Finite Group Databasebeta

← #8943142

Subgroups — #8943142

Order 512.

4568 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58565C214yesmaximal, complemented
2#55127C214yesmaximal, complemented
3#55121C214yesmaximal, complemented
4#52072C212yesmaximal, complemented
5#51668C212yesmaximal, complemented
6#51043C212yesmaximal, complemented
7#50184C212yesmaximal, complemented
8#48778C212yesmaximal, complemented
9#48697C214yesmaximal, complemented
10#48110C214yesmaximal, complemented
11#46401C214yesmaximal, complemented
12#44894C214yesmaximal, complemented
13#43564C214yesmaximal, complemented
14#42918C212yesmaximal, complemented
15#42046C214yesmaximal, complemented
16#41645C214yesmaximal, complemented
17#37956C212yesmaximal, complemented
18#37753C212yesmaximal
19#36708C211yesmaximal, characteristic, complemented
20#35954C212yesmaximal, complemented
21#35846C212yesmaximal, complemented
22#35633C211yesmaximal, characteristic
23#35391C211yesmaximal, characteristic, complemented
24C2×Q82C2212yescomplemented
25C2×#556C2212yes—
26C2×#544C2212yes—
27C2×#544C2211yescharacteristic
28C2×#543C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#525C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C2×#520C2211yescharacteristic
33#2848C2212yes—
34#2838C2214yescomplemented
35#2838C2214yescomplemented
36#2831C2214yescomplemented
37#2821C2214yescomplemented
38#2814C2214yes—
39#2809C2212yescomplemented
40#2805C2214yescomplemented
41#2804C2214yes—
42#2802C2214yescomplemented
43#2796C2214yes—
44#2793C2214yescomplemented
45#2788C2214yes—
46#2788C2214yescomplemented
47#2787C2214yes—
48#2783C2214yescomplemented
49#2779C2214yes—
50#2776C2214yescomplemented
51#2776C2214yescomplemented
52#2776C2214yescomplemented
53#2774C2214yescomplemented
54#2774C2214yescomplemented
55#2766C2214yescomplemented
56#2759C2214yescomplemented
57#2758C2214yescomplemented
58#2758C2214yescomplemented
59#2745C2214yes—
60#2745C2214yes—
61#2745C2214yes—
62#2743C2214yes—
63#2739C2214yes—
64#2739C2214yes—
65#2739C2214yescomplemented
66#2738C2214yescomplemented
67#2737C2214yes—
68#2734C2214yescomplemented
69#2734C2212yescomplemented
70#2734C2214yescomplemented
71#2732C2214yes—
72#2731C2212yescomplemented
73#2731C2212yescomplemented
74#2729C2214yes—
75#2729C2214yes—
76#2723C2214yes—
77#2713C2214yescomplemented
78#2713C2214yescomplemented
79#2711C2214yes—
80#2707C2214yes—
81#2702C2214yes—
82#2698C2214yes—
83#2690C2214yes—
84#2690C2214yes—
85#2689C2214yes—
86#2689C2214yes—
87#2677C2214yes—
88#2677C2214yes—
89#2677C2214yes—
90#2677C2214yescomplemented
91#2677C2214yescomplemented
92#2674C2214yes—
93#2674C2214yes—
94#2674C2214yes—
95#2666C2214yescomplemented
96#2665C2212yes—
97#2665C2214yescomplemented
98#2664C2214yescomplemented
99#2663C2214yes—
100#2659C2212yes—
101#2655C2214yescomplemented
102#2639C2212yes—
103#2638C2212yes—
104#2638C2212yescomplemented
105#2634C2214yescomplemented
106#2632C2214yescomplemented
107#2627C2212yes—
108#2627C2212yes—
109#2625C2212yes—
110#2621C2212yescomplemented
111#2618C2212yes—
112#2599C2214yes—
113#2590C2214yescomplemented
114#2588C2214yescomplemented
115#2587C2214yes—
116#2586C2214yescomplemented
117#2584C2214yescomplemented
118#2583C2212yes—
119#2583C2212yes—
120#2583C2212yescomplemented
121#2581C2212yescomplemented
122#2577C2214yes—
123#2577C2214yes—
124#2576C2214yes—
125#2574C2214yescomplemented
126#2573C2214yes—
127#2573C2214yes—
128#2572C2214yes—
129#2565C2214yescomplemented
130#2561C2212yes—
131#2561C2214yes—
132#2551C2214yescomplemented
133#2550C2214yescomplemented
134#2549C2214yes—
135#2549C2214yes—
136#2546C2212yescomplemented
137#2546C2214yescomplemented
138#2534C2212yes—
139#2534C2212yes—
140#2522C2214yescomplemented
141#2520C2214yescomplemented
142#2516C2214yes—
143#2515C2214yes—
144#2515C2214yes—
145#2502C2212yes—
146#2493C2214yes—
147#2492C2214yescomplemented
148#2486C2212yes—
149#2486C2212yes—
150#2484C2212yes—
151#2484C2212yescomplemented
152#2482C2212yes—
153#2480C2214yes—
154#2478C2214yes—
155#2478C2214yescomplemented
156#2477C2214yes—
157#2475C2214yes—
158#2472C2214yes—
159#2466C2214yes—
160#2466C2214yescomplemented
161#2465C2214yes—
162#2465C2214yes—
163#2465C2214yes—
164#2465C2214yescomplemented
165#2465C2214yescomplemented
166#2462C2214yescomplemented
167#2462C2214yescomplemented
168#2460C2214yes—
169#2458C2214yes—
170#2458C2214yes—
171#2453C2214yescomplemented
172#2453C2214yescomplemented
173#2452C2214yes—
174#2451C2214yescomplemented
175#2449C2214yes—
176#2447C2214yes—
177#2441C2214yescomplemented
178#2440C2214yes—
179#2440C2214yes—
180#2439C2214yes—
181#2434C2212yes—
182#2434C2212yes—
183#2432C2214yes—
184#2429C2214yes—
185#2429C2214yes—
186#2427C2214yes—
187#2421C2214yes—
188#2417C2214yes—
189#2415C2214yes—
190#2411C2214yes—
191#2396C2214yes—
192#2396C2212yescomplemented
193#2395C2212yes—
194#2395C2212yescomplemented
195#2381C2212yescomplemented
196#2381C2212yescomplemented
197#2378C2212yes—
198#2374C2214yes—
199#2369C2212yescomplemented
200#2365C2214yescomplemented
201#2362C2214yes—
202#2360C2214yes—
203#2360C2214yescomplemented
204#2359C2214yes—
205#2357C2212yes—
206#2347C2212yes—
207#2335C2214yes—
208#2329C2212yes—
209#2329C2212yes—
210#2323C2214yes—
211#2316C2211yescharacteristic
212#2315C2212yes—
213#2313C2212yes—
214#2313C2211yescharacteristic
215#2310C2211yescharacteristic
216C2×#385C2212yes—
217#2280C2211yescharacteristic
218#2273C2211yescharacteristic
219C22×#41C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C24×C4C2311yescharacteristic
222Q82—48no—
223#556—48no—
224#544—44no—
225#544—48no—
226#543—44no—
227#536—44no—
228C2×C4⋊Q8C2314yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2314yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2314yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2312yes—
239C2×#126C2314yes—
240C2×#126C2314yes—
241C2×#125C2314yes—
242C2×#125C2314yes—
243C2×#125C2314yes—
244C2×#124C2312yes—
245C2×#124C2314yes—
246#525—44no—
247C2×#123C2314yes—
248C2×#123C2312yes—
249C2×#123C2312yes—
250C2×#123C2312yes—
251C2×C22⋊Q8—44no—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×#121C2312yes—
269C2×#120C2312yes—
270#520—44no—
271C2×C4×Q8C2314yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2314yes—
275C2×C4×Q8C2314yes—
276C2×C4×Q8C2314yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×#117C2312yes—
282C2×#117C2311yescharacteristic
283C2×#117C2311yescharacteristic
284C2×#117C2311yescharacteristic
285C2×#117C2314yes—
286C2×#117C2312yes—
287C2×#117C2312yes—
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2312yes—
294C22×C22⋊C4C2312yes—
295C22×C22⋊C4C2311yescharacteristic
296C22×C22⋊C4C2311yescharacteristic
297C22×C22⋊C4C2312yes—
298#401C2314yes—
299#401C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2312yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2312yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2312yes—
320#400C2314yes—
321#400C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2312yes—
326#399C2314yes—
327#398C2312yes—
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#398C2312yes—
341#398C2312yes—
342#398C2312yes—
343#398C2312yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2312yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2312yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2312yes—
368#397C2314yes—
369#397C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2312yes—
386#395C2312yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2312yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2312yes—
417#393C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2312yes—
433#391C2314yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#390C2314yes—
438#390C2314yes—
439#390C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
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#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
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#388C2314yes—
495#388C2314yes—
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#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
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#384C2314yes—
568#383C2314yes—
569#383C2314yes—
570#383C2314yes—
571#383C2314yes—
572#382C2314yes—
573#382C2312yes—
574#382C2314yes—
575#381C2314yes—
576#381C2314yes—
577#381C2314yes—
578#381C2312yes—
579#381C2312yes—
580#381C2312yes—
581#381C2312yes—
582#381C2314yes—
583#381C2312yes—
584#380C2312yes—
585#380C2312yes—
586#380C2312yes—
587#380C2314yes—
588#380C2314yes—
589#380C2312yes—
590#380C2312yes—
591#380C2314yes—
592#380C2312yes—
593#380C2314yes—
594#380C2312yes—
595#380C2314yes—
596#379C2314yes—
597#379C2312yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2312yes—
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2314yes—
621C2×#95C2312yes—
622C2×#95C2312yes—
623C25C2411yescharacteristic
624C2×#41—24no—
625C2×#41—42no—
626C2×#41—42no—
627C22×Q8—42no—
628C22×Q8—42no—
629C22×Q8—42no—
630C22×Q8C2414yes—
631C22×Q8C2412yes—
632C22×Q8C2414yes—
633C22×Q8C2412yes—
634C22×Q8C2412yes—
635C22×Q8C2412yes—
636C22×Q8C2412yes—
637C22×Q8C2412yes—
638C22×Q8C2411yescharacteristic
639C22×D4C2412yes—
640C22×D4C2411yescharacteristic
641C22×D4C2414yes—
642C23×C4—42no—
643C23×C4—42no—
644C23×C4—42no—
645C23×C4C2411yescharacteristic
646C23×C4C2412yes—
647C23×C4C2411yescharacteristic
648C23×C4C2411yescharacteristic
649C23×C4C2411yescharacteristic
650C23×C4C2412yes—
651C23×C4C2411yescharacteristic
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2412yes—
655C23×C4C2412yes—
656C23×C4C2412yes—
657C23×C4C2412yes—
658C23×C4C2411yescharacteristic
659C23×C4C2412yes—
660C4⋊Q8—28no—
661C4⋊Q8—216no—
662C4⋊Q8—48no—
663C4⋊Q8—44no—
664C4⋊Q8—44no—
665C4⋊Q8—44no—
666C4⋊Q8—48no—
667C4⋊Q8—44no—
668C4⋊Q8—48no—
669C4⋊Q8—48no—
670C4⋊Q8—44no—
671#126—48no—
672#126—48no—
673#125—48no—
674#125—48no—
675#125—48no—
676#124—44no—
677#124—48no—
678#123—216no—
679#123—44no—
680#123—44no—
681#123—44no—
682C22⋊Q8—28no—
683C22⋊Q8—28no—
684C22⋊Q8—216no—
685C22⋊Q8—44no—
686C22⋊Q8—44no—
687C22⋊Q8—44no—
688C22⋊Q8—48no—
689C22⋊Q8—48no—
690C22⋊Q8—48no—
691C22⋊Q8—48no—
692C22⋊Q8—48no—
693C22⋊Q8—48no—
694C22⋊Q8—44no—
695C22⋊Q8—48no—
696C22⋊Q8—44no—
697C22⋊Q8—44no—
698#121—44no—
699#120—44no—
700C4×Q8—44no—
701C4×Q8—48no—
702C4×Q8—48no—
703C4×Q8—48no—
704C4×Q8—48no—
705C4×Q8—44no—
706C4×D4—28no—
707C4×D4—44no—
708C4×D4—48no—
709C4×D4—44no—
710#117—28no—
711#117—42no—
712#117—44no—
713#117—48no—
714#117—42no—
715#117—42no—
716#117—44no—
717C2×C4⋊C4—24no—
718C2×C4⋊C4—24no—
719C2×C4⋊C4—44no—
720C2×C4⋊C4—44no—
721C2×C4⋊C4—44no—
722C2×C4⋊C4—42no—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2411yescharacteristic
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⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C22⋊C4—24no—
781C2×C22⋊C4—28no—
782C2×C22⋊C4—44no—
783C2×C22⋊C4—42no—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2412yes—
826C2×C42C2414yes—
827C2×C42C2414yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2414yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2412yes—
839#95C2412yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2412yes—
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#95C2412yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894C24—22no—
895C24—24no—
896C24—41no—
897C24—41no—
898C24—42no—
899C24C2512yes—
900C24C2511yescharacteristic
901C24C2512yes—
902#41—416no—
903C2×Q8—24no—
904C2×Q8—28no—
905C2×Q8—24no—
906C2×Q8—28no—
907C2×Q8—24no—
908C2×Q8—44no—
909C2×Q8—41no—
910C2×Q8—44no—
911C2×Q8—41no—
912C2×Q8—44no—
913C2×Q8—42no—
914C2×Q8—42no—
915C2×Q8—42no—
916C2×Q8—44no—
917C2×Q8—42no—
918C2×Q8—44no—
919C2×Q8—42no—
920C2×Q8—42no—
921C2×Q8—42no—
922C2×Q8—42no—
923C2×Q8—42no—
924C2×Q8—42no—
925C2×Q8—42no—
926C2×Q8—42no—
927C2×Q8—42no—
928C2×Q8—88no—
929C2×Q8H(5,𝔽2)14yes—
930C2×D4—24no—
931C2×D4—28no—
932C2×D4—24no—
933C2×D4—22no—
934C2×D4—41no—
935C2×D4—42no—
936C2×D4—41no—
937C2×D4—44no—
938C2×D4—44no—
939C22×C4—22no—
940C22×C4—22no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—24no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—41no—
961C22×C4—41no—
962C22×C4—41no—
963C22×C4—42no—
964C22×C4—41no—
965C22×C4—44no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—41no—
969C22×C4—41no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—44no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—88no—
979C22×C4H(5,𝔽2)14yes—
980C22×C42−1+418yes—
981C22×C4C2514yes—
982C22×C4C2514yes—
983C22×C4C2512yes—
984C22×C4C2512yes—
985C22×C4C2514yes—
986C22×C4C2514yes—
987C22×C4C2514yes—
988C22×C4C2514yes—
989C22×C4C2514yes—
990C22×C4C2512yes—
991C22×C4C2512yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C22×C4C2514yes—
995C22×C4C2514yes—
996C22×C4C2512yes—
997C22×C4C2511yescharacteristic
998C22×C4C2512yes—
999C22×C4C2514yes—
1000C22×C4C2511yescharacteristic
1001C4⋊C4—24no—
1002C4⋊C4—24no—
1003C4⋊C4—28no—
1004C4⋊C4—24no—
1005C4⋊C4—28no—
1006C4⋊C4—24no—
1007C4⋊C4—24no—
1008C4⋊C4—28no—
1009C4⋊C4—24no—
1010C4⋊C4—24no—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—41no—
1025C4⋊C4—44no—
1026C4⋊C4—42no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—41no—
1037C4⋊C4—42no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—42no—
1046C4⋊C4—44no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—24no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—24no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—44no—
1080C22⋊C4—42no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C42—28no—
1090C42—24no—
1091C42—24no—
1092C42—28no—
1093C42—44no—
1094C42—44no—
1095C42—44no—
1096C42—42no—
1097C42—42no—
1098C42—42no—
1099C42—44no—
1100C42—44no—
1101C42—44no—
1102C42—42no—
1103C42—44no—
1104C42—44no—
1105C42—42no—
1106C42—42no—
1107C42—42no—
1108C23—28no—
1109C23—22no—
1110C23—22no—
1111C23—21no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—21no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—24no—
1122C23—22no—
1123C23—24no—
1124C23—82no—
1125C23—82no—
1126C23—84no—
1127C23—84no—
1128C23C2×H(5,𝔽2)12yes—
1129C23C2×2−1+414yes—
1130C23C2611yescharacteristic
1131Q8—44no—
1132Q8—416no—
1133Q8—88no—
1134Q8—84no—
1135Q8—84no—
1136Q8—84no—
1137Q8—162no—
1138Q8—162no—
1139Q8—162no—
1140D4—48no—
1141D4—44no—
1142D4—88no—
1143C2×C4—28no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—22no—
1150C2×C4—21no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
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—22no—
1182C2×C4—22no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—44no—
1196C2×C4—48no—
1197C2×C4—48no—
1198C2×C4—84no—
1199C2×C4—84no—
1200C2×C4—84no—
1201C2×C4—82no—
1202C2×C4—84no—
1203C2×C4—82no—
1204C2×C4—82no—
1205C2×C4—82no—
1206C2×C4—162no—
1207C2×C4—162no—
1208C2×C4—162no—
1209C2×C4C2×H(5,𝔽2)14yes—
1210C2×C4C2×H(5,𝔽2)14yes—
1211C2×C4C2×H(5,𝔽2)12yes—
1212C2×C4C2×2−1+418yes—
1213C2×C4#58512yes—
1214C22—22no—
1215C22—22no—
1216C22—24no—
1217C22—22no—
1218C22—24no—
1219C22—24no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—44no—
1230C22—44no—
1231C22—88no—
1232C22C22×H(5,𝔽2)11yescharacteristic
1233C22C22×H(5,𝔽2)11yescharacteristic
1234C22C22×2−1+412yes—
1235C22C2×#58511yescharacteristic
1236C222−1+612yes—
1237C4—22no—
1238C4—22no—
1239C4—24no—
1240C4—24no—
1241C4—28no—
1242C4—42no—
1243C4—42no—
1244C4—42no—
1245C4—44no—
1246C4—44no—
1247C4—42no—
1248C4—44no—
1249C4—42no—
1250C4—42no—
1251C4—44no—
1252C4—44no—
1253C4—44no—
1254C4—44no—
1255C4—44no—
1256C4—44no—
1257C2—42no—
1258C2—44no—
1259C2—82no—
1260C2#6281811yescharacteristic
1261C2#6283311yescharacteristic
1262C2#6287111yescharacteristic
1263C2#6289312yes—
1264C2#6293212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58565C2semidirect
2. #55127C2semidirect
3. #55121C2semidirect
4. #52072C2semidirect
5. #51668C2semidirect
6. #51043C2semidirect
7. #50184C2semidirect
8. #48778C2semidirect
9. #48697C2semidirect
10. #48110C2semidirect
11. #46401C2semidirect
12. #44894C2semidirect
13. #43564C2semidirect
14. #42918C2semidirect
15. #42046C2semidirect
16. #41645C2semidirect
17. #37956C2semidirect
19. #36708C2semidirect
20. #35954C2semidirect
21. #35846C2semidirect
23. #35391C2semidirect
24. C2×Q82C22semidirect
34. #2838C22semidirect
35. #2838C22semidirect
36. #2831C22semidirect
37. #2821C22semidirect
39. #2809C22semidirect
40. #2805C22semidirect
42. #2802C22semidirect
44. #2793C22semidirect
46. #2788C22semidirect
48. #2783C22semidirect
50. #2776C22semidirect
51. #2776C22semidirect
52. #2776C22semidirect
53. #2774C22semidirect
54. #2774C22semidirect
55. #2766C22semidirect
56. #2759C22semidirect
57. #2758C22semidirect
58. #2758C22semidirect
65. #2739C22semidirect
66. #2738C22semidirect
68. #2734C22semidirect
69. #2734C22semidirect
70. #2734C22semidirect
72. #2731C22semidirect
73. #2731C22semidirect
77. #2713C22semidirect
78. #2713C22semidirect
90. #2677C22semidirect
91. #2677C22semidirect
95. #2666C22semidirect
97. #2665C22semidirect
98. #2664C22semidirect
101. #2655C22semidirect
104. #2638C22semidirect
105. #2634C22semidirect
106. #2632C22semidirect
110. #2621C22semidirect
113. #2590C22semidirect
114. #2588C22semidirect
116. #2586C22semidirect
117. #2584C22semidirect
120. #2583C22semidirect
121. #2581C22semidirect
125. #2574C22semidirect
129. #2565C22semidirect
132. #2551C22semidirect
133. #2550C22semidirect
136. #2546C22semidirect
137. #2546C22semidirect
140. #2522C22semidirect
141. #2520C22semidirect
147. #2492C22semidirect
151. #2484C22semidirect
155. #2478C22semidirect
160. #2466C22semidirect
164. #2465C22semidirect
165. #2465C22semidirect
166. #2462C22semidirect
167. #2462C22semidirect
171. #2453C22semidirect
172. #2453C22semidirect
174. #2451C22semidirect
177. #2441C22semidirect
192. #2396C22semidirect
194. #2395C22semidirect
195. #2381C22semidirect
196. #2381C22semidirect
199. #2369C22semidirect
200. #2365C22semidirect
203. #2360C22semidirect

Maximal subgroups

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

subgroupindex
#585652
#551272
#551212
#520722
#516682
#510432
#501842
#487782
#486972
#481102
#464012
#448942
#435642
#429182
#420462
#416452
#379562
#377532
#367082
#359542
#358462
#356332
#353912