Finite Group Databasebeta

← #8391313

Subgroups — #8391313

Order 512.

5404 conjugacy classes of subgroups.

The subgroup lattice has 1274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59624C212yesmaximal
2#59151C212yesmaximal, complemented
3#57212C214yesmaximal, complemented
4#57150C214yesmaximal, complemented
5#51358C214yesmaximal, complemented
6#51076C214yesmaximal, complemented
7#50090C214yesmaximal, complemented
8#47945C214yesmaximal, complemented
9#46325C212yesmaximal, complemented
10#45744C212yesmaximal, complemented
11#44934C214yesmaximal, complemented
12#43891C212yesmaximal, complemented
13#43426C214yesmaximal, complemented
14#43085C212yesmaximal, complemented
15#40495C212yesmaximal, complemented
16#38598C214yesmaximal, complemented
17#38511C214yesmaximal, complemented
18#36708C211yesmaximal, characteristic, complemented
19Q8×#120C212yesmaximal, complemented
20#36531C212yesmaximal, complemented
21#35743C212yesmaximal, complemented
22#35397C211yesmaximal, characteristic
23C2×#2434C211yesmaximal, characteristic, complemented
24C24×Q8C2211yescharacteristic
25C2×#563C2212yescomplemented
26C2×Q82C2212yescomplemented
27C2×D4×Q8C2212yes—
28C2×D4×Q8C2214yes—
29C2×#544C2211yescharacteristic
30C2×#539C2211yescharacteristic
31C22×C4⋊Q8C2212yes—
32C22×C22⋊Q8C2211yescharacteristic
33#2852C2214yes—
34#2848C2212yes—
35#2848C2214yes—
36#2835C2212yes—
37#2834C2212yes—
38#2821C2212yescomplemented
39#2821C2214yescomplemented
40#2817C2212yescomplemented
41#2807C2212yes—
42#2805C2214yescomplemented
43#2799C2214yescomplemented
44#2796C2214yes—
45#2796C2214yes—
46#2790C2214yes—
47#2787C2214yes—
48#2774C2214yescomplemented
49#2770C2214yes—
50#2770C2214yes—
51#2763C2214yes—
52#2762C2214yescomplemented
53#2762C2214yescomplemented
54#2759C2214yescomplemented
55#2759C2214yescomplemented
56#2758C2214yescomplemented
57#2757C2214yes—
58#2734C2212yescomplemented
59#2734C2214yescomplemented
60#2734C2212yescomplemented
61#2734C2214yescomplemented
62#2734C2212yescomplemented
63#2731C2212yescomplemented
64#2729C2214yes—
65#2729C2214yes—
66#2729C2214yescomplemented
67#2729C2214yescomplemented
68#2723C2214yes—
69#2722C2212yes—
70#2720C2214yes—
71#2720C2214yescomplemented
72#2716C2214yescomplemented
73#2716C2214yescomplemented
74#2715C2214yes—
75#2713C2214yescomplemented
76#2713C2214yescomplemented
77#2713C2214yescomplemented
78#2712C2212yes—
79#2698C2214yescomplemented
80#2698C2214yescomplemented
81#2690C2214yes—
82#2690C2214yes—
83#2690C2214yes—
84#2689C2214yescomplemented
85#2680C2214yescomplemented
86#2677C2214yes—
87#2677C2214yes—
88#2677C2212yes—
89#2677C2214yescomplemented
90#2677C2214yescomplemented
91#2677C2214yescomplemented
92#2674C2214yescomplemented
93#2666C2214yescomplemented
94#2666C2214yescomplemented
95#2663C2212yescomplemented
96#2660C2212yescomplemented
97#2652C2214yes—
98#2650C2214yescomplemented
99#2638C2214yes—
100#2634C2212yescomplemented
101#2627C2212yes—
102#2614C2212yescomplemented
103#2605C2214yescomplemented
104#2605C2214yescomplemented
105#2604C2212yescomplemented
106#2602C2214yes—
107#2595C2214yes—
108#2589C2214yes—
109#2588C2214yescomplemented
110#2586C2214yescomplemented
111#2581C2214yescomplemented
112#2580C2214yes—
113#2577C2214yes—
114#2567C2214yescomplemented
115#2564C2212yes—
116#2561C2211yescharacteristic
117#2561C2212yes—
118#2560C2214yes—
119#2560C2214yes—
120#2556C2214yes—
121#2556C2214yescomplemented
122#2551C2214yescomplemented
123#2551C2214yescomplemented
124#2551C2214yescomplemented
125#2550C2214yescomplemented
126#2549C2212yes—
127#2539C2211yescharacteristic
128#2532C2214yescomplemented
129#2530C2214yes—
130#2523C2214yes—
131#2521C2214yes—
132#2520C2214yescomplemented
133#2517C2212yes—
134#2493C2214yes—
135#2488C2214yes—
136#2488C2214yes—
137#2484C2212yes—
138#2482C2212yes—
139#2481C2214yes—
140#2480C2214yes—
141#2473C2214yes—
142#2472C2214yes—
143#2469C2214yescomplemented
144#2468C2214yes—
145#2466C2214yes—
146#2465C2214yes—
147#2465C2214yes—
148#2465C2214yescomplemented
149#2465C2214yescomplemented
150#2462C2214yescomplemented
151#2462C2214yescomplemented
152#2461C2214yes—
153#2455C2212yes—
154#2452C2214yes—
155#2452C2214yes—
156#2451C2214yescomplemented
157#2451C2214yescomplemented
158#2451C2214yescomplemented
159#2451C2214yescomplemented
160#2449C2214yes—
161#2443C2214yes—
162#2440C2214yes—
163#2440C2214yes—
164#2438C2214yes—
165#2438C2214yes—
166#2436C2211yescharacteristic
167#2434C2211yescharacteristic
168#2434C2212yes—
169#2434C2214yes—
170#2434C2214yes—
171#2434C2214yes—
172#2434C2214yes—
173#2434C2212yes—
174#2434C2214yes—
175#2434C2214yes—
176#2434C2214yes—
177#2434C2214yes—
178#2434C2212yescomplemented
179#2434C2214yescomplemented
180#2419C2214yes—
181#2413C2212yes—
182#2411C2212yes—
183#2409C2212yes—
184#2409C2214yes—
185#2409C2214yes—
186#2409C2214yes—
187#2409C2214yes—
188#2399C2214yescomplemented
189C2×#395C2212yes—
190C2×#395C2212yes—
191#2383C2214yes—
192#2381C2212yescomplemented
193#2373C2214yes—
194#2369C2212yescomplemented
195#2368C2212yes—
196#2367C2214yes—
197#2367C2214yes—
198#2360C2214yes—
199#2360C2214yes—
200#2359C2214yes—
201#2353C2212yes—
202#2343C2214yes—
203Q8×C22⋊C4C2212yes—
204Q8×C22⋊C4C2214yes—
205#2334C2214yes—
206#2332C2214yescomplemented
207#2331C2214yescomplemented
208#2326C2214yes—
209#2322C2212yes—
210#2313C2211yescharacteristic
211C4×C22⋊Q8C2214yes—
212C4×#120C2212yes—
213C4×#120C2214yes—
214C2×#391C2212yes—
215C2×#385C2212yes—
216C2×#385C2212yes—
217#2274C2211yescharacteristic
218C2×C4×C22⋊C4C2211yescharacteristic
219C23×Q8—44no—
220C23×Q8—48no—
221C23×Q8C2312yes—
222C23×Q8C2314yes—
223C23×Q8C2312yes—
224C23×Q8C2314yes—
225C23×Q8C2312yes—
226C23×Q8C2311yescharacteristic
227C24×C4C2311yescharacteristic
228C24×C4C2312yes—
229#563—48no—
230Q82—48no—
231D4×Q8—48no—
232D4×Q8—416no—
233#544—44no—
234#539—44no—
235C2×C4⋊Q8—48no—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2314yes—
243C2×C4⋊Q8C2314yes—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2314yes—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2314yes—
248C2×C4⋊Q8C2314yes—
249C2×C4⋊Q8C2314yes—
250C2×C4⋊Q8C2314yes—
251C2×C4⋊Q8C2312yes—
252C2×C4⋊Q8C2314yes—
253C2×#126C2314yes—
254C2×#126C2312yes—
255C2×#126C2314yes—
256C2×#126C2314yes—
257C2×#125C2312yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#124C2314yes—
261C2×#124C2312yes—
262C2×#123C2312yes—
263C2×#123C2314yes—
264C2×#123C2312yes—
265C2×#123C2312yes—
266C2×C22⋊Q8—44no—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2311yescharacteristic
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×#121C2311yescharacteristic
285C2×#120C2312yes—
286C2×C4×Q8C2314yes—
287C2×C4×Q8C2314yes—
288C2×C4×Q8C2314yes—
289C2×C4×Q8C2314yes—
290C2×C4×Q8C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×#117C2312yes—
297C2×#117C2312yes—
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2311yescharacteristic
300C22×C4⋊C4C2314yes—
301C22×C4⋊C4C2314yes—
302C22×C4⋊C4C2311yescharacteristic
303C22×C22⋊C4C2312yes—
304C22×C22⋊C4C2311yescharacteristic
305C22×C22⋊C4C2311yescharacteristic
306C22×C42C2312yes—
307#401C2314yes—
308#400C2312yes—
309#400C2312yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2312yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#399C2312yes—
326#399C2314yes—
327#399C2314yes—
328#399C2312yes—
329#399C2312yes—
330#399C2312yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
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#397C2312yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2312yes—
360#397C2314yes—
361#397C2314yes—
362#397C2312yes—
363#397C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#395C2312yes—
370#395C2314yes—
371#395C2312yes—
372#395C2312yes—
373#395C2312yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2312yes—
381#395C2314yes—
382#395C2312yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2312yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2312yes—
391#395C2312yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#393C2312yes—
408#393C2314yes—
409#393C2312yes—
410#393C2314yes—
411#393C2314yes—
412#393C2312yes—
413#393C2314yes—
414#393C2314yes—
415#393C2312yes—
416#393C2314yes—
417#393C2314yes—
418#392C2312yes—
419#391C2312yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#390C2314yes—
446#390C2314yes—
447#390C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
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#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
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#386C2314yes—
532#386C2314yes—
533#386C2312yes—
534#386C2314yes—
535#386C2312yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2312yes—
542#385C2314yes—
543#385C2312yes—
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#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2312yes—
566#385C2314yes—
567#385C2312yes—
568#385C2312yes—
569#385C2312yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#384C2314yes—
574#384C2314yes—
575#383C2314yes—
576#383C2312yes—
577#383C2314yes—
578#383C2314yes—
579#382C2314yes—
580#382C2314yes—
581#382C2314yes—
582#381C2312yes—
583#381C2314yes—
584#381C2312yes—
585#381C2312yes—
586#381C2314yes—
587#380C2314yes—
588#380C2312yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#379C2312yes—
594#379C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2311yescharacteristic
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2311yescharacteristic
618C4×C22⋊C4C2314yes—
619#376C2314yes—
620#376C2312yes—
621C2×#95C2312yes—
622C2×#95C2314yes—
623C2×#95C2314yes—
624C25C2411yescharacteristic
625C22×Q8—28no—
626C22×Q8—216no—
627C22×Q8—28no—
628C22×Q8—44no—
629C22×Q8—42no—
630C22×Q8—44no—
631C22×Q8—48no—
632C22×Q8—48no—
633C22×Q8—48no—
634C22×Q8—48no—
635C22×Q8—48no—
636C22×Q8—48no—
637C22×Q8—44no—
638C22×Q8—44no—
639C22×Q8—48no—
640C22×Q8—464no—
641C22×Q8C2412yes—
642C22×Q8C2414yes—
643C22×Q8C2414yes—
644C22×Q8C2414yes—
645C22×Q8C2412yes—
646C22×Q8C2414yes—
647C22×Q8C2412yes—
648C22×Q8C2412yes—
649C22×Q8C2412yes—
650C22×Q8C2412yes—
651C22×Q8C2411yescharacteristic
652C22×Q8C2412yes—
653C22×Q8C2412yes—
654C22×D4C2412yes—
655C22×D4C2414yes—
656C22×D4C2411yescharacteristic
657C23×C4—24no—
658C23×C4—44no—
659C23×C4—48no—
660C23×C4—44no—
661C23×C4C2411yescharacteristic
662C23×C4C2411yescharacteristic
663C23×C4C2411yescharacteristic
664C23×C4C2414yes—
665C23×C4C2414yes—
666C23×C4C2412yes—
667C23×C4C2414yes—
668C23×C4C2411yescharacteristic
669C23×C4C2411yescharacteristic
670C23×C4C2412yes—
671C23×C4C2414yes—
672C23×C4C2414yes—
673C23×C4C2412yes—
674C23×C4C2411yescharacteristic
675C4⋊Q8—28no—
676C4⋊Q8—28no—
677C4⋊Q8—216no—
678C4⋊Q8—44no—
679C4⋊Q8—44no—
680C4⋊Q8—44no—
681C4⋊Q8—48no—
682C4⋊Q8—48no—
683C4⋊Q8—48no—
684C4⋊Q8—48no—
685C4⋊Q8—48no—
686C4⋊Q8—48no—
687C4⋊Q8—48no—
688C4⋊Q8—48no—
689C4⋊Q8—44no—
690C4⋊Q8—44no—
691C4⋊Q8—44no—
692#126—216no—
693#126—44no—
694#126—48no—
695#126—48no—
696#125—44no—
697#125—48no—
698#125—48no—
699#124—216no—
700#124—44no—
701#123—28no—
702#123—44no—
703#123—48no—
704#123—44no—
705C22⋊Q8—216no—
706C22⋊Q8—28no—
707C22⋊Q8—216no—
708C22⋊Q8—42no—
709C22⋊Q8—44no—
710C22⋊Q8—48no—
711C22⋊Q8—48no—
712C22⋊Q8—48no—
713C22⋊Q8—48no—
714C22⋊Q8—48no—
715C22⋊Q8—48no—
716C22⋊Q8—44no—
717C22⋊Q8—48no—
718C22⋊Q8—48no—
719C22⋊Q8—48no—
720C22⋊Q8—44no—
721C22⋊Q8—48no—
722#121—42no—
723#120—28no—
724C4×Q8—48no—
725C4×Q8—48no—
726C4×Q8—48no—
727C4×Q8—44no—
728C4×Q8—48no—
729C4×D4—28no—
730C4×D4—48no—
731C4×D4—48no—
732C4×D4—48no—
733C4×D4—48no—
734#117—28no—
735#117—44no—
736C2×C4⋊C4—24no—
737C2×C4⋊C4—24no—
738C2×C4⋊C4—48no—
739C2×C4⋊C4—48no—
740C2×C4⋊C4—42no—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C22⋊C4—28no—
796C2×C22⋊C4—42no—
797C2×C22⋊C4—42no—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C42—44no—
831C2×C42C2414yes—
832C2×C42C2414yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2414yes—
836C2×C42C2412yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2414yes—
842C2×C42C2414yes—
843C2×C42C2414yes—
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2412yes—
848C2×C42C2414yes—
849#95C2412yes—
850#95C2414yes—
851#95C2412yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2412yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2412yes—
869#95C2412yes—
870#95C2412yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
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#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2412yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2412yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909C24—22no—
910C24—24no—
911C24—24no—
912C24—42no—
913C24C2512yes—
914C24C2512yes—
915C24C2511yescharacteristic
916C2×Q8—28no—
917C2×Q8—24no—
918C2×Q8—28no—
919C2×Q8—28no—
920C2×Q8—28no—
921C2×Q8—24no—
922C2×Q8—28no—
923C2×Q8—24no—
924C2×Q8—24no—
925C2×Q8—28no—
926C2×Q8—24no—
927C2×Q8—24no—
928C2×Q8—28no—
929C2×Q8—28no—
930C2×Q8—44no—
931C2×Q8—42no—
932C2×Q8—42no—
933C2×Q8—42no—
934C2×Q8—44no—
935C2×Q8—44no—
936C2×Q8—44no—
937C2×Q8—42no—
938C2×Q8—42no—
939C2×Q8—42no—
940C2×Q8—44no—
941C2×Q8—44no—
942C2×Q8—44no—
943C2×Q8—42no—
944C2×Q8—42no—
945C2×Q8—41no—
946C2×Q8—42no—
947C2×Q8—42no—
948C2×Q8—42no—
949C2×Q8—42no—
950C2×Q8—432no—
951C2×Q8—432no—
952C2×Q8—464no—
953C2×Q8—464no—
954C2×Q8—88no—
955C2×Q8—816no—
956C2×Q8H(5,𝔽2)18yes—
957C2×D4—24no—
958C2×D4—24no—
959C2×D4—24no—
960C2×D4—28no—
961C2×D4—28no—
962C2×D4—44no—
963C2×D4—41no—
964C2×D4—42no—
965C22×C4—22no—
966C22×C4—24no—
967C22×C4—22no—
968C22×C4—22no—
969C22×C4—28no—
970C22×C4—24no—
971C22×C4—28no—
972C22×C4—24no—
973C22×C4—22no—
974C22×C4—22no—
975C22×C4—28no—
976C22×C4—28no—
977C22×C4—28no—
978C22×C4—28no—
979C22×C4—28no—
980C22×C4—28no—
981C22×C4—24no—
982C22×C4—28no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—42no—
991C22×C4—44no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—416no—
998C22×C4—432no—
999C22×C4H(5,𝔽2)14yes—
1000C22×C4C2514yes—
1001C22×C4C2512yes—
1002C22×C4C2514yes—
1003C22×C4C2512yes—
1004C22×C4C2512yes—
1005C22×C4C2512yes—
1006C22×C4C2514yes—
1007C22×C4C2514yes—
1008C22×C4C2514yes—
1009C22×C4C2514yes—
1010C22×C4C2514yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2511yescharacteristic
1014C22×C4C2511yescharacteristic
1015C22×C4C2512yes—
1016C22×C4C2514yes—
1017C22×C4C2512yes—
1018C22×C4C2514yes—
1019C22×C4C2514yes—
1020C4⋊C4—24no—
1021C4⋊C4—24no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—24no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—24no—
1031C4⋊C4—28no—
1032C4⋊C4—28no—
1033C4⋊C4—28no—
1034C4⋊C4—28no—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—28no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—28no—
1041C4⋊C4—28no—
1042C4⋊C4—28no—
1043C4⋊C4—28no—
1044C4⋊C4—28no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—41no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—41no—
1071C4⋊C4—42no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C22⋊C4—28no—
1075C22⋊C4—24no—
1076C22⋊C4—24no—
1077C22⋊C4—24no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—28no—
1081C22⋊C4—28no—
1082C22⋊C4—24no—
1083C22⋊C4—28no—
1084C22⋊C4—28no—
1085C22⋊C4—28no—
1086C22⋊C4—28no—
1087C22⋊C4—28no—
1088C22⋊C4—28no—
1089C22⋊C4—28no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
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—44no—
1102C22⋊C4—42no—
1103C22⋊C4—44no—
1104C22⋊C42−1+418yes—
1105C22⋊C42−1+418yes—
1106C42—24no—
1107C42—24no—
1108C42—24no—
1109C42—28no—
1110C42—28no—
1111C42—28no—
1112C42—28no—
1113C42—44no—
1114C42—44no—
1115C42—44no—
1116C42—44no—
1117C42—44no—
1118C42—42no—
1119C42—44no—
1120C42—44no—
1121C42—42no—
1122C42—42no—
1123C42—42no—
1124C23—22no—
1125C23—22no—
1126C23—28no—
1127C23—22no—
1128C23—24no—
1129C23—22no—
1130C23—24no—
1131C23—24no—
1132C23—22no—
1133C23—22no—
1134C23—24no—
1135C23—22no—
1136C23—416no—
1137C23—44no—
1138C23—44no—
1139C23C2×H(5,𝔽2)12yes—
1140C23C2×2−1+414yes—
1141C23C2×2−1+414yes—
1142C23C2611yescharacteristic
1143Q8—216no—
1144Q8—48no—
1145Q8—416no—
1146Q8—416no—
1147Q8—416no—
1148Q8—48no—
1149Q8—48no—
1150Q8—84no—
1151Q8—84no—
1152Q8—84no—
1153Q8—88no—
1154Q8—161no—
1155Q8—162no—
1156D4—416no—
1157D4—48no—
1158D4—161no—
1159C2×C4—28no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—22no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—44no—
1210C2×C4—416no—
1211C2×C4—48no—
1212C2×C4—416no—
1213C2×C4—416no—
1214C2×C4—416no—
1215C2×C4—48no—
1216C2×C4—44no—
1217C2×C4—44no—
1218C2×C4—84no—
1219C2×C4—88no—
1220C2×C4—82no—
1221C2×C4—82no—
1222C2×C4C2×H(5,𝔽2)14yes—
1223C2×C4C2×H(5,𝔽2)18yes—
1224C2×C4C2×H(5,𝔽2)14yes—
1225C2×C4C2×2−1+418yes—
1226C2×C4C2×2−1+418yes—
1227C22—28no—
1228C22—22no—
1229C22—22no—
1230C22—28no—
1231C22—24no—
1232C22—416no—
1233C22—42no—
1234C22—44no—
1235C22—42no—
1236C22—42no—
1237C22—44no—
1238C22—44no—
1239C22—42no—
1240C22—42no—
1241C22#355014yes—
1242C22C22×H(5,𝔽2)11yescharacteristic
1243C22C22×H(5,𝔽2)12yes—
1244C22C22×2−1+412yes—
1245C22C22×2−1+412yes—
1246C4—28no—
1247C4—28no—
1248C4—24no—
1249C4—24no—
1250C4—28no—
1251C4—42no—
1252C4—42no—
1253C4—42no—
1254C4—44no—
1255C4—44no—
1256C4—44no—
1257C4—44no—
1258C4—44no—
1259C4—41no—
1260C4—44no—
1261C4—42no—
1262C4—42no—
1263C4—41no—
1264C4—42no—
1265C4—44no—
1266C2—24no—
1267C2—44no—
1268C2—82no—
1269C2C2×#355011yescharacteristic
1270C2#6281711yescharacteristic
1271C2#6283311yescharacteristic
1272C2#6301614yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2539C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59151C2semidirect
3. #57212C2semidirect
4. #57150C2semidirect
5. #51358C2semidirect
6. #51076C2semidirect
7. #50090C2semidirect
8. #47945C2semidirect
9. #46325C2semidirect
10. #45744C2semidirect
11. #44934C2semidirect
12. #43891C2semidirect
13. #43426C2semidirect
14. #43085C2semidirect
15. #40495C2semidirect
16. #38598C2semidirect
17. #38511C2semidirect
18. #36708C2semidirect
19. Q8×#120C2semidirect
20. #36531C2semidirect
21. #35743C2semidirect
23. C2×#2434C2semidirect
25. C2×#563C22semidirect
26. C2×Q82C22semidirect
38. #2821C22semidirect
39. #2821C22semidirect
40. #2817C22semidirect
42. #2805C22semidirect
43. #2799C22semidirect
48. #2774C22semidirect
52. #2762C22semidirect
53. #2762C22semidirect
54. #2759C22semidirect
55. #2759C22semidirect
56. #2758C22semidirect
58. #2734C22semidirect
59. #2734C22semidirect
60. #2734C22semidirect
61. #2734C22semidirect
62. #2734C22semidirect
63. #2731C22semidirect
66. #2729C22semidirect
67. #2729C22semidirect
71. #2720C22semidirect
72. #2716C22semidirect
73. #2716C22semidirect
75. #2713C22semidirect
76. #2713C22semidirect
77. #2713C22semidirect
79. #2698C22semidirect
80. #2698C22semidirect
84. #2689C22semidirect
85. #2680C22semidirect
89. #2677C22semidirect
90. #2677C22semidirect
91. #2677C22semidirect
92. #2674C22semidirect
93. #2666C22semidirect
94. #2666C22semidirect
95. #2663C22semidirect
96. #2660C22semidirect
98. #2650C22semidirect
100. #2634C22semidirect
102. #2614C22semidirect
103. #2605C22semidirect
104. #2605C22semidirect
105. #2604C22semidirect
109. #2588C22semidirect
110. #2586C22semidirect
111. #2581C22semidirect
114. #2567C22semidirect
121. #2556C22semidirect
122. #2551C22semidirect
123. #2551C22semidirect
124. #2551C22semidirect
125. #2550C22semidirect
128. #2532C22semidirect
132. #2520C22semidirect
143. #2469C22semidirect
148. #2465C22semidirect
149. #2465C22semidirect
150. #2462C22semidirect
151. #2462C22semidirect
156. #2451C22semidirect
157. #2451C22semidirect
158. #2451C22semidirect
159. #2451C22semidirect
178. #2434C22semidirect
179. #2434C22semidirect
188. #2399C22semidirect
192. #2381C22semidirect
194. #2369C22semidirect
206. #2332C22semidirect
207. #2331C22semidirect

Maximal subgroups

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

subgroupindex
#596242
#591512
#572122
#571502
#513582
#510762
#500902
#479452
#463252
#457442
#449342
#438912
#434262
#430852
#404952
#385982
#385112
#367082
Q8×#1202
#365312
#357432
#353972
C2×#24342