2311yescharacteristic
252C2×#127C2314yes—
253#529—48no—
254C2×#126C2312yes—
255C2×#126C2314yes—
256C2×#126C2314yes—
257C2×#126C2314yes—
258C2×#125C2312yes—
259C2×#125C2311yescharacteristic
260C2×#125C2311yescharacteristic
261C2×#125C2311yescharacteristic
262C2×#125C2314yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2312yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2312yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C2×#121C2314yes—
279C2×#121C2312yes—
280C2×#121C2312yes—
281C2×#121C2314yes—
282C2×#121C2312yes—
283C2×#121C2312yes—
284C2×#121C2312yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×#121C2314yes—
291C4×#41—48no—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2311yescharacteristic
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2314yes—
310C2×#117C2311yescharacteristic
311C2×#117C2314yes—
312C2×#117C2314yes—
313C2×#117C2311yescharacteristic
314C2×#117C2312yes—
315C22×C42C2312yes—
316C22×C42C2311yescharacteristic
317C22×C42C2314yes—
318#401C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2312yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2312yes—
327#400C2314yes—
328#400C2311yescharacteristic
329#400C2314yes—
330#400C2312yes—
331#400C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2311yescharacteristic
336#399C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2312yes—
344#398C2314yes—
345#398C2314yes—
346#398C2312yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2312yes—
353#398C2314yes—
354#398C2311yescharacteristic
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2312yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2311yescharacteristic
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2312yes—
384#396C2314yes—
385#396C2312yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#395C2311yescharacteristic
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#394C2312yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2311yescharacteristic
409#394C2312yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#393C2314yes—
431#393C2312yes—
432#393C2311yescharacteristic
433#392C2314yes—
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#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#390C2314yes—
458#390C2312yes—
459#390C2312yes—
460#390C2314yes—
461#390C2312yes—
462#390C2312yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2314yes—
467#390C2314yes—
468#390C2314yes—
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2314yes—
474#390C2314yes—
475#390C2314yes—
476#390C2312yes—
477#390C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2314yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#388C2312yes—
498#388C2312yes—
499#388C2312yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
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#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2312yes—
532#387C2312yes—
533#387C2312yes—
534#387C2312yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2312yes—
539#387C2312yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2312yes—
545#387C2312yes—
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#387C2312yes—
560#387C2314yes—
561#387C2314yes—
562#387C2312yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2312yes—
572#386C2312yes—
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#386C2312yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2312yes—
601#385C2312yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2312yes—
612#384C2312yes—
613#384C2312yes—
614#384C2312yes—
615#384C2314yes—
616#384C2311yescharacteristic
617#383C2312yes—
618#383C2314yes—
619#383C2312yes—
620#383C2312yes—
621#382C2312yes—
622#382C2311yescharacteristic
623#382C2312yes—
624#382C2312yes—
625#382C2314yes—
626#382C2314yes—
627#381C2312yes—
628#381C2312yes—
629#381C2312yes—
630#381C2314yes—
631#381C2314yes—
632#380C2312yes—
633#380C2314yes—
634#380C2314yes—
635#380C2312yes—
636#380C2312yes—
637#380C2314yes—
638#380C2314yes—
639#380C2312yes—
640#380C2312yes—
641#380C2314yes—
642#380C2314yes—
643#380C2314yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2311yescharacteristic
653C4×C4⋊C4C2311yescharacteristic
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2314yes—
671#376C2312yes—
672#376C2311yescharacteristic
673#376C2311yescharacteristic
674#376C2314yes—
675C2×#95C2314yes—
676C43C2311yescharacteristic
677C43C2311yescharacteristic
678C2×#41—44no—
679C2×#41—44no—
680C2×#41—44no—
681C22×Q8C2412yes—
682C22×Q8C2411yescharacteristic
683C22×D4C2412yes—
684C22×D4C2412yes—
685C22×D4C2414yes—
686C22×D4C2414yes—
687C22×D4C2411yescharacteristic
688C22×D4C2414yes—
689C22×D4C2414yes—
690C22×D4C2414yes—
691C22×D4C2414yes—
692C22×D4C2412yes—
693C22×D4C2414yes—
694C22×D4C2414yes—
695C22×D4C2414yes—
696C22×D4C2414yes—
697C22×D4C2414yes—
698C22×D4C2414yes—
699C23×C4C2411yescharacteristic
700C23×C4C2412yes—
701C23×C4C2414yes—
702C23×C4C2412yes—
703C23×C4C2414yes—
704C23×C4C2412yes—
705C23×C4C2412yes—
706C23×C4C2414yes—
707C23×C4C2414yes—
708C23×C4C2414yes—
709C23×C4C2414yes—
710C4⋊Q8—42no—
711#127—44no—
712#127—44no—
713#127—48no—
714#127—42no—
715#127—42no—
716#127—84no—
717#126—44no—
718#126—48no—
719#126—84no—
720#126—84no—
721#125—42no—
722#125—44no—
723#125—42no—
724#125—42no—
725#125—48no—
726#124—44no—
727#124—44no—
728#124—44no—
729#123—44no—
730#123—48no—
731#123—48no—
732#123—48no—
733#123—48no—
734#123—84no—
735#123—84no—
736#123—84no—
737#123—84no—
738C22⋊Q8—44no—
739C22⋊Q8—44no—
740C22⋊Q8—84no—
741#121—48no—
742#121—48no—
743#121—48no—
744#121—44no—
745#121—44no—
746#121—48no—
747#121—44no—
748#121—44no—
749#121—44no—
750#121—84no—
751#121—84no—
752#121—84no—
753#121—84no—
754C4×Q8—28no—
755C4×Q8—42no—
756C4×Q8—44no—
757C4×D4—28no—
758C4×D4—28no—
759C4×D4—44no—
760C4×D4—48no—
761C4×D4—44no—
762C4×D4—44no—
763C4×D4—44no—
764C4×D4—42no—
765C4×D4—44no—
766C4×D4—48no—
767C4×D4—48no—
768C4×D4—48no—
769C4×D4—84no—
770C4×D4—84no—
771C4×D4—84no—
772#117—24no—
773#117—42no—
774#117—48no—
775#117—48no—
776#117—44no—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2411yescharacteristic
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⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C42—28no—
883C2×C42—48no—
884C2×C42—42no—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2411yescharacteristic
888C2×C42C2411yescharacteristic
889C2×C42C2411yescharacteristic
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2411yescharacteristic
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2411yescharacteristic
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2411yescharacteristic
907#95C2412yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2412yes—
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2411yescharacteristic
923#95C2412yes—
924#95C2412yes—
925#95C2411yescharacteristic
926#95C2414yes—
927#95C2412yes—
928#95C2414yes—
929#95C2414yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2414yes—
938#95C2412yes—
939#95C2414yes—
940#95C2411yescharacteristic
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2412yes—
949#95C2411yescharacteristic
950#95C2414yes—
951#95C2414yes—
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—
966C24C2511yescharacteristic
967C24C2514yes—
968C24C2514yes—
969C24C2512yes—
970#41—432no—
971C2×Q8—24no—
972C2×Q8—24no—
973C2×Q8—24no—
974C2×Q8—41no—
975C2×Q8—42no—
976C2×D4—24no—
977C2×D4—24no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—28no—
983C2×D4—28no—
984C2×D4—44no—
985C2×D4—42no—
986C2×D4—41no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—42no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—42no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—42no—
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—
1023C22×C4—24no—
1024C22×C4—22no—
1025C22×C4—22no—
1026C22×C4—22no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—28no—
1032C22×C4—28no—
1033C22×C4—24no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—42no—
1039C22×C4—44no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—42no—
1045C22×C4—44no—
1046C22×C4—42no—
1047C22×C4—44no—
1048C22×C4—42no—
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×C4C2512yes—
1060C22×C4C2511yescharacteristic
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2514yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2514yes—
1069C22×C4C2512yes—
1070C22×C4C2511yescharacteristic
1071C22×C4C2511yescharacteristic
1072C22×C4C2514yes—
1073C22×C4C2514yes—
1074C22×C4C2514yes—
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—28no—
1086C4⋊C4—24no—
1087C4⋊C4—28no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—41no—
1091C4⋊C4—41no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—41no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—41no—
1103C4⋊C4—42no—
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—44no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
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—42no—
1138C22⋊C4—42no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—42no—
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—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—42no—
1160C22⋊C4—42no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—42no—
1169C22⋊C4—42no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—42no—
1174C22⋊C4—42no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—42no—
1183C22⋊C4—42no—
1184C42—24no—
1185C42—24no—
1186C42—24no—
1187C42—28no—
1188C42—22no—
1189C42—22no—
1190C42—22no—
1191C42—22no—
1192C42—22no—
1193C42—24no—
1194C42—24no—
1195C42—24no—
1196C42—24no—
1197C42—42no—
1198C42—44no—
1199C42—44no—
1200C42—42no—
1201C42—44no—
1202C42—44no—
1203C42—44no—
1204C42—42no—
1205C42H(5,𝔽2)14yes—
1206C23—21no—
1207C23—24no—
1208C23—24no—
1209C23—22no—
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—22no—
1226C23—24no—
1227C23—24no—
1228C23—24no—
1229C23—22no—
1230C23—22no—
1231C23—24no—
1232C23C2611yescharacteristic
1233Q8—48no—
1234Q8—82no—
1235D4—44no—
1236D4—416no—
1237D4—48no—
1238D4—48no—
1239D4—88no—
1240D4—88no—
1241D4—88no—
1242D4—84no—
1243D4—88no—
1244D4—88no—
1245D4—164no—
1246D4—164no—
1247D4—164no—
1248D4—164no—
1249D4—164no—
1250D4—164no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—21no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—22no—
1274C2×C4—21no—
1275C2×C4—22no—
1276C2×C4—21no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—21no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—24no—
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—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—416no—
1312C2×C4—44no—
1313C2×C4—48no—
1314C2×C4—84no—
1315C2×C4—84no—
1316C2×C4—84no—
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—42no—
1328C22—44no—
1329C22—44no—
1330C22—41no—
1331C22—44no—
1332C22—42no—
1333C22—44no—
1334C22—41no—
1335C22—42no—
1336C22—44no—
1337C22—44no—
1338C22—42no—
1339C22—44no—
1340C22—44no—
1341C22—42no—
1342C22—44no—
1343C22—42no—
1344C22—41no—
1345C22—44no—
1346C22—42no—
1347C22—44no—
1348C22—44no—
1349C22—44no—
1350C22—42no—
1351C22—44no—
1352C22—42no—
1353C22C22×H(5,𝔽2)11yescharacteristic
1354C22C2×#58511yescharacteristic
1355C22C2×#58512yes—
1356C22C2×#58511yescharacteristic
1357C22H(7,𝔽2)12yes—
1358C4—24no—
1359C4—24no—
1360C4—42no—
1361C4—41no—
1362C4—41no—
1363C4—42no—
1364C4—44no—
1365C4—41no—
1366C4—41no—
1367C4—42no—
1368C4—42no—
1369C4—42no—
1370C4—44no—
1371C4—41no—
1372C4—42no—
1373C4—44no—
1374C4—42no—
1375C4—42no—
1376C4—44no—
1377C4—44no—
1378C4—44no—
1379C4—42no—
1380C4#352914yes—
1381C2—82no—
1382C2—84no—
1383C2—84no—
1384C2—81no—
1385C2C2×#352911yescharacteristic
1386C2#6283911yescharacteristic
1387C2#6288311yescharacteristic
1388C2#6294112yes—
1389C2#6295512yes—
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. #53132C2semidirect
3. #53105C2semidirect
4. #53076C2semidirect
5. #53074C2semidirect
6. #53060C2semidirect
7. #52683C2semidirect
8. #52682C2semidirect
9. #52632C2semidirect
10. #52622C2semidirect
11. #46079C2semidirect
12. #46010C2semidirect
13. #45722C2semidirect
14. #45649C2semidirect
15. #45596C2semidirect
16. #45546C2semidirect
17. #45533C2semidirect
18. #45522C2semidirect
19. #35570C2semidirect
20. #35561C2semidirect
21. #35549C2semidirect
22. #35323C2semidirect
23. #35278C2semidirect
24. #35211C2semidirect
25. #35156C2semidirect
26. #34879C2semidirect
27. #34727C2semidirect

Maximal subgroups

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

subgroupindex
#531542
#531322
#531052
#530762
#530742
#530602
#526832
#526822
#526322
#526222
#460792
#460102
#457222
#456492
#455962
#455462
#455332
#455222
#355702
#355612
#355492
#353232
#352782
#352112
#351562
#348792
#347272