Finite Group Databasebeta

← #7661779

Subgroups — #7661779

Order 512.

4849 conjugacy classes of subgroups.

The subgroup lattice has 1321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52284C213yesmaximal, complemented
2#42758C213yesmaximal, complemented
3#42671C213yesmaximal, complemented
4#42625C213yesmaximal, complemented
5#42571C213yesmaximal, complemented
6#42545C213yesmaximal, complemented
7#42467C213yesmaximal, complemented
8#40174C213yesmaximal, complemented
9#40121C213yesmaximal, complemented
10#40058C213yesmaximal, complemented
11#40003C213yesmaximal, complemented
12#39236C213yesmaximal, complemented
13#39201C213yesmaximal, complemented
14#37363C213yesmaximal, complemented
15#37336C213yesmaximal, complemented
16#37321C213yesmaximal, complemented
17#36583C211yesmaximal, characteristic, complemented
18#36583C211yesmaximal, characteristic, complemented
19#36466C211yesmaximal, characteristic, complemented
20#36458C211yesmaximal, characteristic, complemented
21#36433C211yesmaximal, characteristic, complemented
22#36431C211yesmaximal, characteristic, complemented
23#36049C211yesmaximal, characteristic, complemented
24#36040C211yesmaximal, characteristic, complemented
25#36040C211yesmaximal, characteristic, complemented
26#36029C211yesmaximal, characteristic
27#36005C211yesmaximal, characteristic, complemented
28#35898C211yesmaximal, characteristic, complemented
29#34336C211yesmaximal, characteristic, complemented
30#34295C211yesmaximal, characteristic, complemented
31#34263C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#550C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#520C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41#2860C2213yes—
42#2859C2213yes—
43#2858C2213yes—
44#2858C2213yes—
45#2854C2213yes—
46#2851C2213yes—
47#2837C2216yes—
48#2830C2216yes—
49#2800C2213yes—
50#2799C2213yes—
51#2798C2216yes—
52#2796C2216yes—
53#2796C2216yes—
54#2793C2213yes—
55#2779C2213yes—
56#2777C2213yes—
57#2773C2213yes—
58#2767C2211yescharacteristic
59#2765C2213yes—
60#2759C2213yes—
61#2751C2213yes—
62#2746C2216yes—
63#2741C2216yes—
64#2737C2216yes—
65#2731C2213yes—
66#2730C2213yes—
67#2729C2213yes—
68#2718C2213yes—
69#2717C2216yes—
70#2715C2213yes—
71#2715C2216yes—
72#2712C2216yes—
73#2712C2216yes—
74#2710C2213yes—
75#2710C2216yes—
76#2710C2216yes—
77#2705C2216yes—
78#2705C2216yes—
79#2705C2216yes—
80#2701C2216yes—
81#2691C2216yes—
82#2686C2216yes—
83#2672C2216yes—
84#2662C2216yes—
85#2652C2216yes—
86#2650C2216yes—
87#2649C2216yes—
88#2644C2213yes—
89#2641C2213yes—
90#2630C2216yes—
91#2628C2213yes—
92#2628C2213yes—
93#2624C2216yes—
94#2624C2213yes—
95#2619C2213yes—
96#2584C2213yes—
97#2584C2213yes—
98#2580C2213yes—
99#2580C2213yes—
100#2580C2213yes—
101#2566C2213yes—
102#2563C2213yes—
103#2563C2213yes—
104#2562C2213yes—
105#2552C2213yes—
106#2551C2213yes—
107#2550C2213yes—
108#2550C2213yes—
109#2548C2213yes—
110#2548C2213yes—
111#2548C2213yes—
112#2547C2213yes—
113#2547C2213yes—
114#2541C2213yes—
115#2535C2213yes—
116#2521C2216yes—
117#2513C2213yes—
118#2513C2213yes—
119#2512C2213yes—
120#2512C2213yes—
121#2512C2213yes—
122#2512C2213yes—
123#2501C2213yes—
124#2500C2213yes—
125#2497C2213yes—
126#2497C2213yes—
127#2496C2213yes—
128#2496C2213yes—
129#2495C2213yes—
130#2494C2213yes—
131#2491C2216yes—
132#2491C2213yes—
133#2491C2213yes—
134#2490C2213yes—
135#2490C2213yes—
136#2490C2213yes—
137#2490C2213yes—
138#2490C2213yes—
139#2490C2213yes—
140#2490C2213yes—
141#2490C2213yes—
142#2490C2213yes—
143#2490C2213yes—
144#2487C2213yes—
145#2485C2213yes—
146#2479C2216yes—
147#2470C2216yes—
148#2468C2216yes—
149#2454C2213yes—
150#2454C2213yes—
151#2454C2213yes—
152#2454C2213yes—
153#2454C2213yes—
154#2452C2213yes—
155#2445C2213yes—
156#2445C2213yes—
157#2445C2213yes—
158#2445C2213yes—
159#2442C2213yes—
160#2442C2213yes—
161#2442C2213yes—
162#2442C2213yes—
163#2441C2213yes—
164#2439C2213yes—
165#2428C2213yes—
166#2428C2213yes—
167#2422C2213yes—
168#2422C2216yes—
169#2422C2213yes—
170#2422C2213yes—
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
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
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#2335C2216yes—
215#2331C2213yes—
216#2330C2213yes—
217#2328C2213yes—
218#2324C2213yes—
219#2324C2216yes—
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
241#557—28no—
242#557—44no—
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×#127C2313yes—
252C2×#127C2313yes—
253C2×#127C2313yes—
254C2×#126C2313yes—
255C2×#126C2316yes—
256C2×#126C2316yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#125C2313yes—
261C2×#125C2313yes—
262C2×#125C2313yes—
263C2×#124C2313yes—
264C2×#124C2313yes—
265C2×#124C2316yes—
266C2×#124C2316yes—
267C2×#124C2316yes—
268C2×#123C2316yes—
269C2×#123C2313yes—
270C2×#123C2316yes—
271C2×#123C2316yes—
272C2×C22⋊Q8C2313yes—
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#401C2313yes—
317#400C2313yes—
318#400C2313yes—
319#400C2316yes—
320#400C2316yes—
321#400C2313yes—
322#400C2313yes—
323#400C2311yescharacteristic
324#400C2311yescharacteristic
325#400C2316yes—
326#400C2311yescharacteristic
327#400C2311yescharacteristic
328#399C2313yes—
329#399C2313yes—
330#399C2316yes—
331#399C2316yes—
332#399C2316yes—
333#399C2316yes—
334#399C2313yes—
335#398C2313yes—
336#398C2313yes—
337#398C2316yes—
338#398C2316yes—
339#398C2311yescharacteristic
340#398C2311yescharacteristic
341#398C2313yes—
342#398C2313yes—
343#397C2313yes—
344#397C2316yes—
345#397C2316yes—
346#397C2316yes—
347#397C2316yes—
348#397C2316yes—
349#397C2313yes—
350#397C2316yes—
351#397C2313yes—
352#397C2313yes—
353#397C2316yes—
354#397C2313yes—
355#397C2316yes—
356#397C2313yes—
357#397C2316yes—
358#397C2313yes—
359#397C2313yes—
360#397C2313yes—
361#396C2316yes—
362#396C2316yes—
363#396C2316yes—
364#396C2316yes—
365#396C2313yes—
366#396C2313yes—
367#396C2313yes—
368#396C2313yes—
369#396C2313yes—
370#396C2313yes—
371#396C2313yes—
372#395C2316yes—
373#395C2316yes—
374#395C2313yes—
375#395C2313yes—
376#394C2316yes—
377#394C2316yes—
378#394C2316yes—
379#394C2313yes—
380#394C2316yes—
381#394C2313yes—
382#394C2313yes—
383#394C2316yes—
384#394C2316yes—
385#394C2316yes—
386#394C2316yes—
387#394C2316yes—
388#394C2313yes—
389#394C2316yes—
390#394C2313yes—
391#394C2316yes—
392#394C2313yes—
393#394C2313yes—
394#394C2316yes—
395#394C2316yes—
396#393C2313yes—
397#393C2313yes—
398#393C2316yes—
399#393C2316yes—
400#393C2313yes—
401#393C2316yes—
402#393C2313yes—
403#392C2316yes—
404#392C2316yes—
405#392C2313yes—
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2316yes—
410#391C2313yes—
411#391C2313yes—
412#391C2313yes—
413#391C2313yes—
414#390C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2316yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2316yes—
426#390C2316yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2313yes—
435#390C2316yes—
436#390C2313yes—
437#390C2313yes—
438#390C2313yes—
439#390C2313yes—
440#390C2313yes—
441#390C2313yes—
442#390C2313yes—
443#390C2316yes—
444#390C2316yes—
445#390C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2311yescharacteristic
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2316yes—
460#389C2316yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2316yes—
471#389C2313yes—
472#389C2316yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#388C2313yes—
478#388C2313yes—
479#388C2313yes—
480#388C2316yes—
481#388C2316yes—
482#388C2316yes—
483#388C2316yes—
484#388C2313yes—
485#388C2316yes—
486#388C2316yes—
487#388C2316yes—
488#388C2313yes—
489#388C2313yes—
490#388C2316yes—
491#388C2313yes—
492#388C2316yes—
493#388C2316yes—
494#388C2313yes—
495#388C2313yes—
496#388C2313yes—
497#388C2313yes—
498#388C2313yes—
499#388C2313yes—
500#388C2313yes—
501#388C2313yes—
502#388C2313yes—
503#388C2313yes—
504#388C2313yes—
505#388C2313yes—
506#387C2311yescharacteristic
507#387C2313yes—
508#387C2313yes—
509#387C2313yes—
510#387C2316yes—
511#387C2313yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2316yes—
516#387C2313yes—
517#387C2313yes—
518#387C2313yes—
519#387C2313yes—
520#387C2313yes—
521#387C2313yes—
522#387C2316yes—
523#387C2313yes—
524#387C2311yescharacteristic
525#387C2311yescharacteristic
526#387C2311yescharacteristic
527#387C2311yescharacteristic
528#387C2311yescharacteristic
529#386C2316yes—
530#386C2316yes—
531#386C2316yes—
532#386C2313yes—
533#386C2316yes—
534#386C2316yes—
535#386C2316yes—
536#386C2313yes—
537#386C2316yes—
538#386C2313yes—
539#385C2313yes—
540#385C2316yes—
541#385C2313yes—
542#385C2313yes—
543#385C2316yes—
544#385C2316yes—
545#385C2316yes—
546#385C2316yes—
547#385C2316yes—
548#385C2313yes—
549#385C2316yes—
550#385C2313yes—
551#384C2313yes—
552#384C2313yes—
553#384C2313yes—
554#384C2313yes—
555#384C2313yes—
556#383C2313yes—
557#382C2313yes—
558#382C2313yes—
559#382C2313yes—
560#382C2313yes—
561#382C2313yes—
562#382C2313yes—
563#382C2311yescharacteristic
564#382C2311yescharacteristic
565#381C2316yes—
566#381C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2316yes—
572#380C2316yes—
573#380C2316yes—
574#380C2316yes—
575#380C2313yes—
576#380C2316yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
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×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2411yescharacteristic
640C22×D4C2413yes—
641C22×D4C2413yes—
642C22×D4C2413yes—
643C22×D4C2416yes—
644C22×D4C2413yes—
645C22×D4C2413yes—
646C22×D4C2413yes—
647C22×D4C2416yes—
648C22×D4C2416yes—
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2413yes—
652C23×C4C2416yes—
653C23×C4C2416yes—
654C23×C4C2413yes—
655C23×C4C2413yes—
656C4⋊Q8—212no—
657C4⋊Q8—46no—
658C4⋊Q8—46no—
659C4⋊Q8—46no—
660#127—212no—
661#127—46no—
662#127—46no—
663#126—46no—
664#126—86no—
665#126—86no—
666#125—212no—
667#125—212no—
668#125—46no—
669#125—46no—
670#125—46no—
671#125—46no—
672#124—46no—
673#124—46no—
674#124—86no—
675#124—86no—
676#124—86no—
677#123—412no—
678#123—46no—
679#123—86no—
680#123—86no—
681C22⋊Q8—46no—
682#121—212no—
683#121—212no—
684#121—412no—
685#121—46no—
686#121—46no—
687#121—46no—
688#121—46no—
689#121—86no—
690C4×Q8—24no—
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—212no—
702C4×Q8—46no—
703C4×Q8—46no—
704C4×Q8#4118yes—
705C4×D4—212no—
706C4×D4—212no—
707C4×D4—212no—
708C4×D4—46no—
709C4×D4—46no—
710C4×D4—46no—
711C4×D4—46no—
712C4×D4—46no—
713C4×D4—46no—
714C4×D4—86no—
715#117—212no—
716#117—46no—
717#117—46no—
718#117—86no—
719C2×C4⋊C4—212no—
720C2×C4⋊C4—46no—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2413yes—
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⋊C4C2411yescharacteristic
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2416yes—
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
763C2×C4⋊C4C2416yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2416yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2416yes—
768C2×C4⋊C4C2416yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊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⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2416yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2416yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2416yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2416yes—
797C2×C22⋊C4C2416yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2416yes—
803C2×C22⋊C4C2416yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2416yes—
806C2×C22⋊C4C2416yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2416yes—
810C2×C22⋊C4C2416yes—
811C2×C22⋊C4C2416yes—
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C42—46no—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2411yescharacteristic
836C2×C42C2411yescharacteristic
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2416yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2416yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2411yescharacteristic
847C2×C42C2413yes—
848#95C2411yescharacteristic
849#95C2411yescharacteristic
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2411yescharacteristic
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2411yescharacteristic
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2416yes—
882#95C2416yes—
883#95C2411yescharacteristic
884#95C2413yes—
885#95C2416yes—
886#95C2411yescharacteristic
887#95C2413yes—
888#95C2411yescharacteristic
889#95C2411yescharacteristic
890#95C2416yes—
891#95C2411yescharacteristic
892#95C2411yescharacteristic
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2416yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2416yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2416yes—
907#95C2416yes—
908C24C2513yes—
909C24C2513yes—
910C24C2513yes—
911#41—416no—
912#41—416no—
913#41—416no—
914C2×Q8—26no—
915C2×Q8—26no—
916C2×Q8—43no—
917C2×Q8—43no—
918C2×Q8—43no—
919C2×Q8—43no—
920C2×Q8—43no—
921C2×Q8—43no—
922C2×Q8—43no—
923C2×Q8C2×#4114yes—
924C2×Q8H(5,𝔽2)14yes—
925C2×Q82−1+414yes—
926C2×D4—26no—
927C2×D4—26no—
928C2×D4—26no—
929C2×D4—26no—
930C2×D4—212no—
931C2×D4—26no—
932C2×D4—26no—
933C2×D4—26no—
934C2×D4—26no—
935C2×D4—26no—
936C2×D4—26no—
937C2×D4—26no—
938C2×D4—43no—
939C2×D4—43no—
940C2×D4—46no—
941C2×D4—46no—
942C2×D4—43no—
943C2×D4—43no—
944C2×D4—43no—
945C2×D4—43no—
946C2×D4—43no—
947C2×D4—46no—
948C2×D4—46no—
949C2×D4—46no—
950C2×D4—46no—
951C2×D4—46no—
952C2×D4—46no—
953C22×C4—26no—
954C22×C4—26no—
955C22×C4—26no—
956C22×C4—26no—
957C22×C4—26no—
958C22×C4—26no—
959C22×C4—26no—
960C22×C4—26no—
961C22×C4—26no—
962C22×C4—212no—
963C22×C4—43no—
964C22×C4—43no—
965C22×C4—46no—
966C22×C4—43no—
967C22×C4—46no—
968C22×C4—43no—
969C22×C4—43no—
970C22×C4—43no—
971C22×C4—46no—
972C22×C4—46no—
973C22×C4—46no—
974C22×C4C2511yescharacteristic
975C22×C4C2511yescharacteristic
976C22×C4C2511yescharacteristic
977C22×C4C2511yescharacteristic
978C22×C4C2513yes—
979C22×C4C2513yes—
980C22×C4C2511yescharacteristic
981C22×C4C2511yescharacteristic
982C22×C4C2513yes—
983C22×C4C2513yes—
984C22×C4C2513yes—
985C22×C4C2513yes—
986C22×C4C2511yescharacteristic
987C22×C4C2513yes—
988C22×C4C2511yescharacteristic
989C22×C4C2511yescharacteristic
990C22×C4C2511yescharacteristic
991C22×C4C2511yescharacteristic
992C22×C4C2513yes—
993C22×C4C2513yes—
994C22×C4C2513yes—
995C22×C4C2513yes—
996C22×C4C2511yescharacteristic
997C22×C4C2511yescharacteristic
998C22×C4C2513yes—
999C22×C4C2511yescharacteristic
1000C22×C4C2511yescharacteristic
1001C22×C4C2513yes—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—22no—
1005C4⋊C4—22no—
1006C4⋊C4—22no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—26no—
1011C4⋊C4—212no—
1012C4⋊C4—26no—
1013C4⋊C4—26no—
1014C4⋊C4—26no—
1015C4⋊C4—26no—
1016C4⋊C4—26no—
1017C4⋊C4—26no—
1018C4⋊C4—26no—
1019C4⋊C4—26no—
1020C4⋊C4—26no—
1021C4⋊C4—22no—
1022C4⋊C4—22no—
1023C4⋊C4—26no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—43no—
1027C4⋊C4—41no—
1028C4⋊C4—43no—
1029C4⋊C4—46no—
1030C4⋊C4—41no—
1031C4⋊C4—41no—
1032C4⋊C4—43no—
1033C4⋊C4—41no—
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—46no—
1044C4⋊C4—43no—
1045C4⋊C4—43no—
1046C4⋊C4—46no—
1047C4⋊C4—46no—
1048C4⋊C4—46no—
1049C4⋊C4—46no—
1050C4⋊C4—43no—
1051C4⋊C4—43no—
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—46no—
1082C22⋊C4—43no—
1083C22⋊C4—43no—
1084C22⋊C4—43no—
1085C22⋊C4—46no—
1086C22⋊C4—46no—
1087C22⋊C4—43no—
1088C22⋊C4—43no—
1089C22⋊C4—43no—
1090C22⋊C4—43no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—46no—
1094C22⋊C4—43no—
1095C22⋊C4—46no—
1096C22⋊C4—43no—
1097C22⋊C4—46no—
1098C22⋊C4—46no—
1099C22⋊C4—46no—
1100C22⋊C4—43no—
1101C22⋊C4—43no—
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—43no—
1123C42—46no—
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—86no—
1151Q8—86no—
1152Q8—86no—
1153Q8#542116yes—
1154D4—412no—
1155D4—412no—
1156D4—412no—
1157D4—86no—
1158D4—812no—
1159D4—86no—
1160D4—86no—
1161D4—166no—
1162D4—166no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—21no—
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—23no—
1196C2×C4—23no—
1197C2×C4—21no—
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—23no—
1215C2×C4—23no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—21no—
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—23no—
1236C2×C4—23no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—412no—
1241C2×C4—412no—
1242C2×C4—412no—
1243C2×C4—812no—
1244C2×C4—86no—
1245C2×C4—86no—
1246C2×C4—166no—
1247C2×C4C22×#4112yes—
1248C2×C4C22×#4116yes—
1249C2×C4C22×#4116yes—
1250C2×C4C2×H(5,𝔽2)16yes—
1251C2×C4C2×2−1+416yes—
1252C2×C4#58512yes—
1253C2×C4#58512yes—
1254C22—43no—
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—
1275C22C23×#4111yescharacteristic
1276C22C22×H(5,𝔽2)11yescharacteristic
1277C22C22×2−1+411yescharacteristic
1278C22C2×#58511yescharacteristic
1279C22C2×#58511yescharacteristic
1280C22H(7,𝔽2)11yescharacteristic
1281C22H(7,𝔽2)11yescharacteristic
1282C4—22no—
1283C4—26no—
1284C4—22no—
1285C4—22no—
1286C4—41no—
1287C4—43no—
1288C4—43no—
1289C4—41no—
1290C4—41no—
1291C4—43no—
1292C4—41no—
1293C4—43no—
1294C4—43no—
1295C4—41no—
1296C4—43no—
1297C4—43no—
1298C4—43no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—43no—
1303C4—43no—
1304C4—41no—
1305C4—43no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4C2×#542112yes—
1310C2—83no—
1311C2—83no—
1312C2—83no—
1313C2C22×#54211yescharacteristic
1314C2#6289911yescharacteristic
1315C2#6292311yescharacteristic
1316C2#6300611yescharacteristic
1317C2#6301011yescharacteristic
1318C2#6303311yescharacteristic
1319C2#6307011yescharacteristic
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. #52284C2semidirect
2. #42758C2semidirect
3. #42671C2semidirect
4. #42625C2semidirect
5. #42571C2semidirect
6. #42545C2semidirect
7. #42467C2semidirect
8. #40174C2semidirect
9. #40121C2semidirect
10. #40058C2semidirect
11. #40003C2semidirect
12. #39236C2semidirect
13. #39201C2semidirect
14. #37363C2semidirect
15. #37336C2semidirect
16. #37321C2semidirect
17. #36583C2semidirect
18. #36583C2semidirect
19. #36466C2semidirect
20. #36458C2semidirect
21. #36433C2semidirect
22. #36431C2semidirect
23. #36049C2semidirect
24. #36040C2semidirect
25. #36040C2semidirect
27. #36005C2semidirect
28. #35898C2semidirect
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
#522842
#427582
#426712
#426252
#425712
#425452
#424672
#401742
#401212
#400582
#400032
#392362
#392012
#373632
#373362
#373212
#365832
#364662
#364582
#364332
#364312
#360492
#360402
#360292
#360052
#358982
#343362
#342952
#342632