Finite Group Databasebeta

← #8934703

Subgroups — #8934703

Order 512.

4910 conjugacy classes of subgroups.

The subgroup lattice has 1323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59975C212yesmaximal, complemented
2#59908C212yesmaximal, complemented
3#59659C212yesmaximal, complemented
4#59613C214yesmaximal, complemented
5#59160C212yesmaximal, complemented
6#52072C211yesmaximal, characteristic, complemented
7#51995C212yesmaximal, complemented
8#51783C212yesmaximal, complemented
9#51749C211yesmaximal, characteristic, complemented
10#51424C214yesmaximal, complemented
11#50757C214yesmaximal, complemented
12#50478C214yesmaximal, complemented
13#49759C214yesmaximal, complemented
14#49562C212yesmaximal, complemented
15#48913C214yesmaximal, complemented
16#48404C214yesmaximal, complemented
17#48396C214yesmaximal, complemented
18#47658C212yesmaximal, complemented
19#47634C214yesmaximal, complemented
20#35677C211yesmaximal, characteristic, complemented
21#35669C212yesmaximal, complemented
22#35481C214yesmaximal, complemented
23#35439C212yesmaximal, complemented
24C2×H(3,𝔽4)C2211yescharacteristic, complemented
25C2×H(3,𝔽4)C2212yescomplemented
26C2×Q82C2211yescharacteristic, complemented
27C2×#555C2212yes—
28C2×#542C2212yes—
29C2×#536C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C22×#124C2211yescharacteristic, complemented
32C2×#519C2211yescharacteristic, complemented
33#2830C2212yescomplemented
34#2803C2214yescomplemented
35#2803C2214yescomplemented
36#2800C2214yescomplemented
37#2800C2214yescomplemented
38#2795C2214yescomplemented
39#2793C2214yescomplemented
40#2786C2214yescomplemented
41#2763C2212yescomplemented
42#2761C2214yescomplemented
43#2761C2214yescomplemented
44#2759C2214yescomplemented
45#2757C2214yescomplemented
46#2756C2214yescomplemented
47#2752C2214yescomplemented
48#2749C2214yescomplemented
49#2740C2214yescomplemented
50#2737C2214yescomplemented
51#2734C2212yescomplemented
52#2733C2212yes—
53#2731C2212yescomplemented
54#2731C2212yescomplemented
55#2731C2214yescomplemented
56#2731C2212yescomplemented
57#2731C2214yescomplemented
58#2730C2214yescomplemented
59#2715C2214yescomplemented
60#2712C2212yes—
61#2712C2214yescomplemented
62#2712C2214yescomplemented
63#2700C2214yescomplemented
64#2700C2214yescomplemented
65#2700C2214yescomplemented
66#2699C2212yes—
67#2697C2214yescomplemented
68#2686C2214yescomplemented
69#2686C2214yescomplemented
70#2685C2214yescomplemented
71#2684C2212yescomplemented
72#2684C2212yescomplemented
73#2683C2212yescomplemented
74#2681C2214yescomplemented
75#2679C2212yescomplemented
76#2678C2214yes—
77#2678C2214yes—
78#2678C2214yescomplemented
79#2677C2214yescomplemented
80#2676C2214yes—
81#2676C2214yes—
82#2674C2214yescomplemented
83#2670C2214yes—
84#2670C2214yescomplemented
85#2669C2214yes—
86#2662C2214yescomplemented
87#2662C2214yescomplemented
88#2648C2214yescomplemented
89#2640C2212yescomplemented
90#2632C2212yescomplemented
91#2620C2214yescomplemented
92#2617C2214yes—
93#2610C2212yes—
94#2610C2214yescomplemented
95#2610C2214yescomplemented
96#2608C2212yescomplemented
97#2602C2214yes—
98#2599C2212yescomplemented
99#2597C2214yescomplemented
100#2595C2214yescomplemented
101#2592C2214yescomplemented
102#2586C2214yescomplemented
103#2576C2214yescomplemented
104#2576C2214yescomplemented
105#2576C2214yescomplemented
106#2576C2214yescomplemented
107#2574C2214yescomplemented
108#2572C2214yescomplemented
109#2568C2212yescomplemented
110#2567C2212yescomplemented
111#2561C2214yescomplemented
112#2561C2212yescomplemented
113#2557C2214yes—
114#2557C2214yes—
115#2555C2214yes—
116#2555C2214yes—
117#2555C2212yes—
118#2548C2212yes—
119#2548C2212yes—
120#2545C2214yescomplemented
121#2545C2214yescomplemented
122#2545C2212yescomplemented
123#2545C2212yescomplemented
124#2545C2212yescomplemented
125#2545C2212yescomplemented
126#2544C2214yes—
127#2538C2214yescomplemented
128#2534C2214yescomplemented
129#2532C2214yescomplemented
130#2527C2214yescomplemented
131#2527C2214yescomplemented
132#2526C2214yescomplemented
133#2526C2214yescomplemented
134#2525C2214yescomplemented
135#2523C2212yescomplemented
136#2518C2214yescomplemented
137#2518C2214yescomplemented
138#2518C2214yescomplemented
139#2518C2214yescomplemented
140#2500C2212yes—
141#2499C2212yescomplemented
142#2491C2214yescomplemented
143#2491C2214yescomplemented
144#2491C2214yescomplemented
145#2474C2214yescomplemented
146#2474C2214yescomplemented
147#2474C2214yescomplemented
148#2474C2214yescomplemented
149#2472C2214yescomplemented
150#2472C2214yescomplemented
151#2472C2214yescomplemented
152#2472C2214yescomplemented
153#2472C2214yescomplemented
154#2470C2214yescomplemented
155#2470C2214yescomplemented
156#2469C2214yescomplemented
157#2469C2214yescomplemented
158#2465C2214yescomplemented
159#2465C2214yescomplemented
160#2465C2214yescomplemented
161#2465C2214yescomplemented
162#2465C2214yescomplemented
163#2463C2212yes—
164#2461C2214yescomplemented
165#2459C2214yescomplemented
166#2459C2214yescomplemented
167#2459C2214yescomplemented
168#2458C2214yescomplemented
169#2457C2214yescomplemented
170#2439C2214yescomplemented
171#2439C2214yescomplemented
172#2436C2212yes—
173#2434C2212yescomplemented
174#2432C2212yes—
175#2426C2214yescomplemented
176#2426C2214yescomplemented
177#2426C2214yescomplemented
178#2426C2214yescomplemented
179#2426C2214yescomplemented
180#2424C2214yes—
181#2424C2214yescomplemented
182#2424C2214yescomplemented
183#2424C2214yescomplemented
184#2411C2214yescomplemented
185#2411C2214yescomplemented
186#2411C2214yescomplemented
187#2410C2214yescomplemented
188#2404C2212yes—
189#2381C2211yescharacteristic, complemented
190#2378C2214yescomplemented
191#2375C2214yescomplemented
192#2372C2211yescharacteristic, complemented
193#2372C2212yescomplemented
194#2367C2214yescomplemented
195#2362C2214yescomplemented
196#2362C2214yescomplemented
197#2358C2214yescomplemented
198#2358C2212yescomplemented
199#2357C2214yescomplemented
200#2356C2214yescomplemented
201#2342C2214yescomplemented
202#2335C2214yescomplemented
203#2333C2214yescomplemented
204#2333C2214yescomplemented
205#2333C2214yescomplemented
206#2332C2212yescomplemented
207#2327C2212yescomplemented
208#2326C2212yescomplemented
209#2309C2211yescharacteristic, complemented
210C4×C4⋊Q8C2212yescomplemented
211C4×#124C2214yescomplemented
212C4×#124C2214yescomplemented
213C4×#124C2212yescomplemented
214#2298C2212yescomplemented
215#2297C2211yescharacteristic
216#2296C2211yescharacteristic, complemented
217#2290C2214yescomplemented
218#2273C2212yescomplemented
219C22×#41C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×D4C2311yescharacteristic
222H(3,𝔽4)—48no—
223H(3,𝔽4)—44no—
224Q82—44no—
225#555—48no—
226#542—48no—
227#536—44no—
228#535—44no—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2312yes—
236C2×#127C2312yes—
237C2×#126C2314yes—
238C2×#124—44no—
239C2×#124C2312yes—
240C2×#124C2314yes—
241C2×#124C2312yes—
242C2×#124C2311yescharacteristic
243C2×#124C2314yes—
244C2×#124C2312yes—
245C2×#124C2312yes—
246C2×#124C2314yes—
247C2×#124C2311yescharacteristic
248C2×#124C2314yes—
249C2×#124C2314yes—
250C2×#124C2314yes—
251C2×#124C2312yes—
252C2×#124C2314yes—
253C2×#124C2312yes—
254C2×#124C2312yes—
255C2×#124C2314yes—
256C2×#124C2314yes—
257C2×#124C2312yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2312yes—
274C2×#121C2314yes—
275C2×#120C2312yes—
276C2×#120C2314yes—
277C2×#120C2312yes—
278C2×#120C2314yes—
279C2×#120C2314yes—
280C2×#120C2312yes—
281C2×#120C2312yes—
282C2×#120C2314yes—
283C2×#120C2314yes—
284#519—44no—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2314yes—
291C2×C4×Q8C2314yes—
292C2×C4×Q8C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×#117C2312yes—
298C2×#117C2311yescharacteristic
299C2×#117C2311yescharacteristic
300C2×#117C2311yescharacteristic
301C2×#117C2314yes—
302C2×#117C2314yes—
303C2×#117C2312yes—
304C22×C22⋊C4C2314yes—
305C22×C22⋊C4C2312yes—
306C22×C22⋊C4C2314yes—
307C22×C22⋊C4C2314yes—
308C22×C42C2311yescharacteristic
309#401C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#399C2314yes—
314#398C2314yes—
315#398C2312yes—
316#398C2314yes—
317#397C2314yes—
318#397C2314yes—
319#397C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2312yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#396C2314yes—
333#396C2314yes—
334#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
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#395C2314yes—
351#395C2314yes—
352#395C2314yes—
353#395C2312yes—
354#395C2312yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2312yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#393C2312yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2312yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#392C2314yes—
401#392C2312yes—
402#392C2314yes—
403#392C2314yes—
404#392C2314yes—
405#392C2314yes—
406#392C2314yes—
407#392C2314yes—
408#392C2314yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2312yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#390C2312yes—
426#390C2312yes—
427#390C2312yes—
428#390C2312yes—
429#390C2312yes—
430#390C2314yes—
431#390C2314yes—
432#390C2314yes—
433#390C2314yes—
434#390C2314yes—
435#390C2314yes—
436#390C2314yes—
437#390C2314yes—
438#390C2314yes—
439#390C2312yes—
440#390C2314yes—
441#390C2314yes—
442#390C2314yes—
443#390C2314yes—
444#390C2314yes—
445#390C2312yes—
446#390C2314yes—
447#390C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
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#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#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
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#387C2314yes—
533#387C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2312yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2312yes—
556#386C2314yes—
557#386C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2312yes—
568#385C2312yes—
569#384C2312yes—
570#384C2312yes—
571#383C2314yes—
572#383C2314yes—
573#383C2312yes—
574#382C2312yes—
575#382C2312yes—
576#382C2314yes—
577#382C2314yes—
578#381C2314yes—
579#381C2314yes—
580#381C2314yes—
581#381C2314yes—
582#381C2314yes—
583#381C2312yes—
584#380C2314yes—
585#380C2314yes—
586#380C2314yes—
587#379C2314yes—
588#379C2314yes—
589#379C2314yes—
590#379C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2312yes—
594C4×C4⋊C4C2312yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2312yes—
599C4×C4⋊C4C2312yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2312yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2312yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2312yes—
618C4×C22⋊C4C2314yes—
619#376C2312yes—
620#376C2312yes—
621#376C2314yes—
622C43C2312yes—
623C25C2412yes—
624C25C2412yes—
625C2×#41—42no—
626C2×#41—42no—
627C2×#41—42no—
628C22×Q8—24no—
629C22×Q8—42no—
630C22×Q8—42no—
631C22×Q8C2412yes—
632C22×Q8C2412yes—
633C22×Q8C2411yescharacteristic
634C22×Q8C2414yes—
635C22×Q8C2412yes—
636C22×Q8C2411yescharacteristic
637C22×Q8C2412yes—
638C22×Q8C2412yes—
639C22×Q8C2411yescharacteristic
640C22×D4—42no—
641C22×D4—42no—
642C22×D4—42no—
643C22×D4C2414yes—
644C22×D4C2412yes—
645C22×D4C2414yes—
646C22×D4C2414yes—
647C22×D4C2412yes—
648C22×D4C2411yescharacteristic
649C22×D4C2412yes—
650C22×D4C2412yes—
651C22×D4C2414yes—
652C22×D4C2414yes—
653C22×D4C2412yes—
654C22×D4C2414yes—
655C22×D4C2414yes—
656C22×D4C2414yes—
657C23×C4C2411yescharacteristic
658C23×C4C2412yes—
659C23×C4C2414yes—
660C23×C4C2414yes—
661C23×C4C2412yes—
662C23×C4C2412yes—
663C23×C4C2412yes—
664C23×C4C2414yes—
665C23×C4C2414yes—
666C4⋊Q8—24no—
667C4⋊Q8—28no—
668C4⋊Q8—42no—
669C4⋊Q8—44no—
670C4⋊Q8—44no—
671C4⋊Q8—44no—
672C4⋊Q8—48no—
673#127—44no—
674#126—48no—
675#124—28no—
676#124—24no—
677#124—28no—
678#124—216no—
679#124—48no—
680#124—44no—
681#124—44no—
682#124—48no—
683#124—44no—
684#124—48no—
685#124—44no—
686#124—42no—
687#124—48no—
688#124—44no—
689#124—48no—
690#124—48no—
691#124—44no—
692#124—48no—
693#124—48no—
694#123—48no—
695#123—48no—
696#123—48no—
697C22⋊Q8—44no—
698C22⋊Q8—48no—
699C22⋊Q8—48no—
700C22⋊Q8—48no—
701C22⋊Q8—48no—
702C22⋊Q8—48no—
703C22⋊Q8—44no—
704#121—48no—
705#121—48no—
706#121—48no—
707#121—48no—
708#121—48no—
709#121—48no—
710#121—44no—
711#120—28no—
712#120—48no—
713#120—48no—
714#120—44no—
715#120—48no—
716#120—48no—
717#120—44no—
718#120—48no—
719#120—44no—
720C4×Q8—44no—
721C4×Q8—44no—
722C4×Q8—48no—
723C4×Q8—44no—
724C4×Q8—44no—
725C4×Q8—44no—
726C4×Q8—44no—
727C4×Q8—48no—
728C4×D4—48no—
729C4×D4—44no—
730C4×D4—48no—
731C4×D4—48no—
732#117—24no—
733#117—28no—
734#117—42no—
735#117—48no—
736#117—48no—
737#117—44no—
738#117—42no—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C22⋊C4—48no—
774C2×C22⋊C4—48no—
775C2×C22⋊C4—44no—
776C2×C22⋊C4—48no—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2412yes—
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⋊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⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
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×C22⋊C4C2411yescharacteristic
835C2×C42—42no—
836C2×C42C2412yes—
837C2×C42C2412yes—
838C2×C42C2412yes—
839C2×C42C2412yes—
840C2×C42C2412yes—
841C2×C42C2411yescharacteristic
842C2×C42C2411yescharacteristic
843C2×C42C2412yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2411yescharacteristic
848C2×C42C2412yes—
849C2×C42C2411yescharacteristic
850C2×C42C2412yes—
851C2×C42C2414yes—
852C2×C42C2412yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861#95C2414yes—
862#95C2412yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2412yes—
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#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2412yes—
902#95C2412yes—
903#95C2414yes—
904#95C2414yes—
905C24—24no—
906C24—44no—
907C24—42no—
908C24—42no—
909C24—44no—
910C24—44no—
911C24—42no—
912C24—42no—
913C24—42no—
914C24—44no—
915C24C2514yes—
916C24C2514yes—
917C24C2512yes—
918C24C2511yescharacteristic
919#41—88no—
920C2×Q8—24no—
921C2×Q8—22no—
922C2×Q8—28no—
923C2×Q8—24no—
924C2×Q8—22no—
925C2×Q8—28no—
926C2×Q8—24no—
927C2×Q8—42no—
928C2×Q8—41no—
929C2×Q8—42no—
930C2×Q8—41no—
931C2×Q8—41no—
932C2×Q8—41no—
933C2×Q8—42no—
934C2×Q8—44no—
935C2×Q8—41no—
936C2×Q8—44no—
937C2×Q8—42no—
938C2×Q8—41no—
939C2×Q8—44no—
940C2×Q8—42no—
941C2×Q8—42no—
942C2×Q8—42no—
943C2×Q8—42no—
944C2×Q8—416no—
945C2×Q8H(5,𝔽2)14yes—
946C2×D4—24no—
947C2×D4—28no—
948C2×D4—28no—
949C2×D4—24no—
950C2×D4—22no—
951C2×D4—24no—
952C2×D4—28no—
953C2×D4—24no—
954C2×D4—44no—
955C2×D4—42no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—42no—
960C2×D4—42no—
961C2×D4—42no—
962C2×D4—42no—
963C2×D4—44no—
964C2×D4—42no—
965C2×D4—44no—
966C2×D4—41no—
967C2×D4—42no—
968C2×D4—41no—
969C2×D4—42no—
970C2×D4—44no—
971C2×D4—42no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—88no—
988C22×C4—22no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—28no—
994C22×C4—28no—
995C22×C4—24no—
996C22×C4—42no—
997C22×C4—42no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—42no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4C2514yes—
1014C22×C4C2514yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2514yes—
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2512yes—
1024C22×C4C2514yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2514yes—
1032C4⋊C4—24no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—28no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—28no—
1041C4⋊C4—28no—
1042C4⋊C4—44no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—44no—
1048C4⋊C4—42no—
1049C4⋊C4—44no—
1050C4⋊C4—42no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—42no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—42no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C22⋊C4—22no—
1067C22⋊C4—24no—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
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—44no—
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—42no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—42no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—42no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4H(5,𝔽2)14yes—
1124C42—24no—
1125C42—24no—
1126C42—24no—
1127C42—24no—
1128C42—24no—
1129C42—22no—
1130C42—22no—
1131C42—24no—
1132C42—28no—
1133C42—28no—
1134C42—42no—
1135C42—44no—
1136C42—41no—
1137C42—41no—
1138C42—42no—
1139C42—42no—
1140C42—44no—
1141C42—44no—
1142C42—44no—
1143C42—42no—
1144C42—44no—
1145C42—42no—
1146C42—44no—
1147C42—42no—
1148C42—42no—
1149C23—21no—
1150C23—24no—
1151C23—21no—
1152C23—24no—
1153C23—22no—
1154C23—24no—
1155C23—24no—
1156C23—24no—
1157C23—22no—
1158C23—24no—
1159C23—24no—
1160C23—24no—
1161C23—24no—
1162C23—24no—
1163C23—24no—
1164C23—24no—
1165C23—24no—
1166C23—24no—
1167C23—22no—
1168C23—24no—
1169C23—24no—
1170C23—24no—
1171C23—48no—
1172C23—84no—
1173C23—88no—
1174C23—88no—
1175C23—162no—
1176C23—162no—
1177C23—164no—
1178C23—164no—
1179C23—162no—
1180C23—162no—
1181C23C2×H(5,𝔽2)12yes—
1182C23C2611yescharacteristic
1183Q8—44no—
1184Q8—48no—
1185Q8—48no—
1186Q8—44no—
1187Q8—88no—
1188Q8—84no—
1189Q8—82no—
1190Q8—162no—
1191Q8—162no—
1192D4—88no—
1193D4—88no—
1194D4—84no—
1195D4—84no—
1196D4—84no—
1197D4—82no—
1198D4—88no—
1199D4—84no—
1200D4—164no—
1201D4—162no—
1202D4—164no—
1203D4—164no—
1204D4—164no—
1205D4—164no—
1206C2×C4—28no—
1207C2×C4—22no—
1208C2×C4—21no—
1209C2×C4—24no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—21no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
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—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—48no—
1254C2×C4—88no—
1255C2×C4—88no—
1256C2×C4—84no—
1257C2×C4—84no—
1258C2×C4—164no—
1259C2×C4—162no—
1260C2×C4—164no—
1261C2×C4C2×H(5,𝔽2)14yes—
1262C2×C4C2×H(5,𝔽2)12yes—
1263C2×C4C2×H(5,𝔽2)14yes—
1264C2×C4#58518yes—
1265C2×C4#58512yes—
1266C22—24no—
1267C22—22no—
1268C22—42no—
1269C22—42no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—44no—
1277C22—44no—
1278C22—44no—
1279C22—44no—
1280C22—42no—
1281C22—44no—
1282C22—44no—
1283C22—44no—
1284C22—42no—
1285C22—44no—
1286C22—44no—
1287C22—44no—
1288C22—42no—
1289C22—168no—
1290C22—168no—
1291C22C22×H(5,𝔽2)11yescharacteristic
1292C22C22×H(5,𝔽2)11yescharacteristic
1293C22C2×#58514yes—
1294C22C2×#58511yescharacteristic
1295C4—28no—
1296C4—24no—
1297C4—22no—
1298C4—22no—
1299C4—24no—
1300C4—44no—
1301C4—44no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—44no—
1307C4—44no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—44no—
1312C4—44no—
1313C4—44no—
1314C2—42no—
1315C2—84no—
1316C2—84no—
1317C2—82no—
1318C2#6281811yescharacteristic
1319C2#6284112yes—
1320C2#6302012yes—
1321C2#6302412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59975C2semidirect
2. #59908C2semidirect
3. #59659C2semidirect
4. #59613C2semidirect
5. #59160C2semidirect
6. #52072C2semidirect
7. #51995C2semidirect
8. #51783C2semidirect
9. #51749C2semidirect
10. #51424C2semidirect
11. #50757C2semidirect
12. #50478C2semidirect
13. #49759C2semidirect
14. #49562C2semidirect
15. #48913C2semidirect
16. #48404C2semidirect
17. #48396C2semidirect
18. #47658C2semidirect
19. #47634C2semidirect
20. #35677C2semidirect
21. #35669C2semidirect
22. #35481C2semidirect
23. #35439C2semidirect
24. C2×H(3,𝔽4)C22semidirect
25. C2×H(3,𝔽4)C22semidirect
26. C2×Q82C22semidirect
31. C22×#124C22semidirect
32. C2×#519C22semidirect
33. #2830C22semidirect
34. #2803C22semidirect
35. #2803C22semidirect
36. #2800C22semidirect
37. #2800C22semidirect
38. #2795C22semidirect
39. #2793C22semidirect
40. #2786C22semidirect
41. #2763C22semidirect
42. #2761C22semidirect
43. #2761C22semidirect
44. #2759C22semidirect
45. #2757C22semidirect
46. #2756C22semidirect
47. #2752C22semidirect
48. #2749C22semidirect
49. #2740C22semidirect
50. #2737C22semidirect
51. #2734C22semidirect
53. #2731C22semidirect
54. #2731C22semidirect
55. #2731C22semidirect
56. #2731C22semidirect
57. #2731C22semidirect
58. #2730C22semidirect
59. #2715C22semidirect
61. #2712C22semidirect
62. #2712C22semidirect
63. #2700C22semidirect
64. #2700C22semidirect
65. #2700C22semidirect
67. #2697C22semidirect
68. #2686C22semidirect
69. #2686C22semidirect
70. #2685C22semidirect
71. #2684C22semidirect
72. #2684C22semidirect
73. #2683C22semidirect
74. #2681C22semidirect
75. #2679C22semidirect
78. #2678C22semidirect
79. #2677C22semidirect
82. #2674C22semidirect
84. #2670C22semidirect
86. #2662C22semidirect
87. #2662C22semidirect
88. #2648C22semidirect
89. #2640C22semidirect
90. #2632C22semidirect
91. #2620C22semidirect
94. #2610C22semidirect
95. #2610C22semidirect
96. #2608C22semidirect
98. #2599C22semidirect
99. #2597C22semidirect
100. #2595C22semidirect
101. #2592C22semidirect
102. #2586C22semidirect
103. #2576C22semidirect
104. #2576C22semidirect
105. #2576C22semidirect
106. #2576C22semidirect
107. #2574C22semidirect
108. #2572C22semidirect
109. #2568C22semidirect
110. #2567C22semidirect
111. #2561C22semidirect
112. #2561C22semidirect
120. #2545C22semidirect
121. #2545C22semidirect
122. #2545C22semidirect
123. #2545C22semidirect
124. #2545C22semidirect
125. #2545C22semidirect
127. #2538C22semidirect
128. #2534C22semidirect
129. #2532C22semidirect
130. #2527C22semidirect
131. #2527C22semidirect
132. #2526C22semidirect
133. #2526C22semidirect
134. #2525C22semidirect
135. #2523C22semidirect
136. #2518C22semidirect
137. #2518C22semidirect
138. #2518C22semidirect
139. #2518C22semidirect
141. #2499C22semidirect
142. #2491C22semidirect
143. #2491C22semidirect
144. #2491C22semidirect
145. #2474C22semidirect
146. #2474C22semidirect
147. #2474C22semidirect
148. #2474C22semidirect
149. #2472C22semidirect
150. #2472C22semidirect
151. #2472C22semidirect
152. #2472C22semidirect
153. #2472C22semidirect
154. #2470C22semidirect
155. #2470C22semidirect
156. #2469C22semidirect
157. #2469C22semidirect
158. #2465C22semidirect
159. #2465C22semidirect
160. #2465C22semidirect
161. #2465C22semidirect
162. #2465C22semidirect
164. #2461C22semidirect
165. #2459C22semidirect
166. #2459C22semidirect
167. #2459C22semidirect
168. #2458C22semidirect
169. #2457C22semidirect
170. #2439C22semidirect
171. #2439C22semidirect
173. #2434C22semidirect
175. #2426C22semidirect
176. #2426C22semidirect
177. #2426C22semidirect
178. #2426C22semidirect
179. #2426C22semidirect
181. #2424C22semidirect
182. #2424C22semidirect
183. #2424C22semidirect
184. #2411C22semidirect
185. #2411C22semidirect
186. #2411C22semidirect
187. #2410C22semidirect
189. #2381C22semidirect
190. #2378C22semidirect
191. #2375C22semidirect
192. #2372C22semidirect
193. #2372C22semidirect
194. #2367C22semidirect
195. #2362C22semidirect
196. #2362C22semidirect
197. #2358C22semidirect
198. #2358C22semidirect
199. #2357C22semidirect
200. #2356C22semidirect
201. #2342C22semidirect
202. #2335C22semidirect
203. #2333C22semidirect
204. #2333C22semidirect
205. #2333C22semidirect
206. #2332C22semidirect
207. #2327C22semidirect
208. #2326C22semidirect
209. #2309C22semidirect
210. C4×C4⋊Q8C22semidirect
211. C4×#124C22semidirect
212. C4×#124C22semidirect
213. C4×#124C22semidirect
214. #2298C22semidirect
216. #2296C22semidirect
217. #2290C22semidirect
218. #2273C22semidirect

Maximal subgroups

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

subgroupindex
#599752
#599082
#596592
#596132
#591602
#520722
#519952
#517832
#517492
#514242
#507572
#504782
#497592
#495622
#489132
#484042
#483962
#476582
#476342
#356772
#356692
#354812
#354392