Finite Group Databasebeta

← #8934696

Subgroups — #8934696

Order 512.

5714 conjugacy classes of subgroups.

The subgroup lattice has 1430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59977C214yesmaximal, complemented
2#59948C212yesmaximal, complemented
3#59885C212yesmaximal, complemented
4#59798C212yesmaximal, complemented
5#59620C212yesmaximal, complemented
6#52076C212yesmaximal, complemented
7#52012C212yesmaximal, complemented
8#51978C211yesmaximal, characteristic, complemented
9#51971C214yesmaximal, complemented
10#51914C214yesmaximal, complemented
11#51902C211yesmaximal, characteristic, complemented
12#51749C212yesmaximal, complemented
13#50468C214yesmaximal, complemented
14#50358C214yesmaximal, complemented
15#49566C214yesmaximal, complemented
16#49190C214yesmaximal, complemented
17#48397C214yesmaximal, complemented
18#47567C212yesmaximal, complemented
19#47565C214yesmaximal, complemented
20#35676C211yesmaximal, characteristic, complemented
21#35660C212yesmaximal, complemented
22#35524C214yesmaximal, complemented
23#35451C212yesmaximal, complemented
24C22×2−1+4C2211yescharacteristic, complemented
25C2×#563C2211yescharacteristic, complemented
26C2×H(3,𝔽4)C2211yescharacteristic
27C2×#560C2212yescomplemented
28C2×#537C2212yescomplemented
29C2×#536C2212yescomplemented
30C2×#535C2211yescharacteristic
31C2×#535C2211yescharacteristic
32C2×#532C2212yes—
33C22×#124C2211yescharacteristic
34C2×#518C2212yescomplemented
35#2841C2212yescomplemented
36#2809C2212yescomplemented
37#2808C2214yescomplemented
38#2803C2214yescomplemented
39#2797C2214yescomplemented
40#2784C2212yescomplemented
41#2779C2214yescomplemented
42#2775C2214yescomplemented
43#2775C2214yescomplemented
44#2764C2212yescomplemented
45#2761C2214yescomplemented
46#2757C2214yescomplemented
47#2756C2214yescomplemented
48#2756C2214yescomplemented
49#2756C2214yescomplemented
50#2752C2212yes—
51#2749C2214yescomplemented
52#2749C2214yescomplemented
53#2733C2212yes—
54#2731C2212yes—
55#2731C2212yescomplemented
56#2729C2214yescomplemented
57#2717C2212yescomplemented
58#2715C2214yescomplemented
59#2714C2214yescomplemented
60#2709C2214yescomplemented
61#2709C2212yescomplemented
62#2704C2214yescomplemented
63#2703C2214yescomplemented
64#2702C2214yescomplemented
65#2702C2214yescomplemented
66#2700C2214yescomplemented
67#2700C2214yescomplemented
68#2699C2212yescomplemented
69#2699C2214yescomplemented
70#2698C2214yescomplemented
71#2697C2214yescomplemented
72#2691C2214yescomplemented
73#2688C2214yescomplemented
74#2685C2214yescomplemented
75#2684C2212yescomplemented
76#2684C2214yescomplemented
77#2682C2214yescomplemented
78#2681C2214yescomplemented
79#2681C2214yescomplemented
80#2678C2214yes—
81#2678C2214yes—
82#2678C2214yescomplemented
83#2678C2214yescomplemented
84#2673C2214yes—
85#2670C2214yes—
86#2669C2214yes—
87#2669C2212yes—
88#2662C2214yes—
89#2662C2214yescomplemented
90#2661C2214yescomplemented
91#2657C2212yes—
92#2641C2212yes—
93#2640C2214yescomplemented
94#2619C2214yescomplemented
95#2612C2214yescomplemented
96#2611C2212yescomplemented
97#2610C2212yes—
98#2610C2214yescomplemented
99#2610C2214yescomplemented
100#2601C2214yescomplemented
101#2601C2214yescomplemented
102#2600C2212yes—
103#2600C2214yescomplemented
104#2591C2214yescomplemented
105#2586C2214yescomplemented
106#2586C2212yescomplemented
107#2574C2214yescomplemented
108#2572C2212yescomplemented
109#2572C2214yescomplemented
110#2572C2214yescomplemented
111#2560C2214yescomplemented
112#2559C2214yescomplemented
113#2559C2214yescomplemented
114#2558C2214yescomplemented
115#2557C2214yescomplemented
116#2557C2214yescomplemented
117#2555C2214yes—
118#2554C2214yescomplemented
119#2554C2214yescomplemented
120#2554C2214yescomplemented
121#2554C2214yescomplemented
122#2543C2214yescomplemented
123#2543C2214yescomplemented
124#2534C2214yes—
125#2534C2214yescomplemented
126#2532C2214yescomplemented
127#2532C2214yescomplemented
128#2532C2214yescomplemented
129#2532C2214yescomplemented
130#2526C2214yescomplemented
131#2488C2214yescomplemented
132#2483C2212yescomplemented
133#2474C2214yes—
134#2474C2214yescomplemented
135#2472C2214yes—
136#2472C2214yescomplemented
137#2472C2214yescomplemented
138#2472C2214yescomplemented
139#2471C2214yescomplemented
140#2461C2214yes—
141#2461C2214yescomplemented
142#2459C2214yes—
143#2459C2214yescomplemented
144#2459C2214yescomplemented
145#2459C2214yescomplemented
146#2459C2214yescomplemented
147#2456C2214yes—
148#2456C2214yescomplemented
149#2456C2214yescomplemented
150#2452C2214yescomplemented
151#2445C2214yes—
152#2439C2214yescomplemented
153#2436C2212yes—
154#2436C2212yescomplemented
155#2436C2214yescomplemented
156#2436C2212yescomplemented
157#2436C2212yescomplemented
158#2434C2212yescomplemented
159#2434C2212yescomplemented
160#2433C2214yes—
161#2432C2212yescomplemented
162#2432C2212yescomplemented
163#2431C2212yes—
164#2431C2212yes—
165#2431C2212yes—
166#2431C2214yescomplemented
167#2431C2212yescomplemented
168#2430C2214yescomplemented
169#2430C2214yescomplemented
170#2430C2214yescomplemented
171#2430C2214yescomplemented
172#2428C2214yescomplemented
173#2425C2214yes—
174#2424C2214yes—
175#2424C2214yescomplemented
176#2420C2214yescomplemented
177#2414C2214yescomplemented
178#2413C2214yescomplemented
179#2409C2214yescomplemented
180#2409C2214yescomplemented
181#2408C2214yescomplemented
182#2407C2214yescomplemented
183#2407C2214yescomplemented
184#2407C2214yescomplemented
185#2405C2212yes—
186#2405C2212yescomplemented
187#2404C2214yescomplemented
188#2404C2214yescomplemented
189#2404C2214yescomplemented
190#2403C2212yes—
191#2379C2214yescomplemented
192#2375C2214yescomplemented
193#2374C2214yescomplemented
194#2373C2214yescomplemented
195#2372C2211yescharacteristic
196#2372C2211yescharacteristic, complemented
197#2372C2212yescomplemented
198#2369C2212yescomplemented
199#2366C2212yescomplemented
200#2363C2214yescomplemented
201#2359C2214yescomplemented
202#2353C2214yescomplemented
203#2353C2214yescomplemented
204#2343C2214yescomplemented
205#2328C2214yescomplemented
206#2324C2214yescomplemented
207#2321C2214yes—
208#2319C2214yescomplemented
209#2312C2212yescomplemented
210#2311C2212yescomplemented
211#2310C2211yescharacteristic, complemented
212C4×#123C2214yescomplemented
213C4×#121C2214yescomplemented
214#2297C2212yescomplemented
215#2297C2211yescharacteristic, complemented
216#2297C2211yescharacteristic, complemented
217C2×#391C2212yescomplemented
218#2290C2214yescomplemented
219C2×2−1+4—44no—
220C2×2−1+4—44no—
221C2×2−1+4—44no—
222C22×#41C2312yes—
223C22×#41C2311yescharacteristic
224C22×#41C2311yescharacteristic
225C22×#41C2312yes—
226C22×#41C2312yes—
227C22×#41C2312yes—
228C22×#41C2312yes—
229C23×Q8C2311yescharacteristic
230C23×Q8C2312yes—
231C23×Q8C2312yes—
232C23×D4C2312yes—
233C23×D4C2311yescharacteristic
234#563—44no—
235H(3,𝔽4)—44no—
236#560—48no—
237#537—48no—
238#536—48no—
239#535—44no—
240#535—44no—
241#532—48no—
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2312yes—
245C2×#127C2312yes—
246C2×#127C2314yes—
247C2×#127C2311yescharacteristic
248C2×#127C2311yescharacteristic
249C2×#127C2312yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#125C2312yes—
254C2×#124—44no—
255C2×#124C2311yescharacteristic
256C2×#124C2311yescharacteristic
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2314yes—
260C2×#124C2314yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2314yes—
265C2×#124C2312yes—
266C2×#124C2312yes—
267C2×#124C2312yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2312yes—
271C2×#123C2312yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2312yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×#121C2314yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×#121C2312yes—
291C2×#121C2314yes—
292C2×#121C2314yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#120C2314yes—
297C2×#120C2314yes—
298C2×#120C2312yes—
299C2×#120C2312yes—
300C2×#120C2314yes—
301C2×#120C2314yes—
302C2×#120C2314yes—
303C2×#120C2314yes—
304#518—48no—
305C2×C4×D4C2314yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2314yes—
313C2×#117C2311yescharacteristic
314C2×#117C2311yescharacteristic
315C2×#117C2312yes—
316C2×#117C2314yes—
317C2×#117C2314yes—
318C22×C4⋊C4C2312yes—
319C22×C22⋊C4C2312yes—
320C22×C22⋊C4C2312yes—
321C22×C22⋊C4C2314yes—
322C22×C22⋊C4C2312yes—
323C22×C42C2311yescharacteristic
324C22×C42C2312yes—
325#400C2314yes—
326#400C2312yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#399C2312yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2312yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#397C2314yes—
339#397C2312yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2312yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2312yes—
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#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#393C2314yes—
395#393C2312yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#392C2312yes—
407#392C2314yes—
408#392C2314yes—
409#392C2314yes—
410#392C2314yes—
411#392C2314yes—
412#392C2314yes—
413#392C2314yes—
414#392C2314yes—
415#392C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2312yes—
434#391C2312yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2314yes—
442#390C2314yes—
443#390C2312yes—
444#390C2312yes—
445#390C2314yes—
446#390C2314yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2314yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#390C2314yes—
457#390C2312yes—
458#390C2314yes—
459#390C2314yes—
460#390C2314yes—
461#390C2312yes—
462#390C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
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#388C2314yes—
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#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
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#386C2312yes—
554#386C2312yes—
555#386C2312yes—
556#386C2314yes—
557#386C2312yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#383C2314yes—
579#383C2314yes—
580#383C2314yes—
581#382C2314yes—
582#382C2314yes—
583#381C2312yes—
584#381C2312yes—
585#381C2314yes—
586#381C2314yes—
587#381C2314yes—
588#381C2314yes—
589#381C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#379C2312yes—
596#379C2312yes—
597#379C2314yes—
598#379C2314yes—
599#379C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2312yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2312yes—
619C4×C22⋊C4C2312yes—
620C4×C22⋊C4C2312yes—
621#376C2314yes—
622#376C2312yes—
623#376C2312yes—
624#376C2314yes—
625C2×#95C2314yes—
626C2×#95C2314yes—
627C25C2412yes—
628C25C2412yes—
6292−1+4—464no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—28no—
633C2×#41—28no—
634C2×#41—42no—
635C2×#41—42no—
636C2×#41—44no—
637C2×#41—44no—
638C2×#41—42no—
639C2×#41—42no—
640C2×#41—44no—
641C2×#41—44no—
642C2×#41—44no—
643C2×#41—44no—
644C2×#41—44no—
645C2×#41—44no—
646C2×#41—44no—
647C2×#41—44no—
648C2×#41—44no—
649C2×#41—44no—
650C2×#41—44no—
651C22×Q8—28no—
652C22×Q8—24no—
653C22×Q8—44no—
654C22×Q8—44no—
655C22×Q8—42no—
656C22×Q8—42no—
657C22×Q8—44no—
658C22×Q8—44no—
659C22×Q8—44no—
660C22×Q8C2412yes—
661C22×Q8C2412yes—
662C22×Q8C2412yes—
663C22×Q8C2412yes—
664C22×Q8C2411yescharacteristic
665C22×Q8C2412yes—
666C22×Q8C2412yes—
667C22×Q8C2411yescharacteristic
668C22×D4—48no—
669C22×D4—42no—
670C22×D4—42no—
671C22×D4—42no—
672C22×D4—44no—
673C22×D4C2414yes—
674C22×D4C2412yes—
675C22×D4C2412yes—
676C22×D4C2412yes—
677C22×D4C2414yes—
678C22×D4C2414yes—
679C22×D4C2414yes—
680C22×D4C2414yes—
681C22×D4C2414yes—
682C22×D4C2411yescharacteristic
683C22×D4C2412yes—
684C22×D4C2414yes—
685C22×D4C2412yes—
686C22×D4C2411yescharacteristic
687C22×D4C2412yes—
688C22×D4C2411yescharacteristic
689C22×D4C2414yes—
690C22×D4C2414yes—
691C22×D4C2414yes—
692C22×D4C2412yes—
693C22×D4C2414yes—
694C22×D4C2414yes—
695C22×D4C2411yescharacteristic
696C23×C4C2412yes—
697C23×C4C2411yescharacteristic
698C23×C4C2412yes—
699C23×C4C2412yes—
700C23×C4C2412yes—
701C23×C4C2412yes—
702C23×C4C2412yes—
703C23×C4C2411yescharacteristic
704C23×C4C2414yes—
705C23×C4C2414yes—
706C23×C4C2414yes—
707C23×C4C2412yes—
708C23×C4C2412yes—
709C23×C4C2414yes—
710C23×C4C2412yes—
711C23×C4C2412yes—
712C23×C4C2411yescharacteristic
713C4⋊Q8—28no—
714C4⋊Q8—44no—
715C4⋊Q8—44no—
716#127—28no—
717#127—48no—
718#127—42no—
719#127—42no—
720#127—44no—
721#126—48no—
722#126—48no—
723#126—48no—
724#125—44no—
725#124—24no—
726#124—24no—
727#124—28no—
728#124—48no—
729#124—44no—
730#124—48no—
731#124—44no—
732#124—44no—
733#124—44no—
734#124—44no—
735#124—48no—
736#124—44no—
737#124—44no—
738#123—48no—
739#123—48no—
740#123—48no—
741#123—48no—
742#123—48no—
743#123—48no—
744#123—44no—
745#123—44no—
746C22⋊Q8—44no—
747C22⋊Q8—48no—
748C22⋊Q8—48no—
749C22⋊Q8—48no—
750C22⋊Q8—48no—
751C22⋊Q8—44no—
752#121—216no—
753#121—48no—
754#121—48no—
755#121—44no—
756#121—48no—
757#121—48no—
758#121—48no—
759#121—48no—
760#121—48no—
761#121—44no—
762#121—44no—
763#121—44no—
764#121—48no—
765#121—48no—
766#120—48no—
767#120—48no—
768#120—48no—
769#120—44no—
770#120—48no—
771#120—44no—
772#120—48no—
773#120—48no—
774C4×D4—216no—
775C4×D4—48no—
776C4×D4—48no—
777C4×D4—48no—
778C4×D4—48no—
779C4×D4—48no—
780C4×D4—48no—
781C4×D4—48no—
782#117—42no—
783#117—42no—
784#117—44no—
785#117—48no—
786#117—48no—
787C2×C4⋊C4—44no—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C22⋊C4—28no—
817C2×C22⋊C4—48no—
818C2×C22⋊C4—44no—
819C2×C22⋊C4—44no—
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⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C42—44no—
879C2×C42—42no—
880C2×C42C2414yes—
881C2×C42C2411yescharacteristic
882C2×C42C2412yes—
883C2×C42C2411yescharacteristic
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2414yes—
896C2×C42C2412yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2412yes—
906#95C2414yes—
907#95C2412yes—
908#95C2414yes—
909#95C2414yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2412yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939C24—24no—
940C24—42no—
941C24—44no—
942C24—44no—
943C24—42no—
944C24—42no—
945C24—44no—
946C24—42no—
947C24—42no—
948C24—44no—
949C24C2512yes—
950C24C2512yes—
951C24C2514yes—
952C24C2512yes—
953C24C2511yescharacteristic
954C24C2512yes—
955#41—416no—
956#41—416no—
957#41—432no—
958#41—432no—
959#41—432no—
960#41—432no—
961#41—816no—
962C2×Q8—24no—
963C2×Q8—24no—
964C2×Q8—24no—
965C2×Q8—24no—
966C2×Q8—24no—
967C2×Q8—22no—
968C2×Q8—24no—
969C2×Q8—24no—
970C2×Q8—24no—
971C2×Q8—41no—
972C2×Q8—42no—
973C2×Q8—41no—
974C2×Q8—41no—
975C2×Q8—42no—
976C2×Q8—42no—
977C2×Q8—41no—
978C2×Q8—42no—
979C2×Q8—42no—
980C2×Q8—42no—
981C2×Q8—42no—
982C2×Q8—42no—
983C2×Q8—44no—
984C2×Q8—416no—
985C2×Q8—432no—
986C2×Q8—432no—
987C2×Q8H(5,𝔽2)14yes—
988C2×D4—28no—
989C2×D4—24no—
990C2×D4—24no—
991C2×D4—24no—
992C2×D4—24no—
993C2×D4—24no—
994C2×D4—28no—
995C2×D4—28no—
996C2×D4—28no—
997C2×D4—28no—
998C2×D4—24no—
999C2×D4—24no—
1000C2×D4—22no—
1001C2×D4—24no—
1002C2×D4—22no—
1003C2×D4—24no—
1004C2×D4—22no—
1005C2×D4—28no—
1006C2×D4—28no—
1007C2×D4—28no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—41no—
1012C2×D4—41no—
1013C2×D4—41no—
1014C2×D4—41no—
1015C2×D4—42no—
1016C2×D4—42no—
1017C2×D4—42no—
1018C2×D4—42no—
1019C2×D4—42no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—42no—
1025C2×D4—41no—
1026C2×D4—41no—
1027C2×D4—42no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—41no—
1035C2×D4—42no—
1036C2×D4—41no—
1037C2×D4—42no—
1038C2×D4—44no—
1039C2×D4—42no—
1040C2×D4—44no—
1041C2×D4—44no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—44no—
1047C2×D4—44no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—44no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C2×D4—44no—
1054C2×D4—44no—
1055C2×D4—432no—
1056C2×D4—88no—
1057C2×D4H(5,𝔽2)14yes—
1058C22×C4—22no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—22no—
1062C22×C4—22no—
1063C22×C4—24no—
1064C22×C4—22no—
1065C22×C4—24no—
1066C22×C4—24no—
1067C22×C4—24no—
1068C22×C4—28no—
1069C22×C4—24no—
1070C22×C4—24no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—24no—
1074C22×C4—28no—
1075C22×C4—28no—
1076C22×C4—28no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—42no—
1080C22×C4—42no—
1081C22×C4—41no—
1082C22×C4—42no—
1083C22×C4—41no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—42no—
1087C22×C4—41no—
1088C22×C4—41no—
1089C22×C4—42no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—42no—
1098C22×C4—44no—
1099C22×C4—42no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—42no—
1103C22×C4—42no—
1104C22×C4—44no—
1105C22×C4H(5,𝔽2)14yes—
1106C22×C4C2512yes—
1107C22×C4C2514yes—
1108C22×C4C2514yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2514yes—
1112C22×C4C2514yes—
1113C22×C4C2512yes—
1114C22×C4C2514yes—
1115C22×C4C2514yes—
1116C22×C4C2514yes—
1117C22×C4C2514yes—
1118C22×C4C2512yes—
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C22×C4C2512yes—
1122C22×C4C2514yes—
1123C4⋊C4—28no—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—28no—
1127C4⋊C4—28no—
1128C4⋊C4—28no—
1129C4⋊C4—28no—
1130C4⋊C4—28no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C22⋊C4—28no—
1152C22⋊C4—28no—
1153C22⋊C4—28no—
1154C22⋊C4—28no—
1155C22⋊C4—28no—
1156C22⋊C4—28no—
1157C22⋊C4—28no—
1158C22⋊C4—28no—
1159C22⋊C4—28no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—28no—
1164C22⋊C4—28no—
1165C22⋊C4—28no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—42no—
1172C22⋊C4—42no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—42no—
1186C22⋊C4—44no—
1187C22⋊C4—42no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—42no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C42—28no—
1210C42—22no—
1211C42—24no—
1212C42—22no—
1213C42—24no—
1214C42—24no—
1215C42—28no—
1216C42—42no—
1217C42—42no—
1218C42—42no—
1219C42—42no—
1220C42—44no—
1221C42—44no—
1222C42—44no—
1223C42—44no—
1224C42—44no—
1225C42—44no—
1226C23—22no—
1227C23—21no—
1228C23—21no—
1229C23—22no—
1230C23—24no—
1231C23—24no—
1232C23—24no—
1233C23—22no—
1234C23—24no—
1235C23—22no—
1236C23—22no—
1237C23—22no—
1238C23—24no—
1239C23—24no—
1240C23—22no—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23—22no—
1245C23—24no—
1246C23—24no—
1247C23—24no—
1248C23—24no—
1249C23—24no—
1250C23—24no—
1251C23—24no—
1252C23—24no—
1253C23—24no—
1254C23—24no—
1255C23—48no—
1256C23—48no—
1257C23—84no—
1258C23—84no—
1259C23—164no—
1260C23—164no—
1261C23—164no—
1262C23—164no—
1263C23—162no—
1264C23—162no—
1265C23C2×H(5,𝔽2)12yes—
1266C23C2×H(5,𝔽2)14yes—
1267C23C2611yescharacteristic
1268Q8—44no—
1269Q8—48no—
1270Q8—48no—
1271Q8—48no—
1272Q8—44no—
1273Q8—48no—
1274Q8—84no—
1275Q8—162no—
1276D4—44no—
1277D4—416no—
1278D4—48no—
1279D4—48no—
1280D4—416no—
1281D4—44no—
1282D4—48no—
1283D4—48no—
1284D4—88no—
1285D4—82no—
1286D4—84no—
1287D4—82no—
1288D4—84no—
1289D4—88no—
1290D4—88no—
1291D4—88no—
1292D4—88no—
1293D4—164no—
1294D4—164no—
1295D4—164no—
1296D4—164no—
1297D4—162no—
1298D4—164no—
1299C2×C4—28no—
1300C2×C4—216no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—44no—
1346C2×C4—48no—
1347C2×C4—48no—
1348C2×C4—48no—
1349C2×C4—48no—
1350C2×C4—48no—
1351C2×C4—44no—
1352C2×C4—48no—
1353C2×C4—88no—
1354C2×C4—88no—
1355C2×C4—88no—
1356C2×C4—84no—
1357C2×C4—162no—
1358C2×C4—164no—
1359C2×C4—162no—
1360C2×C4C2×H(5,𝔽2)14yes—
1361C2×C4C2×H(5,𝔽2)14yes—
1362C2×C4C2×H(5,𝔽2)12yes—
1363C2×C4C2×H(5,𝔽2)12yes—
1364C2×C4#58518yes—
1365C22—24no—
1366C22—24no—
1367C22—24no—
1368C22—22no—
1369C22—24no—
1370C22—42no—
1371C22—44no—
1372C22—42no—
1373C22—44no—
1374C22—44no—
1375C22—44no—
1376C22—44no—
1377C22—42no—
1378C22—44no—
1379C22—42no—
1380C22—44no—
1381C22—44no—
1382C22—44no—
1383C22—44no—
1384C22—44no—
1385C22—42no—
1386C22—44no—
1387C22—42no—
1388C22—42no—
1389C22—42no—
1390C22—44no—
1391C22—42no—
1392C22—44no—
1393C22—42no—
1394C22—44no—
1395C22—42no—
1396C22—168no—
1397C22—168no—
1398C22C22×H(5,𝔽2)11yescharacteristic
1399C22C22×H(5,𝔽2)11yescharacteristic
1400C22C22×H(5,𝔽2)11yescharacteristic
1401C22C2×#58514yes—
1402C4—24no—
1403C4—22no—
1404C4—22no—
1405C4—24no—
1406C4—28no—
1407C4—44no—
1408C4—44no—
1409C4—44no—
1410C4—44no—
1411C4—42no—
1412C4—42no—
1413C4—44no—
1414C4—42no—
1415C4—42no—
1416C4—44no—
1417C4—44no—
1418C4—44no—
1419C2—44no—
1420C2—42no—
1421C2—82no—
1422C2—82no—
1423C2—84no—
1424C2—82no—
1425C2#6281711yescharacteristic
1426C2#6282112yes—
1427C2#6302412yes—
1428C2#6303512yes—
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. #59977C2semidirect
2. #59948C2semidirect
3. #59885C2semidirect
4. #59798C2semidirect
5. #59620C2semidirect
6. #52076C2semidirect
7. #52012C2semidirect
8. #51978C2semidirect
9. #51971C2semidirect
10. #51914C2semidirect
11. #51902C2semidirect
12. #51749C2semidirect
13. #50468C2semidirect
14. #50358C2semidirect
15. #49566C2semidirect
16. #49190C2semidirect
17. #48397C2semidirect
18. #47567C2semidirect
19. #47565C2semidirect
20. #35676C2semidirect
21. #35660C2semidirect
22. #35524C2semidirect
23. #35451C2semidirect
24. C22×2−1+4C22semidirect
25. C2×#563C22semidirect
27. C2×#560C22semidirect
28. C2×#537C22semidirect
29. C2×#536C22semidirect
34. C2×#518C22semidirect
35. #2841C22semidirect
36. #2809C22semidirect
37. #2808C22semidirect
38. #2803C22semidirect
39. #2797C22semidirect
40. #2784C22semidirect
41. #2779C22semidirect
42. #2775C22semidirect
43. #2775C22semidirect
44. #2764C22semidirect
45. #2761C22semidirect
46. #2757C22semidirect
47. #2756C22semidirect
48. #2756C22semidirect
49. #2756C22semidirect
51. #2749C22semidirect
52. #2749C22semidirect
55. #2731C22semidirect
56. #2729C22semidirect
57. #2717C22semidirect
58. #2715C22semidirect
59. #2714C22semidirect
60. #2709C22semidirect
61. #2709C22semidirect
62. #2704C22semidirect
63. #2703C22semidirect
64. #2702C22semidirect
65. #2702C22semidirect
66. #2700C22semidirect
67. #2700C22semidirect
68. #2699C22semidirect
69. #2699C22semidirect
70. #2698C22semidirect
71. #2697C22semidirect
72. #2691C22semidirect
73. #2688C22semidirect
74. #2685C22semidirect
75. #2684C22semidirect
76. #2684C22semidirect
77. #2682C22semidirect
78. #2681C22semidirect
79. #2681C22semidirect
82. #2678C22semidirect
83. #2678C22semidirect
89. #2662C22semidirect
90. #2661C22semidirect
93. #2640C22semidirect
94. #2619C22semidirect
95. #2612C22semidirect
96. #2611C22semidirect
98. #2610C22semidirect
99. #2610C22semidirect
100. #2601C22semidirect
101. #2601C22semidirect
103. #2600C22semidirect
104. #2591C22semidirect
105. #2586C22semidirect
106. #2586C22semidirect
107. #2574C22semidirect
108. #2572C22semidirect
109. #2572C22semidirect
110. #2572C22semidirect
111. #2560C22semidirect
112. #2559C22semidirect
113. #2559C22semidirect
114. #2558C22semidirect
115. #2557C22semidirect
116. #2557C22semidirect
118. #2554C22semidirect
119. #2554C22semidirect
120. #2554C22semidirect
121. #2554C22semidirect
122. #2543C22semidirect
123. #2543C22semidirect
125. #2534C22semidirect
126. #2532C22semidirect
127. #2532C22semidirect
128. #2532C22semidirect
129. #2532C22semidirect
130. #2526C22semidirect
131. #2488C22semidirect
132. #2483C22semidirect
134. #2474C22semidirect
136. #2472C22semidirect
137. #2472C22semidirect
138. #2472C22semidirect
139. #2471C22semidirect
141. #2461C22semidirect
143. #2459C22semidirect
144. #2459C22semidirect
145. #2459C22semidirect
146. #2459C22semidirect
148. #2456C22semidirect
149. #2456C22semidirect
150. #2452C22semidirect
152. #2439C22semidirect
154. #2436C22semidirect
155. #2436C22semidirect
156. #2436C22semidirect
157. #2436C22semidirect
158. #2434C22semidirect
159. #2434C22semidirect
161. #2432C22semidirect
162. #2432C22semidirect
166. #2431C22semidirect
167. #2431C22semidirect
168. #2430C22semidirect
169. #2430C22semidirect
170. #2430C22semidirect
171. #2430C22semidirect
172. #2428C22semidirect
175. #2424C22semidirect
176. #2420C22semidirect
177. #2414C22semidirect
178. #2413C22semidirect
179. #2409C22semidirect
180. #2409C22semidirect
181. #2408C22semidirect
182. #2407C22semidirect
183. #2407C22semidirect
184. #2407C22semidirect
186. #2405C22semidirect
187. #2404C22semidirect
188. #2404C22semidirect
189. #2404C22semidirect
191. #2379C22semidirect
192. #2375C22semidirect
193. #2374C22semidirect
194. #2373C22semidirect
196. #2372C22semidirect
197. #2372C22semidirect
198. #2369C22semidirect
199. #2366C22semidirect
200. #2363C22semidirect
201. #2359C22semidirect
202. #2353C22semidirect
203. #2353C22semidirect
204. #2343C22semidirect
205. #2328C22semidirect
206. #2324C22semidirect
208. #2319C22semidirect
209. #2312C22semidirect
210. #2311C22semidirect
211. #2310C22semidirect
212. C4×#123C22semidirect
213. C4×#121C22semidirect
214. #2297C22semidirect
215. #2297C22semidirect
216. #2297C22semidirect
217. C2×#391C22semidirect
218. #2290C22semidirect

Maximal subgroups

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

subgroupindex
#599772
#599482
#598852
#597982
#596202
#520762
#520122
#519782
#519712
#519142
#519022
#517492
#504682
#503582
#495662
#491902
#483972
#475672
#475652
#356762
#356602
#355242
#354512