Finite Group Databasebeta

← #8075410

Subgroups — #8075410

Order 512.

4709 conjugacy classes of subgroups.

The subgroup lattice has 1260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59948C212yesmaximal, complemented
2#59928C211yesmaximal, characteristic, complemented
3#59880C212yesmaximal, complemented
4#59761C214yesmaximal, complemented
5#51999C212yesmaximal, complemented
6#51802C214yesmaximal, complemented
7#51749C212yesmaximal, complemented
8#51681C212yesmaximal, complemented
9#49251C214yesmaximal, complemented
10#48416C214yesmaximal, complemented
11#47452C212yesmaximal, complemented
12#47117C214yesmaximal, complemented
13#44450C212yesmaximal, complemented
14#44399C214yesmaximal, complemented
15#43671C214yesmaximal, complemented
16#43205C214yesmaximal, complemented
17#43042C214yesmaximal, complemented
18#40253C214yesmaximal, complemented
19#39761C212yesmaximal, complemented
20#39360C211yesmaximal, characteristic, complemented
21#38085C212yesmaximal, complemented
22#34524C211yesmaximal, characteristic, complemented
23#34409C212yesmaximal, complemented
24C2×H(3,𝔽4)C2211yescharacteristic
25C2×#553C2212yes—
26C2×D4×Q8C2211yescharacteristic, complemented
27C2×#547C2211yescharacteristic
28C2×#538C2212yescomplemented
29C2×#536C2212yes—
30#2868C2211yescharacteristic, complemented
31#2850C2212yes—
32#2834C2212yescomplemented
33#2811C2211yescharacteristic, complemented
34#2809C2211yescharacteristic, complemented
35#2808C2212yes—
36#2805C2212yescomplemented
37#2804C2212yescomplemented
38#2799C2214yescomplemented
39#2796C2214yescomplemented
40#2793C2214yescomplemented
41#2793C2214yescomplemented
42#2791C2214yescomplemented
43#2790C2214yescomplemented
44#2787C2214yescomplemented
45#2786C2214yes—
46#2786C2214yes—
47#2783C2214yescomplemented
48#2782C2214yescomplemented
49#2775C2214yescomplemented
50#2764C2214yescomplemented
51#2759C2214yescomplemented
52#2759C2214yescomplemented
53#2755C2214yescomplemented
54#2750C2214yes—
55#2743C2214yes—
56#2740C2214yes—
57#2738C2214yescomplemented
58#2736C2212yescomplemented
59#2735C2212yescomplemented
60#2732C2212yes—
61#2731C2212yes—
62#2731C2212yes—
63#2725C2214yescomplemented
64#2724C2214yescomplemented
65#2716C2214yescomplemented
66#2716C2214yescomplemented
67#2716C2214yescomplemented
68#2706C2214yes—
69#2702C2214yes—
70#2700C2214yes—
71#2700C2214yes—
72#2700C2214yes—
73#2700C2214yescomplemented
74#2688C2214yes—
75#2687C2214yescomplemented
76#2687C2214yescomplemented
77#2686C2214yes—
78#2684C2214yes—
79#2682C2212yes—
80#2680C2214yescomplemented
81#2680C2214yescomplemented
82#2678C2214yes—
83#2678C2214yes—
84#2665C2214yescomplemented
85#2651C2214yes—
86#2642C2212yescomplemented
87#2640C2214yes—
88#2621C2212yescomplemented
89#2620C2212yes—
90#2612C2214yescomplemented
91#2612C2212yescomplemented
92#2610C2214yes—
93#2605C2214yescomplemented
94#2602C2214yes—
95#2600C2214yes—
96#2599C2214yescomplemented
97#2598C2214yes—
98#2597C2214yescomplemented
99#2596C2214yescomplemented
100#2595C2214yescomplemented
101#2589C2214yescomplemented
102#2582C2212yescomplemented
103#2577C2214yescomplemented
104#2574C2214yescomplemented
105#2574C2214yescomplemented
106#2573C2214yescomplemented
107#2573C2214yescomplemented
108#2572C2214yescomplemented
109#2565C2212yescomplemented
110#2564C2212yes—
111#2557C2214yes—
112#2557C2214yes—
113#2557C2214yes—
114#2557C2214yes—
115#2556C2214yescomplemented
116#2547C2211yescharacteristic
117#2547C2212yes—
118#2546C2211yescharacteristic, complemented
119#2538C2212yes—
120#2534C2214yescomplemented
121#2534C2214yescomplemented
122#2533C2214yescomplemented
123#2532C2214yescomplemented
124#2532C2214yescomplemented
125#2531C2214yes—
126#2530C2214yescomplemented
127#2527C2214yescomplemented
128#2527C2214yescomplemented
129#2525C2214yescomplemented
130#2523C2214yescomplemented
131#2523C2212yescomplemented
132#2515C2214yescomplemented
133#2512C2214yes—
134#2511C2214yescomplemented
135#2510C2214yes—
136#2503C2212yescomplemented
137#2502C2212yescomplemented
138#2499C2214yescomplemented
139#2499C2212yescomplemented
140#2496C2214yescomplemented
141#2492C2214yescomplemented
142#2488C2214yescomplemented
143#2481C2214yes—
144#2480C2214yescomplemented
145#2477C2214yescomplemented
146#2477C2214yescomplemented
147#2474C2214yes—
148#2474C2214yescomplemented
149#2472C2214yes—
150#2472C2214yes—
151#2466C2214yes—
152#2463C2214yes—
153#2458C2214yescomplemented
154#2455C2214yes—
155#2450C2214yes—
156#2450C2214yescomplemented
157#2450C2214yescomplemented
158#2447C2214yescomplemented
159#2444C2214yescomplemented
160#2444C2214yescomplemented
161#2440C2214yescomplemented
162#2439C2214yescomplemented
163#2437C2214yescomplemented
164#2436C2212yes—
165#2436C2212yes—
166#2434C2212yescomplemented
167#2432C2212yes—
168#2425C2214yes—
169#2423C2214yescomplemented
170#2422C2214yescomplemented
171#2419C2214yescomplemented
172#2418C2214yescomplemented
173#2413C2214yescomplemented
174#2404C2214yes—
175#2392C2214yes—
176C2×#397C2212yescomplemented
177#2381C2212yescomplemented
178#2379C2212yes—
179#2379C2211yescharacteristic
180#2378C2214yescomplemented
181#2372C2212yes—
182#2372C2212yes—
183#2372C2214yes—
184#2369C2212yescomplemented
185#2368C2214yescomplemented
186#2368C2214yescomplemented
187#2364C2212yescomplemented
188#2363C2214yescomplemented
189#2359C2214yescomplemented
190#2359C2214yescomplemented
191#2359C2214yescomplemented
192#2358C2214yes—
193#2358C2212yes—
194#2355C2212yescomplemented
195#2354C2212yes—
196#2343C2214yescomplemented
197#2343C2214yescomplemented
198#2342C2214yescomplemented
199#2339C2214yes—
200#2337C2214yes—
201#2332C2214yescomplemented
202#2331C2214yescomplemented
203#2329C2214yescomplemented
204#2326C2214yes—
205#2326C2212yes—
206#2322C2214yescomplemented
207#2321C2214yes—
208#2321C2212yes—
209#2318C2214yes—
210#2310C2212yescomplemented
211C4×#124C2211yescharacteristic
212C4×#124C2212yes—
213C4×#123C2214yescomplemented
214#2295C2212yescomplemented
215C2×#391C2212yescomplemented
216#2293C2211yescharacteristic, complemented
217#2290C2214yescomplemented
218#2290C2212yescomplemented
219C22×#41C2312yes—
220C23×Q8C2312yes—
221H(3,𝔽4)—28no—
222#553—48no—
223D4×Q8—44no—
224#547—44no—
225#538—48no—
226#536—216no—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#125C2312yes—
236C2×#124C2312yes—
237C2×#124C2314yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2314yes—
241C2×#124C2312yes—
242C2×#124C2312yes—
243C2×#124C2311yescharacteristic
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×#121C2314yes—
260C2×#121C2312yes—
261C2×#121C2312yes—
262C2×#121C2312yes—
263C2×#120C2312yes—
264C2×#120C2314yes—
265C2×#120C2314yes—
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2314yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×#117C2312yes—
280C2×#117C2312yes—
281C2×#117C2314yes—
282C2×#117C2312yes—
283C2×#117C2314yes—
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2312yes—
286C22×C22⋊C4C2314yes—
287C22×C22⋊C4C2312yes—
288C22×C22⋊C4C2314yes—
289C22×C42C2312yes—
290#401C2314yes—
291#400C2312yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#399C2312yes—
306#399C2314yes—
307#399C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2312yes—
325#397C2314yes—
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#397C2312yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#395C2312yes—
354#395C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#393C2312yes—
370#393C2314yes—
371#393C2314yes—
372#393C2314yes—
373#393C2314yes—
374#393C2314yes—
375#393C2314yes—
376#393C2314yes—
377#393C2314yes—
378#393C2314yes—
379#393C2314yes—
380#392C2314yes—
381#392C2314yes—
382#392C2314yes—
383#391C2312yes—
384#391C2312yes—
385#391C2312yes—
386#391C2312yes—
387#391C2314yes—
388#391C2312yes—
389#391C2314yes—
390#391C2312yes—
391#391C2312yes—
392#391C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2312yes—
401#391C2312yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2314yes—
410#391C2311yescharacteristic
411#391C2312yes—
412#390C2312yes—
413#390C2314yes—
414#390C2314yes—
415#390C2314yes—
416#390C2314yes—
417#390C2314yes—
418#390C2312yes—
419#390C2311yescharacteristic
420#390C2312yes—
421#389C2312yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2312yes—
431#389C2314yes—
432#389C2312yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2312yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2312yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#384C2312yes—
554#384C2312yes—
555#384C2312yes—
556#384C2312yes—
557#384C2314yes—
558#383C2314yes—
559#383C2314yes—
560#383C2314yes—
561#383C2314yes—
562#382C2312yes—
563#382C2314yes—
564#382C2314yes—
565#382C2312yes—
566#382C2311yescharacteristic
567#381C2314yes—
568#381C2314yes—
569#381C2314yes—
570#381C2314yes—
571#381C2314yes—
572#381C2314yes—
573#381C2314yes—
574#380C2314yes—
575#380C2314yes—
576#380C2314yes—
577#380C2314yes—
578#380C2314yes—
579#380C2314yes—
580#380C2314yes—
581#379C2312yes—
582#379C2314yes—
583#379C2314yes—
584C4×C4⋊C4C2312yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2311yescharacteristic
594C4×C22⋊C4C2312yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2312yes—
611#376C2314yes—
612#376C2312yes—
613#376C2314yes—
614#376C2314yes—
615C2×#95C2312yes—
616C2×#95C2314yes—
617C2×#95C2314yes—
618C2×#95C2314yes—
619C43C2311yescharacteristic
620C25C2412yes—
621C2×#41—28no—
622C2×#41—44no—
623C2×#41—82no—
624C22×Q8—28no—
625C22×Q8—44no—
626C22×Q8—82no—
627C22×Q8C2412yes—
628C22×Q8C2412yes—
629C22×Q8C2412yes—
630C22×Q8C2412yes—
631C22×Q8C2412yes—
632C22×Q8C2412yes—
633C22×Q8C2412yes—
634C22×Q8C2411yescharacteristic
635C22×D4C2414yes—
636C22×D4C2412yes—
637C22×D4C2414yes—
638C22×D4C2412yes—
639C22×D4C2414yes—
640C22×D4C2414yes—
641C22×D4C2411yescharacteristic
642C22×D4C2411yescharacteristic
643C23×C4C2412yes—
644C23×C4C2412yes—
645C23×C4C2412yes—
646C23×C4C2412yes—
647C23×C4C2414yes—
648C23×C4C2414yes—
649C23×C4C2414yes—
650C23×C4C2412yes—
651C23×C4C2414yes—
652C23×C4C2414yes—
653C23×C4C2414yes—
654C4⋊Q8—28no—
655C4⋊Q8—28no—
656C4⋊Q8—42no—
657C4⋊Q8—44no—
658C4⋊Q8—42no—
659C4⋊Q8—82no—
660#126—48no—
661#126—48no—
662#125—44no—
663#124—28no—
664#124—28no—
665#124—216no—
666#124—28no—
667#124—48no—
668#124—82no—
669#124—82no—
670#124#4118yes—
671#123—216no—
672#123—216no—
673#123—48no—
674#123—48no—
675#123—48no—
676#123—48no—
677C22⋊Q8—216no—
678C22⋊Q8—216no—
679C22⋊Q8—44no—
680C22⋊Q8—44no—
681C22⋊Q8—44no—
682C22⋊Q8—44no—
683C22⋊Q8—48no—
684C22⋊Q8—44no—
685C22⋊Q8—84no—
686#121—28no—
687#121—216no—
688#121—44no—
689#121—44no—
690#120—28no—
691#120—216no—
692#120—48no—
693C4×Q8—44no—
694C4×Q8—42no—
695C4×Q8—44no—
696C4×D4—24no—
697C4×D4—28no—
698C4×D4—48no—
699C4×D4—44no—
700C4×D4—44no—
701C4×D4—42no—
702C4×D4—48no—
703C4×D4—48no—
704C4×D4—48no—
705C4×D4—84no—
706#117—28no—
707#117—48no—
708#117—44no—
709#117—84no—
710#117—82no—
711C2×C4⋊C4—44no—
712C2×C4⋊C4—44no—
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C22⋊C4—48no—
760C2×C22⋊C4—44no—
761C2×C22⋊C4—84no—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
806C2×C42—82no—
807C2×C42C2414yes—
808C2×C42C2412yes—
809C2×C42C2412yes—
810C2×C42C2411yescharacteristic
811C2×C42C2412yes—
812C2×C42C2412yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2412yes—
823C2×C42C2411yescharacteristic
824C2×C42C2412yes—
825C2×C42C2414yes—
826C2×C42C2414yes—
827C2×C42C2411yescharacteristic
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2412yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2412yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
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#95C2412yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884C24—24no—
885C24—42no—
886C24—44no—
887C24—44no—
888C24—42no—
889C24C2514yes—
890C24C2512yes—
891C24C2512yes—
892#41—816no—
893C2×Q8—24no—
894C2×Q8—24no—
895C2×Q8—24no—
896C2×Q8—24no—
897C2×Q8—24no—
898C2×Q8—24no—
899C2×Q8—41no—
900C2×Q8—41no—
901C2×Q8—42no—
902C2×Q8—42no—
903C2×Q8—42no—
904C2×Q8—42no—
905C2×Q8—42no—
906C2×Q8—42no—
907C2×Q8—42no—
908C2×Q8—42no—
909C2×Q8—42no—
910C2×Q8—42no—
911C2×Q8—42no—
912C2×Q8—42no—
913C2×Q8—42no—
914C2×Q8—44no—
915C2×Q8—816no—
916C2×Q8C2×#4114yes—
917C2×D4—28no—
918C2×D4—28no—
919C2×D4—28no—
920C2×D4—28no—
921C2×D4—28no—
922C2×D4—24no—
923C2×D4—24no—
924C2×D4—41no—
925C2×D4—44no—
926C2×D4—42no—
927C2×D4—41no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4—44no—
938C2×D4C2×#4114yes—
939C2×D4H(5,𝔽2)14yes—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—24no—
943C22×C4—28no—
944C22×C4—28no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—24no—
949C22×C4—28no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—44no—
954C22×C4—44no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—42no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4C2514yes—
972C22×C4C2514yes—
973C22×C4C2514yes—
974C22×C4C2514yes—
975C22×C4C2512yes—
976C22×C4C2514yes—
977C22×C4C2512yes—
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2512yes—
981C22×C4C2512yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2512yes—
985C22×C4C2511yescharacteristic
986C22×C4C2511yescharacteristic
987C22×C4C2512yes—
988C22×C4C2512yes—
989C22×C4C2511yescharacteristic
990C22×C4C2512yes—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—22no—
997C4⋊C4—24no—
998C4⋊C4—24no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—24no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—42no—
1017C4⋊C4—44no—
1018C4⋊C4—41no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—42no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—42no—
1026C4⋊C4—41no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—41no—
1030C4⋊C4—41no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—42no—
1037C22⋊C4—24no—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—24no—
1042C22⋊C4—24no—
1043C22⋊C4—24no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4C2×#41116yes—
1081C42—24no—
1082C42—24no—
1083C42—24no—
1084C42—22no—
1085C42—28no—
1086C42—24no—
1087C42—42no—
1088C42—44no—
1089C42—42no—
1090C42—42no—
1091C42—44no—
1092C42—44no—
1093C42—44no—
1094C42—44no—
1095C42—44no—
1096C42—42no—
1097C42—44no—
1098C42—44no—
1099C42—44no—
1100C42—41no—
1101C42C2×#4114yes—
1102C23—22no—
1103C23—22no—
1104C23—24no—
1105C23—24no—
1106C23—22no—
1107C23—22no—
1108C23—24no—
1109C23—24no—
1110C23—24no—
1111C23—24no—
1112C23—24no—
1113C23—24no—
1114C23—24no—
1115C23—24no—
1116C23—24no—
1117C23—84no—
1118C23—88no—
1119C23—88no—
1120C23—162no—
1121C23—162no—
1122C23C22×#4114yes—
1123C23C2×H(5,𝔽2)14yes—
1124C23C2611yescharacteristic
1125Q8—44no—
1126Q8—84no—
1127Q8—84no—
1128Q8—84no—
1129Q8—84no—
1130Q8—84no—
1131Q8—84no—
1132Q8—162no—
1133D4—44no—
1134D4—44no—
1135D4—416no—
1136D4—84no—
1137D4—84no—
1138D4—88no—
1139D4—88no—
1140D4—88no—
1141C2×C4—22no—
1142C2×C4—21no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—22no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—48no—
1193C2×C4—48no—
1194C2×C4—48no—
1195C2×C4—88no—
1196C2×C4—84no—
1197C2×C4—88no—
1198C2×C4—88no—
1199C2×C4—88no—
1200C2×C4—162no—
1201C2×C4—164no—
1202C2×C4—164no—
1203C2×C4C22×#4112yes—
1204C2×C4C22×#4114yes—
1205C2×C4C22×#4114yes—
1206C2×C4C2×H(5,𝔽2)12yes—
1207C2×C4#58514yes—
1208C22—24no—
1209C22—24no—
1210C22—28no—
1211C22—24no—
1212C22—24no—
1213C22—44no—
1214C22—42no—
1215C22—44no—
1216C22—44no—
1217C22—42no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—168no—
1226C22C23×#4111yescharacteristic
1227C22C22×H(5,𝔽2)11yescharacteristic
1228C22C2×#58512yes—
1229C22H(7,𝔽2)11yescharacteristic
1230C222−1+612yes—
1231C4—22no—
1232C4—24no—
1233C4—24no—
1234C4—24no—
1235C4—22no—
1236C4—42no—
1237C4—42no—
1238C4—42no—
1239C4—44no—
1240C4—44no—
1241C4—44no—
1242C4—41no—
1243C4—44no—
1244C4—44no—
1245C4—42no—
1246C4—44no—
1247C4—44no—
1248C4—44no—
1249C4—42no—
1250C4—44no—
1251C2—44no—
1252C2—44no—
1253C2—84no—
1254C2#6286912yes—
1255C2#6287111yescharacteristic
1256C2#6298311yescharacteristic
1257C2#6299512yes—
1258C2#6302411yescharacteristic
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. #59948C2semidirect
2. #59928C2semidirect
3. #59880C2semidirect
4. #59761C2semidirect
5. #51999C2semidirect
6. #51802C2semidirect
7. #51749C2semidirect
8. #51681C2semidirect
9. #49251C2semidirect
10. #48416C2semidirect
11. #47452C2semidirect
12. #47117C2semidirect
13. #44450C2semidirect
14. #44399C2semidirect
15. #43671C2semidirect
16. #43205C2semidirect
17. #43042C2semidirect
18. #40253C2semidirect
19. #39761C2semidirect
20. #39360C2semidirect
21. #38085C2semidirect
22. #34524C2semidirect
23. #34409C2semidirect
26. C2×D4×Q8C22semidirect
28. C2×#538C22semidirect
30. #2868C22semidirect
32. #2834C22semidirect
33. #2811C22semidirect
34. #2809C22semidirect
36. #2805C22semidirect
37. #2804C22semidirect
38. #2799C22semidirect
39. #2796C22semidirect
40. #2793C22semidirect
41. #2793C22semidirect
42. #2791C22semidirect
43. #2790C22semidirect
44. #2787C22semidirect
47. #2783C22semidirect
48. #2782C22semidirect
49. #2775C22semidirect
50. #2764C22semidirect
51. #2759C22semidirect
52. #2759C22semidirect
53. #2755C22semidirect
57. #2738C22semidirect
58. #2736C22semidirect
59. #2735C22semidirect
63. #2725C22semidirect
64. #2724C22semidirect
65. #2716C22semidirect
66. #2716C22semidirect
67. #2716C22semidirect
73. #2700C22semidirect
75. #2687C22semidirect
76. #2687C22semidirect
80. #2680C22semidirect
81. #2680C22semidirect
84. #2665C22semidirect
86. #2642C22semidirect
88. #2621C22semidirect
90. #2612C22semidirect
91. #2612C22semidirect
93. #2605C22semidirect
96. #2599C22semidirect
98. #2597C22semidirect
99. #2596C22semidirect
100. #2595C22semidirect
101. #2589C22semidirect
102. #2582C22semidirect
103. #2577C22semidirect
104. #2574C22semidirect
105. #2574C22semidirect
106. #2573C22semidirect
107. #2573C22semidirect
108. #2572C22semidirect
109. #2565C22semidirect
115. #2556C22semidirect
118. #2546C22semidirect
120. #2534C22semidirect
121. #2534C22semidirect
122. #2533C22semidirect
123. #2532C22semidirect
124. #2532C22semidirect
126. #2530C22semidirect
127. #2527C22semidirect
128. #2527C22semidirect
129. #2525C22semidirect
130. #2523C22semidirect
131. #2523C22semidirect
132. #2515C22semidirect
134. #2511C22semidirect
136. #2503C22semidirect
137. #2502C22semidirect
138. #2499C22semidirect
139. #2499C22semidirect
140. #2496C22semidirect
141. #2492C22semidirect
142. #2488C22semidirect
144. #2480C22semidirect
145. #2477C22semidirect
146. #2477C22semidirect
148. #2474C22semidirect
153. #2458C22semidirect
156. #2450C22semidirect
157. #2450C22semidirect
158. #2447C22semidirect
159. #2444C22semidirect
160. #2444C22semidirect
161. #2440C22semidirect
162. #2439C22semidirect
163. #2437C22semidirect
166. #2434C22semidirect
169. #2423C22semidirect
170. #2422C22semidirect
171. #2419C22semidirect
172. #2418C22semidirect
173. #2413C22semidirect
176. C2×#397C22semidirect
177. #2381C22semidirect
180. #2378C22semidirect
184. #2369C22semidirect
185. #2368C22semidirect
186. #2368C22semidirect
187. #2364C22semidirect
188. #2363C22semidirect
189. #2359C22semidirect
190. #2359C22semidirect
191. #2359C22semidirect
194. #2355C22semidirect
196. #2343C22semidirect
197. #2343C22semidirect
198. #2342C22semidirect
201. #2332C22semidirect
202. #2331C22semidirect
203. #2329C22semidirect
206. #2322C22semidirect
210. #2310C22semidirect
213. C4×#123C22semidirect
214. #2295C22semidirect
215. C2×#391C22semidirect
216. #2293C22semidirect
217. #2290C22semidirect
218. #2290C22semidirect

Maximal subgroups

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

subgroupindex
#599482
#599282
#598802
#597612
#519992
#518022
#517492
#516812
#492512
#484162
#474522
#471172
#444502
#443992
#436712
#432052
#430422
#402532
#397612
#393602
#380852
#345242
#344092