Finite Group Databasebeta

← #8757198

Subgroups — #8757198

Order 512.

3940 conjugacy classes of subgroups.

The subgroup lattice has 1151 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58350C214yesmaximal, complemented
2#55793C214yesmaximal, complemented
3#55474C214yesmaximal, complemented
4#54461C214yesmaximal, complemented
5#54317C214yesmaximal, complemented
6#54127C214yesmaximal, complemented
7#50756C214yesmaximal, complemented
8#50182C212yesmaximal, complemented
9#49594C212yesmaximal, complemented
10#48560C214yesmaximal, complemented
11#47802C212yesmaximal, complemented
12#47785C212yesmaximal, complemented
13#47140C214yesmaximal, complemented
14#46667C214yesmaximal, complemented
15#46247C212yesmaximal, complemented
16#46244C212yesmaximal, complemented
17#46233C212yesmaximal, complemented
18#46145C211yesmaximal, characteristic, complemented
19#46009C212yesmaximal, complemented
20#46008C212yesmaximal, complemented
21#45991C211yesmaximal, characteristic
22#35339C211yesmaximal, characteristic, complemented
23#35135C212yesmaximal, complemented
24#2864C2212yes—
25#2864C2212yes—
26#2861C2212yes—
27#2859C2212yes—
28#2851C2212yes—
29#2850C2212yes—
30#2845C2212yes—
31#2844C2211yescharacteristic
32#2844C2211yescharacteristic
33#2844C2212yes—
34#2838C2214yes—
35#2836C2214yes—
36#2835C2214yes—
37#2834C2214yes—
38#2827C2214yes—
39#2823C2212yes—
40#2822C2211yescharacteristic
41#2822C2214yes—
42#2820C2212yes—
43#2819C2211yescharacteristic
44#2807C2214yes—
45#2806C2214yes—
46#2802C2214yes—
47#2802C2214yes—
48#2800C2214yes—
49#2797C2214yes—
50#2797C2214yes—
51#2793C2214yes—
52#2792C2212yes—
53#2792C2214yes—
54#2792C2214yes—
55#2792C2214yes—
56#2791C2214yes—
57#2790C2214yes—
58#2790C2214yes—
59#2789C2212yes—
60#2789C2214yes—
61#2787C2214yes—
62#2787C2214yes—
63#2786C2214yes—
64#2785C2212yes—
65#2782C2212yes—
66#2782C2212yes—
67#2780C2214yes—
68#2777C2214yes—
69#2775C2214yes—
70#2774C2214yes—
71#2773C2214yes—
72#2773C2214yes—
73#2772C2214yes—
74#2769C2212yes—
75#2769C2214yes—
76#2769C2212yes—
77#2768C2214yes—
78#2767C2214yes—
79#2766C2214yes—
80#2766C2214yes—
81#2766C2214yes—
82#2766C2214yes—
83#2765C2214yes—
84#2765C2214yes—
85#2765C2214yes—
86#2763C2214yes—
87#2762C2214yes—
88#2761C2214yes—
89#2757C2214yes—
90#2757C2214yes—
91#2754C2214yes—
92#2753C2214yes—
93#2748C2214yes—
94#2746C2214yes—
95#2746C2214yes—
96#2741C2214yes—
97#2740C2214yes—
98#2740C2214yes—
99#2732C2214yes—
100#2727C2214yes—
101#2722C2214yes—
102#2721C2214yes—
103#2720C2214yes—
104#2719C2214yes—
105#2718C2214yes—
106#2707C2214yes—
107#2704C2214yes—
108#2704C2214yes—
109#2701C2214yes—
110#2694C2214yes—
111#2694C2214yes—
112#2691C2214yes—
113#2689C2214yes—
114#2680C2214yes—
115#2680C2212yes—
116#2667C2212yes—
117#2667C2212yes—
118#2654C2214yes—
119#2654C2214yes—
120#2654C2214yes—
121#2652C2214yes—
122#2649C2214yes—
123#2647C2212yes—
124#2647C2212yes—
125#2637C2214yes—
126#2624C2212yes—
127#2616C2212yes—
128#2609C2214yes—
129#2609C2212yes—
130#2602C2214yes—
131#2601C2214yes—
132#2599C2214yes—
133#2599C2214yes—
134#2595C2214yes—
135#2594C2214yes—
136#2594C2214yes—
137#2591C2212yes—
138#2590C2214yes—
139#2587C2214yes—
140#2585C2214yes—
141#2584C2214yes—
142#2583C2212yes—
143#2583C2214yes—
144#2575C2214yes—
145#2571C2212yes—
146#2570C2214yes—
147#2570C2214yes—
148#2570C2214yes—
149#2569C2214yes—
150#2569C2214yes—
151#2556C2214yes—
152#2556C2214yes—
153#2530C2214yes—
154#2529C2214yes—
155#2523C2214yes—
156#2522C2214yes—
157#2520C2214yes—
158#2520C2214yes—
159#2519C2214yes—
160#2518C2214yes—
161#2515C2214yes—
162#2512C2212yes—
163#2511C2212yes—
164#2506C2214yes—
165#2493C2214yes—
166#2490C2212yes—
167#2489C2212yes—
168#2489C2214yes—
169#2488C2214yes—
170#2484C2212yes—
171#2481C2214yes—
172#2479C2214yes—
173#2479C2214yes—
174#2479C2214yes—
175#2478C2214yes—
176#2478C2214yes—
177#2475C2214yes—
178#2473C2214yes—
179#2473C2214yes—
180#2471C2214yes—
181#2470C2214yes—
182#2470C2214yes—
183#2470C2214yes—
184#2470C2214yes—
185#2462C2214yes—
186#2462C2214yes—
187#2462C2214yes—
188#2454C2212yes—
189#2453C2212yes—
190#2453C2214yes—
191#2449C2214yes—
192#2438C2214yes—
193#2430C2214yes—
194#2423C2212yes—
195#2422C2212yes—
196#2406C2214yes—
197#2406C2212yes—
198#2382C2212yes—
199#2382C2212yes—
200#2379C2212yes—
201#2379C2212yes—
202#2378C2212yes—
203#2377C2212yes—
204#2347C2212yes—
205#2341C2212yes—
206#2335C2214yes—
207#2334C2214yes—
208#2334C2214yes—
209#2317C2211yescharacteristic
210#2317C2211yescharacteristic
211#2317C2214yes—
212#2316C2211yescharacteristic
213#2316C2211yescharacteristic
214C4×#125C2212yes—
215C4×#124C2212yes—
216#2285C2211yescharacteristic
217C2×#382C2211yescharacteristic
218C4×#117C2211yescharacteristic
219C22×#41C2312yes—
220C2×#126C2314yes—
221C2×#126C2314yes—
222C2×#126C2314yes—
223C2×#125C2312yes—
224C2×#125C2314yes—
225C2×#125C2314yes—
226C2×#125C2314yes—
227C2×#125C2312yes—
228C2×#125C2312yes—
229C2×#124C2312yes—
230C2×#123C2314yes—
231C2×#123C2314yes—
232C2×#123C2314yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2314yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2312yes—
241C2×C4×D4C2312yes—
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2314yes—
247C2×#117C2312yes—
248C2×#117C2314yes—
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2314yes—
252C22×C42C2311yescharacteristic
253#401C2314yes—
254#401C2314yes—
255#401C2314yes—
256#400C2314yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2312yes—
269#400C2312yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2312yes—
276#400C2312yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#399C2314yes—
281#399C2314yes—
282#399C2314yes—
283#399C2314yes—
284#399C2314yes—
285#399C2314yes—
286#399C2314yes—
287#399C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2312yes—
293#398C2314yes—
294#398C2312yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2312yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2312yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2312yes—
360#395C2314yes—
361#395C2312yes—
362#395C2312yes—
363#395C2312yes—
364#395C2314yes—
365#395C2314yes—
366#394C2312yes—
367#394C2312yes—
368#394C2314yes—
369#394C2312yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2312yes—
376#394C2314yes—
377#394C2314yes—
378#393C2314yes—
379#393C2314yes—
380#392C2314yes—
381#391C2312yes—
382#391C2312yes—
383#391C2312yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2312yes—
389#390C2314yes—
390#390C2312yes—
391#390C2312yes—
392#390C2314yes—
393#390C2314yes—
394#390C2314yes—
395#390C2312yes—
396#390C2312yes—
397#389C2312yes—
398#389C2312yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#389C2314yes—
410#389C2312yes—
411#389C2314yes—
412#389C2312yes—
413#389C2314yes—
414#389C2312yes—
415#389C2312yes—
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#389C2312yes—
431#389C2312yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
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#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
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#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#384C2312yes—
554#384C2312yes—
555#384C2314yes—
556#384C2312yes—
557#384C2312yes—
558#384C2312yes—
559#383C2314yes—
560#383C2314yes—
561#383C2314yes—
562#382C2312yes—
563#382C2311yescharacteristic
564#382C2312yes—
565#382C2314yes—
566#382C2311yescharacteristic
567#382C2312yes—
568#382C2312yes—
569#382C2314yes—
570#382C2314yes—
571#382C2314yes—
572#382C2314yes—
573#382C2314yes—
574#382C2314yes—
575#382C2312yes—
576#382C2311yescharacteristic
577#382C2311yescharacteristic
578#381C2314yes—
579#381C2312yes—
580#381C2312yes—
581#381C2314yes—
582#380C2312yes—
583#380C2312yes—
584#380C2312yes—
585#380C2312yes—
586#380C2314yes—
587#380C2314yes—
588#380C2312yes—
589#380C2312yes—
590#380C2314yes—
591#380C2314yes—
592C4×C4⋊C4C2312yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2312yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2312yes—
597C4×C4⋊C4C2312yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C22⋊C4C2312yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2312yes—
611#376C2312yes—
612C2×#95C2314yes—
613C43C2312yes—
614C2×#41—44no—
615C2×#41—84no—
616C22×Q8C2412yes—
617C22×Q8C2412yes—
618C22×Q8C2412yes—
619C22×D4C2412yes—
620C22×D4C2414yes—
621C22×D4C2412yes—
622C22×D4C2412yes—
623C23×C4C2411yescharacteristic
624C23×C4C2412yes—
625C23×C4C2412yes—
626C23×C4C2412yes—
627C23×C4C2414yes—
628C23×C4C2414yes—
629C23×C4C2414yes—
630#126—48no—
631#126—48no—
632#126—84no—
633#125—28no—
634#125—84no—
635#125—82no—
636#125—84no—
637#125—84no—
638#125—82no—
639#124—28no—
640#123—48no—
641#123—84no—
642#123—84no—
643C22⋊Q8—44no—
644C22⋊Q8—84no—
645C22⋊Q8—84no—
646C22⋊Q8—82no—
647#121—44no—
648#121—82no—
649C4×Q8—82no—
650C4×Q8—84no—
651C4×D4—82no—
652#117—42no—
653#117—42no—
654#117—48no—
655#117—44no—
656#117—42no—
657#117—42no—
658#117—84no—
659C2×C4⋊C4—42no—
660C2×C4⋊C4—42no—
661C2×C4⋊C4—84no—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2412yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2411yescharacteristic
733C2×C22⋊C4C2411yescharacteristic
734C2×C22⋊C4C2412yes—
735C2×C22⋊C4C2412yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C42—24no—
758C2×C42C2412yes—
759C2×C42C2412yes—
760C2×C42C2411yescharacteristic
761C2×C42C2412yes—
762C2×C42C2414yes—
763C2×C42C2414yes—
764C2×C42C2412yes—
765C2×C42C2412yes—
766C2×C42C2414yes—
767C2×C42C2414yes—
768C2×C42C2412yes—
769C2×C42C2414yes—
770C2×C42C2414yes—
771C2×C42C2412yes—
772C2×C42C2414yes—
773C2×C42C2414yes—
774C2×C42C2412yes—
775C2×C42C2412yes—
776C2×C42C2414yes—
777C2×C42C2411yescharacteristic
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2412yes—
783#95C2412yes—
784#95C2412yes—
785#95C2412yes—
786#95C2412yes—
787#95C2412yes—
788#95C2412yes—
789#95C2414yes—
790#95C2412yes—
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—
815#95C2414yes—
816#95C2414yes—
817#95C2412yes—
818#95C2412yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2412yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2412yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844C24C2514yes—
845C24C2511yescharacteristic
846#41—816no—
847C2×Q8—24no—
848C2×Q8—44no—
849C2×Q8—42no—
850C2×Q8—42no—
851C2×Q8—42no—
852C2×Q8—42no—
853C2×Q8—44no—
854C2×D4—28no—
855C2×D4—24no—
856C2×D4—42no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—44no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—42no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—42no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4C2512yes—
884C22×C4C2514yes—
885C22×C4C2512yes—
886C22×C4C2512yes—
887C22×C4C2514yes—
888C22×C4C2514yes—
889C22×C4C2512yes—
890C22×C4C2512yes—
891C22×C4C2514yes—
892C22×C4C2514yes—
893C22×C4C2514yes—
894C22×C4C2512yes—
895C22×C4C2512yes—
896C22×C4C2512yes—
897C22×C4C2514yes—
898C22×C4C2514yes—
899C22×C4C2512yes—
900C22×C4C2514yes—
901C22×C4C2512yes—
902C22×C4C2511yescharacteristic
903C22×C4C2511yescharacteristic
904C4⋊C4—28no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—28no—
908C4⋊C4—24no—
909C4⋊C4—28no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—44no—
917C4⋊C4—44no—
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—44no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—41no—
932C4⋊C4—41no—
933C4⋊C4—44no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—44no—
948C4⋊C4—42no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C22⋊C4—28no—
968C22⋊C4—24no—
969C22⋊C4—28no—
970C22⋊C4—28no—
971C22⋊C4—28no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—42no—
980C22⋊C4—44no—
981C22⋊C4—42no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C42—24no—
1000C42—22no—
1001C42—24no—
1002C42—24no—
1003C42—42no—
1004C42—42no—
1005C42—44no—
1006C42—42no—
1007C42—42no—
1008C42—44no—
1009C42—44no—
1010C42—44no—
1011C42—44no—
1012C42—42no—
1013C42—44no—
1014C42—44no—
1015C42—42no—
1016C42—44no—
1017C42—44no—
1018C422−1+414yes—
1019C23—21no—
1020C23—21no—
1021C23—22no—
1022C23—22no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—24no—
1029C23—24no—
1030C23#58512yes—
1031C23C2611yescharacteristic
1032Q8—48no—
1033Q8—84no—
1034Q8—162no—
1035D4—84no—
1036D4—88no—
1037D4—84no—
1038D4—162no—
1039C2×C4—28no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—416no—
1097C2×C4—84no—
1098C2×C4—84no—
1099C2×C4—84no—
1100C2×C4—88no—
1101C2×C4—164no—
1102C2×C4C2×2−1+412yes—
1103C2×C4C2×2−1+414yes—
1104C2×C4#58512yes—
1105C22—22no—
1106C22—22no—
1107C22—22no—
1108C22—42no—
1109C22—42no—
1110C22—44no—
1111C22—44no—
1112C22—44no—
1113C22—44no—
1114C22—44no—
1115C22—44no—
1116C22—44no—
1117C22C22×2−1+411yescharacteristic
1118C22C2×#58511yescharacteristic
1119C22C2×#58511yescharacteristic
1120C22H(7,𝔽2)12yes—
1121C222−1+612yes—
1122C4—22no—
1123C4—22no—
1124C4—24no—
1125C4—42no—
1126C4—44no—
1127C4—42no—
1128C4—42no—
1129C4—44no—
1130C4—44no—
1131C4—42no—
1132C4—44no—
1133C4—42no—
1134C4—44no—
1135C4—44no—
1136C4—42no—
1137C4—42no—
1138C4—42no—
1139C4—44no—
1140C4—44no—
1141C4—42no—
1142C4—44no—
1143C2—42no—
1144C2—84no—
1145C2#6282511yescharacteristic
1146C2#6287912yes—
1147C2#6304611yescharacteristic
1148C2#6304712yes—
1149C2#6306411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#45991C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58350C2semidirect
2. #55793C2semidirect
3. #55474C2semidirect
4. #54461C2semidirect
5. #54317C2semidirect
6. #54127C2semidirect
7. #50756C2semidirect
8. #50182C2semidirect
9. #49594C2semidirect
10. #48560C2semidirect
11. #47802C2semidirect
12. #47785C2semidirect
13. #47140C2semidirect
14. #46667C2semidirect
15. #46247C2semidirect
16. #46244C2semidirect
17. #46233C2semidirect
18. #46145C2semidirect
19. #46009C2semidirect
20. #46008C2semidirect
22. #35339C2semidirect
23. #35135C2semidirect

Maximal subgroups

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

subgroupindex
#583502
#557932
#554742
#544612
#543172
#541272
#507562
#501822
#495942
#485602
#478022
#477852
#471402
#466672
#462472
#462442
#462332
#461452
#460092
#460082
#459912
#353392
#351352