Finite Group Databasebeta

← #7662371

Subgroups — #7662371

Order 512.

4853 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52285C213yesmaximal, complemented
2#42751C213yesmaximal, complemented
3#42666C213yesmaximal, complemented
4#42624C213yesmaximal, complemented
5#42564C213yesmaximal, complemented
6#42537C213yesmaximal, complemented
7#42472C213yesmaximal, complemented
8#40171C213yesmaximal, complemented
9#40117C213yesmaximal, complemented
10#40050C213yesmaximal, complemented
11#40002C213yesmaximal, complemented
12#39240C213yesmaximal, complemented
13#39201C213yesmaximal, complemented
14#37363C213yesmaximal, complemented
15#37336C213yesmaximal, complemented
16#37322C213yesmaximal, complemented
17#36585C211yesmaximal, characteristic, complemented
18#36583C211yesmaximal, characteristic, complemented
19#36474C211yesmaximal, characteristic, complemented
20#36457C211yesmaximal, characteristic, complemented
21#36433C211yesmaximal, characteristic, complemented
22#36431C211yesmaximal, characteristic, complemented
23#36076C211yesmaximal, characteristic, complemented
24#36059C211yesmaximal, characteristic, complemented
25#36049C211yesmaximal, characteristic, complemented
26#36040C211yesmaximal, characteristic, complemented
27#36029C211yesmaximal, characteristic
28#35748C211yesmaximal, characteristic, complemented
29#34336C211yesmaximal, characteristic, complemented
30#34295C211yesmaximal, characteristic, complemented
31#34263C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#550C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#520C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41#2862C2213yes—
42#2860C2213yes—
43#2858C2213yes—
44#2858C2213yes—
45#2854C2213yes—
46#2851C2213yes—
47#2838C2216yes—
48#2829C2216yes—
49#2801C2213yes—
50#2798C2213yes—
51#2796C2213yes—
52#2795C2213yes—
53#2790C2213yes—
54#2772C2213yes—
55#2762C2211yescharacteristic
56#2759C2216yes—
57#2757C2213yes—
58#2755C2213yes—
59#2754C2213yes—
60#2751C2216yes—
61#2751C2216yes—
62#2746C2216yes—
63#2741C2216yes—
64#2739C2213yes—
65#2737C2216yes—
66#2730C2216yes—
67#2730C2216yes—
68#2730C2216yes—
69#2717C2216yes—
70#2716C2213yes—
71#2712C2213yes—
72#2712C2216yes—
73#2712C2216yes—
74#2710C2216yes—
75#2710C2216yes—
76#2705C2213yes—
77#2701C2216yes—
78#2700C2213yes—
79#2700C2216yes—
80#2691C2216yes—
81#2686C2216yes—
82#2674C2213yes—
83#2672C2216yes—
84#2663C2216yes—
85#2653C2216yes—
86#2651C2216yes—
87#2651C2216yes—
88#2644C2213yes—
89#2641C2213yes—
90#2638C2216yes—
91#2628C2213yes—
92#2628C2213yes—
93#2624C2216yes—
94#2624C2213yes—
95#2619C2213yes—
96#2580C2213yes—
97#2580C2213yes—
98#2580C2213yes—
99#2567C2213yes—
100#2566C2213yes—
101#2563C2213yes—
102#2563C2213yes—
103#2562C2213yes—
104#2550C2213yes—
105#2550C2213yes—
106#2550C2213yes—
107#2550C2213yes—
108#2548C2213yes—
109#2548C2213yes—
110#2548C2213yes—
111#2547C2213yes—
112#2546C2213yes—
113#2542C2213yes—
114#2541C2213yes—
115#2535C2213yes—
116#2515C2216yes—
117#2513C2213yes—
118#2513C2213yes—
119#2513C2213yes—
120#2513C2213yes—
121#2513C2213yes—
122#2513C2213yes—
123#2504C2213yes—
124#2500C2213yes—
125#2495C2213yes—
126#2495C2213yes—
127#2495C2213yes—
128#2494C2213yes—
129#2494C2213yes—
130#2494C2213yes—
131#2491C2216yes—
132#2491C2213yes—
133#2491C2213yes—
134#2491C2213yes—
135#2491C2213yes—
136#2491C2213yes—
137#2491C2213yes—
138#2490C2213yes—
139#2490C2213yes—
140#2490C2213yes—
141#2490C2213yes—
142#2490C2213yes—
143#2490C2213yes—
144#2486C2213yes—
145#2485C2213yes—
146#2477C2216yes—
147#2474C2216yes—
148#2461C2216yes—
149#2454C2213yes—
150#2454C2213yes—
151#2454C2213yes—
152#2452C2213yes—
153#2452C2213yes—
154#2452C2213yes—
155#2445C2213yes—
156#2445C2213yes—
157#2445C2213yes—
158#2445C2213yes—
159#2442C2213yes—
160#2442C2213yes—
161#2441C2213yes—
162#2440C2213yes—
163#2440C2213yes—
164#2439C2213yes—
165#2428C2213yes—
166#2428C2213yes—
167#2422C2216yes—
168#2422C2213yes—
169#2420C2213yes—
170#2420C2213yes—
171#2420C2213yes—
172#2416C2213yes—
173#2416C2213yes—
174#2401C2213yes—
175#2398C2213yes—
176#2396C2213yes—
177#2396C2213yes—
178#2395C2213yes—
179#2392C2213yes—
180#2370C2213yes—
181#2370C2213yes—
182#2369C2213yes—
183#2366C2213yes—
184#2363C2213yes—
185#2361C2213yes—
186#2357C2213yes—
187#2355C2213yes—
188#2354C2213yes—
189#2352C2213yes—
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197#2351C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200#2345C2213yes—
201#2344C2213yes—
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205#2341C2211yescharacteristic
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214#2337C2216yes—
215#2331C2213yes—
216#2330C2213yes—
217#2328C2213yes—
218#2324C2216yes—
219#2324C2213yes—
220#2319C2213yes—
221#2314C2213yes—
222C4×C4⋊Q8C2213yes—
223C4×#125C2213yes—
224C4×#126C2213yes—
225C4×#124C2213yes—
226C4×#124C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×#123C2213yes—
229C4×#121C2213yes—
230#2298C2213yes—
231#2295C2213yes—
232#2293C2213yes—
233#2290C2213yes—
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C22×#41C2311yescharacteristic
241Q82—44no—
242#557—28no—
243#557—44no—
244#550—28no—
245#550—44no—
246#550—44no—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×#127C2313yes—
254C2×#127C2313yes—
255C2×#127C2313yes—
256C2×#126C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#125C2313yes—
261C2×#124C2316yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#124C2316yes—
265C2×#124C2316yes—
266C2×#124C2316yes—
267C2×#123C2313yes—
268C2×#123C2316yes—
269C2×#123C2316yes—
270C2×C22⋊Q8C2313yes—
271C2×C22⋊Q8C2316yes—
272C2×C22⋊Q8C2316yes—
273C2×#121C2313yes—
274C2×#121C2313yes—
275C2×#121C2316yes—
276C2×#121C2313yes—
277C2×#121C2313yes—
278C2×#121C2313yes—
279C2×#121C2313yes—
280C2×#121C2316yes—
281#520—28no—
282#520—44no—
283C4×#41—44no—
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2313yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2316yes—
309C2×#117C2313yes—
310C2×#117C2313yes—
311C2×#117C2313yes—
312C2×#117C2316yes—
313C22×C4⋊C4C2313yes—
314C22×C4⋊C4C2313yes—
315C22×C42C2313yes—
316#401C2316yes—
317#401C2311yescharacteristic
318#400C2313yes—
319#400C2316yes—
320#400C2313yes—
321#400C2311yescharacteristic
322#400C2311yescharacteristic
323#400C2311yescharacteristic
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#399C2313yes—
328#399C2313yes—
329#399C2316yes—
330#399C2316yes—
331#399C2313yes—
332#399C2316yes—
333#398C2316yes—
334#398C2313yes—
335#398C2313yes—
336#398C2311yescharacteristic
337#398C2313yes—
338#398C2313yes—
339#398C2316yes—
340#398C2313yes—
341#397C2313yes—
342#397C2316yes—
343#397C2316yes—
344#397C2316yes—
345#397C2316yes—
346#397C2313yes—
347#397C2316yes—
348#397C2316yes—
349#397C2313yes—
350#397C2316yes—
351#397C2316yes—
352#397C2316yes—
353#397C2313yes—
354#397C2313yes—
355#397C2313yes—
356#397C2313yes—
357#397C2313yes—
358#397C2313yes—
359#397C2316yes—
360#396C2316yes—
361#396C2316yes—
362#396C2313yes—
363#396C2313yes—
364#396C2313yes—
365#396C2313yes—
366#396C2313yes—
367#396C2313yes—
368#396C2313yes—
369#395C2316yes—
370#395C2316yes—
371#395C2316yes—
372#395C2313yes—
373#395C2311yescharacteristic
374#394C2316yes—
375#394C2316yes—
376#394C2316yes—
377#394C2316yes—
378#394C2316yes—
379#394C2316yes—
380#394C2313yes—
381#394C2316yes—
382#394C2313yes—
383#394C2316yes—
384#394C2316yes—
385#394C2313yes—
386#394C2316yes—
387#394C2313yes—
388#394C2313yes—
389#394C2313yes—
390#394C2316yes—
391#394C2316yes—
392#394C2316yes—
393#394C2313yes—
394#393C2313yes—
395#393C2316yes—
396#393C2316yes—
397#393C2316yes—
398#393C2313yes—
399#393C2316yes—
400#393C2316yes—
401#393C2313yes—
402#393C2313yes—
403#392C2316yes—
404#392C2316yes—
405#392C2313yes—
406#391C2311yescharacteristic
407#391C2313yes—
408#391C2316yes—
409#391C2313yes—
410#391C2316yes—
411#391C2313yes—
412#391C2316yes—
413#391C2316yes—
414#391C2313yes—
415#391C2311yescharacteristic
416#391C2313yes—
417#390C2316yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2316yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2316yes—
427#390C2316yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2313yes—
435#390C2313yes—
436#390C2313yes—
437#390C2313yes—
438#390C2313yes—
439#390C2313yes—
440#390C2313yes—
441#390C2313yes—
442#390C2313yes—
443#390C2313yes—
444#390C2313yes—
445#390C2313yes—
446#390C2316yes—
447#390C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2316yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#388C2313yes—
477#388C2313yes—
478#388C2313yes—
479#388C2316yes—
480#388C2316yes—
481#388C2316yes—
482#388C2316yes—
483#388C2313yes—
484#388C2316yes—
485#388C2316yes—
486#388C2313yes—
487#388C2313yes—
488#388C2316yes—
489#388C2316yes—
490#388C2313yes—
491#388C2316yes—
492#388C2316yes—
493#388C2313yes—
494#388C2313yes—
495#388C2313yes—
496#388C2313yes—
497#388C2316yes—
498#388C2316yes—
499#388C2313yes—
500#388C2313yes—
501#388C2313yes—
502#388C2313yes—
503#388C2313yes—
504#388C2313yes—
505#388C2313yes—
506#388C2313yes—
507#387C2313yes—
508#387C2313yes—
509#387C2313yes—
510#387C2313yes—
511#387C2316yes—
512#387C2313yes—
513#387C2316yes—
514#387C2316yes—
515#387C2316yes—
516#387C2313yes—
517#387C2316yes—
518#387C2313yes—
519#387C2313yes—
520#387C2313yes—
521#387C2313yes—
522#387C2313yes—
523#387C2311yescharacteristic
524#387C2311yescharacteristic
525#387C2313yes—
526#387C2311yescharacteristic
527#387C2311yescharacteristic
528#387C2311yescharacteristic
529#386C2313yes—
530#386C2316yes—
531#386C2316yes—
532#386C2313yes—
533#386C2316yes—
534#386C2316yes—
535#386C2316yes—
536#386C2316yes—
537#386C2316yes—
538#386C2313yes—
539#386C2316yes—
540#385C2313yes—
541#385C2316yes—
542#385C2313yes—
543#385C2316yes—
544#385C2313yes—
545#385C2316yes—
546#385C2316yes—
547#385C2316yes—
548#385C2316yes—
549#385C2313yes—
550#385C2313yes—
551#384C2313yes—
552#384C2313yes—
553#384C2313yes—
554#383C2311yescharacteristic
555#383C2316yes—
556#382C2313yes—
557#382C2313yes—
558#382C2313yes—
559#382C2313yes—
560#382C2313yes—
561#382C2313yes—
562#382C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2311yescharacteristic
566#381C2316yes—
567#381C2316yes—
568#381C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2316yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2316yes—
578#380C2313yes—
579#380C2316yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2316yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2316yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2316yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623#376C2313yes—
624#376C2313yes—
625C43C2313yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C22×Q8C2411yescharacteristic
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2416yes—
640C22×Q8C2411yescharacteristic
641C22×D4C2413yes—
642C22×D4C2413yes—
643C22×D4C2413yes—
644C22×D4C2416yes—
645C22×D4C2413yes—
646C22×D4C2413yes—
647C22×D4C2413yes—
648C22×D4C2416yes—
649C22×D4C2416yes—
650C23×C4C2413yes—
651C23×C4C2413yes—
652C23×C4C2413yes—
653C23×C4C2416yes—
654C23×C4C2416yes—
655C23×C4C2413yes—
656C23×C4C2413yes—
657C4⋊Q8—212no—
658C4⋊Q8—46no—
659C4⋊Q8—46no—
660C4⋊Q8—46no—
661C4⋊Q8—46no—
662C4⋊Q8—46no—
663#127—212no—
664#127—46no—
665#127—46no—
666#126—46no—
667#125—212no—
668#125—212no—
669#125—46no—
670#125—46no—
671#124—46no—
672#124—46no—
673#124—412no—
674#124—86no—
675#124—86no—
676#124—86no—
677#123—46no—
678#123—86no—
679#123—86no—
680C22⋊Q8—46no—
681C22⋊Q8—86no—
682C22⋊Q8—86no—
683#121—212no—
684#121—212no—
685#121—412no—
686#121—46no—
687#121—46no—
688#121—46no—
689#121—46no—
690#121—86no—
691C4×Q8—24no—
692C4×Q8—24no—
693C4×Q8—24no—
694C4×Q8—24no—
695C4×Q8—24no—
696C4×Q8—24no—
697C4×Q8—24no—
698C4×Q8—24no—
699C4×Q8—24no—
700C4×Q8—24no—
701C4×Q8—24no—
702C4×Q8—212no—
703C4×Q8—46no—
704C4×Q8—46no—
705C4×Q8#4118yes—
706C4×D4—212no—
707C4×D4—212no—
708C4×D4—212no—
709C4×D4—46no—
710C4×D4—46no—
711C4×D4—46no—
712C4×D4—46no—
713C4×D4—46no—
714C4×D4—46no—
715C4×D4—86no—
716#117—212no—
717#117—46no—
718#117—46no—
719#117—86no—
720C2×C4⋊C4—212no—
721C2×C4⋊C4—46no—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2416yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2416yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2416yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2416yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2416yes—
795C2×C22⋊C4C2416yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2416yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2416yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2416yes—
803C2×C22⋊C4C2416yes—
804C2×C22⋊C4C2416yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2416yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2416yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C42—46no—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2411yescharacteristic
834C2×C42C2411yescharacteristic
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2416yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2416yes—
843C2×C42C2413yes—
844C2×C42C2411yescharacteristic
845C2×C42C2413yes—
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2411yescharacteristic
856#95C2411yescharacteristic
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2411yescharacteristic
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2416yes—
880#95C2416yes—
881#95C2411yescharacteristic
882#95C2416yes—
883#95C2413yes—
884#95C2411yescharacteristic
885#95C2411yescharacteristic
886#95C2411yescharacteristic
887#95C2413yes—
888#95C2411yescharacteristic
889#95C2416yes—
890#95C2411yescharacteristic
891#95C2411yescharacteristic
892#95C2411yescharacteristic
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2416yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2416yes—
904#95C2416yes—
905#95C2416yes—
906#95C2416yes—
907#95C2416yes—
908C24C2513yes—
909C24C2513yes—
910C24C2513yes—
911#41—416no—
912#41—416no—
913#41—416no—
914C2×Q8—26no—
915C2×Q8—22no—
916C2×Q8—22no—
917C2×Q8—26no—
918C2×Q8—41no—
919C2×Q8—43no—
920C2×Q8—43no—
921C2×Q8—43no—
922C2×Q8—43no—
923C2×Q8—46no—
924C2×Q8—46no—
925C2×Q8—46no—
926C2×Q8C2×#4114yes—
927C2×Q8H(5,𝔽2)14yes—
928C2×Q82−1+414yes—
929C2×D4—26no—
930C2×D4—26no—
931C2×D4—26no—
932C2×D4—26no—
933C2×D4—212no—
934C2×D4—26no—
935C2×D4—26no—
936C2×D4—26no—
937C2×D4—26no—
938C2×D4—26no—
939C2×D4—26no—
940C2×D4—26no—
941C2×D4—43no—
942C2×D4—43no—
943C2×D4—46no—
944C2×D4—46no—
945C2×D4—43no—
946C2×D4—43no—
947C2×D4—43no—
948C2×D4—43no—
949C2×D4—43no—
950C2×D4—46no—
951C2×D4—46no—
952C2×D4—46no—
953C2×D4—46no—
954C2×D4—46no—
955C2×D4—46no—
956C22×C4—26no—
957C22×C4—26no—
958C22×C4—26no—
959C22×C4—26no—
960C22×C4—26no—
961C22×C4—26no—
962C22×C4—26no—
963C22×C4—26no—
964C22×C4—26no—
965C22×C4—212no—
966C22×C4—43no—
967C22×C4—43no—
968C22×C4—46no—
969C22×C4—43no—
970C22×C4—46no—
971C22×C4—43no—
972C22×C4—43no—
973C22×C4—43no—
974C22×C4—46no—
975C22×C4—46no—
976C22×C4—46no—
977C22×C4C2511yescharacteristic
978C22×C4C2511yescharacteristic
979C22×C4C2511yescharacteristic
980C22×C4C2511yescharacteristic
981C22×C4C2511yescharacteristic
982C22×C4C2513yes—
983C22×C4C2511yescharacteristic
984C22×C4C2513yes—
985C22×C4C2513yes—
986C22×C4C2513yes—
987C22×C4C2513yes—
988C22×C4C2513yes—
989C22×C4C2513yes—
990C22×C4C2513yes—
991C22×C4C2513yes—
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C22×C4C2513yes—
995C22×C4C2511yescharacteristic
996C22×C4C2511yescharacteristic
997C22×C4C2511yescharacteristic
998C22×C4C2511yescharacteristic
999C22×C4C2513yes—
1000C22×C4C2511yescharacteristic
1001C22×C4C2513yes—
1002C22×C4C2511yescharacteristic
1003C22×C4C2511yescharacteristic
1004C22×C4C2513yes—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—22no—
1008C4⋊C4—22no—
1009C4⋊C4—22no—
1010C4⋊C4—26no—
1011C4⋊C4—26no—
1012C4⋊C4—26no—
1013C4⋊C4—26no—
1014C4⋊C4—212no—
1015C4⋊C4—26no—
1016C4⋊C4—26no—
1017C4⋊C4—26no—
1018C4⋊C4—26no—
1019C4⋊C4—26no—
1020C4⋊C4—26no—
1021C4⋊C4—26no—
1022C4⋊C4—26no—
1023C4⋊C4—26no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—26no—
1027C4⋊C4—43no—
1028C4⋊C4—41no—
1029C4⋊C4—43no—
1030C4⋊C4—46no—
1031C4⋊C4—41no—
1032C4⋊C4—41no—
1033C4⋊C4—43no—
1034C4⋊C4—41no—
1035C4⋊C4—43no—
1036C4⋊C4—43no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4—43no—
1040C4⋊C4—43no—
1041C4⋊C4—43no—
1042C4⋊C4—43no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4—43no—
1046C4⋊C4—43no—
1047C4⋊C4—46no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—46no—
1052C4⋊C4—43no—
1053C4⋊C4—43no—
1054C4⋊C4—43no—
1055C4⋊C4—43no—
1056C4⋊C4C2×#41112yes—
1057C22⋊C4—26no—
1058C22⋊C4—26no—
1059C22⋊C4—26no—
1060C22⋊C4—26no—
1061C22⋊C4—26no—
1062C22⋊C4—26no—
1063C22⋊C4—26no—
1064C22⋊C4—26no—
1065C22⋊C4—43no—
1066C22⋊C4—43no—
1067C22⋊C4—46no—
1068C22⋊C4—43no—
1069C22⋊C4—46no—
1070C22⋊C4—43no—
1071C22⋊C4—43no—
1072C22⋊C4—43no—
1073C22⋊C4—43no—
1074C22⋊C4—43no—
1075C22⋊C4—46no—
1076C22⋊C4—46no—
1077C22⋊C4—43no—
1078C22⋊C4—46no—
1079C22⋊C4—43no—
1080C22⋊C4—43no—
1081C22⋊C4—43no—
1082C22⋊C4—46no—
1083C22⋊C4—43no—
1084C22⋊C4—43no—
1085C22⋊C4—43no—
1086C22⋊C4—46no—
1087C22⋊C4—43no—
1088C22⋊C4—46no—
1089C22⋊C4—46no—
1090C22⋊C4—46no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—43no—
1094C22⋊C4—46no—
1095C22⋊C4—46no—
1096C22⋊C4—43no—
1097C22⋊C4—43no—
1098C22⋊C4—43no—
1099C22⋊C4—43no—
1100C22⋊C4—43no—
1101C22⋊C4—46no—
1102C22⋊C4—43no—
1103C22⋊C4—43no—
1104C42—26no—
1105C42—26no—
1106C42—26no—
1107C42—26no—
1108C42—26no—
1109C42—26no—
1110C42—26no—
1111C42—26no—
1112C42—26no—
1113C42—26no—
1114C42—26no—
1115C42—22no—
1116C42—22no—
1117C42—41no—
1118C42—43no—
1119C42—43no—
1120C42—46no—
1121C42—43no—
1122C42—46no—
1123C42—43no—
1124C42—43no—
1125C42—43no—
1126C42—43no—
1127C42C2×#41112yes—
1128C23—23no—
1129C23—23no—
1130C23—23no—
1131C23—23no—
1132C23—23no—
1133C23—23no—
1134C23—23no—
1135C23—23no—
1136C23—23no—
1137C23—23no—
1138C23—23no—
1139C23—23no—
1140C23—23no—
1141C23—23no—
1142C23—23no—
1143C23—23no—
1144C23—23no—
1145C23—23no—
1146C23—23no—
1147C23—23no—
1148C23—23no—
1149C23C2611yescharacteristic
1150Q8—44no—
1151Q8—86no—
1152Q8—86no—
1153Q8—166no—
1154Q8#542116yes—
1155D4—412no—
1156D4—412no—
1157D4—412no—
1158D4—86no—
1159D4—812no—
1160D4—86no—
1161D4—86no—
1162D4—166no—
1163D4—166no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—23no—
1189C2×C4—23no—
1190C2×C4—23no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—23no—
1208C2×C4—23no—
1209C2×C4—23no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—23no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—23no—
1222C2×C4—21no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—23no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—21no—
1241C2×C4—412no—
1242C2×C4—412no—
1243C2×C4—412no—
1244C2×C4—812no—
1245C2×C4—86no—
1246C2×C4—86no—
1247C2×C4—166no—
1248C2×C4C22×#4112yes—
1249C2×C4C22×#4116yes—
1250C2×C4C22×#4116yes—
1251C2×C4C2×H(5,𝔽2)16yes—
1252C2×C4C2×2−1+416yes—
1253C2×C4#58512yes—
1254C2×C4#58512yes—
1255C22—43no—
1256C22—43no—
1257C22—43no—
1258C22—43no—
1259C22—43no—
1260C22—43no—
1261C22—43no—
1262C22—43no—
1263C22—43no—
1264C22—43no—
1265C22—43no—
1266C22—43no—
1267C22—43no—
1268C22—43no—
1269C22—43no—
1270C22—43no—
1271C22—43no—
1272C22—43no—
1273C22—43no—
1274C22—43no—
1275C22—43no—
1276C22C23×#4111yescharacteristic
1277C22C22×H(5,𝔽2)11yescharacteristic
1278C22C22×2−1+411yescharacteristic
1279C22C2×#58511yescharacteristic
1280C22C2×#58511yescharacteristic
1281C22H(7,𝔽2)11yescharacteristic
1282C22H(7,𝔽2)11yescharacteristic
1283C4—22no—
1284C4—26no—
1285C4—22no—
1286C4—22no—
1287C4—41no—
1288C4—43no—
1289C4—43no—
1290C4—41no—
1291C4—41no—
1292C4—43no—
1293C4—41no—
1294C4—43no—
1295C4—43no—
1296C4—41no—
1297C4—41no—
1298C4—43no—
1299C4—43no—
1300C4—41no—
1301C4—43no—
1302C4—43no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—43no—
1309C4—43no—
1310C4C2×#542112yes—
1311C2—83no—
1312C2—83no—
1313C2—83no—
1314C2C22×#54211yescharacteristic
1315C2#6295211yescharacteristic
1316C2#6295211yescharacteristic
1317C2#6300611yescharacteristic
1318C2#6301011yescharacteristic
1319C2#6302011yescharacteristic
1320C2#6306611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36029C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52285C2semidirect
2. #42751C2semidirect
3. #42666C2semidirect
4. #42624C2semidirect
5. #42564C2semidirect
6. #42537C2semidirect
7. #42472C2semidirect
8. #40171C2semidirect
9. #40117C2semidirect
10. #40050C2semidirect
11. #40002C2semidirect
12. #39240C2semidirect
13. #39201C2semidirect
14. #37363C2semidirect
15. #37336C2semidirect
16. #37322C2semidirect
17. #36585C2semidirect
18. #36583C2semidirect
19. #36474C2semidirect
20. #36457C2semidirect
21. #36433C2semidirect
22. #36431C2semidirect
23. #36076C2semidirect
24. #36059C2semidirect
25. #36049C2semidirect
26. #36040C2semidirect
28. #35748C2semidirect
29. #34336C2semidirect
30. #34295C2semidirect
31. #34263C2semidirect

Maximal subgroups

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

subgroupindex
#522852
#427512
#426662
#426242
#425642
#425372
#424722
#401712
#401172
#400502
#400022
#392402
#392012
#373632
#373362
#373222
#365852
#365832
#364742
#364572
#364332
#364312
#360762
#360592
#360492
#360402
#360292
#357482
#343362
#342952
#342632