Finite Group Databasebeta

← #8757171

Subgroups — #8757171

Order 512.

4192 conjugacy classes of subgroups.

The subgroup lattice has 1113 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58743C214yesmaximal, complemented
2#58690C214yesmaximal, complemented
3#57433C214yesmaximal, complemented
4#55753C214yesmaximal, complemented
5#55548C214yesmaximal, complemented
6#54196C214yesmaximal, complemented
7#50705C214yesmaximal, complemented
8#49702C214yesmaximal, complemented
9#48188C214yesmaximal, complemented
10#47022C214yesmaximal, complemented
11#46800C214yesmaximal, complemented
12#46663C214yesmaximal, complemented
13#46229C211yesmaximal, characteristic, complemented
14#46226C211yesmaximal, characteristic
15#46150C212yesmaximal, complemented
16#46149C212yesmaximal, complemented
17#46023C212yesmaximal, complemented
18#46022C212yesmaximal, complemented
19#45979C212yesmaximal, complemented
20#35335C211yesmaximal, characteristic, complemented
21#35137C212yesmaximal, complemented
22C2×#564C2211yescharacteristic
23C2×#563C2212yes—
24C2×#562C2211yescharacteristic
25C2×#533C2211yescharacteristic
26C22×#125C2211yescharacteristic
27#2862C2212yes—
28#2861C2212yes—
29#2859C2212yes—
30#2859C2212yes—
31#2851C2212yes—
32#2850C2212yes—
33#2841C2214yes—
34#2838C2214yes—
35#2837C2214yes—
36#2834C2214yes—
37#2833C2214yes—
38#2831C2214yes—
39#2822C2212yes—
40#2822C2212yes—
41#2820C2212yes—
42#2820C2212yes—
43#2817C2214yes—
44#2811C2214yes—
45#2809C2214yes—
46#2808C2214yes—
47#2806C2214yes—
48#2805C2214yes—
49#2800C2214yes—
50#2796C2214yes—
51#2793C2214yes—
52#2792C2214yes—
53#2788C2214yes—
54#2788C2214yes—
55#2788C2214yes—
56#2786C2214yes—
57#2783C2214yes—
58#2781C2214yes—
59#2778C2214yes—
60#2776C2214yes—
61#2776C2214yes—
62#2774C2214yes—
63#2772C2214yes—
64#2772C2214yes—
65#2766C2214yes—
66#2766C2214yes—
67#2764C2214yes—
68#2763C2214yes—
69#2762C2214yes—
70#2762C2214yes—
71#2759C2214yes—
72#2759C2214yes—
73#2757C2214yes—
74#2755C2214yes—
75#2755C2214yes—
76#2754C2214yes—
77#2754C2214yes—
78#2729C2214yes—
79#2728C2214yes—
80#2725C2214yes—
81#2725C2214yes—
82#2721C2214yes—
83#2721C2214yes—
84#2720C2214yes—
85#2720C2214yes—
86#2720C2214yes—
87#2718C2214yes—
88#2717C2214yes—
89#2713C2214yes—
90#2713C2214yes—
91#2713C2214yes—
92#2712C2214yes—
93#2707C2214yes—
94#2704C2214yes—
95#2704C2214yes—
96#2704C2214yes—
97#2704C2214yes—
98#2701C2214yes—
99#2700C2214yes—
100#2694C2214yes—
101#2692C2214yes—
102#2690C2214yes—
103#2690C2214yes—
104#2689C2214yes—
105#2687C2214yes—
106#2683C2214yes—
107#2683C2214yes—
108#2681C2214yes—
109#2680C2214yes—
110#2676C2214yes—
111#2674C2214yes—
112#2666C2214yes—
113#2666C2214yes—
114#2660C2212yes—
115#2660C2212yes—
116#2653C2214yes—
117#2653C2214yes—
118#2652C2214yes—
119#2650C2214yes—
120#2632C2214yes—
121#2630C2214yes—
122#2598C2214yes—
123#2589C2214yes—
124#2587C2214yes—
125#2586C2214yes—
126#2584C2214yes—
127#2584C2214yes—
128#2583C2214yes—
129#2583C2214yes—
130#2582C2214yes—
131#2581C2214yes—
132#2576C2214yes—
133#2573C2214yes—
134#2565C2214yes—
135#2559C2214yes—
136#2558C2214yes—
137#2558C2214yes—
138#2556C2214yes—
139#2553C2214yes—
140#2550C2214yes—
141#2550C2214yes—
142#2549C2214yes—
143#2549C2214yes—
144#2532C2214yes—
145#2527C2214yes—
146#2519C2214yes—
147#2519C2214yes—
148#2514C2214yes—
149#2514C2212yes—
150#2513C2212yes—
151#2511C2214yes—
152#2499C2214yes—
153#2492C2212yes—
154#2491C2212yes—
155#2489C2214yes—
156#2488C2214yes—
157#2481C2214yes—
158#2481C2214yes—
159#2477C2214yes—
160#2475C2214yes—
161#2474C2214yes—
162#2474C2214yes—
163#2471C2214yes—
164#2465C2214yes—
165#2465C2214yes—
166#2465C2214yes—
167#2465C2214yes—
168#2462C2214yes—
169#2453C2214yes—
170#2453C2214yes—
171#2452C2212yes—
172#2451C2212yes—
173#2450C2214yes—
174#2449C2214yes—
175#2446C2214yes—
176#2443C2214yes—
177#2440C2214yes—
178#2439C2214yes—
179#2438C2214yes—
180#2429C2214yes—
181#2429C2214yes—
182#2426C2214yes—
183#2425C2214yes—
184#2423C2214yes—
185#2421C2212yes—
186#2420C2212yes—
187#2417C2214yes—
188#2415C2214yes—
189#2382C2211yescharacteristic
190#2382C2211yescharacteristic
191#2382C2212yes—
192#2379C2214yes—
193#2367C2214yes—
194#2337C2214yes—
195#2332C2214yes—
196#2329C2214yes—
197#2323C2214yes—
198#2317C2212yes—
199#2317C2212yes—
200C4×#125C2212yes—
201C4×#124C2212yes—
202C4×#117C2211yescharacteristic
203#564—44no—
204#563—48no—
205#562—44no—
206#533—44no—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×#126C2314yes—
212C2×#126C2314yes—
213C2×#125—44no—
214C2×#125C2312yes—
215C2×#125C2311yescharacteristic
216C2×#125C2312yes—
217C2×#125C2311yescharacteristic
218C2×#125C2314yes—
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×#125C2314yes—
224C2×#125C2314yes—
225C2×#124C2312yes—
226C2×#124C2314yes—
227C2×#124C2314yes—
228C2×#123C2314yes—
229C2×#123C2314yes—
230C2×#123C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×#121C2314yes—
243C2×#121C2312yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2312yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2312yes—
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2312yes—
253C2×#117C2314yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2314yes—
256C22×C42C2311yescharacteristic
257#401C2314yes—
258#401C2314yes—
259#401C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#399C2314yes—
281#399C2314yes—
282#399C2314yes—
283#399C2314yes—
284#399C2314yes—
285#398C2314yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#397C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#397C2314yes—
318#397C2314yes—
319#397C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#396C2314yes—
329#396C2314yes—
330#396C2314yes—
331#396C2314yes—
332#396C2314yes—
333#396C2314yes—
334#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#396C2314yes—
342#396C2314yes—
343#395C2314yes—
344#395C2314yes—
345#395C2314yes—
346#395C2314yes—
347#395C2314yes—
348#395C2314yes—
349#395C2314yes—
350#395C2314yes—
351#395C2314yes—
352#395C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#393C2314yes—
370#393C2314yes—
371#393C2314yes—
372#393C2314yes—
373#393C2314yes—
374#393C2314yes—
375#393C2314yes—
376#392C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2312yes—
391#391C2312yes—
392#391C2312yes—
393#391C2314yes—
394#391C2314yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2312yes—
401#390C2312yes—
402#390C2312yes—
403#390C2312yes—
404#390C2314yes—
405#390C2314yes—
406#390C2312yes—
407#389C2312yes—
408#389C2312yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2312yes—
432#389C2312yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#384C2312yes—
538#384C2312yes—
539#384C2312yes—
540#384C2312yes—
541#384C2314yes—
542#383C2314yes—
543#383C2314yes—
544#383C2314yes—
545#382C2312yes—
546#382C2312yes—
547#382C2314yes—
548#382C2312yes—
549#382C2312yes—
550#382C2312yes—
551#382C2312yes—
552#382C2314yes—
553#382C2312yes—
554#382C2312yes—
555#382C2314yes—
556#381C2314yes—
557#381C2314yes—
558#380C2314yes—
559#380C2314yes—
560#380C2312yes—
561#380C2312yes—
562#380C2314yes—
563#380C2314yes—
564#380C2314yes—
565C4×C4⋊C4C2314yes—
566C4×C4⋊C4C2314yes—
567C4×C4⋊C4C2312yes—
568C4×C4⋊C4C2312yes—
569C4×C4⋊C4C2314yes—
570C4×C4⋊C4C2312yes—
571C4×C4⋊C4C2312yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2314yes—
574C4×C22⋊C4C2314yes—
575C4×C22⋊C4C2314yes—
576C4×C22⋊C4C2314yes—
577C4×C22⋊C4C2312yes—
578C4×C22⋊C4C2312yes—
579C4×C22⋊C4C2314yes—
580C4×C22⋊C4C2314yes—
581C4×C22⋊C4C2314yes—
582#376C2312yes—
583C2×#95C2314yes—
584C43C2312yes—
585C22×Q8C2412yes—
586C22×Q8C2414yes—
587C22×Q8C2414yes—
588C22×Q8C2414yes—
589C22×Q8C2414yes—
590C22×D4C2412yes—
591C22×D4C2414yes—
592C22×D4C2414yes—
593C23×C4C2411yescharacteristic
594C23×C4C2412yes—
595C23×C4C2414yes—
596C23×C4C2414yes—
597C23×C4C2414yes—
598C23×C4C2414yes—
599C4⋊Q8—44no—
600C4⋊Q8—48no—
601C4⋊Q8—82no—
602C4⋊Q8—82no—
603#126—48no—
604#126—48no—
605#125—28no—
606#125—24no—
607#125—24no—
608#125—28no—
609#125—48no—
610#125—42no—
611#125—42no—
612#125—48no—
613#125—48no—
614#125—48no—
615#125—84no—
616#124—216no—
617#124—28no—
618#124—84no—
619#123—48no—
620#123—48no—
621#123—84no—
622C22⋊Q8—216no—
623C22⋊Q8—48no—
624C22⋊Q8—48no—
625C22⋊Q8—48no—
626C22⋊Q8—48no—
627C22⋊Q8—84no—
628C22⋊Q8—84no—
629C22⋊Q8—84no—
630C22⋊Q8—82no—
631C22⋊Q8—84no—
632C22⋊Q8—84no—
633#121—48no—
634#121—82no—
635C4×Q8—48no—
636C4×Q8—84no—
637C4×Q8—82no—
638C4×Q8—84no—
639C4×D4—84no—
640C4×D4—82no—
641#117—24no—
642#117—24no—
643#117—44no—
644#117—84no—
645C2×C4⋊C4—44no—
646C2×C4⋊C4—48no—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2411yescharacteristic
704C2×C22⋊C4C2412yes—
705C2×C22⋊C4C2411yescharacteristic
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2411yescharacteristic
735C2×C42—24no—
736C2×C42C2412yes—
737C2×C42C2412yes—
738C2×C42C2412yes—
739C2×C42C2414yes—
740C2×C42C2411yescharacteristic
741C2×C42C2414yes—
742C2×C42C2414yes—
743C2×C42C2414yes—
744C2×C42C2412yes—
745C2×C42C2414yes—
746C2×C42C2414yes—
747C2×C42C2414yes—
748C2×C42C2414yes—
749C2×C42C2414yes—
750C2×C42C2414yes—
751C2×C42C2412yes—
752C2×C42C2412yes—
753C2×C42C2412yes—
754C2×C42C2411yescharacteristic
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2412yes—
760#95C2412yes—
761#95C2412yes—
762#95C2412yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815C24C2514yes—
816C24C2511yescharacteristic
817C2×Q8—24no—
818C2×Q8—28no—
819C2×Q8—28no—
820C2×Q8—44no—
821C2×Q8—44no—
822C2×Q8—42no—
823C2×Q8—44no—
824C2×Q8—44no—
825C2×Q8—44no—
826C2×Q8—42no—
827C2×Q8—44no—
828C2×Q8—44no—
829C2×Q8—44no—
830C2×Q8—44no—
831C2×Q8—44no—
832C2×D4—28no—
833C2×D4—24no—
834C2×D4—42no—
835C2×D4—44no—
836C2×D4—42no—
837C2×D4—44no—
838C2×D4—44no—
839C2×D4—44no—
840C2×D4—44no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—24no—
845C22×C4—28no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4C2512yes—
860C22×C4C2514yes—
861C22×C4C2514yes—
862C22×C4C2514yes—
863C22×C4C2512yes—
864C22×C4C2514yes—
865C22×C4C2514yes—
866C22×C4C2512yes—
867C22×C4C2514yes—
868C22×C4C2514yes—
869C22×C4C2514yes—
870C22×C4C2514yes—
871C22×C4C2514yes—
872C22×C4C2514yes—
873C22×C4C2511yescharacteristic
874C22×C4C2512yes—
875C22×C4C2512yes—
876C22×C4C2512yes—
877C22×C4C2511yescharacteristic
878C4⋊C4—24no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—22no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—42no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—42no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C42−1+414yes—
935C22⋊C4—22no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—24no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C42−1+414yes—
966C42—24no—
967C42—22no—
968C42—24no—
969C42—24no—
970C42—28no—
971C42—42no—
972C42—42no—
973C42—44no—
974C42—44no—
975C42—44no—
976C42—42no—
977C42—44no—
978C42—44no—
979C42—44no—
980C42—44no—
981C42—44no—
982C42—44no—
983C42—42no—
984C42H(5,𝔽2)14yes—
985C23—21no—
986C23—21no—
987C23—22no—
988C23—22no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23C2×2−1+412yes—
997C23C2611yescharacteristic
998Q8—88no—
999Q8—88no—
1000Q8—84no—
1001Q8—88no—
1002Q8—164no—
1003D4—84no—
1004D4—88no—
1005D4—164no—
1006C2×C4—28no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—88no—
1060C2×C4—84no—
1061C2×C4—88no—
1062C2×C4—164no—
1063C2×C4—164no—
1064C2×C4C2×H(5,𝔽2)12yes—
1065C2×C4C2×H(5,𝔽2)14yes—
1066C2×C4C2×2−1+414yes—
1067C2×C4C2×2−1+414yes—
1068C2×C4C2×2−1+412yes—
1069C22—24no—
1070C22—22no—
1071C22—41no—
1072C22—41no—
1073C22—42no—
1074C22—44no—
1075C22—44no—
1076C22—44no—
1077C22—44no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22C22×H(5,𝔽2)11yescharacteristic
1082C22C22×2−1+411yescharacteristic
1083C22C22×2−1+411yescharacteristic
1084C22H(7,𝔽2)12yes—
1085C222−1+612yes—
1086C4—24no—
1087C4—24no—
1088C4—22no—
1089C4—22no—
1090C4—24no—
1091C4—44no—
1092C4—44no—
1093C4—42no—
1094C4—42no—
1095C4—44no—
1096C4—44no—
1097C4—44no—
1098C4—44no—
1099C4—44no—
1100C4—42no—
1101C4—44no—
1102C4—44no—
1103C4—44no—
1104C4—44no—
1105C2—42no—
1106C2—84no—
1107C2#6283311yescharacteristic
1108C2#6287812yes—
1109C2#6305411yescharacteristic
1110C2#6305711yescharacteristic
1111C2#6305812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#46226C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58743C2semidirect
2. #58690C2semidirect
3. #57433C2semidirect
4. #55753C2semidirect
5. #55548C2semidirect
6. #54196C2semidirect
7. #50705C2semidirect
8. #49702C2semidirect
9. #48188C2semidirect
10. #47022C2semidirect
11. #46800C2semidirect
12. #46663C2semidirect
13. #46229C2semidirect
15. #46150C2semidirect
16. #46149C2semidirect
17. #46023C2semidirect
18. #46022C2semidirect
19. #45979C2semidirect
20. #35335C2semidirect
21. #35137C2semidirect

Maximal subgroups

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

subgroupindex
#587432
#586902
#574332
#557532
#555482
#541962
#507052
#497022
#481882
#470222
#468002
#466632
#462292
#462262
#461502
#461492
#460232
#460222
#459792
#353352
#351372