Finite Group Databasebeta

← #7630757

Subgroups — #7630757

Order 512.

4864 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36038C214yesmaximal, complemented
2#36027C214yesmaximal, complemented
3#35835C214yesmaximal, complemented
4#35829C214yesmaximal, complemented
5#35820C214yesmaximal, complemented
6#35814C214yesmaximal, complemented
7#35746C214yesmaximal, complemented
8#35735C214yesmaximal, complemented
9#35120C211yesmaximal, characteristic, complemented
10#35119C211yesmaximal, characteristic
11#35111C212yesmaximal, complemented
12#35099C212yesmaximal, complemented
13#35098C212yesmaximal, complemented
14#35092C212yesmaximal, complemented
15#35042C212yesmaximal, complemented
16#35024C212yesmaximal, complemented
17#35021C212yesmaximal, complemented
18#35013C211yesmaximal, characteristic, complemented
19#35004C211yesmaximal, characteristic
20#34602C212yesmaximal, complemented
21#34595C211yesmaximal, characteristic, complemented
22#34594C211yesmaximal, characteristic
23#34584C212yesmaximal, complemented
24#34278C212yesmaximal, complemented
25#34224C212yesmaximal, complemented
26#34219C212yesmaximal, complemented
27C2×#2276C211yesmaximal, characteristic, complemented
28C2×#539C2212yes—
29C2×#529C2212yes—
30C2×#529C2212yes—
31C22×C4×Q8C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34#2855C2212yes—
35#2855C2212yes—
36#2855C2212yes—
37#2854C2212yes—
38#2854C2212yes—
39#2854C2212yes—
40#2853C2214yes—
41#2852C2214yes—
42#2851C2212yes—
43#2850C2212yes—
44#2666C2214yes—
45#2666C2214yes—
46#2664C2214yes—
47#2662C2214yes—
48#2659C2211yescharacteristic
49#2659C2211yescharacteristic
50#2659C2211yescharacteristic
51#2656C2211yescharacteristic
52#2655C2214yes—
53#2654C2214yes—
54#2651C2214yes—
55#2650C2214yes—
56#2646C2212yes—
57#2646C2212yes—
58#2643C2214yes—
59#2639C2212yes—
60#2639C2212yes—
61#2637C2214yes—
62#2637C2214yes—
63#2634C2214yes—
64#2632C2214yes—
65#2627C2212yes—
66#2627C2212yes—
67#2627C2212yes—
68#2623C2214yes—
69#2623C2214yes—
70#2618C2212yes—
71#2618C2212yes—
72#2618C2212yes—
73#2614C2214yes—
74#2612C2214yes—
75#2612C2214yes—
76#2611C2214yes—
77#2610C2214yes—
78#2606C2214yes—
79#2605C2214yes—
80#2604C2214yes—
81#2604C2214yes—
82#2604C2214yes—
83#2603C2214yes—
84#2599C2214yes—
85#2599C2214yes—
86#2597C2214yes—
87#2596C2214yes—
88#2596C2214yes—
89#2594C2214yes—
90#2593C2214yes—
91#2592C2212yes—
92#2592C2212yes—
93#2590C2214yes—
94#2589C2214yes—
95#2586C2214yes—
96#2585C2214yes—
97#2585C2214yes—
98#2584C2212yes—
99#2584C2212yes—
100#2581C2212yes—
101#2581C2212yes—
102#2580C2212yes—
103#2580C2212yes—
104#2577C2214yes—
105#2575C2214yes—
106#2574C2214yes—
107#2573C2214yes—
108#2556C2214yes—
109#2554C2214yes—
110#2533C2214yes—
111#2533C2214yes—
112#2532C2214yes—
113#2532C2214yes—
114#2531C2214yes—
115#2530C2214yes—
116#2529C2214yes—
117#2528C2214yes—
118#2527C2214yes—
119#2526C2214yes—
120#2525C2214yes—
121#2525C2214yes—
122#2524C2214yes—
123#2524C2214yes—
124#2522C2214yes—
125#2521C2214yes—
126#2520C2214yes—
127#2520C2214yes—
128#2519C2214yes—
129#2519C2214yes—
130#2516C2214yes—
131#2515C2214yes—
132#2514C2212yes—
133#2513C2212yes—
134#2509C2212yes—
135#2508C2212yes—
136#2479C2214yes—
137#2478C2214yes—
138#2469C2214yes—
139#2469C2214yes—
140#2469C2214yes—
141#2468C2214yes—
142#2465C2214yes—
143#2465C2214yes—
144#2462C2214yes—
145#2462C2214yes—
146#2462C2214yes—
147#2461C2214yes—
148#2458C2214yes—
149#2458C2214yes—
150#2454C2212yes—
151#2453C2212yes—
152#2448C2212yes—
153#2447C2212yes—
154#2402C2214yes—
155#2402C2214yes—
156#2401C2214yes—
157#2399C2214yes—
158#2399C2214yes—
159#2398C2214yes—
160#2396C2214yes—
161#2396C2214yes—
162#2396C2214yes—
163#2396C2214yes—
164#2395C2214yes—
165#2392C2214yes—
166#2374C2214yes—
167#2373C2214yes—
168#2373C2214yes—
169#2373C2214yes—
170#2373C2214yes—
171#2373C2214yes—
172#2373C2214yes—
173#2372C2214yes—
174#2371C2214yes—
175#2371C2214yes—
176#2370C2214yes—
177#2370C2212yes—
178#2370C2212yes—
179#2368C2214yes—
180#2367C2212yes—
181#2367C2212yes—
182#2362C2214yes—
183#2359C2214yes—
184#2357C2212yes—
185#2356C2214yes—
186#2356C2212yes—
187#2353C2214yes—
188#2351C2212yes—
189#2349C2212yes—
190#2347C2214yes—
191#2346C2214yes—
192#2343C2214yes—
193#2343C2214yes—
194#2329C2212yes—
195#2329C2212yes—
196#2329C2212yes—
197#2325C2212yes—
198#2325C2212yes—
199#2325C2212yes—
200#2322C2214yes—
201#2322C2214yes—
202#2322C2214yes—
203#2318C2214yes—
204#2318C2214yes—
205#2313C2212yes—
206C4×C22⋊Q8C2212yes—
207C4×C22⋊Q8C2212yes—
208C4×C22⋊Q8C2212yes—
209C4×#123C2214yes—
210C4×#123C2214yes—
211C4×#123C2214yes—
212C4×#121C2212yes—
213C4×#121C2212yes—
214C4×#121C2212yes—
215#2290C2214yes—
216#2283C2212yes—
217#2283C2212yes—
218#2276C2214yes—
219#2276C2214yes—
220#2276C2214yes—
221#2276C2214yes—
222#2275C2214yes—
223C2×C4×C4⋊C4C2211yescharacteristic
224C2×C4×C4⋊C4C2211yescharacteristic
225C2×C4×C4⋊C4C2211yescharacteristic
226C2×C4×C4⋊C4C2211yescharacteristic
227C2×C4×C4⋊C4C2211yescharacteristic
228C2×C4×C4⋊C4C2211yescharacteristic
229C2×C4×C4⋊C4C2211yescharacteristic
230C2×C4×C4⋊C4C2211yescharacteristic
231C2×C4×C4⋊C4C2211yescharacteristic
232C2×#376C2211yescharacteristic
233C2×#376C2211yescharacteristic
234C2×#376C2211yescharacteristic
235C23×Q8C2311yescharacteristic
236#539—216no—
237#529—216no—
238#529—216no—
239C2×#126C2314yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#125C2312yes—
244C2×#125C2312yes—
245C2×#125C2314yes—
246C2×#125C2312yes—
247C2×#124C2312yes—
248C2×#124C2312yes—
249C2×#124C2312yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2312yes—
258C2×#121C2312yes—
259C2×#121C2312yes—
260C2×#121C2312yes—
261C2×C4×Q8—28no—
262C2×C4×Q8—28no—
263C2×C4×Q8—28no—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2314yes—
271C2×C4×Q8C2314yes—
272C2×C4×Q8C2314yes—
273C2×C4×Q8C2314yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×#117C2314yes—
286C2×#117C2314yes—
287C2×#117C2314yes—
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2311yescharacteristic
297C22×C42C2311yescharacteristic
298C22×C42C2311yescharacteristic
299C22×C42C2311yescharacteristic
300C22×C42C2311yescharacteristic
301C22×C42C2311yescharacteristic
302C22×C42C2311yescharacteristic
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305C22×C42C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2311yescharacteristic
310C22×C42C2311yescharacteristic
311C22×C42C2311yescharacteristic
312#401C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#393C2314yes—
386#393C2314yes—
387#393C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#392C2314yes—
392#391C2312yes—
393#391C2312yes—
394#391C2312yes—
395#391C2312yes—
396#391C2312yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2312yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#390C2312yes—
406#390C2312yes—
407#390C2312yes—
408#390C2312yes—
409#390C2312yes—
410#390C2312yes—
411#390C2312yes—
412#390C2312yes—
413#390C2312yes—
414#390C2312yes—
415#389C2312yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#383C2314yes—
557#383C2314yes—
558#383C2314yes—
559#383C2314yes—
560#383C2314yes—
561#382C2314yes—
562#382C2314yes—
563#382C2312yes—
564#382C2312yes—
565#382C2312yes—
566#382C2312yes—
567#382C2312yes—
568#382C2312yes—
569#381C2314yes—
570#381C2314yes—
571#381C2314yes—
572#381C2314yes—
573#381C2314yes—
574#380C2312yes—
575#380C2312yes—
576#380C2314yes—
577#380C2314yes—
578#380C2312yes—
579#380C2312yes—
580#380C2312yes—
581#380C2312yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2312yes—
584C4×C4⋊C4C2312yes—
585C4×C4⋊C4C2312yes—
586C4×C4⋊C4C2312yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2312yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2312yes—
597C4×C4⋊C4C2312yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2312yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2312yes—
604C4×C4⋊C4C2312yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2312yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2314yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2314yes—
643#376C2314yes—
644#376C2314yes—
645#376C2314yes—
646#376C2314yes—
647#376C2314yes—
648#376C2314yes—
649#376C2314yes—
650#376C2314yes—
651#376C2314yes—
652#376C2314yes—
653C2×#95C2311yescharacteristic
654C2×#95C2311yescharacteristic
655C2×#95C2311yescharacteristic
656C2×#95C2311yescharacteristic
657C2×#95C2311yescharacteristic
658C2×#95C2314yes—
659C2×#95C2311yescharacteristic
660C2×#95C2311yescharacteristic
661C2×#95C2311yescharacteristic
662C2×#95C2311yescharacteristic
663C2×#95C2311yescharacteristic
664C22×Q8—24no—
665C22×Q8—24no—
666C22×Q8—24no—
667C22×Q8C2412yes—
668C22×Q8C2412yes—
669C22×Q8C2412yes—
670C22×Q8C2412yes—
671C22×Q8C2412yes—
672C22×D4C2414yes—
673C22×D4C2412yes—
674C22×D4C2412yes—
675C22×D4C2412yes—
676C23×C4C2411yescharacteristic
677C23×C4C2411yescharacteristic
678C23×C4C2411yescharacteristic
679C23×C4C2411yescharacteristic
680C23×C4C2411yescharacteristic
681C23×C4C2411yescharacteristic
682C23×C4C2411yescharacteristic
683C23×C4C2411yescharacteristic
684C23×C4C2414yes—
685C23×C4C2414yes—
686C23×C4C2414yes—
687C23×C4C2411yescharacteristic
688C23×C4C2411yescharacteristic
689C23×C4C2411yescharacteristic
690C23×C4C2411yescharacteristic
691C23×C4C2411yescharacteristic
692C23×C4C2411yescharacteristic
693C23×C4C2411yescharacteristic
694#126—216no—
695#126—216no—
696#126—216no—
697#126—84no—
698#125—216no—
699#125—28no—
700#125—28no—
701#125—82no—
702#124—28no—
703#124—28no—
704#124—82no—
705#123—216no—
706#123—216no—
707#123—216no—
708#123—216no—
709C22⋊Q8—28no—
710C22⋊Q8—28no—
711C22⋊Q8—28no—
712C22⋊Q8—216no—
713#121—28no—
714#121—28no—
715#121—28no—
716C4×Q8—216no—
717C4×Q8—216no—
718C4×Q8—28no—
719C4×Q8—28no—
720C4×Q8—216no—
721C4×Q8—216no—
722C4×Q8—28no—
723C4×Q8—28no—
724C4×Q8—28no—
725C4×Q8—28no—
726C4×Q8—82no—
727C4×Q8—82no—
728C4×Q8—82no—
729C4×D4—216no—
730C4×D4—216no—
731C4×D4—216no—
732C4×D4—28no—
733C4×D4—28no—
734C4×D4—82no—
735C4×D4—82no—
736C4×D4—82no—
737#117—216no—
738#117—216no—
739#117—84no—
740C2×C4⋊C4—24no—
741C2×C4⋊C4—24no—
742C2×C4⋊C4—24no—
743C2×C4⋊C4—24no—
744C2×C4⋊C4—24no—
745C2×C4⋊C4—24no—
746C2×C4⋊C4—24no—
747C2×C4⋊C4—24no—
748C2×C4⋊C4#4118yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C42—24no—
835C2×C42—24no—
836C2×C42—24no—
837C2×C42—24no—
838C2×C42—24no—
839C2×C42—24no—
840C2×C42—24no—
841C2×C42—81no—
842C2×C42—81no—
843C2×C42—81no—
844C2×C42—81no—
845C2×C42—81no—
846C2×C42—81no—
847C2×C42#4118yes—
848C2×C42#4118yes—
849C2×C42C2414yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2412yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2412yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2414yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2412yes—
879C2×C42C2412yes—
880C2×C42C2412yes—
881C2×C42C2412yes—
882#95C2412yes—
883#95C2414yes—
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2414yes—
889#95C2414yes—
890#95C2412yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2412yes—
895#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944C24C2514yes—
945C24C2511yescharacteristic
946C2×Q8—232no—
947C2×Q8—24no—
948C2×Q8—24no—
949C2×Q8—24no—
950C2×Q8—24no—
951C2×Q8—24no—
952C2×Q8—24no—
953C2×Q8—24no—
954C2×Q8—24no—
955C2×Q8—24no—
956C2×Q8—42no—
957C2×Q8—42no—
958C2×Q8—42no—
959C2×Q8—42no—
960C2×Q8—42no—
961C2×Q8—42no—
962C2×D4—28no—
963C2×D4—28no—
964C2×D4—28no—
965C2×D4—24no—
966C2×D4—24no—
967C2×D4—24no—
968C2×D4—42no—
969C2×D4—42no—
970C2×D4—42no—
971C2×D4—42no—
972C2×D4—42no—
973C2×D4—42no—
974C22×C4—22no—
975C22×C4—22no—
976C22×C4—22no—
977C22×C4—22no—
978C22×C4—22no—
979C22×C4—22no—
980C22×C4—22no—
981C22×C4—22no—
982C22×C4—22no—
983C22×C4—22no—
984C22×C4—22no—
985C22×C4—22no—
986C22×C4—28no—
987C22×C4—28no—
988C22×C4—28no—
989C22×C4—41no—
990C22×C4—41no—
991C22×C4—41no—
992C22×C4—41no—
993C22×C4—41no—
994C22×C4—41no—
995C22×C4—41no—
996C22×C4—41no—
997C22×C4—41no—
998C22×C4—41no—
999C22×C4—41no—
1000C22×C4—41no—
1001C22×C4—41no—
1002C22×C4—41no—
1003C22×C4—41no—
1004C22×C4—41no—
1005C22×C4—41no—
1006C22×C4—41no—
1007C22×C4—41no—
1008C22×C4—41no—
1009C22×C4—41no—
1010C22×C4—41no—
1011C22×C4—41no—
1012C22×C4—41no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4C2×#4114yes—
1020C22×C4C2×#4114yes—
1021C22×C4C2×#4114yes—
1022C22×C4C2×#4114yes—
1023C22×C4C2×#4114yes—
1024C22×C4C2×#4114yes—
1025C22×C4C2×#4114yes—
1026C22×C4C2×#4114yes—
1027C22×C4C2×#4114yes—
1028C22×C4C2512yes—
1029C22×C4C2514yes—
1030C22×C4C2514yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2511yescharacteristic
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2511yescharacteristic
1039C22×C4C2514yes—
1040C22×C4C2514yes—
1041C22×C4C2514yes—
1042C22×C4C2512yes—
1043C22×C4C2511yescharacteristic
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2511yescharacteristic
1049C22×C4C2511yescharacteristic
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2511yescharacteristic
1053C4⋊C4—24no—
1054C4⋊C4—22no—
1055C4⋊C4—22no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—28no—
1059C4⋊C4—24no—
1060C4⋊C4—22no—
1061C4⋊C4—22no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—28no—
1069C4⋊C4—28no—
1070C4⋊C4—28no—
1071C4⋊C4—28no—
1072C4⋊C4—28no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—28no—
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—24no—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—24no—
1085C4⋊C4—28no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4C2×#41116yes—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—28no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C42—28no—
1139C42—24no—
1140C42—24no—
1141C42—28no—
1142C42—28no—
1143C42—24no—
1144C42—24no—
1145C42—24no—
1146C42—24no—
1147C42—28no—
1148C42—28no—
1149C42—28no—
1150C42—28no—
1151C42—44no—
1152C42—42no—
1153C42—42no—
1154C42—42no—
1155C42—42no—
1156C42—42no—
1157C42—42no—
1158C42—42no—
1159C42—42no—
1160C42—44no—
1161C42—44no—
1162C42—44no—
1163C42—44no—
1164C42—44no—
1165C42—44no—
1166C42—44no—
1167C42C2×#4118yes—
1168C42C2×#4118yes—
1169C42C2×#4118yes—
1170C42C2×#4118yes—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—24no—
1176C23—24no—
1177C23—24no—
1178C23—24no—
1179C23—24no—
1180C23—24no—
1181C23—24no—
1182C23C22×#4112yes—
1183C23C22×#4112yes—
1184C23C22×#4112yes—
1185C23C2611yescharacteristic
1186Q8—216no—
1187Q8—216no—
1188Q8—48no—
1189Q8—84no—
1190Q8—84no—
1191D4—48no—
1192D4—416no—
1193D4—84no—
1194D4—84no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—22no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—21no—
1217C2×C4—28no—
1218C2×C4—28no—
1219C2×C4—28no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—21no—
1225C2×C4—22no—
1226C2×C4—21no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—21no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—21no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—21no—
1262C2×C4—44no—
1263C2×C4—44no—
1264C2×C4—44no—
1265C2×C4—44no—
1266C2×C4—44no—
1267C2×C4—44no—
1268C2×C4—44no—
1269C2×C4—44no—
1270C2×C4—44no—
1271C2×C4—44no—
1272C2×C4—44no—
1273C2×C4—44no—
1274C2×C4—88no—
1275C2×C4—88no—
1276C2×C4—88no—
1277C2×C4C22×#4114yes—
1278C2×C4C22×#4114yes—
1279C2×C4C22×#4112yes—
1280C2×C4C22×#4114yes—
1281C2×C4C22×#4114yes—
1282C2×C4C22×#4114yes—
1283C2×C4C22×#4112yes—
1284C2×C4C22×#4112yes—
1285C2×C4C22×#4112yes—
1286C2×C4C22×#4114yes—
1287C2×C4C22×#4114yes—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—44no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—44no—
1299C22—44no—
1300C22—44no—
1301C22#344414yes—
1302C22C23×#4111yescharacteristic
1303C22C23×#4111yescharacteristic
1304C22C23×#4111yescharacteristic
1305C22H(7,𝔽2)11yescharacteristic
1306C222−1+611yescharacteristic
1307C222−1+611yescharacteristic
1308C222−1+611yescharacteristic
1309C4—24no—
1310C4—24no—
1311C4—24no—
1312C4—22no—
1313C4—22no—
1314C4—24no—
1315C4—24no—
1316C4—24no—
1317C4—24no—
1318C4—22no—
1319C4—22no—
1320C4—42no—
1321C4—42no—
1322C4—44no—
1323C4—42no—
1324C4—44no—
1325C4—44no—
1326C4—42no—
1327C4—41no—
1328C4—42no—
1329C4—41no—
1330C4—44no—
1331C4—44no—
1332C4—44no—
1333C4—44no—
1334C2—24no—
1335C2—84no—
1336C2C2×#344411yescharacteristic
1337C2#6284511yescharacteristic
1338C2#6284711yescharacteristic
1339C2#6285011yescharacteristic
1340C2#6285611yescharacteristic
1341C2#6286011yescharacteristic
1342C2#6286011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2656C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36038C2semidirect
2. #36027C2semidirect
3. #35835C2semidirect
4. #35829C2semidirect
5. #35820C2semidirect
6. #35814C2semidirect
7. #35746C2semidirect
8. #35735C2semidirect
9. #35120C2semidirect
11. #35111C2semidirect
12. #35099C2semidirect
13. #35098C2semidirect
14. #35092C2semidirect
15. #35042C2semidirect
16. #35024C2semidirect
17. #35021C2semidirect
18. #35013C2semidirect
20. #34602C2semidirect
21. #34595C2semidirect
23. #34584C2semidirect
24. #34278C2semidirect
25. #34224C2semidirect
26. #34219C2semidirect
27. C2×#2276C2semidirect

Maximal subgroups

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

subgroupindex
#360382
#360272
#358352
#358292
#358202
#358142
#357462
#357352
#351202
#351192
#351112
#350992
#350982
#350922
#350422
#350242
#350212
#350132
#350042
#346022
#345952
#345942
#345842
#342782
#342242
#342192
C2×#22762