Finite Group Databasebeta

← #8757210

Subgroups — #8757210

Order 512.

4832 conjugacy classes of subgroups.

The subgroup lattice has 1355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58885C214yesmaximal, complemented
2#57494C214yesmaximal, complemented
3#56292C214yesmaximal, complemented
4#55800C214yesmaximal, complemented
5#55330C214yesmaximal, complemented
6#53808C214yesmaximal, complemented
7#50821C214yesmaximal, complemented
8#50219C212yesmaximal, complemented
9#49660C212yesmaximal, complemented
10#48309C214yesmaximal, complemented
11#46962C214yesmaximal, complemented
12#46427C212yesmaximal, complemented
13#46423C212yesmaximal, complemented
14#46366C214yesmaximal, complemented
15#46228C211yesmaximal, characteristic, complemented
16#46225C211yesmaximal, characteristic, complemented
17#46134C212yesmaximal, complemented
18#45991C212yesmaximal, complemented
19#45989C212yesmaximal, complemented
20#45989C212yesmaximal, complemented
21#45973C212yesmaximal, complemented
22#35328C211yesmaximal, characteristic, complemented
23#35130C212yesmaximal, complemented
24C2×#563C2211yescharacteristic, complemented
25C2×H(3,𝔽4)C2211yescharacteristic
26C2×#538C2212yescomplemented
27C2×#537C2211yescharacteristic
28C2×#537C2212yes—
29C2×#537C2211yescharacteristic, complemented
30C2×#532C2211yescharacteristic
31C2×#529C2212yes—
32C2×C4×#41C2211yescharacteristic, complemented
33#2851C2212yescomplemented
34#2851C2212yescomplemented
35#2850C2212yes—
36#2850C2212yes—
37#2850C2212yes—
38#2850C2212yescomplemented
39#2844C2212yescomplemented
40#2838C2214yescomplemented
41#2837C2214yes—
42#2827C2214yescomplemented
43#2825C2214yes—
44#2820C2212yes—
45#2820C2212yes—
46#2819C2212yes—
47#2817C2212yescomplemented
48#2816C2212yes—
49#2816C2214yes—
50#2814C2214yescomplemented
51#2797C2214yes—
52#2785C2214yescomplemented
53#2782C2214yescomplemented
54#2778C2214yescomplemented
55#2775C2214yescomplemented
56#2775C2214yescomplemented
57#2773C2214yescomplemented
58#2773C2214yescomplemented
59#2768C2214yescomplemented
60#2768C2214yescomplemented
61#2765C2214yescomplemented
62#2765C2214yescomplemented
63#2763C2214yescomplemented
64#2763C2214yescomplemented
65#2762C2214yescomplemented
66#2762C2214yescomplemented
67#2756C2214yescomplemented
68#2755C2214yescomplemented
69#2753C2214yes—
70#2753C2214yescomplemented
71#2749C2214yes—
72#2748C2212yescomplemented
73#2746C2214yescomplemented
74#2744C2214yescomplemented
75#2739C2214yescomplemented
76#2738C2214yescomplemented
77#2734C2212yescomplemented
78#2731C2212yes—
79#2730C2214yes—
80#2727C2214yescomplemented
81#2723C2214yes—
82#2723C2214yes—
83#2723C2214yes—
84#2723C2214yescomplemented
85#2723C2214yescomplemented
86#2715C2214yes—
87#2709C2212yes—
88#2709C2212yes—
89#2708C2214yes—
90#2705C2214yescomplemented
91#2703C2214yes—
92#2703C2214yes—
93#2701C2214yes—
94#2700C2214yescomplemented
95#2698C2214yescomplemented
96#2698C2214yescomplemented
97#2696C2214yes—
98#2692C2214yes—
99#2692C2214yescomplemented
100#2691C2214yes—
101#2691C2214yescomplemented
102#2688C2214yes—
103#2686C2214yes—
104#2685C2214yes—
105#2685C2214yescomplemented
106#2684C2212yescomplemented
107#2683C2212yescomplemented
108#2682C2214yescomplemented
109#2681C2214yescomplemented
110#2678C2214yes—
111#2676C2214yes—
112#2676C2214yes—
113#2674C2214yescomplemented
114#2672C2214yes—
115#2672C2214yescomplemented
116#2671C2214yescomplemented
117#2671C2214yescomplemented
118#2669C2214yes—
119#2669C2212yes—
120#2668C2214yes—
121#2668C2214yescomplemented
122#2668C2214yescomplemented
123#2666C2214yescomplemented
124#2653C2214yes—
125#2653C2214yescomplemented
126#2648C2214yescomplemented
127#2637C2214yescomplemented
128#2636C2214yes—
129#2636C2214yescomplemented
130#2622C2214yescomplemented
131#2621C2212yescomplemented
132#2619C2212yes—
133#2609C2214yescomplemented
134#2609C2214yescomplemented
135#2591C2214yescomplemented
136#2583C2212yescomplemented
137#2581C2212yescomplemented
138#2580C2212yes—
139#2578C2214yescomplemented
140#2577C2214yescomplemented
141#2564C2214yescomplemented
142#2564C2214yescomplemented
143#2561C2212yescomplemented
144#2555C2214yes—
145#2553C2214yes—
146#2549C2214yescomplemented
147#2549C2214yescomplemented
148#2543C2214yescomplemented
149#2543C2214yescomplemented
150#2536C2214yescomplemented
151#2536C2212yescomplemented
152#2535C2212yes—
153#2535C2214yescomplemented
154#2518C2214yescomplemented
155#2510C2214yescomplemented
156#2510C2214yescomplemented
157#2498C2214yescomplemented
158#2494C2214yescomplemented
159#2488C2214yescomplemented
160#2488C2214yescomplemented
161#2481C2214yescomplemented
162#2481C2214yescomplemented
163#2481C2214yescomplemented
164#2474C2214yes—
165#2471C2214yescomplemented
166#2467C2214yes—
167#2467C2214yescomplemented
168#2466C2214yescomplemented
169#2465C2214yescomplemented
170#2464C2214yes—
171#2461C2214yes—
172#2459C2214yes—
173#2449C2214yescomplemented
174#2449C2214yescomplemented
175#2449C2214yescomplemented
176#2448C2214yes—
177#2444C2214yes—
178#2444C2214yes—
179#2439C2214yescomplemented
180#2437C2214yescomplemented
181#2432C2212yes—
182#2431C2212yes—
183#2430C2214yes—
184#2430C2214yescomplemented
185#2430C2214yescomplemented
186#2428C2214yes—
187#2427C2214yescomplemented
188#2424C2214yes—
189#2424C2214yes—
190#2420C2214yescomplemented
191#2418C2214yes—
192#2417C2212yescomplemented
193#2417C2212yescomplemented
194#2416C2212yes—
195#2416C2212yes—
196#2411C2214yes—
197#2407C2214yes—
198#2407C2214yescomplemented
199#2406C2214yescomplemented
200#2406C2212yescomplemented
201#2404C2212yes—
202#2404C2214yescomplemented
203#2382C2212yescomplemented
204#2380C2212yes—
205#2379C2211yescharacteristic
206#2379C2212yes—
207#2379C2212yescomplemented
208#2379C2211yescharacteristic, complemented
209#2374C2212yescomplemented
210#2358C2212yescomplemented
211#2333C2212yescomplemented
212#2333C2212yescomplemented
213#2325C2214yescomplemented
214#2325C2214yescomplemented
215#2311C2211yescharacteristic
216#2311C2211yescharacteristic, complemented
217C2×#382C2211yescharacteristic, complemented
218C2×#382C2212yescomplemented
219C22×#41C2311yescharacteristic
220C22×#41C2311yescharacteristic
221C22×#41C2311yescharacteristic
222C22×#41C2314yes—
223#563—44no—
224H(3,𝔽4)—44no—
225#538—48no—
226#537—48no—
227#537—44no—
228#537—44no—
229#532—44no—
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2312yes—
232C2×#127C2311yescharacteristic
233C2×#127C2312yes—
234#529—48no—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#126C2314yes—
238C2×#126C2314yes—
239C2×#125C2312yes—
240C2×#124C2311yescharacteristic
241C2×#124C2312yes—
242C2×#124C2311yescharacteristic
243C2×#124C2312yes—
244C2×#124C2312yes—
245C2×#124C2314yes—
246C2×#124C2314yes—
247C2×#123C2312yes—
248C2×#123C2312yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×#121C2314yes—
267C2×#121C2312yes—
268C2×#121C2312yes—
269C2×#121C2312yes—
270C2×#121C2314yes—
271C2×#121C2312yes—
272C2×#121C2312yes—
273C2×#121C2314yes—
274C2×#121C2312yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#121C2312yes—
282C2×#121C2312yes—
283C2×#120C2312yes—
284C2×#120C2312yes—
285C2×#120C2314yes—
286C2×#120C2314yes—
287C2×#120C2314yes—
288C4×#41—44no—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2314yes—
299C2×#117C2311yescharacteristic
300C2×#117C2312yes—
301C2×#117C2314yes—
302C22×C4⋊C4C2311yescharacteristic
303C22×C4⋊C4C2311yescharacteristic
304C22×C4⋊C4C2312yes—
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2312yes—
307C22×C22⋊C4C2312yes—
308C22×C22⋊C4C2314yes—
309C22×C42C2312yes—
310C22×C42C2311yescharacteristic
311#401C2314yes—
312#401C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2314yes—
437#391C2314yes—
438#391C2312yes—
439#391C2314yes—
440#391C2314yes—
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2312yes—
445#390C2314yes—
446#390C2314yes—
447#390C2312yes—
448#390C2312yes—
449#390C2314yes—
450#390C2314yes—
451#390C2314yes—
452#390C2314yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
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#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2312yes—
520#386C2312yes—
521#386C2312yes—
522#386C2312yes—
523#386C2314yes—
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#386C2312yes—
542#386C2314yes—
543#386C2312yes—
544#386C2312yes—
545#386C2314yes—
546#386C2314yes—
547#386C2312yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
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#385C2314yes—
579#383C2314yes—
580#383C2314yes—
581#382C2312yes—
582#382C2312yes—
583#382C2312yes—
584#382C2312yes—
585#382C2312yes—
586#382C2314yes—
587#382C2312yes—
588#382C2314yes—
589#382C2314yes—
590#382C2314yes—
591#382C2314yes—
592#382C2314yes—
593#381C2314yes—
594#381C2312yes—
595#381C2312yes—
596#381C2314yes—
597#381C2314yes—
598#380C2312yes—
599#380C2312yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2314yes—
604#380C2314yes—
605#380C2314yes—
606#380C2312yes—
607#380C2312yes—
608#380C2314yes—
609#380C2314yes—
610#379C2314yes—
611#379C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2314yes—
620C2×#95C2314yes—
621C2×#95C2314yes—
622C2×#95C2314yes—
623C25C2412yes—
624C2×#41—24no—
625C2×#41—42no—
626C2×#41—42no—
627C2×#41—42no—
628C2×#41—42no—
629C2×#41—48no—
630C2×#41—42no—
631C2×#41—42no—
632C2×#41—42no—
633C2×#41—42no—
634C2×#41—84no—
635C2×#41—84no—
636C22×Q8C2411yescharacteristic
637C22×Q8C2412yes—
638C22×Q8C2411yescharacteristic
639C22×Q8C2411yescharacteristic
640C22×Q8C2414yes—
641C22×Q8C2412yes—
642C22×D4C2412yes—
643C22×D4C2412yes—
644C22×D4C2414yes—
645C22×D4C2414yes—
646C22×D4C2414yes—
647C22×D4C2411yescharacteristic
648C22×D4C2414yes—
649C22×D4C2412yes—
650C22×D4C2414yes—
651C22×D4C2412yes—
652C22×D4C2411yescharacteristic
653C22×D4C2414yes—
654C22×D4C2412yes—
655C22×D4C2414yes—
656C22×D4C2414yes—
657C22×D4C2414yes—
658C22×D4C2411yescharacteristic
659C23×C4C2411yescharacteristic
660C23×C4C2412yes—
661C23×C4C2412yes—
662C23×C4C2412yes—
663C23×C4C2412yes—
664C23×C4C2414yes—
665C23×C4C2412yes—
666C23×C4C2412yes—
667C23×C4C2414yes—
668C23×C4C2412yes—
669C23×C4C2414yes—
670C23×C4C2412yes—
671C23×C4C2412yes—
672C23×C4C2412yes—
673C23×C4C2414yes—
674C23×C4C2412yes—
675C4⋊Q8—42no—
676C4⋊Q8—44no—
677#127—42no—
678#127—44no—
679#126—48no—
680#126—48no—
681#126—48no—
682#126—84no—
683#125—28no—
684#124—28no—
685#124—24no—
686#124—24no—
687#124—44no—
688#124—48no—
689#124—44no—
690#124—48no—
691#123—44no—
692#123—48no—
693#123—48no—
694#123—44no—
695#123—84no—
696#123—84no—
697C22⋊Q8—48no—
698C22⋊Q8—44no—
699C22⋊Q8—44no—
700C22⋊Q8—48no—
701C22⋊Q8—48no—
702C22⋊Q8—44no—
703C22⋊Q8—44no—
704C22⋊Q8—44no—
705C22⋊Q8—44no—
706C22⋊Q8—84no—
707C22⋊Q8—84no—
708C22⋊Q8—82no—
709C22⋊Q8—82no—
710#121—28no—
711#121—216no—
712#121—28no—
713#121—48no—
714#121—44no—
715#121—48no—
716#121—48no—
717#121—48no—
718#121—48no—
719#121—48no—
720#121—44no—
721#121—44no—
722#121—44no—
723#121—82no—
724#121—82no—
725#121—84no—
726#121—84no—
727#120—44no—
728#120—48no—
729#120—44no—
730#120—48no—
731#120—84no—
732C4×Q8—44no—
733C4×Q8—44no—
734C4×D4—48no—
735C4×D4—44no—
736C4×D4—44no—
737C4×D4—44no—
738C4×D4—44no—
739C4×D4—48no—
740C4×D4—48no—
741C4×D4—84no—
742#117—42no—
743#117—44no—
744#117—48no—
745C2×C4⋊C4—42no—
746C2×C4⋊C4—44no—
747C2×C4⋊C4—42no—
748C2×C4⋊C4—82no—
749C2×C4⋊C4—82no—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C22⋊C4—44no—
792C2×C22⋊C4—84no—
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×C22⋊C4C2414yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2411yescharacteristic
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⋊C4C2412yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C42—28no—
848C2×C42—24no—
849C2×C42C2412yes—
850C2×C42C2411yescharacteristic
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2414yes—
862C2×C42C2411yescharacteristic
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#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909C24—42no—
910C24—44no—
911C24—42no—
912C24—44no—
913C24—42no—
914C24C2514yes—
915C24C2512yes—
916C24C2512yes—
917C24C2512yes—
918C24C2511yescharacteristic
919#41—416no—
920#41—88no—
921#41—88no—
922#41—832no—
923C2×Q8—22no—
924C2×Q8—24no—
925C2×Q8—22no—
926C2×Q8—22no—
927C2×Q8—41no—
928C2×Q8—41no—
929C2×Q8—41no—
930C2×Q8—41no—
931C2×Q8—44no—
932C2×Q8—42no—
933C2×Q8—44no—
934C2×Q8—44no—
935C2×Q8—42no—
936C2×Q8—41no—
937C2×Q8—41no—
938C2×Q8—42no—
939C2×Q8—42no—
940C2×Q8—42no—
941C2×D4—24no—
942C2×D4—24no—
943C2×D4—28no—
944C2×D4—28no—
945C2×D4—28no—
946C2×D4—28no—
947C2×D4—28no—
948C2×D4—24no—
949C2×D4—24no—
950C2×D4—24no—
951C2×D4—22no—
952C2×D4—22no—
953C2×D4—41no—
954C2×D4—42no—
955C2×D4—41no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—41no—
962C2×D4—41no—
963C2×D4—42no—
964C2×D4—44no—
965C2×D4—42no—
966C2×D4—42no—
967C2×D4—42no—
968C2×D4—44no—
969C2×D4—42no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—42no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—41no—
981C2×D4—41no—
982C2×D4—44no—
983C2×D4—42no—
984C2×D4—44no—
985C2×D4—42no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—42no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4H(5,𝔽2)14yes—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—24no—
996C22×C4—28no—
997C22×C4—24no—
998C22×C4—24no—
999C22×C4—24no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—44no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4—44no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—42no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—44no—
1029C22×C4—44no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4C2514yes—
1037C22×C4C2514yes—
1038C22×C4C2512yes—
1039C22×C4C2514yes—
1040C22×C4C2512yes—
1041C22×C4C2514yes—
1042C22×C4C2514yes—
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2514yes—
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2514yes—
1049C22×C4C2512yes—
1050C22×C4C2514yes—
1051C22×C4C2512yes—
1052C22×C4C2511yescharacteristic
1053C22×C4C2511yescharacteristic
1054C4⋊C4—24no—
1055C4⋊C4—28no—
1056C4⋊C4—24no—
1057C4⋊C4—28no—
1058C4⋊C4—24no—
1059C4⋊C4—28no—
1060C4⋊C4—24no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—44no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—42no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—42no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C22⋊C4—28no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—28no—
1099C22⋊C4—28no—
1100C22⋊C4—28no—
1101C22⋊C4—28no—
1102C22⋊C4—28no—
1103C22⋊C4—28no—
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—41no—
1117C22⋊C4—42no—
1118C22⋊C4—41no—
1119C22⋊C4—42no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—42no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—42no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—42no—
1146C22⋊C4—42no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C42—24no—
1150C42—22no—
1151C42—24no—
1152C42—24no—
1153C42—24no—
1154C42—44no—
1155C42—44no—
1156C42—44no—
1157C42—44no—
1158C42—42no—
1159C42—42no—
1160C42—42no—
1161C42—42no—
1162C42H(5,𝔽2)14yes—
1163C23—22no—
1164C23—21no—
1165C23—21no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—22no—
1172C23—22no—
1173C23—22no—
1174C23—24no—
1175C23—22no—
1176C23—24no—
1177C23—22no—
1178C23—22no—
1179C23—22no—
1180C23—24no—
1181C23—22no—
1182C23—24no—
1183C23—24no—
1184C23—24no—
1185C23—24no—
1186C23—24no—
1187C23—24no—
1188C23—24no—
1189C23—24no—
1190C23—88no—
1191C23—84no—
1192C23—162no—
1193C23—162no—
1194C23—164no—
1195C23C2×H(5,𝔽2)14yes—
1196C23#58512yes—
1197C23C2611yescharacteristic
1198Q8—44no—
1199Q8—84no—
1200Q8—82no—
1201Q8—82no—
1202Q8—88no—
1203Q8—162no—
1204D4—44no—
1205D4—48no—
1206D4—84no—
1207D4—82no—
1208D4—82no—
1209D4—88no—
1210D4—88no—
1211D4—88no—
1212D4—88no—
1213D4—88no—
1214D4—84no—
1215D4—84no—
1216D4—88no—
1217D4—88no—
1218D4—164no—
1219D4—162no—
1220D4—164no—
1221C2×C4—28no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—48no—
1274C2×C4—48no—
1275C2×C4—48no—
1276C2×C4—84no—
1277C2×C4—84no—
1278C2×C4—84no—
1279C2×C4—84no—
1280C2×C4—88no—
1281C2×C4—88no—
1282C2×C4—88no—
1283C2×C4—162no—
1284C2×C4—162no—
1285C2×C4—164no—
1286C2×C4—162no—
1287C2×C4—162no—
1288C2×C4C2×H(5,𝔽2)14yes—
1289C2×C4C2×H(5,𝔽2)12yes—
1290C2×C4C2×H(5,𝔽2)12yes—
1291C22—24no—
1292C22—24no—
1293C22—24no—
1294C22—22no—
1295C22—24no—
1296C22—41no—
1297C22—42no—
1298C22—42no—
1299C22—41no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—44no—
1305C22—42no—
1306C22—44no—
1307C22—44no—
1308C22—44no—
1309C22—44no—
1310C22—42no—
1311C22—42no—
1312C22—44no—
1313C22—42no—
1314C22—42no—
1315C22—44no—
1316C22—44no—
1317C22—44no—
1318C22—44no—
1319C22—44no—
1320C22—168no—
1321C22C22×H(5,𝔽2)11yescharacteristic
1322C22C22×H(5,𝔽2)11yescharacteristic
1323C22C2×#58511yescharacteristic
1324C22H(7,𝔽2)12yes—
1325C222−1+612yes—
1326C4—22no—
1327C4—22no—
1328C4—24no—
1329C4—44no—
1330C4—44no—
1331C4—44no—
1332C4—44no—
1333C4—44no—
1334C4—44no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—44no—
1339C4—42no—
1340C4—44no—
1341C4—42no—
1342C4—42no—
1343C4—44no—
1344C2—44no—
1345C2—42no—
1346C2—82no—
1347C2—84no—
1348C2—82no—
1349C2#6281811yescharacteristic
1350C2#6287512yes—
1351C2#6304511yescharacteristic
1352C2#6305912yes—
1353C2#6306311yescharacteristic
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. #58885C2semidirect
2. #57494C2semidirect
3. #56292C2semidirect
4. #55800C2semidirect
5. #55330C2semidirect
6. #53808C2semidirect
7. #50821C2semidirect
8. #50219C2semidirect
9. #49660C2semidirect
10. #48309C2semidirect
11. #46962C2semidirect
12. #46427C2semidirect
13. #46423C2semidirect
14. #46366C2semidirect
15. #46228C2semidirect
16. #46225C2semidirect
17. #46134C2semidirect
18. #45991C2semidirect
19. #45989C2semidirect
20. #45989C2semidirect
21. #45973C2semidirect
22. #35328C2semidirect
23. #35130C2semidirect
24. C2×#563C22semidirect
26. C2×#538C22semidirect
29. C2×#537C22semidirect
32. C2×C4×#41C22semidirect
33. #2851C22semidirect
34. #2851C22semidirect
38. #2850C22semidirect
39. #2844C22semidirect
40. #2838C22semidirect
42. #2827C22semidirect
47. #2817C22semidirect
50. #2814C22semidirect
52. #2785C22semidirect
53. #2782C22semidirect
54. #2778C22semidirect
55. #2775C22semidirect
56. #2775C22semidirect
57. #2773C22semidirect
58. #2773C22semidirect
59. #2768C22semidirect
60. #2768C22semidirect
61. #2765C22semidirect
62. #2765C22semidirect
63. #2763C22semidirect
64. #2763C22semidirect
65. #2762C22semidirect
66. #2762C22semidirect
67. #2756C22semidirect
68. #2755C22semidirect
70. #2753C22semidirect
72. #2748C22semidirect
73. #2746C22semidirect
74. #2744C22semidirect
75. #2739C22semidirect
76. #2738C22semidirect
77. #2734C22semidirect
80. #2727C22semidirect
84. #2723C22semidirect
85. #2723C22semidirect
90. #2705C22semidirect
94. #2700C22semidirect
95. #2698C22semidirect
96. #2698C22semidirect
99. #2692C22semidirect
101. #2691C22semidirect
105. #2685C22semidirect
106. #2684C22semidirect
107. #2683C22semidirect
108. #2682C22semidirect
109. #2681C22semidirect
113. #2674C22semidirect
115. #2672C22semidirect
116. #2671C22semidirect
117. #2671C22semidirect
121. #2668C22semidirect
122. #2668C22semidirect
123. #2666C22semidirect
125. #2653C22semidirect
126. #2648C22semidirect
127. #2637C22semidirect
129. #2636C22semidirect
130. #2622C22semidirect
131. #2621C22semidirect
133. #2609C22semidirect
134. #2609C22semidirect
135. #2591C22semidirect
136. #2583C22semidirect
137. #2581C22semidirect
139. #2578C22semidirect
140. #2577C22semidirect
141. #2564C22semidirect
142. #2564C22semidirect
143. #2561C22semidirect
146. #2549C22semidirect
147. #2549C22semidirect
148. #2543C22semidirect
149. #2543C22semidirect
150. #2536C22semidirect
151. #2536C22semidirect
153. #2535C22semidirect
154. #2518C22semidirect
155. #2510C22semidirect
156. #2510C22semidirect
157. #2498C22semidirect
158. #2494C22semidirect
159. #2488C22semidirect
160. #2488C22semidirect
161. #2481C22semidirect
162. #2481C22semidirect
163. #2481C22semidirect
165. #2471C22semidirect
167. #2467C22semidirect
168. #2466C22semidirect
169. #2465C22semidirect
173. #2449C22semidirect
174. #2449C22semidirect
175. #2449C22semidirect
179. #2439C22semidirect
180. #2437C22semidirect
184. #2430C22semidirect
185. #2430C22semidirect
187. #2427C22semidirect
190. #2420C22semidirect
192. #2417C22semidirect
193. #2417C22semidirect
198. #2407C22semidirect
199. #2406C22semidirect
200. #2406C22semidirect
202. #2404C22semidirect
203. #2382C22semidirect
207. #2379C22semidirect
208. #2379C22semidirect
209. #2374C22semidirect
210. #2358C22semidirect
211. #2333C22semidirect
212. #2333C22semidirect
213. #2325C22semidirect
214. #2325C22semidirect
216. #2311C22semidirect
217. C2×#382C22semidirect
218. C2×#382C22semidirect

Maximal subgroups

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

subgroupindex
#588852
#574942
#562922
#558002
#553302
#538082
#508212
#502192
#496602
#483092
#469622
#464272
#464232
#463662
#462282
#462252
#461342
#459912
#459892
#459732
#353282
#351302