Finite Group Databasebeta

← #7690767

Subgroups — #7690767

Order 512.

5446 conjugacy classes of subgroups.

The subgroup lattice has 1359 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59546C213yesmaximal, complemented
2#59486C213yesmaximal, complemented
3#59425C213yesmaximal, complemented
4#59380C213yesmaximal, complemented
5#59281C213yesmaximal, complemented
6#45366C213yesmaximal, complemented
7#45251C213yesmaximal, complemented
8#45192C213yesmaximal, complemented
9#45116C213yesmaximal, complemented
10#39563C213yesmaximal, complemented
11#39044C213yesmaximal, complemented
12#38251C213yesmaximal, complemented
13#37974C213yesmaximal, complemented
14Q8×#124C211yesmaximal, characteristic, complemented
15Q8×#123C211yesmaximal, characteristic, complemented
16#36482C211yesmaximal, characteristic, complemented
17#36456C211yesmaximal, characteristic, complemented
18#36448C211yesmaximal, characteristic, complemented
19#36390C213yesmaximal, complemented
20#36277C213yesmaximal, complemented
21#35983C211yesmaximal, characteristic, complemented
22#35883C211yesmaximal, characteristic, complemented
23#35711C211yesmaximal, characteristic, complemented
24#35687C211yesmaximal, characteristic
25#34861C213yesmaximal, complemented
26#34291C211yesmaximal, characteristic, complemented
27#34263C211yesmaximal, characteristic, complemented
28#34259C211yesmaximal, characteristic, complemented
29#34257C211yesmaximal, characteristic, complemented
30C4×#548C211yesmaximal, characteristic, complemented
31#34128C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2863C2213yes—
43#2862C2213yes—
44#2857C2213yes—
45#2855C2213yes—
46#2855C2213yes—
47#2799C2216yes—
48#2789C2216yes—
49#2786C2216yes—
50#2760C2216yes—
51#2758C2216yes—
52#2751C2216yes—
53#2751C2216yes—
54#2750C2216yes—
55#2745C2216yes—
56#2744C2216yes—
57#2743C2216yes—
58#2743C2216yes—
59#2739C2216yes—
60#2737C2216yes—
61#2645C2213yes—
62#2628C2213yes—
63#2625C2213yes—
64#2616C2213yes—
65#2609C2216yes—
66#2607C2216yes—
67#2605C2213yes—
68#2605C2216yes—
69#2603C2213yes—
70#2601C2213yes—
71#2598C2213yes—
72#2597C2213yes—
73#2589C2213yes—
74#2588C2216yes—
75#2581C2213yes—
76#2576C2213yes—
77#2572C2216yes—
78#2572C2216yes—
79#2569C2216yes—
80#2568C2213yes—
81#2568C2213yes—
82#2564C2216yes—
83#2563C2213yes—
84#2563C2213yes—
85#2560C2216yes—
86#2557C2211yescharacteristic
87#2538C2213yes—
88#2531C2213yes—
89#2527C2216yes—
90#2527C2213yes—
91#2527C2216yes—
92#2526C2216yes—
93#2520C2213yes—
94#2516C2213yes—
95#2515C2216yes—
96#2514C2213yes—
97#2514C2213yes—
98#2514C2213yes—
99#2514C2213yes—
100#2511C2213yes—
101#2511C2213yes—
102#2503C2213yes—
103#2503C2213yes—
104#2502C2213yes—
105#2497C2213yes—
106#2496C2213yes—
107#2495C2213yes—
108#2495C2213yes—
109#2494C2213yes—
110#2494C2213yes—
111#2493C2216yes—
112#2493C2216yes—
113#2492C2213yes—
114#2492C2213yes—
115#2492C2213yes—
116#2492C2213yes—
117#2487C2213yes—
118#2487C2213yes—
119#2486C2213yes—
120#2477C2216yes—
121#2477C2213yes—
122#2471C2213yes—
123#2471C2216yes—
124#2461C2213yes—
125#2457C2213yes—
126#2452C2213yes—
127#2452C2213yes—
128#2451C2213yes—
129#2451C2213yes—
130#2447C2213yes—
131#2447C2213yes—
132#2446C2213yes—
133#2446C2213yes—
134#2446C2213yes—
135#2446C2213yes—
136#2439C2213yes—
137#2439C2213yes—
138#2439C2213yes—
139#2439C2213yes—
140#2438C2216yes—
141#2434C2213yes—
142#2432C2213yes—
143#2432C2213yes—
144#2423C2213yes—
145#2423C2213yes—
146#2421C2213yes—
147#2421C2213yes—
148#2420C2213yes—
149#2420C2213yes—
150#2409C2213yes—
151#2407C2213yes—
152#2407C2213yes—
153#2401C2213yes—
154#2396C2213yes—
155#2395C2213yes—
156#2388C2213yes—
157#2368C2216yes—
158#2367C2213yes—
159#2365C2213yes—
160#2362C2213yes—
161#2362C2213yes—
162#2361C2213yes—
163#2360C2213yes—
164#2357C2213yes—
165#2356C2213yes—
166#2356C2213yes—
167#2354C2213yes—
168#2353C2216yes—
169#2352C2213yes—
170#2352C2213yes—
171#2351C2211yescharacteristic
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175#2351C2211yescharacteristic
176#2351C2211yescharacteristic
177Q8×C4⋊C4C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179#2345C2213yes—
180#2344C2213yes—
181#2344C2213yes—
182#2344C2213yes—
183#2343C2216yes—
184#2341C2213yes—
185#2341C2211yescharacteristic
186#2341C2211yescharacteristic
187#2341C2211yescharacteristic
188#2341C2213yes—
189Q8×C22⋊C4C2213yes—
190Q8×C22⋊C4C2211yescharacteristic
191Q8×C22⋊C4C2211yescharacteristic
192Q8×C22⋊C4C2211yescharacteristic
193Q8×C22⋊C4C2211yescharacteristic
194Q8×C22⋊C4C2211yescharacteristic
195Q8×C22⋊C4C2211yescharacteristic
196Q8×C22⋊C4C2211yescharacteristic
197Q8×C22⋊C4C2213yes—
198Q8×C22⋊C4C2211yescharacteristic
199Q8×C22⋊C4C2211yescharacteristic
200Q8×C22⋊C4C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202#2339C2213yes—
203#2339C2213yes—
204#2339C2213yes—
205#2339C2213yes—
206#2327C2213yes—
207#2323C2213yes—
208#2319C2213yes—
209#2314C2213yes—
210#2311C2213yes—
211#2311C2213yes—
212#2311C2213yes—
213#2310C2213yes—
214C4×#126C2213yes—
215C4×#124C2213yes—
216C4×#124C2213yes—
217C4×C22⋊Q8C2213yes—
218C4×C22⋊Q8C2213yes—
219C4×C22⋊Q8C2213yes—
220C4×#123C2213yes—
221C4×#123C2213yes—
222C4×#121C2213yes—
223#2298C2213yes—
224#2297C2213yes—
225#2297C2213yes—
226#2297C2213yes—
227#2295C2213yes—
228#2295C2213yes—
229C2×#391C2213yes—
230#2293C2213yes—
231#2290C2213yes—
232#2283C2213yes—
233#2276C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×D4C2213yes—
237C4×#117C2213yes—
238C2×2−1+4—28no—
239C2×2−1+4—28no—
240C2×2−1+4—44no—
241C22×#41C2313yes—
242C22×#41C2313yes—
243C22×#41C2313yes—
244C22×#41C2311yescharacteristic
245C23×Q8C2311yescharacteristic
246C23×Q8C2311yescharacteristic
247C23×Q8C2313yes—
248C23×Q8C2311yescharacteristic
249Q82—44no—
250D4×Q8—28no—
251D4×Q8—44no—
252#548—28no—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2313yes—
256C2×C4⋊Q8C2313yes—
257C2×C4⋊Q8C2313yes—
258C2×#126C2313yes—
259C2×#124C2313yes—
260C2×#124C2311yescharacteristic
261C2×#123C2311yescharacteristic
262C2×#123C2313yes—
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2313yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2316yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×#121C2313yes—
271#520—28no—
272#519—44no—
273C4×#41—44no—
274C2×C4×Q8—28no—
275C2×C4×Q8—44no—
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2313yes—
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×#117C2313yes—
304C2×#117C2313yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2316yes—
309C2×#117C2313yes—
310C22×C4⋊C4C2313yes—
311C22×C4⋊C4C2313yes—
312C22×C4⋊C4C2313yes—
313C22×C42C2313yes—
314C22×C42C2313yes—
315C22×C42C2313yes—
316#401C2313yes—
317#401C2316yes—
318#401C2316yes—
319#400C2316yes—
320#400C2313yes—
321#400C2316yes—
322#400C2316yes—
323#400C2316yes—
324#400C2313yes—
325#400C2316yes—
326#400C2316yes—
327#400C2316yes—
328#400C2313yes—
329#400C2313yes—
330#400C2313yes—
331#400C2316yes—
332#400C2316yes—
333#400C2316yes—
334#400C2316yes—
335#399C2316yes—
336#399C2313yes—
337#399C2313yes—
338#398C2316yes—
339#398C2313yes—
340#398C2316yes—
341#398C2313yes—
342#398C2313yes—
343#398C2316yes—
344#397C2316yes—
345#397C2313yes—
346#397C2313yes—
347#397C2313yes—
348#397C2313yes—
349#397C2316yes—
350#397C2311yescharacteristic
351#397C2311yescharacteristic
352#397C2316yes—
353#397C2316yes—
354#396C2313yes—
355#396C2313yes—
356#396C2313yes—
357#396C2316yes—
358#396C2316yes—
359#395C2316yes—
360#395C2313yes—
361#395C2316yes—
362#395C2313yes—
363#394C2316yes—
364#394C2313yes—
365#394C2316yes—
366#394C2313yes—
367#394C2313yes—
368#394C2313yes—
369#394C2313yes—
370#393C2316yes—
371#393C2316yes—
372#393C2316yes—
373#393C2316yes—
374#393C2316yes—
375#393C2313yes—
376#393C2311yescharacteristic
377#392C2313yes—
378#392C2313yes—
379#392C2311yescharacteristic
380#391C2316yes—
381#391C2313yes—
382#391C2316yes—
383#391C2313yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#391C2313yes—
388#391C2316yes—
389#391C2313yes—
390#391C2313yes—
391#391C2313yes—
392#391C2313yes—
393#391C2313yes—
394#391C2313yes—
395#391C2316yes—
396#391C2316yes—
397#391C2313yes—
398#391C2313yes—
399#391C2313yes—
400#391C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2313yes—
410#391C2313yes—
411#391C2313yes—
412#391C2316yes—
413#391C2311yescharacteristic
414#391C2316yes—
415#390C2316yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2311yescharacteristic
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2316yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#388C2311yescharacteristic
446#388C2313yes—
447#388C2313yes—
448#388C2313yes—
449#388C2316yes—
450#388C2316yes—
451#388C2316yes—
452#388C2313yes—
453#388C2316yes—
454#388C2316yes—
455#388C2313yes—
456#388C2313yes—
457#388C2313yes—
458#388C2313yes—
459#388C2313yes—
460#388C2313yes—
461#388C2313yes—
462#388C2313yes—
463#388C2313yes—
464#388C2313yes—
465#388C2313yes—
466#388C2316yes—
467#388C2316yes—
468#388C2313yes—
469#387C2313yes—
470#387C2313yes—
471#387C2313yes—
472#387C2316yes—
473#387C2316yes—
474#387C2316yes—
475#387C2316yes—
476#387C2316yes—
477#387C2316yes—
478#387C2313yes—
479#387C2316yes—
480#387C2313yes—
481#387C2316yes—
482#387C2316yes—
483#387C2313yes—
484#387C2316yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2313yes—
489#387C2313yes—
490#387C2313yes—
491#387C2316yes—
492#387C2316yes—
493#387C2313yes—
494#387C2316yes—
495#387C2316yes—
496#387C2313yes—
497#387C2316yes—
498#387C2316yes—
499#387C2313yes—
500#387C2313yes—
501#387C2313yes—
502#387C2311yescharacteristic
503#386C2313yes—
504#386C2316yes—
505#386C2316yes—
506#386C2313yes—
507#386C2313yes—
508#386C2316yes—
509#386C2316yes—
510#386C2316yes—
511#386C2313yes—
512#386C2316yes—
513#386C2313yes—
514#386C2313yes—
515#386C2313yes—
516#386C2311yescharacteristic
517#386C2313yes—
518#386C2311yescharacteristic
519#386C2313yes—
520#386C2311yescharacteristic
521#385C2313yes—
522#385C2313yes—
523#385C2316yes—
524#385C2316yes—
525#385C2313yes—
526#385C2313yes—
527#385C2316yes—
528#385C2316yes—
529#385C2313yes—
530#385C2313yes—
531#385C2316yes—
532#385C2316yes—
533#384C2313yes—
534#384C2313yes—
535#383C2313yes—
536#383C2316yes—
537#383C2316yes—
538#383C2316yes—
539#382C2316yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#381C2316yes—
548#381C2316yes—
549#381C2313yes—
550#381C2313yes—
551#381C2316yes—
552#381C2316yes—
553#381C2316yes—
554#381C2316yes—
555#381C2316yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2316yes—
560#380C2313yes—
561#380C2313yes—
562#380C2316yes—
563#380C2316yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2316yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2316yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C22⋊C4C2313yes—
598C4×C22⋊C4C2313yes—
599C4×C22⋊C4C2313yes—
600C4×C22⋊C4C2316yes—
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2316yes—
604C4×C22⋊C4C2316yes—
605C4×C22⋊C4C2316yes—
606C4×C22⋊C4C2311yescharacteristic
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2311yescharacteristic
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
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—
622#376C2313yes—
623#376C2313yes—
624#376C2316yes—
625#376C2313yes—
626C2×#95C2316yes—
627C2×#95C2316yes—
628C43C2313yes—
629C43C2313yes—
6302−1+4—464no—
631C2×#41—24no—
632C2×#41—212no—
633C2×#41—24no—
634C2×#41—212no—
635C2×#41—212no—
636C2×#41—212no—
637C2×#41—212no—
638C2×#41—212no—
639C2×#41—46no—
640C2×#41—46no—
641C2×#41—46no—
642C2×#41#4118yes—
643C22×Q8—24no—
644C22×Q8—24no—
645C22×Q8—24no—
646C22×Q8—24no—
647C22×Q8—212no—
648C22×Q8—24no—
649C22×Q8—24no—
650C22×Q8—24no—
651C22×Q8—24no—
652C22×Q8—212no—
653C22×Q8—46no—
654C22×Q8#4118yes—
655C22×Q8C2413yes—
656C22×Q8C2413yes—
657C22×Q8C2411yescharacteristic
658C22×Q8C2413yes—
659C22×Q8C2413yes—
660C22×Q8C2416yes—
661C22×Q8C2411yescharacteristic
662C22×D4C2413yes—
663C22×D4C2411yescharacteristic
664C22×D4C2411yescharacteristic
665C22×D4C2413yes—
666C22×D4C2411yescharacteristic
667C22×D4C2413yes—
668C22×D4C2413yes—
669C23×C4C2413yes—
670C23×C4C2413yes—
671C23×C4C2411yescharacteristic
672C23×C4C2416yes—
673C23×C4C2413yes—
674C23×C4C2413yes—
675C23×C4C2413yes—
676C23×C4C2413yes—
677C23×C4C2416yes—
678C23×C4C2413yes—
679C23×C4C2413yes—
680C23×C4C2411yescharacteristic
681C4⋊Q8—212no—
682C4⋊Q8—46no—
683C4⋊Q8—46no—
684C4⋊Q8—46no—
685C4⋊Q8—46no—
686#126—46no—
687#124—212no—
688#124—24no—
689#123—24no—
690#123—46no—
691C22⋊Q8—212no—
692C22⋊Q8—212no—
693C22⋊Q8—212no—
694C22⋊Q8—46no—
695C22⋊Q8—412no—
696C22⋊Q8—46no—
697C22⋊Q8—46no—
698#121—212no—
699C4×Q8—212no—
700C4×Q8—212no—
701C4×Q8—24no—
702C4×Q8—24no—
703C4×Q8—24no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—24no—
710C4×Q8—24no—
711C4×Q8—24no—
712C4×Q8—46no—
713C4×Q8—46no—
714C4×Q8—46no—
715C4×Q8—46no—
716C4×Q8—46no—
717C4×D4—212no—
718C4×D4—212no—
719C4×D4—212no—
720C4×D4—212no—
721C4×D4—212no—
722C4×D4—46no—
723C4×D4—46no—
724C4×D4—46no—
725C4×D4—46no—
726#117—212no—
727#117—46no—
728#117—46no—
729#117—412no—
730#117—46no—
731#117—46no—
732#117—46no—
733C2×C4⋊C4—212no—
734C2×C4⋊C4—212no—
735C2×C4⋊C4—46no—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2416yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2411yescharacteristic
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2416yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2416yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2411yescharacteristic
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2416yes—
790C2×C22⋊C4C2411yescharacteristic
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2411yescharacteristic
793C2×C22⋊C4C2411yescharacteristic
794C2×C22⋊C4C2411yescharacteristic
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2411yescharacteristic
798C2×C22⋊C4C2416yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2416yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2411yescharacteristic
817C2×C22⋊C4C2411yescharacteristic
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2411yescharacteristic
822C2×C42—212no—
823C2×C42—46no—
824C2×C42—46no—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2411yescharacteristic
842C2×C42C2413yes—
843C2×C42C2416yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2416yes—
847C2×C42C2413yes—
848C2×C42C2413yes—
849C2×C42C2411yescharacteristic
850C2×C42C2413yes—
851C2×C42C2411yescharacteristic
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2416yes—
857#95C2416yes—
858#95C2416yes—
859#95C2416yes—
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2416yes—
872#95C2416yes—
873#95C2416yes—
874#95C2411yescharacteristic
875#95C2411yescharacteristic
876#95C2413yes—
877#95C2413yes—
878#95C2411yescharacteristic
879#95C2411yescharacteristic
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2416yes—
886#95C2416yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2416yes—
892#95C2416yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2416yes—
897#95C2413yes—
898#95C2413yes—
899#95C2416yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2416yes—
905#95C2416yes—
906#95C2411yescharacteristic
907#95C2411yescharacteristic
908#95C2411yescharacteristic
909#95C2416yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2416yes—
917#95C2416yes—
918#95C2416yes—
919C24C2511yescharacteristic
920C24C2511yescharacteristic
921C24C2513yes—
922C24C2511yescharacteristic
923#41—232no—
924#41—448no—
925#41—448no—
926#41—448no—
927C2×Q8—232no—
928C2×Q8—26no—
929C2×Q8—26no—
930C2×Q8—26no—
931C2×Q8—26no—
932C2×Q8—26no—
933C2×Q8—26no—
934C2×Q8—26no—
935C2×Q8—26no—
936C2×Q8—26no—
937C2×Q8—26no—
938C2×Q8—22no—
939C2×Q8—22no—
940C2×Q8—41no—
941C2×Q8—43no—
942C2×Q8—46no—
943C2×Q8—46no—
944C2×Q8—46no—
945C2×Q8—448no—
946C2×Q8—416no—
947C2×Q8—416no—
948C2×Q8C2×#41112yes—
949C2×Q8C2×#4114yes—
950C2×Q8C2×#4114yes—
951C2×Q8H(5,𝔽2)14yes—
952C2×D4—22no—
953C2×D4—26no—
954C2×D4—26no—
955C2×D4—22no—
956C2×D4—26no—
957C2×D4—26no—
958C2×D4—26no—
959C2×D4—22no—
960C2×D4—22no—
961C2×D4—26no—
962C2×D4—26no—
963C2×D4—22no—
964C2×D4—26no—
965C2×D4—22no—
966C2×D4—41no—
967C2×D4—43no—
968C2×D4—41no—
969C2×D4—41no—
970C2×D4—43no—
971C2×D4—43no—
972C2×D4C2×#41112yes—
973C22×C4—26no—
974C22×C4—26no—
975C22×C4—26no—
976C22×C4—26no—
977C22×C4—22no—
978C22×C4—26no—
979C22×C4—212no—
980C22×C4—212no—
981C22×C4—26no—
982C22×C4—26no—
983C22×C4—26no—
984C22×C4—212no—
985C22×C4—26no—
986C22×C4—26no—
987C22×C4—26no—
988C22×C4—26no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—26no—
992C22×C4—26no—
993C22×C4—41no—
994C22×C4—43no—
995C22×C4—43no—
996C22×C4—41no—
997C22×C4—41no—
998C22×C4—46no—
999C22×C4—43no—
1000C22×C4—43no—
1001C22×C4—43no—
1002C22×C4—46no—
1003C22×C4—43no—
1004C22×C4—43no—
1005C22×C4—43no—
1006C22×C4—46no—
1007C22×C4C2×#41112yes—
1008C22×C4C2×#41112yes—
1009C22×C4C2513yes—
1010C22×C4C2511yescharacteristic
1011C22×C4C2511yescharacteristic
1012C22×C4C2513yes—
1013C22×C4C2513yes—
1014C22×C4C2513yes—
1015C22×C4C2511yescharacteristic
1016C22×C4C2513yes—
1017C22×C4C2511yescharacteristic
1018C22×C4C2513yes—
1019C22×C4C2511yescharacteristic
1020C22×C4C2513yes—
1021C22×C4C2513yes—
1022C22×C4C2511yescharacteristic
1023C22×C4C2513yes—
1024C22×C4C2513yes—
1025C22×C4C2513yes—
1026C22×C4C2513yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2513yes—
1029C22×C4C2511yescharacteristic
1030C22×C4C2513yes—
1031C22×C4C2511yescharacteristic
1032C22×C4C2511yescharacteristic
1033C22×C4C2511yescharacteristic
1034C22×C4C2511yescharacteristic
1035C22×C4C2513yes—
1036C4⋊C4—26no—
1037C4⋊C4—26no—
1038C4⋊C4—26no—
1039C4⋊C4—212no—
1040C4⋊C4—26no—
1041C4⋊C4—26no—
1042C4⋊C4—22no—
1043C4⋊C4—26no—
1044C4⋊C4—26no—
1045C4⋊C4—26no—
1046C4⋊C4—26no—
1047C4⋊C4—212no—
1048C4⋊C4—26no—
1049C4⋊C4—26no—
1050C4⋊C4—26no—
1051C4⋊C4—26no—
1052C4⋊C4—26no—
1053C4⋊C4—26no—
1054C4⋊C4—22no—
1055C4⋊C4—22no—
1056C4⋊C4—26no—
1057C4⋊C4—26no—
1058C4⋊C4—26no—
1059C4⋊C4—26no—
1060C4⋊C4—46no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—43no—
1064C4⋊C4—46no—
1065C4⋊C4—43no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—43no—
1070C4⋊C4—43no—
1071C4⋊C4—43no—
1072C4⋊C4—43no—
1073C4⋊C4—43no—
1074C4⋊C4—43no—
1075C4⋊C4—46no—
1076C4⋊C4—46no—
1077C4⋊C4—43no—
1078C4⋊C4—43no—
1079C22⋊C4—26no—
1080C22⋊C4—26no—
1081C22⋊C4—26no—
1082C22⋊C4—26no—
1083C22⋊C4—212no—
1084C22⋊C4—22no—
1085C22⋊C4—22no—
1086C22⋊C4—22no—
1087C22⋊C4—26no—
1088C22⋊C4—26no—
1089C22⋊C4—22no—
1090C22⋊C4—22no—
1091C22⋊C4—22no—
1092C22⋊C4—22no—
1093C22⋊C4—22no—
1094C22⋊C4—26no—
1095C22⋊C4—22no—
1096C22⋊C4—43no—
1097C22⋊C4—43no—
1098C22⋊C4—41no—
1099C22⋊C4—43no—
1100C22⋊C4—43no—
1101C22⋊C4—41no—
1102C22⋊C4—43no—
1103C22⋊C4—43no—
1104C22⋊C4—46no—
1105C22⋊C4—43no—
1106C22⋊C4—41no—
1107C22⋊C4—43no—
1108C22⋊C4—46no—
1109C22⋊C4—43no—
1110C22⋊C4—43no—
1111C22⋊C4—43no—
1112C22⋊C4—43no—
1113C22⋊C4—46no—
1114C22⋊C4—43no—
1115C22⋊C4—46no—
1116C22⋊C4—43no—
1117C22⋊C4—43no—
1118C22⋊C4—43no—
1119C22⋊C4—43no—
1120C22⋊C4—43no—
1121C22⋊C42−1+414yescomplemented
1122C42—26no—
1123C42—26no—
1124C42—26no—
1125C42—26no—
1126C42—26no—
1127C42—26no—
1128C42—26no—
1129C42—26no—
1130C42—26no—
1131C42—26no—
1132C42—26no—
1133C42—26no—
1134C42—26no—
1135C42—26no—
1136C42—22no—
1137C42—26no—
1138C42—26no—
1139C42—41no—
1140C42—43no—
1141C42—43no—
1142C42—43no—
1143C42—41no—
1144C42—43no—
1145C42—46no—
1146C42—43no—
1147C42—43no—
1148C42—46no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—23no—
1153C23—21no—
1154C23—21no—
1155C23—23no—
1156C23—21no—
1157C23—23no—
1158C23—23no—
1159C23—21no—
1160C23—21no—
1161C23—23no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—23no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23C22×#4116yes—
1175C23C22×#4112yes—
1176C23C2×2−1+412yes—
1177C23C2611yescharacteristic
1178Q8—224no—
1179Q8—44no—
1180Q8—412no—
1181Q8—412no—
1182Q8—412no—
1183Q8—166no—
1184Q8#551116yes—
1185D4—224no—
1186D4—44no—
1187D4—44no—
1188D4—412no—
1189D4—44no—
1190D4—412no—
1191D4—412no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—23no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—23no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—224no—
1205C2×C4—224no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
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—21no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—23no—
1237C2×C4—21no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—21no—
1249C2×C4—23no—
1250C2×C4—23no—
1251C2×C4—23no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—21no—
1259C2×C4—23no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—23no—
1263C2×C4—23no—
1264C2×C4—21no—
1265C2×C4—23no—
1266C2×C4—44no—
1267C2×C4—424no—
1268C2×C4—44no—
1269C2×C4—412no—
1270C2×C4—412no—
1271C2×C4—412no—
1272C2×C4—86no—
1273C2×C4—86no—
1274C2×C4—812no—
1275C2×C4—86no—
1276C2×C4C22×#4116yes—
1277C2×C4C22×#4112yes—
1278C2×C4C22×#4116yes—
1279C2×C4C22×#4116yes—
1280C2×C4C2×H(5,𝔽2)16yes—
1281C2×C4C2×2−1+412yes—
1282C2×C4C2×2−1+412yes—
1283C2×C4#58512yes—
1284C2×C4#58512yes—
1285C22—26no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—26no—
1292C22—22no—
1293C22—26no—
1294C22—41no—
1295C22—41no—
1296C22—43no—
1297C22—43no—
1298C22—41no—
1299C22—41no—
1300C22—43no—
1301C22—41no—
1302C22—41no—
1303C22—43no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22C23×#4111yescharacteristic
1314C22C23×#4111yescharacteristic
1315C22C22×H(5,𝔽2)11yescharacteristic
1316C22C22×2−1+411yescharacteristic
1317C22C2×#58511yescharacteristic
1318C22C2×#58511yescharacteristic
1319C222−1+611yescharacteristic
1320C4—22no—
1321C4—22no—
1322C4—22no—
1323C4—22no—
1324C4—22no—
1325C4—26no—
1326C4—41no—
1327C4—43no—
1328C4—43no—
1329C4—41no—
1330C4—41no—
1331C4—43no—
1332C4—43no—
1333C4—41no—
1334C4—43no—
1335C4—43no—
1336C4—43no—
1337C4—41no—
1338C4—41no—
1339C4—43no—
1340C4—41no—
1341C4—43no—
1342C4—43no—
1343C4—43no—
1344C4—43no—
1345C4—43no—
1346C4C2×#551112yes—
1347C2—46no—
1348C2—42no—
1349C2—42no—
1350C2—81no—
1351C2C22×#55111yescharacteristic
1352C2#6279311yescharacteristic
1353C2#6280511yescharacteristic
1354C2#6291911yescharacteristic
1355C2#6299511yescharacteristic
1356C2#6299811yescharacteristic
1357C2#6301511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35687C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59546C2semidirect
2. #59486C2semidirect
3. #59425C2semidirect
4. #59380C2semidirect
5. #59281C2semidirect
6. #45366C2semidirect
7. #45251C2semidirect
8. #45192C2semidirect
9. #45116C2semidirect
10. #39563C2semidirect
11. #39044C2semidirect
12. #38251C2semidirect
13. #37974C2semidirect
14. Q8×#124C2semidirect
15. Q8×#123C2semidirect
16. #36482C2semidirect
17. #36456C2semidirect
18. #36448C2semidirect
19. #36390C2semidirect
20. #36277C2semidirect
21. #35983C2semidirect
22. #35883C2semidirect
23. #35711C2semidirect
25. #34861C2semidirect
26. #34291C2semidirect
27. #34263C2semidirect
28. #34259C2semidirect
29. #34257C2semidirect
30. C4×#548C2semidirect
31. #34128C2semidirect
1121. C22⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#595462
#594862
#594252
#593802
#592812
#453662
#452512
#451922
#451162
#395632
#390442
#382512
#379742
Q8×#1242
Q8×#1232
#364822
#364562
#364482
#363902
#362772
#359832
#358832
#357112
#356872
#348612
#342912
#342632
#342592
#342572
C4×#5482
#341282