Finite Group Databasebeta

← #8096599

Subgroups — #8096599

Order 512.

4445 conjugacy classes of subgroups.

The subgroup lattice has 1439 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53106C212yesmaximal, complemented
2#53057C212yesmaximal, complemented
3#52980C212yesmaximal, complemented
4#52507C214yesmaximal, complemented
5#52494C214yesmaximal, complemented
6#52443C214yesmaximal, complemented
7#52306C211yesmaximal, characteristic, complemented
8#52169C212yesmaximal, complemented
9#46340C212yesmaximal, complemented
10#46290C212yesmaximal, complemented
11#46194C214yesmaximal, complemented
12#46157C211yesmaximal, characteristic, complemented
13#46062C212yesmaximal, complemented
14#46062C212yesmaximal, complemented
15#46015C211yesmaximal, characteristic, complemented
16#45998C211yesmaximal, characteristic, complemented
17#45895C214yesmaximal, complemented
18#45807C212yesmaximal, complemented
19#45801C212yesmaximal, complemented
20#45767C214yesmaximal, complemented
21#36495C212yesmaximal, complemented
22#36476C212yesmaximal, complemented
23#36463C211yesmaximal, characteristic, complemented
24#36453C211yesmaximal, characteristic, complemented
25#36407C211yesmaximal, characteristic, complemented
26#36113C212yesmaximal, complemented
27#35843C212yesmaximal, complemented
28#35785C212yesmaximal, complemented
29#35722C212yesmaximal, complemented
30C2×#563C2212yes—
31C2×#529C2214yes—
32#2862C2212yes—
33#2860C2212yes—
34#2860C2212yes—
35#2859C2211yescharacteristic
36#2859C2211yescharacteristic
37#2858C2211yescharacteristic
38#2857C2212yes—
39#2855C2212yes—
40#2855C2214yes—
41#2854C2212yes—
42#2853C2214yes—
43#2852C2214yes—
44#2838C2214yes—
45#2837C2214yes—
46#2837C2214yes—
47#2834C2214yes—
48#2832C2214yes—
49#2832C2214yes—
50#2830C2214yes—
51#2829C2214yes—
52#2829C2214yes—
53#2824C2214yes—
54#2822C2212yes—
55#2820C2212yes—
56#2819C2212yes—
57#2819C2214yes—
58#2816C2214yes—
59#2816C2214yes—
60#2813C2214yes—
61#2813C2214yes—
62#2810C2212yes—
63#2809C2211yescharacteristic
64#2808C2212yes—
65#2787C2214yes—
66#2775C2212yes—
67#2775C2212yes—
68#2769C2212yes—
69#2767C2214yes—
70#2759C2214yes—
71#2759C2214yes—
72#2745C2214yes—
73#2745C2214yes—
74#2741C2214yes—
75#2734C2211yescharacteristic
76#2731C2212yes—
77#2731C2214yes—
78#2731C2214yes—
79#2730C2214yes—
80#2727C2214yes—
81#2727C2211yescharacteristic
82#2727C2211yescharacteristic
83#2727C2212yes—
84#2726C2212yes—
85#2723C2214yes—
86#2721C2212yes—
87#2721C2212yes—
88#2721C2214yes—
89#2719C2214yes—
90#2718C2214yes—
91#2718C2214yes—
92#2716C2214yes—
93#2716C2214yes—
94#2715C2214yes—
95#2715C2214yes—
96#2715C2214yes—
97#2711C2214yes—
98#2710C2214yes—
99#2707C2214yes—
100#2706C2214yes—
101#2702C2214yes—
102#2702C2214yes—
103#2702C2214yes—
104#2695C2214yes—
105#2687C2214yes—
106#2686C2214yes—
107#2683C2212yes—
108#2682C2212yes—
109#2676C2214yes—
110#2676C2214yes—
111#2674C2214yes—
112#2674C2214yes—
113#2671C2214yes—
114#2665C2214yes—
115#2653C2214yes—
116#2648C2214yes—
117#2629C2212yes—
118#2624C2212yes—
119#2619C2212yes—
120#2608C2214yes—
121#2607C2214yes—
122#2607C2214yes—
123#2595C2214yes—
124#2594C2214yes—
125#2593C2214yes—
126#2590C2214yes—
127#2589C2214yes—
128#2589C2214yes—
129#2589C2214yes—
130#2586C2214yes—
131#2584C2212yes—
132#2580C2212yes—
133#2580C2212yes—
134#2578C2214yes—
135#2576C2214yes—
136#2574C2214yes—
137#2570C2212yes—
138#2570C2212yes—
139#2570C2212yes—
140#2563C2211yescharacteristic
141#2563C2212yes—
142#2559C2214yes—
143#2557C2214yes—
144#2556C2214yes—
145#2552C2211yescharacteristic
146#2551C2212yes—
147#2551C2211yescharacteristic
148#2548C2212yes—
149#2542C2212yes—
150#2541C2211yescharacteristic
151#2538C2211yescharacteristic
152#2537C2211yescharacteristic
153#2520C2214yes—
154#2516C2214yes—
155#2513C2212yes—
156#2513C2212yes—
157#2512C2212yes—
158#2512C2212yes—
159#2509C2212yes—
160#2509C2212yes—
161#2508C2212yes—
162#2507C2212yes—
163#2506C2212yes—
164#2500C2212yes—
165#2500C2212yes—
166#2494C2212yes—
167#2494C2212yes—
168#2494C2212yes—
169#2492C2214yes—
170#2491C2212yes—
171#2491C2212yes—
172#2490C2212yes—
173#2490C2212yes—
174#2479C2214yes—
175#2477C2214yes—
176#2476C2214yes—
177#2474C2214yes—
178#2468C2214yes—
179#2467C2214yes—
180#2467C2214yes—
181#2466C2214yes—
182#2466C2214yes—
183#2460C2214yes—
184#2460C2214yes—
185#2459C2214yes—
186#2459C2214yes—
187#2459C2214yes—
188#2459C2214yes—
189#2458C2214yes—
190#2457C2214yes—
191#2457C2214yes—
192#2454C2212yes—
193#2454C2212yes—
194#2452C2212yes—
195#2452C2212yes—
196#2447C2214yes—
197#2446C2214yes—
198#2445C2212yes—
199#2445C2212yes—
200#2445C2212yes—
201#2441C2212yes—
202#2439C2214yes—
203#2439C2212yes—
204#2439C2212yes—
205#2439C2212yes—
206#2439C2212yes—
207#2428C2212yes—
208#2428C2212yes—
209#2427C2212yes—
210#2423C2214yes—
211#2422C2212yes—
212#2420C2212yes—
213#2420C2212yes—
214#2420C2212yes—
215#2414C2212yes—
216#2396C2212yes—
217#2396C2214yes—
218#2396C2212yes—
219#2395C2212yes—
220#2392C2214yes—
221#2392C2214yes—
222#2382C2212yes—
223#2379C2212yes—
224#2378C2214yes—
225#2378C2214yes—
226#2376C2214yes—
227#2370C2212yes—
228#2369C2211yescharacteristic
229#2369C2212yes—
230#2366C2212yes—
231#2366C2211yescharacteristic
232#2365C2212yes—
233#2361C2212yes—
234#2361C2212yes—
235#2361C2212yes—
236#2357C2212yes—
237#2357C2212yes—
238#2355C2212yes—
239#2355C2211yescharacteristic
240#2354C2211yescharacteristic
241#2354C2211yescharacteristic
242D4×C4⋊C4C2211yescharacteristic
243#2345C2212yes—
244#2344C2212yes—
245C4×C4⋊Q8C2212yes—
246C4×#125C2211yescharacteristic
247C4×#125C2211yescharacteristic
248C4×#126C2212yes—
249C4×#126C2212yes—
250C4×#124C2211yescharacteristic
251C4×C22⋊Q8C2214yes—
252C4×#121C2212yes—
253C4×#121C2212yes—
254C4×#121C2214yes—
255#2296C2212yes—
256#2274C2212yes—
257C42×D4C2212yes—
258C42×D4C2211yescharacteristic
259#563—48no—
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2312yes—
266C2×#127C2311yescharacteristic
267C2×#127C2312yes—
268#529—416no—
269C2×#126C2312yes—
270C2×#126C2312yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#125C2311yescharacteristic
276C2×#125C2311yescharacteristic
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#124C2311yescharacteristic
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2314yes—
285C2×#124C2314yes—
286C2×#124C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×#121C2312yes—
297C2×#121C2314yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2314yes—
307C2×C4×D4C2311yescharacteristic
308C2×C4×D4C2312yes—
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2314yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2312yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2312yes—
320C2×#117C2312yes—
321C2×#117C2314yes—
322C2×#117C2312yes—
323C2×#117C2312yes—
324C2×#117C2312yes—
325C22×C4⋊C4C2312yes—
326C22×C42C2314yes—
327C22×C42C2312yes—
328#401C2314yes—
329#401C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2312yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2312yes—
340#400C2312yes—
341#400C2314yes—
342#399C2312yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#399C2314yes—
348#399C2314yes—
349#399C2314yes—
350#399C2312yes—
351#399C2312yes—
352#398C2312yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2314yes—
364#398C2314yes—
365#398C2312yes—
366#398C2312yes—
367#398C2312yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2312yes—
372#397C2312yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2312yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2312yes—
394#396C2314yes—
395#396C2312yes—
396#396C2314yes—
397#396C2312yes—
398#396C2314yes—
399#396C2312yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2312yes—
404#395C2312yes—
405#395C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
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#394C2312yes—
431#394C2314yes—
432#394C2312yes—
433#394C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2312yes—
441#393C2314yes—
442#393C2314yes—
443#393C2314yes—
444#393C2314yes—
445#393C2312yes—
446#393C2314yes—
447#393C2314yes—
448#392C2314yes—
449#392C2314yes—
450#392C2314yes—
451#392C2314yes—
452#392C2314yes—
453#392C2314yes—
454#391C2312yes—
455#391C2312yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2314yes—
465#391C2311yescharacteristic
466#391C2314yes—
467#391C2312yes—
468#391C2314yes—
469#391C2314yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2314yes—
474#390C2314yes—
475#390C2312yes—
476#390C2312yes—
477#390C2314yes—
478#390C2314yes—
479#390C2312yes—
480#390C2312yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2312yes—
485#390C2312yes—
486#390C2312yes—
487#390C2312yes—
488#390C2312yes—
489#390C2311yescharacteristic
490#389C2311yescharacteristic
491#389C2311yescharacteristic
492#389C2311yescharacteristic
493#389C2311yescharacteristic
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2314yes—
527#389C2314yes—
528#388C2312yes—
529#388C2312yes—
530#388C2312yes—
531#388C2312yes—
532#388C2312yes—
533#388C2312yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2312yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2312yes—
567#387C2312yes—
568#387C2312yes—
569#387C2312yes—
570#387C2312yes—
571#387C2312yes—
572#387C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#384C2312yes—
631#384C2311yescharacteristic
632#384C2311yescharacteristic
633#384C2312yes—
634#384C2312yes—
635#384C2311yescharacteristic
636#384C2311yescharacteristic
637#383C2312yes—
638#383C2312yes—
639#382C2311yescharacteristic
640#382C2311yescharacteristic
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2314yes—
646#382C2312yes—
647#382C2312yes—
648#382C2312yes—
649#382C2311yescharacteristic
650#381C2314yes—
651#381C2314yes—
652#381C2314yes—
653#381C2314yes—
654#381C2314yes—
655#380C2312yes—
656#380C2314yes—
657#380C2312yes—
658#380C2314yes—
659#380C2314yes—
660#380C2314yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2314yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C43C2312yes—
713C43C2311yescharacteristic
714C22×Q8C2414yes—
715C22×Q8C2411yescharacteristic
716C22×Q8C2412yes—
717C22×Q8C2414yes—
718C22×Q8C2412yes—
719C22×D4C2411yescharacteristic
720C22×D4C2412yes—
721C22×D4C2411yescharacteristic
722C22×D4C2412yes—
723C22×D4C2414yes—
724C22×D4C2414yes—
725C22×D4C2414yes—
726C22×D4C2414yes—
727C22×D4C2414yes—
728C22×D4C2412yes—
729C23×C4C2412yes—
730C23×C4C2412yes—
731C23×C4C2414yes—
732C23×C4C2414yes—
733C23×C4C2412yes—
734C23×C4C2414yes—
735C23×C4C2412yes—
736C23×C4C2414yes—
737C4⋊Q8—42no—
738C4⋊Q8—44no—
739C4⋊Q8—44no—
740C4⋊Q8—44no—
741C4⋊Q8—48no—
742C4⋊Q8—82no—
743#127—44no—
744#127—42no—
745#126—28no—
746#126—48no—
747#126—44no—
748#126—48no—
749#126—48no—
750#126—84no—
751#125—24no—
752#125—44no—
753#125—42no—
754#125—44no—
755#125—44no—
756#125—48no—
757#124—44no—
758#124—44no—
759#124—42no—
760#124—48no—
761#124—84no—
762#124—84no—
763#123—48no—
764#123—48no—
765#123—48no—
766#123—48no—
767C22⋊Q8—216no—
768C22⋊Q8—48no—
769C22⋊Q8—48no—
770C22⋊Q8—48no—
771C22⋊Q8—82no—
772#121—48no—
773#121—48no—
774#121—44no—
775#121—44no—
776#121—44no—
777#121—44no—
778#121—44no—
779#121—82no—
780C4×Q8—44no—
781C4×Q8—42no—
782C4×Q8—48no—
783C4×D4—24no—
784C4×D4—28no—
785C4×D4—48no—
786C4×D4—42no—
787C4×D4—44no—
788C4×D4—42no—
789C4×D4—44no—
790C4×D4—42no—
791C4×D4—48no—
792C4×D4—48no—
793C4×D4—82no—
794C4×D4—82no—
795C4×D4—84no—
796#117—28no—
797#117—44no—
798#117—48no—
799#117—44no—
800#117—82no—
801C2×C4⋊C4—28no—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2411yescharacteristic
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C42—48no—
919C2×C42—82no—
920C2×C42C2414yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2411yescharacteristic
924C2×C42C2412yes—
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2411yescharacteristic
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932C2×C42C2412yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2411yescharacteristic
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010C24C2512yes—
1011C24C2512yes—
1012C24C2514yes—
1013C2×Q8—28no—
1014C2×Q8—22no—
1015C2×Q8—41no—
1016C2×Q8—42no—
1017C2×Q8—44no—
1018C2×Q8—41no—
1019C2×Q8—42no—
1020C2×Q8—44no—
1021C2×Q8—42no—
1022C2×Q8—44no—
1023C2×Q8—42no—
1024C2×Q8—42no—
1025C2×Q8—44no—
1026C2×Q8—44no—
1027C2×Q8—42no—
1028C2×D4—22no—
1029C2×D4—24no—
1030C2×D4—22no—
1031C2×D4—24no—
1032C2×D4—24no—
1033C2×D4—22no—
1034C2×D4—22no—
1035C2×D4—24no—
1036C2×D4—41no—
1037C2×D4—41no—
1038C2×D4—44no—
1039C2×D4—44no—
1040C2×D4—44no—
1041C2×D4—42no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—44no—
1047C2×D4—44no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—42no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C2×D4—42no—
1054C2×D4—44no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—44no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—28no—
1064C22×C4—28no—
1065C22×C4—28no—
1066C22×C4—24no—
1067C22×C4—24no—
1068C22×C4—42no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—42no—
1075C22×C4—42no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4C2512yes—
1083C22×C4C2511yescharacteristic
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2511yescharacteristic
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2514yes—
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2514yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2511yescharacteristic
1104C22×C4C2512yes—
1105C22×C4C2511yescharacteristic
1106C22×C4C2511yescharacteristic
1107C22×C4C2511yescharacteristic
1108C4⋊C4—24no—
1109C4⋊C4—28no—
1110C4⋊C4—24no—
1111C4⋊C4—28no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—22no—
1116C4⋊C4—28no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—22no—
1123C4⋊C4—22no—
1124C4⋊C4—22no—
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—22no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—44no—
1134C4⋊C4—41no—
1135C4⋊C4—42no—
1136C4⋊C4—41no—
1137C4⋊C4—44no—
1138C4⋊C4—41no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—41no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—41no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—41no—
1172C4⋊C4H(5,𝔽2)14yes—
1173C4⋊C42−1+414yes—
1174C22⋊C4—28no—
1175C22⋊C4—24no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—28no—
1179C22⋊C4—28no—
1180C22⋊C4—24no—
1181C22⋊C4—28no—
1182C22⋊C4—24no—
1183C22⋊C4—28no—
1184C22⋊C4—42no—
1185C22⋊C4—42no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—42no—
1190C22⋊C4—42no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—42no—
1217C22⋊C4—44no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C42—24no—
1225C42—28no—
1226C42—22no—
1227C42—22no—
1228C42—24no—
1229C42—24no—
1230C42—24no—
1231C42—22no—
1232C42—24no—
1233C42—22no—
1234C42—24no—
1235C42—22no—
1236C42—22no—
1237C42—44no—
1238C42—44no—
1239C42—41no—
1240C42—42no—
1241C42—42no—
1242C42—42no—
1243C42—44no—
1244C42—44no—
1245C42—44no—
1246C42—44no—
1247C42—42no—
1248C42—44no—
1249C42—42no—
1250C42—42no—
1251C23—22no—
1252C23—22no—
1253C23—24no—
1254C23—22no—
1255C23—24no—
1256C23—22no—
1257C23—24no—
1258C23—22no—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—22no—
1263C23—22no—
1264C23—22no—
1265C23—24no—
1266C23—24no—
1267C23—24no—
1268C23—22no—
1269C23—24no—
1270C23—22no—
1271C23—22no—
1272C23C2611yescharacteristic
1273Q8—88no—
1274Q8—82no—
1275Q8—84no—
1276Q8—162no—
1277Q8—164no—
1278D4—44no—
1279D4—44no—
1280D4—48no—
1281D4—84no—
1282D4—88no—
1283D4—88no—
1284D4—88no—
1285D4—88no—
1286D4—162no—
1287D4—164no—
1288C2×C4—22no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—21no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—48no—
1359C2×C4—48no—
1360C2×C4—88no—
1361C2×C4—84no—
1362C2×C4—88no—
1363C2×C4—88no—
1364C2×C4—84no—
1365C2×C4—88no—
1366C2×C4C2×H(5,𝔽2)14yes—
1367C2×C4C2×H(5,𝔽2)12yes—
1368C2×C4C2×2−1+414yes—
1369C2×C4C2×2−1+412yes—
1370C2×C4#58512yes—
1371C2×C4#58512yes—
1372C2×C4#58512yes—
1373C2×C4#58512yes—
1374C22—44no—
1375C22—42no—
1376C22—42no—
1377C22—44no—
1378C22—42no—
1379C22—42no—
1380C22—44no—
1381C22—42no—
1382C22—42no—
1383C22—42no—
1384C22—42no—
1385C22—44no—
1386C22—42no—
1387C22—42no—
1388C22—44no—
1389C22—42no—
1390C22—42no—
1391C22—44no—
1392C22—42no—
1393C22—44no—
1394C22—42no—
1395C22C22×H(5,𝔽2)11yescharacteristic
1396C22C22×2−1+411yescharacteristic
1397C22C2×#58511yescharacteristic
1398C22C2×#58511yescharacteristic
1399C22C2×#58511yescharacteristic
1400C22C2×#58511yescharacteristic
1401C22H(7,𝔽2)11yescharacteristic
1402C4—24no—
1403C4—22no—
1404C4—22no—
1405C4—24no—
1406C4—22no—
1407C4—44no—
1408C4—41no—
1409C4—44no—
1410C4—41no—
1411C4—42no—
1412C4—42no—
1413C4—44no—
1414C4—42no—
1415C4—41no—
1416C4—42no—
1417C4—42no—
1418C4—42no—
1419C4—42no—
1420C4—42no—
1421C4—44no—
1422C4—42no—
1423C4—42no—
1424C4—42no—
1425C4—44no—
1426C4—42no—
1427C4#353114yes—
1428C2—84no—
1429C2—82no—
1430C2—82no—
1431C2C2×#353111yescharacteristic
1432C2#6290811yescharacteristic
1433C2#6294411yescharacteristic
1434C2#6296511yescharacteristic
1435C2#6302111yescharacteristic
1436C2#6302211yescharacteristic
1437C2#6303411yescharacteristic
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. #53106C2semidirect
2. #53057C2semidirect
3. #52980C2semidirect
4. #52507C2semidirect
5. #52494C2semidirect
6. #52443C2semidirect
7. #52306C2semidirect
8. #52169C2semidirect
9. #46340C2semidirect
10. #46290C2semidirect
11. #46194C2semidirect
12. #46157C2semidirect
13. #46062C2semidirect
14. #46062C2semidirect
15. #46015C2semidirect
16. #45998C2semidirect
17. #45895C2semidirect
18. #45807C2semidirect
19. #45801C2semidirect
20. #45767C2semidirect
21. #36495C2semidirect
22. #36476C2semidirect
23. #36463C2semidirect
24. #36453C2semidirect
25. #36407C2semidirect
26. #36113C2semidirect
27. #35843C2semidirect
28. #35785C2semidirect
29. #35722C2semidirect

Maximal subgroups

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

subgroupindex
#531062
#530572
#529802
#525072
#524942
#524432
#523062
#521692
#463402
#462902
#461942
#461572
#460622
#460152
#459982
#458952
#458072
#458012
#457672
#364952
#364762
#364632
#364532
#364072
#361132
#358432
#357852
#357222