Finite Group Databasebeta

← #7658965

Subgroups — #7658965

Order 512.

4338 conjugacy classes of subgroups.

The subgroup lattice has 1306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42333C212yesmaximal, complemented
2#42322C214yesmaximal, complemented
3#42244C214yesmaximal, complemented
4#42163C212yesmaximal, complemented
5#42075C214yesmaximal, complemented
6#41680C214yesmaximal, complemented
7#41673C214yesmaximal, complemented
8#41443C212yesmaximal, complemented
9#41436C212yesmaximal, complemented
10#41055C214yesmaximal, complemented
11#41042C214yesmaximal, complemented
12#37612C212yesmaximal, complemented
13#37606C211yesmaximal, characteristic
14#37599C212yesmaximal, complemented
15#37599C212yesmaximal, complemented
16#37563C211yesmaximal, characteristic, complemented
17#37537C211yesmaximal, characteristic, complemented
18#36699C211yesmaximal, characteristic, complemented
19#36698C212yesmaximal, complemented
20#36074C212yesmaximal, complemented
21#36046C212yesmaximal, complemented
22#36002C212yesmaximal, complemented
23#35954C212yesmaximal, complemented
24#35814C214yesmaximal, complemented
25#34240C211yesmaximal, characteristic, complemented
26#34231C211yesmaximal, characteristic, complemented
27#34227C211yesmaximal, characteristic, complemented
28C2×#533C2211yescharacteristic
29C2×#529C2211yescharacteristic
30C22×#124C2211yescharacteristic
31#2844C2212yescomplemented
32#2844C2212yescomplemented
33#2838C2214yescomplemented
34#2838C2214yescomplemented
35#2836C2214yescomplemented
36#2836C2214yescomplemented
37#2833C2214yescomplemented
38#2830C2214yes—
39#2822C2211yescharacteristic, complemented
40#2822C2211yescharacteristic, complemented
41#2821C2212yescomplemented
42#2821C2212yescomplemented
43#2820C2212yes—
44#2820C2212yes—
45#2820C2212yes—
46#2820C2211yescharacteristic, complemented
47#2820C2211yescharacteristic, complemented
48#2819C2212yes—
49#2817C2212yes—
50#2816C2212yes—
51#2814C2214yes—
52#2804C2214yescomplemented
53#2799C2214yescomplemented
54#2798C2214yescomplemented
55#2786C2214yes—
56#2771C2214yescomplemented
57#2759C2214yescomplemented
58#2759C2214yescomplemented
59#2752C2214yes—
60#2751C2214yescomplemented
61#2745C2214yes—
62#2745C2214yescomplemented
63#2739C2214yes—
64#2736C2214yes—
65#2735C2214yes—
66#2732C2214yescomplemented
67#2716C2214yescomplemented
68#2713C2214yescomplemented
69#2712C2214yes—
70#2700C2214yes—
71#2697C2214yes—
72#2695C2214yes—
73#2694C2214yescomplemented
74#2687C2214yes—
75#2684C2214yes—
76#2665C2214yes—
77#2665C2214yes—
78#2665C2212yes—
79#2665C2212yes—
80#2665C2214yescomplemented
81#2665C2214yescomplemented
82#2663C2214yescomplemented
83#2663C2214yescomplemented
84#2662C2214yes—
85#2662C2214yes—
86#2662C2214yescomplemented
87#2658C2212yes—
88#2654C2214yescomplemented
89#2654C2214yescomplemented
90#2650C2214yescomplemented
91#2650C2214yescomplemented
92#2650C2214yescomplemented
93#2650C2214yescomplemented
94#2649C2214yescomplemented
95#2649C2214yescomplemented
96#2648C2214yes—
97#2648C2214yescomplemented
98#2640C2212yes—
99#2638C2214yes—
100#2634C2214yescomplemented
101#2632C2214yes—
102#2632C2212yes—
103#2631C2212yes—
104#2626C2214yes—
105#2614C2212yes—
106#2613C2212yes—
107#2610C2214yes—
108#2605C2214yescomplemented
109#2605C2212yescomplemented
110#2605C2212yescomplemented
111#2605C2214yescomplemented
112#2604C2214yescomplemented
113#2596C2214yescomplemented
114#2593C2214yes—
115#2592C2214yescomplemented
116#2589C2214yescomplemented
117#2588C2214yescomplemented
118#2586C2214yescomplemented
119#2576C2214yescomplemented
120#2573C2214yes—
121#2573C2214yescomplemented
122#2573C2214yescomplemented
123#2572C2214yescomplemented
124#2561C2212yes—
125#2561C2214yes—
126#2560C2214yes—
127#2558C2214yes—
128#2557C2214yes—
129#2557C2214yes—
130#2556C2214yescomplemented
131#2556C2214yescomplemented
132#2545C2212yes—
133#2545C2212yes—
134#2539C2212yes—
135#2534C2212yes—
136#2534C2212yes—
137#2532C2214yescomplemented
138#2532C2214yescomplemented
139#2531C2214yescomplemented
140#2529C2214yescomplemented
141#2527C2214yes—
142#2527C2214yescomplemented
143#2525C2214yescomplemented
144#2521C2214yescomplemented
145#2521C2214yescomplemented
146#2521C2214yescomplemented
147#2516C2214yescomplemented
148#2516C2214yescomplemented
149#2515C2214yescomplemented
150#2510C2214yescomplemented
151#2492C2214yescomplemented
152#2489C2214yescomplemented
153#2488C2214yescomplemented
154#2482C2212yes—
155#2482C2212yes—
156#2480C2214yes—
157#2479C2214yescomplemented
158#2474C2214yes—
159#2472C2214yes—
160#2469C2214yescomplemented
161#2469C2214yescomplemented
162#2465C2214yescomplemented
163#2465C2214yescomplemented
164#2465C2214yescomplemented
165#2461C2214yes—
166#2461C2214yescomplemented
167#2458C2214yes—
168#2458C2214yescomplemented
169#2457C2214yes—
170#2457C2214yescomplemented
171#2451C2214yescomplemented
172#2448C2214yescomplemented
173#2435C2212yes—
174#2434C2212yes—
175#2411C2214yes—
176#2401C2214yescomplemented
177#2401C2214yescomplemented
178#2399C2214yescomplemented
179#2399C2212yescomplemented
180#2398C2212yescomplemented
181#2396C2214yescomplemented
182#2396C2214yescomplemented
183#2396C2214yescomplemented
184#2395C2214yes—
185#2395C2212yes—
186#2395C2212yes—
187#2374C2214yes—
188#2374C2214yescomplemented
189#2373C2214yescomplemented
190#2373C2214yescomplemented
191#2372C2212yes—
192#2372C2212yes—
193#2372C2214yescomplemented
194#2369C2212yescomplemented
195#2367C2212yes—
196#2367C2212yes—
197#2365C2212yescomplemented
198#2362C2214yes—
199#2362C2214yescomplemented
200#2357C2212yes—
201#2356C2212yescomplemented
202#2356C2212yescomplemented
203#2353C2212yes—
204#2347C2211yescharacteristic
205#2347C2211yescharacteristic
206#2347C2212yescomplemented
207#2346C2211yescharacteristic
208#2346C2211yescharacteristic
209#2343C2212yescomplemented
210#2342C2214yes—
211Q8×C22⋊C4C2212yes—
212D4×C22⋊C4C2212yes—
213#2337C2214yes—
214#2332C2214yes—
215#2324C2212yes—
216#2323C2212yes—
217#2320C2212yescomplemented
218#2320C2211yescharacteristic, complemented
219#2319C2211yescharacteristic, complemented
220#2312C2212yes—
221C4×#125C2212yescomplemented
222C4×#125C2212yescomplemented
223C4×#125C2212yescomplemented
224C4×#124C2212yes—
225C4×#124C2212yes—
226C4×#124C2212yescomplemented
227#2283C2211yescharacteristic
228#2283C2211yescharacteristic
229#2283C2211yescharacteristic
230#2276C2211yescharacteristic, complemented
231#2276C2212yescomplemented
232#2275C2211yescharacteristic, complemented
233#2273C2212yes—
234C4×#117C2211yescharacteristic
235C23×Q8C2311yescharacteristic
236C23×D4C2311yescharacteristic
237#533—28no—
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2312yes—
242#529—28no—
243C2×#126C2312yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#125C2311yescharacteristic
247C2×#125C2311yescharacteristic
248C2×#125C2311yescharacteristic
249C2×#125C2314yes—
250C2×#124—28no—
251C2×#124C2311yescharacteristic
252C2×#124C2312yes—
253C2×#124C2312yes—
254C2×#124C2312yes—
255C2×#124C2312yes—
256C2×#124C2314yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2314yes—
260C2×#123C2312yes—
261C2×#123C2314yes—
262C2×#123C2312yes—
263C2×#123C2312yes—
264C2×#123C2314yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2311yescharacteristic
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×#121C2311yescharacteristic
272C2×#120C2312yes—
273C2×#120C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2314yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2314yes—
282C2×C4×D4C2311yescharacteristic
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×#117C2312yes—
288C2×#117C2311yescharacteristic
289C2×#117C2311yescharacteristic
290C2×#117C2312yes—
291C2×#117C2314yes—
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2314yes—
295C22×C42C2311yescharacteristic
296#401C2314yes—
297#401C2314yes—
298#400C2314yes—
299#400C2312yes—
300#400C2312yes—
301#400C2312yes—
302#400C2312yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
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#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2312yes—
325#399C2312yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#398C2314yes—
330#398C2312yes—
331#398C2312yes—
332#398C2312yes—
333#398C2312yes—
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#397C2312yes—
350#397C2312yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#395C2312yes—
379#395C2312yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#394C2314yes—
394#394C2312yes—
395#394C2312yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2312yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2312yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2312yes—
442#391C2314yes—
443#391C2314yes—
444#390C2312yes—
445#390C2312yes—
446#390C2312yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2312yes—
451#390C2314yes—
452#390C2314yes—
453#390C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
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#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
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#387C2314yes—
543#387C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#383C2312yes—
565#383C2312yes—
566#383C2314yes—
567#383C2312yes—
568#383C2312yes—
569#383C2312yes—
570#383C2312yes—
571#382C2312yes—
572#382C2312yes—
573#382C2311yescharacteristic
574#382C2311yescharacteristic
575#382C2312yes—
576#382C2312yes—
577#382C2312yes—
578#381C2312yes—
579#381C2314yes—
580#381C2312yes—
581#381C2312yes—
582#381C2314yes—
583#381C2312yes—
584#381C2312yes—
585#381C2312yes—
586#381C2314yes—
587#380C2314yes—
588#380C2312yes—
589#380C2312yes—
590#380C2312yes—
591#380C2311yescharacteristic
592#380C2311yescharacteristic
593#380C2314yes—
594#380C2314yes—
595#379C2312yes—
596#379C2312yes—
597#379C2314yes—
598#379C2314yes—
599#379C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2312yes—
604C4×C4⋊C4C2312yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2311yescharacteristic
615C4×C4⋊C4C2311yescharacteristic
616C4×C4⋊C4C2311yescharacteristic
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2311yescharacteristic
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2312yes—
631C4×C22⋊C4C2311yescharacteristic
632C4×C22⋊C4C2312yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2312yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2311yescharacteristic
644C4×C22⋊C4C2312yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2312yes—
650#376C2311yescharacteristic
651#376C2312yes—
652#376C2312yes—
653#376C2312yes—
654#376C2312yes—
655#376C2314yes—
656#376C2312yes—
657#376C2312yes—
658#376C2311yescharacteristic
659C2×#95C2312yes—
660C43C2312yes—
661C25C2412yes—
662C22×Q8—24no—
663C22×Q8—81no—
664C22×Q8—81no—
665C22×Q8C2411yescharacteristic
666C22×Q8C2412yes—
667C22×Q8C2412yes—
668C22×Q8C2412yes—
669C22×Q8C2412yes—
670C22×Q8C2414yes—
671C22×Q8C2414yes—
672C22×D4—24no—
673C22×D4—81no—
674C22×D4—81no—
675C22×D4C2411yescharacteristic
676C22×D4C2412yes—
677C22×D4C2412yes—
678C22×D4C2412yes—
679C22×D4C2414yes—
680C22×D4C2414yes—
681C23×C4C2412yes—
682C23×C4C2414yes—
683C23×C4C2412yes—
684C23×C4C2414yes—
685C23×C4C2414yes—
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2411yescharacteristic
689C4⋊Q8—24no—
690C4⋊Q8—24no—
691C4⋊Q8—82no—
692C4⋊Q8—82no—
693#126—28no—
694#126—48no—
695#126—84no—
696#125—24no—
697#125—24no—
698#125—24no—
699#125—84no—
700#124—28no—
701#124—28no—
702#124—28no—
703#124—28no—
704#124—24no—
705#124—48no—
706#124—84no—
707#124—82no—
708#124—82no—
709#123—28no—
710#123—48no—
711#123—84no—
712#123—82no—
713#123—82no—
714C22⋊Q8—24no—
715C22⋊Q8—28no—
716C22⋊Q8—28no—
717C22⋊Q8—48no—
718C22⋊Q8—84no—
719C22⋊Q8—84no—
720#121—24no—
721#120—82no—
722#120—82no—
723C4×Q8—24no—
724C4×Q8—28no—
725C4×Q8—28no—
726C4×Q8—44no—
727C4×Q8—48no—
728C4×Q8—84no—
729C4×Q8—82no—
730C4×Q8—82no—
731C4×D4—28no—
732C4×D4—24no—
733C4×D4—44no—
734C4×D4—82no—
735C4×D4—82no—
736#117—24no—
737#117—24no—
738#117—28no—
739#117—44no—
740#117—84no—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C22⋊C4—28no—
791C2×C22⋊C4—28no—
792C2×C22⋊C4—48no—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
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×C42#4118yes—
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2412yes—
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2411yescharacteristic
863C2×C42C2411yescharacteristic
864C2×C42C2411yescharacteristic
865C2×C42C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2412yes—
868#95C2414yes—
869#95C2411yescharacteristic
870#95C2411yescharacteristic
871#95C2412yes—
872#95C2411yescharacteristic
873#95C2412yes—
874#95C2412yes—
875#95C2412yes—
876#95C2414yes—
877#95C2414yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2412yes—
891#95C2412yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930C24—24no—
931C24—44no—
932C24—42no—
933C24—42no—
934C24—44no—
935C24C2514yes—
936C24C2512yes—
937C24C2511yescharacteristic
938C2×Q8—22no—
939C2×Q8—24no—
940C2×Q8—24no—
941C2×Q8—24no—
942C2×Q8—24no—
943C2×Q8—42no—
944C2×Q8—44no—
945C2×Q8—42no—
946C2×Q8—42no—
947C2×Q8—44no—
948C2×Q8—44no—
949C2×Q8—42no—
950C2×Q8—42no—
951C2×Q8—42no—
952C2×Q8—42no—
953C2×Q8—44no—
954C2×Q8—44no—
955C2×Q8—44no—
956C2×Q8—44no—
957C2×Q8—88no—
958C2×D4—24no—
959C2×D4—22no—
960C2×D4—24no—
961C2×D4—24no—
962C2×D4—42no—
963C2×D4—42no—
964C2×D4—42no—
965C2×D4—42no—
966C2×D4—42no—
967C2×D4—42no—
968C2×D4—42no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—88no—
976C22×C4—24no—
977C22×C4—24no—
978C22×C4—28no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—41no—
982C22×C4—41no—
983C22×C4—44no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4C2×#4114yes—
995C22×C4C2×#4114yes—
996C22×C4C2×#4114yes—
997C22×C4C2512yes—
998C22×C4C2512yes—
999C22×C4C2512yes—
1000C22×C4C2514yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2514yes—
1004C22×C4C2514yes—
1005C22×C4C2512yes—
1006C22×C4C2512yes—
1007C22×C4C2512yes—
1008C22×C4C2514yes—
1009C22×C4C2514yes—
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2511yescharacteristic
1015C22×C4C2511yescharacteristic
1016C22×C4C2511yescharacteristic
1017C22×C4C2511yescharacteristic
1018C22×C4C2511yescharacteristic
1019C22×C4C2511yescharacteristic
1020C22×C4C2512yes—
1021C4⋊C4—24no—
1022C4⋊C4—24no—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—24no—
1029C4⋊C4—22no—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—24no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—24no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—42no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C22⋊C4—24no—
1071C22⋊C4—24no—
1072C22⋊C4—24no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—28no—
1077C22⋊C4—24no—
1078C22⋊C4—24no—
1079C22⋊C4—24no—
1080C22⋊C4—24no—
1081C22⋊C4—24no—
1082C22⋊C4—28no—
1083C22⋊C4—28no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—42no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C42—24no—
1117C42—24no—
1118C42—24no—
1119C42—24no—
1120C42—28no—
1121C42—42no—
1122C42—44no—
1123C42—42no—
1124C42—44no—
1125C42—42no—
1126C42—44no—
1127C42—44no—
1128C42—42no—
1129C42—42no—
1130C42—44no—
1131C42—44no—
1132C42—44no—
1133C42—44no—
1134C42—44no—
1135C42—44no—
1136C42—42no—
1137C42—42no—
1138C42C2×#4114yes—
1139C42C2×#4114yes—
1140C42C2×#4114yes—
1141C42C2×#4114yes—
1142C23—22no—
1143C23—21no—
1144C23—21no—
1145C23—22no—
1146C23—22no—
1147C23—24no—
1148C23—24no—
1149C23—24no—
1150C23—24no—
1151C23—22no—
1152C23—22no—
1153C23—24no—
1154C23—24no—
1155C23—24no—
1156C23—24no—
1157C23—24no—
1158C23—48no—
1159C23—84no—
1160C23—84no—
1161C23—164no—
1162C23—164no—
1163C23C22×#4112yes—
1164C23C2611yescharacteristic
1165Q8—44no—
1166Q8—48no—
1167Q8—48no—
1168Q8—84no—
1169Q8—84no—
1170Q8—88no—
1171Q8—164no—
1172D4—44no—
1173D4—48no—
1174D4—84no—
1175D4—84no—
1176D4—164no—
1177D4—164no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—44no—
1236C2×C4—44no—
1237C2×C4—44no—
1238C2×C4—88no—
1239C2×C4—84no—
1240C2×C4—84no—
1241C2×C4—164no—
1242C2×C4—164no—
1243C2×C4C22×#4112yes—
1244C2×C4C22×#4112yes—
1245C2×C4C22×#4112yes—
1246C2×C4C22×#4112yes—
1247C2×C4C22×#4112yes—
1248C2×C4C22×#4112yes—
1249C2×C4#58514yes—
1250C22—22no—
1251C22—22no—
1252C22—22no—
1253C22—42no—
1254C22—42no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—42no—
1263C22—42no—
1264C22—44no—
1265C22—42no—
1266C22—44no—
1267C22—168no—
1268C22C23×#4111yescharacteristic
1269C22C2×#58512yes—
1270C22H(7,𝔽2)11yescharacteristic
1271C22H(7,𝔽2)11yescharacteristic
1272C222−1+612yes—
1273C4—24no—
1274C4—22no—
1275C4—22no—
1276C4—22no—
1277C4—22no—
1278C4—22no—
1279C4—22no—
1280C4—42no—
1281C4—44no—
1282C4—44no—
1283C4—44no—
1284C4—42no—
1285C4—42no—
1286C4—44no—
1287C4—44no—
1288C4—44no—
1289C4—44no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C2—42no—
1298C2—82no—
1299C2—84no—
1300C2#6268611yescharacteristic
1301C2#6285511yescharacteristic
1302C2#6286011yescharacteristic
1303C2#6305912yes—
1304C2#6306912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37606C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42333C2semidirect
2. #42322C2semidirect
3. #42244C2semidirect
4. #42163C2semidirect
5. #42075C2semidirect
6. #41680C2semidirect
7. #41673C2semidirect
8. #41443C2semidirect
9. #41436C2semidirect
10. #41055C2semidirect
11. #41042C2semidirect
12. #37612C2semidirect
14. #37599C2semidirect
15. #37599C2semidirect
16. #37563C2semidirect
17. #37537C2semidirect
18. #36699C2semidirect
19. #36698C2semidirect
20. #36074C2semidirect
21. #36046C2semidirect
22. #36002C2semidirect
23. #35954C2semidirect
24. #35814C2semidirect
25. #34240C2semidirect
26. #34231C2semidirect
27. #34227C2semidirect
31. #2844C22semidirect
32. #2844C22semidirect
33. #2838C22semidirect
34. #2838C22semidirect
35. #2836C22semidirect
36. #2836C22semidirect
37. #2833C22semidirect
39. #2822C22semidirect
40. #2822C22semidirect
41. #2821C22semidirect
42. #2821C22semidirect
46. #2820C22semidirect
47. #2820C22semidirect
52. #2804C22semidirect
53. #2799C22semidirect
54. #2798C22semidirect
56. #2771C22semidirect
57. #2759C22semidirect
58. #2759C22semidirect
60. #2751C22semidirect
62. #2745C22semidirect
66. #2732C22semidirect
67. #2716C22semidirect
68. #2713C22semidirect
73. #2694C22semidirect
80. #2665C22semidirect
81. #2665C22semidirect
82. #2663C22semidirect
83. #2663C22semidirect
86. #2662C22semidirect
88. #2654C22semidirect
89. #2654C22semidirect
90. #2650C22semidirect
91. #2650C22semidirect
92. #2650C22semidirect
93. #2650C22semidirect
94. #2649C22semidirect
95. #2649C22semidirect
97. #2648C22semidirect
100. #2634C22semidirect
108. #2605C22semidirect
109. #2605C22semidirect
110. #2605C22semidirect
111. #2605C22semidirect
112. #2604C22semidirect
113. #2596C22semidirect
115. #2592C22semidirect
116. #2589C22semidirect
117. #2588C22semidirect
118. #2586C22semidirect
119. #2576C22semidirect
121. #2573C22semidirect
122. #2573C22semidirect
123. #2572C22semidirect
130. #2556C22semidirect
131. #2556C22semidirect
137. #2532C22semidirect
138. #2532C22semidirect
139. #2531C22semidirect
140. #2529C22semidirect
142. #2527C22semidirect
143. #2525C22semidirect
144. #2521C22semidirect
145. #2521C22semidirect
146. #2521C22semidirect
147. #2516C22semidirect
148. #2516C22semidirect
149. #2515C22semidirect
150. #2510C22semidirect
151. #2492C22semidirect
152. #2489C22semidirect
153. #2488C22semidirect
157. #2479C22semidirect
160. #2469C22semidirect
161. #2469C22semidirect
162. #2465C22semidirect
163. #2465C22semidirect
164. #2465C22semidirect
166. #2461C22semidirect
168. #2458C22semidirect
170. #2457C22semidirect
171. #2451C22semidirect
172. #2448C22semidirect
176. #2401C22semidirect
177. #2401C22semidirect
178. #2399C22semidirect
179. #2399C22semidirect
180. #2398C22semidirect
181. #2396C22semidirect
182. #2396C22semidirect
183. #2396C22semidirect
188. #2374C22semidirect
189. #2373C22semidirect
190. #2373C22semidirect
193. #2372C22semidirect
194. #2369C22semidirect
197. #2365C22semidirect
199. #2362C22semidirect
201. #2356C22semidirect
202. #2356C22semidirect
206. #2347C22semidirect
209. #2343C22semidirect
217. #2320C22semidirect
218. #2320C22semidirect
219. #2319C22semidirect
221. C4×#125C22semidirect
222. C4×#125C22semidirect
223. C4×#125C22semidirect
226. C4×#124C22semidirect
230. #2276C22semidirect
231. #2276C22semidirect
232. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#423332
#423222
#422442
#421632
#420752
#416802
#416732
#414432
#414362
#410552
#410422
#376122
#376062
#375992
#375632
#375372
#366992
#366982
#360742
#360462
#360022
#359542
#358142
#342402
#342312
#342272