Finite Group Databasebeta

← #8096273

Subgroups — #8096273

Order 512.

4886 conjugacy classes of subgroups.

The subgroup lattice has 1396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52953C212yesmaximal, complemented
2#52948C214yesmaximal, complemented
3#52714C212yesmaximal, complemented
4#52549C212yesmaximal, complemented
5#52326C214yesmaximal, complemented
6#52321C214yesmaximal, complemented
7#52287C211yesmaximal, characteristic, complemented
8#52167C211yesmaximal, characteristic, complemented
9C2×#2734C211yesmaximal, characteristic, complemented
10#46325C212yesmaximal, complemented
11#46316C211yesmaximal, characteristic, complemented
12#46312C211yesmaximal, characteristic, complemented
13#46269C212yesmaximal, complemented
14#46228C212yesmaximal, complemented
15#46099C211yesmaximal, characteristic, complemented
16#46090C212yesmaximal, complemented
17#46040C214yesmaximal, complemented
18#45958C212yesmaximal, complemented
19#45826C214yesmaximal, complemented
20#45798C214yesmaximal, complemented
21#45792C212yesmaximal, complemented
22#36376C211yesmaximal, characteristic, complemented
23#36309C214yesmaximal, complemented
24#36305C212yesmaximal, complemented
25#36122C212yesmaximal, complemented
26#36001C212yesmaximal, complemented
27#35740C214yesmaximal, complemented
28C2×#563C2212yes—
29C2×#552C2211yescharacteristic
30C2×#548C2211yescharacteristic
31C2×#548C2212yes—
32C2×#532C2212yes—
33C22×C4⋊Q8C2212yes—
34C2×#520C2212yes—
35#2865C2214yes—
36#2861C2211yescharacteristic
37#2860C2212yes—
38#2858C2212yes—
39#2857C2211yescharacteristic
40#2857C2212yes—
41#2856C2212yes—
42#2855C2212yes—
43#2852C2214yes—
44#2851C2214yes—
45#2850C2211yescharacteristic
46#2850C2212yes—
47#2841C2214yes—
48#2841C2214yes—
49#2841C2214yes—
50#2837C2214yes—
51#2832C2212yes—
52#2832C2214yes—
53#2831C2214yes—
54#2831C2214yes—
55#2830C2214yes—
56#2830C2212yes—
57#2830C2214yes—
58#2829C2214yes—
59#2829C2214yes—
60#2827C2214yes—
61#2823C2212yes—
62#2821C2214yes—
63#2820C2214yes—
64#2814C2214yes—
65#2811C2211yescharacteristic
66#2808C2212yes—
67#2806C2212yes—
68#2806C2214yes—
69#2804C2212yes—
70#2803C2214yes—
71#2797C2214yes—
72#2792C2212yes—
73#2792C2214yes—
74#2790C2214yes—
75#2790C2214yes—
76#2788C2214yes—
77#2784C2214yes—
78#2780C2214yes—
79#2772C2214yes—
80#2768C2214yes—
81#2763C2214yes—
82#2757C2214yes—
83#2755C2214yes—
84#2748C2214yes—
85#2737C2214yes—
86#2734C2214yes—
87#2734C2212yes—
88#2734C2211yescharacteristic
89#2734C2214yes—
90#2734C2212yes—
91#2734C2212yes—
92#2734C2212yes—
93#2734C2211yescharacteristic
94#2733C2211yescharacteristic
95#2732C2212yes—
96#2731C2212yes—
97#2729C2214yes—
98#2716C2214yes—
99#2713C2214yes—
100#2712C2214yes—
101#2710C2214yes—
102#2709C2214yes—
103#2705C2214yes—
104#2704C2214yes—
105#2700C2214yes—
106#2699C2212yes—
107#2692C2214yes—
108#2691C2214yes—
109#2691C2214yes—
110#2686C2214yes—
111#2682C2212yes—
112#2677C2214yes—
113#2674C2214yes—
114#2673C2214yes—
115#2672C2214yes—
116#2672C2214yes—
117#2638C2214yes—
118#2637C2212yes—
119#2633C2212yes—
120#2632C2214yes—
121#2623C2212yes—
122#2618C2214yes—
123#2610C2214yes—
124#2603C2212yes—
125#2599C2214yes—
126#2599C2212yes—
127#2590C2214yes—
128#2589C2214yes—
129#2587C2214yes—
130#2585C2214yes—
131#2584C2212yes—
132#2583C2214yes—
133#2573C2214yes—
134#2565C2211yescharacteristic
135#2556C2214yes—
136#2545C2211yescharacteristic
137#2545C2212yes—
138#2545C2212yes—
139#2543C2214yes—
140#2536C2212yes—
141#2531C2214yes—
142#2530C2214yes—
143#2526C2214yes—
144#2525C2214yes—
145#2524C2214yes—
146#2523C2214yes—
147#2521C2214yes—
148#2519C2214yes—
149#2515C2214yes—
150#2509C2212yes—
151#2501C2211yescharacteristic
152#2499C2211yescharacteristic
153#2495C2212yes—
154#2491C2214yes—
155#2491C2214yes—
156#2488C2214yes—
157#2481C2214yes—
158#2479C2214yes—
159#2475C2214yes—
160#2474C2214yes—
161#2474C2214yes—
162#2473C2214yes—
163#2473C2214yes—
164#2466C2214yes—
165#2466C2214yes—
166#2465C2214yes—
167#2465C2214yes—
168#2461C2214yes—
169#2461C2214yes—
170#2458C2214yes—
171#2452C2214yes—
172#2452C2214yes—
173#2450C2214yes—
174#2449C2214yes—
175#2449C2214yes—
176#2449C2214yes—
177#2449C2214yes—
178#2447C2212yes—
179#2444C2214yes—
180#2443C2214yes—
181#2443C2214yes—
182#2443C2214yes—
183#2436C2212yes—
184#2436C2212yes—
185#2434C2211yescharacteristic
186#2432C2211yescharacteristic
187#2432C2212yes—
188#2432C2212yes—
189#2430C2214yes—
190#2430C2214yes—
191#2430C2212yes—
192#2426C2212yes—
193#2425C2214yes—
194#2425C2214yes—
195#2425C2214yes—
196#2419C2214yes—
197#2417C2212yes—
198#2416C2214yes—
199#2416C2214yes—
200#2416C2212yes—
201#2409C2214yes—
202#2406C2212yes—
203#2406C2214yes—
204#2399C2214yes—
205#2399C2212yes—
206#2392C2212yes—
207C2×#398C2212yes—
208#2388C2214yes—
209C2×#395C2214yes—
210#2381C2212yes—
211#2379C2212yes—
212#2377C2214yes—
213#2376C2214yes—
214#2376C2214yes—
215#2361C2214yes—
216#2361C2214yes—
217#2361C2212yes—
218#2360C2212yes—
219#2359C2214yes—
220#2359C2214yes—
221#2353C2214yes—
222#2343C2212yes—
223C4×C4⋊Q8C2211yescharacteristic
224C4×C4⋊Q8C2212yes—
225C4×#123C2214yes—
226C4×#121C2212yes—
227#2297C2211yescharacteristic
228#2295C2214yes—
229#2295C2212yes—
230C2×#391C2211yescharacteristic
231C2×#389C2212yes—
232C2×#387C2214yes—
233C42×D4C2211yescharacteristic
234C42×D4C2212yes—
235C22×#41C2311yescharacteristic
236C22×#41C2312yes—
237C22×#41C2312yes—
238C23×Q8C2311yescharacteristic
239C23×Q8C2312yes—
240#563—48no—
241#552—44no—
242#548—48no—
243#548—44no—
244#532—48no—
245C2×C4⋊Q8—48no—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2311yescharacteristic
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2312yes—
251C2×C4⋊Q8C2314yes—
252C2×C4⋊Q8C2314yes—
253C2×C4⋊Q8C2311yescharacteristic
254C2×#127C2312yes—
255C2×#126C2314yes—
256C2×#126C2314yes—
257C2×#126C2312yes—
258C2×#125C2314yes—
259C2×#125C2311yescharacteristic
260C2×#125C2312yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2311yescharacteristic
266C2×#124C2314yes—
267C2×#124C2311yescharacteristic
268C2×#124C2312yes—
269C2×#124C2312yes—
270C2×#124C2312yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2312yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2311yescharacteristic
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2311yescharacteristic
283C2×C22⋊Q8C2311yescharacteristic
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2311yescharacteristic
291C2×#121C2314yes—
292C2×#121C2314yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298#520—48no—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2311yescharacteristic
308C2×C4×D4C2312yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×#117C2312yes—
317C2×#117C2311yescharacteristic
318C2×#117C2314yes—
319C22×C4⋊C4C2312yes—
320C22×C4⋊C4C2314yes—
321C22×C4⋊C4C2314yes—
322C22×C4⋊C4C2314yes—
323C22×C4⋊C4C2312yes—
324C22×C4⋊C4C2311yescharacteristic
325C22×C4⋊C4C2312yes—
326C22×C42C2312yes—
327C22×C42C2312yes—
328C22×C42C2311yescharacteristic
329C22×C42C2311yescharacteristic
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2312yes—
349#398C2314yes—
350#398C2312yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2312yes—
361#398C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2312yes—
366#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2312yes—
379#397C2314yes—
380#397C2314yes—
381#397C2312yes—
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#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2312yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2312yes—
411#395C2312yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2312yes—
421#394C2314yes—
422#394C2314yes—
423#394C2312yes—
424#394C2312yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2312yes—
440#393C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2314yes—
444#393C2314yes—
445#393C2314yes—
446#393C2314yes—
447#393C2314yes—
448#392C2314yes—
449#392C2312yes—
450#392C2314yes—
451#392C2314yes—
452#391C2312yes—
453#391C2311yescharacteristic
454#391C2312yes—
455#391C2311yescharacteristic
456#391C2311yescharacteristic
457#391C2311yescharacteristic
458#391C2314yes—
459#391C2312yes—
460#391C2311yescharacteristic
461#391C2312yes—
462#391C2314yes—
463#391C2312yes—
464#391C2311yescharacteristic
465#391C2312yes—
466#391C2312yes—
467#391C2311yescharacteristic
468#391C2314yes—
469#391C2314yes—
470#391C2314yes—
471#390C2314yes—
472#390C2314yes—
473#390C2311yescharacteristic
474#390C2314yes—
475#390C2314yes—
476#390C2312yes—
477#390C2311yescharacteristic
478#390C2312yes—
479#390C2312yes—
480#390C2314yes—
481#390C2314yes—
482#390C2312yes—
483#390C2312yes—
484#390C2311yescharacteristic
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2314yes—
506#389C2312yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
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#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
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#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
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#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#384C2311yescharacteristic
613#384C2312yes—
614#384C2311yescharacteristic
615#383C2314yes—
616#383C2312yes—
617#383C2314yes—
618#382C2314yes—
619#382C2311yescharacteristic
620#382C2312yes—
621#382C2312yes—
622#381C2314yes—
623#381C2314yes—
624#381C2314yes—
625#381C2312yes—
626#380C2312yes—
627#380C2314yes—
628#380C2314yes—
629#380C2314yes—
630#380C2314yes—
631#380C2314yes—
632#380C2312yes—
633#380C2314yes—
634#380C2314yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2311yescharacteristic
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2312yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2312yes—
652C4×C22⋊C4C2312yes—
653C4×C22⋊C4C2311yescharacteristic
654C4×C22⋊C4C2311yescharacteristic
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2314yes—
657#376C2312yes—
658#376C2314yes—
659C2×#95C2312yes—
660C2×#95C2314yes—
661C2×#95C2314yes—
662C2×#95C2314yes—
663C43C2312yes—
664C43C2311yescharacteristic
665C2×#41—24no—
666C2×#41—42no—
667C2×#41—44no—
668C2×#41—44no—
669C2×#41—48no—
670C2×#41—44no—
671C2×#41—81no—
672C2×#41—82no—
673C22×Q8—24no—
674C22×Q8—42no—
675C22×Q8—44no—
676C22×Q8—44no—
677C22×Q8—81no—
678C22×Q8—82no—
679C22×Q8C2411yescharacteristic
680C22×Q8C2412yes—
681C22×Q8C2412yes—
682C22×Q8C2412yes—
683C22×Q8C2412yes—
684C22×Q8C2411yescharacteristic
685C22×Q8C2412yes—
686C22×Q8C2414yes—
687C22×Q8C2411yescharacteristic
688C22×D4C2412yes—
689C22×D4C2411yescharacteristic
690C22×D4C2414yes—
691C22×D4C2414yes—
692C22×D4C2414yes—
693C22×D4C2412yes—
694C22×D4C2411yescharacteristic
695C22×D4C2412yes—
696C22×D4C2412yes—
697C22×D4C2412yes—
698C22×D4C2414yes—
699C23×C4C2412yes—
700C23×C4C2411yescharacteristic
701C23×C4C2414yes—
702C23×C4C2412yes—
703C23×C4C2412yes—
704C23×C4C2411yescharacteristic
705C23×C4C2412yes—
706C23×C4C2414yes—
707C23×C4C2414yes—
708C23×C4C2414yes—
709C23×C4C2412yes—
710C23×C4C2414yes—
711C23×C4C2414yes—
712C4⋊Q8—28no—
713C4⋊Q8—28no—
714C4⋊Q8—24no—
715C4⋊Q8—44no—
716C4⋊Q8—44no—
717C4⋊Q8—48no—
718C4⋊Q8—48no—
719C4⋊Q8—81no—
720#127—44no—
721#126—44no—
722#126—48no—
723#126—48no—
724#125—44no—
725#125—42no—
726#125—48no—
727#124—28no—
728#124—48no—
729#124—44no—
730#124—44no—
731#124—42no—
732#124—44no—
733#124—81no—
734#124—82no—
735#124—82no—
736#124—82no—
737#123—216no—
738#123—48no—
739#123—48no—
740#123—44no—
741#123—48no—
742#123—84no—
743C22⋊Q8—44no—
744C22⋊Q8—42no—
745C22⋊Q8—48no—
746C22⋊Q8—48no—
747C22⋊Q8—44no—
748C22⋊Q8—48no—
749C22⋊Q8—42no—
750C22⋊Q8—44no—
751C22⋊Q8—42no—
752C22⋊Q8—84no—
753C22⋊Q8—82no—
754#121—28no—
755#121—48no—
756#121—48no—
757#121—48no—
758#121—48no—
759#121—44no—
760#121—42no—
761#121—44no—
762#121—44no—
763#121—48no—
764C4×Q8—28no—
765C4×Q8—44no—
766C4×Q8—44no—
767C4×Q8—42no—
768C4×Q8—42no—
769C4×Q8—44no—
770C4×D4—216no—
771C4×D4—28no—
772C4×D4—24no—
773C4×D4—44no—
774C4×D4—44no—
775C4×D4—48no—
776C4×D4—48no—
777C4×D4—48no—
778C4×D4—44no—
779C4×D4—48no—
780C4×D4—82no—
781#117—28no—
782#117—42no—
783#117—48no—
784C2×C4⋊C4—28no—
785C2×C4⋊C4—48no—
786C2×C4⋊C4—48no—
787C2×C4⋊C4—48no—
788C2×C4⋊C4—44no—
789C2×C4⋊C4—42no—
790C2×C4⋊C4—82no—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2411yescharacteristic
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2411yescharacteristic
891C2×C42—44no—
892C2×C42—44no—
893C2×C42—81no—
894C2×C42—81no—
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2411yescharacteristic
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2411yescharacteristic
913C2×C42C2412yes—
914C2×C42C2414yes—
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917#95C2414yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2412yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2412yes—
936#95C2414yes—
937#95C2412yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2412yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
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—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969C24C2514yes—
970C24C2511yescharacteristic
971C24C2512yes—
972C24C2511yescharacteristic
973#41—432no—
974#41—88no—
975#41—816no—
976C2×Q8—24no—
977C2×Q8—22no—
978C2×Q8—24no—
979C2×Q8—22no—
980C2×Q8—24no—
981C2×Q8—24no—
982C2×Q8—42no—
983C2×Q8—41no—
984C2×Q8—42no—
985C2×Q8—41no—
986C2×Q8—42no—
987C2×Q8—44no—
988C2×Q8—41no—
989C2×Q8—41no—
990C2×Q8—42no—
991C2×Q8—42no—
992C2×Q8—44no—
993C2×Q8—42no—
994C2×Q8—42no—
995C2×Q8—44no—
996C2×Q8—41no—
997C2×Q8—42no—
998C2×Q8—42no—
999C2×Q8—44no—
1000C2×Q8—41no—
1001C2×Q8—88no—
1002C2×Q8—816no—
1003C2×Q8H(5,𝔽2)14yes—
1004C2×D4—28no—
1005C2×D4—24no—
1006C2×D4—22no—
1007C2×D4—24no—
1008C2×D4—28no—
1009C2×D4—28no—
1010C2×D4—28no—
1011C2×D4—22no—
1012C2×D4—24no—
1013C2×D4—24no—
1014C2×D4—24no—
1015C2×D4—28no—
1016C2×D4—28no—
1017C2×D4—42no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—42no—
1022C2×D4—44no—
1023C2×D4—41no—
1024C2×D4—42no—
1025C2×D4—42no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—42no—
1030C2×D4—44no—
1031C2×D4—41no—
1032C2×D4—42no—
1033C2×D4—42no—
1034C22×C4—24no—
1035C22×C4—22no—
1036C22×C4—24no—
1037C22×C4—28no—
1038C22×C4—24no—
1039C22×C4—28no—
1040C22×C4—28no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—24no—
1046C22×C4—22no—
1047C22×C4—24no—
1048C22×C4—28no—
1049C22×C4—28no—
1050C22×C4—24no—
1051C22×C4—28no—
1052C22×C4—44no—
1053C22×C4—42no—
1054C22×C4—41no—
1055C22×C4—41no—
1056C22×C4—44no—
1057C22×C4—42no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—42no—
1061C22×C4—44no—
1062C22×C4—42no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—42no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4C2512yes—
1073C22×C4C2514yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2514yes—
1077C22×C4C2514yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2514yes—
1084C22×C4C2512yes—
1085C22×C4C2511yescharacteristic
1086C22×C4C2514yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2511yescharacteristic
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C22×C4C2512yes—
1094C22×C4C2514yes—
1095C4⋊C4—24no—
1096C4⋊C4—28no—
1097C4⋊C4—28no—
1098C4⋊C4—28no—
1099C4⋊C4—28no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—22no—
1104C4⋊C4—28no—
1105C4⋊C4—24no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—44no—
1110C4⋊C4—41no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—41no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—41no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—41no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C42−1+418yes—
1150C22⋊C4—24no—
1151C22⋊C4—28no—
1152C22⋊C4—24no—
1153C22⋊C4—28no—
1154C22⋊C4—24no—
1155C22⋊C4—22no—
1156C22⋊C4—28no—
1157C22⋊C4—28no—
1158C22⋊C4—28no—
1159C22⋊C4—28no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—44no—
1163C22⋊C4—42no—
1164C22⋊C4—42no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—42no—
1178C22⋊C4—42no—
1179C22⋊C4—42no—
1180C22⋊C4—44no—
1181C22⋊C4—42no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4H(5,𝔽2)14yes—
1195C42—24no—
1196C42—24no—
1197C42—24no—
1198C42—24no—
1199C42—24no—
1200C42—28no—
1201C42—24no—
1202C42—22no—
1203C42—22no—
1204C42—24no—
1205C42—28no—
1206C42—44no—
1207C42—44no—
1208C42—41no—
1209C42—42no—
1210C42—42no—
1211C42—41no—
1212C42—41no—
1213C42—44no—
1214C42—44no—
1215C42—42no—
1216C42—42no—
1217C23—21no—
1218C23—22no—
1219C23—21no—
1220C23—24no—
1221C23—21no—
1222C23—22no—
1223C23—24no—
1224C23—21no—
1225C23—22no—
1226C23—24no—
1227C23—24no—
1228C23—24no—
1229C23—22no—
1230C23—24no—
1231C23—22no—
1232C23—24no—
1233C23—24no—
1234C23—21no—
1235C23—24no—
1236C23—22no—
1237C23C2×H(5,𝔽2)12yes—
1238C23#58514yes—
1239C23C2611yescharacteristic
1240Q8—44no—
1241Q8—48no—
1242Q8—48no—
1243Q8—82no—
1244Q8—84no—
1245Q8—84no—
1246Q8—84no—
1247Q8—82no—
1248Q8—88no—
1249D4—48no—
1250D4—48no—
1251D4—44no—
1252D4—416no—
1253D4—88no—
1254D4—88no—
1255D4—84no—
1256D4—84no—
1257D4—84no—
1258D4—82no—
1259D4—88no—
1260C2×C4—24no—
1261C2×C4—21no—
1262C2×C4—22no—
1263C2×C4—21no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—21no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—21no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—21no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—21no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—44no—
1318C2×C4—48no—
1319C2×C4—416no—
1320C2×C4—48no—
1321C2×C4—44no—
1322C2×C4—48no—
1323C2×C4—416no—
1324C2×C4—48no—
1325C2×C4—88no—
1326C2×C4—84no—
1327C2×C4—88no—
1328C2×C4—88no—
1329C2×C4—164no—
1330C2×C4C2×H(5,𝔽2)12yes—
1331C2×C4C2×H(5,𝔽2)14yes—
1332C2×C4C2×H(5,𝔽2)12yes—
1333C2×C4C2×H(5,𝔽2)12yes—
1334C2×C4C2×2−1+414yes—
1335C2×C4C2×2−1+418yes—
1336C22—24no—
1337C22—22no—
1338C22—22no—
1339C22—24no—
1340C22—44no—
1341C22—42no—
1342C22—44no—
1343C22—44no—
1344C22—41no—
1345C22—42no—
1346C22—44no—
1347C22—42no—
1348C22—41no—
1349C22—44no—
1350C22—44no—
1351C22—41no—
1352C22—42no—
1353C22—42no—
1354C22—44no—
1355C22—44no—
1356C22—44no—
1357C22#352914yes—
1358C22C22×H(5,𝔽2)11yescharacteristic
1359C22C22×H(5,𝔽2)11yescharacteristic
1360C22C22×2−1+412yes—
1361C22C2×#58512yes—
1362C22H(7,𝔽2)11yescharacteristic
1363C4—28no—
1364C4—22no—
1365C4—22no—
1366C4—24no—
1367C4—22no—
1368C4—24no—
1369C4—42no—
1370C4—44no—
1371C4—44no—
1372C4—42no—
1373C4—41no—
1374C4—42no—
1375C4—44no—
1376C4—44no—
1377C4—42no—
1378C4—42no—
1379C4—42no—
1380C4—44no—
1381C4—42no—
1382C4—41no—
1383C4—42no—
1384C4—42no—
1385C4—44no—
1386C2—24no—
1387C2—82no—
1388C2—81no—
1389C2—84no—
1390C2C2×#352911yescharacteristic
1391C2#6289211yescharacteristic
1392C2#6295812yes—
1393C2#6301512yes—
1394C2#6303711yescharacteristic
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. #52953C2semidirect
2. #52948C2semidirect
3. #52714C2semidirect
4. #52549C2semidirect
5. #52326C2semidirect
6. #52321C2semidirect
7. #52287C2semidirect
8. #52167C2semidirect
9. C2×#2734C2semidirect
10. #46325C2semidirect
11. #46316C2semidirect
12. #46312C2semidirect
13. #46269C2semidirect
14. #46228C2semidirect
15. #46099C2semidirect
16. #46090C2semidirect
17. #46040C2semidirect
18. #45958C2semidirect
19. #45826C2semidirect
20. #45798C2semidirect
21. #45792C2semidirect
22. #36376C2semidirect
23. #36309C2semidirect
24. #36305C2semidirect
25. #36122C2semidirect
26. #36001C2semidirect
27. #35740C2semidirect

Maximal subgroups

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

subgroupindex
#529532
#529482
#527142
#525492
#523262
#523212
#522872
#521672
C2×#27342
#463252
#463162
#463122
#462692
#462282
#460992
#460902
#460402
#459582
#458262
#457982
#457922
#363762
#363092
#363052
#361222
#360012
#357402