Finite Group Databasebeta

← #7732647

Subgroups — #7732647

Order 512.

5236 conjugacy classes of subgroups.

The subgroup lattice has 1413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51224C212yesmaximal, complemented
2#51086C212yesmaximal, complemented
3#50914C212yesmaximal, complemented
4#50713C212yesmaximal, complemented
5#47710C214yesmaximal, complemented
6#47708C214yesmaximal, complemented
7#44446C214yesmaximal, complemented
8#43888C214yesmaximal, complemented
9#40302C214yesmaximal, complemented
10#39806C212yesmaximal, complemented
11#39804C212yesmaximal, complemented
12#39743C212yesmaximal, complemented
13#39738C212yesmaximal, complemented
14#38702C214yesmaximal, complemented
15#38483C214yesmaximal, complemented
16#37556C211yesmaximal, characteristic, complemented
17#37022C212yesmaximal, complemented
18#36833C212yesmaximal, complemented
19#36396C214yesmaximal, complemented
20#35470C212yesmaximal, complemented
21#35436C212yesmaximal, complemented
22#35303C211yesmaximal, characteristic, complemented
23#35166C211yesmaximal, characteristic, complemented
24C2×#2605C211yesmaximal, characteristic, complemented
25#34388C211yesmaximal, characteristic, complemented
26#34222C211yesmaximal, characteristic, complemented
27#34083C211yesmaximal, characteristic, complemented
28C2×#553C2214yes—
29C2×#548C2214yes—
30C2×#537C2214yes—
31C2×#532C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C2×#529C2211yescharacteristic
34#2861C2214yes—
35#2856C2212yes—
36#2856C2212yes—
37#2856C2212yes—
38#2850C2214yes—
39#2850C2212yes—
40#2821C2212yes—
41#2818C2212yes—
42#2798C2214yes—
43#2797C2214yes—
44#2797C2214yes—
45#2793C2214yes—
46#2791C2214yes—
47#2786C2214yes—
48#2773C2214yes—
49#2754C2214yes—
50#2754C2214yes—
51#2752C2214yes—
52#2752C2214yes—
53#2740C2214yes—
54#2733C2214yes—
55#2732C2214yes—
56#2730C2214yes—
57#2730C2214yes—
58#2721C2214yes—
59#2714C2214yes—
60#2712C2214yes—
61#2710C2214yes—
62#2709C2214yes—
63#2703C2214yes—
64#2703C2214yes—
65#2700C2214yes—
66#2700C2214yes—
67#2698C2214yes—
68#2698C2214yes—
69#2694C2214yes—
70#2692C2214yes—
71#2692C2214yes—
72#2690C2214yes—
73#2690C2214yes—
74#2688C2214yes—
75#2688C2214yes—
76#2686C2214yes—
77#2686C2214yes—
78#2673C2214yes—
79#2673C2214yes—
80#2672C2214yes—
81#2672C2214yes—
82#2660C2211yescharacteristic
83#2657C2211yescharacteristic
84#2656C2211yescharacteristic
85#2656C2212yes—
86#2656C2211yescharacteristic
87#2656C2212yes—
88#2651C2214yes—
89#2648C2214yes—
90#2641C2211yescharacteristic
91#2640C2211yescharacteristic
92#2639C2211yescharacteristic
93#2639C2211yescharacteristic
94#2633C2212yes—
95#2632C2212yes—
96#2631C2212yes—
97#2631C2212yes—
98#2610C2212yes—
99#2610C2212yes—
100#2607C2214yes—
101#2605C2212yes—
102#2605C2214yes—
103#2605C2214yes—
104#2605C2212yes—
105#2605C2212yes—
106#2605C2212yes—
107#2603C2214yes—
108#2602C2214yes—
109#2598C2212yes—
110#2598C2212yes—
111#2589C2214yes—
112#2575C2214yes—
113#2565C2214yes—
114#2560C2214yes—
115#2560C2214yes—
116#2560C2214yes—
117#2560C2214yes—
118#2559C2214yes—
119#2559C2214yes—
120#2557C2214yes—
121#2557C2214yes—
122#2557C2214yes—
123#2557C2214yes—
124#2557C2214yes—
125#2557C2214yes—
126#2555C2214yes—
127#2555C2214yes—
128#2549C2214yes—
129#2549C2214yes—
130#2544C2214yes—
131#2543C2214yes—
132#2543C2214yes—
133#2543C2214yes—
134#2543C2214yes—
135#2543C2214yes—
136#2543C2214yes—
137#2542C2212yes—
138#2542C2212yes—
139#2541C2212yes—
140#2541C2212yes—
141#2540C2214yes—
142#2540C2212yes—
143#2540C2212yes—
144#2531C2214yes—
145#2526C2214yes—
146#2517C2214yes—
147#2504C2214yes—
148#2499C2214yes—
149#2488C2214yes—
150#2488C2214yes—
151#2479C2214yes—
152#2477C2214yes—
153#2477C2214yes—
154#2476C2214yes—
155#2471C2214yes—
156#2471C2214yes—
157#2467C2214yes—
158#2465C2214yes—
159#2465C2214yes—
160#2459C2214yes—
161#2456C2214yes—
162#2448C2214yes—
163#2444C2214yes—
164#2444C2214yes—
165#2444C2214yes—
166#2444C2214yes—
167#2443C2214yes—
168#2443C2214yes—
169#2436C2214yes—
170#2431C2214yes—
171#2431C2214yes—
172#2430C2214yes—
173#2430C2214yes—
174#2430C2212yes—
175#2430C2214yes—
176#2430C2212yes—
177#2423C2214yes—
178#2416C2214yes—
179#2416C2214yes—
180#2407C2214yes—
181C2×#400C2212yes—
182C2×#395C2212yes—
183#2381C2212yes—
184#2380C2212yes—
185#2372C2214yes—
186#2364C2214yes—
187#2364C2214yes—
188#2364C2214yes—
189#2364C2214yes—
190#2353C2212yes—
191#2353C2214yes—
192#2353C2212yes—
193#2339C2214yes—
194#2339C2212yes—
195#2339C2212yes—
196#2337C2212yes—
197#2337C2212yes—
198#2337C2212yes—
199#2336C2212yes—
200#2335C2214yes—
201#2334C2214yes—
202#2333C2214yes—
203#2331C2212yes—
204#2329C2212yes—
205#2328C2212yes—
206#2328C2212yes—
207#2326C2212yes—
208#2325C2212yes—
209#2325C2212yes—
210#2325C2212yes—
211#2322C2214yes—
212#2319C2211yescharacteristic
213#2319C2211yescharacteristic
214#2318C2214yes—
215C4×#124C2214yes—
216C4×#121C2212yes—
217C4×#121C2212yes—
218#2298C2212yes—
219#2297C2214yes—
220#2296C2212yes—
221#2295C2212yes—
222C2×#391C2212yes—
223C2×#391C2212yes—
224#2290C2212yes—
225#2290C2212yes—
226C2×#387C2212yes—
227C2×#387C2212yes—
228#2283C2211yescharacteristic
229C2×#383C2211yescharacteristic
230#2275C2211yescharacteristic
231#2275C2211yescharacteristic
232C42×D4C2212yes—
233C2×C4×C4⋊C4C2211yescharacteristic
234C2×#376C2211yescharacteristic
235C22×#41C2312yes—
236C22×#41C2312yes—
237C22×#41C2314yes—
238C23×Q8C2312yes—
239#553—416no—
240#548—416no—
241#537—416no—
242#532—28no—
243#532—28no—
244C2×C4⋊Q8C2311yescharacteristic
245C2×C4⋊Q8C2311yescharacteristic
246C2×#127C2311yescharacteristic
247C2×#127C2311yescharacteristic
248C2×#127C2312yes—
249C2×#127C2312yes—
250C2×#127C2312yes—
251#529—28no—
252C2×#126C2312yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#125C2311yescharacteristic
256C2×#125C2314yes—
257C2×#124C2312yes—
258C2×#124C2311yescharacteristic
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2314yes—
262C2×#124C2314yes—
263C2×#124C2314yes—
264C2×#124C2314yes—
265C2×#124C2314yes—
266C2×#123C2312yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×C22⋊Q8C2311yescharacteristic
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×#121C2312yes—
280C2×#121C2311yescharacteristic
281C2×#121C2312yes—
282C2×#121C2312yes—
283C2×#121C2314yes—
284C2×#121C2314yes—
285C2×#121C2311yescharacteristic
286C2×#121C2311yescharacteristic
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×#121C2314yes—
291C2×#121C2314yes—
292C2×#121C2314yes—
293C2×#121C2314yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2314yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2314yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2311yescharacteristic
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2314yes—
317C2×#117C2312yes—
318C2×#117C2314yes—
319C2×#117C2312yes—
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2312yes—
323C22×C4⋊C4C2312yes—
324C22×C42C2312yes—
325C22×C42C2312yes—
326C22×C42C2311yescharacteristic
327C22×C42C2311yescharacteristic
328C22×C42C2311yescharacteristic
329#400C2312yes—
330#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#399C2312yes—
338#399C2312yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2312yes—
344#399C2312yes—
345#399C2314yes—
346#399C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2312yes—
362#397C2312yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2312yes—
383#395C2312yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2312yes—
389#394C2312yes—
390#394C2314yes—
391#394C2314yes—
392#394C2312yes—
393#394C2312yes—
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#393C2312yes—
409#393C2312yes—
410#393C2312yes—
411#393C2312yes—
412#392C2312yes—
413#392C2312yes—
414#392C2314yes—
415#392C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2312yes—
419#392C2312yes—
420#392C2312yes—
421#392C2312yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2312yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#390C2312yes—
446#390C2312yes—
447#390C2314yes—
448#390C2314yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2314yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2312yes—
460#390C2312yes—
461#390C2314yes—
462#390C2314yes—
463#390C2314yes—
464#389C2312yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
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#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
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#386C2314yes—
534#386C2314yes—
535#386C2314yes—
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#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#384C2312yes—
588#384C2312yes—
589#384C2312yes—
590#383C2312yes—
591#383C2312yes—
592#383C2312yes—
593#383C2312yes—
594#383C2312yes—
595#382C2314yes—
596#382C2312yes—
597#382C2314yes—
598#382C2312yes—
599#381C2314yes—
600#381C2312yes—
601#381C2312yes—
602#381C2314yes—
603#381C2312yes—
604#381C2314yes—
605#380C2314yes—
606#380C2312yes—
607#380C2312yes—
608#380C2312yes—
609#380C2314yes—
610#380C2314yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2311yescharacteristic
614C4×C4⋊C4C2311yescharacteristic
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C22⋊C4C2314yes—
623C4×C22⋊C4C2314yes—
624C4×C22⋊C4C2314yes—
625C4×C22⋊C4C2314yes—
626C4×C22⋊C4C2314yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2312yes—
630C4×C22⋊C4C2314yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2312yes—
634C4×C22⋊C4C2312yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2312yes—
639C4×C22⋊C4C2312yes—
640#376C2311yescharacteristic
641#376C2312yes—
642#376C2312yes—
643#376C2311yescharacteristic
644#376C2311yescharacteristic
645#376C2311yescharacteristic
646#376C2312yes—
647#376C2312yes—
648C2×#95C2314yes—
649C2×#95C2311yescharacteristic
650C2×#95C2311yescharacteristic
651C2×#95C2312yes—
652C2×#95C2311yescharacteristic
653C2×#95C2312yes—
654C2×#95C2311yescharacteristic
655C2×#95C2312yes—
656C2×#95C2312yes—
657C2×#95C2312yes—
658C2×#95C2312yes—
659C2×#95C2312yes—
660C2×#95C2312yes—
661C2×#95C2312yes—
662C2×#95C2312yes—
663C43C2312yes—
664C2×#41—28no—
665C2×#41—28no—
666C2×#41—48no—
667C2×#41—48no—
668C2×#41—48no—
669C2×#41—48no—
670C2×#41—84no—
671C22×Q8—28no—
672C22×Q8—44no—
673C22×Q8—82no—
674C22×Q8C2414yes—
675C22×Q8C2411yescharacteristic
676C22×Q8C2412yes—
677C22×Q8C2412yes—
678C22×Q8C2414yes—
679C22×D4C2412yes—
680C22×D4C2414yes—
681C22×D4C2412yes—
682C22×D4C2412yes—
683C22×D4C2411yescharacteristic
684C22×D4C2411yescharacteristic
685C22×D4C2414yes—
686C22×D4C2411yescharacteristic
687C22×D4C2412yes—
688C22×D4C2412yes—
689C22×D4C2412yes—
690C22×D4C2412yes—
691C22×D4C2412yes—
692C22×D4C2414yes—
693C22×D4C2414yes—
694C22×D4C2414yes—
695C22×D4C2414yes—
696C22×D4C2414yes—
697C22×D4C2414yes—
698C22×D4C2414yes—
699C23×C4C2412yes—
700C23×C4C2411yescharacteristic
701C23×C4C2412yes—
702C23×C4C2412yes—
703C23×C4C2412yes—
704C23×C4C2412yes—
705C23×C4C2412yes—
706C23×C4C2414yes—
707C23×C4C2414yes—
708C23×C4C2412yes—
709C23×C4C2412yes—
710C23×C4C2414yes—
711C23×C4C2414yes—
712C23×C4C2414yes—
713C23×C4C2414yes—
714C23×C4C2411yescharacteristic
715C23×C4C2411yescharacteristic
716C23×C4C2412yes—
717C4⋊Q8—24no—
718C4⋊Q8—24no—
719#127—24no—
720#127—24no—
721#127—44no—
722#127—82no—
723#127—82no—
724#126—28no—
725#126—48no—
726#126—48no—
727#125—24no—
728#125—48no—
729#124—24no—
730#124—28no—
731#124—28no—
732#124—44no—
733#124—48no—
734#124—48no—
735#124—48no—
736#124—48no—
737#124—84no—
738#123—28no—
739#123—48no—
740#123—48no—
741#123—48no—
742#123—84no—
743C22⋊Q8—24no—
744C22⋊Q8—48no—
745C22⋊Q8—48no—
746C22⋊Q8—48no—
747C22⋊Q8—48no—
748C22⋊Q8—48no—
749C22⋊Q8—48no—
750C22⋊Q8—48no—
751#121—24no—
752#121—28no—
753#121—28no—
754#121—24no—
755#121—24no—
756#121—28no—
757#121—216no—
758#121—216no—
759#121—48no—
760#121—48no—
761#121—48no—
762#121—48no—
763#121—48no—
764#121—48no—
765#121—48no—
766#121—48no—
767#121—48no—
768#121—48no—
769#121—48no—
770#121—48no—
771#121—84no—
772C4×Q8—24no—
773C4×Q8—48no—
774C4×D4—28no—
775C4×D4—216no—
776C4×D4—24no—
777C4×D4—24no—
778C4×D4—24no—
779C4×D4—28no—
780C4×D4—28no—
781C4×D4—28no—
782C4×D4—44no—
783C4×D4—48no—
784C4×D4—44no—
785C4×D4—48no—
786C4×D4—48no—
787C4×D4—48no—
788C4×D4—48no—
789#117—28no—
790#117—48no—
791#117—82no—
792C2×C4⋊C4—28no—
793C2×C4⋊C4—28no—
794C2×C4⋊C4—44no—
795C2×C4⋊C4—82no—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C42—44no—
884C2×C42—81no—
885C2×C42—82no—
886C2×C42—81no—
887C2×C42#4118yescomplemented
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910#95C2411yescharacteristic
911#95C2411yescharacteristic
912#95C2414yes—
913#95C2412yes—
914#95C2411yescharacteristic
915#95C2411yescharacteristic
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2412yes—
926#95C2412yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965C24C2512yes—
966C24C2514yes—
967C24C2512yes—
968C24C2512yes—
969C24C2511yescharacteristic
970#41—816no—
971#41—816no—
972#41—832no—
973C2×Q8—22no—
974C2×Q8—24no—
975C2×Q8—24no—
976C2×Q8—28no—
977C2×Q8—28no—
978C2×Q8—28no—
979C2×Q8—44no—
980C2×Q8—44no—
981C2×Q8—44no—
982C2×Q8—42no—
983C2×Q8—44no—
984C2×Q8—44no—
985C2×Q8—816no—
986C2×D4—24no—
987C2×D4—24no—
988C2×D4—24no—
989C2×D4—28no—
990C2×D4—28no—
991C2×D4—28no—
992C2×D4—28no—
993C2×D4—28no—
994C2×D4—28no—
995C2×D4—22no—
996C2×D4—22no—
997C2×D4—22no—
998C2×D4—24no—
999C2×D4—24no—
1000C2×D4—24no—
1001C2×D4—24no—
1002C2×D4—24no—
1003C2×D4—28no—
1004C2×D4—28no—
1005C2×D4—28no—
1006C2×D4—42no—
1007C2×D4—42no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—42no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—42no—
1018C2×D4—42no—
1019C2×D4—42no—
1020C2×D4—42no—
1021C2×D4—44no—
1022C2×D4—42no—
1023C2×D4—42no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—24no—
1045C22×C4—28no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—28no—
1050C22×C4—28no—
1051C22×C4—42no—
1052C22×C4—41no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—44no—
1056C22×C4—42no—
1057C22×C4—41no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—44no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—42no—
1075C22×C4—42no—
1076C22×C4—42no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4C2×#4114yes—
1085C22×C4C2×#4114yes—
1086C22×C4C2×#4114yes—
1087C22×C4H(5,𝔽2)18yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2514yes—
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2514yes—
1101C22×C4C2512yes—
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2511yescharacteristic
1105C22×C4C2511yescharacteristic
1106C22×C4C2511yescharacteristic
1107C22×C4C2511yescharacteristic
1108C22×C4C2514yes—
1109C22×C4C2512yes—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—22no—
1113C4⋊C4—22no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—22no—
1118C4⋊C4—24no—
1119C4⋊C4—22no—
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—28no—
1123C4⋊C4—28no—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—28no—
1127C4⋊C4—28no—
1128C4⋊C4—28no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C22⋊C4—24no—
1147C22⋊C4—28no—
1148C22⋊C4—24no—
1149C22⋊C4—24no—
1150C22⋊C4—24no—
1151C22⋊C4—24no—
1152C22⋊C4—28no—
1153C22⋊C4—28no—
1154C22⋊C4—24no—
1155C22⋊C4—24no—
1156C22⋊C4—24no—
1157C22⋊C4—24no—
1158C22⋊C4—28no—
1159C22⋊C4—28no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—28no—
1164C22⋊C4—28no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C42—24no—
1198C42—28no—
1199C42—24no—
1200C42—24no—
1201C42—42no—
1202C42—42no—
1203C42—42no—
1204C42—42no—
1205C42—42no—
1206C42—44no—
1207C42—42no—
1208C42—42no—
1209C42—42no—
1210C42—44no—
1211C42—44no—
1212C42—44no—
1213C42—44no—
1214C42—44no—
1215C42C2×#4114yes—
1216C42C2×#4114yes—
1217C42C2×#4114yes—
1218C42C2×#4114yes—
1219C23—22no—
1220C23—21no—
1221C23—21no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—24no—
1226C23—24no—
1227C23—24no—
1228C23—24no—
1229C23—24no—
1230C23—24no—
1231C23—24no—
1232C23—24no—
1233C23—24no—
1234C23—24no—
1235C23—24no—
1236C23—22no—
1237C23—22no—
1238C23—24no—
1239C23—22no—
1240C23—22no—
1241C23—24no—
1242C23—22no—
1243C23—22no—
1244C23C22×#4112yes—
1245C23C2×H(5,𝔽2)14yes—
1246C23C2611yescharacteristic
1247Q8—416no—
1248Q8—82no—
1249Q8—88no—
1250Q8—84no—
1251Q8—84no—
1252D4—44no—
1253D4—44no—
1254D4—48no—
1255D4—48no—
1256D4—416no—
1257D4—48no—
1258D4—82no—
1259D4—84no—
1260D4—84no—
1261D4—84no—
1262D4—88no—
1263D4—84no—
1264D4—84no—
1265D4—88no—
1266D4—88no—
1267D4—88no—
1268D4—164no—
1269D4—164no—
1270D4—164no—
1271D4—164no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—28no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—44no—
1324C2×C4—44no—
1325C2×C4—48no—
1326C2×C4—48no—
1327C2×C4—48no—
1328C2×C4—416no—
1329C2×C4—84no—
1330C2×C4—84no—
1331C2×C4—88no—
1332C2×C4—88no—
1333C2×C4—84no—
1334C2×C4—84no—
1335C2×C4—84no—
1336C2×C4—84no—
1337C2×C4—88no—
1338C2×C4—164no—
1339C2×C4—164no—
1340C2×C4C22×#4112yes—
1341C2×C4C22×#4112yes—
1342C2×C4C22×#4112yes—
1343C2×C4C22×#4112yes—
1344C2×C4C22×#4112yes—
1345C2×C4C22×#4112yes—
1346C2×C4C2×H(5,𝔽2)18yes—
1347C2×C4#58514yes—
1348C22—22no—
1349C22—22no—
1350C22—24no—
1351C22—24no—
1352C22—42no—
1353C22—42no—
1354C22—44no—
1355C22—42no—
1356C22—42no—
1357C22—42no—
1358C22—42no—
1359C22—44no—
1360C22—42no—
1361C22—42no—
1362C22—44no—
1363C22—42no—
1364C22—44no—
1365C22—44no—
1366C22—44no—
1367C22—44no—
1368C22—44no—
1369C22—44no—
1370C22—44no—
1371C22—44no—
1372C22—44no—
1373C22—44no—
1374C22#350814yes—
1375C22C23×#4111yescharacteristic
1376C22C22×H(5,𝔽2)12yes—
1377C22C2×#58512yes—
1378C22H(7,𝔽2)11yescharacteristic
1379C222−1+611yescharacteristic
1380C4—22no—
1381C4—22no—
1382C4—22no—
1383C4—22no—
1384C4—22no—
1385C4—22no—
1386C4—28no—
1387C4—24no—
1388C4—42no—
1389C4—44no—
1390C4—42no—
1391C4—42no—
1392C4—42no—
1393C4—42no—
1394C4—44no—
1395C4—42no—
1396C4—44no—
1397C4—44no—
1398C4—42no—
1399C4—44no—
1400C4—42no—
1401C4—44no—
1402C2—24no—
1403C2—82no—
1404C2—82no—
1405C2—84no—
1406C2—82no—
1407C2C2×#350811yescharacteristic
1408C2#6281511yescharacteristic
1409C2#6285611yescharacteristic
1410C2#6290012yes—
1411C2#6293112yes—
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. #51224C2semidirect
2. #51086C2semidirect
3. #50914C2semidirect
4. #50713C2semidirect
5. #47710C2semidirect
6. #47708C2semidirect
7. #44446C2semidirect
8. #43888C2semidirect
9. #40302C2semidirect
10. #39806C2semidirect
11. #39804C2semidirect
12. #39743C2semidirect
13. #39738C2semidirect
14. #38702C2semidirect
15. #38483C2semidirect
16. #37556C2semidirect
17. #37022C2semidirect
18. #36833C2semidirect
19. #36396C2semidirect
20. #35470C2semidirect
21. #35436C2semidirect
22. #35303C2semidirect
23. #35166C2semidirect
24. C2×#2605C2semidirect
25. #34388C2semidirect
26. #34222C2semidirect
27. #34083C2semidirect
887. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#512242
#510862
#509142
#507132
#477102
#477082
#444462
#438882
#403022
#398062
#398042
#397432
#397382
#387022
#384832
#375562
#370222
#368332
#363962
#354702
#354362
#353032
#351662
C2×#26052
#343882
#342222
#340832