Finite Group Databasebeta

← #7726953

Subgroups — #7726953

Order 512.

4640 conjugacy classes of subgroups.

The subgroup lattice has 1358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51765C214yesmaximal, complemented
2#51576C214yesmaximal, complemented
3#47812C214yesmaximal, complemented
4#47811C214yesmaximal, complemented
5#43965C212yesmaximal, complemented
6#43964C212yesmaximal, complemented
7#43083C212yesmaximal, complemented
8#43082C212yesmaximal, complemented
9#40282C214yesmaximal, complemented
10#39550C212yesmaximal, complemented
11#39540C212yesmaximal, complemented
12#39508C212yesmaximal, complemented
13#39503C212yesmaximal, complemented
14#38683C214yesmaximal, complemented
15#38396C214yesmaximal, complemented
16#37546C211yesmaximal, characteristic, complemented
17#37031C212yesmaximal, complemented
18#37022C212yesmaximal, complemented
19#36295C214yesmaximal, complemented
20#35508C212yesmaximal, complemented
21#35500C212yesmaximal, complemented
22#35304C211yesmaximal, characteristic, complemented
23#35118C211yesmaximal, characteristic, complemented
24C2×#2610C211yesmaximal, characteristic, complemented
25#34377C211yesmaximal, characteristic, complemented
26#34220C211yesmaximal, characteristic, complemented
27#34048C211yesmaximal, characteristic, complemented
28C2×#529C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C22×#117C2211yescharacteristic
31#2866C2214yescomplemented
32#2861C2214yescomplemented
33#2857C2212yes—
34#2853C2212yes—
35#2851C2212yes—
36#2849C2212yes—
37#2820C2212yescomplemented
38#2819C2212yescomplemented
39#2808C2214yescomplemented
40#2808C2214yescomplemented
41#2808C2214yescomplemented
42#2803C2214yes—
43#2803C2214yescomplemented
44#2803C2214yescomplemented
45#2803C2214yescomplemented
46#2798C2214yescomplemented
47#2797C2214yescomplemented
48#2793C2214yescomplemented
49#2787C2214yescomplemented
50#2786C2214yescomplemented
51#2784C2214yescomplemented
52#2779C2214yescomplemented
53#2779C2214yescomplemented
54#2778C2214yescomplemented
55#2774C2214yescomplemented
56#2762C2214yescomplemented
57#2761C2214yescomplemented
58#2759C2214yescomplemented
59#2759C2214yescomplemented
60#2759C2214yescomplemented
61#2757C2214yescomplemented
62#2756C2214yescomplemented
63#2753C2214yes—
64#2751C2214yescomplemented
65#2745C2214yescomplemented
66#2737C2214yescomplemented
67#2733C2214yescomplemented
68#2716C2214yescomplemented
69#2714C2214yes—
70#2708C2214yescomplemented
71#2707C2214yescomplemented
72#2703C2214yes—
73#2700C2214yescomplemented
74#2695C2214yescomplemented
75#2694C2214yescomplemented
76#2690C2214yescomplemented
77#2686C2214yescomplemented
78#2686C2214yescomplemented
79#2662C2212yescomplemented
80#2662C2212yescomplemented
81#2660C2212yescomplemented
82#2653C2214yescomplemented
83#2648C2214yescomplemented
84#2647C2212yescomplemented
85#2627C2211yescharacteristic
86#2626C2211yescharacteristic
87#2626C2212yes—
88#2620C2214yescomplemented
89#2618C2211yescharacteristic
90#2617C2211yescharacteristic
91#2617C2212yes—
92#2612C2214yescomplemented
93#2611C2212yescomplemented
94#2610C2214yes—
95#2610C2212yes—
96#2610C2212yes—
97#2610C2212yes—
98#2610C2212yes—
99#2610C2214yes—
100#2610C2212yescomplemented
101#2609C2214yescomplemented
102#2606C2212yescomplemented
103#2605C2212yescomplemented
104#2602C2214yes—
105#2601C2214yescomplemented
106#2601C2214yescomplemented
107#2600C2214yescomplemented
108#2599C2214yescomplemented
109#2599C2212yescomplemented
110#2598C2212yescomplemented
111#2596C2214yescomplemented
112#2595C2214yescomplemented
113#2595C2214yescomplemented
114#2594C2214yescomplemented
115#2594C2214yescomplemented
116#2593C2214yescomplemented
117#2592C2214yescomplemented
118#2592C2212yescomplemented
119#2578C2214yescomplemented
120#2577C2214yescomplemented
121#2576C2214yescomplemented
122#2574C2214yescomplemented
123#2569C2212yes—
124#2561C2214yes—
125#2560C2214yescomplemented
126#2559C2214yescomplemented
127#2558C2214yescomplemented
128#2557C2214yescomplemented
129#2554C2214yes—
130#2549C2212yes—
131#2543C2214yes—
132#2540C2212yescomplemented
133#2532C2214yescomplemented
134#2531C2214yescomplemented
135#2531C2214yescomplemented
136#2531C2214yescomplemented
137#2529C2214yescomplemented
138#2527C2214yescomplemented
139#2525C2214yescomplemented
140#2525C2214yescomplemented
141#2520C2214yescomplemented
142#2513C2214yescomplemented
143#2510C2214yes—
144#2500C2214yescomplemented
145#2493C2214yes—
146#2491C2214yescomplemented
147#2485C2214yescomplemented
148#2480C2214yes—
149#2480C2214yes—
150#2479C2214yescomplemented
151#2476C2214yescomplemented
152#2475C2214yescomplemented
153#2474C2214yescomplemented
154#2473C2214yes—
155#2472C2214yes—
156#2472C2214yes—
157#2469C2214yescomplemented
158#2469C2214yescomplemented
159#2468C2214yescomplemented
160#2462C2214yescomplemented
161#2460C2214yescomplemented
162#2459C2214yescomplemented
163#2458C2214yescomplemented
164#2456C2214yes—
165#2438C2214yes—
166#2438C2214yescomplemented
167#2419C2214yes—
168#2414C2214yescomplemented
169#2412C2214yes—
170#2411C2214yes—
171#2409C2212yes—
172#2408C2212yes—
173#2408C2214yes—
174#2405C2214yes—
175C2×#395C2211yescharacteristic
176C2×#394C2211yescharacteristic
177C2×#393C2211yescharacteristic
178C2×#392C2211yescharacteristic
179#2379C2214yescomplemented
180#2373C2214yescomplemented
181#2368C2214yes—
182#2367C2214yescomplemented
183#2359C2214yes—
184#2358C2214yes—
185#2353C2212yes—
186#2352C2214yes—
187#2349C2212yes—
188#2346C2212yescomplemented
189#2343C2212yescomplemented
190#2342C2214yes—
191#2342C2214yes—
192Q8×C22⋊C4C2212yes—
193D4×C22⋊C4C2212yes—
194#2337C2212yescomplemented
195#2337C2212yescomplemented
196#2335C2214yescomplemented
197#2333C2214yescomplemented
198#2331C2212yescomplemented
199#2330C2212yescomplemented
200#2330C2212yescomplemented
201#2326C2214yescomplemented
202#2326C2212yescomplemented
203#2322C2212yes—
204#2321C2212yes—
205#2320C2211yescharacteristic, complemented
206#2319C2211yescharacteristic, complemented
207#2315C2212yes—
208#2314C2214yescomplemented
209#2314C2214yescomplemented
210#2313C2212yes—
211#2313C2212yes—
212#2312C2212yes—
213#2312C2212yes—
214#2312C2212yes—
215C4×#126C2214yescomplemented
216C4×C22⋊Q8C2212yes—
217C4×#121C2212yes—
218#2298C2212yescomplemented
219#2298C2212yescomplemented
220#2298C2212yescomplemented
221#2298C2212yescomplemented
222#2293C2214yescomplemented
223C2×#390C2212yes—
224C2×#388C2212yes—
225C2×#388C2212yes—
226C2×#386C2212yes—
227#2285C2211yescharacteristic
228#2285C2211yescharacteristic
229#2283C2211yescharacteristic
230#2280C2212yes—
231#2276C2211yescharacteristic, complemented
232#2275C2211yescharacteristic, complemented
233C4×#117C2212yes—
234C2×#376C2211yescharacteristic
235C23×Q8C2311yescharacteristic
236C23×D4C2311yescharacteristic
237C23×D4C2312yes—
238C24×C4C2311yescharacteristic
239C2×C4⋊Q8C2312yes—
240#529—28no—
241C2×#126C2312yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#125C2311yescharacteristic
245C2×#125C2312yes—
246C2×#125C2314yes—
247C2×#124—28no—
248C2×#124C2311yescharacteristic
249C2×#124C2312yes—
250C2×#124C2312yes—
251C2×#124C2312yes—
252C2×#124C2312yes—
253C2×#124C2314yes—
254C2×#124C2314yes—
255C2×#123C2312yes—
256C2×#123C2312yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×C22⋊Q8C2311yescharacteristic
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×#121C2311yescharacteristic
263C2×#121C2314yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#120C2312yes—
267C2×#120C2314yes—
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2314yes—
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×#117—28no—
278C2×#117C2312yes—
279C2×#117C2312yes—
280C2×#117C2312yes—
281C2×#117C2312yes—
282C2×#117C2312yes—
283C2×#117C2312yes—
284C2×#117C2312yes—
285C2×#117C2314yes—
286C2×#117C2314yes—
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2312yes—
290C22×C22⋊C4C2311yescharacteristic
291C22×C22⋊C4C2311yescharacteristic
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2312yes—
295C22×C22⋊C4C2314yes—
296C22×C22⋊C4C2312yes—
297C22×C22⋊C4C2312yes—
298C22×C22⋊C4C2312yes—
299C22×C42C2311yescharacteristic
300C22×C42C2312yes—
301C22×C42C2311yescharacteristic
302#401C2314yes—
303#401C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2312yes—
311#400C2314yes—
312#400C2314yes—
313#399C2314yes—
314#399C2312yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2312yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2312yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#395C2312yes—
352#395C2312yes—
353#395C2314yes—
354#395C2314yes—
355#395C2312yes—
356#395C2314yes—
357#395C2312yes—
358#395C2312yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2312yes—
363#394C2312yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2312yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2312yes—
374#394C2314yes—
375#394C2312yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#393C2312yes—
383#393C2314yes—
384#393C2314yes—
385#393C2312yes—
386#393C2314yes—
387#393C2312yes—
388#393C2314yes—
389#393C2314yes—
390#393C2312yes—
391#393C2312yes—
392#393C2314yes—
393#392C2314yes—
394#392C2312yes—
395#392C2312yes—
396#392C2312yes—
397#392C2314yes—
398#392C2312yes—
399#392C2312yes—
400#392C2314yes—
401#392C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2312yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#390C2314yes—
413#390C2312yes—
414#390C2314yes—
415#390C2314yes—
416#390C2314yes—
417#390C2314yes—
418#390C2314yes—
419#390C2314yes—
420#390C2314yes—
421#390C2314yes—
422#390C2314yes—
423#390C2314yes—
424#390C2314yes—
425#390C2314yes—
426#390C2314yes—
427#389C2312yes—
428#389C2312yes—
429#389C2314yes—
430#389C2314yes—
431#389C2312yes—
432#389C2312yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2312yes—
437#389C2312yes—
438#389C2314yes—
439#389C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
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#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2312yes—
538#386C2312yes—
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#385C2314yes—
554#385C2314yes—
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#384C2312yes—
573#384C2312yes—
574#384C2312yes—
575#383C2314yes—
576#383C2312yes—
577#383C2314yes—
578#383C2312yes—
579#382C2312yes—
580#382C2312yes—
581#382C2314yes—
582#382C2312yes—
583#382C2312yes—
584#382C2312yes—
585#381C2312yes—
586#381C2314yes—
587#381C2312yes—
588#381C2314yes—
589#381C2312yes—
590#381C2314yes—
591#380C2312yes—
592#380C2311yescharacteristic
593#380C2312yes—
594#380C2312yes—
595#380C2312yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2311yescharacteristic
600#380C2314yes—
601#380C2314yes—
602#380C2312yes—
603#380C2314yes—
604#380C2314yes—
605#380C2314yes—
606#379C2314yes—
607#379C2314yes—
608#379C2314yes—
609#379C2312yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2311yescharacteristic
617C4×C4⋊C4C2311yescharacteristic
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2311yescharacteristic
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2311yescharacteristic
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2312yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2312yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2312yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2312yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2312yes—
642C4×C22⋊C4C2312yes—
643#376C2311yescharacteristic
644#376C2312yes—
645#376C2312yes—
646#376C2312yes—
647#376C2311yescharacteristic
648#376C2311yescharacteristic
649#376C2312yes—
650#376C2311yescharacteristic
651#376C2312yes—
652#376C2312yes—
653C2×#95C2311yescharacteristic
654C2×#95C2312yes—
655C2×#95C2311yescharacteristic
656C2×#95C2312yes—
657C2×#95C2312yes—
658C2×#95C2312yes—
659C43C2312yes—
660C43C2312yes—
661C25C2412yes—
662C25C2411yescharacteristic
663C22×Q8—24no—
664C22×Q8—82no—
665C22×Q8C2411yescharacteristic
666C22×Q8C2412yes—
667C22×Q8C2412yes—
668C22×Q8C2414yes—
669C22×D4—24no—
670C22×D4—44no—
671C22×D4—44no—
672C22×D4—82no—
673C22×D4—82no—
674C22×D4C2412yes—
675C22×D4C2411yescharacteristic
676C22×D4C2412yes—
677C22×D4C2414yes—
678C22×D4C2412yes—
679C22×D4C2414yes—
680C22×D4C2414yes—
681C22×D4C2414yes—
682C22×D4C2414yes—
683C23×C4—24no—
684C23×C4—42no—
685C23×C4—42no—
686C23×C4C2411yescharacteristic
687C23×C4C2412yes—
688C23×C4C2411yescharacteristic
689C23×C4C2411yescharacteristic
690C23×C4C2412yes—
691C23×C4C2411yescharacteristic
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2414yes—
696C23×C4C2412yes—
697C23×C4C2414yes—
698C23×C4C2414yes—
699C23×C4C2411yescharacteristic
700C23×C4C2411yescharacteristic
701C4⋊Q8—44no—
702#126—28no—
703#126—48no—
704#126—84no—
705#125—24no—
706#125—44no—
707#125—84no—
708#124—28no—
709#124—28no—
710#124—28no—
711#124—28no—
712#124—24no—
713#124—84no—
714#124—84no—
715#123—28no—
716#123—44no—
717#123—48no—
718#123—84no—
719C22⋊Q8—24no—
720C22⋊Q8—48no—
721C22⋊Q8—84no—
722#121—24no—
723#121—48no—
724#121—84no—
725#121—84no—
726#120—48no—
727#120—44no—
728C4×Q8—24no—
729C4×Q8—44no—
730C4×Q8—84no—
731C4×D4—28no—
732C4×D4—24no—
733C4×D4—44no—
734C4×D4—48no—
735C4×D4—48no—
736C4×D4—84no—
737#117—28no—
738#117—28no—
739#117—28no—
740#117—28no—
741#117—28no—
742#117—44no—
743#117—44no—
744#117—84no—
745#117—84no—
746C2×C4⋊C4—24no—
747C2×C4⋊C4—24no—
748C2×C4⋊C4—82no—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
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⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C22⋊C4—24no—
791C2×C22⋊C4—24no—
792C2×C22⋊C4—28no—
793C2×C22⋊C4—28no—
794C2×C22⋊C4—44no—
795C2×C22⋊C4—48no—
796C2×C22⋊C4—44no—
797C2×C22⋊C4—82no—
798C2×C22⋊C4—82no—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
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×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×C42—24no—
852C2×C42—44no—
853C2×C42#4118yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2412yes—
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2412yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2411yescharacteristic
876C2×C42C2411yescharacteristic
877C2×C42C2411yescharacteristic
878C2×C42C2411yescharacteristic
879#95C2411yescharacteristic
880#95C2411yescharacteristic
881#95C2412yes—
882#95C2411yescharacteristic
883#95C2411yescharacteristic
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2412yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2412yes—
900#95C2414yes—
901#95C2412yes—
902#95C2412yes—
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#95C2412yes—
923#95C2414yes—
924#95C2412yes—
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—
938C24—22no—
939C24—22no—
940C24—24no—
941C24—24no—
942C24—24no—
943C24—22no—
944C24—42no—
945C24—42no—
946C24—42no—
947C24—42no—
948C24—42no—
949C24—42no—
950C24C2512yes—
951C24C2514yes—
952C24C2512yes—
953C24C2511yescharacteristic
954C2×Q8—22no—
955C2×Q8—24no—
956C2×Q8—24no—
957C2×Q8—42no—
958C2×Q8—44no—
959C2×Q8—44no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—44no—
963C2×Q8—88no—
964C2×D4—24no—
965C2×D4—24no—
966C2×D4—24no—
967C2×D4—22no—
968C2×D4—24no—
969C2×D4—24no—
970C2×D4—28no—
971C2×D4—42no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—88no—
989C2×D4—816no—
990C22×C4—22no—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—24no—
995C22×C4—22no—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—24no—
999C22×C4—24no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—24no—
1004C22×C4—28no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—42no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—44no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—416no—
1028C22×C4C2×#4114yes—
1029C22×C4C2×#4114yes—
1030C22×C4C2×#4114yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2514yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2514yes—
1039C22×C4C2514yes—
1040C22×C4C2514yes—
1041C22×C4C2514yes—
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2511yescharacteristic
1048C22×C4C2511yescharacteristic
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C22×C4C2511yescharacteristic
1052C22×C4C2511yescharacteristic
1053C22×C4C2512yes—
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—22no—
1061C4⋊C4—24no—
1062C4⋊C4—22no—
1063C4⋊C4—24no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—42no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—42no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C22⋊C4—24no—
1096C22⋊C4—24no—
1097C22⋊C4—28no—
1098C22⋊C4—28no—
1099C22⋊C4—24no—
1100C22⋊C4—24no—
1101C22⋊C4—24no—
1102C22⋊C4—24no—
1103C22⋊C4—24no—
1104C22⋊C4—28no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—24no—
1109C22⋊C4—24no—
1110C22⋊C4—24no—
1111C22⋊C4—24no—
1112C22⋊C4—28no—
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—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C42—24no—
1148C42—24no—
1149C42—24no—
1150C42—24no—
1151C42—24no—
1152C42—42no—
1153C42—42no—
1154C42—42no—
1155C42—42no—
1156C42—42no—
1157C42—42no—
1158C42—44no—
1159C42—44no—
1160C42—44no—
1161C42—44no—
1162C42—44no—
1163C42—44no—
1164C42—44no—
1165C42—44no—
1166C42—44no—
1167C42—44no—
1168C42C2×#4114yes—
1169C42C2×#4114yes—
1170C42C2×#4114yes—
1171C42C2×#4114yes—
1172C23—22no—
1173C23—22no—
1174C23—22no—
1175C23—22no—
1176C23—24no—
1177C23—24no—
1178C23—22no—
1179C23—24no—
1180C23—24no—
1181C23—24no—
1182C23—22no—
1183C23—24no—
1184C23—24no—
1185C23—22no—
1186C23—22no—
1187C23—24no—
1188C23—24no—
1189C23—24no—
1190C23—24no—
1191C23—48no—
1192C23—44no—
1193C23—48no—
1194C23—82no—
1195C23—82no—
1196C23—84no—
1197C23—84no—
1198C23—84no—
1199C23—84no—
1200C23—84no—
1201C23—84no—
1202C23—84no—
1203C23C22×#4112yes—
1204C23#58512yes—
1205C23#58512yes—
1206C23C2611yescharacteristic
1207Q8—44no—
1208Q8—48no—
1209Q8—84no—
1210Q8—164no—
1211D4—44no—
1212D4—48no—
1213D4—48no—
1214D4—84no—
1215D4—88no—
1216D4—88no—
1217D4—88no—
1218D4—164no—
1219D4—164no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—28no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—22no—
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—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—44no—
1276C2×C4—44no—
1277C2×C4—48no—
1278C2×C4—48no—
1279C2×C4—48no—
1280C2×C4—44no—
1281C2×C4—84no—
1282C2×C4—88no—
1283C2×C4—82no—
1284C2×C4—82no—
1285C2×C4—84no—
1286C2×C4—84no—
1287C2×C4—88no—
1288C2×C4—164no—
1289C2×C4C22×#4112yes—
1290C2×C4C22×#4112yes—
1291C2×C4C22×#4112yes—
1292C2×C4C22×#4112yes—
1293C2×C4C22×#4112yes—
1294C2×C4C22×#4112yes—
1295C2×C4#58514yes—
1296C22—22no—
1297C22—22no—
1298C22—24no—
1299C22—24no—
1300C22—42no—
1301C22—42no—
1302C22—44no—
1303C22—42no—
1304C22—42no—
1305C22—44no—
1306C22—42no—
1307C22—44no—
1308C22—42no—
1309C22—44no—
1310C22—44no—
1311C22—44no—
1312C22—44no—
1313C22—44no—
1314C22—44no—
1315C22—44no—
1316C22—44no—
1317C22—88no—
1318C22—168no—
1319C22#349314yes—
1320C22C23×#4111yescharacteristic
1321C22C2×#58511yescharacteristic
1322C22C2×#58511yescharacteristic
1323C22C2×#58512yes—
1324C22H(7,𝔽2)12yes—
1325C4—22no—
1326C4—22no—
1327C4—22no—
1328C4—22no—
1329C4—22no—
1330C4—22no—
1331C4—24no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—44no—
1339C4—42no—
1340C4—42no—
1341C4—44no—
1342C4—44no—
1343C4—44no—
1344C4—42no—
1345C4—44no—
1346C4—44no—
1347C4—44no—
1348C2—24no—
1349C2—82no—
1350C2—82no—
1351C2—84no—
1352C2C2×#349311yescharacteristic
1353C2#6281511yescharacteristic
1354C2#6285511yescharacteristic
1355C2#6291012yes—
1356C2#6293312yes—
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. #51765C2semidirect
2. #51576C2semidirect
3. #47812C2semidirect
4. #47811C2semidirect
5. #43965C2semidirect
6. #43964C2semidirect
7. #43083C2semidirect
8. #43082C2semidirect
9. #40282C2semidirect
10. #39550C2semidirect
11. #39540C2semidirect
12. #39508C2semidirect
13. #39503C2semidirect
14. #38683C2semidirect
15. #38396C2semidirect
16. #37546C2semidirect
17. #37031C2semidirect
18. #37022C2semidirect
19. #36295C2semidirect
20. #35508C2semidirect
21. #35500C2semidirect
22. #35304C2semidirect
23. #35118C2semidirect
24. C2×#2610C2semidirect
25. #34377C2semidirect
26. #34220C2semidirect
27. #34048C2semidirect
31. #2866C22semidirect
32. #2861C22semidirect
37. #2820C22semidirect
38. #2819C22semidirect
39. #2808C22semidirect
40. #2808C22semidirect
41. #2808C22semidirect
43. #2803C22semidirect
44. #2803C22semidirect
45. #2803C22semidirect
46. #2798C22semidirect
47. #2797C22semidirect
48. #2793C22semidirect
49. #2787C22semidirect
50. #2786C22semidirect
51. #2784C22semidirect
52. #2779C22semidirect
53. #2779C22semidirect
54. #2778C22semidirect
55. #2774C22semidirect
56. #2762C22semidirect
57. #2761C22semidirect
58. #2759C22semidirect
59. #2759C22semidirect
60. #2759C22semidirect
61. #2757C22semidirect
62. #2756C22semidirect
64. #2751C22semidirect
65. #2745C22semidirect
66. #2737C22semidirect
67. #2733C22semidirect
68. #2716C22semidirect
70. #2708C22semidirect
71. #2707C22semidirect
73. #2700C22semidirect
74. #2695C22semidirect
75. #2694C22semidirect
76. #2690C22semidirect
77. #2686C22semidirect
78. #2686C22semidirect
79. #2662C22semidirect
80. #2662C22semidirect
81. #2660C22semidirect
82. #2653C22semidirect
83. #2648C22semidirect
84. #2647C22semidirect
88. #2620C22semidirect
92. #2612C22semidirect
93. #2611C22semidirect
100. #2610C22semidirect
101. #2609C22semidirect
102. #2606C22semidirect
103. #2605C22semidirect
105. #2601C22semidirect
106. #2601C22semidirect
107. #2600C22semidirect
108. #2599C22semidirect
109. #2599C22semidirect
110. #2598C22semidirect
111. #2596C22semidirect
112. #2595C22semidirect
113. #2595C22semidirect
114. #2594C22semidirect
115. #2594C22semidirect
116. #2593C22semidirect
117. #2592C22semidirect
118. #2592C22semidirect
119. #2578C22semidirect
120. #2577C22semidirect
121. #2576C22semidirect
122. #2574C22semidirect
125. #2560C22semidirect
126. #2559C22semidirect
127. #2558C22semidirect
128. #2557C22semidirect
132. #2540C22semidirect
133. #2532C22semidirect
134. #2531C22semidirect
135. #2531C22semidirect
136. #2531C22semidirect
137. #2529C22semidirect
138. #2527C22semidirect
139. #2525C22semidirect
140. #2525C22semidirect
141. #2520C22semidirect
142. #2513C22semidirect
144. #2500C22semidirect
146. #2491C22semidirect
147. #2485C22semidirect
150. #2479C22semidirect
151. #2476C22semidirect
152. #2475C22semidirect
153. #2474C22semidirect
157. #2469C22semidirect
158. #2469C22semidirect
159. #2468C22semidirect
160. #2462C22semidirect
161. #2460C22semidirect
162. #2459C22semidirect
163. #2458C22semidirect
166. #2438C22semidirect
168. #2414C22semidirect
179. #2379C22semidirect
180. #2373C22semidirect
182. #2367C22semidirect
188. #2346C22semidirect
189. #2343C22semidirect
194. #2337C22semidirect
195. #2337C22semidirect
196. #2335C22semidirect
197. #2333C22semidirect
198. #2331C22semidirect
199. #2330C22semidirect
200. #2330C22semidirect
201. #2326C22semidirect
202. #2326C22semidirect
205. #2320C22semidirect
206. #2319C22semidirect
208. #2314C22semidirect
209. #2314C22semidirect
215. C4×#126C22semidirect
218. #2298C22semidirect
219. #2298C22semidirect
220. #2298C22semidirect
221. #2298C22semidirect
222. #2293C22semidirect
231. #2276C22semidirect
232. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#517652
#515762
#478122
#478112
#439652
#439642
#430832
#430822
#402822
#395502
#395402
#395082
#395032
#386832
#383962
#375462
#370312
#370222
#362952
#355082
#355002
#353042
#351182
C2×#26102
#343772
#342202
#340482