Finite Group Databasebeta

← #7675033

Subgroups — #7675033

Order 512.

4972 conjugacy classes of subgroups.

The subgroup lattice has 1476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59961C212yesmaximal, complemented
2#59903C212yesmaximal, complemented
3#59501C212yesmaximal, complemented
4#59487C212yesmaximal, complemented
5#59435C212yesmaximal, complemented
6#59380C212yesmaximal, complemented
7#59276C212yesmaximal, complemented
8#59262C212yesmaximal, complemented
9#44643C214yesmaximal, complemented
10#44591C214yesmaximal, complemented
11#43832C214yesmaximal, complemented
12#43788C214yesmaximal, complemented
13#39743C211yesmaximal, characteristic
14#39624C211yesmaximal, characteristic, complemented
15#38939C212yesmaximal, complemented
16#38935C214yesmaximal, complemented
17#37951C212yesmaximal, complemented
18#37771C212yesmaximal, complemented
19#36483C212yesmaximal, complemented
20#36176C211yesmaximal, characteristic, complemented
21#36117C211yesmaximal, characteristic, complemented
22#35464C214yesmaximal, complemented
23#35119C212yesmaximal, complemented
24#35006C211yesmaximal, characteristic, complemented
25#34763C212yesmaximal, complemented
26#34327C212yesmaximal, complemented
27#34219C212yesmaximal, complemented
28C2×#2356C211yesmaximal, characteristic, complemented
29C4×#539C211yesmaximal, characteristic, complemented
30C2×#548C2212yes—
31C2×#539C2211yescharacteristic
32C2×#539C2212yes—
33C2×#529C2212yes—
34C2×#529C2214yes—
35C22×C4×Q8C2211yescharacteristic
36#2857C2211yescharacteristic
37#2856C2211yescharacteristic
38#2854C2212yes—
39#2854C2214yes—
40#2854C2212yes—
41#2854C2212yes—
42#2811C2212yes—
43#2806C2212yes—
44#2806C2214yes—
45#2785C2214yes—
46#2781C2214yes—
47#2775C2214yes—
48#2775C2214yes—
49#2775C2214yes—
50#2775C2214yes—
51#2769C2214yes—
52#2769C2214yes—
53#2769C2214yes—
54#2756C2214yes—
55#2756C2214yes—
56#2744C2214yes—
57#2744C2214yes—
58#2737C2214yes—
59#2737C2214yes—
60#2737C2214yes—
61#2733C2212yes—
62#2732C2212yes—
63#2730C2214yes—
64#2730C2214yes—
65#2721C2214yes—
66#2721C2214yes—
67#2705C2214yes—
68#2659C2212yes—
69#2656C2212yes—
70#2639C2212yes—
71#2639C2214yes—
72#2618C2212yes—
73#2612C2214yes—
74#2611C2214yes—
75#2611C2214yes—
76#2611C2214yes—
77#2610C2214yes—
78#2610C2214yes—
79#2604C2214yes—
80#2604C2214yes—
81#2604C2214yes—
82#2603C2214yes—
83#2603C2214yes—
84#2602C2214yes—
85#2601C2214yes—
86#2582C2212yes—
87#2574C2214yes—
88#2572C2214yes—
89#2572C2214yes—
90#2571C2212yes—
91#2571C2211yescharacteristic
92#2567C2212yes—
93#2565C2214yes—
94#2564C2214yes—
95#2563C2212yes—
96#2563C2211yescharacteristic
97#2560C2214yes—
98#2560C2214yes—
99#2558C2214yes—
100#2557C2214yes—
101#2556C2214yes—
102#2553C2214yes—
103#2552C2211yescharacteristic
104#2549C2214yes—
105#2548C2211yescharacteristic
106#2543C2214yes—
107#2532C2214yes—
108#2532C2214yes—
109#2532C2214yes—
110#2531C2214yes—
111#2529C2214yes—
112#2521C2214yes—
113#2521C2214yes—
114#2519C2214yes—
115#2519C2214yes—
116#2518C2214yes—
117#2518C2214yes—
118#2513C2212yes—
119#2513C2212yes—
120#2512C2212yes—
121#2512C2212yes—
122#2512C2212yes—
123#2508C2212yes—
124#2508C2212yes—
125#2506C2214yes—
126#2506C2212yes—
127#2506C2212yes—
128#2501C2212yes—
129#2501C2214yes—
130#2500C2212yes—
131#2499C2214yes—
132#2498C2214yes—
133#2496C2214yes—
134#2496C2212yes—
135#2495C2214yes—
136#2495C2214yes—
137#2495C2212yes—
138#2495C2212yes—
139#2491C2212yes—
140#2488C2214yes—
141#2488C2214yes—
142#2488C2214yes—
143#2486C2214yes—
144#2486C2212yes—
145#2479C2214yes—
146#2471C2214yes—
147#2467C2214yes—
148#2454C2212yes—
149#2452C2212yes—
150#2451C2212yes—
151#2451C2212yes—
152#2448C2212yes—
153#2448C2214yes—
154#2448C2212yes—
155#2448C2212yes—
156#2448C2214yes—
157#2448C2212yes—
158#2445C2212yes—
159#2441C2214yes—
160#2440C2212yes—
161#2439C2212yes—
162#2431C2212yes—
163#2425C2214yes—
164#2425C2214yes—
165#2425C2214yes—
166#2423C2214yes—
167#2423C2214yes—
168#2423C2214yes—
169#2423C2212yes—
170#2423C2212yes—
171#2423C2212yes—
172#2420C2212yes—
173#2416C2212yes—
174#2407C2212yes—
175#2396C2214yes—
176#2395C2214yes—
177#2373C2214yes—
178#2373C2214yes—
179#2372C2214yes—
180#2372C2214yes—
181#2371C2214yes—
182#2369C2211yescharacteristic
183#2368C2214yes—
184#2367C2212yes—
185#2366C2211yescharacteristic
186#2364C2214yes—
187#2362C2212yes—
188#2361C2212yes—
189#2356C2214yes—
190#2356C2214yes—
191#2356C2212yes—
192#2356C2212yes—
193#2356C2214yes—
194#2356C2212yes—
195#2356C2212yes—
196#2356C2212yes—
197#2354C2212yes—
198#2354C2211yescharacteristic
199#2353C2214yes—
200#2353C2214yes—
201#2352C2212yes—
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2212yes—
204Q8×C4⋊C4C2212yes—
205#2346C2214yes—
206#2346C2212yes—
207#2343C2214yes—
208#2341C2212yes—
209#2341C2212yes—
210Q8×C22⋊C4C2212yes—
211#2339C2212yes—
212#2337C2214yes—
213#2336C2212yes—
214#2335C2212yes—
215#2334C2212yes—
216#2332C2212yes—
217#2332C2214yes—
218#2329C2211yescharacteristic
219#2329C2212yes—
220#2325C2214yes—
221#2325C2211yescharacteristic
222#2325C2212yes—
223#2325C2212yes—
224#2322C2212yes—
225#2318C2212yes—
226#2318C2214yes—
227#2313C2211yescharacteristic
228C4×C4⋊Q8C2212yes—
229C4×#125C2212yes—
230C4×#126C2212yes—
231C4×#124C2212yes—
232C4×C22⋊Q8C2211yescharacteristic
233C4×C22⋊Q8C2212yes—
234C4×C22⋊Q8C2212yes—
235C4×#123C2214yes—
236C4×#123C2212yes—
237C4×#123C2212yes—
238C4×#123C2214yes—
239C4×#121C2212yes—
240C4×#121C2211yescharacteristic
241C4×#121C2212yes—
242#2297C2212yes—
243#2295C2212yes—
244C2×#391C2211yescharacteristic
245C2×#391C2211yescharacteristic
246#2293C2212yes—
247C2×#387C2212yes—
248C2×#387C2212yes—
249#2285C2212yes—
250#2283C2212yes—
251C2×#383C2212yes—
252C2×#382C2211yescharacteristic
253#2275C2214yes—
254C42×D4C2212yes—
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×#376C2212yes—
259C22×#41C2312yes—
260C23×Q8C2311yescharacteristic
261#548—216no—
262#539—28no—
263#539—48no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×#127C2311yescharacteristic
267#529—216no—
268#529—416no—
269C2×#126C2312yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#125C2314yes—
278C2×#124C2314yes—
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#124C2314yes—
282C2×#123C2312yes—
283C2×#123C2312yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2311yescharacteristic
296C2×#121C2312yes—
297C2×#121C2311yescharacteristic
298C2×#121C2314yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×#121C2312yes—
303C2×C4×Q8—28no—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2314yes—
309C2×C4×Q8C2314yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2314yes—
323C2×C4×D4C2312yes—
324C2×#117C2314yes—
325C2×#117C2314yes—
326C2×#117C2312yes—
327C2×#117C2314yes—
328C22×C4⋊C4C2311yescharacteristic
329C22×C4⋊C4C2311yescharacteristic
330C22×C4⋊C4C2311yescharacteristic
331C22×C4⋊C4C2312yes—
332C22×C4⋊C4C2311yescharacteristic
333C22×C4⋊C4C2311yescharacteristic
334C22×C42C2312yes—
335C22×C42C2311yescharacteristic
336C22×C42C2312yes—
337C22×C42C2312yes—
338C22×C42C2311yescharacteristic
339C22×C42C2311yescharacteristic
340C22×C42C2312yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#392C2314yes—
411#392C2314yes—
412#392C2314yes—
413#391C2312yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2312yes—
419#391C2312yes—
420#391C2314yes—
421#391C2312yes—
422#391C2312yes—
423#391C2311yescharacteristic
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#390C2312yes—
434#390C2314yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2311yescharacteristic
439#390C2314yes—
440#390C2314yes—
441#390C2312yes—
442#390C2314yes—
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#390C2312yes—
447#390C2312yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2312yes—
466#389C2311yescharacteristic
467#389C2311yescharacteristic
468#389C2314yes—
469#389C2312yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#388C2312yes—
483#388C2312yes—
484#388C2312yes—
485#388C2312yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2312yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2312yes—
504#388C2312yes—
505#388C2314yes—
506#388C2314yes—
507#388C2312yes—
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#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#387C2312yes—
529#387C2312yes—
530#387C2312yes—
531#387C2314yes—
532#387C2314yes—
533#387C2312yes—
534#387C2312yes—
535#387C2312yes—
536#387C2312yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2312yes—
541#387C2312yes—
542#387C2312yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2312yes—
550#387C2314yes—
551#387C2314yes—
552#387C2312yes—
553#387C2314yes—
554#387C2314yes—
555#387C2312yes—
556#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2312yes—
575#386C2312yes—
576#386C2314yes—
577#386C2314yes—
578#386C2312yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#385C2312yes—
587#385C2314yes—
588#385C2312yes—
589#385C2312yes—
590#385C2314yes—
591#385C2314yes—
592#385C2312yes—
593#385C2312yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#384C2312yes—
598#384C2314yes—
599#384C2311yescharacteristic
600#384C2312yes—
601#384C2311yescharacteristic
602#384C2312yes—
603#384C2314yes—
604#383C2312yes—
605#383C2314yes—
606#383C2314yes—
607#383C2314yes—
608#383C2314yes—
609#383C2314yes—
610#383C2314yes—
611#383C2314yes—
612#382C2312yes—
613#382C2312yes—
614#382C2312yes—
615#382C2312yes—
616#382C2314yes—
617#382C2314yes—
618#382C2312yes—
619#382C2314yes—
620#382C2312yes—
621#382C2314yes—
622#382C2314yes—
623#381C2312yes—
624#381C2312yes—
625#381C2314yes—
626#381C2314yes—
627#381C2314yes—
628#380C2314yes—
629#380C2312yes—
630#380C2312yes—
631#380C2314yes—
632#380C2314yes—
633#380C2314yes—
634#380C2311yescharacteristic
635#380C2311yescharacteristic
636#380C2312yes—
637#380C2314yes—
638#380C2312yes—
639#380C2314yes—
640#380C2312yes—
641#380C2312yes—
642#380C2312yes—
643#380C2314yes—
644C4×C4⋊C4C2311yescharacteristic
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2311yescharacteristic
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2312yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699#376C2314yes—
700#376C2314yes—
701#376C2314yes—
702#376C2314yes—
703#376C2314yes—
704#376C2314yes—
705#376C2314yes—
706C2×#95C2314yes—
707C2×#95C2312yes—
708C2×#95C2311yescharacteristic
709C2×#95C2311yescharacteristic
710C2×#95C2312yes—
711C2×#95C2312yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C2×#95C2312yes—
715C2×#95C2312yes—
716C2×#95C2312yes—
717C43C2312yes—
718C2×#41—28no—
719C2×#41—44no—
720C2×#41—44no—
721C22×Q8—42no—
722C22×Q8—42no—
723C22×Q8#4118yes—
724C22×Q8C2412yes—
725C22×Q8C2414yes—
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×D4C2414yes—
730C22×D4C2412yes—
731C22×D4C2412yes—
732C22×D4C2411yescharacteristic
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2414yes—
736C22×D4C2412yes—
737C23×C4C2411yescharacteristic
738C23×C4C2412yes—
739C23×C4C2412yes—
740C23×C4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2411yescharacteristic
743C23×C4C2412yes—
744C23×C4C2411yescharacteristic
745C23×C4C2412yes—
746C23×C4C2414yes—
747C23×C4C2414yes—
748C23×C4C2412yes—
749C23×C4C2414yes—
750C23×C4C2411yescharacteristic
751C23×C4C2412yes—
752C23×C4C2411yescharacteristic
753C23×C4C2411yescharacteristic
754C4⋊Q8—42no—
755C4⋊Q8—44no—
756#127—42no—
757#126—216no—
758#126—28no—
759#126—48no—
760#126—48no—
761#126—48no—
762#125—28no—
763#125—28no—
764#125—48no—
765#125—48no—
766#124—28no—
767#124—28no—
768#124—216no—
769#124—48no—
770#123—28no—
771#123—216no—
772#123—28no—
773#123—48no—
774#123—48no—
775#123—48no—
776#123—48no—
777C22⋊Q8—28no—
778C22⋊Q8—28no—
779C22⋊Q8—216no—
780C22⋊Q8—48no—
781C22⋊Q8—44no—
782C22⋊Q8—48no—
783C22⋊Q8#4118yescomplemented
784#121—28no—
785#121—24no—
786#121—28no—
787#121—216no—
788#121—44no—
789#121—48no—
790#121—44no—
791C4×Q8—28no—
792C4×Q8—28no—
793C4×Q8—216no—
794C4×Q8—28no—
795C4×Q8—28no—
796C4×Q8—42no—
797C4×Q8—48no—
798C4×Q8—44no—
799C4×Q8—44no—
800C4×D4—28no—
801C4×D4—216no—
802C4×D4—28no—
803C4×D4—216no—
804C4×D4—28no—
805C4×D4—216no—
806C4×D4—28no—
807C4×D4—44no—
808C4×D4—44no—
809C4×D4—42no—
810C4×D4—48no—
811#117—216no—
812#117—48no—
813#117—48no—
814#117—44no—
815C2×C4⋊C4—24no—
816C2×C4⋊C4—28no—
817C2×C4⋊C4—24no—
818C2×C4⋊C4—24no—
819C2×C4⋊C4—42no—
820C2×C4⋊C4—42no—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2411yescharacteristic
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C42—24no—
923C2×C42—28no—
924C2×C42—28no—
925C2×C42—28no—
926C2×C42—42no—
927C2×C42—44no—
928C2×C42—42no—
929C2×C42C2412yes—
930C2×C42C2414yes—
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2411yescharacteristic
941C2×C42C2412yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2411yescharacteristic
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2414yes—
956C2×C42C2412yes—
957C2×C42C2412yes—
958C2×C42C2412yes—
959C2×C42C2411yescharacteristic
960C2×C42C2411yescharacteristic
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2414yes—
1026#95C2412yes—
1027C24C2512yes—
1028C24C2514yes—
1029C24C2511yescharacteristic
1030#41—816no—
1031C2×Q8—24no—
1032C2×Q8—24no—
1033C2×Q8—41no—
1034C2×Q8—42no—
1035C2×Q8—42no—
1036C2×Q8—41no—
1037C2×Q8—44no—
1038C2×Q8—44no—
1039C2×Q8—44no—
1040C2×Q8—42no—
1041C2×Q8—42no—
1042C2×Q8—42no—
1043C2×Q8—416no—
1044C2×Q8C2×#4118yes—
1045C2×Q8C2×#4114yes—
1046C2×Q8C2×#4118yes—
1047C2×D4—24no—
1048C2×D4—28no—
1049C2×D4—28no—
1050C2×D4—24no—
1051C2×D4—24no—
1052C2×D4—28no—
1053C2×D4—24no—
1054C2×D4—24no—
1055C2×D4—22no—
1056C2×D4—28no—
1057C2×D4—24no—
1058C2×D4—24no—
1059C2×D4—44no—
1060C2×D4—41no—
1061C2×D4—44no—
1062C2×D4—42no—
1063C2×D4—41no—
1064C2×D4—42no—
1065C2×D4—44no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C2×D4—42no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C22×C4—22no—
1072C22×C4—22no—
1073C22×C4—22no—
1074C22×C4—22no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—22no—
1078C22×C4—24no—
1079C22×C4—22no—
1080C22×C4—24no—
1081C22×C4—22no—
1082C22×C4—24no—
1083C22×C4—22no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—28no—
1089C22×C4—24no—
1090C22×C4—28no—
1091C22×C4—28no—
1092C22×C4—41no—
1093C22×C4—42no—
1094C22×C4—41no—
1095C22×C4—41no—
1096C22×C4—42no—
1097C22×C4—41no—
1098C22×C4—41no—
1099C22×C4—41no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—41no—
1104C22×C4—41no—
1105C22×C4—42no—
1106C22×C4—42no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—42no—
1112C22×C4—42no—
1113C22×C4—41no—
1114C22×C4—41no—
1115C22×C4—42no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4C2×#4114yes—
1119C22×C4C2×#4114yes—
1120C22×C4C2×#4118yes—
1121C22×C4H(5,𝔽2)14yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2511yescharacteristic
1129C22×C4C2514yes—
1130C22×C4C2511yescharacteristic
1131C22×C4C2512yes—
1132C22×C4C2514yes—
1133C22×C4C2514yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2514yes—
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2511yescharacteristic
1141C22×C4C2514yes—
1142C22×C4C2512yes—
1143C22×C4C2511yescharacteristic
1144C22×C4C2511yescharacteristic
1145C22×C4C2512yes—
1146C22×C4C2512yes—
1147C22×C4C2511yescharacteristic
1148C4⋊C4—28no—
1149C4⋊C4—28no—
1150C4⋊C4—24no—
1151C4⋊C4—22no—
1152C4⋊C4—22no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—28no—
1156C4⋊C4—28no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—28no—
1160C4⋊C4—28no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—28no—
1164C4⋊C4—22no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—28no—
1170C4⋊C4—24no—
1171C4⋊C4—22no—
1172C4⋊C4—22no—
1173C4⋊C4—24no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—41no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—41no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—41no—
1190C4⋊C4—44no—
1191C4⋊C4—42no—
1192C4⋊C4—41no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—42no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—42no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—42no—
1205C4⋊C4C2×#4118yes—
1206C4⋊C4C2×#4114yes—
1207C22⋊C4—24no—
1208C22⋊C4—28no—
1209C22⋊C4—24no—
1210C22⋊C4—28no—
1211C22⋊C4—28no—
1212C22⋊C4—28no—
1213C22⋊C4—24no—
1214C22⋊C4—28no—
1215C22⋊C4—24no—
1216C22⋊C4—28no—
1217C22⋊C4—28no—
1218C22⋊C4—28no—
1219C22⋊C4—28no—
1220C22⋊C4—24no—
1221C22⋊C4—24no—
1222C22⋊C4—24no—
1223C22⋊C4—28no—
1224C22⋊C4—24no—
1225C22⋊C4—42no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—42no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4C2×#4118yes—
1249C42—24no—
1250C42—24no—
1251C42—28no—
1252C42—28no—
1253C42—24no—
1254C42—24no—
1255C42—24no—
1256C42—24no—
1257C42—28no—
1258C42—28no—
1259C42—24no—
1260C42—24no—
1261C42—28no—
1262C42—28no—
1263C42—24no—
1264C42—28no—
1265C42—24no—
1266C42—22no—
1267C42—24no—
1268C42—22no—
1269C42—24no—
1270C42—42no—
1271C42—42no—
1272C42—41no—
1273C42—41no—
1274C42—42no—
1275C42—42no—
1276C42—44no—
1277C42—42no—
1278C42—44no—
1279C42—44no—
1280C42—44no—
1281C23—21no—
1282C23—21no—
1283C23—21no—
1284C23—21no—
1285C23—22no—
1286C23—24no—
1287C23—22no—
1288C23—24no—
1289C23—22no—
1290C23—24no—
1291C23—22no—
1292C23—24no—
1293C23—22no—
1294C23—24no—
1295C23—22no—
1296C23—24no—
1297C23—24no—
1298C23—22no—
1299C23C22×#4112yes—
1300C23C22×#4112yes—
1301C23C2×H(5,𝔽2)12yes—
1302C23C2611yescharacteristic
1303Q8—216no—
1304Q8—48no—
1305Q8—44no—
1306Q8—88no—
1307Q8—162no—
1308D4—416no—
1309D4—48no—
1310D4—48no—
1311D4—82no—
1312D4—84no—
1313D4—88no—
1314D4—88no—
1315D4—162no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—21no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—21no—
1328C2×C4—22no—
1329C2×C4—21no—
1330C2×C4—28no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—22no—
1360C2×C4—21no—
1361C2×C4—22no—
1362C2×C4—21no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—22no—
1382C2×C4—21no—
1383C2×C4—24no—
1384C2×C4—21no—
1385C2×C4—44no—
1386C2×C4—48no—
1387C2×C4—44no—
1388C2×C4—48no—
1389C2×C4—44no—
1390C2×C4—48no—
1391C2×C4—44no—
1392C2×C4—48no—
1393C2×C4—84no—
1394C2×C4—88no—
1395C2×C4—88no—
1396C2×C4—88no—
1397C2×C4—82no—
1398C2×C4—84no—
1399C2×C4—82no—
1400C2×C4—84no—
1401C2×C4C22×#4112yes—
1402C2×C4C22×#4112yes—
1403C2×C4C22×#4118yes—
1404C2×C4C22×#4112yes—
1405C2×C4C22×#4114yes—
1406C2×C4C22×#4114yes—
1407C2×C4C22×#4112yes—
1408C2×C4C2×H(5,𝔽2)14yes—
1409C2×C4#58512yes—
1410C2×C4#58512yes—
1411C22—22no—
1412C22—22no—
1413C22—22no—
1414C22—22no—
1415C22—22no—
1416C22—22no—
1417C22—42no—
1418C22—44no—
1419C22—44no—
1420C22—42no—
1421C22—42no—
1422C22—44no—
1423C22—42no—
1424C22—44no—
1425C22—42no—
1426C22—44no—
1427C22—42no—
1428C22—44no—
1429C22—42no—
1430C22—44no—
1431C22#348314yes—
1432C22C23×#4111yescharacteristic
1433C22C23×#4111yescharacteristic
1434C22C22×H(5,𝔽2)11yescharacteristic
1435C22C2×#58511yescharacteristic
1436C22C2×#58511yescharacteristic
1437C222−1+611yescharacteristic
1438C222−1+611yescharacteristic
1439C4—22no—
1440C4—22no—
1441C4—24no—
1442C4—24no—
1443C4—22no—
1444C4—28no—
1445C4—24no—
1446C4—42no—
1447C4—42no—
1448C4—42no—
1449C4—42no—
1450C4—42no—
1451C4—42no—
1452C4—42no—
1453C4—41no—
1454C4—44no—
1455C4—41no—
1456C4—44no—
1457C4—44no—
1458C4—42no—
1459C4—42no—
1460C4—42no—
1461C4—42no—
1462C4—44no—
1463C4—42no—
1464C4#349114yes—
1465C2—24no—
1466C2—82no—
1467C2—84no—
1468C2C2×#348311yescharacteristic
1469C2C2×#349111yescharacteristic
1470C2#6285011yescharacteristic
1471C2#6290111yescharacteristic
1472C2#6296011yescharacteristic
1473C2#6299111yescharacteristic
1474C2#6300911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#39743C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59961C2semidirect
2. #59903C2semidirect
3. #59501C2semidirect
4. #59487C2semidirect
5. #59435C2semidirect
6. #59380C2semidirect
7. #59276C2semidirect
8. #59262C2semidirect
9. #44643C2semidirect
10. #44591C2semidirect
11. #43832C2semidirect
12. #43788C2semidirect
14. #39624C2semidirect
15. #38939C2semidirect
16. #38935C2semidirect
17. #37951C2semidirect
18. #37771C2semidirect
19. #36483C2semidirect
20. #36176C2semidirect
21. #36117C2semidirect
22. #35464C2semidirect
23. #35119C2semidirect
24. #35006C2semidirect
25. #34763C2semidirect
26. #34327C2semidirect
27. #34219C2semidirect
28. C2×#2356C2semidirect
29. C4×#539C2semidirect
783. C22⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#599612
#599032
#595012
#594872
#594352
#593802
#592762
#592622
#446432
#445912
#438322
#437882
#397432
#396242
#389392
#389352
#379512
#377712
#364832
#361762
#361172
#354642
#351192
#350062
#347632
#343272
#342192
C2×#23562
C4×#5392