Finite Group Databasebeta

← #7682459

Subgroups — #7682459

Order 512.

5418 conjugacy classes of subgroups.

The subgroup lattice has 1305 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60037C212yesmaximal, complemented
2#60018C212yesmaximal, complemented
3#59940C212yesmaximal, complemented
4#59939C212yesmaximal, complemented
5#59915C212yesmaximal, complemented
6#59861C211yesmaximal, characteristic, complemented
7#59814C211yesmaximal, characteristic
8#59618C214yesmaximal, complemented
9#59385C214yesmaximal, complemented
10#59340C212yesmaximal, complemented
11#59305C212yesmaximal, complemented
12#44413C214yesmaximal, complemented
13#44380C214yesmaximal, complemented
14#44301C214yesmaximal, complemented
15#44173C214yesmaximal, complemented
16#43059C214yesmaximal, complemented
17#43026C214yesmaximal, complemented
18#35453C212yesmaximal, complemented
19#35376C214yesmaximal, complemented
20#34956C212yesmaximal, complemented
21C2×#2566C211yesmaximal, characteristic, complemented
22#34288C214yesmaximal, complemented
23#34278C212yesmaximal, complemented
24C2×#546C2214yes—
25C2×#539C2212yes—
26C22×#125C2211yescharacteristic, complemented
27C2×#520C2212yes—
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2212yescomplemented
30#2808C2212yescomplemented
31#2804C2211yescharacteristic
32#2797C2214yescomplemented
33#2793C2214yescomplemented
34#2790C2214yescomplemented
35#2790C2214yescomplemented
36#2790C2214yescomplemented
37#2789C2212yescomplemented
38#2786C2214yescomplemented
39#2782C2212yescomplemented
40#2779C2214yescomplemented
41#2772C2214yescomplemented
42#2757C2214yescomplemented
43#2750C2214yescomplemented
44#2748C2212yes—
45#2744C2214yescomplemented
46#2725C2214yescomplemented
47#2724C2211yescharacteristic
48#2715C2214yescomplemented
49#2707C2214yescomplemented
50#2704C2214yescomplemented
51#2701C2214yescomplemented
52#2700C2214yescomplemented
53#2697C2212yes—
54#2697C2214yescomplemented
55#2691C2214yescomplemented
56#2683C2211yescharacteristic
57#2682C2212yes—
58#2681C2214yescomplemented
59#2679C2211yescharacteristic
60#2612C2212yescomplemented
61#2609C2212yescomplemented
62#2608C2214yescomplemented
63#2603C2214yes—
64#2600C2214yes—
65#2600C2214yescomplemented
66#2597C2214yescomplemented
67#2594C2214yescomplemented
68#2593C2212yescomplemented
69#2589C2214yescomplemented
70#2587C2214yescomplemented
71#2587C2214yescomplemented
72#2579C2212yes—
73#2579C2214yescomplemented
74#2579C2212yescomplemented
75#2579C2214yescomplemented
76#2579C2214yescomplemented
77#2578C2214yescomplemented
78#2576C2214yescomplemented
79#2576C2214yescomplemented
80#2576C2214yescomplemented
81#2573C2214yescomplemented
82#2566C2212yes—
83#2566C2212yes—
84#2566C2214yescomplemented
85#2566C2212yescomplemented
86#2566C2212yescomplemented
87#2566C2214yescomplemented
88#2566C2214yescomplemented
89#2561C2214yescomplemented
90#2558C2214yescomplemented
91#2556C2214yescomplemented
92#2555C2212yes—
93#2554C2214yescomplemented
94#2552C2212yescomplemented
95#2538C2212yescomplemented
96#2534C2214yes—
97#2534C2214yes—
98#2534C2212yes—
99#2534C2214yescomplemented
100#2534C2212yescomplemented
101#2531C2214yescomplemented
102#2530C2214yescomplemented
103#2527C2214yescomplemented
104#2522C2214yescomplemented
105#2520C2214yescomplemented
106#2515C2214yescomplemented
107#2515C2214yescomplemented
108#2507C2214yescomplemented
109#2505C2214yescomplemented
110#2502C2214yescomplemented
111#2497C2214yescomplemented
112#2493C2214yescomplemented
113#2486C2214yescomplemented
114#2484C2212yescomplemented
115#2484C2212yescomplemented
116#2483C2212yescomplemented
117#2481C2214yescomplemented
118#2480C2214yescomplemented
119#2480C2214yescomplemented
120#2478C2214yescomplemented
121#2477C2214yescomplemented
122#2475C2214yescomplemented
123#2475C2214yescomplemented
124#2475C2214yescomplemented
125#2473C2214yescomplemented
126#2473C2214yescomplemented
127#2471C2214yes—
128#2470C2214yescomplemented
129#2466C2214yescomplemented
130#2466C2214yescomplemented
131#2462C2214yescomplemented
132#2462C2214yescomplemented
133#2461C2214yes—
134#2460C2214yescomplemented
135#2460C2214yescomplemented
136#2460C2214yescomplemented
137#2460C2214yescomplemented
138#2458C2214yescomplemented
139#2450C2214yescomplemented
140#2450C2214yescomplemented
141#2442C2214yescomplemented
142#2437C2214yescomplemented
143#2425C2214yescomplemented
144#2424C2214yes—
145#2419C2214yescomplemented
146#2419C2214yescomplemented
147#2418C2214yes—
148#2417C2214yescomplemented
149#2411C2214yescomplemented
150#2406C2212yes—
151#2406C2212yes—
152#2405C2212yes—
153#2405C2212yescomplemented
154#2403C2212yes—
155#2392C2214yes—
156#2392C2214yescomplemented
157C2×#396C2214yescomplemented
158#2374C2212yes—
159#2374C2212yes—
160#2374C2214yescomplemented
161#2373C2214yescomplemented
162#2373C2214yescomplemented
163#2371C2214yescomplemented
164#2370C2214yescomplemented
165#2368C2214yescomplemented
166#2367C2214yescomplemented
167#2362C2214yescomplemented
168#2361C2214yes—
169#2361C2214yescomplemented
170#2361C2214yescomplemented
171#2360C2214yescomplemented
172#2359C2214yescomplemented
173#2359C2214yescomplemented
174#2359C2214yescomplemented
175#2358C2212yes—
176#2358C2212yes—
177#2358C2214yes—
178#2358C2214yescomplemented
179#2355C2212yescomplemented
180D4×C4⋊C4C2214yescomplemented
181D4×C4⋊C4C2214yescomplemented
182D4×C4⋊C4C2212yescomplemented
183#2343C2214yescomplemented
184#2342C2214yescomplemented
185#2342C2214yescomplemented
186#2339C2214yes—
187D4×C22⋊C4C2214yescomplemented
188#2329C2212yescomplemented
189#2326C2214yescomplemented
190#2325C2212yes—
191#2325C2214yescomplemented
192#2324C2214yescomplemented
193#2322C2214yescomplemented
194#2322C2214yescomplemented
195#2322C2214yescomplemented
196#2313C2212yescomplemented
197#2313C2212yescomplemented
198C4×C22⋊Q8C2214yescomplemented
199C4×C22⋊Q8C2212yescomplemented
200C4×#123C2212yes—
201C4×#123C2214yescomplemented
202C4×#123C2212yescomplemented
203C4×#121C2212yes—
204C4×#120C2212yes—
205C4×#120C2214yes—
206C4×#120C2214yescomplemented
207C4×#120C2212yescomplemented
208C2×#390C2211yescharacteristic
209C2×#390C2211yescharacteristic
210#2290C2214yescomplemented
211#2290C2214yescomplemented
212C2×#385C2214yescomplemented
213C2×#385C2214yescomplemented
214C2×#384C2211yescharacteristic, complemented
215C2×#382C2211yescharacteristic, complemented
216#2280C2212yescomplemented
217#2275C2214yescomplemented
218C2×C4×C4⋊C4C2211yescharacteristic, complemented
219C22×#41C2312yes—
220C23×D4C2312yes—
221C23×D4C2311yescharacteristic
222C24×C4C2312yes—
223C24×C4C2312yes—
224#546—232no—
225#539—216no—
226C2×#126C2314yes—
227C2×#126C2314yes—
228C2×#125—44no—
229C2×#125C2314yes—
230C2×#125C2312yes—
231C2×#125C2312yes—
232C2×#125C2314yes—
233C2×#125C2314yes—
234C2×#124C2314yes—
235C2×#123C2314yes—
236C2×#123C2314yes—
237C2×#123C2314yes—
238C2×#123C2314yes—
239C2×#123C2312yes—
240C2×#123C2312yes—
241C2×#123C2314yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2314yes—
246C2×#121C2314yes—
247C2×#121C2314yes—
248C2×#121C2312yes—
249C2×#120C2312yes—
250C2×#120C2314yes—
251C2×#120C2314yes—
252C2×#120C2312yes—
253#520—48no—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2312yes—
256C2×C4×D4—44no—
257C2×C4×D4—48no—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×#117C2314yes—
277C2×#117C2312yes—
278C2×#117C2314yes—
279C2×#117C2314yes—
280C22×C4⋊C4C2312yes—
281C22×C4⋊C4C2312yes—
282C22×C4⋊C4C2314yes—
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2314yes—
289C22×C4⋊C4C2314yes—
290C22×C22⋊C4C2314yes—
291C22×C22⋊C4C2314yes—
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2312yes—
295C22×C22⋊C4C2314yes—
296C22×C22⋊C4C2314yes—
297C22×C42C2311yescharacteristic
298C22×C42C2312yes—
299C22×C42C2311yescharacteristic
300C22×C42C2311yescharacteristic
301#401C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2312yes—
307#400C2312yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#399C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2312yes—
321#398C2312yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#396C2314yes—
342#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#395C2312yes—
358#395C2312yes—
359#395C2314yes—
360#394C2312yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2312yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#393C2314yes—
374#393C2314yes—
375#392C2314yes—
376#392C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2314yes—
380#391C2314yes—
381#391C2312yes—
382#390C2311yescharacteristic
383#390C2312yes—
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2314yes—
387#390C2314yes—
388#390C2312yes—
389#390C2312yes—
390#390C2311yescharacteristic
391#390C2314yes—
392#390C2314yes—
393#390C2314yes—
394#390C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2312yes—
409#389C2312yes—
410#389C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#386C2314yes—
480#386C2314yes—
481#386C2314yes—
482#386C2314yes—
483#386C2314yes—
484#386C2314yes—
485#386C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2312yes—
490#386C2312yes—
491#386C2314yes—
492#386C2314yes—
493#386C2312yes—
494#386C2312yes—
495#386C2314yes—
496#386C2314yes—
497#386C2314yes—
498#386C2314yes—
499#386C2314yes—
500#386C2314yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2312yes—
522#385C2314yes—
523#385C2312yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2312yes—
531#385C2312yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#384C2312yes—
542#384C2312yes—
543#384C2312yes—
544#384C2312yes—
545#384C2314yes—
546#383C2314yes—
547#382C2312yes—
548#382C2312yes—
549#382C2312yes—
550#382C2312yes—
551#382C2314yes—
552#381C2312yes—
553#381C2314yes—
554#381C2314yes—
555#381C2312yes—
556#381C2312yes—
557#381C2314yes—
558#381C2314yes—
559#381C2314yes—
560#381C2312yes—
561#380C2314yes—
562#380C2312yes—
563#380C2312yes—
564#380C2314yes—
565#380C2312yes—
566#380C2314yes—
567#380C2314yes—
568#380C2312yes—
569#380C2314yes—
570#380C2314yes—
571#380C2314yes—
572#380C2314yes—
573#379C2312yes—
574#379C2314yes—
575#379C2314yes—
576#379C2312yes—
577#379C2312yes—
578#379C2312yes—
579C4×C4⋊C4C2312yes—
580C4×C4⋊C4C2312yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2312yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2312yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2312yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614#376C2314yes—
615#376C2314yes—
616C2×#95C2312yes—
617C2×#95C2314yes—
618C2×#95C2314yes—
619C2×#95C2314yes—
620C25C2412yes—
621C25C2412yes—
622C2×#41—216no—
623C2×#41—44no—
624C22×Q8C2412yes—
625C22×Q8C2412yes—
626C22×D4—216no—
627C22×D4—24no—
628C22×D4—42no—
629C22×D4—42no—
630C22×D4—44no—
631C22×D4C2414yes—
632C22×D4C2412yes—
633C22×D4C2412yes—
634C22×D4C2414yes—
635C22×D4C2414yes—
636C22×D4C2411yescharacteristic
637C22×D4C2414yes—
638C22×D4C2412yes—
639C22×D4C2411yescharacteristic
640C23×C4—28no—
641C23×C4—44no—
642C23×C4—84no—
643C23×C4—84no—
644C23×C4C2411yescharacteristic
645C23×C4C2412yes—
646C23×C4C2411yescharacteristic
647C23×C4C2414yes—
648C23×C4C2412yes—
649C23×C4C2412yes—
650C23×C4C2412yes—
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2414yes—
655C23×C4C2414yes—
656C23×C4C2414yes—
657C23×C4C2412yes—
658C23×C4C2412yes—
659C23×C4C2412yes—
660C23×C4C2414yes—
661C23×C4C2412yes—
662C23×C4C2414yes—
663C23×C4C2412yes—
664C23×C4C2411yescharacteristic
665#126—216no—
666#126—84no—
667#125—216no—
668#125—44no—
669#125—48no—
670#125—44no—
671#125—84no—
672#124—216no—
673#123—216no—
674#123—216no—
675#123—216no—
676#123—28no—
677#123—216no—
678#123—44no—
679#123—84no—
680C22⋊Q8—28no—
681C22⋊Q8—216no—
682C22⋊Q8—216no—
683C22⋊Q8—84no—
684#121—216no—
685#121—216no—
686#121#41116yes—
687#120—216no—
688#120—216no—
689#120—28no—
690#120—44no—
691C4×Q8—44no—
692C4×Q8—48no—
693C4×D4—216no—
694C4×D4—216no—
695C4×D4—216no—
696C4×D4—216no—
697C4×D4—44no—
698C4×D4—44no—
699C4×D4—44no—
700C4×D4—44no—
701C4×D4—44no—
702C4×D4—48no—
703C4×D4—48no—
704C4×D4—48no—
705C4×D4—48no—
706C4×D4—48no—
707C4×D4—84no—
708C4×D4—84no—
709C4×D4—84no—
710C4×D4—84no—
711#117—48no—
712#117—48no—
713#117—44no—
714#117—84no—
715C2×C4⋊C4—28no—
716C2×C4⋊C4—28no—
717C2×C4⋊C4—44no—
718C2×C4⋊C4—48no—
719C2×C4⋊C4—42no—
720C2×C4⋊C4—42no—
721C2×C4⋊C4—42no—
722C2×C4⋊C4—44no—
723C2×C4⋊C4—84no—
724C2×C4⋊C4—84no—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C22⋊C4—216no—
774C2×C22⋊C4—216no—
775C2×C22⋊C4—44no—
776C2×C22⋊C4—44no—
777C2×C22⋊C4—44no—
778C2×C22⋊C4—84no—
779C2×C22⋊C4—84no—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C42—24no—
827C2×C42—44no—
828C2×C42—42no—
829C2×C42—42no—
830C2×C42C2412yes—
831C2×C42C2414yes—
832C2×C42C2414yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2412yes—
836C2×C42C2414yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2414yes—
842C2×C42C2414yes—
843C2×C42C2414yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2411yescharacteristic
847C2×C42C2412yes—
848C2×C42C2411yescharacteristic
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
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#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#95C2412yes—
894#95C2412yes—
895#95C2412yes—
896#95C2412yes—
897C24—24no—
898C24—28no—
899C24—28no—
900C24—24no—
901C24—24no—
902C24—42no—
903C24—44no—
904C24—44no—
905C24—42no—
906C24—42no—
907C24C2512yes—
908C24C2514yes—
909C24C2512yes—
910C24C2511yescharacteristic
911#41—432no—
912C2×Q8—28no—
913C2×Q8—24no—
914C2×Q8—42no—
915C2×Q8—42no—
916C2×Q8—42no—
917C2×D4—28no—
918C2×D4—28no—
919C2×D4—28no—
920C2×D4—28no—
921C2×D4—28no—
922C2×D4—28no—
923C2×D4—24no—
924C2×D4—28no—
925C2×D4—28no—
926C2×D4—22no—
927C2×D4—24no—
928C2×D4—41no—
929C2×D4—42no—
930C2×D4—41no—
931C2×D4—44no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—44no—
936C2×D4—41no—
937C2×D4—41no—
938C2×D4—416no—
939C2×D4—44no—
940C2×D4—44no—
941C2×D4—432no—
942C2×D4C2×#41116yes—
943C2×D4C2×#4118yes—
944C2×D42−1+414yes—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—28no—
949C22×C4—24no—
950C22×C4—28no—
951C22×C4—22no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—28no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—24no—
958C22×C4—28no—
959C22×C4—28no—
960C22×C4—24no—
961C22×C4—24no—
962C22×C4—28no—
963C22×C4—24no—
964C22×C4—28no—
965C22×C4—24no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—44no—
969C22×C4—42no—
970C22×C4—44no—
971C22×C4—42no—
972C22×C4—44no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—42no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—816no—
996C22×C4—816no—
997C22×C4C2×#4118yes—
998C22×C4H(5,𝔽2)14yes—
999C22×C4C2514yes—
1000C22×C4C2514yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2514yes—
1004C22×C4C2514yes—
1005C22×C4C2512yes—
1006C22×C4C2512yes—
1007C22×C4C2512yes—
1008C22×C4C2514yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2514yes—
1012C22×C4C2514yes—
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2512yes—
1016C22×C4C2511yescharacteristic
1017C22×C4C2511yescharacteristic
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—24no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—28no—
1033C4⋊C4—42no—
1034C4⋊C4—41no—
1035C4⋊C4—42no—
1036C4⋊C4—41no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—41no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—41no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—42no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—42no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—42no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—42no—
1064C4⋊C4—44no—
1065C4⋊C4C2×#4118yes—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—24no—
1075C22⋊C4—24no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—28no—
1081C22⋊C4—28no—
1082C22⋊C4—28no—
1083C22⋊C4—28no—
1084C22⋊C4—28no—
1085C22⋊C4—28no—
1086C22⋊C4—28no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—42no—
1109C22⋊C4—44no—
1110C22⋊C4—42no—
1111C22⋊C4C2×#41116yes—
1112C42—28no—
1113C42—28no—
1114C42—24no—
1115C42—24no—
1116C42—28no—
1117C42—24no—
1118C42—24no—
1119C42—41no—
1120C42—41no—
1121C42—42no—
1122C42—44no—
1123C42—44no—
1124C42—44no—
1125C42—44no—
1126C42—44no—
1127C42—44no—
1128C42—44no—
1129C42—44no—
1130C42—44no—
1131C23—21no—
1132C23—21no—
1133C23—22no—
1134C23—24no—
1135C23—24no—
1136C23—24no—
1137C23—22no—
1138C23—24no—
1139C23—24no—
1140C23—22no—
1141C23—24no—
1142C23—24no—
1143C23—24no—
1144C23—24no—
1145C23—22no—
1146C23—22no—
1147C23—22no—
1148C23—24no—
1149C23—48no—
1150C23—48no—
1151C23—416no—
1152C23—416no—
1153C23—48no—
1154C23—84no—
1155C23—88no—
1156C23—88no—
1157C23—84no—
1158C23—84no—
1159C23C22×#4118yes—
1160C23C22×#4114yes—
1161C23C2×H(5,𝔽2)12yes—
1162C23C2×2−1+414yes—
1163C23C2611yescharacteristic
1164Q8—48no—
1165Q8—84no—
1166D4—232no—
1167D4—44no—
1168D4—48no—
1169D4—48no—
1170D4—416no—
1171D4—44no—
1172D4—416no—
1173D4—48no—
1174D4—88no—
1175C2×C4—28no—
1176C2×C4—24no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—24no—
1180C2×C4—21no—
1181C2×C4—22no—
1182C2×C4—22no—
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—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—22no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—44no—
1222C2×C4—48no—
1223C2×C4—48no—
1224C2×C4—416no—
1225C2×C4—48no—
1226C2×C4—48no—
1227C2×C4—44no—
1228C2×C4—48no—
1229C2×C4—88no—
1230C2×C4—84no—
1231C2×C4—84no—
1232C2×C4—88no—
1233C2×C4—84no—
1234C2×C4—88no—
1235C2×C4—84no—
1236C2×C4—84no—
1237C2×C4—84no—
1238C2×C4—88no—
1239C2×C4—84no—
1240C2×C4—164no—
1241C2×C4C22×#4114yes—
1242C2×C4C22×#4118yes—
1243C2×C4C22×#4114yes—
1244C2×C4C2×H(5,𝔽2)14yes—
1245C2×C4C2×2−1+412yes—
1246C2×C4#58512yes—
1247C22—24no—
1248C22—24no—
1249C22—22no—
1250C22—22no—
1251C22—28no—
1252C22—28no—
1253C22—28no—
1254C22—24no—
1255C22—28no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—42no—
1261C22—44no—
1262C22—42no—
1263C22—44no—
1264C22—44no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—816no—
1269C22—816no—
1270C22#348114yes—
1271C22C23×#4112yes—
1272C22C22×H(5,𝔽2)11yescharacteristic
1273C22C22×2−1+411yescharacteristic
1274C22C2×#58511yescharacteristic
1275C22H(7,𝔽2)12yes—
1276C4—24no—
1277C4—24no—
1278C4—22no—
1279C4—22no—
1280C4—24no—
1281C4—28no—
1282C4—44no—
1283C4—44no—
1284C4—44no—
1285C4—44no—
1286C4—44no—
1287C4—44no—
1288C4—42no—
1289C4—42no—
1290C4—44no—
1291C4—44no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C2—24no—
1296C2—48no—
1297C2—44no—
1298C2—82no—
1299C2C2×#348111yescharacteristic
1300C2#6281911yescharacteristic
1301C2#6286211yescharacteristic
1302C2#6299212yes—
1303C2#6300012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#59814C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60037C2semidirect
2. #60018C2semidirect
3. #59940C2semidirect
4. #59939C2semidirect
5. #59915C2semidirect
6. #59861C2semidirect
8. #59618C2semidirect
9. #59385C2semidirect
10. #59340C2semidirect
11. #59305C2semidirect
12. #44413C2semidirect
13. #44380C2semidirect
14. #44301C2semidirect
15. #44173C2semidirect
16. #43059C2semidirect
17. #43026C2semidirect
18. #35453C2semidirect
19. #35376C2semidirect
20. #34956C2semidirect
21. C2×#2566C2semidirect
22. #34288C2semidirect
23. #34278C2semidirect
26. C22×#125C22semidirect
29. C22×C4×D4C22semidirect
30. #2808C22semidirect
32. #2797C22semidirect
33. #2793C22semidirect
34. #2790C22semidirect
35. #2790C22semidirect
36. #2790C22semidirect
37. #2789C22semidirect
38. #2786C22semidirect
39. #2782C22semidirect
40. #2779C22semidirect
41. #2772C22semidirect
42. #2757C22semidirect
43. #2750C22semidirect
45. #2744C22semidirect
46. #2725C22semidirect
48. #2715C22semidirect
49. #2707C22semidirect
50. #2704C22semidirect
51. #2701C22semidirect
52. #2700C22semidirect
54. #2697C22semidirect
55. #2691C22semidirect
58. #2681C22semidirect
60. #2612C22semidirect
61. #2609C22semidirect
62. #2608C22semidirect
65. #2600C22semidirect
66. #2597C22semidirect
67. #2594C22semidirect
68. #2593C22semidirect
69. #2589C22semidirect
70. #2587C22semidirect
71. #2587C22semidirect
73. #2579C22semidirect
74. #2579C22semidirect
75. #2579C22semidirect
76. #2579C22semidirect
77. #2578C22semidirect
78. #2576C22semidirect
79. #2576C22semidirect
80. #2576C22semidirect
81. #2573C22semidirect
84. #2566C22semidirect
85. #2566C22semidirect
86. #2566C22semidirect
87. #2566C22semidirect
88. #2566C22semidirect
89. #2561C22semidirect
90. #2558C22semidirect
91. #2556C22semidirect
93. #2554C22semidirect
94. #2552C22semidirect
95. #2538C22semidirect
99. #2534C22semidirect
100. #2534C22semidirect
101. #2531C22semidirect
102. #2530C22semidirect
103. #2527C22semidirect
104. #2522C22semidirect
105. #2520C22semidirect
106. #2515C22semidirect
107. #2515C22semidirect
108. #2507C22semidirect
109. #2505C22semidirect
110. #2502C22semidirect
111. #2497C22semidirect
112. #2493C22semidirect
113. #2486C22semidirect
114. #2484C22semidirect
115. #2484C22semidirect
116. #2483C22semidirect
117. #2481C22semidirect
118. #2480C22semidirect
119. #2480C22semidirect
120. #2478C22semidirect
121. #2477C22semidirect
122. #2475C22semidirect
123. #2475C22semidirect
124. #2475C22semidirect
125. #2473C22semidirect
126. #2473C22semidirect
128. #2470C22semidirect
129. #2466C22semidirect
130. #2466C22semidirect
131. #2462C22semidirect
132. #2462C22semidirect
134. #2460C22semidirect
135. #2460C22semidirect
136. #2460C22semidirect
137. #2460C22semidirect
138. #2458C22semidirect
139. #2450C22semidirect
140. #2450C22semidirect
141. #2442C22semidirect
142. #2437C22semidirect
143. #2425C22semidirect
145. #2419C22semidirect
146. #2419C22semidirect
148. #2417C22semidirect
149. #2411C22semidirect
153. #2405C22semidirect
156. #2392C22semidirect
157. C2×#396C22semidirect
160. #2374C22semidirect
161. #2373C22semidirect
162. #2373C22semidirect
163. #2371C22semidirect
164. #2370C22semidirect
165. #2368C22semidirect
166. #2367C22semidirect
167. #2362C22semidirect
169. #2361C22semidirect
170. #2361C22semidirect
171. #2360C22semidirect
172. #2359C22semidirect
173. #2359C22semidirect
174. #2359C22semidirect
178. #2358C22semidirect
179. #2355C22semidirect
180. D4×C4⋊C4C22semidirect
181. D4×C4⋊C4C22semidirect
182. D4×C4⋊C4C22semidirect
183. #2343C22semidirect
184. #2342C22semidirect
185. #2342C22semidirect
187. D4×C22⋊C4C22semidirect
188. #2329C22semidirect
189. #2326C22semidirect
191. #2325C22semidirect
192. #2324C22semidirect
193. #2322C22semidirect
194. #2322C22semidirect
195. #2322C22semidirect
196. #2313C22semidirect
197. #2313C22semidirect
198. C4×C22⋊Q8C22semidirect
199. C4×C22⋊Q8C22semidirect
201. C4×#123C22semidirect
202. C4×#123C22semidirect
206. C4×#120C22semidirect
207. C4×#120C22semidirect
210. #2290C22semidirect
211. #2290C22semidirect
212. C2×#385C22semidirect
213. C2×#385C22semidirect
214. C2×#384C22semidirect
215. C2×#382C22semidirect
216. #2280C22semidirect
217. #2275C22semidirect
218. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#600372
#600182
#599402
#599392
#599152
#598612
#598142
#596182
#593852
#593402
#593052
#444132
#443802
#443012
#441732
#430592
#430262
#354532
#353762
#349562
C2×#25662
#342882
#342782