Finite Group Databasebeta

← #8957951

Subgroups — #8957951

Order 512.

5158 conjugacy classes of subgroups.

The subgroup lattice has 1402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57852C214yesmaximal, complemented
2#57667C214yesmaximal, complemented
3#55687C214yesmaximal, complemented
4#52012C212yesmaximal, complemented
5#51993C212yesmaximal, complemented
6#51833C214yesmaximal, complemented
7#51745C214yesmaximal, complemented
8#51040C212yesmaximal, complemented
9#50185C212yesmaximal, complemented
10#48776C212yesmaximal, complemented
11#47042C214yesmaximal, complemented
12#43420C214yesmaximal, complemented
13#43375C214yesmaximal, complemented
14#41443C212yesmaximal, complemented
15#41284C214yesmaximal, complemented
16#40701C214yesmaximal, complemented
17#37941C212yesmaximal, complemented
18#37745C212yesmaximal, complemented
19#36717C211yesmaximal, characteristic, complemented
20#36032C212yesmaximal, complemented
21#35995C212yesmaximal, complemented
22#35563C211yesmaximal, characteristic, complemented
23#35351C211yesmaximal, characteristic, complemented
24C2×#560C2212yescomplemented
25C2×#553C2212yes—
26C2×#537C2212yescomplemented
27C2×#535C2211yescharacteristic
28C2×#534C2211yescharacteristic
29C2×#525C2211yescharacteristic, complemented
30C22×#121C2211yescharacteristic
31C2×#520C2211yescharacteristic, complemented
32C2×#518C2211yescharacteristic, complemented
33#2847C2212yes—
34#2836C2214yescomplemented
35#2831C2214yescomplemented
36#2829C2214yescomplemented
37#2827C2214yescomplemented
38#2824C2214yescomplemented
39#2804C2212yescomplemented
40#2796C2214yescomplemented
41#2796C2214yescomplemented
42#2784C2214yescomplemented
43#2780C2214yescomplemented
44#2779C2214yescomplemented
45#2777C2214yescomplemented
46#2774C2214yescomplemented
47#2770C2214yescomplemented
48#2756C2214yescomplemented
49#2752C2214yescomplemented
50#2751C2214yescomplemented
51#2750C2214yescomplemented
52#2750C2214yescomplemented
53#2749C2214yescomplemented
54#2749C2214yescomplemented
55#2743C2214yescomplemented
56#2740C2214yescomplemented
57#2739C2214yescomplemented
58#2737C2214yescomplemented
59#2736C2214yes—
60#2723C2214yescomplemented
61#2717C2212yescomplemented
62#2710C2214yescomplemented
63#2709C2214yescomplemented
64#2703C2214yes—
65#2703C2214yes—
66#2703C2214yescomplemented
67#2703C2214yescomplemented
68#2703C2214yescomplemented
69#2701C2214yes—
70#2697C2214yes—
71#2697C2212yescomplemented
72#2697C2214yescomplemented
73#2696C2214yescomplemented
74#2695C2214yescomplemented
75#2694C2214yescomplemented
76#2692C2214yescomplemented
77#2689C2214yescomplemented
78#2688C2214yescomplemented
79#2688C2214yescomplemented
80#2688C2214yescomplemented
81#2687C2214yescomplemented
82#2685C2214yescomplemented
83#2684C2214yescomplemented
84#2684C2212yescomplemented
85#2682C2214yescomplemented
86#2678C2214yescomplemented
87#2678C2214yescomplemented
88#2673C2214yescomplemented
89#2672C2214yescomplemented
90#2671C2214yes—
91#2669C2214yes—
92#2669C2214yes—
93#2668C2214yescomplemented
94#2668C2214yescomplemented
95#2665C2212yescomplemented
96#2663C2214yescomplemented
97#2662C2214yescomplemented
98#2650C2214yescomplemented
99#2649C2214yescomplemented
100#2648C2214yescomplemented
101#2646C2212yescomplemented
102#2639C2214yescomplemented
103#2639C2212yescomplemented
104#2636C2214yescomplemented
105#2635C2212yes—
106#2634C2212yescomplemented
107#2627C2212yescomplemented
108#2624C2212yes—
109#2618C2212yescomplemented
110#2618C2212yescomplemented
111#2617C2212yes—
112#2611C2212yescomplemented
113#2610C2214yescomplemented
114#2603C2214yescomplemented
115#2602C2214yescomplemented
116#2601C2214yescomplemented
117#2600C2214yescomplemented
118#2598C2214yescomplemented
119#2598C2212yescomplemented
120#2596C2214yescomplemented
121#2591C2212yes—
122#2589C2214yescomplemented
123#2559C2214yescomplemented
124#2543C2212yescomplemented
125#2543C2214yescomplemented
126#2535C2214yescomplemented
127#2534C2212yes—
128#2534C2212yescomplemented
129#2533C2214yescomplemented
130#2532C2214yescomplemented
131#2531C2214yescomplemented
132#2529C2214yescomplemented
133#2526C2214yescomplemented
134#2522C2214yescomplemented
135#2516C2214yescomplemented
136#2488C2214yescomplemented
137#2487C2212yescomplemented
138#2484C2212yescomplemented
139#2483C2212yescomplemented
140#2482C2212yes—
141#2481C2214yescomplemented
142#2481C2214yescomplemented
143#2477C2214yescomplemented
144#2472C2214yescomplemented
145#2471C2214yescomplemented
146#2471C2214yescomplemented
147#2470C2214yescomplemented
148#2469C2214yescomplemented
149#2464C2214yescomplemented
150#2459C2214yescomplemented
151#2457C2214yescomplemented
152#2456C2214yescomplemented
153#2455C2214yescomplemented
154#2454C2214yescomplemented
155#2450C2214yescomplemented
156#2444C2214yescomplemented
157#2444C2214yescomplemented
158#2444C2214yescomplemented
159#2443C2214yescomplemented
160#2443C2214yescomplemented
161#2443C2214yescomplemented
162#2443C2214yescomplemented
163#2433C2212yes—
164#2431C2214yescomplemented
165#2430C2214yescomplemented
166#2430C2214yescomplemented
167#2430C2214yescomplemented
168#2428C2214yescomplemented
169#2428C2214yescomplemented
170#2426C2214yescomplemented
171#2425C2214yescomplemented
172#2424C2214yescomplemented
173#2424C2214yescomplemented
174#2424C2214yescomplemented
175#2419C2214yescomplemented
176#2418C2214yescomplemented
177#2418C2214yescomplemented
178#2418C2214yescomplemented
179#2416C2214yescomplemented
180#2414C2214yescomplemented
181#2411C2214yescomplemented
182#2408C2214yes—
183#2408C2212yes—
184#2408C2212yescomplemented
185#2405C2212yes—
186#2405C2214yes—
187#2404C2214yescomplemented
188#2404C2214yescomplemented
189#2403C2212yes—
190#2403C2212yes—
191#2398C2212yescomplemented
192#2397C2214yescomplemented
193#2395C2212yescomplemented
194C2×#400C2212yescomplemented
195#2377C2212yes—
196#2376C2212yescomplemented
197#2366C2212yescomplemented
198#2366C2214yescomplemented
199#2364C2214yescomplemented
200#2361C2214yescomplemented
201#2359C2214yescomplemented
202#2359C2214yescomplemented
203#2358C2212yescomplemented
204#2353C2212yescomplemented
205#2346C2212yescomplemented
206#2339C2214yescomplemented
207#2325C2212yescomplemented
208#2325C2212yescomplemented
209#2325C2214yescomplemented
210#2321C2214yescomplemented
211#2316C2211yescharacteristic, complemented
212#2316C2212yescomplemented
213#2312C2211yescharacteristic
214#2309C2211yescharacteristic
215#2308C2212yes—
216#2308C2211yescharacteristic, complemented
217C2×#385C2212yescomplemented
218#2280C2211yescharacteristic, complemented
219C22×#41C2311yescharacteristic
220C22×#41C2314yes—
221C23×D4C2311yescharacteristic
222C23×D4C2311yescharacteristic
223C23×D4C2311yescharacteristic
224C23×D4C2312yes—
225C24×C4C2311yescharacteristic
226#560—48no—
227#553—48no—
228#537—48no—
229#535—44no—
230#534—44no—
231C2×#127C2312yes—
232C2×#127C2314yes—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#125C2312yes—
236C2×#124C2312yes—
237C2×#124C2314yes—
238#525—44no—
239C2×#123C2314yes—
240C2×#123C2314yes—
241C2×#123C2312yes—
242C2×#123C2314yes—
243C2×#123C2312yes—
244C2×#123C2314yes—
245C2×#123C2312yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×#121—44no—
253C2×#121C2312yes—
254C2×#121C2312yes—
255C2×#121C2314yes—
256C2×#121C2312yes—
257C2×#121C2314yes—
258C2×#121C2312yes—
259C2×#121C2312yes—
260C2×#121C2314yes—
261C2×#121C2312yes—
262C2×#121C2314yes—
263C2×#121C2314yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#120C2314yes—
272C2×#120C2312yes—
273C2×#120C2312yes—
274C2×#120C2312yes—
275C2×#120C2314yes—
276C2×#120C2312yes—
277C2×#120C2312yes—
278C2×#120C2314yes—
279C2×#120C2314yes—
280C2×#120C2314yes—
281#520—44no—
282#518—44no—
283C2×C4×Q8C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×#117C2312yes—
298C2×#117C2311yescharacteristic
299C2×#117C2311yescharacteristic
300C2×#117C2311yescharacteristic
301C2×#117C2312yes—
302C2×#117C2314yes—
303C22×C4⋊C4C2311yescharacteristic
304C22×C4⋊C4C2312yes—
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2312yes—
307C22×C4⋊C4C2312yes—
308C22×C22⋊C4C2311yescharacteristic
309C22×C22⋊C4C2312yes—
310C22×C22⋊C4C2312yes—
311C22×C22⋊C4C2311yescharacteristic
312C22×C22⋊C4C2312yes—
313C22×C22⋊C4C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2312yes—
321#400C2312yes—
322#400C2312yes—
323#400C2312yes—
324#400C2314yes—
325#400C2312yes—
326#400C2312yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2312yes—
337#399C2314yes—
338#399C2312yes—
339#399C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2312yes—
346#398C2314yes—
347#398C2312yes—
348#398C2312yes—
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#397C2314yes—
364#397C2312yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2312yes—
395#394C2312yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2312yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2312yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#390C2314yes—
438#390C2312yes—
439#390C2312yes—
440#390C2314yes—
441#390C2314yes—
442#390C2314yes—
443#390C2314yes—
444#390C2314yes—
445#390C2314yes—
446#390C2314yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
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#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#387C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
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#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2312yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2312yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2312yes—
547#386C2314yes—
548#386C2312yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#385C2314yes—
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#383C2312yes—
576#383C2314yes—
577#382C2314yes—
578#381C2314yes—
579#381C2312yes—
580#381C2314yes—
581#381C2314yes—
582#381C2314yes—
583#381C2314yes—
584#381C2312yes—
585#380C2312yes—
586#380C2312yes—
587#380C2312yes—
588#380C2312yes—
589#380C2312yes—
590#380C2314yes—
591#380C2312yes—
592#380C2314yes—
593#380C2314yes—
594#380C2312yes—
595#380C2312yes—
596#380C2314yes—
597#380C2314yes—
598#379C2314yes—
599#379C2312yes—
600#379C2312yes—
601#379C2312yes—
602#379C2312yes—
603#379C2314yes—
604#379C2314yes—
605#379C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616#376C2314yes—
617#376C2312yes—
618C2×#95C2312yes—
619C2×#95C2312yes—
620C2×#95C2314yes—
621C2×#95C2314yes—
622C2×#95C2312yes—
623C25C2411yescharacteristic
624C25C2411yescharacteristic
625C25C2411yescharacteristic
626C25C2412yes—
627C2×#41—24no—
628C2×#41—42no—
629C2×#41—42no—
630C2×#41—48no—
631C2×#41—48no—
632C2×#41—84no—
633C22×Q8C2411yescharacteristic
634C22×Q8C2414yes—
635C22×D4—24no—
636C22×D4—42no—
637C22×D4—42no—
638C22×D4—42no—
639C22×D4—42no—
640C22×D4—44no—
641C22×D4—44no—
642C22×D4—44no—
643C22×D4—84no—
644C22×D4C2412yes—
645C22×D4C2414yes—
646C22×D4C2414yes—
647C22×D4C2414yes—
648C22×D4C2412yes—
649C22×D4C2414yes—
650C22×D4C2414yes—
651C22×D4C2414yes—
652C22×D4C2414yes—
653C22×D4C2414yes—
654C22×D4C2412yes—
655C22×D4C2414yes—
656C22×D4C2414yes—
657C22×D4C2412yes—
658C22×D4C2414yes—
659C22×D4C2412yes—
660C22×D4C2414yes—
661C22×D4C2414yes—
662C22×D4C2411yescharacteristic
663C23×C4—42no—
664C23×C4—42no—
665C23×C4—42no—
666C23×C4C2411yescharacteristic
667C23×C4C2412yes—
668C23×C4C2411yescharacteristic
669C23×C4C2412yes—
670C23×C4C2411yescharacteristic
671C23×C4C2412yes—
672C23×C4C2412yes—
673C23×C4C2412yes—
674C23×C4C2412yes—
675C23×C4C2414yes—
676C23×C4C2412yes—
677C23×C4C2412yes—
678C23×C4C2412yes—
679C23×C4C2414yes—
680C23×C4C2412yes—
681C23×C4C2414yes—
682C23×C4C2414yes—
683C23×C4C2412yes—
684C23×C4C2412yes—
685C23×C4C2411yescharacteristic
686#127—28no—
687#127—48no—
688#126—48no—
689#126—48no—
690#125—44no—
691#124—44no—
692#124—84no—
693#123—48no—
694#123—44no—
695#123—48no—
696#123—48no—
697#123—48no—
698#123—48no—
699#123—44no—
700#123—44no—
701#123—84no—
702#123—84no—
703C22⋊Q8—48no—
704C22⋊Q8—48no—
705C22⋊Q8—44no—
706#121—28no—
707#121—216no—
708#121—28no—
709#121—44no—
710#121—44no—
711#121—48no—
712#121—48no—
713#121—48no—
714#121—48no—
715#121—48no—
716#121—48no—
717#121—48no—
718#121—48no—
719#121—44no—
720#121—44no—
721#121—48no—
722#121—48no—
723#121—84no—
724#120—44no—
725#120—48no—
726#120—44no—
727#120—48no—
728#120—44no—
729#120—44no—
730#120—44no—
731#120—48no—
732#120—84no—
733#120—84no—
734C4×Q8—44no—
735C4×D4—28no—
736C4×D4—48no—
737C4×D4—48no—
738C4×D4—48no—
739C4×D4—44no—
740C4×D4—44no—
741C4×D4—44no—
742C4×D4—48no—
743C4×D4—84no—
744C4×D4—84no—
745C4×D4—84no—
746C4×D4—84no—
747C4×D4—84no—
748#117—28no—
749#117—42no—
750#117—44no—
751#117—42no—
752#117—42no—
753#117—84no—
754C2×C4⋊C4—24no—
755C2×C4⋊C4—44no—
756C2×C4⋊C4—44no—
757C2×C4⋊C4—44no—
758C2×C4⋊C4—44no—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C22⋊C4—24no—
796C2×C22⋊C4—44no—
797C2×C22⋊C4—44no—
798C2×C22⋊C4—44no—
799C2×C22⋊C4—42no—
800C2×C22⋊C4—84no—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C42C2414yes—
861C2×C42C2412yes—
862C2×C42C2412yes—
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2412yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871#95C2414yes—
872#95C2412yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2412yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2412yes—
886#95C2412yes—
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—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915C24—22no—
916C24—24no—
917C24—22no—
918C24—22no—
919C24—42no—
920C24—42no—
921C24—41no—
922C24—42no—
923C24—41no—
924C24—44no—
925C24—42no—
926C24—41no—
927C24—41no—
928C24—42no—
929C24—44no—
930C24—42no—
931C24—42no—
932C24—41no—
933C24—41no—
934C24—42no—
935C24C2512yes—
936C24C2514yes—
937C24C2512yes—
938C24C2511yescharacteristic
939C24C2512yes—
940C24C2512yes—
941#41—416no—
942#41—832no—
943C2×Q8—22no—
944C2×Q8—41no—
945C2×Q8—41no—
946C2×Q8—44no—
947C2×Q8—44no—
948C2×Q8—44no—
949C2×D4—24no—
950C2×D4—28no—
951C2×D4—24no—
952C2×D4—28no—
953C2×D4—28no—
954C2×D4—28no—
955C2×D4—28no—
956C2×D4—28no—
957C2×D4—28no—
958C2×D4—28no—
959C2×D4—28no—
960C2×D4—28no—
961C2×D4—28no—
962C2×D4—28no—
963C2×D4—24no—
964C2×D4—24no—
965C2×D4—24no—
966C2×D4—41no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—41no—
970C2×D4—42no—
971C2×D4—44no—
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—42no—
982C2×D4—42no—
983C2×D4—42no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—42no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—42no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—42no—
1002C2×D4—42no—
1003C2×D4—44no—
1004C2×D4—416no—
1005C2×D4—88no—
1006C2×D4—88no—
1007C2×D4—816no—
1008C2×D4H(5,𝔽2)14yes—
1009C22×C4—22no—
1010C22×C4—22no—
1011C22×C4—22no—
1012C22×C4—24no—
1013C22×C4—24no—
1014C22×C4—24no—
1015C22×C4—22no—
1016C22×C4—22no—
1017C22×C4—28no—
1018C22×C4—24no—
1019C22×C4—24no—
1020C22×C4—24no—
1021C22×C4—24no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—42no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—44no—
1029C22×C4—42no—
1030C22×C4—44no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—41no—
1036C22×C4—42no—
1037C22×C4—44no—
1038C22×C4—42no—
1039C22×C4—41no—
1040C22×C4—42no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—44no—
1048C22×C4—42no—
1049C22×C4—44no—
1050C22×C4—42no—
1051C22×C4—42no—
1052C22×C4—44no—
1053C22×C4—42no—
1054C22×C4—44no—
1055C22×C4—42no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—42no—
1060C22×C4—44no—
1061C22×C4—42no—
1062C22×C4—88no—
1063C22×C4H(5,𝔽2)14yes—
1064C22×C4C2512yes—
1065C22×C4C2514yes—
1066C22×C4C2514yes—
1067C22×C4C2514yes—
1068C22×C4C2514yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2514yes—
1073C22×C4C2512yes—
1074C22×C4C2514yes—
1075C22×C4C2512yes—
1076C22×C4C2514yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2511yescharacteristic
1080C22×C4C2511yescharacteristic
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—28no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—41no—
1091C4⋊C4—44no—
1092C4⋊C4—42no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—41no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C22⋊C4—28no—
1118C22⋊C4—24no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—24no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—42no—
1137C22⋊C4—42no—
1138C22⋊C4—42no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—42no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—42no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—42no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—42no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C42—28no—
1177C42—24no—
1178C42—24no—
1179C42—42no—
1180C42—42no—
1181C42—42no—
1182C42—44no—
1183C42—44no—
1184C42—44no—
1185C42—44no—
1186C42—44no—
1187C23—28no—
1188C23—22no—
1189C23—21no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—21no—
1197C23—24no—
1198C23—22no—
1199C23—24no—
1200C23—22no—
1201C23—22no—
1202C23—22no—
1203C23—24no—
1204C23—24no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23—24no—
1209C23—24no—
1210C23—22no—
1211C23—24no—
1212C23—22no—
1213C23—24no—
1214C23—24no—
1215C23—24no—
1216C23—24no—
1217C23—24no—
1218C23—24no—
1219C23—44no—
1220C23—44no—
1221C23—82no—
1222C23—82no—
1223C23—84no—
1224C23—84no—
1225C23—82no—
1226C23—82no—
1227C23—82no—
1228C23—82no—
1229C23—84no—
1230C23—88no—
1231C23—162no—
1232C23—162no—
1233C23—162no—
1234C23—162no—
1235C23—162no—
1236C23—162no—
1237C23—164no—
1238C23C2×H(5,𝔽2)12yes—
1239C23C2×H(5,𝔽2)14yes—
1240C23#58514yes—
1241C23C2611yescharacteristic
1242Q8—44no—
1243Q8—88no—
1244D4—44no—
1245D4—416no—
1246D4—48no—
1247D4—416no—
1248D4—84no—
1249D4—84no—
1250D4—84no—
1251D4—88no—
1252D4—88no—
1253D4—88no—
1254D4—88no—
1255D4—88no—
1256D4—88no—
1257D4—88no—
1258D4—88no—
1259D4—88no—
1260D4—88no—
1261D4—162no—
1262D4—164no—
1263C2×C4—28no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—24no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—44no—
1309C2×C4—48no—
1310C2×C4—48no—
1311C2×C4—48no—
1312C2×C4—84no—
1313C2×C4—84no—
1314C2×C4—84no—
1315C2×C4—82no—
1316C2×C4—82no—
1317C2×C4—88no—
1318C2×C4—84no—
1319C2×C4—88no—
1320C2×C4—162no—
1321C2×C4—162no—
1322C2×C4—162no—
1323C2×C4—164no—
1324C2×C4—164no—
1325C2×C4—162no—
1326C2×C4—162no—
1327C2×C4C2×H(5,𝔽2)14yes—
1328C2×C4C2×H(5,𝔽2)12yes—
1329C2×C4#58512yes—
1330C22—22no—
1331C22—24no—
1332C22—22no—
1333C22—24no—
1334C22—22no—
1335C22—24no—
1336C22—28no—
1337C22—24no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—44no—
1345C22—42no—
1346C22—42no—
1347C22—42no—
1348C22—42no—
1349C22—44no—
1350C22—42no—
1351C22—42no—
1352C22—44no—
1353C22—42no—
1354C22—44no—
1355C22—42no—
1356C22—44no—
1357C22—44no—
1358C22—44no—
1359C22—44no—
1360C22—44no—
1361C22—44no—
1362C22—44no—
1363C22—44no—
1364C22—88no—
1365C22—164no—
1366C22—164no—
1367C22—168no—
1368C22C22×H(5,𝔽2)11yescharacteristic
1369C22C22×H(5,𝔽2)11yescharacteristic
1370C22C2×#58511yescharacteristic
1371C22C2×#58512yes—
1372C22H(7,𝔽2)12yes—
1373C4—22no—
1374C4—22no—
1375C4—24no—
1376C4—42no—
1377C4—42no—
1378C4—44no—
1379C4—42no—
1380C4—42no—
1381C4—44no—
1382C4—42no—
1383C4—44no—
1384C4—44no—
1385C4—44no—
1386C4—44no—
1387C4—44no—
1388C4—44no—
1389C4—44no—
1390C2—44no—
1391C2—44no—
1392C2—42no—
1393C2—82no—
1394C2—84no—
1395C2—82no—
1396C2#6281811yescharacteristic
1397C2#6282011yescharacteristic
1398C2#6287611yescharacteristic
1399C2#6291812yes—
1400C2#6293512yes—
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. #57852C2semidirect
2. #57667C2semidirect
3. #55687C2semidirect
4. #52012C2semidirect
5. #51993C2semidirect
6. #51833C2semidirect
7. #51745C2semidirect
8. #51040C2semidirect
9. #50185C2semidirect
10. #48776C2semidirect
11. #47042C2semidirect
12. #43420C2semidirect
13. #43375C2semidirect
14. #41443C2semidirect
15. #41284C2semidirect
16. #40701C2semidirect
17. #37941C2semidirect
18. #37745C2semidirect
19. #36717C2semidirect
20. #36032C2semidirect
21. #35995C2semidirect
22. #35563C2semidirect
23. #35351C2semidirect
24. C2×#560C22semidirect
26. C2×#537C22semidirect
29. C2×#525C22semidirect
31. C2×#520C22semidirect
32. C2×#518C22semidirect
34. #2836C22semidirect
35. #2831C22semidirect
36. #2829C22semidirect
37. #2827C22semidirect
38. #2824C22semidirect
39. #2804C22semidirect
40. #2796C22semidirect
41. #2796C22semidirect
42. #2784C22semidirect
43. #2780C22semidirect
44. #2779C22semidirect
45. #2777C22semidirect
46. #2774C22semidirect
47. #2770C22semidirect
48. #2756C22semidirect
49. #2752C22semidirect
50. #2751C22semidirect
51. #2750C22semidirect
52. #2750C22semidirect
53. #2749C22semidirect
54. #2749C22semidirect
55. #2743C22semidirect
56. #2740C22semidirect
57. #2739C22semidirect
58. #2737C22semidirect
60. #2723C22semidirect
61. #2717C22semidirect
62. #2710C22semidirect
63. #2709C22semidirect
66. #2703C22semidirect
67. #2703C22semidirect
68. #2703C22semidirect
71. #2697C22semidirect
72. #2697C22semidirect
73. #2696C22semidirect
74. #2695C22semidirect
75. #2694C22semidirect
76. #2692C22semidirect
77. #2689C22semidirect
78. #2688C22semidirect
79. #2688C22semidirect
80. #2688C22semidirect
81. #2687C22semidirect
82. #2685C22semidirect
83. #2684C22semidirect
84. #2684C22semidirect
85. #2682C22semidirect
86. #2678C22semidirect
87. #2678C22semidirect
88. #2673C22semidirect
89. #2672C22semidirect
93. #2668C22semidirect
94. #2668C22semidirect
95. #2665C22semidirect
96. #2663C22semidirect
97. #2662C22semidirect
98. #2650C22semidirect
99. #2649C22semidirect
100. #2648C22semidirect
101. #2646C22semidirect
102. #2639C22semidirect
103. #2639C22semidirect
104. #2636C22semidirect
106. #2634C22semidirect
107. #2627C22semidirect
109. #2618C22semidirect
110. #2618C22semidirect
112. #2611C22semidirect
113. #2610C22semidirect
114. #2603C22semidirect
115. #2602C22semidirect
116. #2601C22semidirect
117. #2600C22semidirect
118. #2598C22semidirect
119. #2598C22semidirect
120. #2596C22semidirect
122. #2589C22semidirect
123. #2559C22semidirect
124. #2543C22semidirect
125. #2543C22semidirect
126. #2535C22semidirect
128. #2534C22semidirect
129. #2533C22semidirect
130. #2532C22semidirect
131. #2531C22semidirect
132. #2529C22semidirect
133. #2526C22semidirect
134. #2522C22semidirect
135. #2516C22semidirect
136. #2488C22semidirect
137. #2487C22semidirect
138. #2484C22semidirect
139. #2483C22semidirect
141. #2481C22semidirect
142. #2481C22semidirect
143. #2477C22semidirect
144. #2472C22semidirect
145. #2471C22semidirect
146. #2471C22semidirect
147. #2470C22semidirect
148. #2469C22semidirect
149. #2464C22semidirect
150. #2459C22semidirect
151. #2457C22semidirect
152. #2456C22semidirect
153. #2455C22semidirect
154. #2454C22semidirect
155. #2450C22semidirect
156. #2444C22semidirect
157. #2444C22semidirect
158. #2444C22semidirect
159. #2443C22semidirect
160. #2443C22semidirect
161. #2443C22semidirect
162. #2443C22semidirect
164. #2431C22semidirect
165. #2430C22semidirect
166. #2430C22semidirect
167. #2430C22semidirect
168. #2428C22semidirect
169. #2428C22semidirect
170. #2426C22semidirect
171. #2425C22semidirect
172. #2424C22semidirect
173. #2424C22semidirect
174. #2424C22semidirect
175. #2419C22semidirect
176. #2418C22semidirect
177. #2418C22semidirect
178. #2418C22semidirect
179. #2416C22semidirect
180. #2414C22semidirect
181. #2411C22semidirect
184. #2408C22semidirect
187. #2404C22semidirect
188. #2404C22semidirect
191. #2398C22semidirect
192. #2397C22semidirect
193. #2395C22semidirect
194. C2×#400C22semidirect
196. #2376C22semidirect
197. #2366C22semidirect
198. #2366C22semidirect
199. #2364C22semidirect
200. #2361C22semidirect
201. #2359C22semidirect
202. #2359C22semidirect
203. #2358C22semidirect
204. #2353C22semidirect
205. #2346C22semidirect
206. #2339C22semidirect
207. #2325C22semidirect
208. #2325C22semidirect
209. #2325C22semidirect
210. #2321C22semidirect
211. #2316C22semidirect
212. #2316C22semidirect
216. #2308C22semidirect
217. C2×#385C22semidirect
218. #2280C22semidirect

Maximal subgroups

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

subgroupindex
#578522
#576672
#556872
#520122
#519932
#518332
#517452
#510402
#501852
#487762
#470422
#434202
#433752
#414432
#412842
#407012
#379412
#377452
#367172
#360322
#359952
#355632
#353512