Finite Group Databasebeta

← #7658076

Subgroups — #7658076

Order 512.

4575 conjugacy classes of subgroups.

The subgroup lattice has 1345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42147C214yesmaximal, complemented
2#42139C214yesmaximal, complemented
3#41930C214yesmaximal, complemented
4#41898C214yesmaximal, complemented
5#41597C214yesmaximal, complemented
6#41579C214yesmaximal, complemented
7#39750C211yesmaximal, characteristic, complemented
8#39740C211yesmaximal, characteristic, complemented
9#39284C212yesmaximal, complemented
10#39283C212yesmaximal, complemented
11#39131C212yesmaximal, complemented
12#37773C212yesmaximal, complemented
13#37767C212yesmaximal, complemented
14#37628C212yesmaximal, complemented
15#37579C212yesmaximal, complemented
16#37570C212yesmaximal, complemented
17#36513C212yesmaximal, complemented
18#36151C211yesmaximal, characteristic, complemented
19#36136C211yesmaximal, characteristic, complemented
20#35966C214yesmaximal, complemented
21#35893C214yesmaximal, complemented
22#35331C211yesmaximal, characteristic, complemented
23#35299C212yesmaximal, complemented
24#34631C212yesmaximal, complemented
25#34629C211yesmaximal, characteristic, complemented
26#34322C212yesmaximal, complemented
27#34151C211yesmaximal, characteristic, complemented
28C2×#556C2212yes—
29C2×#542C2212yes—
30C2×#533C2212yes—
31C2×#529C2211yescharacteristic
32C2×#529C2212yes—
33#2863C2212yes—
34#2862C2211yescharacteristic
35#2860C2212yes—
36#2858C2211yescharacteristic
37#2857C2212yes—
38#2850C2212yes—
39#2850C2212yes—
40#2837C2214yes—
41#2836C2214yes—
42#2836C2214yes—
43#2836C2214yes—
44#2829C2214yes—
45#2828C2214yes—
46#2802C2214yes—
47#2799C2214yes—
48#2779C2214yes—
49#2778C2214yes—
50#2777C2214yes—
51#2772C2214yes—
52#2766C2214yes—
53#2755C2214yes—
54#2753C2214yes—
55#2750C2214yes—
56#2732C2214yes—
57#2732C2214yes—
58#2732C2214yes—
59#2730C2214yes—
60#2730C2214yes—
61#2727C2214yes—
62#2721C2214yes—
63#2721C2214yes—
64#2715C2214yes—
65#2714C2214yes—
66#2706C2214yes—
67#2698C2214yes—
68#2695C2214yes—
69#2694C2214yes—
70#2667C2214yes—
71#2664C2214yes—
72#2664C2214yes—
73#2663C2214yes—
74#2663C2214yes—
75#2661C2214yes—
76#2660C2212yes—
77#2658C2212yes—
78#2655C2214yes—
79#2654C2214yes—
80#2654C2214yes—
81#2652C2214yes—
82#2651C2214yes—
83#2651C2214yes—
84#2649C2214yes—
85#2648C2214yes—
86#2648C2214yes—
87#2648C2214yes—
88#2647C2211yescharacteristic
89#2647C2214yes—
90#2645C2212yes—
91#2644C2214yes—
92#2642C2211yescharacteristic
93#2640C2212yes—
94#2629C2211yescharacteristic
95#2625C2212yes—
96#2625C2212yes—
97#2624C2212yes—
98#2621C2211yescharacteristic
99#2621C2211yescharacteristic
100#2621C2212yes—
101#2621C2212yes—
102#2620C2212yes—
103#2620C2212yes—
104#2619C2211yescharacteristic
105#2601C2214yes—
106#2596C2214yes—
107#2596C2214yes—
108#2594C2214yes—
109#2591C2214yes—
110#2590C2214yes—
111#2589C2214yes—
112#2588C2214yes—
113#2587C2214yes—
114#2585C2214yes—
115#2578C2214yes—
116#2576C2214yes—
117#2571C2212yes—
118#2570C2212yes—
119#2570C2212yes—
120#2560C2214yes—
121#2560C2214yes—
122#2560C2214yes—
123#2559C2214yes—
124#2557C2214yes—
125#2557C2214yes—
126#2554C2214yes—
127#2554C2214yes—
128#2546C2212yes—
129#2545C2212yes—
130#2544C2212yes—
131#2542C2212yes—
132#2540C2212yes—
133#2540C2212yes—
134#2538C2212yes—
135#2536C2212yes—
136#2535C2212yes—
137#2532C2214yes—
138#2531C2214yes—
139#2531C2214yes—
140#2529C2214yes—
141#2526C2214yes—
142#2525C2214yes—
143#2520C2214yes—
144#2518C2214yes—
145#2513C2214yes—
146#2512C2214yes—
147#2507C2214yes—
148#2489C2214yes—
149#2481C2214yes—
150#2479C2214yes—
151#2479C2214yes—
152#2479C2214yes—
153#2479C2214yes—
154#2479C2214yes—
155#2478C2214yes—
156#2478C2214yes—
157#2477C2214yes—
158#2476C2214yes—
159#2471C2214yes—
160#2471C2214yes—
161#2471C2214yes—
162#2470C2214yes—
163#2461C2214yes—
164#2456C2214yes—
165#2453C2214yes—
166#2449C2214yes—
167#2448C2214yes—
168#2429C2212yes—
169#2429C2212yes—
170#2429C2212yes—
171#2428C2212yes—
172#2427C2212yes—
173#2426C2212yes—
174#2423C2214yes—
175#2423C2212yes—
176#2422C2212yes—
177#2421C2212yes—
178#2421C2212yes—
179#2421C2212yes—
180#2420C2212yes—
181#2415C2214yes—
182#2413C2214yes—
183#2402C2214yes—
184#2401C2214yes—
185#2396C2214yes—
186#2396C2214yes—
187#2395C2214yes—
188#2395C2214yes—
189#2374C2212yes—
190#2374C2212yes—
191#2374C2214yes—
192#2373C2214yes—
193#2373C2214yes—
194#2373C2212yes—
195#2373C2214yes—
196#2373C2212yes—
197#2370C2212yes—
198#2367C2212yes—
199#2367C2212yes—
200#2367C2212yes—
201#2365C2212yes—
202#2363C2214yes—
203#2363C2212yes—
204#2362C2214yes—
205#2362C2212yes—
206#2360C2214yes—
207#2355C2212yes—
208#2351C2212yes—
209#2351C2212yes—
210D4×C4⋊C4C2212yes—
211#2346C2214yes—
212#2334C2214yes—
213#2334C2214yes—
214#2331C2212yes—
215#2328C2211yescharacteristic
216#2327C2211yescharacteristic
217#2326C2212yes—
218#2324C2212yes—
219#2323C2214yes—
220#2323C2212yes—
221C4×C4⋊Q8C2212yes—
222C4×C4⋊Q8C2211yescharacteristic
223C4×C4⋊Q8C2212yes—
224C4×#125C2211yescharacteristic
225C4×#124C2212yes—
226C4×#124C2212yes—
227C4×#124C2212yes—
228C4×C22⋊Q8C2212yes—
229#2298C2212yes—
230#2295C2212yes—
231#2295C2212yes—
232#2295C2211yescharacteristic
233#2293C2212yes—
234#2293C2212yes—
235#2293C2211yescharacteristic
236#2290C2212yes—
237#2274C2214yes—
238C42×Q8C2211yescharacteristic
239C42×D4C2211yescharacteristic
240C4×#117C2211yescharacteristic
241C4×#117C2212yes—
242C4×#117C2211yescharacteristic
243#556—216no—
244#542—48no—
245#533—48no—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2311yescharacteristic
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2311yescharacteristic
251C2×#127C2311yescharacteristic
252#529—28no—
253#529—48no—
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#126C2312yes—
257C2×#126C2314yes—
258C2×#126C2314yes—
259C2×#126C2314yes—
260C2×#125C2311yescharacteristic
261C2×#125C2311yescharacteristic
262C2×#125C2314yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2312yes—
266C2×#124C2311yescharacteristic
267C2×#124C2312yes—
268C2×#124C2314yes—
269C2×#123C2312yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2311yescharacteristic
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×#121C2311yescharacteristic
285C2×#121C2312yes—
286C2×#121C2314yes—
287C2×#121C2312yes—
288C2×#121C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2314yes—
297C2×C4×Q8C2311yescharacteristic
298C2×C4×D4C2312yes—
299C2×C4×D4C2311yescharacteristic
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2314yes—
305C2×#117C2312yes—
306C2×#117C2314yes—
307C2×#117C2311yescharacteristic
308C2×#117C2314yes—
309C2×#117C2312yes—
310C2×#117C2314yes—
311C2×#117C2314yes—
312C2×#117C2311yescharacteristic
313C2×#117C2312yes—
314C22×C4⋊C4C2314yes—
315C22×C42C2311yescharacteristic
316C22×C42C2312yes—
317#401C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2314yes—
337#399C2314yes—
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#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
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#397C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#395C2314yes—
398#395C2314yes—
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#393C2314yes—
415#393C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2314yes—
430#391C2312yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#390C2314yes—
437#390C2314yes—
438#390C2314yes—
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2314yes—
445#390C2312yes—
446#390C2314yes—
447#390C2314yes—
448#390C2312yes—
449#390C2314yes—
450#390C2314yes—
451#390C2314yes—
452#390C2314yes—
453#389C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2312yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2312yes—
501#388C2312yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2312yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2312yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2312yes—
518#388C2312yes—
519#388C2312yes—
520#388C2314yes—
521#388C2314yes—
522#388C2312yes—
523#388C2312yes—
524#388C2312yes—
525#388C2312yes—
526#388C2312yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2312yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2312yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
560#387C2312yes—
561#387C2312yes—
562#387C2312yes—
563#387C2312yes—
564#387C2312yes—
565#387C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2312yes—
577#386C2312yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2312yes—
592#385C2312yes—
593#384C2312yes—
594#384C2312yes—
595#384C2311yescharacteristic
596#384C2314yes—
597#383C2314yes—
598#382C2311yescharacteristic
599#382C2311yescharacteristic
600#382C2312yes—
601#382C2312yes—
602#382C2312yes—
603#382C2311yescharacteristic
604#382C2314yes—
605#382C2314yes—
606#382C2314yes—
607#381C2314yes—
608#380C2314yes—
609#380C2312yes—
610#380C2314yes—
611#380C2312yes—
612#380C2312yes—
613#380C2314yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2311yescharacteristic
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2311yescharacteristic
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2314yes—
645C4×C22⋊C4C2312yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2312yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2312yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2311yescharacteristic
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2311yescharacteristic
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2312yes—
668#376C2312yes—
669#376C2311yescharacteristic
670#376C2314yes—
671#376C2314yes—
672#376C2311yescharacteristic
673#376C2311yescharacteristic
674#376C2311yescharacteristic
675C43C2311yescharacteristic
676C43C2312yes—
677C43C2312yes—
678C43C2311yescharacteristic
679C22×Q8C2412yes—
680C22×Q8C2412yes—
681C22×Q8C2414yes—
682C22×Q8C2411yescharacteristic
683C22×D4C2412yes—
684C22×D4C2411yescharacteristic
685C22×D4C2412yes—
686C22×D4C2414yes—
687C22×D4C2414yes—
688C22×D4C2414yes—
689C22×D4C2414yes—
690C23×C4C2411yescharacteristic
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2414yes—
694C23×C4C2414yes—
695C23×C4C2411yescharacteristic
696C23×C4C2412yes—
697C23×C4C2411yescharacteristic
698C23×C4C2414yes—
699C4⋊Q8—28no—
700C4⋊Q8—24no—
701C4⋊Q8—28no—
702C4⋊Q8—44no—
703C4⋊Q8—42no—
704#127—42no—
705#126—28no—
706#126—216no—
707#126—216no—
708#126—48no—
709#126—48no—
710#126—48no—
711#125—24no—
712#125—24no—
713#125—48no—
714#124—24no—
715#124—28no—
716#124—28no—
717#124—28no—
718#124—44no—
719#124—48no—
720#123—28no—
721#123—48no—
722#123—48no—
723#123—48no—
724C22⋊Q8—24no—
725C22⋊Q8—216no—
726C22⋊Q8—48no—
727C22⋊Q8—48no—
728C22⋊Q8—44no—
729C22⋊Q8—44no—
730C22⋊Q8—44no—
731C22⋊Q8—48no—
732C22⋊Q8—44no—
733C22⋊Q8—44no—
734C22⋊Q8—44no—
735#121—24no—
736#121—48no—
737#121—44no—
738#121—44no—
739#121—44no—
740C4×Q8—28no—
741C4×Q8—28no—
742C4×Q8—44no—
743C4×Q8—44no—
744C4×Q8—48no—
745C4×Q8—44no—
746C4×Q8—44no—
747C4×Q8—44no—
748C4×Q8#4118yes—
749C4×D4—24no—
750C4×D4—28no—
751C4×D4—28no—
752C4×D4—44no—
753C4×D4—44no—
754C4×D4—44no—
755C4×D4—48no—
756#117—216no—
757#117—28no—
758#117—24no—
759#117—44no—
760#117—42no—
761#117—48no—
762#117—44no—
763#117—48no—
764#117—48no—
765C2×C4⋊C4—48no—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C42—24no—
867C2×C42—28no—
868C2×C42C2411yescharacteristic
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2411yescharacteristic
872C2×C42C2411yescharacteristic
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2411yescharacteristic
878C2×C42C2412yes—
879C2×C42C2411yescharacteristic
880C2×C42C2412yes—
881C2×C42C2411yescharacteristic
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2412yes—
888C2×C42C2414yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902#95C2414yes—
903#95C2411yescharacteristic
904#95C2411yescharacteristic
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
915#95C2411yescharacteristic
916#95C2411yescharacteristic
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2414yes—
936#95C2412yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2412yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963C24C2514yes—
964C24C2512yes—
965C24C2511yescharacteristic
966C2×Q8—24no—
967C2×Q8—24no—
968C2×Q8—24no—
969C2×Q8—24no—
970C2×Q8—28no—
971C2×Q8—24no—
972C2×Q8—24no—
973C2×Q8—42no—
974C2×Q8—44no—
975C2×Q8—44no—
976C2×Q8C2×#4114yes—
977C2×D4—22no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—42no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—42no—
986C2×D4—42no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—24no—
1000C22×C4—28no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—22no—
1004C22×C4—24no—
1005C22×C4—22no—
1006C22×C4—24no—
1007C22×C4—22no—
1008C22×C4—24no—
1009C22×C4—28no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—44no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—44no—
1018C22×C4—42no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4C2511yescharacteristic
1023C22×C4C2512yes—
1024C22×C4C2514yes—
1025C22×C4C2512yes—
1026C22×C4C2511yescharacteristic
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2514yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2514yes—
1036C22×C4C2514yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2512yes—
1039C22×C4C2511yescharacteristic
1040C22×C4C2512yes—
1041C22×C4C2511yescharacteristic
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2511yescharacteristic
1046C4⋊C4—24no—
1047C4⋊C4—28no—
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—22no—
1051C4⋊C4—24no—
1052C4⋊C4—28no—
1053C4⋊C4—28no—
1054C4⋊C4—28no—
1055C4⋊C4—24no—
1056C4⋊C4—28no—
1057C4⋊C4—28no—
1058C4⋊C4—28no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—24no—
1065C4⋊C4—28no—
1066C4⋊C4—24no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—42no—
1075C4⋊C4—44no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—44no—
1080C4⋊C4—42no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4C2×#4118yes—
1099C4⋊C4C2×#4114yes—
1100C22⋊C4—24no—
1101C22⋊C4—24no—
1102C22⋊C4—28no—
1103C22⋊C4—28no—
1104C22⋊C4—24no—
1105C22⋊C4—24no—
1106C22⋊C4—24no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—24no—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—24no—
1115C22⋊C4—24no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—42no—
1120C22⋊C4—42no—
1121C22⋊C4—44no—
1122C22⋊C4—42no—
1123C22⋊C4—42no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—42no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C42—22no—
1147C42—22no—
1148C42—22no—
1149C42—28no—
1150C42—28no—
1151C42—24no—
1152C42—24no—
1153C42—24no—
1154C42—22no—
1155C42—22no—
1156C42—24no—
1157C42—24no—
1158C42—24no—
1159C42—22no—
1160C42—42no—
1161C42—42no—
1162C42—44no—
1163C42—42no—
1164C42—44no—
1165C42—42no—
1166C42—42no—
1167C42—42no—
1168C42—44no—
1169C42—42no—
1170C42—44no—
1171C42—44no—
1172C42—44no—
1173C42—42no—
1174C42—42no—
1175C42—42no—
1176C42—44no—
1177C42C2×#4114yes—
1178C42C2×#4118yes—
1179C42H(5,𝔽2)14yes—
1180C23—24no—
1181C23—22no—
1182C23—21no—
1183C23—21no—
1184C23—24no—
1185C23—22no—
1186C23—24no—
1187C23—22no—
1188C23—22no—
1189C23—21no—
1190C23—22no—
1191C23—22no—
1192C23—24no—
1193C23—24no—
1194C23—24no—
1195C23—24no—
1196C23—22no—
1197C23—22no—
1198C23—22no—
1199C23C2611yescharacteristic
1200Q8—44no—
1201Q8—48no—
1202Q8—48no—
1203Q8—88no—
1204D4—44no—
1205D4—48no—
1206D4—84no—
1207D4—88no—
1208D4—164no—
1209D4—164no—
1210D4—164no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—21no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—21no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—48no—
1271C2×C4—416no—
1272C2×C4—44no—
1273C2×C4—44no—
1274C2×C4—48no—
1275C2×C4—82no—
1276C2×C4—88no—
1277C2×C4—84no—
1278C2×C4—164no—
1279C2×C4C22×#4112yes—
1280C2×C4C22×#4114yes—
1281C2×C4C22×#4112yes—
1282C2×C4C22×#4114yes—
1283C2×C4C22×#4112yes—
1284C2×C4C2×H(5,𝔽2)14yes—
1285C2×C4C2×H(5,𝔽2)12yes—
1286C2×C4#58514yes—
1287C2×C4#58512yes—
1288C22—42no—
1289C22—41no—
1290C22—44no—
1291C22—41no—
1292C22—42no—
1293C22—44no—
1294C22—44no—
1295C22—41no—
1296C22—42no—
1297C22—42no—
1298C22—44no—
1299C22—42no—
1300C22—44no—
1301C22—42no—
1302C22—42no—
1303C22—44no—
1304C22—44no—
1305C22—42no—
1306C22—42no—
1307C22C23×#4111yescharacteristic
1308C22C22×H(5,𝔽2)11yescharacteristic
1309C22C2×#58511yescharacteristic
1310C22C2×#58512yes—
1311C222−1+612yes—
1312C4—22no—
1313C4—24no—
1314C4—24no—
1315C4—22no—
1316C4—24no—
1317C4—24no—
1318C4—41no—
1319C4—42no—
1320C4—44no—
1321C4—44no—
1322C4—41no—
1323C4—41no—
1324C4—44no—
1325C4—42no—
1326C4—44no—
1327C4—42no—
1328C4—44no—
1329C4—44no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—44no—
1334C4—42no—
1335C4#351714yes—
1336C2—81no—
1337C2—82no—
1338C2—84no—
1339C2#6268611yescharacteristic
1340C2C2×#351711yescharacteristic
1341C2#6286111yescharacteristic
1342C2#6295412yes—
1343C2#6296812yes—
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. #42147C2semidirect
2. #42139C2semidirect
3. #41930C2semidirect
4. #41898C2semidirect
5. #41597C2semidirect
6. #41579C2semidirect
7. #39750C2semidirect
8. #39740C2semidirect
9. #39284C2semidirect
10. #39283C2semidirect
11. #39131C2semidirect
12. #37773C2semidirect
13. #37767C2semidirect
14. #37628C2semidirect
15. #37579C2semidirect
16. #37570C2semidirect
17. #36513C2semidirect
18. #36151C2semidirect
19. #36136C2semidirect
20. #35966C2semidirect
21. #35893C2semidirect
22. #35331C2semidirect
23. #35299C2semidirect
24. #34631C2semidirect
25. #34629C2semidirect
26. #34322C2semidirect
27. #34151C2semidirect

Maximal subgroups

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

subgroupindex
#421472
#421392
#419302
#418982
#415972
#415792
#397502
#397402
#392842
#392832
#391312
#377732
#377672
#376282
#375792
#375702
#365132
#361512
#361362
#359662
#358932
#353312
#352992
#346312
#346292
#343222
#341512