Finite Group Databasebeta

← #8701608

Subgroups — #8701608

Order 512.

4447 conjugacy classes of subgroups.

The subgroup lattice has 1441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59873C212yesmaximal, complemented
2#59403C212yesmaximal, complemented
3#59331C212yesmaximal, complemented
4#59230C212yesmaximal, complemented
5#57374C214yesmaximal, complemented
6#57174C214yesmaximal, complemented
7#55833C214yesmaximal, complemented
8#52304C211yesmaximal, characteristic, complemented
9#51016C214yesmaximal, complemented
10#50871C214yesmaximal, complemented
11#49210C214yesmaximal, complemented
12#46157C211yesmaximal, characteristic, complemented
13#46015C211yesmaximal, characteristic, complemented
14#45998C211yesmaximal, characteristic, complemented
15#45172C212yesmaximal, complemented
16#45033C212yesmaximal, complemented
17#44947C212yesmaximal, complemented
18#42738C212yesmaximal, complemented
19#42590C212yesmaximal, complemented
20#42509C212yesmaximal, complemented
21#40149C212yesmaximal, complemented
22#39915C212yesmaximal, complemented
23#39409C212yesmaximal, complemented
24#37157C212yesmaximal, complemented
25#37155C212yesmaximal, complemented
26#37130C212yesmaximal, complemented
27#36464C211yesmaximal, characteristic, complemented
28#36463C211yesmaximal, characteristic, complemented
29#36290C211yesmaximal, characteristic, complemented
30C2×#563C2212yes—
31C2×#539C2214yes—
32#2859C2211yescharacteristic
33#2859C2211yescharacteristic
34#2858C2211yescharacteristic
35#2854C2212yes—
36#2854C2212yes—
37#2854C2212yes—
38#2851C2212yes—
39#2836C2214yes—
40#2831C2214yes—
41#2824C2214yes—
42#2822C2212yes—
43#2820C2212yes—
44#2819C2212yes—
45#2810C2212yes—
46#2808C2212yes—
47#2805C2211yescharacteristic
48#2805C2211yescharacteristic
49#2789C2212yes—
50#2784C2214yes—
51#2784C2214yes—
52#2781C2214yes—
53#2781C2214yes—
54#2778C2214yes—
55#2767C2214yes—
56#2765C2212yes—
57#2765C2212yes—
58#2764C2214yes—
59#2762C2214yes—
60#2756C2214yes—
61#2755C2214yes—
62#2751C2214yes—
63#2750C2214yes—
64#2750C2214yes—
65#2748C2214yes—
66#2748C2214yes—
67#2741C2214yes—
68#2740C2214yes—
69#2740C2214yes—
70#2739C2214yes—
71#2728C2214yes—
72#2727C2212yes—
73#2726C2212yes—
74#2725C2214yes—
75#2724C2211yescharacteristic
76#2723C2214yes—
77#2722C2214yes—
78#2719C2214yes—
79#2717C2212yes—
80#2716C2214yes—
81#2714C2214yes—
82#2711C2214yes—
83#2710C2214yes—
84#2707C2214yes—
85#2707C2214yes—
86#2705C2214yes—
87#2704C2214yes—
88#2703C2214yes—
89#2702C2214yes—
90#2698C2214yes—
91#2696C2214yes—
92#2696C2214yes—
93#2693C2214yes—
94#2693C2214yes—
95#2692C2214yes—
96#2692C2214yes—
97#2691C2214yes—
98#2691C2214yes—
99#2690C2212yes—
100#2690C2212yes—
101#2688C2214yes—
102#2687C2214yes—
103#2687C2214yes—
104#2683C2211yescharacteristic
105#2683C2212yes—
106#2682C2212yes—
107#2681C2214yes—
108#2674C2214yes—
109#2664C2214yes—
110#2653C2214yes—
111#2651C2214yes—
112#2650C2214yes—
113#2647C2212yes—
114#2642C2214yes—
115#2637C2214yes—
116#2636C2214yes—
117#2630C2214yes—
118#2618C2214yes—
119#2603C2214yes—
120#2596C2214yes—
121#2591C2214yes—
122#2580C2212yes—
123#2580C2212yes—
124#2574C2214yes—
125#2574C2214yes—
126#2573C2214yes—
127#2571C2211yescharacteristic
128#2570C2212yes—
129#2570C2212yes—
130#2570C2212yes—
131#2564C2214yes—
132#2564C2214yes—
133#2563C2214yes—
134#2563C2212yes—
135#2563C2211yescharacteristic
136#2560C2214yes—
137#2559C2214yes—
138#2559C2214yes—
139#2558C2214yes—
140#2557C2214yes—
141#2552C2211yescharacteristic
142#2551C2212yes—
143#2543C2214yes—
144#2542C2212yes—
145#2541C2211yescharacteristic
146#2538C2212yes—
147#2538C2212yes—
148#2538C2211yescharacteristic
149#2537C2211yescharacteristic
150#2533C2214yes—
151#2532C2214yes—
152#2519C2214yes—
153#2518C2214yes—
154#2515C2214yes—
155#2513C2212yes—
156#2512C2212yes—
157#2512C2212yes—
158#2512C2212yes—
159#2512C2212yes—
160#2509C2212yes—
161#2509C2212yes—
162#2508C2212yes—
163#2508C2212yes—
164#2507C2212yes—
165#2507C2212yes—
166#2506C2212yes—
167#2506C2212yes—
168#2505C2214yes—
169#2500C2212yes—
170#2500C2212yes—
171#2497C2212yes—
172#2496C2212yes—
173#2495C2212yes—
174#2495C2212yes—
175#2493C2214yes—
176#2492C2214yes—
177#2490C2212yes—
178#2489C2214yes—
179#2488C2214yes—
180#2488C2214yes—
181#2481C2214yes—
182#2481C2214yes—
183#2473C2214yes—
184#2469C2214yes—
185#2468C2214yes—
186#2466C2214yes—
187#2460C2214yes—
188#2460C2214yes—
189#2459C2214yes—
190#2457C2214yes—
191#2456C2214yes—
192#2452C2212yes—
193#2450C2214yes—
194#2450C2214yes—
195#2445C2212yes—
196#2445C2212yes—
197#2442C2212yes—
198#2442C2212yes—
199#2439C2212yes—
200#2439C2212yes—
201#2439C2212yes—
202#2428C2212yes—
203#2428C2212yes—
204#2428C2212yes—
205#2426C2212yes—
206#2422C2212yes—
207#2422C2212yes—
208#2420C2214yes—
209#2420C2212yes—
210#2420C2212yes—
211#2420C2212yes—
212#2417C2214yes—
213#2416C2214yes—
214#2414C2212yes—
215#2401C2212yes—
216#2401C2212yes—
217#2399C2212yes—
218#2382C2212yes—
219#2379C2212yes—
220#2373C2214yes—
221#2369C2211yescharacteristic
222#2366C2212yes—
223#2366C2211yescharacteristic
224#2366C2212yes—
225#2363C2212yes—
226#2363C2212yes—
227#2363C2212yes—
228#2357C2212yes—
229#2355C2212yes—
230#2354C2211yescharacteristic
231#2353C2214yes—
232Q8×C4⋊C4C2211yescharacteristic
233#2349C2212yes—
234#2349C2212yes—
235D4×C4⋊C4C2211yescharacteristic
236D4×C4⋊C4C2212yes—
237D4×C4⋊C4C2211yescharacteristic
238#2347C2212yes—
239#2346C2212yes—
240#2345C2214yes—
241#2332C2214yes—
242#2331C2212yes—
243#2328C2212yes—
244#2325C2214yes—
245#2319C2212yes—
246C4×#125C2211yescharacteristic
247C4×#125C2211yescharacteristic
248C4×#124C2211yescharacteristic
249C4×C22⋊Q8C2212yes—
250C4×C22⋊Q8C2212yes—
251C4×C22⋊Q8C2212yes—
252C4×#123C2212yes—
253C4×#121C2212yes—
254C4×#121C2212yes—
255C4×#121C2212yes—
256C2×#389C2212yes—
257#2285C2212yes—
258C42×D4C2211yescharacteristic
259#563—48no—
260#539—416no—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2314yes—
264C2×#127C2312yes—
265C2×#127C2311yescharacteristic
266C2×#126C2314yes—
267C2×#126C2314yes—
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#125C2311yescharacteristic
272C2×#125C2311yescharacteristic
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2314yes—
276C2×#125C2314yes—
277C2×#125C2312yes—
278C2×#124C2311yescharacteristic
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×#121C2312yes—
296C2×#121C2314yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2314yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×D4C2311yescharacteristic
308C2×C4×D4C2312yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2311yescharacteristic
311C2×C4×D4C2314yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2312yes—
320C2×C4×D4C2314yes—
321C2×#117C2312yes—
322C2×#117C2312yes—
323C22×C4⋊C4C2312yes—
324C22×C4⋊C4C2314yes—
325C22×C4⋊C4C2312yes—
326C22×C42C2312yes—
327C22×C42C2312yes—
328#401C2312yes—
329#401C2312yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2312yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2312yes—
342#400C2314yes—
343#400C2312yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2312yes—
350#400C2312yes—
351#400C2314yes—
352#400C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2312yes—
378#397C2314yes—
379#397C2314yes—
380#397C2312yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2312yes—
388#397C2314yes—
389#397C2312yes—
390#397C2312yes—
391#397C2312yes—
392#397C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2312yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2312yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#395C2312yes—
410#395C2312yes—
411#395C2314yes—
412#395C2314yes—
413#395C2312yes—
414#395C2312yes—
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#394C2314yes—
431#394C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2314yes—
441#392C2314yes—
442#392C2314yes—
443#392C2314yes—
444#392C2314yes—
445#392C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2312yes—
454#391C2312yes—
455#391C2311yescharacteristic
456#390C2314yes—
457#390C2312yes—
458#390C2312yes—
459#390C2314yes—
460#390C2314yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2312yes—
465#390C2312yes—
466#390C2311yescharacteristic
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2314yes—
474#390C2314yes—
475#390C2314yes—
476#390C2312yes—
477#389C2311yescharacteristic
478#389C2311yescharacteristic
479#389C2311yescharacteristic
480#389C2311yescharacteristic
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2312yes—
493#389C2314yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#388C2312yes—
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#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2312yes—
543#388C2312yes—
544#388C2312yes—
545#388C2314yes—
546#387C2314yes—
547#387C2312yes—
548#387C2312yes—
549#387C2312yes—
550#387C2312yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2312yes—
561#387C2312yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2312yes—
568#387C2314yes—
569#387C2314yes—
570#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2312yes—
578#387C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2312yes—
601#386C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2312yes—
612#385C2314yes—
613#385C2312yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2312yes—
618#385C2314yes—
619#385C2314yes—
620#385C2312yes—
621#385C2312yes—
622#384C2311yescharacteristic
623#384C2311yescharacteristic
624#384C2312yes—
625#384C2311yescharacteristic
626#384C2311yescharacteristic
627#384C2312yes—
628#384C2312yes—
629#383C2314yes—
630#383C2314yes—
631#382C2311yescharacteristic
632#382C2311yescharacteristic
633#382C2312yes—
634#382C2312yes—
635#382C2314yes—
636#382C2314yes—
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#382C2312yes—
642#382C2312yes—
643#382C2314yes—
644#382C2311yescharacteristic
645#381C2314yes—
646#381C2314yes—
647#381C2314yes—
648#381C2314yes—
649#381C2312yes—
650#380C2312yes—
651#380C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2312yes—
655#380C2312yes—
656#380C2314yes—
657#380C2314yes—
658#380C2312yes—
659#380C2314yes—
660#380C2314yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2314yes—
666#380C2314yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709#376C2312yes—
710#376C2314yes—
711C2×#95C2314yes—
712C2×#95C2314yes—
713C43C2311yescharacteristic
714C22×Q8C2411yescharacteristic
715C22×Q8C2412yes—
716C22×Q8C2414yes—
717C22×Q8C2412yes—
718C22×D4C2412yes—
719C22×D4C2411yescharacteristic
720C22×D4C2414yes—
721C22×D4C2412yes—
722C22×D4C2414yes—
723C22×D4C2411yescharacteristic
724C22×D4C2414yes—
725C22×D4C2414yes—
726C22×D4C2414yes—
727C22×D4C2412yes—
728C23×C4C2412yes—
729C23×C4C2412yes—
730C23×C4C2414yes—
731C23×C4C2412yes—
732C23×C4C2412yes—
733C23×C4C2412yes—
734C23×C4C2414yes—
735C23×C4C2414yes—
736C23×C4C2414yes—
737C23×C4C2412yes—
738C23×C4C2414yes—
739C4⋊Q8—44no—
740C4⋊Q8—42no—
741C4⋊Q8—48no—
742#127—28no—
743#127—42no—
744#126—216no—
745#126—48no—
746#126—48no—
747#126—84no—
748#126—84no—
749#125—24no—
750#125—44no—
751#125—42no—
752#125—48no—
753#125—44no—
754#125—48no—
755#125—82no—
756#124—44no—
757#124—44no—
758#124—42no—
759#123—48no—
760#123—48no—
761#123—48no—
762#123—48no—
763#123—48no—
764#123—44no—
765C22⋊Q8—28no—
766C22⋊Q8—48no—
767C22⋊Q8—44no—
768C22⋊Q8—48no—
769C22⋊Q8—48no—
770C22⋊Q8—48no—
771C22⋊Q8—44no—
772C22⋊Q8—48no—
773#121—28no—
774#121—48no—
775#121—48no—
776#121—44no—
777#121—44no—
778#121—44no—
779#121—82no—
780#121—84no—
781#121—82no—
782C4×Q8—44no—
783C4×Q8—42no—
784C4×Q8—82no—
785C4×D4—24no—
786C4×D4—44no—
787C4×D4—44no—
788C4×D4—42no—
789C4×D4—44no—
790C4×D4—44no—
791C4×D4—44no—
792C4×D4—42no—
793C4×D4—42no—
794C4×D4—48no—
795C4×D4—48no—
796C4×D4—48no—
797C4×D4—82no—
798C4×D4—84no—
799#117—44no—
800#117—44no—
801C2×C4⋊C4—28no—
802C2×C4⋊C4—48no—
803C2×C4⋊C4—82no—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C42—44no—
918C2×C42—82no—
919C2×C42C2411yescharacteristic
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2414yes—
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928C2×C42C2411yescharacteristic
929C2×C42C2411yescharacteristic
930C2×C42C2412yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2412yes—
937C2×C42C2414yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2411yescharacteristic
941C2×C42C2412yes—
942C2×C42C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010C24C2514yes—
1011C24C2512yes—
1012C24C2512yes—
1013C2×Q8—24no—
1014C2×Q8—22no—
1015C2×Q8—41no—
1016C2×Q8—41no—
1017C2×Q8—42no—
1018C2×Q8—42no—
1019C2×Q8—44no—
1020C2×Q8—44no—
1021C2×Q8—42no—
1022C2×Q8—42no—
1023C2×Q8—44no—
1024C2×Q8—42no—
1025C2×D4—28no—
1026C2×D4—28no—
1027C2×D4—28no—
1028C2×D4—24no—
1029C2×D4—22no—
1030C2×D4—22no—
1031C2×D4—24no—
1032C2×D4—24no—
1033C2×D4—24no—
1034C2×D4—22no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—41no—
1038C2×D4—44no—
1039C2×D4—42no—
1040C2×D4—44no—
1041C2×D4—44no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C2×D4—41no—
1045C2×D4—44no—
1046C2×D4—44no—
1047C2×D4—42no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—44no—
1051C2×D4—42no—
1052C2×D4—42no—
1053C2×D4—42no—
1054C2×D42−1+414yes—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—28no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—42no—
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×C4—44no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2511yescharacteristic
1093C22×C4C2511yescharacteristic
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2514yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2514yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2514yes—
1103C22×C4C2514yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2514yes—
1107C22×C4C2512yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2512yes—
1110C22×C4C2511yescharacteristic
1111C22×C4C2511yescharacteristic
1112C22×C4C2511yescharacteristic
1113C22×C4C2511yescharacteristic
1114C4⋊C4—28no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—22no—
1119C4⋊C4—24no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—22no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—22no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—22no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—22no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—22no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—41no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—41no—
1144C4⋊C4—44no—
1145C4⋊C4—41no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—41no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—41no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—41no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4H(5,𝔽2)14yes—
1180C22⋊C4—24no—
1181C22⋊C4—28no—
1182C22⋊C4—28no—
1183C22⋊C4—24no—
1184C22⋊C4—28no—
1185C22⋊C4—24no—
1186C22⋊C4—28no—
1187C22⋊C4—28no—
1188C22⋊C4—24no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—42no—
1194C22⋊C4—42no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
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—42no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—42no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—42no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—44no—
1227C42—28no—
1228C42—22no—
1229C42—22no—
1230C42—24no—
1231C42—24no—
1232C42—24no—
1233C42—22no—
1234C42—24no—
1235C42—24no—
1236C42—22no—
1237C42—22no—
1238C42—22no—
1239C42—42no—
1240C42—42no—
1241C42—41no—
1242C42—42no—
1243C42—42no—
1244C42—42no—
1245C42—44no—
1246C42—44no—
1247C42—44no—
1248C42—44no—
1249C42—44no—
1250C42—44no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23—24no—
1258C23—22no—
1259C23—22no—
1260C23—24no—
1261C23—24no—
1262C23—22no—
1263C23—22no—
1264C23—22no—
1265C23—24no—
1266C23—24no—
1267C23—24no—
1268C23—22no—
1269C23—24no—
1270C23—22no—
1271C23C2×2−1+414yes—
1272C23C2611yescharacteristic
1273Q8—44no—
1274Q8—84no—
1275Q8—164no—
1276Q8—162no—
1277D4—28no—
1278D4—48no—
1279D4—82no—
1280D4—84no—
1281D4—88no—
1282D4—88no—
1283D4—88no—
1284D4—88no—
1285D4—164no—
1286D4—162no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—22no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
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—84no—
1363C2×C4—84no—
1364C2×C4—84no—
1365C2×C4—164no—
1366C2×C4—164no—
1367C2×C4—164no—
1368C2×C4—164no—
1369C2×C4C2×H(5,𝔽2)14yes—
1370C2×C4C2×H(5,𝔽2)12yes—
1371C2×C4C2×2−1+412yes—
1372C2×C4#58512yes—
1373C2×C4#58512yes—
1374C2×C4#58512yes—
1375C2×C4#58512yes—
1376C22—24no—
1377C22—24no—
1378C22—24no—
1379C22—42no—
1380C22—42no—
1381C22—42no—
1382C22—42no—
1383C22—42no—
1384C22—44no—
1385C22—42no—
1386C22—44no—
1387C22—44no—
1388C22—42no—
1389C22—44no—
1390C22—42no—
1391C22—42no—
1392C22—44no—
1393C22—42no—
1394C22—44no—
1395C22—44no—
1396C22—42no—
1397C22C22×H(5,𝔽2)11yescharacteristic
1398C22C22×2−1+411yescharacteristic
1399C22C2×#58511yescharacteristic
1400C22C2×#58511yescharacteristic
1401C22C2×#58511yescharacteristic
1402C22C2×#58511yescharacteristic
1403C22H(7,𝔽2)11yescharacteristic
1404C4—24no—
1405C4—22no—
1406C4—22no—
1407C4—22no—
1408C4—42no—
1409C4—41no—
1410C4—44no—
1411C4—42no—
1412C4—42no—
1413C4—41no—
1414C4—42no—
1415C4—42no—
1416C4—44no—
1417C4—41no—
1418C4—44no—
1419C4—42no—
1420C4—42no—
1421C4—42no—
1422C4—42no—
1423C4—42no—
1424C4—44no—
1425C4—42no—
1426C4—42no—
1427C4—42no—
1428C4—44no—
1429C4#355314yes—
1430C2—44no—
1431C2—82no—
1432C2—84no—
1433C2C2×#355311yescharacteristic
1434C2#6290811yescharacteristic
1435C2#6294411yescharacteristic
1436C2#6296511yescharacteristic
1437C2#6302411yescharacteristic
1438C2#6302511yescharacteristic
1439C2#6303511yescharacteristic
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. #59873C2semidirect
2. #59403C2semidirect
3. #59331C2semidirect
4. #59230C2semidirect
5. #57374C2semidirect
6. #57174C2semidirect
7. #55833C2semidirect
8. #52304C2semidirect
9. #51016C2semidirect
10. #50871C2semidirect
11. #49210C2semidirect
12. #46157C2semidirect
13. #46015C2semidirect
14. #45998C2semidirect
15. #45172C2semidirect
16. #45033C2semidirect
17. #44947C2semidirect
18. #42738C2semidirect
19. #42590C2semidirect
20. #42509C2semidirect
21. #40149C2semidirect
22. #39915C2semidirect
23. #39409C2semidirect
24. #37157C2semidirect
25. #37155C2semidirect
26. #37130C2semidirect
27. #36464C2semidirect
28. #36463C2semidirect
29. #36290C2semidirect

Maximal subgroups

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

subgroupindex
#598732
#594032
#593312
#592302
#573742
#571742
#558332
#523042
#510162
#508712
#492102
#461572
#460152
#459982
#451722
#450332
#449472
#427382
#425902
#425092
#401492
#399152
#394092
#371572
#371552
#371302
#364642
#364632
#362902