Finite Group Databasebeta

← #8757617

Subgroups — #8757617

Order 512.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57025C214yesmaximal, complemented
2#56843C214yesmaximal, complemented
3#56642C214yesmaximal, complemented
4#56641C214yesmaximal, complemented
5#54564C214yesmaximal, complemented
6#54320C214yesmaximal, complemented
7#52083C211yesmaximal, characteristic
8#52079C212yesmaximal, complemented
9#52075C212yesmaximal, complemented
10#52072C211yesmaximal, characteristic, complemented
11#51999C212yesmaximal, complemented
12#51726C212yesmaximal, complemented
13#51586C212yesmaximal, complemented
14#47075C214yesmaximal, complemented
15#47065C214yesmaximal, complemented
16#47032C212yesmaximal, complemented
17#47003C212yesmaximal, complemented
18#46325C212yesmaximal, complemented
19#46311C212yesmaximal, complemented
20#46131C214yesmaximal, complemented
21#45981C214yesmaximal, complemented
22#35316C211yesmaximal, characteristic, complemented
23#35211C212yesmaximal, complemented
24C2×#563C2212yes—
25C2×#563C2212yes—
26C2×Q82C2211yescharacteristic
27C2×#555C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C2×#529C2212yes—
32C2×C4×#41C2211yescharacteristic
33#2857C2214yes—
34#2852C2214yes—
35#2852C2214yes—
36#2843C2212yes—
37#2841C2212yes—
38#2836C2214yes—
39#2831C2214yes—
40#2830C2214yes—
41#2827C2214yes—
42#2826C2214yes—
43#2824C2214yes—
44#2823C2212yes—
45#2821C2214yes—
46#2816C2212yes—
47#2803C2214yes—
48#2791C2214yes—
49#2790C2214yes—
50#2785C2212yes—
51#2784C2214yes—
52#2783C2214yes—
53#2781C2214yes—
54#2777C2214yes—
55#2771C2212yes—
56#2769C2212yes—
57#2768C2214yes—
58#2767C2214yes—
59#2766C2214yes—
60#2764C2214yes—
61#2763C2214yes—
62#2762C2214yes—
63#2762C2214yes—
64#2761C2214yes—
65#2761C2214yes—
66#2760C2212yes—
67#2756C2214yes—
68#2755C2214yes—
69#2754C2214yes—
70#2753C2214yes—
71#2750C2214yes—
72#2750C2214yes—
73#2750C2214yes—
74#2748C2214yes—
75#2747C2214yes—
76#2746C2214yes—
77#2744C2214yes—
78#2744C2214yes—
79#2742C2214yes—
80#2741C2214yes—
81#2740C2214yes—
82#2739C2214yes—
83#2737C2214yes—
84#2737C2214yes—
85#2734C2212yes—
86#2734C2212yes—
87#2734C2212yes—
88#2733C2212yes—
89#2731C2212yes—
90#2731C2212yes—
91#2731C2212yes—
92#2731C2212yes—
93#2730C2214yes—
94#2729C2214yes—
95#2729C2214yes—
96#2725C2214yes—
97#2719C2214yes—
98#2716C2214yes—
99#2716C2214yes—
100#2715C2214yes—
101#2713C2214yes—
102#2713C2214yes—
103#2707C2214yes—
104#2707C2214yes—
105#2706C2214yes—
106#2705C2214yes—
107#2701C2214yes—
108#2696C2214yes—
109#2695C2214yes—
110#2691C2214yes—
111#2683C2214yes—
112#2681C2214yes—
113#2677C2214yes—
114#2677C2214yes—
115#2676C2214yes—
116#2674C2214yes—
117#2674C2214yes—
118#2674C2214yes—
119#2673C2214yes—
120#2672C2214yes—
121#2666C2214yes—
122#2662C2214yes—
123#2651C2214yes—
124#2637C2214yes—
125#2632C2212yes—
126#2631C2212yes—
127#2630C2214yes—
128#2630C2214yes—
129#2629C2214yes—
130#2621C2214yes—
131#2611C2214yes—
132#2609C2214yes—
133#2609C2214yes—
134#2608C2212yes—
135#2604C2214yes—
136#2601C2214yes—
137#2600C2214yes—
138#2600C2212yes—
139#2600C2214yes—
140#2599C2212yes—
141#2598C2212yes—
142#2596C2214yes—
143#2595C2214yes—
144#2589C2214yes—
145#2585C2214yes—
146#2570C2214yes—
147#2566C2212yes—
148#2565C2212yes—
149#2560C2214yes—
150#2556C2214yes—
151#2547C2212yes—
152#2547C2212yes—
153#2546C2212yes—
154#2546C2212yes—
155#2545C2212yes—
156#2544C2212yes—
157#2533C2214yes—
158#2528C2214yes—
159#2525C2214yes—
160#2524C2214yes—
161#2520C2214yes—
162#2515C2214yes—
163#2510C2214yes—
164#2500C2212yes—
165#2499C2212yes—
166#2486C2214yes—
167#2486C2214yes—
168#2481C2214yes—
169#2478C2214yes—
170#2477C2214yes—
171#2477C2214yes—
172#2474C2214yes—
173#2473C2214yes—
174#2471C2214yes—
175#2469C2214yes—
176#2468C2214yes—
177#2467C2214yes—
178#2466C2214yes—
179#2465C2214yes—
180#2465C2214yes—
181#2462C2214yes—
182#2462C2214yes—
183#2461C2214yes—
184#2458C2214yes—
185#2458C2214yes—
186#2457C2214yes—
187#2454C2214yes—
188#2450C2214yes—
189#2450C2214yes—
190#2449C2214yes—
191#2445C2214yes—
192#2443C2214yes—
193#2439C2214yes—
194#2438C2214yes—
195#2438C2214yes—
196#2436C2212yes—
197#2434C2212yes—
198#2432C2212yes—
199#2431C2212yes—
200#2429C2214yes—
201#2425C2214yes—
202#2409C2214yes—
203#2383C2214yes—
204#2381C2211yescharacteristic
205#2381C2211yescharacteristic
206#2381C2212yes—
207#2369C2212yes—
208#2333C2212yes—
209#2332C2212yes—
210#2328C2212yes—
211#2327C2212yes—
212#2326C2212yes—
213#2326C2212yes—
214#2318C2214yes—
215#2310C2211yescharacteristic
216#2310C2211yescharacteristic
217#2285C2211yescharacteristic
218#2283C2212yes—
219C22×#41C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222#563—48no—
223#563—48no—
224Q82—44no—
225#555—44no—
226#536—44no—
227#536—44no—
228C2×C4⋊Q8—44no—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2312yes—
240C2×#127C2312yes—
241#529—48no—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#125C2312yes—
247C2×#125C2314yes—
248C2×#125C2314yes—
249C2×#124C2312yes—
250C2×#124C2312yes—
251C2×#124C2311yescharacteristic
252C2×#124C2311yescharacteristic
253C2×#124C2312yes—
254C2×#124C2312yes—
255C2×#124C2312yes—
256C2×#124C2312yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×#121C2312yes—
271C2×#121C2312yes—
272C2×#121C2314yes—
273C4×#41—44no—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2314yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2314yes—
285C2×#117C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C2×#117C2311yescharacteristic
288C2×#117C2312yes—
289C2×#117C2314yes—
290C2×#117C2314yes—
291C22×C4⋊C4C2314yes—
292C22×C42C2311yescharacteristic
293C22×C42C2312yes—
294#401C2314yes—
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#400C2314yes—
308#400C2314yes—
309#400C2312yes—
310#400C2314yes—
311#400C2314yes—
312#399C2314yes—
313#399C2314yes—
314#399C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2312yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2312yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2312yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2312yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2312yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2312yes—
411#393C2314yes—
412#393C2314yes—
413#392C2314yes—
414#392C2314yes—
415#392C2312yes—
416#392C2314yes—
417#392C2314yes—
418#391C2314yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2314yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#390C2314yes—
436#390C2312yes—
437#390C2312yes—
438#390C2314yes—
439#390C2312yes—
440#390C2312yes—
441#390C2314yes—
442#390C2314yes—
443#390C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
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#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
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#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#384C2312yes—
575#384C2312yes—
576#384C2312yes—
577#383C2314yes—
578#383C2314yes—
579#383C2312yes—
580#383C2312yes—
581#383C2314yes—
582#382C2312yes—
583#382C2312yes—
584#382C2314yes—
585#382C2314yes—
586#382C2314yes—
587#382C2312yes—
588#382C2314yes—
589#381C2312yes—
590#381C2312yes—
591#381C2312yes—
592#381C2312yes—
593#381C2314yes—
594#381C2314yes—
595#381C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2314yes—
604#380C2314yes—
605#380C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2312yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2312yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2312yes—
619C4×C22⋊C4C2312yes—
620#376C2312yes—
621#376C2312yes—
622C2×#95C2314yes—
623C2×#41—24no—
624C2×#41—42no—
625C2×#41—42no—
626C22×Q8—42no—
627C22×Q8—42no—
628C22×Q8—42no—
629C22×Q8—42no—
630C22×Q8—42no—
631C22×Q8—42no—
632C22×Q8C2412yes—
633C22×Q8C2412yes—
634C22×Q8C2412yes—
635C22×Q8C2412yes—
636C22×Q8C2411yescharacteristic
637C22×Q8C2411yescharacteristic
638C22×Q8C2412yes—
639C22×Q8C2412yes—
640C22×Q8C2411yescharacteristic
641C22×D4C2412yes—
642C22×D4C2411yescharacteristic
643C22×D4C2412yes—
644C22×D4C2414yes—
645C22×D4C2412yes—
646C22×D4C2414yes—
647C22×D4C2412yes—
648C22×D4C2414yes—
649C23×C4C2411yescharacteristic
650C23×C4C2412yes—
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2412yes—
655C23×C4C2412yes—
656C23×C4C2414yes—
657C23×C4C2414yes—
658C23×C4C2414yes—
659C4⋊Q8—24no—
660C4⋊Q8—24no—
661C4⋊Q8—28no—
662C4⋊Q8—28no—
663C4⋊Q8—28no—
664C4⋊Q8—44no—
665C4⋊Q8—44no—
666C4⋊Q8—44no—
667C4⋊Q8—48no—
668C4⋊Q8—44no—
669C4⋊Q8—44no—
670#127—44no—
671#126—216no—
672#126—48no—
673#126—48no—
674#126—48no—
675#125—44no—
676#125—48no—
677#125—48no—
678#124—28no—
679#124—44no—
680#124—42no—
681#124—42no—
682#124—44no—
683#124—44no—
684#124—44no—
685#124—44no—
686#123—48no—
687#123—48no—
688#123—48no—
689#123—48no—
690#123—48no—
691C22⋊Q8—44no—
692C22⋊Q8—48no—
693C22⋊Q8—48no—
694C22⋊Q8—48no—
695C22⋊Q8—48no—
696C22⋊Q8—44no—
697C22⋊Q8—48no—
698C22⋊Q8—48no—
699#121—44no—
700#121—48no—
701#121—44no—
702C4×Q8—44no—
703C4×Q8—44no—
704C4×Q8—44no—
705C4×Q8—48no—
706C4×D4—44no—
707C4×D4—44no—
708C4×D4—44no—
709C4×D4—44no—
710C4×D4—44no—
711C4×D4—48no—
712C4×D4—48no—
713#117—42no—
714#117—44no—
715#117—42no—
716#117—42no—
717#117—48no—
718#117—48no—
719C2×C4⋊C4—48no—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2411yescharacteristic
776C2×C22⋊C4C2411yescharacteristic
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C42—28no—
811C2×C42—24no—
812C2×C42C2412yes—
813C2×C42C2412yes—
814C2×C42C2411yescharacteristic
815C2×C42C2411yescharacteristic
816C2×C42C2411yescharacteristic
817C2×C42C2412yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2414yes—
832C2×C42C2414yes—
833C2×C42C2411yescharacteristic
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2412yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2412yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2412yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2412yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890C24C2514yes—
891C24C2512yes—
892C24C2511yescharacteristic
893#41—416no—
894C2×Q8—24no—
895C2×Q8—24no—
896C2×Q8—24no—
897C2×Q8—22no—
898C2×Q8—22no—
899C2×Q8—24no—
900C2×Q8—42no—
901C2×Q8—41no—
902C2×Q8—44no—
903C2×Q8—41no—
904C2×Q8—42no—
905C2×Q8—42no—
906C2×Q8—42no—
907C2×Q8—42no—
908C2×Q8—41no—
909C2×Q8—41no—
910C2×Q8—42no—
911C2×Q8—42no—
912C2×Q8—42no—
913C2×Q8—42no—
914C2×Q8—41no—
915C2×Q8—41no—
916C2×Q8—42no—
917C2×Q8—42no—
918C2×Q8—42no—
919C2×Q8—88no—
920C2×Q8—88no—
921C2×Q8H(5,𝔽2)14yes—
922C2×D4—24no—
923C2×D4—28no—
924C2×D4—24no—
925C2×D4—22no—
926C2×D4—24no—
927C2×D4—42no—
928C2×D4—41no—
929C2×D4—41no—
930C2×D4—42no—
931C2×D4—44no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4—44no—
938C2×D4—44no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—42no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—44no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—24no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—44no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4C2514yes—
973C22×C4C2512yes—
974C22×C4C2512yes—
975C22×C4C2514yes—
976C22×C4C2512yes—
977C22×C4C2514yes—
978C22×C4C2514yes—
979C22×C4C2512yes—
980C22×C4C2512yes—
981C22×C4C2514yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2514yes—
987C22×C4C2514yes—
988C22×C4C2511yescharacteristic
989C22×C4C2512yes—
990C22×C4C2511yescharacteristic
991C22×C4C2512yes—
992C4⋊C4—28no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—44no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—41no—
1062C22⋊C4—42no—
1063C22⋊C4—41no—
1064C22⋊C4—42no—
1065C22⋊C4—44no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C42—24no—
1083C42—22no—
1084C42—24no—
1085C42—24no—
1086C42—24no—
1087C42—24no—
1088C42—22no—
1089C42—22no—
1090C42—24no—
1091C42—24no—
1092C42—44no—
1093C42—44no—
1094C42—42no—
1095C42—44no—
1096C42—44no—
1097C42—44no—
1098C42—42no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—42no—
1103C42H(5,𝔽2)14yes—
1104C23—21no—
1105C23—21no—
1106C23—24no—
1107C23—24no—
1108C23—24no—
1109C23—22no—
1110C23—22no—
1111C23—24no—
1112C23—22no—
1113C23—24no—
1114C23—24no—
1115C23—24no—
1116C23—24no—
1117C23—24no—
1118C23—24no—
1119C23#58512yes—
1120C23C2611yescharacteristic
1121Q8—44no—
1122Q8—48no—
1123Q8—84no—
1124Q8—84no—
1125Q8—84no—
1126Q8—84no—
1127Q8—82no—
1128Q8—82no—
1129Q8—162no—
1130D4—48no—
1131D4—44no—
1132D4—84no—
1133D4—88no—
1134D4—84no—
1135D4—88no—
1136D4—164no—
1137D4—162no—
1138C2×C4—28no—
1139C2×C4—22no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—22no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—48no—
1190C2×C4—48no—
1191C2×C4—84no—
1192C2×C4—84no—
1193C2×C4—84no—
1194C2×C4—84no—
1195C2×C4—88no—
1196C2×C4—88no—
1197C2×C4—164no—
1198C2×C4C2×H(5,𝔽2)12yes—
1199C2×C4C2×H(5,𝔽2)14yes—
1200C2×C4C2×H(5,𝔽2)12yes—
1201C2×C4C2×H(5,𝔽2)14yes—
1202C22—24no—
1203C22—22no—
1204C22—42no—
1205C22—42no—
1206C22—44no—
1207C22—44no—
1208C22—44no—
1209C22—44no—
1210C22—44no—
1211C22—44no—
1212C22—42no—
1213C22—44no—
1214C22—42no—
1215C22—42no—
1216C22—44no—
1217C22—44no—
1218C22C22×H(5,𝔽2)11yescharacteristic
1219C22C22×H(5,𝔽2)11yescharacteristic
1220C22C2×#58511yescharacteristic
1221C222−1+614yes—
1222C4—22no—
1223C4—22no—
1224C4—24no—
1225C4—24no—
1226C4—44no—
1227C4—44no—
1228C4—42no—
1229C4—42no—
1230C4—44no—
1231C4—44no—
1232C4—44no—
1233C4—44no—
1234C4—42no—
1235C4—42no—
1236C4—44no—
1237C4—42no—
1238C4—42no—
1239C4—44no—
1240C4—42no—
1241C4—44no—
1242C2—42no—
1243C2—84no—
1244C2—82no—
1245C2#6281811yescharacteristic
1246C2#6288612yes—
1247C2#6304412yes—
1248C2#6306412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#52083C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #57025C2semidirect
2. #56843C2semidirect
3. #56642C2semidirect
4. #56641C2semidirect
5. #54564C2semidirect
6. #54320C2semidirect
8. #52079C2semidirect
9. #52075C2semidirect
10. #52072C2semidirect
11. #51999C2semidirect
12. #51726C2semidirect
13. #51586C2semidirect
14. #47075C2semidirect
15. #47065C2semidirect
16. #47032C2semidirect
17. #47003C2semidirect
18. #46325C2semidirect
19. #46311C2semidirect
20. #46131C2semidirect
21. #45981C2semidirect
22. #35316C2semidirect
23. #35211C2semidirect

Maximal subgroups

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

subgroupindex
#570252
#568432
#566422
#566412
#545642
#543202
#520832
#520792
#520752
#520722
#519992
#517262
#515862
#470752
#470652
#470322
#470032
#463252
#463112
#461312
#459812
#353162
#352112