Finite Group Databasebeta

← #8347632

Subgroups — #8347632

Order 512.

5344 conjugacy classes of subgroups.

The subgroup lattice has 1280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59367C212yesmaximal, complemented
2#58226C214yesmaximal, complemented
3#55395C214yesmaximal, complemented
4#55192C214yesmaximal, complemented
5#54913C214yesmaximal, complemented
6#52414C212yesmaximal, complemented
7#49557C214yesmaximal, complemented
8#48008C214yesmaximal, complemented
9#45474C212yesmaximal, complemented
10#43891C212yesmaximal, complemented
11#43553C212yesmaximal, complemented
12#43085C212yesmaximal, complemented
13#42427C214yesmaximal, complemented
14#40923C214yesmaximal, complemented
15#40892C214yesmaximal, complemented
16#40491C212yesmaximal, complemented
17#39150C212yesmaximal, complemented
18#37715C214yesmaximal, complemented
19#36711C211yesmaximal, characteristic, complemented
20Q8×#120C212yesmaximal, complemented
21#35705C212yesmaximal, complemented
22#35394C211yesmaximal, characteristic
23C2×#2614C211yesmaximal, characteristic, complemented
24C24×Q8C2211yescharacteristic
25C2×D4×Q8C2212yes—
26C2×D4×Q8C2214yescomplemented
27C2×#544C2211yescharacteristic
28C2×#542C2214yes—
29C2×#538C2211yescharacteristic
30C22×#123C2211yescharacteristic
31C22×#123C2212yes—
32#2848C2214yes—
33#2848C2212yes—
34#2844C2212yescomplemented
35#2841C2212yescomplemented
36#2838C2214yescomplemented
37#2838C2214yescomplemented
38#2832C2214yescomplemented
39#2831C2214yescomplemented
40#2830C2212yescomplemented
41#2821C2212yescomplemented
42#2817C2214yescomplemented
43#2817C2212yescomplemented
44#2816C2212yescomplemented
45#2811C2212yescomplemented
46#2806C2214yescomplemented
47#2805C2214yescomplemented
48#2792C2214yescomplemented
49#2792C2212yescomplemented
50#2789C2212yescomplemented
51#2774C2214yescomplemented
52#2771C2212yescomplemented
53#2771C2212yescomplemented
54#2765C2214yescomplemented
55#2764C2212yescomplemented
56#2762C2214yescomplemented
57#2759C2214yescomplemented
58#2759C2214yescomplemented
59#2754C2214yescomplemented
60#2752C2212yescomplemented
61#2751C2214yescomplemented
62#2745C2214yescomplemented
63#2745C2214yescomplemented
64#2745C2214yescomplemented
65#2742C2214yescomplemented
66#2740C2214yescomplemented
67#2738C2214yescomplemented
68#2737C2214yescomplemented
69#2734C2214yescomplemented
70#2734C2214yescomplemented
71#2731C2214yescomplemented
72#2723C2214yescomplemented
73#2720C2214yescomplemented
74#2718C2214yes—
75#2717C2214yes—
76#2716C2214yescomplemented
77#2713C2214yescomplemented
78#2710C2214yes—
79#2705C2214yes—
80#2701C2214yes—
81#2700C2214yescomplemented
82#2700C2214yescomplemented
83#2698C2214yescomplemented
84#2694C2214yes—
85#2694C2214yes—
86#2692C2214yescomplemented
87#2689C2214yescomplemented
88#2689C2214yescomplemented
89#2689C2214yescomplemented
90#2689C2214yescomplemented
91#2687C2214yes—
92#2683C2212yescomplemented
93#2681C2214yescomplemented
94#2677C2214yescomplemented
95#2674C2214yes—
96#2674C2214yes—
97#2674C2214yes—
98#2674C2214yescomplemented
99#2674C2214yescomplemented
100#2672C2214yes—
101#2665C2214yescomplemented
102#2663C2214yes—
103#2663C2212yescomplemented
104#2663C2214yescomplemented
105#2653C2214yescomplemented
106#2650C2214yescomplemented
107#2643C2214yes—
108#2640C2212yescomplemented
109#2632C2212yescomplemented
110#2630C2214yes—
111#2628C2214yescomplemented
112#2626C2212yes—
113#2614C2214yes—
114#2614C2214yes—
115#2614C2214yes—
116#2614C2214yes—
117#2614C2212yescomplemented
118#2607C2214yescomplemented
119#2607C2212yescomplemented
120#2605C2214yescomplemented
121#2604C2212yescomplemented
122#2600C2212yescomplemented
123#2589C2214yescomplemented
124#2586C2214yescomplemented
125#2586C2212yescomplemented
126#2583C2212yes—
127#2581C2214yescomplemented
128#2575C2214yescomplemented
129#2574C2214yescomplemented
130#2573C2214yescomplemented
131#2567C2214yescomplemented
132#2564C2212yes—
133#2561C2211yescharacteristic
134#2557C2214yes—
135#2556C2214yescomplemented
136#2553C2214yes—
137#2551C2212yescomplemented
138#2551C2214yescomplemented
139#2549C2214yes—
140#2549C2212yes—
141#2539C2211yescharacteristic
142#2527C2214yescomplemented
143#2516C2214yescomplemented
144#2505C2214yes—
145#2504C2211yescharacteristic
146#2502C2211yescharacteristic
147#2493C2214yes—
148#2492C2214yescomplemented
149#2492C2214yescomplemented
150#2488C2214yes—
151#2482C2212yes—
152#2482C2212yes—
153#2481C2214yes—
154#2480C2214yes—
155#2477C2214yescomplemented
156#2472C2214yes—
157#2472C2214yes—
158#2470C2214yes—
159#2469C2214yescomplemented
160#2466C2214yescomplemented
161#2465C2214yescomplemented
162#2465C2214yescomplemented
163#2464C2214yes—
164#2462C2214yescomplemented
165#2461C2214yes—
166#2459C2214yescomplemented
167#2458C2214yes—
168#2451C2214yescomplemented
169#2449C2214yes—
170#2447C2214yescomplemented
171#2447C2214yescomplemented
172#2444C2214yes—
173#2440C2214yes—
174#2439C2214yescomplemented
175#2438C2214yes—
176#2437C2214yes—
177#2436C2212yescomplemented
178#2435C2212yes—
179#2434C2214yes—
180#2434C2212yes—
181#2434C2214yescomplemented
182#2434C2214yescomplemented
183#2434C2214yescomplemented
184#2434C2214yescomplemented
185#2422C2214yes—
186#2422C2214yes—
187#2418C2214yes—
188#2412C2212yes—
189#2410C2212yes—
190#2409C2212yes—
191#2409C2214yes—
192#2409C2214yescomplemented
193#2409C2214yescomplemented
194#2409C2214yescomplemented
195#2396C2214yescomplemented
196C2×#395C2212yes—
197C2×#395C2212yes—
198C2×#393C2212yes—
199C2×#393C2212yes—
200#2378C2214yescomplemented
201#2368C2214yes—
202#2368C2212yes—
203#2360C2214yes—
204#2359C2214yes—
205#2357C2214yescomplemented
206#2353C2212yes—
207#2342C2214yes—
208Q8×C22⋊C4C2212yes—
209Q8×C22⋊C4C2214yescomplemented
210#2335C2214yes—
211#2329C2214yes—
212#2322C2212yes—
213#2313C2211yescharacteristic
214C4×#120C2212yes—
215C4×#120C2214yes—
216C2×#381C2212yes—
217C2×#381C2211yescharacteristic
218#2273C2211yescharacteristic
219C23×Q8—44no—
220C23×Q8—48no—
221C23×Q8C2312yes—
222C23×Q8C2314yes—
223C23×Q8C2314yes—
224C23×Q8C2312yes—
225C23×Q8C2312yes—
226C23×D4C2311yescharacteristic
227C24×C4C2312yes—
228C24×C4C2311yescharacteristic
229D4×Q8—48no—
230D4×Q8—416no—
231#544—44no—
232#542—416no—
233#538—44no—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2314yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2314yes—
241C2×#126C2312yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#125C2314yes—
245C2×#124C2312yes—
246C2×#124C2314yes—
247C2×#124C2314yes—
248C2×#124C2314yes—
249C2×#123—44no—
250C2×#123—48no—
251C2×#123C2312yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×#123C2312yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2311yescharacteristic
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×#121C2312yes—
276C2×#121C2314yes—
277C2×#121C2311yescharacteristic
278C2×#120C2312yes—
279C2×#120C2312yes—
280C2×C4×Q8C2314yes—
281C2×C4×Q8C2314yes—
282C2×C4×Q8C2312yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2314yes—
288C2×#117C2314yes—
289C2×#117C2312yes—
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2314yes—
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2311yescharacteristic
295C22×C22⋊C4C2311yescharacteristic
296C22×C22⋊C4C2314yes—
297C22×C22⋊C4C2311yescharacteristic
298C22×C22⋊C4C2312yes—
299#401C2314yes—
300#401C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2312yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#399C2312yes—
318#399C2312yes—
319#399C2314yes—
320#399C2312yes—
321#399C2314yes—
322#399C2314yes—
323#399C2312yes—
324#399C2312yes—
325#399C2314yes—
326#399C2312yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2312yes—
331#398C2312yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#397C2312yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2312yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2312yes—
356#397C2314yes—
357#397C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#395C2312yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2312yes—
373#395C2312yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2312yes—
378#395C2314yes—
379#395C2312yes—
380#395C2314yes—
381#395C2314yes—
382#395C2312yes—
383#395C2314yes—
384#395C2312yes—
385#395C2314yes—
386#395C2312yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2312yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#393C2312yes—
408#393C2312yes—
409#393C2312yes—
410#393C2312yes—
411#393C2312yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2312yes—
419#393C2314yes—
420#393C2314yes—
421#393C2312yes—
422#393C2314yes—
423#393C2312yes—
424#393C2314yes—
425#393C2314yes—
426#393C2312yes—
427#393C2314yes—
428#393C2312yes—
429#392C2312yes—
430#392C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2312yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#390C2312yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#390C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
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#386C2314yes—
531#386C2312yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2312yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2312yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2312yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#384C2312yes—
567#384C2314yes—
568#383C2312yes—
569#383C2314yes—
570#382C2314yes—
571#382C2314yes—
572#382C2312yes—
573#381C2312yes—
574#381C2312yes—
575#381C2312yes—
576#381C2314yes—
577#381C2312yes—
578#381C2314yes—
579#381C2314yes—
580#381C2314yes—
581#381C2312yes—
582#381C2314yes—
583#381C2314yes—
584#381C2312yes—
585#381C2312yes—
586#380C2314yes—
587#380C2312yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#379C2312yes—
596#379C2314yes—
597#379C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C22⋊C4C2311yescharacteristic
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2312yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2311yescharacteristic
618#376C2312yes—
619C2×#95C2312yes—
620C2×#95C2312yes—
621C2×#95C2314yes—
622C2×#95C2314yes—
623C25C2411yescharacteristic
624C25C2411yescharacteristic
625C22×Q8—28no—
626C22×Q8—216no—
627C22×Q8—44no—
628C22×Q8—48no—
629C22×Q8—48no—
630C22×Q8—48no—
631C22×Q8—48no—
632C22×Q8—48no—
633C22×Q8—48no—
634C22×Q8—48no—
635C22×Q8—44no—
636C22×Q8—48no—
637C22×Q8—464no—
638C22×Q8C2412yes—
639C22×Q8C2414yes—
640C22×Q8C2412yes—
641C22×Q8C2414yes—
642C22×Q8C2414yes—
643C22×Q8C2412yes—
644C22×Q8C2412yes—
645C22×Q8C2414yes—
646C22×Q8C2412yes—
647C22×Q8C2411yescharacteristic
648C22×Q8C2412yes—
649C22×D4—42no—
650C22×D4—44no—
651C22×D4C2412yes—
652C22×D4C2414yes—
653C22×D4C2414yes—
654C22×D4C2412yes—
655C22×D4C2412yes—
656C22×D4C2411yescharacteristic
657C23×C4—24no—
658C23×C4—28no—
659C23×C4—44no—
660C23×C4—44no—
661C23×C4—44no—
662C23×C4C2411yescharacteristic
663C23×C4C2414yes—
664C23×C4C2414yes—
665C23×C4C2414yes—
666C23×C4C2411yescharacteristic
667C23×C4C2414yes—
668C23×C4C2411yescharacteristic
669C23×C4C2414yes—
670C23×C4C2411yescharacteristic
671C23×C4C2412yes—
672C23×C4C2414yes—
673C23×C4C2412yes—
674C23×C4C2411yescharacteristic
675C23×C4C2412yes—
676C4⋊Q8—48no—
677C4⋊Q8—44no—
678C4⋊Q8—48no—
679C4⋊Q8—48no—
680C4⋊Q8—48no—
681C4⋊Q8—48no—
682C4⋊Q8—48no—
683#126—44no—
684#126—48no—
685#126—48no—
686#125—48no—
687#124—44no—
688#124—48no—
689#124—48no—
690#124—48no—
691#123—216no—
692#123—28no—
693#123—48no—
694#123—48no—
695#123—48no—
696#123—48no—
697#123—44no—
698#123—48no—
699#123—48no—
700C22⋊Q8—216no—
701C22⋊Q8—28no—
702C22⋊Q8—216no—
703C22⋊Q8—42no—
704C22⋊Q8—44no—
705C22⋊Q8—48no—
706C22⋊Q8—48no—
707C22⋊Q8—48no—
708C22⋊Q8—48no—
709C22⋊Q8—48no—
710C22⋊Q8—48no—
711C22⋊Q8—48no—
712C22⋊Q8—48no—
713C22⋊Q8—48no—
714C22⋊Q8—44no—
715#121—44no—
716#121—48no—
717#121—42no—
718#120—28no—
719#120—44no—
720C4×Q8—48no—
721C4×Q8—48no—
722C4×Q8—44no—
723C4×D4—28no—
724C4×D4—216no—
725C4×D4—48no—
726C4×D4—48no—
727C4×D4—48no—
728#117—48no—
729#117—44no—
730C2×C4⋊C4—24no—
731C2×C4⋊C4—48no—
732C2×C4⋊C4—42no—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C22⋊C4—24no—
780C2×C22⋊C4—28no—
781C2×C22⋊C4—48no—
782C2×C22⋊C4—44no—
783C2×C22⋊C4—42no—
784C2×C22⋊C4—42no—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
828C2×C42C2414yes—
829C2×C42C2412yes—
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2414yes—
836C2×C42C2414yes—
837C2×C42C2414yes—
838C2×C42C2412yes—
839C2×C42C2412yes—
840C2×C42C2414yes—
841#95C2412yes—
842#95C2414yes—
843#95C2412yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2412yes—
851#95C2414yes—
852#95C2412yes—
853#95C2414yes—
854#95C2414yes—
855#95C2412yes—
856#95C2414yes—
857#95C2414yes—
858#95C2412yes—
859#95C2412yes—
860#95C2414yes—
861#95C2414yes—
862#95C2412yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2412yes—
876#95C2412yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2412yes—
893#95C2414yes—
894#95C2414yes—
895#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901C24—24no—
902C24—22no—
903C24—24no—
904C24—22no—
905C24—24no—
906C24—42no—
907C24—42no—
908C24—42no—
909C24C2512yes—
910C24C2512yes—
911C24C2512yes—
912C24C2511yescharacteristic
913C2×Q8—24no—
914C2×Q8—28no—
915C2×Q8—28no—
916C2×Q8—28no—
917C2×Q8—28no—
918C2×Q8—24no—
919C2×Q8—28no—
920C2×Q8—28no—
921C2×Q8—24no—
922C2×Q8—28no—
923C2×Q8—42no—
924C2×Q8—44no—
925C2×Q8—44no—
926C2×Q8—44no—
927C2×Q8—44no—
928C2×Q8—42no—
929C2×Q8—44no—
930C2×Q8—44no—
931C2×Q8—44no—
932C2×Q8—44no—
933C2×Q8—44no—
934C2×Q8—44no—
935C2×Q8—41no—
936C2×Q8—44no—
937C2×Q8—42no—
938C2×Q8—42no—
939C2×Q8—432no—
940C2×Q8—464no—
941C2×Q8—432no—
942C2×Q8—464no—
943C2×Q8—816no—
944C2×D4—24no—
945C2×D4—28no—
946C2×D4—24no—
947C2×D4—24no—
948C2×D4—28no—
949C2×D4—28no—
950C2×D4—44no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—42no—
954C2×D4—42no—
955C2×D4—41no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—42no—
959C2×D4—88no—
960C22×C4—22no—
961C22×C4—22no—
962C22×C4—28no—
963C22×C4—28no—
964C22×C4—28no—
965C22×C4—24no—
966C22×C4—24no—
967C22×C4—22no—
968C22×C4—22no—
969C22×C4—28no—
970C22×C4—28no—
971C22×C4—28no—
972C22×C4—28no—
973C22×C4—24no—
974C22×C4—28no—
975C22×C4—28no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—44no—
986C22×C4—42no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—42no—
994C22×C4—416no—
995C22×C4—432no—
996C22×C4H(5,𝔽2)14yes—
997C22×C4H(5,𝔽2)18yes—
998C22×C4C2512yes—
999C22×C4C2512yes—
1000C22×C4C2514yes—
1001C22×C4C2514yes—
1002C22×C4C2512yes—
1003C22×C4C2514yes—
1004C22×C4C2514yes—
1005C22×C4C2511yescharacteristic
1006C22×C4C2511yescharacteristic
1007C22×C4C2514yes—
1008C22×C4C2514yes—
1009C22×C4C2512yes—
1010C22×C4C2514yes—
1011C22×C4C2514yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—24no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—24no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—42no—
1041C4⋊C4—44no—
1042C4⋊C4—42no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—42no—
1051C4⋊C4—41no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—41no—
1060C4⋊C4—42no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—24no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—28no—
1069C22⋊C4—24no—
1070C22⋊C4—28no—
1071C22⋊C4—24no—
1072C22⋊C4—24no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—24no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—44no—
1083C22⋊C4—42no—
1084C22⋊C4—44no—
1085C22⋊C4—42no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—44no—
1101C22⋊C4—42no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C42−1+418yes—
1106C42—28no—
1107C42—24no—
1108C42—42no—
1109C42—44no—
1110C42—44no—
1111C42—42no—
1112C42—44no—
1113C42—44no—
1114C42—44no—
1115C42—44no—
1116C42—44no—
1117C42—44no—
1118C42—44no—
1119C23—22no—
1120C23—22no—
1121C23—28no—
1122C23—22no—
1123C23—22no—
1124C23—24no—
1125C23—24no—
1126C23—24no—
1127C23—22no—
1128C23—24no—
1129C23—22no—
1130C23—22no—
1131C23—22no—
1132C23—22no—
1133C23—22no—
1134C23—24no—
1135C23—24no—
1136C23—416no—
1137C23—44no—
1138C23—44no—
1139C23—44no—
1140C23—82no—
1141C23—82no—
1142C23—88no—
1143C23C2×H(5,𝔽2)14yes—
1144C23C2×H(5,𝔽2)12yes—
1145C23C2×2−1+414yes—
1146C23C2611yescharacteristic
1147Q8—216no—
1148Q8—48no—
1149Q8—416no—
1150Q8—416no—
1151Q8—48no—
1152Q8—48no—
1153Q8—88no—
1154Q8—88no—
1155Q8—84no—
1156Q8—162no—
1157Q8—161no—
1158D4—416no—
1159D4—48no—
1160D4—88no—
1161D4—162no—
1162D4—161no—
1163D4—162no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—22no—
1185C2×C4—24no—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—44no—
1211C2×C4—48no—
1212C2×C4—416no—
1213C2×C4—416no—
1214C2×C4—416no—
1215C2×C4—44no—
1216C2×C4—48no—
1217C2×C4—44no—
1218C2×C4—88no—
1219C2×C4—84no—
1220C2×C4—88no—
1221C2×C4—82no—
1222C2×C4—88no—
1223C2×C4—82no—
1224C2×C4C2×H(5,𝔽2)14yes—
1225C2×C4C2×H(5,𝔽2)18yes—
1226C2×C4C2×2−1+418yes—
1227C22—22no—
1228C22—22no—
1229C22—28no—
1230C22—24no—
1231C22—28no—
1232C22—416no—
1233C22—42no—
1234C22—42no—
1235C22—44no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—164no—
1247C22#355014yes—
1248C22C22×H(5,𝔽2)11yescharacteristic
1249C22C22×H(5,𝔽2)12yes—
1250C22C22×2−1+412yes—
1251C222−1+612yes—
1252C4—28no—
1253C4—24no—
1254C4—28no—
1255C4—42no—
1256C4—42no—
1257C4—42no—
1258C4—44no—
1259C4—42no—
1260C4—42no—
1261C4—44no—
1262C4—44no—
1263C4—41no—
1264C4—41no—
1265C4—42no—
1266C4—44no—
1267C4—44no—
1268C4—44no—
1269C4—44no—
1270C4—44no—
1271C2—24no—
1272C2—44no—
1273C2—82no—
1274C2—82no—
1275C2C2×#355011yescharacteristic
1276C2#6281711yescharacteristic
1277C2#6288711yescharacteristic
1278C2#6294214yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35394C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59367C2semidirect
2. #58226C2semidirect
3. #55395C2semidirect
4. #55192C2semidirect
5. #54913C2semidirect
6. #52414C2semidirect
7. #49557C2semidirect
8. #48008C2semidirect
9. #45474C2semidirect
10. #43891C2semidirect
11. #43553C2semidirect
12. #43085C2semidirect
13. #42427C2semidirect
14. #40923C2semidirect
15. #40892C2semidirect
16. #40491C2semidirect
17. #39150C2semidirect
18. #37715C2semidirect
19. #36711C2semidirect
20. Q8×#120C2semidirect
21. #35705C2semidirect
23. C2×#2614C2semidirect
26. C2×D4×Q8C22semidirect
34. #2844C22semidirect
35. #2841C22semidirect
36. #2838C22semidirect
37. #2838C22semidirect
38. #2832C22semidirect
39. #2831C22semidirect
40. #2830C22semidirect
41. #2821C22semidirect
42. #2817C22semidirect
43. #2817C22semidirect
44. #2816C22semidirect
45. #2811C22semidirect
46. #2806C22semidirect
47. #2805C22semidirect
48. #2792C22semidirect
49. #2792C22semidirect
50. #2789C22semidirect
51. #2774C22semidirect
52. #2771C22semidirect
53. #2771C22semidirect
54. #2765C22semidirect
55. #2764C22semidirect
56. #2762C22semidirect
57. #2759C22semidirect
58. #2759C22semidirect
59. #2754C22semidirect
60. #2752C22semidirect
61. #2751C22semidirect
62. #2745C22semidirect
63. #2745C22semidirect
64. #2745C22semidirect
65. #2742C22semidirect
66. #2740C22semidirect
67. #2738C22semidirect
68. #2737C22semidirect
69. #2734C22semidirect
70. #2734C22semidirect
71. #2731C22semidirect
72. #2723C22semidirect
73. #2720C22semidirect
76. #2716C22semidirect
77. #2713C22semidirect
81. #2700C22semidirect
82. #2700C22semidirect
83. #2698C22semidirect
86. #2692C22semidirect
87. #2689C22semidirect
88. #2689C22semidirect
89. #2689C22semidirect
90. #2689C22semidirect
92. #2683C22semidirect
93. #2681C22semidirect
94. #2677C22semidirect
98. #2674C22semidirect
99. #2674C22semidirect
101. #2665C22semidirect
103. #2663C22semidirect
104. #2663C22semidirect
105. #2653C22semidirect
106. #2650C22semidirect
108. #2640C22semidirect
109. #2632C22semidirect
111. #2628C22semidirect
117. #2614C22semidirect
118. #2607C22semidirect
119. #2607C22semidirect
120. #2605C22semidirect
121. #2604C22semidirect
122. #2600C22semidirect
123. #2589C22semidirect
124. #2586C22semidirect
125. #2586C22semidirect
127. #2581C22semidirect
128. #2575C22semidirect
129. #2574C22semidirect
130. #2573C22semidirect
131. #2567C22semidirect
135. #2556C22semidirect
137. #2551C22semidirect
138. #2551C22semidirect
142. #2527C22semidirect
143. #2516C22semidirect
148. #2492C22semidirect
149. #2492C22semidirect
155. #2477C22semidirect
159. #2469C22semidirect
160. #2466C22semidirect
161. #2465C22semidirect
162. #2465C22semidirect
164. #2462C22semidirect
166. #2459C22semidirect
168. #2451C22semidirect
170. #2447C22semidirect
171. #2447C22semidirect
174. #2439C22semidirect
177. #2436C22semidirect
181. #2434C22semidirect
182. #2434C22semidirect
183. #2434C22semidirect
184. #2434C22semidirect
192. #2409C22semidirect
193. #2409C22semidirect
194. #2409C22semidirect
195. #2396C22semidirect
200. #2378C22semidirect
205. #2357C22semidirect
209. Q8×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#593672
#582262
#553952
#551922
#549132
#524142
#495572
#480082
#454742
#438912
#435532
#430852
#424272
#409232
#408922
#404912
#391502
#377152
#367112
Q8×#1202
#357052
#353942
C2×#26142