Finite Group Databasebeta

← #7658921

Subgroups — #7658921

Order 512.

4650 conjugacy classes of subgroups.

The subgroup lattice has 1386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42399C212yesmaximal, complemented
2#42081C214yesmaximal, complemented
3#42074C214yesmaximal, complemented
4#41978C212yesmaximal, complemented
5#41968C214yesmaximal, complemented
6#41058C214yesmaximal, complemented
7#41039C214yesmaximal, complemented
8#41021C214yesmaximal, complemented
9#41010C214yesmaximal, complemented
10#40656C212yesmaximal, complemented
11#40651C212yesmaximal, complemented
12#37610C212yesmaximal, complemented
13#37606C211yesmaximal, characteristic, complemented
14#37604C212yesmaximal, complemented
15#37604C212yesmaximal, complemented
16#37564C211yesmaximal, characteristic, complemented
17#37536C211yesmaximal, characteristic, complemented
18#36695C212yesmaximal, complemented
19#36687C211yesmaximal, characteristic, complemented
20#35992C212yesmaximal, complemented
21#35980C212yesmaximal, complemented
22#35932C212yesmaximal, complemented
23#35907C212yesmaximal, complemented
24#35784C214yesmaximal, complemented
25#34240C211yesmaximal, characteristic, complemented
26#34232C211yesmaximal, characteristic, complemented
27#34227C211yesmaximal, characteristic, complemented
28C2×#532C2211yescharacteristic
29C2×#529C2211yescharacteristic
30C22×#124C2211yescharacteristic
31#2845C2212yescomplemented
32#2845C2212yescomplemented
33#2837C2214yescomplemented
34#2837C2214yescomplemented
35#2831C2214yescomplemented
36#2831C2214yescomplemented
37#2829C2214yes—
38#2829C2214yescomplemented
39#2821C2212yescomplemented
40#2820C2212yes—
41#2820C2211yescharacteristic, complemented
42#2820C2211yescharacteristic, complemented
43#2819C2212yes—
44#2819C2212yes—
45#2819C2212yes—
46#2819C2211yescharacteristic, complemented
47#2819C2211yescharacteristic, complemented
48#2818C2212yescomplemented
49#2816C2212yes—
50#2815C2212yes—
51#2813C2214yes—
52#2803C2214yescomplemented
53#2797C2214yescomplemented
54#2796C2214yes—
55#2796C2214yescomplemented
56#2789C2214yescomplemented
57#2787C2214yescomplemented
58#2783C2214yescomplemented
59#2754C2214yescomplemented
60#2746C2214yes—
61#2740C2214yes—
62#2724C2214yescomplemented
63#2715C2214yescomplemented
64#2714C2214yescomplemented
65#2710C2214yescomplemented
66#2709C2214yes—
67#2706C2214yes—
68#2705C2214yes—
69#2697C2214yes—
70#2693C2214yes—
71#2685C2214yes—
72#2682C2214yescomplemented
73#2678C2214yes—
74#2673C2214yes—
75#2668C2214yes—
76#2667C2212yes—
77#2667C2214yes—
78#2667C2214yes—
79#2667C2212yes—
80#2662C2214yes—
81#2661C2214yes—
82#2661C2214yes—
83#2661C2214yescomplemented
84#2661C2214yescomplemented
85#2661C2214yescomplemented
86#2661C2214yescomplemented
87#2657C2212yes—
88#2653C2214yescomplemented
89#2653C2214yescomplemented
90#2653C2214yescomplemented
91#2653C2214yescomplemented
92#2653C2214yescomplemented
93#2653C2214yescomplemented
94#2651C2214yescomplemented
95#2651C2214yescomplemented
96#2640C2212yes—
97#2637C2214yescomplemented
98#2637C2214yescomplemented
99#2632C2212yes—
100#2631C2212yes—
101#2631C2214yes—
102#2630C2214yes—
103#2630C2214yescomplemented
104#2617C2214yes—
105#2614C2212yes—
106#2613C2212yes—
107#2610C2214yes—
108#2606C2214yescomplemented
109#2606C2212yescomplemented
110#2606C2212yescomplemented
111#2606C2214yescomplemented
112#2602C2214yescomplemented
113#2597C2214yescomplemented
114#2595C2214yes—
115#2594C2214yescomplemented
116#2589C2214yescomplemented
117#2588C2214yescomplemented
118#2576C2214yes—
119#2576C2214yescomplemented
120#2574C2214yescomplemented
121#2574C2214yescomplemented
122#2561C2212yes—
123#2557C2214yescomplemented
124#2554C2214yes—
125#2554C2214yes—
126#2554C2214yescomplemented
127#2553C2214yescomplemented
128#2553C2214yescomplemented
129#2553C2214yescomplemented
130#2544C2212yes—
131#2544C2212yes—
132#2539C2212yes—
133#2539C2214yes—
134#2534C2212yes—
135#2534C2212yes—
136#2531C2214yescomplemented
137#2526C2214yescomplemented
138#2518C2214yescomplemented
139#2516C2214yes—
140#2513C2214yescomplemented
141#2510C2214yescomplemented
142#2478C2214yescomplemented
143#2474C2214yescomplemented
144#2471C2214yes—
145#2471C2214yes—
146#2467C2214yescomplemented
147#2464C2214yes—
148#2464C2214yes—
149#2464C2214yescomplemented
150#2464C2214yescomplemented
151#2464C2214yescomplemented
152#2464C2214yescomplemented
153#2458C2214yescomplemented
154#2458C2214yescomplemented
155#2458C2214yescomplemented
156#2458C2214yescomplemented
157#2458C2214yescomplemented
158#2458C2214yescomplemented
159#2457C2214yescomplemented
160#2456C2214yescomplemented
161#2455C2214yescomplemented
162#2445C2214yes—
163#2444C2214yescomplemented
164#2436C2212yes—
165#2433C2212yes—
166#2428C2214yes—
167#2425C2214yescomplemented
168#2425C2214yescomplemented
169#2424C2214yes—
170#2420C2214yescomplemented
171#2418C2214yes—
172#2414C2214yescomplemented
173#2411C2214yes—
174#2404C2212yes—
175#2404C2212yes—
176#2398C2212yescomplemented
177#2397C2212yescomplemented
178#2396C2214yescomplemented
179#2396C2214yescomplemented
180#2395C2214yescomplemented
181#2395C2214yescomplemented
182#2392C2214yes—
183#2392C2214yescomplemented
184#2392C2214yescomplemented
185#2388C2212yes—
186#2388C2212yes—
187#2374C2214yes—
188#2374C2214yescomplemented
189#2373C2214yescomplemented
190#2372C2212yes—
191#2372C2212yes—
192#2367C2212yes—
193#2367C2212yes—
194#2366C2212yescomplemented
195#2365C2212yescomplemented
196#2364C2214yescomplemented
197#2363C2214yes—
198#2363C2214yescomplemented
199#2359C2214yescomplemented
200#2357C2212yes—
201#2353C2212yes—
202#2353C2212yescomplemented
203#2353C2212yescomplemented
204#2347C2212yescomplemented
205#2343C2212yescomplemented
206#2342C2214yes—
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209Q8×C22⋊C4C2212yes—
210#2339C2211yescharacteristic
211#2339C2211yescharacteristic
212D4×C22⋊C4C2212yes—
213#2337C2214yes—
214#2333C2214yes—
215#2324C2212yes—
216#2323C2212yes—
217#2320C2211yescharacteristic, complemented
218#2319C2211yescharacteristic, complemented
219#2319C2212yescomplemented
220#2312C2212yes—
221C4×#125C2212yescomplemented
222C4×#124C2212yes—
223C4×#124C2212yes—
224C4×#124C2212yescomplemented
225C4×#124C2212yescomplemented
226C4×#124C2212yescomplemented
227#2283C2211yescharacteristic
228#2283C2211yescharacteristic
229#2283C2211yescharacteristic
230#2276C2211yescharacteristic, complemented
231#2275C2211yescharacteristic, complemented
232#2275C2212yescomplemented
233#2273C2212yes—
234C4×#117C2211yescharacteristic
235C22×#41C2311yescharacteristic
236C22×#41C2311yescharacteristic
237C23×Q8C2311yescharacteristic
238C23×D4C2311yescharacteristic
239#532—28no—
240C2×C4⋊Q8C2311yescharacteristic
241C2×#127C2311yescharacteristic
242C2×#127C2312yes—
243C2×#127C2312yes—
244#529—28no—
245C2×#126C2312yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#125C2311yescharacteristic
249C2×#124—28no—
250C2×#124C2312yes—
251C2×#124C2311yescharacteristic
252C2×#124C2311yescharacteristic
253C2×#124C2311yescharacteristic
254C2×#124C2312yes—
255C2×#124C2312yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#123C2312yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2312yes—
263C2×#123C2312yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×C22⋊Q8C2311yescharacteristic
271C2×#121C2312yes—
272C2×#121C2311yescharacteristic
273C2×#121C2312yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#120C2312yes—
281C2×#120C2312yes—
282C2×#120C2314yes—
283C2×#120C2314yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×#117C2312yes—
305C2×#117C2312yes—
306C2×#117C2314yes—
307C2×#117C2314yes—
308C22×C22⋊C4C2312yes—
309C22×C22⋊C4C2312yes—
310C22×C22⋊C4C2314yes—
311C22×C42C2311yescharacteristic
312#401C2314yes—
313#401C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#399C2312yes—
320#399C2312yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#397C2314yes—
345#397C2312yes—
346#397C2312yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
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#395C2314yes—
377#395C2312yes—
378#395C2312yes—
379#395C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2312yes—
384#394C2312yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
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#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#393C2312yes—
411#393C2312yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2312yes—
419#393C2312yes—
420#393C2314yes—
421#392C2312yes—
422#392C2312yes—
423#392C2314yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2312yes—
432#392C2312yes—
433#392C2314yes—
434#392C2314yes—
435#392C2314yes—
436#392C2314yes—
437#392C2314yes—
438#392C2314yes—
439#392C2314yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2314yes—
447#391C2312yes—
448#391C2314yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#390C2312yes—
457#390C2312yes—
458#390C2312yes—
459#390C2314yes—
460#390C2314yes—
461#390C2314yes—
462#390C2314yes—
463#390C2314yes—
464#390C2314yes—
465#390C2312yes—
466#390C2314yes—
467#390C2314yes—
468#390C2314yes—
469#390C2314yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
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#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
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#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#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#383C2312yes—
577#383C2312yes—
578#383C2312yes—
579#383C2312yes—
580#382C2312yes—
581#382C2312yes—
582#382C2311yescharacteristic
583#382C2311yescharacteristic
584#382C2314yes—
585#382C2314yes—
586#382C2312yes—
587#381C2312yes—
588#381C2312yes—
589#381C2312yes—
590#381C2312yes—
591#381C2312yes—
592#381C2312yes—
593#381C2312yes—
594#381C2312yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2312yes—
599#380C2312yes—
600#380C2312yes—
601#380C2312yes—
602#380C2312yes—
603#380C2311yescharacteristic
604#380C2311yescharacteristic
605#379C2312yes—
606#379C2312yes—
607#379C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2311yescharacteristic
613C4×C4⋊C4C2311yescharacteristic
614C4×C4⋊C4C2311yescharacteristic
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2311yescharacteristic
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2312yes—
624C4×C22⋊C4C2312yes—
625C4×C22⋊C4C2311yescharacteristic
626C4×C22⋊C4C2312yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2314yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2312yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2311yescharacteristic
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2312yes—
640C4×C22⋊C4C2312yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2312yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2312yes—
650C4×C22⋊C4C2314yes—
651#376C2311yescharacteristic
652#376C2312yes—
653#376C2312yes—
654#376C2312yes—
655#376C2312yes—
656#376C2311yescharacteristic
657C2×#95C2312yes—
658C2×#95C2312yes—
659C2×#95C2312yes—
660C43C2312yes—
661C25C2412yes—
662C2×#41—24no—
663C2×#41—24no—
664C2×#41—82no—
665C2×#41—82no—
666C22×Q8—24no—
667C22×Q8—81no—
668C22×Q8—81no—
669C22×Q8C2411yescharacteristic
670C22×Q8C2412yes—
671C22×Q8C2411yescharacteristic
672C22×Q8C2411yescharacteristic
673C22×Q8C2412yes—
674C22×D4—24no—
675C22×D4—81no—
676C22×D4—81no—
677C22×D4C2411yescharacteristic
678C22×D4C2412yes—
679C22×D4C2412yes—
680C22×D4C2411yescharacteristic
681C22×D4C2411yescharacteristic
682C22×D4C2412yes—
683C22×D4C2412yes—
684C22×D4C2412yes—
685C22×D4C2412yes—
686C22×D4C2412yes—
687C22×D4C2414yes—
688C22×D4C2414yes—
689C22×D4C2414yes—
690C22×D4C2414yes—
691C22×D4C2414yes—
692C22×D4C2414yes—
693C22×D4C2414yes—
694C22×D4C2414yes—
695C23×C4C2412yes—
696C23×C4C2414yes—
697C23×C4C2412yes—
698C23×C4C2414yes—
699C23×C4C2412yes—
700C23×C4C2412yes—
701C23×C4C2414yes—
702C23×C4C2414yes—
703C23×C4C2414yes—
704C23×C4C2411yescharacteristic
705C23×C4C2411yescharacteristic
706C23×C4C2411yescharacteristic
707C4⋊Q8—24no—
708#127—24no—
709#127—82no—
710#127—82no—
711#126—28no—
712#126—84no—
713#126—84no—
714#125—24no—
715#124—28no—
716#124—28no—
717#124—28no—
718#124—28no—
719#124—24no—
720#124—24no—
721#124—24no—
722#124—82no—
723#124—82no—
724#123—28no—
725#123—48no—
726#123—48no—
727#123—84no—
728#123—84no—
729#123—84no—
730#123—82no—
731#123—82no—
732#123—84no—
733#123—84no—
734#123—84no—
735C22⋊Q8—24no—
736#121—24no—
737#121—28no—
738#121—28no—
739#121—48no—
740#121—48no—
741#121—84no—
742#121—84no—
743#121—84no—
744#121—84no—
745#120—84no—
746#120—82no—
747#120—84no—
748#120—82no—
749C4×Q8—24no—
750C4×Q8—44no—
751C4×Q8—82no—
752C4×Q8—82no—
753C4×Q8—82no—
754C4×Q8—82no—
755C4×D4—28no—
756C4×D4—24no—
757C4×D4—28no—
758C4×D4—28no—
759C4×D4—44no—
760C4×D4—48no—
761C4×D4—84no—
762C4×D4—84no—
763C4×D4—84no—
764C4×D4—84no—
765C4×D4—82no—
766C4×D4—82no—
767C4×D4—82no—
768C4×D4—82no—
769#117—28no—
770#117—44no—
771#117—84no—
772#117—84no—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C22⋊C4—28no—
813C2×C22⋊C4—28no—
814C2×C22⋊C4—48no—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
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×C42#4118yes—
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2412yes—
881C2×C42C2414yes—
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2411yescharacteristic
893C2×C42C2411yescharacteristic
894C2×C42C2411yescharacteristic
895C2×C42C2411yescharacteristic
896#95C2411yescharacteristic
897#95C2411yescharacteristic
898#95C2411yescharacteristic
899#95C2412yes—
900#95C2412yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2411yescharacteristic
905#95C2412yes—
906#95C2412yes—
907#95C2414yes—
908#95C2412yes—
909#95C2412yes—
910#95C2414yes—
911#95C2412yes—
912#95C2412yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2412yes—
917#95C2412yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948C24—24no—
949C24—44no—
950C24—44no—
951C24—42no—
952C24—42no—
953C24C2514yes—
954C24C2512yes—
955C24C2512yes—
956C24C2512yes—
957C24C2511yescharacteristic
958#41—88no—
959#41—88no—
960C2×Q8—22no—
961C2×Q8—24no—
962C2×Q8—22no—
963C2×Q8—22no—
964C2×Q8—24no—
965C2×Q8—42no—
966C2×Q8—42no—
967C2×Q8—42no—
968C2×Q8—42no—
969C2×Q8—42no—
970C2×Q8—42no—
971C2×Q8—42no—
972C2×Q8—88no—
973C2×D4—24no—
974C2×D4—24no—
975C2×D4—24no—
976C2×D4—22no—
977C2×D4—24no—
978C2×D4—24no—
979C2×D4—22no—
980C2×D4—22no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—42no—
984C2×D4—44no—
985C2×D4—42no—
986C2×D4—42no—
987C2×D4—42no—
988C2×D4—42no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—42no—
995C2×D4—42no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—42no—
1006C2×D4—42no—
1007C2×D4—42no—
1008C2×D4—42no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—88no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—28no—
1027C22×C4—28no—
1028C22×C4—42no—
1029C22×C4—41no—
1030C22×C4—41no—
1031C22×C4—42no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—42no—
1040C22×C4—42no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4—44no—
1050C22×C4C2×#4114yes—
1051C22×C4C2×#4114yes—
1052C22×C4C2×#4114yes—
1053C22×C4C2512yes—
1054C22×C4C2514yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2514yes—
1058C22×C4C2514yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2514yes—
1064C22×C4C2514yes—
1065C22×C4C2512yes—
1066C22×C4C2514yes—
1067C22×C4C2512yes—
1068C22×C4C2511yescharacteristic
1069C22×C4C2511yescharacteristic
1070C22×C4C2511yescharacteristic
1071C22×C4C2511yescharacteristic
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C22×C4C2512yes—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—22no—
1080C4⋊C4—24no—
1081C4⋊C4—22no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—28no—
1085C4⋊C4—42no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C22⋊C4—24no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—28no—
1118C22⋊C4—28no—
1119C22⋊C4—24no—
1120C22⋊C4—24no—
1121C22⋊C4—24no—
1122C22⋊C4—24no—
1123C22⋊C4—24no—
1124C22⋊C4—24no—
1125C22⋊C4—24no—
1126C22⋊C4—24no—
1127C22⋊C4—24no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—42no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—42no—
1153C22⋊C4—44no—
1154C22⋊C4—42no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C42—24no—
1173C42—24no—
1174C42—42no—
1175C42—44no—
1176C42—44no—
1177C42—44no—
1178C42—44no—
1179C42—44no—
1180C42—44no—
1181C42—42no—
1182C42—42no—
1183C42—42no—
1184C42—42no—
1185C42—44no—
1186C42—44no—
1187C42—44no—
1188C42—42no—
1189C42—42no—
1190C42C2×#4114yes—
1191C42C2×#4114yes—
1192C42C2×#4114yes—
1193C42C2×#4114yes—
1194C23—22no—
1195C23—21no—
1196C23—21no—
1197C23—22no—
1198C23—22no—
1199C23—24no—
1200C23—22no—
1201C23—22no—
1202C23—24no—
1203C23—24no—
1204C23—24no—
1205C23—24no—
1206C23—24no—
1207C23—22no—
1208C23—24no—
1209C23—22no—
1210C23—22no—
1211C23—22no—
1212C23—24no—
1213C23—24no—
1214C23—24no—
1215C23—22no—
1216C23—24no—
1217C23—22no—
1218C23—24no—
1219C23—24no—
1220C23—48no—
1221C23—84no—
1222C23—84no—
1223C23—164no—
1224C23—164no—
1225C23C22×#4112yes—
1226C23C2611yescharacteristic
1227Q8—44no—
1228Q8—48no—
1229Q8—44no—
1230Q8—44no—
1231Q8—84no—
1232D4—48no—
1233D4—44no—
1234D4—48no—
1235D4—44no—
1236D4—44no—
1237D4—84no—
1238D4—84no—
1239D4—84no—
1240D4—84no—
1241D4—84no—
1242D4—88no—
1243D4—88no—
1244D4—88no—
1245D4—88no—
1246D4—164no—
1247D4—164no—
1248D4—164no—
1249D4—164no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—21no—
1255C2×C4—22no—
1256C2×C4—21no—
1257C2×C4—22no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—44no—
1302C2×C4—44no—
1303C2×C4—44no—
1304C2×C4—88no—
1305C2×C4—88no—
1306C2×C4—84no—
1307C2×C4—84no—
1308C2×C4—84no—
1309C2×C4—84no—
1310C2×C4—164no—
1311C2×C4—164no—
1312C2×C4—164no—
1313C2×C4C22×#4112yes—
1314C2×C4C22×#4112yes—
1315C2×C4C22×#4112yes—
1316C2×C4C22×#4112yes—
1317C2×C4C22×#4112yes—
1318C2×C4C22×#4112yes—
1319C2×C4#58514yes—
1320C22—22no—
1321C22—22no—
1322C22—22no—
1323C22—42no—
1324C22—42no—
1325C22—44no—
1326C22—44no—
1327C22—44no—
1328C22—44no—
1329C22—44no—
1330C22—44no—
1331C22—44no—
1332C22—44no—
1333C22—44no—
1334C22—44no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22—44no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—44no—
1343C22—42no—
1344C22—42no—
1345C22—42no—
1346C22—44no—
1347C22—168no—
1348C22C23×#4111yescharacteristic
1349C22C2×#58512yes—
1350C22H(7,𝔽2)11yescharacteristic
1351C22H(7,𝔽2)12yes—
1352C22H(7,𝔽2)11yescharacteristic
1353C4—24no—
1354C4—22no—
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—22no—
1359C4—22no—
1360C4—44no—
1361C4—44no—
1362C4—42no—
1363C4—44no—
1364C4—42no—
1365C4—42no—
1366C4—44no—
1367C4—44no—
1368C4—44no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—44no—
1373C4—42no—
1374C4—42no—
1375C2—42no—
1376C2—82no—
1377C2—82no—
1378C2—82no—
1379C2—84no—
1380C2#6268611yescharacteristic
1381C2#6285511yescharacteristic
1382C2#6285511yescharacteristic
1383C2#6305512yes—
1384C2#6306012yes—
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. #42399C2semidirect
2. #42081C2semidirect
3. #42074C2semidirect
4. #41978C2semidirect
5. #41968C2semidirect
6. #41058C2semidirect
7. #41039C2semidirect
8. #41021C2semidirect
9. #41010C2semidirect
10. #40656C2semidirect
11. #40651C2semidirect
12. #37610C2semidirect
13. #37606C2semidirect
14. #37604C2semidirect
15. #37604C2semidirect
16. #37564C2semidirect
17. #37536C2semidirect
18. #36695C2semidirect
19. #36687C2semidirect
20. #35992C2semidirect
21. #35980C2semidirect
22. #35932C2semidirect
23. #35907C2semidirect
24. #35784C2semidirect
25. #34240C2semidirect
26. #34232C2semidirect
27. #34227C2semidirect
31. #2845C22semidirect
32. #2845C22semidirect
33. #2837C22semidirect
34. #2837C22semidirect
35. #2831C22semidirect
36. #2831C22semidirect
38. #2829C22semidirect
39. #2821C22semidirect
41. #2820C22semidirect
42. #2820C22semidirect
46. #2819C22semidirect
47. #2819C22semidirect
48. #2818C22semidirect
52. #2803C22semidirect
53. #2797C22semidirect
55. #2796C22semidirect
56. #2789C22semidirect
57. #2787C22semidirect
58. #2783C22semidirect
59. #2754C22semidirect
62. #2724C22semidirect
63. #2715C22semidirect
64. #2714C22semidirect
65. #2710C22semidirect
72. #2682C22semidirect
83. #2661C22semidirect
84. #2661C22semidirect
85. #2661C22semidirect
86. #2661C22semidirect
88. #2653C22semidirect
89. #2653C22semidirect
90. #2653C22semidirect
91. #2653C22semidirect
92. #2653C22semidirect
93. #2653C22semidirect
94. #2651C22semidirect
95. #2651C22semidirect
97. #2637C22semidirect
98. #2637C22semidirect
103. #2630C22semidirect
108. #2606C22semidirect
109. #2606C22semidirect
110. #2606C22semidirect
111. #2606C22semidirect
112. #2602C22semidirect
113. #2597C22semidirect
115. #2594C22semidirect
116. #2589C22semidirect
117. #2588C22semidirect
119. #2576C22semidirect
120. #2574C22semidirect
121. #2574C22semidirect
123. #2557C22semidirect
126. #2554C22semidirect
127. #2553C22semidirect
128. #2553C22semidirect
129. #2553C22semidirect
136. #2531C22semidirect
137. #2526C22semidirect
138. #2518C22semidirect
140. #2513C22semidirect
141. #2510C22semidirect
142. #2478C22semidirect
143. #2474C22semidirect
146. #2467C22semidirect
149. #2464C22semidirect
150. #2464C22semidirect
151. #2464C22semidirect
152. #2464C22semidirect
153. #2458C22semidirect
154. #2458C22semidirect
155. #2458C22semidirect
156. #2458C22semidirect
157. #2458C22semidirect
158. #2458C22semidirect
159. #2457C22semidirect
160. #2456C22semidirect
161. #2455C22semidirect
163. #2444C22semidirect
167. #2425C22semidirect
168. #2425C22semidirect
170. #2420C22semidirect
172. #2414C22semidirect
176. #2398C22semidirect
177. #2397C22semidirect
178. #2396C22semidirect
179. #2396C22semidirect
180. #2395C22semidirect
181. #2395C22semidirect
183. #2392C22semidirect
184. #2392C22semidirect
188. #2374C22semidirect
189. #2373C22semidirect
194. #2366C22semidirect
195. #2365C22semidirect
196. #2364C22semidirect
198. #2363C22semidirect
199. #2359C22semidirect
202. #2353C22semidirect
203. #2353C22semidirect
204. #2347C22semidirect
205. #2343C22semidirect
217. #2320C22semidirect
218. #2319C22semidirect
219. #2319C22semidirect
221. C4×#125C22semidirect
224. C4×#124C22semidirect
225. C4×#124C22semidirect
226. C4×#124C22semidirect
230. #2276C22semidirect
231. #2275C22semidirect
232. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#423992
#420812
#420742
#419782
#419682
#410582
#410392
#410212
#410102
#406562
#406512
#376102
#376062
#376042
#375642
#375362
#366952
#366872
#359922
#359802
#359322
#359072
#357842
#342402
#342322
#342272