Finite Group Databasebeta

← #8121468

Subgroups — #8121468

Order 512.

3906 conjugacy classes of subgroups.

The subgroup lattice has 1059 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57259C214yesmaximal, complemented
2#56762C214yesmaximal, complemented
3#56469C214yesmaximal, complemented
4#56469C214yesmaximal, complemented
5#52452C214yesmaximal
6#47757C214yesmaximal, complemented
7#47427C214yesmaximal, complemented
8#47131C214yesmaximal, complemented
9#47131C214yesmaximal, complemented
10#43125C214yesmaximal
11#39752C212yesmaximal
12#39748C212yesmaximal
13#39679C212yesmaximal
14#39676C212yesmaximal
15#38395C214yesmaximal
16#38057C214yesmaximal
17#36979C212yesmaximal
18#35120C212yesmaximal
19#35087C211yesmaximal, characteristic
20#35087C211yesmaximal, characteristic
21C2×#2605C211yesmaximal, characteristic
22#2857C2211yescharacteristic
23#2857C2211yescharacteristic
24#2855C2212yes—
25#2855C2212yes—
26#2855C2214yes—
27#2851C2211yescharacteristic
28#2851C2211yescharacteristic
29#2839C2214yes—
30#2839C2214yes—
31#2839C2214yes—
32#2839C2214yes—
33#2839C2214yes—
34#2839C2214yes—
35#2839C2214yes—
36#2822C2214yes—
37#2810C2214yes—
38#2809C2214yes—
39#2809C2214yes—
40#2806C2214yes—
41#2806C2214yes—
42#2805C2214yes—
43#2805C2214yes—
44#2802C2214yes—
45#2802C2214yes—
46#2799C2214yes—
47#2799C2214yes—
48#2799C2214yes—
49#2799C2214yes—
50#2791C2214yes—
51#2776C2214yes—
52#2776C2214yes—
53#2776C2214yes—
54#2774C2214yes—
55#2774C2214yes—
56#2774C2214yes—
57#2774C2214yes—
58#2769C2214yes—
59#2769C2214yes—
60#2769C2214yes—
61#2767C2214yes—
62#2767C2214yes—
63#2767C2214yes—
64#2767C2214yes—
65#2766C2214yes—
66#2762C2214yes—
67#2762C2214yes—
68#2762C2214yes—
69#2762C2214yes—
70#2762C2214yes—
71#2762C2214yes—
72#2762C2214yes—
73#2762C2214yes—
74#2758C2214yes—
75#2758C2214yes—
76#2758C2214yes—
77#2758C2214yes—
78#2758C2214yes—
79#2755C2214yes—
80#2755C2214yes—
81#2755C2214yes—
82#2755C2214yes—
83#2755C2214yes—
84#2719C2214yes—
85#2719C2214yes—
86#2719C2214yes—
87#2719C2214yes—
88#2713C2214yes—
89#2713C2214yes—
90#2713C2214yes—
91#2713C2214yes—
92#2713C2214yes—
93#2659C2212yes—
94#2659C2212yes—
95#2659C2212yes—
96#2655C2214yes—
97#2655C2214yes—
98#2655C2214yes—
99#2655C2214yes—
100#2646C2214yes—
101#2646C2212yes—
102#2645C2214yes—
103#2642C2214yes—
104#2612C2214yes—
105#2612C2214yes—
106#2612C2214yes—
107#2612C2214yes—
108#2606C2214yes—
109#2606C2214yes—
110#2605C2214yes—
111#2605C2214yes—
112#2605C2214yes—
113#2605C2214yes—
114#2605C2214yes—
115#2605C2214yes—
116#2590C2214yes—
117#2590C2214yes—
118#2588C2214yes—
119#2588C2214yes—
120#2588C2214yes—
121#2584C2214yes—
122#2583C2214yes—
123#2581C2214yes—
124#2581C2214yes—
125#2581C2214yes—
126#2569C2214yes—
127#2569C2214yes—
128#2569C2214yes—
129#2569C2214yes—
130#2565C2214yes—
131#2550C2214yes—
132#2550C2214yes—
133#2533C2214yes—
134#2533C2214yes—
135#2528C2214yes—
136#2528C2214yes—
137#2520C2214yes—
138#2520C2214yes—
139#2520C2214yes—
140#2514C2212yes—
141#2514C2212yes—
142#2514C2214yes—
143#2508C2214yes—
144#2506C2212yes—
145#2506C2212yes—
146#2505C2214yes—
147#2505C2214yes—
148#2505C2214yes—
149#2505C2214yes—
150#2505C2214yes—
151#2493C2214yes—
152#2493C2214yes—
153#2493C2214yes—
154#2493C2214yes—
155#2473C2214yes—
156#2473C2214yes—
157#2473C2214yes—
158#2462C2214yes—
159#2462C2214yes—
160#2462C2214yes—
161#2462C2214yes—
162#2453C2212yes—
163#2453C2212yes—
164#2453C2214yes—
165#2453C2214yes—
166#2451C2214yes—
167#2451C2214yes—
168#2451C2214yes—
169#2446C2212yes—
170#2446C2212yes—
171#2446C2214yes—
172#2446C2214yes—
173#2442C2214yes—
174#2442C2214yes—
175#2434C2214yes—
176C2×#400C2212yes—
177C2×#395C2212yes—
178#2368C2214yes—
179#2360C2214yes—
180#2345C2214yes—
181Q8×C22⋊C4C2214yes—
182#2336C2214yes—
183#2336C2214yes—
184#2336C2214yes—
185#2336C2214yes—
186#2329C2212yes—
187#2329C2212yes—
188#2329C2214yes—
189#2329C2212yes—
190#2329C2212yes—
191#2327C2214yes—
192#2320C2214yes—
193C4×C22⋊Q8C2212yes—
194C4×C22⋊Q8C2212yes—
195C2×#391C2212yes—
196C2×#391C2212yes—
197C2×#387C2212yes—
198C2×#387C2212yes—
199#2283C2214yes—
200C2×#383C2211yescharacteristic
201C2×C4×C4⋊C4C2211yescharacteristic
202C2×#376C2211yescharacteristic
203C23×Q8C2312yes—
204C2×C4⋊Q8C2314yes—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2314yes—
208C2×#125C2314yes—
209C2×#125C2314yes—
210C2×#125C2314yes—
211C2×#125C2314yes—
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2312yes—
218C2×C4×Q8C2314yes—
219C2×C4×Q8C2314yes—
220C2×C4×Q8C2314yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2312yes—
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2312yes—
227C22×C42C2311yescharacteristic
228C22×C42C2312yes—
229C22×C42C2311yescharacteristic
230C22×C42C2311yescharacteristic
231#401C2314yes—
232#401C2314yes—
233#401C2314yes—
234#401C2314yes—
235#400C2314yes—
236#400C2314yes—
237#400C2314yes—
238#400C2314yes—
239#400C2314yes—
240#400C2314yes—
241#400C2314yes—
242#400C2314yes—
243#400C2314yes—
244#400C2314yes—
245#400C2314yes—
246#400C2314yes—
247#400C2314yes—
248#400C2314yes—
249#400C2314yes—
250#400C2314yes—
251#400C2314yes—
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2314yes—
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#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
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#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#395C2314yes—
328#395C2314yes—
329#395C2314yes—
330#395C2314yes—
331#395C2314yes—
332#395C2314yes—
333#395C2314yes—
334#395C2314yes—
335#395C2314yes—
336#395C2314yes—
337#395C2314yes—
338#395C2314yes—
339#395C2314yes—
340#395C2314yes—
341#395C2314yes—
342#395C2314yes—
343#391C2314yes—
344#391C2314yes—
345#391C2314yes—
346#391C2314yes—
347#391C2314yes—
348#391C2314yes—
349#391C2314yes—
350#391C2314yes—
351#391C2314yes—
352#391C2314yes—
353#391C2314yes—
354#391C2314yes—
355#391C2314yes—
356#391C2312yes—
357#391C2314yes—
358#391C2314yes—
359#391C2314yes—
360#391C2314yes—
361#391C2314yes—
362#391C2314yes—
363#391C2312yes—
364#391C2312yes—
365#391C2314yes—
366#391C2312yes—
367#391C2312yes—
368#391C2312yes—
369#391C2314yes—
370#391C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2314yes—
374#391C2314yes—
375#391C2314yes—
376#391C2312yes—
377#391C2312yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2312yes—
403#389C2314yes—
404#389C2314yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#389C2312yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2312yes—
416#389C2312yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2314yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
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#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#384C2311yescharacteristic
516#384C2311yescharacteristic
517#383C2314yes—
518#383C2314yes—
519#383C2314yes—
520#383C2314yes—
521#383C2314yes—
522#383C2314yes—
523#383C2314yes—
524#383C2314yes—
525#382C2314yes—
526#382C2314yes—
527#382C2314yes—
528#382C2314yes—
529#382C2314yes—
530#382C2314yes—
531#382C2311yescharacteristic
532#382C2311yescharacteristic
533#382C2314yes—
534#382C2314yes—
535#382C2314yes—
536#381C2314yes—
537#381C2314yes—
538#380C2314yes—
539#380C2314yes—
540#380C2314yes—
541#380C2314yes—
542#380C2314yes—
543#380C2314yes—
544#380C2312yes—
545#380C2312yes—
546#380C2314yes—
547C4×C4⋊C4C2314yes—
548C4×C4⋊C4C2314yes—
549C4×C4⋊C4C2314yes—
550C4×C4⋊C4C2314yes—
551C4×C4⋊C4C2314yes—
552C4×C4⋊C4C2314yes—
553C4×C4⋊C4C2314yes—
554C4×C4⋊C4C2312yes—
555C4×C4⋊C4C2312yes—
556C4×C4⋊C4C2312yes—
557C4×C4⋊C4C2314yes—
558C4×C4⋊C4C2314yes—
559C4×C4⋊C4C2312yes—
560C4×C4⋊C4C2312yes—
561C4×C4⋊C4C2312yes—
562C4×C22⋊C4C2314yes—
563C4×C22⋊C4C2314yes—
564C4×C22⋊C4C2314yes—
565C4×C22⋊C4C2314yes—
566C4×C22⋊C4C2314yes—
567C4×C22⋊C4C2314yes—
568#376C2314yes—
569#376C2314yes—
570#376C2314yes—
571#376C2314yes—
572C2×#95C2312yes—
573C2×#95C2312yes—
574C2×#95C2312yes—
575C2×#95C2312yes—
576C2×#95C2311yescharacteristic
577C2×#95C2312yes—
578C2×#95C2312yes—
579C2×#95C2312yes—
580C2×#95C2311yescharacteristic
581C2×#95C2312yes—
582C2×#95C2311yescharacteristic
583C2×#95C2311yescharacteristic
584C22×Q8—28no—
585C22×Q8—44no—
586C22×Q8—82no—
587C22×Q8C2414yes—
588C22×Q8C2414yes—
589C22×Q8C2412yes—
590C22×Q8C2412yes—
591C22×Q8C2414yes—
592C23×C4C2411yescharacteristic
593C23×C4C2412yes—
594C23×C4C2412yes—
595C23×C4C2412yes—
596C23×C4C2411yescharacteristic
597C23×C4C2412yes—
598C23×C4C2412yes—
599C23×C4C2412yes—
600C23×C4C2411yescharacteristic
601C4⋊Q8—48no—
602C4⋊Q8—81no—
603C4⋊Q8—81no—
604C4⋊Q8—84no—
605#125—48no—
606#125—48no—
607#125—48no—
608#125—48no—
609#125—81no—
610#125—81no—
611#125—84no—
612C22⋊Q8—216no—
613C22⋊Q8—28no—
614C22⋊Q8—28no—
615C4×Q8—48no—
616C4×Q8—82no—
617C4×Q8—82no—
618C4×Q8—84no—
619C4×Q8—84no—
620C2×C4⋊C4—28no—
621C2×C4⋊C4—44no—
622C2×C4⋊C4—44no—
623C2×C4⋊C4—82no—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C42—24no—
688C2×C42—28no—
689C2×C42—81no—
690C2×C42—81no—
691C2×C42C2414yes—
692C2×C42C2414yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2414yes—
696C2×C42C2414yes—
697C2×C42C2414yes—
698C2×C42C2414yes—
699C2×C42C2414yes—
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2414yes—
705C2×C42C2414yes—
706C2×C42C2414yes—
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2414yes—
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2412yes—
718#95C2412yes—
719#95C2412yes—
720#95C2414yes—
721#95C2412yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
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—
795C24C2511yescharacteristic
796C2×Q8—28no—
797C2×Q8—24no—
798C2×Q8—24no—
799C2×Q8—28no—
800C2×Q8—28no—
801C2×Q8—28no—
802C2×Q8—44no—
803C2×Q8—42no—
804C2×Q8—42no—
805C2×Q8—44no—
806C2×Q8—44no—
807C2×Q8—44no—
808C2×Q8—44no—
809C2×Q8—42no—
810C2×Q8—42no—
811C2×Q8—816no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—41no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—41no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C42−1+418yes—
836C22×C42−1+414yes—
837C22×C4C2512yes—
838C22×C4C2514yes—
839C22×C4C2514yes—
840C22×C4C2514yes—
841C22×C4C2512yes—
842C22×C4C2514yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2514yes—
851C22×C4C2514yes—
852C22×C4C2512yes—
853C22×C4C2511yescharacteristic
854C22×C4C2511yescharacteristic
855C22×C4C2514yes—
856C22×C4C2512yes—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—24no—
867C4⋊C4—28no—
868C4⋊C4—24no—
869C4⋊C4—28no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—42no—
873C4⋊C4—44no—
874C4⋊C4—42no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
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—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C42—24no—
921C42—24no—
922C42—28no—
923C42—28no—
924C42—28no—
925C42—42no—
926C42—42no—
927C42—41no—
928C42—41no—
929C42—41no—
930C42—41no—
931C42—44no—
932C42—44no—
933C42—44no—
934C42—44no—
935C42—44no—
936C42—44no—
937C42—44no—
938C42—44no—
939C42—44no—
940C42—44no—
941C42—44no—
942C23—22no—
943C23—21no—
944C23—21no—
945C23C2×2−1+412yes—
946C23C2×2−1+414yes—
947C23C2611yescharacteristic
948Q8—416no—
949Q8—84no—
950Q8—84no—
951Q8—88no—
952Q8—88no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—44no—
1010C2×C4—48no—
1011C2×C4—48no—
1012C2×C4—44no—
1013C2×C4—44no—
1014C2×C4—84no—
1015C2×C4—84no—
1016C2×C4—84no—
1017C2×C4—84no—
1018C2×C4C2×2−1+412yes—
1019C2×C4C2×2−1+412yes—
1020C2×C4C2×2−1+418yes—
1021C2×C4#58514yes—
1022C22—22no—
1023C22—22no—
1024C22—24no—
1025C22—24no—
1026C22#355614yes—
1027C22C22×2−1+411yescharacteristic
1028C22C22×2−1+412yes—
1029C22C2×#58512yes—
1030C22H(7,𝔽2)11yescharacteristic
1031C222−1+611yescharacteristic
1032C4—22no—
1033C4—22no—
1034C4—28no—
1035C4—24no—
1036C4—42no—
1037C4—44no—
1038C4—44no—
1039C4—42no—
1040C4—44no—
1041C4—44no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—44no—
1046C4—44no—
1047C4—44no—
1048C4—44no—
1049C4—44no—
1050C4—44no—
1051C4—44no—
1052C2—24no—
1053C2C2×#355611yescharacteristic
1054C2#6283811yescharacteristic
1055C2#6286511yescharacteristic
1056C2#6290312yes—
1057C2#6295912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #57259C2semidirect
2. #56762C2semidirect
3. #56469C2semidirect
4. #56469C2semidirect
6. #47757C2semidirect
7. #47427C2semidirect
8. #47131C2semidirect
9. #47131C2semidirect

Maximal subgroups

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

subgroupindex
#572592
#567622
#564692
#524522
#477572
#474272
#471312
#431252
#397522
#397482
#396792
#396762
#383952
#380572
#369792
#351202
#350872
C2×#26052