Finite Group Databasebeta

← #8095662

Subgroups — #8095662

Order 512.

3851 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53157C211yesmaximal, characteristic, complemented
2#53150C211yesmaximal, characteristic, complemented
3#53139C212yesmaximal, complemented
4#53077C211yesmaximal, characteristic, complemented
5#53075C211yesmaximal, characteristic, complemented
6#53054C212yesmaximal
7#52793C214yesmaximal, complemented
8#52786C214yesmaximal, complemented
9#52654C214yesmaximal
10#52627C214yesmaximal, complemented
11#46207C214yesmaximal, complemented
12#46204C214yesmaximal, complemented
13#46051C212yesmaximal, complemented
14#46011C212yesmaximal, complemented
15#45883C214yesmaximal, complemented
16#45879C214yesmaximal, complemented
17#45627C212yesmaximal, complemented
18#45525C212yesmaximal, complemented
19#35655C212yesmaximal, complemented
20#35646C212yesmaximal, complemented
21#35582C212yesmaximal, complemented
22#35323C211yesmaximal, characteristic, complemented
23#35283C211yesmaximal, characteristic, complemented
24#35213C212yesmaximal, complemented
25#35163C212yesmaximal, complemented
26#34879C211yesmaximal, characteristic
27#34803C212yesmaximal, complemented
28#2868C2211yescharacteristic
29#2866C2214yes—
30#2864C2214yes—
31#2863C2214yes—
32#2863C2214yes—
33#2863C2212yes—
34#2862C2211yescharacteristic
35#2857C2212yes—
36#2857C2211yescharacteristic
37#2851C2211yescharacteristic
38#2839C2214yes—
39#2839C2214yes—
40#2839C2214yes—
41#2838C2214yes—
42#2838C2214yes—
43#2838C2214yes—
44#2837C2214yes—
45#2837C2214yes—
46#2836C2214yes—
47#2836C2214yes—
48#2833C2214yes—
49#2833C2214yes—
50#2833C2214yes—
51#2832C2214yes—
52#2832C2214yes—
53#2831C2214yes—
54#2831C2214yes—
55#2829C2214yes—
56#2821C2214yes—
57#2814C2214yes—
58#2808C2214yes—
59#2802C2214yes—
60#2802C2214yes—
61#2799C2214yes—
62#2799C2214yes—
63#2798C2214yes—
64#2798C2214yes—
65#2798C2214yes—
66#2794C2214yes—
67#2793C2214yes—
68#2791C2214yes—
69#2789C2214yes—
70#2783C2214yes—
71#2777C2214yes—
72#2777C2214yes—
73#2776C2214yes—
74#2775C2214yes—
75#2774C2214yes—
76#2772C2214yes—
77#2769C2214yes—
78#2767C2214yes—
79#2767C2214yes—
80#2762C2214yes—
81#2759C2214yes—
82#2759C2214yes—
83#2758C2214yes—
84#2758C2214yes—
85#2755C2214yes—
86#2755C2214yes—
87#2747C2214yes—
88#2745C2214yes—
89#2741C2214yes—
90#2729C2214yes—
91#2723C2214yes—
92#2721C2214yes—
93#2716C2214yes—
94#2716C2214yes—
95#2716C2214yes—
96#2713C2214yes—
97#2707C2214yes—
98#2667C2214yes—
99#2665C2214yes—
100#2652C2214yes—
101#2649C2214yes—
102#2647C2211yescharacteristic
103#2647C2211yescharacteristic
104#2647C2211yescharacteristic
105#2642C2211yescharacteristic
106#2628C2212yes—
107#2625C2212yes—
108#2612C2214yes—
109#2612C2214yes—
110#2612C2214yes—
111#2608C2214yes—
112#2607C2214yes—
113#2606C2214yes—
114#2605C2214yes—
115#2595C2214yes—
116#2590C2214yes—
117#2590C2214yes—
118#2589C2214yes—
119#2586C2214yes—
120#2584C2212yes—
121#2582C2212yes—
122#2577C2214yes—
123#2577C2214yes—
124#2574C2212yes—
125#2574C2214yes—
126#2573C2212yes—
127#2572C2212yes—
128#2570C2212yes—
129#2570C2212yes—
130#2570C2212yes—
131#2568C2212yes—
132#2565C2212yes—
133#2563C2212yes—
134#2553C2212yes—
135#2551C2212yes—
136#2550C2214yes—
137#2550C2212yes—
138#2550C2212yes—
139#2536C2212yes—
140#2533C2214yes—
141#2533C2214yes—
142#2533C2214yes—
143#2532C2214yes—
144#2532C2214yes—
145#2530C2214yes—
146#2529C2214yes—
147#2528C2214yes—
148#2528C2214yes—
149#2527C2214yes—
150#2527C2214yes—
151#2527C2214yes—
152#2524C2214yes—
153#2524C2214yes—
154#2524C2212yes—
155#2523C2214yes—
156#2520C2214yes—
157#2518C2214yes—
158#2517C2214yes—
159#2516C2214yes—
160#2515C2214yes—
161#2515C2212yes—
162#2514C2214yes—
163#2514C2212yes—
164#2514C2212yes—
165#2511C2214yes—
166#2511C2212yes—
167#2509C2212yes—
168#2509C2212yes—
169#2508C2212yes—
170#2508C2212yes—
171#2506C2212yes—
172#2499C2212yes—
173#2499C2212yes—
174#2497C2212yes—
175#2496C2212yes—
176#2495C2212yes—
177#2494C2212yes—
178#2494C2212yes—
179#2492C2214yes—
180#2492C2212yes—
181#2492C2212yes—
182#2489C2212yes—
183#2485C2212yes—
184#2485C2212yes—
185#2468C2212yes—
186#2466C2214yes—
187#2462C2214yes—
188#2457C2212yes—
189#2451C2212yes—
190#2451C2212yes—
191#2451C2214yes—
192#2451C2212yes—
193#2446C2212yes—
194#2446C2214yes—
195#2441C2212yes—
196#2441C2212yes—
197#2441C2212yes—
198#2439C2212yes—
199#2439C2212yes—
200#2439C2212yes—
201#2429C2212yes—
202#2423C2212yes—
203#2423C2214yes—
204#2421C2212yes—
205#2421C2212yes—
206#2415C2212yes—
207#2415C2212yes—
208#2402C2211yescharacteristic
209#2401C2214yes—
210#2398C2211yescharacteristic
211#2398C2214yes—
212#2396C2211yescharacteristic
213#2392C2211yescharacteristic
214#2382C2214yes—
215#2381C2214yes—
216#2381C2214yes—
217#2378C2214yes—
218#2331C2212yes—
219#2331C2212yes—
220#2330C2212yes—
221#2330C2211yescharacteristic
222#2327C2211yescharacteristic
223#2323C2212yes—
224#2320C2212yes—
225#2314C2211yescharacteristic
226#2314C2211yescharacteristic
227C4×C4⋊Q8C2212yes—
228C4×#126C2214yes—
229C4×#126C2212yes—
230C4×C22⋊Q8C2212yes—
231C4×C22⋊Q8C2212yes—
232C4×#123C2212yes—
233#2295C2211yescharacteristic
234#2295C2214yes—
235#2295C2212yes—
236#2290C2212yes—
237#2283C2212yes—
238#2283C2212yes—
239#2276C2212yes—
240C42×D4C2211yescharacteristic
241C4×#117C2211yescharacteristic
242C4×#117C2212yes—
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2314yes—
246C2×C4⋊Q8C2311yescharacteristic
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2314yes—
249C2×#126C2312yes—
250C2×#126C2314yes—
251C2×#125C2312yes—
252C2×#125C2311yescharacteristic
253C2×#125C2314yes—
254C2×#123C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2314yes—
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×D4C2312yes—
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2312yes—
267C2×#117C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C2×#117C2312yes—
270C2×#117C2312yes—
271C22×C42C2312yes—
272C22×C42C2311yescharacteristic
273#401C2314yes—
274#401C2314yes—
275#401C2314yes—
276#401C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2312yes—
284#400C2311yescharacteristic
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2312yes—
308#400C2314yes—
309#400C2314yes—
310#400C2312yes—
311#400C2314yes—
312#400C2314yes—
313#399C2314yes—
314#399C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2311yescharacteristic
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2312yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2312yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2312yes—
346#398C2311yescharacteristic
347#397C2314yes—
348#397C2314yes—
349#397C2312yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2311yescharacteristic
365#397C2314yes—
366#396C2312yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2312yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2311yescharacteristic
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#394C2312yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2311yescharacteristic
393#394C2312yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2311yescharacteristic
399#393C2312yes—
400#393C2314yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#392C2311yescharacteristic
405#391C2314yes—
406#391C2312yes—
407#391C2312yes—
408#391C2314yes—
409#391C2312yes—
410#391C2314yes—
411#391C2312yes—
412#391C2312yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2312yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2312yes—
422#391C2312yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2312yes—
435#390C2314yes—
436#389C2312yes—
437#389C2312yes—
438#389C2314yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#388C2312yes—
475#388C2312yes—
476#388C2312yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2312yes—
483#388C2312yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2312yes—
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#388C2314yes—
501#388C2312yes—
502#387C2312yes—
503#387C2312yes—
504#387C2314yes—
505#387C2314yes—
506#387C2312yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2312yes—
519#387C2312yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2312yes—
525#387C2312yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2312yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#386C2312yes—
575#386C2312yes—
576#386C2312yes—
577#385C2312yes—
578#385C2314yes—
579#385C2312yes—
580#385C2314yes—
581#385C2314yes—
582#385C2312yes—
583#384C2312yes—
584#384C2311yescharacteristic
585#384C2311yescharacteristic
586#384C2311yescharacteristic
587#384C2312yes—
588#384C2314yes—
589#383C2312yes—
590#383C2314yes—
591#383C2314yes—
592#383C2312yes—
593#383C2312yes—
594#383C2314yes—
595#383C2314yes—
596#383C2314yes—
597#383C2314yes—
598#382C2314yes—
599#382C2312yes—
600#382C2311yescharacteristic
601#382C2312yes—
602#382C2311yescharacteristic
603#382C2312yes—
604#382C2312yes—
605#382C2314yes—
606#382C2312yes—
607#382C2311yescharacteristic
608#382C2314yes—
609#382C2314yes—
610#382C2312yes—
611#382C2314yes—
612#381C2312yes—
613#381C2312yes—
614#381C2312yes—
615#381C2314yes—
616#380C2312yes—
617#380C2312yes—
618#380C2312yes—
619#380C2312yes—
620#380C2312yes—
621#380C2312yes—
622#380C2312yes—
623#380C2314yes—
624#380C2314yes—
625#380C2312yes—
626#380C2312yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2311yescharacteristic
645C4×C4⋊C4C2311yescharacteristic
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C22⋊C4C2312yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2312yes—
653C4×C22⋊C4C2312yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664#376C2312yes—
665#376C2311yescharacteristic
666#376C2314yes—
667#376C2314yes—
668#376C2314yes—
669#376C2314yes—
670#376C2311yescharacteristic
671C43C2311yescharacteristic
672C43C2314yes—
673C43C2311yescharacteristic
674C22×Q8C2412yes—
675C22×Q8C2414yes—
676C22×Q8C2411yescharacteristic
677C22×Q8C2414yes—
678C22×Q8C2414yes—
679C22×D4C2411yescharacteristic
680C22×D4C2412yes—
681C23×C4C2412yes—
682C23×C4C2411yescharacteristic
683C23×C4C2412yes—
684C23×C4C2412yes—
685C23×C4C2412yes—
686C4⋊Q8—44no—
687C4⋊Q8—44no—
688C4⋊Q8—44no—
689C4⋊Q8—48no—
690C4⋊Q8—42no—
691C4⋊Q8—48no—
692#126—44no—
693#126—48no—
694#125—42no—
695#125—44no—
696#125—48no—
697#123—44no—
698C22⋊Q8—44no—
699C22⋊Q8—44no—
700C22⋊Q8—44no—
701C22⋊Q8—48no—
702C4×Q8—28no—
703C4×Q8—42no—
704C4×Q8—48no—
705C4×Q8—44no—
706C4×Q8—44no—
707C4×D4—44no—
708C4×D4—42no—
709C4×D4—44no—
710#117—24no—
711#117—42no—
712#117—44no—
713#117—44no—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2411yescharacteristic
778C2×C22⋊C4C2411yescharacteristic
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2414yes—
802C2×C42—28no—
803C2×C42—42no—
804C2×C42C2411yescharacteristic
805C2×C42C2411yescharacteristic
806C2×C42C2411yescharacteristic
807C2×C42C2412yes—
808C2×C42C2412yes—
809C2×C42C2412yes—
810C2×C42C2414yes—
811C2×C42C2411yescharacteristic
812C2×C42C2412yes—
813C2×C42C2411yescharacteristic
814C2×C42C2412yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2414yes—
827C2×C42C2412yes—
828C2×C42C2414yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2411yescharacteristic
832#95C2412yes—
833#95C2412yes—
834#95C2412yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2412yes—
839#95C2412yes—
840#95C2414yes—
841#95C2412yes—
842#95C2412yes—
843#95C2412yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2412yes—
856#95C2411yescharacteristic
857#95C2412yes—
858#95C2411yescharacteristic
859#95C2412yes—
860#95C2414yes—
861#95C2412yes—
862#95C2414yes—
863#95C2412yes—
864#95C2412yes—
865#95C2412yes—
866#95C2414yes—
867#95C2414yes—
868#95C2412yes—
869#95C2412yes—
870#95C2412yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2412yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2414yes—
883#95C2412yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2412yes—
888#95C2411yescharacteristic
889#95C2411yescharacteristic
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919C24C2511yescharacteristic
920C24C2512yes—
921C2×Q8—24no—
922C2×Q8—24no—
923C2×Q8—24no—
924C2×Q8—28no—
925C2×Q8—41no—
926C2×Q8—44no—
927C2×Q8—44no—
928C2×Q8—42no—
929C2×Q8—44no—
930C2×Q8—44no—
931C2×Q8—44no—
932C2×Q8—44no—
933C2×Q8—44no—
934C2×Q8—44no—
935C2×D4—41no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C22×C4—24no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—24no—
944C22×C4—24no—
945C22×C4—22no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—24no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4C2512yes—
956C22×C4C2511yescharacteristic
957C22×C4C2512yes—
958C22×C4C2512yes—
959C22×C4C2512yes—
960C22×C4C2514yes—
961C22×C4C2514yes—
962C22×C4C2512yes—
963C22×C4C2511yescharacteristic
964C22×C4C2512yes—
965C22×C4C2514yes—
966C22×C4C2511yescharacteristic
967C22×C4C2511yescharacteristic
968C22×C4C2514yes—
969C22×C4C2514yes—
970C22×C4C2514yes—
971C22×C4C2512yes—
972C22×C4C2512yes—
973C22×C4C2514yes—
974C22×C4C2514yes—
975C22×C4C2511yescharacteristic
976C22×C4C2512yes—
977C22×C4C2512yes—
978C22×C4C2512yes—
979C22×C4C2511yescharacteristic
980C4⋊C4—24no—
981C4⋊C4—24no—
982C4⋊C4—28no—
983C4⋊C4—24no—
984C4⋊C4—24no—
985C4⋊C4—24no—
986C4⋊C4—24no—
987C4⋊C4—24no—
988C4⋊C4—28no—
989C4⋊C4—24no—
990C4⋊C4—28no—
991C4⋊C4—24no—
992C4⋊C4—28no—
993C4⋊C4—24no—
994C4⋊C4—42no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—42no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—41no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—42no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C22⋊C4—24no—
1041C22⋊C4—24no—
1042C22⋊C4—24no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—44no—
1046C22⋊C4—42no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—42no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C42—24no—
1069C42—24no—
1070C42—24no—
1071C42—22no—
1072C42—28no—
1073C42—22no—
1074C42—22no—
1075C42—22no—
1076C42—22no—
1077C42—24no—
1078C42—24no—
1079C42—24no—
1080C42—24no—
1081C42—42no—
1082C42—42no—
1083C42—44no—
1084C42—42no—
1085C42—44no—
1086C42—44no—
1087C42—44no—
1088C42—44no—
1089C42—44no—
1090C42—44no—
1091C42—44no—
1092C42—44no—
1093C42—44no—
1094C42—44no—
1095C422−1+414yes—
1096C23—21no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—21no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—21no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23C2611yescharacteristic
1109Q8—48no—
1110Q8—88no—
1111Q8—82no—
1112Q8—164no—
1113Q8—164no—
1114D4—44no—
1115D4—84no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—21no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—24no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—24no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—48no—
1183C2×C4—44no—
1184C2×C4—84no—
1185C2×C4—84no—
1186C2×C4—84no—
1187C2×C4C2×2−1+414yes—
1188C2×C4C2×2−1+412yes—
1189C2×C4#58514yes—
1190C2×C4#58512yes—
1191C2×C4#58512yes—
1192C22—42no—
1193C22—41no—
1194C22—41no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—41no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22C22×2−1+411yescharacteristic
1205C22C2×#58511yescharacteristic
1206C22C2×#58512yes—
1207C22C2×#58511yescharacteristic
1208C222−1+612yes—
1209C4—24no—
1210C4—24no—
1211C4—42no—
1212C4—41no—
1213C4—44no—
1214C4—44no—
1215C4—41no—
1216C4—41no—
1217C4—44no—
1218C4—42no—
1219C4—41no—
1220C4—42no—
1221C4—42no—
1222C4—44no—
1223C4—44no—
1224C4—44no—
1225C4—42no—
1226C4—42no—
1227C4—41no—
1228C4—44no—
1229C4—42no—
1230C4—44no—
1231C4—42no—
1232C4—42no—
1233C4#353114yes—
1234C2—82no—
1235C2—81no—
1236C2C2×#353111yescharacteristic
1237C2#6283911yescharacteristic
1238C2#6289011yescharacteristic
1239C2#6294012yes—
1240C2#6295912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#392C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53157C2semidirect
2. #53150C2semidirect
3. #53139C2semidirect
4. #53077C2semidirect
5. #53075C2semidirect
7. #52793C2semidirect
8. #52786C2semidirect
10. #52627C2semidirect
11. #46207C2semidirect
12. #46204C2semidirect
13. #46051C2semidirect
14. #46011C2semidirect
15. #45883C2semidirect
16. #45879C2semidirect
17. #45627C2semidirect
18. #45525C2semidirect
19. #35655C2semidirect
20. #35646C2semidirect
21. #35582C2semidirect
22. #35323C2semidirect
23. #35283C2semidirect
24. #35213C2semidirect
25. #35163C2semidirect
27. #34803C2semidirect

Maximal subgroups

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

subgroupindex
#531572
#531502
#531392
#530772
#530752
#530542
#527932
#527862
#526542
#526272
#462072
#462042
#460512
#460112
#458832
#458792
#456272
#455252
#356552
#356462
#355822
#353232
#352832
#352132
#351632
#348792
#348032