Finite Group Databasebeta

← #7657719

Subgroups — #7657719

Order 512.

4414 conjugacy classes of subgroups.

The subgroup lattice has 1410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42394C214yesmaximal, complemented
2#42216C214yesmaximal, complemented
3#42163C212yesmaximal, complemented
4#42162C212yesmaximal, complemented
5#42042C214yesmaximal, complemented
6#40971C214yesmaximal, complemented
7#40955C214yesmaximal, complemented
8#39273C212yesmaximal, complemented
9#39268C212yesmaximal, complemented
10#38240C212yesmaximal, complemented
11#38236C212yesmaximal, complemented
12#38119C212yesmaximal, complemented
13#38117C212yesmaximal, complemented
14#37633C211yesmaximal, characteristic, complemented
15#37598C212yesmaximal, complemented
16#37591C212yesmaximal, complemented
17#37559C211yesmaximal, characteristic
18#36392C212yesmaximal, complemented
19#36368C212yesmaximal, complemented
20#35760C212yesmaximal, complemented
21#35754C212yesmaximal, complemented
22#35735C214yesmaximal, complemented
23#35321C212yesmaximal, complemented
24#35304C211yesmaximal, characteristic, complemented
25#34637C211yesmaximal, characteristic, complemented
26#34621C212yesmaximal, complemented
27#34231C211yesmaximal, characteristic, complemented
28#34226C211yesmaximal, characteristic, complemented
29#34149C211yesmaximal, characteristic, complemented
30C2×#533C2211yescharacteristic
31C2×#532C2211yescharacteristic
32C2×#529C2211yescharacteristic
33#2863C2212yes—
34#2863C2212yes—
35#2857C2212yes—
36#2855C2212yes—
37#2855C2212yes—
38#2851C2212yes—
39#2839C2214yes—
40#2838C2214yes—
41#2830C2214yes—
42#2829C2214yes—
43#2816C2212yes—
44#2815C2212yes—
45#2814C2214yes—
46#2808C2214yes—
47#2808C2214yes—
48#2798C2214yes—
49#2798C2214yes—
50#2797C2214yes—
51#2796C2214yes—
52#2796C2214yes—
53#2793C2214yes—
54#2786C2214yes—
55#2783C2214yes—
56#2777C2214yes—
57#2775C2214yes—
58#2773C2214yes—
59#2759C2214yes—
60#2759C2214yes—
61#2757C2214yes—
62#2756C2214yes—
63#2753C2214yes—
64#2752C2214yes—
65#2751C2214yes—
66#2730C2214yes—
67#2723C2214yes—
68#2716C2214yes—
69#2712C2214yes—
70#2666C2214yes—
71#2662C2214yes—
72#2661C2214yes—
73#2660C2212yes—
74#2655C2214yes—
75#2654C2214yes—
76#2651C2214yes—
77#2651C2214yes—
78#2651C2214yes—
79#2650C2214yes—
80#2648C2214yes—
81#2648C2214yes—
82#2647C2212yes—
83#2644C2212yes—
84#2644C2212yes—
85#2642C2211yescharacteristic
86#2642C2211yescharacteristic
87#2641C2211yescharacteristic
88#2641C2211yescharacteristic
89#2640C2212yes—
90#2640C2212yes—
91#2639C2214yes—
92#2639C2212yes—
93#2639C2212yes—
94#2638C2214yes—
95#2637C2214yes—
96#2633C2212yes—
97#2631C2212yes—
98#2630C2214yes—
99#2629C2212yes—
100#2629C2212yes—
101#2624C2212yes—
102#2624C2212yes—
103#2621C2212yes—
104#2621C2212yes—
105#2620C2212yes—
106#2619C2212yes—
107#2612C2214yes—
108#2607C2214yes—
109#2606C2212yes—
110#2605C2212yes—
111#2603C2214yes—
112#2602C2214yes—
113#2600C2214yes—
114#2599C2214yes—
115#2598C2214yes—
116#2597C2214yes—
117#2592C2212yes—
118#2585C2214yes—
119#2585C2214yes—
120#2580C2214yes—
121#2578C2214yes—
122#2578C2214yes—
123#2577C2214yes—
124#2576C2214yes—
125#2576C2214yes—
126#2575C2214yes—
127#2573C2214yes—
128#2573C2214yes—
129#2573C2214yes—
130#2572C2214yes—
131#2569C2212yes—
132#2567C2211yescharacteristic
133#2565C2212yes—
134#2563C2211yescharacteristic
135#2549C2212yes—
136#2547C2211yescharacteristic
137#2546C2211yescharacteristic
138#2545C2212yes—
139#2540C2212yes—
140#2531C2214yes—
141#2530C2214yes—
142#2525C2214yes—
143#2524C2214yes—
144#2524C2214yes—
145#2523C2214yes—
146#2523C2214yes—
147#2523C2214yes—
148#2522C2214yes—
149#2521C2214yes—
150#2520C2214yes—
151#2518C2214yes—
152#2518C2214yes—
153#2517C2214yes—
154#2517C2214yes—
155#2515C2214yes—
156#2515C2214yes—
157#2514C2212yes—
158#2513C2212yes—
159#2512C2212yes—
160#2511C2212yes—
161#2499C2214yes—
162#2492C2212yes—
163#2491C2212yes—
164#2490C2212yes—
165#2489C2212yes—
166#2485C2212yes—
167#2485C2212yes—
168#2478C2214yes—
169#2477C2214yes—
170#2468C2214yes—
171#2465C2214yes—
172#2463C2214yes—
173#2461C2214yes—
174#2459C2214yes—
175#2458C2214yes—
176#2457C2214yes—
177#2454C2212yes—
178#2453C2212yes—
179#2452C2212yes—
180#2451C2212yes—
181#2447C2214yes—
182#2439C2214yes—
183#2438C2214yes—
184#2423C2212yes—
185#2422C2212yes—
186#2421C2212yes—
187#2420C2212yes—
188#2407C2212yes—
189#2407C2212yes—
190#2398C2214yes—
191#2398C2212yes—
192#2398C2212yes—
193#2395C2214yes—
194#2395C2214yes—
195#2392C2214yes—
196#2392C2214yes—
197#2373C2212yes—
198#2373C2212yes—
199#2372C2211yescharacteristic
200#2372C2211yescharacteristic
201#2371C2211yescharacteristic
202#2371C2211yescharacteristic
203#2369C2212yes—
204#2368C2214yes—
205#2368C2212yes—
206#2367C2212yes—
207#2367C2212yes—
208#2365C2212yes—
209#2364C2212yes—
210#2363C2214yes—
211#2362C2214yes—
212#2359C2214yes—
213#2359C2212yes—
214#2359C2212yes—
215#2357C2212yes—
216#2356C2212yes—
217#2356C2212yes—
218#2353C2214yes—
219#2349C2212yes—
220#2347C2211yescharacteristic
221#2347C2211yescharacteristic
222#2346C2211yescharacteristic
223#2346C2211yescharacteristic
224#2343C2214yes—
225#2341C2212yes—
226#2339C2212yes—
227#2332C2214yes—
228#2331C2212yes—
229#2330C2212yes—
230#2324C2214yes—
231#2323C2212yes—
232#2323C2212yes—
233#2320C2212yes—
234#2320C2212yes—
235#2320C2212yes—
236#2319C2212yes—
237C4×C4⋊Q8C2212yes—
238C4×#127C2212yes—
239C4×#125C2212yes—
240C4×#125C2212yes—
241C4×#121C2212yes—
242C4×#121C2212yes—
243#2298C2212yes—
244#2297C2212yes—
245#2297C2212yes—
246#2295C2212yes—
247#2293C2212yes—
248#2293C2212yes—
249#2290C2212yes—
250#2290C2212yes—
251#2285C2211yescharacteristic
252#2283C2211yescharacteristic
253#2276C2212yes—
254#2275C2212yes—
255C42×D4C2212yes—
256C4×#117C2212yes—
257C4×#117C2211yescharacteristic
258C2×#376C2211yescharacteristic
259C22×#41C2312yes—
260#533—28no—
261#532—28no—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×#127C2311yescharacteristic
268#529—28no—
269C2×#126C2312yes—
270C2×#126C2314yes—
271C2×#125C2311yescharacteristic
272C2×#125C2311yescharacteristic
273C2×#125C2311yescharacteristic
274C2×#125C2312yes—
275C2×#124C2312yes—
276C2×#124C2311yescharacteristic
277C2×#124C2312yes—
278C2×#124C2314yes—
279C2×#123C2312yes—
280C2×#123C2314yes—
281C2×C22⋊Q8C2311yescharacteristic
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2311yescharacteristic
291C2×#121C2312yes—
292C2×#121C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2314yes—
299C2×C4×D4C2311yescharacteristic
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2314yes—
311C2×#117C2311yescharacteristic
312C2×#117C2311yescharacteristic
313C2×#117C2312yes—
314C2×#117C2312yes—
315C2×#117C2312yes—
316C2×#117C2314yes—
317C2×#117C2314yes—
318C2×#117C2312yes—
319C22×C42C2312yes—
320C22×C42C2312yes—
321C22×C42C2311yescharacteristic
322#401C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2312yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2312yes—
334#400C2312yes—
335#400C2314yes—
336#400C2312yes—
337#400C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
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#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
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#394C2312yes—
412#394C2312yes—
413#394C2312yes—
414#394C2314yes—
415#394C2312yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2314yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2314yes—
451#390C2314yes—
452#390C2314yes—
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2314yes—
460#390C2312yes—
461#390C2312yes—
462#390C2314yes—
463#390C2312yes—
464#390C2312yes—
465#390C2312yes—
466#390C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2312yes—
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#388C2312yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2312yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2312yes—
522#388C2312yes—
523#388C2312yes—
524#388C2312yes—
525#388C2312yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
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#387C2312yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2312yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2312yes—
565#387C2314yes—
566#387C2312yes—
567#387C2312yes—
568#387C2312yes—
569#387C2312yes—
570#387C2312yes—
571#387C2312yes—
572#387C2314yes—
573#387C2312yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2312yes—
589#386C2312yes—
590#386C2312yes—
591#386C2312yes—
592#386C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2312yes—
603#385C2314yes—
604#385C2314yes—
605#385C2312yes—
606#385C2312yes—
607#385C2312yes—
608#384C2312yes—
609#384C2312yes—
610#384C2312yes—
611#383C2312yes—
612#383C2314yes—
613#383C2314yes—
614#383C2312yes—
615#383C2314yes—
616#383C2314yes—
617#383C2314yes—
618#383C2312yes—
619#382C2312yes—
620#382C2312yes—
621#382C2312yes—
622#382C2312yes—
623#382C2314yes—
624#382C2314yes—
625#382C2314yes—
626#382C2312yes—
627#382C2312yes—
628#381C2312yes—
629#381C2314yes—
630#381C2314yes—
631#381C2314yes—
632#381C2314yes—
633#380C2312yes—
634#380C2312yes—
635#380C2314yes—
636#380C2312yes—
637#380C2314yes—
638#380C2314yes—
639#380C2312yes—
640#380C2312yes—
641#380C2311yescharacteristic
642#380C2311yescharacteristic
643#380C2312yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2311yescharacteristic
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2311yescharacteristic
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2312yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2311yescharacteristic
688C4×C22⋊C4C2311yescharacteristic
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697#376C2311yescharacteristic
698#376C2312yes—
699#376C2312yes—
700#376C2312yes—
701#376C2312yes—
702#376C2312yes—
703#376C2311yescharacteristic
704#376C2311yescharacteristic
705#376C2311yescharacteristic
706#376C2312yes—
707#376C2311yescharacteristic
708#376C2311yescharacteristic
709C2×#95C2311yescharacteristic
710C2×#95C2314yes—
711C2×#95C2311yescharacteristic
712C2×#95C2312yes—
713C43C2312yes—
714C43C2312yes—
715C2×#41—28no—
716C2×#41—44no—
717C2×#41—44no—
718C22×Q8C2412yes—
719C22×Q8C2412yes—
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×Q8C2414yes—
723C22×D4C2412yes—
724C22×D4C2412yes—
725C22×D4C2412yes—
726C22×D4C2412yes—
727C22×D4C2411yescharacteristic
728C22×D4C2414yes—
729C22×D4C2414yes—
730C22×D4C2414yes—
731C23×C4C2412yes—
732C23×C4C2411yescharacteristic
733C23×C4C2414yes—
734C23×C4C2414yes—
735C23×C4C2412yes—
736C23×C4C2414yes—
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2412yes—
740C23×C4C2411yescharacteristic
741C23×C4C2411yescharacteristic
742C4⋊Q8—24no—
743C4⋊Q8—24no—
744C4⋊Q8—24no—
745C4⋊Q8—44no—
746C4⋊Q8—82no—
747#127—24no—
748#126—28no—
749#126—84no—
750#125—24no—
751#125—24no—
752#125—24no—
753#125—44no—
754#124—24no—
755#124—28no—
756#124—82no—
757#124—84no—
758#123—28no—
759#123—48no—
760C22⋊Q8—24no—
761C22⋊Q8—28no—
762C22⋊Q8—28no—
763C22⋊Q8—48no—
764C22⋊Q8—44no—
765C22⋊Q8—44no—
766C22⋊Q8—84no—
767#121—24no—
768#121—28no—
769#121—28no—
770#121—44no—
771#121—44no—
772C4×Q8—24no—
773C4×Q8—28no—
774C4×Q8—28no—
775C4×Q8—48no—
776C4×Q8—44no—
777C4×Q8—44no—
778C4×D4—28no—
779C4×D4—24no—
780C4×D4—28no—
781C4×D4—28no—
782C4×D4—44no—
783C4×D4—44no—
784C4×D4—44no—
785C4×D4—48no—
786C4×D4—48no—
787C4×D4—44no—
788C4×D4—84no—
789C4×D4—84no—
790#117—24no—
791#117—24no—
792#117—28no—
793#117—44no—
794#117—48no—
795#117—44no—
796#117—84no—
797#117—82no—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C42—44no—
898C2×C42—44no—
899C2×C42#4118yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2411yescharacteristic
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932#95C2411yescharacteristic
933#95C2411yescharacteristic
934#95C2412yes—
935#95C2411yescharacteristic
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2411yescharacteristic
941#95C2412yes—
942#95C2411yescharacteristic
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2411yescharacteristic
947#95C2412yes—
948#95C2411yescharacteristic
949#95C2412yes—
950#95C2411yescharacteristic
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006C24C2512yes—
1007C24C2514yes—
1008C24C2511yescharacteristic
1009#41—816no—
1010C2×Q8—24no—
1011C2×Q8—24no—
1012C2×Q8—22no—
1013C2×Q8—24no—
1014C2×Q8—24no—
1015C2×Q8—24no—
1016C2×Q8—44no—
1017C2×Q8—42no—
1018C2×Q8—41no—
1019C2×Q8—41no—
1020C2×Q8—42no—
1021C2×Q8—44no—
1022C2×Q8—44no—
1023C2×Q8—44no—
1024C2×D4—24no—
1025C2×D4—28no—
1026C2×D4—24no—
1027C2×D4—24no—
1028C2×D4—24no—
1029C2×D4—22no—
1030C2×D4—24no—
1031C2×D4—24no—
1032C2×D4—44no—
1033C2×D4—42no—
1034C2×D4—42no—
1035C2×D4—42no—
1036C2×D4—42no—
1037C2×D4—44no—
1038C2×D4—44no—
1039C2×D4—44no—
1040C2×D4—44no—
1041C2×D4—44no—
1042C2×D4—41no—
1043C2×D4—41no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—44no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—28no—
1052C22×C4—28no—
1053C22×C4—24no—
1054C22×C4—28no—
1055C22×C4—42no—
1056C22×C4—41no—
1057C22×C4—41no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—44no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4C2×#4114yes—
1076C22×C4C2×#4114yes—
1077C22×C4C2×#4114yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2514yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2514yes—
1095C22×C4C2514yes—
1096C22×C4C2512yes—
1097C22×C4C2511yescharacteristic
1098C22×C4C2511yescharacteristic
1099C22×C4C2511yescharacteristic
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2512yes—
1103C22×C4C2511yescharacteristic
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—22no—
1107C4⋊C4—22no—
1108C4⋊C4—22no—
1109C4⋊C4—22no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—22no—
1113C4⋊C4—24no—
1114C4⋊C4—22no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C22⋊C4—24no—
1158C22⋊C4—24no—
1159C22⋊C4—24no—
1160C22⋊C4—24no—
1161C22⋊C4—24no—
1162C22⋊C4—28no—
1163C22⋊C4—28no—
1164C22⋊C4—24no—
1165C22⋊C4—24no—
1166C22⋊C4—24no—
1167C22⋊C4—24no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—42no—
1171C22⋊C4—44no—
1172C22⋊C4—42no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—42no—
1176C22⋊C4—42no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—42no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—42no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—42no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C42—24no—
1204C42—24no—
1205C42—24no—
1206C42—24no—
1207C42—24no—
1208C42—24no—
1209C42—24no—
1210C42—24no—
1211C42—28no—
1212C42—24no—
1213C42—42no—
1214C42—42no—
1215C42—42no—
1216C42—42no—
1217C42—42no—
1218C42—42no—
1219C42—42no—
1220C42—42no—
1221C42—44no—
1222C42—42no—
1223C42—42no—
1224C42—42no—
1225C42—42no—
1226C42—44no—
1227C42—44no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42C2×#4114yes—
1232C42C2×#4114yes—
1233C42C2×#4114yes—
1234C42C2×#4114yes—
1235C23—22no—
1236C23—22no—
1237C23—21no—
1238C23—21no—
1239C23—22no—
1240C23—24no—
1241C23—22no—
1242C23—24no—
1243C23—22no—
1244C23—22no—
1245C23—24no—
1246C23—22no—
1247C23—24no—
1248C23—24no—
1249C23—24no—
1250C23—22no—
1251C23—24no—
1252C23—22no—
1253C23C22×#4112yes—
1254C23C2611yescharacteristic
1255Q8—48no—
1256Q8—48no—
1257Q8—82no—
1258Q8—84no—
1259Q8—164no—
1260D4—48no—
1261D4—48no—
1262D4—48no—
1263D4—48no—
1264D4—82no—
1265D4—88no—
1266D4—88no—
1267D4—88no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—28no—
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—22no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—44no—
1334C2×C4—44no—
1335C2×C4—48no—
1336C2×C4—88no—
1337C2×C4—84no—
1338C2×C4—88no—
1339C2×C4—88no—
1340C2×C4—84no—
1341C2×C4—84no—
1342C2×C4—84no—
1343C2×C4C22×#4112yes—
1344C2×C4C22×#4112yes—
1345C2×C4C22×#4112yes—
1346C2×C4C22×#4112yes—
1347C2×C4C22×#4112yes—
1348C2×C4C22×#4112yes—
1349C2×C4#58514yes—
1350C2×C4#58514yes—
1351C22—22no—
1352C22—22no—
1353C22—22no—
1354C22—42no—
1355C22—42no—
1356C22—42no—
1357C22—44no—
1358C22—44no—
1359C22—42no—
1360C22—42no—
1361C22—42no—
1362C22—44no—
1363C22—44no—
1364C22—44no—
1365C22—44no—
1366C22—42no—
1367C22—42no—
1368C22—44no—
1369C22—42no—
1370C22C23×#4111yescharacteristic
1371C22C2×#58512yes—
1372C22C2×#58512yes—
1373C22H(7,𝔽2)11yescharacteristic
1374C222−1+611yescharacteristic
1375C4—22no—
1376C4—22no—
1377C4—22no—
1378C4—24no—
1379C4—22no—
1380C4—22no—
1381C4—42no—
1382C4—44no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—42no—
1388C4—42no—
1389C4—42no—
1390C4—44no—
1391C4—42no—
1392C4—44no—
1393C4—42no—
1394C4—44no—
1395C4—42no—
1396C4—44no—
1397C4—42no—
1398C4—42no—
1399C4—42no—
1400C4#351014yes—
1401C2—42no—
1402C2—82no—
1403C2—84no—
1404C2#6268611yescharacteristic
1405C2C2×#351011yescharacteristic
1406C2#6285611yescharacteristic
1407C2#6293612yes—
1408C2#6294112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37559C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42394C2semidirect
2. #42216C2semidirect
3. #42163C2semidirect
4. #42162C2semidirect
5. #42042C2semidirect
6. #40971C2semidirect
7. #40955C2semidirect
8. #39273C2semidirect
9. #39268C2semidirect
10. #38240C2semidirect
11. #38236C2semidirect
12. #38119C2semidirect
13. #38117C2semidirect
14. #37633C2semidirect
15. #37598C2semidirect
16. #37591C2semidirect
18. #36392C2semidirect
19. #36368C2semidirect
20. #35760C2semidirect
21. #35754C2semidirect
22. #35735C2semidirect
23. #35321C2semidirect
24. #35304C2semidirect
25. #34637C2semidirect
26. #34621C2semidirect
27. #34231C2semidirect
28. #34226C2semidirect
29. #34149C2semidirect

Maximal subgroups

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

subgroupindex
#423942
#422162
#421632
#421622
#420422
#409712
#409552
#392732
#392682
#382402
#382362
#381192
#381172
#376332
#375982
#375912
#375592
#363922
#363682
#357602
#357542
#357352
#353212
#353042
#346372
#346212
#342312
#342262
#341492