Finite Group Databasebeta

← #8935136

Subgroups — #8935136

Order 512.

5430 conjugacy classes of subgroups.

The subgroup lattice has 1339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58598C214yesmaximal, complemented
2#58007C214yesmaximal, complemented
3#56675C214yesmaximal, complemented
4#52007C214yesmaximal, complemented
5#51986C214yesmaximal, complemented
6#51336C212yesmaximal, complemented
7#49549C212yesmaximal, complemented
8#48566C214yesmaximal, complemented
9#47882C212yesmaximal, complemented
10#47141C212yesmaximal, complemented
11#47004C212yesmaximal, complemented
12#43370C214yesmaximal, complemented
13#43003C214yesmaximal, complemented
14#41180C214yesmaximal, complemented
15#40943C214yesmaximal, complemented
16#40653C212yesmaximal, complemented
17#37753C212yesmaximal, complemented
18#37752C212yesmaximal, complemented
19#36708C211yesmaximal, characteristic, complemented
20#35703C212yesmaximal, complemented
21#35687C212yesmaximal, complemented
22#35659C211yesmaximal, characteristic, complemented
23#35349C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic, complemented
25C2×D4×Q8C2214yescomplemented
26C2×#548C2212yes—
27C2×#544C2212yescomplemented
28C2×#544C2211yescharacteristic, complemented
29C2×#543C2212yes—
30C2×#525C2212yes—
31C22×C22⋊Q8C2211yescharacteristic
32C2×#518C2211yescharacteristic
33#2848C2212yes—
34#2837C2214yescomplemented
35#2832C2214yescomplemented
36#2830C2214yescomplemented
37#2826C2212yescomplemented
38#2826C2214yescomplemented
39#2812C2212yes—
40#2808C2214yescomplemented
41#2799C2214yescomplemented
42#2799C2214yescomplemented
43#2797C2214yes—
44#2797C2214yescomplemented
45#2788C2214yescomplemented
46#2770C2214yescomplemented
47#2764C2212yes—
48#2764C2214yescomplemented
49#2758C2214yescomplemented
50#2758C2214yescomplemented
51#2756C2214yes—
52#2756C2214yescomplemented
53#2752C2212yes—
54#2751C2214yescomplemented
55#2750C2214yes—
56#2750C2214yes—
57#2749C2214yes—
58#2747C2214yescomplemented
59#2747C2214yescomplemented
60#2740C2214yescomplemented
61#2737C2214yescomplemented
62#2731C2214yescomplemented
63#2729C2214yes—
64#2729C2214yescomplemented
65#2729C2214yescomplemented
66#2728C2214yes—
67#2728C2214yescomplemented
68#2717C2214yescomplemented
69#2713C2214yescomplemented
70#2713C2214yescomplemented
71#2712C2212yescomplemented
72#2711C2214yes—
73#2711C2214yescomplemented
74#2710C2214yescomplemented
75#2708C2214yes—
76#2707C2214yescomplemented
77#2704C2214yescomplemented
78#2703C2214yes—
79#2696C2214yes—
80#2692C2214yes—
81#2692C2214yes—
82#2692C2214yescomplemented
83#2692C2214yescomplemented
84#2690C2214yes—
85#2690C2214yescomplemented
86#2690C2214yescomplemented
87#2690C2214yescomplemented
88#2681C2214yes—
89#2677C2214yes—
90#2677C2212yescomplemented
91#2677C2214yescomplemented
92#2677C2214yescomplemented
93#2677C2214yescomplemented
94#2676C2214yes—
95#2674C2214yescomplemented
96#2665C2212yescomplemented
97#2652C2214yescomplemented
98#2651C2214yescomplemented
99#2648C2214yescomplemented
100#2648C2214yescomplemented
101#2639C2212yes—
102#2639C2212yescomplemented
103#2638C2212yes—
104#2634C2214yescomplemented
105#2633C2214yescomplemented
106#2631C2212yes—
107#2627C2212yescomplemented
108#2618C2212yescomplemented
109#2617C2212yes—
110#2617C2212yes—
111#2616C2212yescomplemented
112#2616C2214yescomplemented
113#2610C2212yes—
114#2605C2214yescomplemented
115#2599C2212yes—
116#2599C2214yescomplemented
117#2598C2214yes—
118#2579C2212yes—
119#2579C2212yes—
120#2578C2214yes—
121#2578C2214yes—
122#2578C2214yescomplemented
123#2578C2214yescomplemented
124#2577C2214yescomplemented
125#2564C2214yescomplemented
126#2561C2212yes—
127#2549C2214yescomplemented
128#2549C2214yescomplemented
129#2543C2212yes—
130#2530C2214yescomplemented
131#2523C2212yescomplemented
132#2523C2214yescomplemented
133#2523C2214yescomplemented
134#2492C2214yes—
135#2492C2214yescomplemented
136#2487C2212yes—
137#2484C2212yescomplemented
138#2482C2212yes—
139#2477C2214yes—
140#2477C2214yes—
141#2477C2214yes—
142#2477C2214yescomplemented
143#2476C2214yes—
144#2475C2214yescomplemented
145#2474C2214yescomplemented
146#2472C2214yes—
147#2472C2214yes—
148#2465C2214yes—
149#2465C2214yescomplemented
150#2463C2214yes—
151#2463C2214yes—
152#2462C2214yescomplemented
153#2460C2214yes—
154#2460C2214yescomplemented
155#2460C2214yescomplemented
156#2460C2214yescomplemented
157#2459C2214yes—
158#2452C2214yes—
159#2452C2214yescomplemented
160#2450C2214yes—
161#2450C2214yes—
162#2450C2214yescomplemented
163#2450C2214yescomplemented
164#2449C2214yes—
165#2449C2214yescomplemented
166#2444C2214yes—
167#2438C2214yes—
168#2437C2214yes—
169#2437C2212yes—
170#2434C2214yescomplemented
171#2434C2214yescomplemented
172#2434C2212yescomplemented
173#2432C2214yescomplemented
174#2432C2214yescomplemented
175#2432C2214yescomplemented
176#2427C2214yes—
177#2411C2214yes—
178#2410C2214yes—
179#2409C2212yes—
180#2409C2212yes—
181#2409C2214yes—
182#2409C2214yescomplemented
183#2409C2214yescomplemented
184#2407C2214yes—
185#2407C2214yes—
186#2407C2214yes—
187#2407C2214yescomplemented
188#2407C2214yescomplemented
189#2406C2212yescomplemented
190#2406C2212yescomplemented
191#2404C2212yes—
192#2404C2212yes—
193#2398C2212yes—
194#2388C2212yes—
195#2388C2214yescomplemented
196C2×#393C2212yes—
197#2381C2214yescomplemented
198#2378C2212yescomplemented
199#2368C2214yescomplemented
200#2364C2214yes—
201#2359C2214yescomplemented
202#2358C2214yes—
203#2358C2214yes—
204#2353C2212yes—
205#2341C2212yescomplemented
206Q8×C22⋊C4C2214yescomplemented
207#2337C2214yescomplemented
208#2329C2212yes—
209#2329C2212yescomplemented
210#2321C2214yes—
211#2315C2211yescharacteristic
212#2315C2211yescharacteristic
213#2313C2211yescharacteristic, complemented
214#2311C2212yescomplemented
215#2310C2211yescharacteristic, complemented
216#2308C2211yescharacteristic
217C2×#386C2211yescharacteristic
218C2×#385C2211yescharacteristic
219C2×2−1+4—48no—
220C2×2−1+4—44no—
221C22×#41C2312yes—
222C22×#41C2312yes—
223C22×#41C2314yes—
224C22×#41C2312yes—
225C23×Q8C2311yescharacteristic
226C23×Q8C2314yes—
227C23×Q8C2312yes—
228C23×D4C2311yescharacteristic
229C24×C4C2311yescharacteristic
230D4×Q8—416no—
231#548—48no—
232#544—44no—
233#544—48no—
234#543—48no—
235C2×C4⋊Q8C2314yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2314yes—
240C2×#125C2314yes—
241C2×#125C2314yes—
242C2×#125C2314yes—
243C2×#124C2314yes—
244C2×#124C2312yes—
245C2×#124C2314yes—
246#525—48no—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×C22⋊Q8—44no—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×#121C2312yes—
271C2×#121C2312yes—
272C2×#121C2312yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#120C2314yes—
276C2×#120C2314yes—
277#518—44no—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2314yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×#117C2312yes—
291C2×#117C2314yes—
292C2×#117C2312yes—
293C2×#117C2312yes—
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2312yes—
297C22×C4⋊C4C2311yescharacteristic
298C22×C22⋊C4C2311yescharacteristic
299C22×C22⋊C4C2311yescharacteristic
300C22×C22⋊C4C2311yescharacteristic
301C22×C22⋊C4C2311yescharacteristic
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2314yes—
304C22×C22⋊C4C2312yes—
305C22×C22⋊C4C2312yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#399C2314yes—
322#399C2312yes—
323#399C2314yes—
324#399C2314yes—
325#399C2312yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2312yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#397C2312yes—
340#397C2312yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2312yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2312yes—
356#397C2314yes—
357#397C2314yes—
358#397C2312yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2312yes—
371#395C2314yes—
372#395C2314yes—
373#395C2312yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2312yes—
388#394C2314yes—
389#394C2314yes—
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#394C2314yes—
404#393C2312yes—
405#393C2312yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2312yes—
412#393C2312yes—
413#393C2312yes—
414#393C2312yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2312yes—
419#393C2312yes—
420#393C2314yes—
421#392C2314yes—
422#392C2312yes—
423#392C2314yes—
424#392C2312yes—
425#392C2312yes—
426#392C2314yes—
427#392C2312yes—
428#392C2314yes—
429#392C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2314yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
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#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#386C2312yes—
520#386C2314yes—
521#386C2312yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2312yes—
536#386C2312yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2312yes—
549#385C2314yes—
550#385C2314yes—
551#385C2312yes—
552#385C2314yes—
553#385C2312yes—
554#385C2312yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2312yes—
560#385C2312yes—
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#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#383C2314yes—
580#383C2314yes—
581#383C2314yes—
582#383C2314yes—
583#383C2312yes—
584#381C2314yes—
585#381C2312yes—
586#381C2312yes—
587#381C2312yes—
588#381C2312yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2312yes—
594#380C2314yes—
595#380C2312yes—
596#380C2312yes—
597#380C2314yes—
598#380C2312yes—
599#380C2312yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2312yes—
604#379C2314yes—
605#379C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619#376C2312yes—
620C2×#95C2314yes—
621C2×#95C2312yes—
622C2×#95C2312yes—
623C2×#95C2312yes—
624C25C2411yescharacteristic
625C25C2411yescharacteristic
6262−1+4—464no—
627C2×#41—28no—
628C2×#41—28no—
629C2×#41—44no—
630C2×#41—48no—
631C2×#41—44no—
632C2×#41—44no—
633C2×#41—48no—
634C2×#41—48no—
635C2×#41—48no—
636C2×#41—48no—
637C22×Q8—216no—
638C22×Q8—24no—
639C22×Q8—44no—
640C22×Q8—48no—
641C22×Q8—48no—
642C22×Q8—44no—
643C22×Q8—48no—
644C22×Q8C2412yes—
645C22×Q8C2414yes—
646C22×Q8C2412yes—
647C22×Q8C2414yes—
648C22×Q8C2412yes—
649C22×Q8C2412yes—
650C22×Q8C2414yes—
651C22×Q8C2412yes—
652C22×D4—24no—
653C22×D4—42no—
654C22×D4—42no—
655C22×D4C2412yes—
656C22×D4C2412yes—
657C22×D4C2414yes—
658C22×D4C2414yes—
659C22×D4C2414yes—
660C22×D4C2414yes—
661C22×D4C2414yes—
662C22×D4C2412yes—
663C22×D4C2412yes—
664C22×D4C2412yes—
665C23×C4—44no—
666C23×C4—42no—
667C23×C4C2411yescharacteristic
668C23×C4C2414yes—
669C23×C4C2414yes—
670C23×C4C2411yescharacteristic
671C23×C4C2411yescharacteristic
672C23×C4C2412yes—
673C23×C4C2411yescharacteristic
674C23×C4C2412yes—
675C23×C4C2414yes—
676C23×C4C2412yes—
677C23×C4C2411yescharacteristic
678C23×C4C2412yes—
679C23×C4C2411yescharacteristic
680C23×C4C2414yes—
681C23×C4C2412yes—
682C23×C4C2411yescharacteristic
683C23×C4C2411yescharacteristic
684C23×C4C2412yes—
685C23×C4C2414yes—
686C23×C4C2411yescharacteristic
687C4⋊Q8—216no—
688C4⋊Q8—48no—
689C4⋊Q8—48no—
690C4⋊Q8—48no—
691C4⋊Q8—48no—
692#125—48no—
693#125—48no—
694#125—48no—
695#124—44no—
696#124—48no—
697#124—48no—
698#123—48no—
699#123—48no—
700C22⋊Q8—28no—
701C22⋊Q8—28no—
702C22⋊Q8—216no—
703C22⋊Q8—28no—
704C22⋊Q8—44no—
705C22⋊Q8—48no—
706C22⋊Q8—48no—
707C22⋊Q8—48no—
708C22⋊Q8—48no—
709C22⋊Q8—48no—
710C22⋊Q8—48no—
711C22⋊Q8—48no—
712C22⋊Q8—48no—
713C22⋊Q8—48no—
714C22⋊Q8—44no—
715C22⋊Q8—44no—
716C22⋊Q8—48no—
717C22⋊Q8—48no—
718C22⋊Q8—48no—
719C22⋊Q8—48no—
720#121—48no—
721#121—48no—
722#121—44no—
723#121—44no—
724#121—44no—
725#120—216no—
726#120—48no—
727C4×Q8—44no—
728C4×Q8—48no—
729C4×D4—28no—
730C4×D4—44no—
731C4×D4—48no—
732C4×D4—44no—
733C4×D4—48no—
734C4×D4—48no—
735C4×D4—48no—
736C4×D4—48no—
737C4×D4—48no—
738C4×D4—44no—
739#117—44no—
740#117—48no—
741#117—44no—
742#117—44no—
743C2×C4⋊C4—24no—
744C2×C4⋊C4—44no—
745C2×C4⋊C4—42no—
746C2×C4⋊C4—42no—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C22⋊C4—24no—
789C2×C22⋊C4—44no—
790C2×C22⋊C4—48no—
791C2×C22⋊C4—44no—
792C2×C22⋊C4—42no—
793C2×C22⋊C4—42no—
794C2×C22⋊C4—42no—
795C2×C22⋊C4—42no—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C42C2412yes—
846C2×C42C2414yes—
847C2×C42C2414yes—
848C2×C42C2412yes—
849C2×C42C2414yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856#95C2412yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2412yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2412yes—
868#95C2414yes—
869#95C2412yes—
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#95C2412yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2412yes—
895#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2412yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910C24—22no—
911C24—22no—
912C24—22no—
913C24—42no—
914C24—41no—
915C24—41no—
916C24—42no—
917C24—42no—
918C24—42no—
919C242−1+414yescomplemented
920C24C2514yes—
921C24C2511yescharacteristic
922C24C2511yescharacteristic
923C24C2512yes—
924C24C2511yescharacteristic
925#41—432no—
926#41—432no—
927#41—464no—
928#41—432no—
929C2×Q8—28no—
930C2×Q8—24no—
931C2×Q8—28no—
932C2×Q8—28no—
933C2×Q8—28no—
934C2×Q8—24no—
935C2×Q8—28no—
936C2×Q8—42no—
937C2×Q8—44no—
938C2×Q8—42no—
939C2×Q8—42no—
940C2×Q8—44no—
941C2×Q8—44no—
942C2×Q8—44no—
943C2×Q8—44no—
944C2×Q8—42no—
945C2×Q8—42no—
946C2×Q8—42no—
947C2×Q8—44no—
948C2×Q8—44no—
949C2×Q8—416no—
950C2×Q8—464no—
951C2×Q8—816no—
952C2×Q8H(5,𝔽2)18yes—
953C2×D4—24no—
954C2×D4—28no—
955C2×D4—28no—
956C2×D4—24no—
957C2×D4—24no—
958C2×D4—24no—
959C2×D4—28no—
960C2×D4—28no—
961C2×D4—28no—
962C2×D4—28no—
963C2×D4—24no—
964C2×D4—24no—
965C2×D4—44no—
966C2×D4—42no—
967C2×D4—42no—
968C2×D4—44no—
969C2×D4—42no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—42no—
973C2×D4—42no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—416no—
982C22×C4—22no—
983C22×C4—24no—
984C22×C4—22no—
985C22×C4—22no—
986C22×C4—22no—
987C22×C4—24no—
988C22×C4—22no—
989C22×C4—22no—
990C22×C4—28no—
991C22×C4—28no—
992C22×C4—28no—
993C22×C4—28no—
994C22×C4—28no—
995C22×C4—24no—
996C22×C4—28no—
997C22×C4—24no—
998C22×C4—24no—
999C22×C4—42no—
1000C22×C4—41no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—41no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—42no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—42no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—41no—
1020C22×C4—42no—
1021C22×C4—41no—
1022C22×C4—44no—
1023C22×C4—42no—
1024C22×C4—42no—
1025C22×C4—42no—
1026C22×C4—44no—
1027C22×C4—42no—
1028C22×C4—44no—
1029C22×C4—44no—
1030C22×C4—42no—
1031C22×C4—88no—
1032C22×C4H(5,𝔽2)14yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2514yes—
1036C22×C4C2514yes—
1037C22×C4C2514yes—
1038C22×C4C2512yes—
1039C22×C4C2514yes—
1040C22×C4C2512yes—
1041C22×C4C2514yes—
1042C22×C4C2514yes—
1043C22×C4C2512yes—
1044C22×C4C2514yes—
1045C22×C4C2514yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2514yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C4⋊C4—28no—
1052C4⋊C4—28no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—28no—
1057C4⋊C4—28no—
1058C4⋊C4—28no—
1059C4⋊C4—28no—
1060C4⋊C4—28no—
1061C4⋊C4—28no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—42no—
1073C4⋊C4—44no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—42no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—42no—
1086C4⋊C4—44no—
1087C4⋊C4—42no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C22⋊C4—24no—
1093C22⋊C4—28no—
1094C22⋊C4—28no—
1095C22⋊C4—28no—
1096C22⋊C4—28no—
1097C22⋊C4—24no—
1098C22⋊C4—28no—
1099C22⋊C4—24no—
1100C22⋊C4—24no—
1101C22⋊C4—24no—
1102C22⋊C4—28no—
1103C22⋊C4—28no—
1104C22⋊C4—28no—
1105C22⋊C4—28no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C42—24no—
1142C42—28no—
1143C42—44no—
1144C42—44no—
1145C42—42no—
1146C42—44no—
1147C42—44no—
1148C42—44no—
1149C42—44no—
1150C42—44no—
1151C42—44no—
1152C23—28no—
1153C23—21no—
1154C23—24no—
1155C23—22no—
1156C23—22no—
1157C23—21no—
1158C23—22no—
1159C23—22no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—22no—
1165C23—22no—
1166C23—24no—
1167C23—22no—
1168C23—22no—
1169C23—24no—
1170C23—24no—
1171C23—24no—
1172C23—24no—
1173C23—24no—
1174C23—24no—
1175C23—24no—
1176C23—44no—
1177C23—48no—
1178C23—82no—
1179C23—82no—
1180C23—84no—
1181C23—84no—
1182C23—161no—
1183C23—161no—
1184C23—162no—
1185C23C2×H(5,𝔽2)12yes—
1186C23C2×2−1+412yes—
1187C23C2×2−1+414yes—
1188C23#58512yes—
1189C23C2611yescharacteristic
1190Q8—216no—
1191Q8—48no—
1192Q8—416no—
1193Q8—48no—
1194Q8—88no—
1195Q8—84no—
1196Q8—162no—
1197Q8—164no—
1198D4—416no—
1199D4—48no—
1200D4—48no—
1201D4—48no—
1202D4—48no—
1203D4—416no—
1204D4—48no—
1205D4—88no—
1206D4—88no—
1207D4—88no—
1208C2×C4—28no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—44no—
1255C2×C4—416no—
1256C2×C4—416no—
1257C2×C4—416no—
1258C2×C4—44no—
1259C2×C4—48no—
1260C2×C4—44no—
1261C2×C4—44no—
1262C2×C4—84no—
1263C2×C4—84no—
1264C2×C4—84no—
1265C2×C4—88no—
1266C2×C4—82no—
1267C2×C4—82no—
1268C2×C4—161no—
1269C2×C4—162no—
1270C2×C4—161no—
1271C2×C4—164no—
1272C2×C4—162no—
1273C2×C4C2×H(5,𝔽2)18yes—
1274C2×C4C2×H(5,𝔽2)14yes—
1275C2×C4C2×H(5,𝔽2)14yes—
1276C22—22no—
1277C22—22no—
1278C22—24no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—28no—
1283C22—24no—
1284C22—24no—
1285C22—42no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—42no—
1290C22—41no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—44no—
1295C22—42no—
1296C22—44no—
1297C22—44no—
1298C22—44no—
1299C22—44no—
1300C22—44no—
1301C22—44no—
1302C22—44no—
1303C22—88no—
1304C22—164no—
1305C22C22×H(5,𝔽2)11yescharacteristic
1306C22C22×H(5,𝔽2)12yes—
1307C22C22×2−1+411yescharacteristic
1308C22C2×#58511yescharacteristic
1309C222−1+612yes—
1310C4—24no—
1311C4—28no—
1312C4—24no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—44no—
1317C4—42no—
1318C4—44no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—44no—
1323C4—44no—
1324C4—44no—
1325C4—44no—
1326C4—44no—
1327C4—44no—
1328C2—42no—
1329C2—42no—
1330C2—42no—
1331C2—44no—
1332C2—84no—
1333C2#6281711yescharacteristic
1334C2#6281911yescharacteristic
1335C2#6288711yescharacteristic
1336C2#6289312yes—
1337C2#6291912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58598C2semidirect
2. #58007C2semidirect
3. #56675C2semidirect
4. #52007C2semidirect
5. #51986C2semidirect
6. #51336C2semidirect
7. #49549C2semidirect
8. #48566C2semidirect
9. #47882C2semidirect
10. #47141C2semidirect
11. #47004C2semidirect
12. #43370C2semidirect
13. #43003C2semidirect
14. #41180C2semidirect
15. #40943C2semidirect
16. #40653C2semidirect
17. #37753C2semidirect
18. #37752C2semidirect
19. #36708C2semidirect
20. #35703C2semidirect
21. #35687C2semidirect
22. #35659C2semidirect
23. #35349C2semidirect
24. C22×2−1+4C22semidirect
25. C2×D4×Q8C22semidirect
27. C2×#544C22semidirect
28. C2×#544C22semidirect
34. #2837C22semidirect
35. #2832C22semidirect
36. #2830C22semidirect
37. #2826C22semidirect
38. #2826C22semidirect
40. #2808C22semidirect
41. #2799C22semidirect
42. #2799C22semidirect
44. #2797C22semidirect
45. #2788C22semidirect
46. #2770C22semidirect
48. #2764C22semidirect
49. #2758C22semidirect
50. #2758C22semidirect
52. #2756C22semidirect
54. #2751C22semidirect
58. #2747C22semidirect
59. #2747C22semidirect
60. #2740C22semidirect
61. #2737C22semidirect
62. #2731C22semidirect
64. #2729C22semidirect
65. #2729C22semidirect
67. #2728C22semidirect
68. #2717C22semidirect
69. #2713C22semidirect
70. #2713C22semidirect
71. #2712C22semidirect
73. #2711C22semidirect
74. #2710C22semidirect
76. #2707C22semidirect
77. #2704C22semidirect
82. #2692C22semidirect
83. #2692C22semidirect
85. #2690C22semidirect
86. #2690C22semidirect
87. #2690C22semidirect
90. #2677C22semidirect
91. #2677C22semidirect
92. #2677C22semidirect
93. #2677C22semidirect
95. #2674C22semidirect
96. #2665C22semidirect
97. #2652C22semidirect
98. #2651C22semidirect
99. #2648C22semidirect
100. #2648C22semidirect
102. #2639C22semidirect
104. #2634C22semidirect
105. #2633C22semidirect
107. #2627C22semidirect
108. #2618C22semidirect
111. #2616C22semidirect
112. #2616C22semidirect
114. #2605C22semidirect
116. #2599C22semidirect
122. #2578C22semidirect
123. #2578C22semidirect
124. #2577C22semidirect
125. #2564C22semidirect
127. #2549C22semidirect
128. #2549C22semidirect
130. #2530C22semidirect
131. #2523C22semidirect
132. #2523C22semidirect
133. #2523C22semidirect
135. #2492C22semidirect
137. #2484C22semidirect
142. #2477C22semidirect
144. #2475C22semidirect
145. #2474C22semidirect
149. #2465C22semidirect
152. #2462C22semidirect
154. #2460C22semidirect
155. #2460C22semidirect
156. #2460C22semidirect
159. #2452C22semidirect
162. #2450C22semidirect
163. #2450C22semidirect
165. #2449C22semidirect
170. #2434C22semidirect
171. #2434C22semidirect
172. #2434C22semidirect
173. #2432C22semidirect
174. #2432C22semidirect
175. #2432C22semidirect
182. #2409C22semidirect
183. #2409C22semidirect
187. #2407C22semidirect
188. #2407C22semidirect
189. #2406C22semidirect
190. #2406C22semidirect
195. #2388C22semidirect
197. #2381C22semidirect
198. #2378C22semidirect
199. #2368C22semidirect
201. #2359C22semidirect
205. #2341C22semidirect
206. Q8×C22⋊C4C22semidirect
207. #2337C22semidirect
209. #2329C22semidirect
213. #2313C22semidirect
214. #2311C22semidirect
215. #2310C22semidirect
919. C242−1+4semidirect

Maximal subgroups

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

subgroupindex
#585982
#580072
#566752
#520072
#519862
#513362
#495492
#485662
#478822
#471412
#470042
#433702
#430032
#411802
#409432
#406532
#377532
#377522
#367082
#357032
#356872
#356592
#353492