Finite Group Databasebeta

← #8942877

Subgroups — #8942877

Order 512.

5092 conjugacy classes of subgroups.

The subgroup lattice has 1391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#54957C214yesmaximal, complemented
2#54949C214yesmaximal, complemented
3#54572C214yesmaximal, complemented
4#52083C212yesmaximal, complemented
5#51831C212yesmaximal, complemented
6#51045C212yesmaximal, complemented
7#49593C212yesmaximal, complemented
8#48709C214yesmaximal, complemented
9#48051C214yesmaximal, complemented
10#47831C212yesmaximal, complemented
11#46481C214yesmaximal, complemented
12#44270C214yesmaximal, complemented
13#44170C214yesmaximal, complemented
14#42985C212yesmaximal, complemented
15#42112C214yesmaximal, complemented
16#42099C214yesmaximal, complemented
17#37940C212yesmaximal, complemented
18#37769C212yesmaximal, complemented
19#36707C211yesmaximal, characteristic, complemented
20#35907C212yesmaximal, complemented
21#35704C212yesmaximal, complemented
22#35633C211yesmaximal, characteristic, complemented
23#35377C211yesmaximal, characteristic, complemented
24C2×#555C2212yescomplemented
25C2×#550C2212yes—
26C2×#538C2212yescomplemented
27C2×#537C2211yescharacteristic, complemented
28C2×#536C2211yescharacteristic, complemented
29C2×#534C2211yescharacteristic
30C2×#525C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C2×#520C2211yescharacteristic, complemented
33#2847C2212yes—
34#2828C2214yescomplemented
35#2827C2214yescomplemented
36#2826C2214yes—
37#2825C2214yescomplemented
38#2815C2214yescomplemented
39#2809C2212yescomplemented
40#2800C2214yescomplemented
41#2797C2214yes—
42#2797C2214yescomplemented
43#2788C2214yescomplemented
44#2781C2214yescomplemented
45#2780C2214yes—
46#2778C2214yes—
47#2778C2214yescomplemented
48#2775C2214yescomplemented
49#2773C2214yescomplemented
50#2772C2214yescomplemented
51#2772C2214yescomplemented
52#2765C2214yescomplemented
53#2754C2214yescomplemented
54#2751C2214yescomplemented
55#2746C2214yescomplemented
56#2746C2214yescomplemented
57#2738C2214yescomplemented
58#2733C2212yescomplemented
59#2733C2212yescomplemented
60#2733C2212yescomplemented
61#2731C2214yescomplemented
62#2730C2214yes—
63#2710C2214yescomplemented
64#2708C2214yes—
65#2706C2214yescomplemented
66#2706C2214yescomplemented
67#2705C2214yescomplemented
68#2703C2214yes—
69#2701C2214yescomplemented
70#2701C2214yescomplemented
71#2699C2214yes—
72#2693C2214yescomplemented
73#2692C2214yescomplemented
74#2692C2214yescomplemented
75#2691C2214yescomplemented
76#2688C2214yescomplemented
77#2688C2214yescomplemented
78#2688C2214yescomplemented
79#2682C2214yescomplemented
80#2678C2214yescomplemented
81#2678C2214yescomplemented
82#2676C2214yescomplemented
83#2676C2214yescomplemented
84#2676C2214yescomplemented
85#2676C2214yescomplemented
86#2673C2214yes—
87#2673C2214yes—
88#2673C2214yes—
89#2673C2214yes—
90#2673C2214yescomplemented
91#2673C2214yescomplemented
92#2671C2214yes—
93#2669C2214yes—
94#2669C2214yes—
95#2667C2212yescomplemented
96#2656C2212yescomplemented
97#2655C2214yescomplemented
98#2653C2214yescomplemented
99#2653C2214yescomplemented
100#2646C2212yescomplemented
101#2639C2214yescomplemented
102#2638C2214yescomplemented
103#2635C2212yes—
104#2635C2212yescomplemented
105#2631C2214yescomplemented
106#2630C2214yescomplemented
107#2619C2212yescomplemented
108#2618C2212yescomplemented
109#2617C2212yescomplemented
110#2617C2212yescomplemented
111#2615C2212yes—
112#2602C2214yescomplemented
113#2601C2214yescomplemented
114#2601C2214yescomplemented
115#2598C2214yescomplemented
116#2591C2212yes—
117#2591C2212yes—
118#2591C2212yescomplemented
119#2581C2212yescomplemented
120#2578C2214yes—
121#2576C2214yescomplemented
122#2576C2214yescomplemented
123#2575C2214yescomplemented
124#2574C2214yescomplemented
125#2557C2214yescomplemented
126#2548C2212yescomplemented
127#2543C2214yescomplemented
128#2539C2212yes—
129#2535C2214yescomplemented
130#2534C2212yes—
131#2534C2212yes—
132#2531C2214yescomplemented
133#2528C2214yescomplemented
134#2527C2214yescomplemented
135#2526C2214yescomplemented
136#2526C2214yescomplemented
137#2510C2214yescomplemented
138#2505C2214yescomplemented
139#2504C2212yes—
140#2488C2214yes—
141#2488C2214yes—
142#2486C2212yescomplemented
143#2486C2212yescomplemented
144#2478C2214yescomplemented
145#2477C2214yescomplemented
146#2477C2214yescomplemented
147#2476C2214yescomplemented
148#2476C2214yescomplemented
149#2476C2214yescomplemented
150#2472C2214yes—
151#2472C2214yes—
152#2471C2214yescomplemented
153#2471C2214yescomplemented
154#2471C2214yescomplemented
155#2467C2214yes—
156#2464C2214yes—
157#2464C2214yescomplemented
158#2458C2214yes—
159#2457C2214yes—
160#2457C2214yescomplemented
161#2456C2214yes—
162#2456C2214yescomplemented
163#2456C2214yescomplemented
164#2455C2214yescomplemented
165#2445C2214yescomplemented
166#2436C2212yes—
167#2436C2212yescomplemented
168#2433C2214yes—
169#2431C2214yescomplemented
170#2429C2214yescomplemented
171#2428C2214yes—
172#2428C2214yescomplemented
173#2427C2214yescomplemented
174#2425C2214yescomplemented
175#2424C2214yes—
176#2424C2214yes—
177#2424C2214yescomplemented
178#2421C2214yescomplemented
179#2420C2214yescomplemented
180#2418C2214yes—
181#2418C2214yescomplemented
182#2417C2214yescomplemented
183#2415C2214yescomplemented
184#2411C2214yescomplemented
185#2410C2214yes—
186#2407C2214yescomplemented
187#2406C2212yescomplemented
188#2406C2212yescomplemented
189#2404C2212yes—
190#2404C2214yes—
191#2396C2212yescomplemented
192#2392C2214yescomplemented
193#2388C2212yescomplemented
194#2388C2212yescomplemented
195#2381C2212yescomplemented
196#2379C2212yescomplemented
197#2377C2212yes—
198#2372C2212yescomplemented
199#2367C2214yescomplemented
200#2364C2214yescomplemented
201#2364C2214yescomplemented
202#2361C2214yescomplemented
203#2359C2214yescomplemented
204#2358C2214yescomplemented
205#2357C2212yescomplemented
206#2339C2212yescomplemented
207#2329C2212yescomplemented
208#2328C2214yes—
209#2325C2212yescomplemented
210#2324C2214yes—
211#2316C2211yescharacteristic, complemented
212#2315C2212yescomplemented
213#2313C2211yescharacteristic, complemented
214#2310C2211yescharacteristic, complemented
215#2308C2212yes—
216C2×#386C2212yes—
217#2280C2211yescharacteristic
218#2273C2211yescharacteristic
219C22×#41C2311yescharacteristic
220C22×#41C2312yes—
221C22×#41C2312yes—
222C23×Q8C2311yescharacteristic
223C23×D4C2312yes—
224C24×C4C2311yescharacteristic
225#555—48no—
226#550—48no—
227#538—48no—
228#537—44no—
229#536—44no—
230#534—44no—
231C2×C4⋊Q8C2312yes—
232C2×#127C2314yes—
233C2×#127C2312yes—
234C2×#127C2314yes—
235C2×#126C2314yes—
236C2×#124C2314yes—
237C2×#124C2312yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2312yes—
241C2×#124C2312yes—
242#525—44no—
243C2×#123C2314yes—
244C2×#123C2312yes—
245C2×#123C2314yes—
246C2×#123C2312yes—
247C2×#123C2314yes—
248C2×#123C2312yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×C22⋊Q8—44no—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×#121C2312yes—
260C2×#121C2314yes—
261C2×#121C2312yes—
262C2×#121C2312yes—
263C2×#121C2312yes—
264C2×#121C2312yes—
265C2×#121C2312yes—
266C2×#121C2314yes—
267C2×#121C2312yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2312yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#120C2314yes—
280C2×#120C2314yes—
281C2×#120C2314yes—
282C2×#120C2312yes—
283C2×#120C2314yes—
284C2×#120C2314yes—
285#520—44no—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2314yes—
299C2×#117C2311yescharacteristic
300C2×#117C2311yescharacteristic
301C2×#117C2311yescharacteristic
302C2×#117C2314yes—
303C2×#117C2314yes—
304C2×#117C2312yes—
305C22×C4⋊C4C2311yescharacteristic
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2311yescharacteristic
308C22×C4⋊C4C2312yes—
309C22×C22⋊C4C2311yescharacteristic
310C22×C22⋊C4C2311yescharacteristic
311C22×C22⋊C4C2312yes—
312C22×C22⋊C4C2312yes—
313C22×C22⋊C4C2312yes—
314C22×C22⋊C4C2314yes—
315#401C2314yes—
316#401C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2312yes—
324#400C2312yes—
325#400C2312yes—
326#400C2314yes—
327#400C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2312yes—
332#399C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#397C2314yes—
343#397C2314yes—
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#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#395C2312yes—
371#395C2312yes—
372#395C2312yes—
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#394C2312yes—
388#394C2312yes—
389#394C2312yes—
390#394C2312yes—
391#394C2314yes—
392#394C2312yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2312yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2312yes—
409#393C2314yes—
410#393C2314yes—
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#392C2312yes—
424#392C2312yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#391C2312yes—
436#391C2312yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#390C2314yes—
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#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#388C2314yes—
496#388C2314yes—
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#387C2314yes—
516#387C2314yes—
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#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#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
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#383C2314yes—
577#382C2314yes—
578#382C2314yes—
579#382C2312yes—
580#382C2314yes—
581#381C2314yes—
582#381C2312yes—
583#381C2312yes—
584#381C2312yes—
585#381C2314yes—
586#381C2312yes—
587#381C2314yes—
588#381C2312yes—
589#380C2312yes—
590#380C2314yes—
591#380C2312yes—
592#380C2312yes—
593#380C2312yes—
594#380C2312yes—
595#380C2312yes—
596#380C2314yes—
597#380C2314yes—
598#380C2312yes—
599#380C2314yes—
600#380C2314yes—
601#379C2314yes—
602#379C2312yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2312yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2312yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619#376C2314yes—
620C2×#95C2312yes—
621C2×#95C2312yes—
622C2×#95C2314yes—
623C25C2411yescharacteristic
624C25C2412yes—
625C2×#41—24no—
626C2×#41—28no—
627C2×#41—42no—
628C2×#41—42no—
629C2×#41—44no—
630C2×#41—84no—
631C2×#41—84no—
632C22×Q8—42no—
633C22×Q8—42no—
634C22×Q8—42no—
635C22×Q8C2412yes—
636C22×Q8C2412yes—
637C22×Q8C2412yes—
638C22×Q8C2411yescharacteristic
639C22×D4—44no—
640C22×D4—44no—
641C22×D4—44no—
642C22×D4C2412yes—
643C22×D4C2412yes—
644C22×D4C2411yescharacteristic
645C22×D4C2414yes—
646C22×D4C2414yes—
647C22×D4C2414yes—
648C22×D4C2414yes—
649C22×D4C2412yes—
650C22×D4C2414yes—
651C22×D4C2414yes—
652C22×D4C2414yes—
653C22×D4C2414yes—
654C22×D4C2414yes—
655C22×D4C2414yes—
656C22×D4C2412yes—
657C22×D4C2414yes—
658C22×D4C2414yes—
659C22×D4C2414yes—
660C22×D4C2412yes—
661C22×D4C2412yes—
662C22×D4C2414yes—
663C23×C4—42no—
664C23×C4—42no—
665C23×C4—42no—
666C23×C4C2411yescharacteristic
667C23×C4C2412yes—
668C23×C4C2411yescharacteristic
669C23×C4C2411yescharacteristic
670C23×C4C2411yescharacteristic
671C23×C4C2412yes—
672C23×C4C2412yes—
673C23×C4C2411yescharacteristic
674C23×C4C2412yes—
675C23×C4C2414yes—
676C23×C4C2412yes—
677C23×C4C2412yes—
678C23×C4C2412yes—
679C23×C4C2414yes—
680C23×C4C2414yes—
681C23×C4C2412yes—
682C23×C4C2414yes—
683C23×C4C2414yes—
684C23×C4C2411yescharacteristic
685C4⋊Q8—28no—
686#127—44no—
687#127—48no—
688#127—48no—
689#126—48no—
690#124—216no—
691#124—44no—
692#124—44no—
693#124—44no—
694#124—44no—
695#124—44no—
696#123—48no—
697#123—48no—
698#123—48no—
699#123—44no—
700#123—44no—
701#123—44no—
702#123—84no—
703#123—84no—
704#123—84no—
705#123—84no—
706C22⋊Q8—28no—
707C22⋊Q8—48no—
708C22⋊Q8—48no—
709C22⋊Q8—48no—
710C22⋊Q8—48no—
711#121—28no—
712#121—48no—
713#121—44no—
714#121—44no—
715#121—48no—
716#121—48no—
717#121—48no—
718#121—48no—
719#121—48no—
720#121—48no—
721#121—48no—
722#121—44no—
723#121—48no—
724#121—44no—
725#121—48no—
726#121—44no—
727#121—44no—
728#121—44no—
729#121—84no—
730#121—84no—
731#120—44no—
732#120—48no—
733#120—48no—
734#120—48no—
735#120—84no—
736#120—84no—
737C4×Q8—44no—
738C4×Q8—44no—
739C4×D4—28no—
740C4×D4—48no—
741C4×D4—48no—
742C4×D4—44no—
743C4×D4—48no—
744C4×D4—48no—
745C4×D4—44no—
746C4×D4—84no—
747C4×D4—84no—
748C4×D4—84no—
749C4×D4—84no—
750#117—42no—
751#117—44no—
752#117—48no—
753#117—48no—
754#117—42no—
755#117—42no—
756C2×C4⋊C4—24no—
757C2×C4⋊C4—24no—
758C2×C4⋊C4—44no—
759C2×C4⋊C4—42no—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
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⋊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⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C42C2414yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2412yes—
862C2×C42C2412yes—
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2414yes—
871#95C2412yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2412yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2412yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2412yes—
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—24no—
918C24—42no—
919C24—42no—
920C24—41no—
921C24—42no—
922C24—41no—
923C24—42no—
924C24—42no—
925C24—42no—
926C24—42no—
927C24C2514yes—
928C24C2514yes—
929C24C2512yes—
930C24C2511yescharacteristic
931C24C2512yes—
932#41—416no—
933#41—816no—
934#41—816no—
935C2×Q8—24no—
936C2×Q8—24no—
937C2×Q8—24no—
938C2×Q8—41no—
939C2×Q8—41no—
940C2×Q8—44no—
941C2×Q8—42no—
942C2×Q8—42no—
943C2×Q8—42no—
944C2×Q8—42no—
945C2×Q8—88no—
946C2×Q8H(5,𝔽2)14yes—
947C2×D4—24no—
948C2×D4—28no—
949C2×D4—28no—
950C2×D4—28no—
951C2×D4—28no—
952C2×D4—28no—
953C2×D4—28no—
954C2×D4—24no—
955C2×D4—24no—
956C2×D4—22no—
957C2×D4—24no—
958C2×D4—28no—
959C2×D4—41no—
960C2×D4—44no—
961C2×D4—42no—
962C2×D4—41no—
963C2×D4—44no—
964C2×D4—44no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
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—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—42no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—42no—
994C2×D4—42no—
995C2×D4—42no—
996C2×D4—42no—
997C2×D4—42no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—42no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—42no—
1005C2×D4—42no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—816no—
1009C22×C4—22no—
1010C22×C4—22no—
1011C22×C4—22no—
1012C22×C4—22no—
1013C22×C4—22no—
1014C22×C4—22no—
1015C22×C4—22no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—24no—
1019C22×C4—24no—
1020C22×C4—24no—
1021C22×C4—28no—
1022C22×C4—24no—
1023C22×C4—42no—
1024C22×C4—42no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4—42no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—41no—
1040C22×C4—42no—
1041C22×C4—41no—
1042C22×C4—41no—
1043C22×C4—44no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—41no—
1047C22×C4—42no—
1048C22×C4—41no—
1049C22×C4—41no—
1050C22×C4—42no—
1051C22×C4—42no—
1052C22×C4—42no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—44no—
1056C22×C4—42no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—42no—
1061C22×C4—88no—
1062C22×C4H(5,𝔽2)14yes—
1063C22×C4C2514yes—
1064C22×C4C2514yes—
1065C22×C4C2514yes—
1066C22×C4C2514yes—
1067C22×C4C2514yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2514yes—
1073C22×C4C2514yes—
1074C22×C4C2512yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2511yescharacteristic
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2511yescharacteristic
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—28no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—24no—
1090C4⋊C4—41no—
1091C4⋊C4—42no—
1092C4⋊C4—44no—
1093C4⋊C4—41no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C22⋊C4—24no—
1117C22⋊C4—28no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—24no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
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—42no—
1138C22⋊C4—42no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—42no—
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—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C42—28no—
1173C42—24no—
1174C42—24no—
1175C42—42no—
1176C42—42no—
1177C42—42no—
1178C42—42no—
1179C42—42no—
1180C42—44no—
1181C42—44no—
1182C42—44no—
1183C42—42no—
1184C42—42no—
1185C42—44no—
1186C23—28no—
1187C23—22no—
1188C23—22no—
1189C23—21no—
1190C23—22no—
1191C23—21no—
1192C23—22no—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—22no—
1197C23—24no—
1198C23—24no—
1199C23—22no—
1200C23—24no—
1201C23—22no—
1202C23—24no—
1203C23—24no—
1204C23—24no—
1205C23—24no—
1206C23—24no—
1207C23—24no—
1208C23—22no—
1209C23—24no—
1210C23—24no—
1211C23—24no—
1212C23—24no—
1213C23—24no—
1214C23—24no—
1215C23—24no—
1216C23—48no—
1217C23—82no—
1218C23—82no—
1219C23—84no—
1220C23—84no—
1221C23—84no—
1222C23—84no—
1223C23—162no—
1224C23—162no—
1225C23—162no—
1226C23—162no—
1227C23C2×H(5,𝔽2)12yes—
1228C23#58514yes—
1229C23C2611yescharacteristic
1230Q8—44no—
1231Q8—48no—
1232Q8—84no—
1233Q8—84no—
1234D4—48no—
1235D4—44no—
1236D4—48no—
1237D4—88no—
1238D4—84no—
1239D4—88no—
1240D4—88no—
1241D4—88no—
1242D4—88no—
1243D4—88no—
1244D4—88no—
1245D4—88no—
1246D4—88no—
1247D4—88no—
1248D4—88no—
1249D4—162no—
1250D4—162no—
1251D4—162no—
1252D4—164no—
1253D4—164no—
1254D4—164no—
1255C2×C4—28no—
1256C2×C4—22no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—22no—
1261C2×C4—21no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—44no—
1303C2×C4—48no—
1304C2×C4—84no—
1305C2×C4—84no—
1306C2×C4—84no—
1307C2×C4—88no—
1308C2×C4—82no—
1309C2×C4—82no—
1310C2×C4—84no—
1311C2×C4—82no—
1312C2×C4—82no—
1313C2×C4—88no—
1314C2×C4—88no—
1315C2×C4—88no—
1316C2×C4—162no—
1317C2×C4—162no—
1318C2×C4—164no—
1319C2×C4—162no—
1320C2×C4C2×H(5,𝔽2)12yes—
1321C2×C4C2×H(5,𝔽2)14yes—
1322C2×C4C2×H(5,𝔽2)14yes—
1323C2×C4#58512yes—
1324C22—22no—
1325C22—24no—
1326C22—22no—
1327C22—22no—
1328C22—24no—
1329C22—24no—
1330C22—42no—
1331C22—42no—
1332C22—42no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—44no—
1338C22—44no—
1339C22—44no—
1340C22—42no—
1341C22—44no—
1342C22—42no—
1343C22—44no—
1344C22—44no—
1345C22—44no—
1346C22—44no—
1347C22—44no—
1348C22—44no—
1349C22—44no—
1350C22—44no—
1351C22—44no—
1352C22—44no—
1353C22—44no—
1354C22—44no—
1355C22—88no—
1356C22—168no—
1357C22C22×H(5,𝔽2)11yescharacteristic
1358C22C22×H(5,𝔽2)11yescharacteristic
1359C22C2×#58511yescharacteristic
1360C22C2×#58512yes—
1361C22H(7,𝔽2)12yes—
1362C4—22no—
1363C4—22no—
1364C4—24no—
1365C4—24no—
1366C4—42no—
1367C4—42no—
1368C4—42no—
1369C4—44no—
1370C4—42no—
1371C4—42no—
1372C4—44no—
1373C4—42no—
1374C4—44no—
1375C4—44no—
1376C4—44no—
1377C4—44no—
1378C4—44no—
1379C4—44no—
1380C2—42no—
1381C2—44no—
1382C2—82no—
1383C2—84no—
1384C2—84no—
1385C2#6281811yescharacteristic
1386C2#6282411yescharacteristic
1387C2#6286211yescharacteristic
1388C2#6289912yes—
1389C2#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. #54957C2semidirect
2. #54949C2semidirect
3. #54572C2semidirect
4. #52083C2semidirect
5. #51831C2semidirect
6. #51045C2semidirect
7. #49593C2semidirect
8. #48709C2semidirect
9. #48051C2semidirect
10. #47831C2semidirect
11. #46481C2semidirect
12. #44270C2semidirect
13. #44170C2semidirect
14. #42985C2semidirect
15. #42112C2semidirect
16. #42099C2semidirect
17. #37940C2semidirect
18. #37769C2semidirect
19. #36707C2semidirect
20. #35907C2semidirect
21. #35704C2semidirect
22. #35633C2semidirect
23. #35377C2semidirect
24. C2×#555C22semidirect
26. C2×#538C22semidirect
27. C2×#537C22semidirect
28. C2×#536C22semidirect
32. C2×#520C22semidirect
34. #2828C22semidirect
35. #2827C22semidirect
37. #2825C22semidirect
38. #2815C22semidirect
39. #2809C22semidirect
40. #2800C22semidirect
42. #2797C22semidirect
43. #2788C22semidirect
44. #2781C22semidirect
47. #2778C22semidirect
48. #2775C22semidirect
49. #2773C22semidirect
50. #2772C22semidirect
51. #2772C22semidirect
52. #2765C22semidirect
53. #2754C22semidirect
54. #2751C22semidirect
55. #2746C22semidirect
56. #2746C22semidirect
57. #2738C22semidirect
58. #2733C22semidirect
59. #2733C22semidirect
60. #2733C22semidirect
61. #2731C22semidirect
63. #2710C22semidirect
65. #2706C22semidirect
66. #2706C22semidirect
67. #2705C22semidirect
69. #2701C22semidirect
70. #2701C22semidirect
72. #2693C22semidirect
73. #2692C22semidirect
74. #2692C22semidirect
75. #2691C22semidirect
76. #2688C22semidirect
77. #2688C22semidirect
78. #2688C22semidirect
79. #2682C22semidirect
80. #2678C22semidirect
81. #2678C22semidirect
82. #2676C22semidirect
83. #2676C22semidirect
84. #2676C22semidirect
85. #2676C22semidirect
90. #2673C22semidirect
91. #2673C22semidirect
95. #2667C22semidirect
96. #2656C22semidirect
97. #2655C22semidirect
98. #2653C22semidirect
99. #2653C22semidirect
100. #2646C22semidirect
101. #2639C22semidirect
102. #2638C22semidirect
104. #2635C22semidirect
105. #2631C22semidirect
106. #2630C22semidirect
107. #2619C22semidirect
108. #2618C22semidirect
109. #2617C22semidirect
110. #2617C22semidirect
112. #2602C22semidirect
113. #2601C22semidirect
114. #2601C22semidirect
115. #2598C22semidirect
118. #2591C22semidirect
119. #2581C22semidirect
121. #2576C22semidirect
122. #2576C22semidirect
123. #2575C22semidirect
124. #2574C22semidirect
125. #2557C22semidirect
126. #2548C22semidirect
127. #2543C22semidirect
129. #2535C22semidirect
132. #2531C22semidirect
133. #2528C22semidirect
134. #2527C22semidirect
135. #2526C22semidirect
136. #2526C22semidirect
137. #2510C22semidirect
138. #2505C22semidirect
142. #2486C22semidirect
143. #2486C22semidirect
144. #2478C22semidirect
145. #2477C22semidirect
146. #2477C22semidirect
147. #2476C22semidirect
148. #2476C22semidirect
149. #2476C22semidirect
152. #2471C22semidirect
153. #2471C22semidirect
154. #2471C22semidirect
157. #2464C22semidirect
160. #2457C22semidirect
162. #2456C22semidirect
163. #2456C22semidirect
164. #2455C22semidirect
165. #2445C22semidirect
167. #2436C22semidirect
169. #2431C22semidirect
170. #2429C22semidirect
172. #2428C22semidirect
173. #2427C22semidirect
174. #2425C22semidirect
177. #2424C22semidirect
178. #2421C22semidirect
179. #2420C22semidirect
181. #2418C22semidirect
182. #2417C22semidirect
183. #2415C22semidirect
184. #2411C22semidirect
186. #2407C22semidirect
187. #2406C22semidirect
188. #2406C22semidirect
191. #2396C22semidirect
192. #2392C22semidirect
193. #2388C22semidirect
194. #2388C22semidirect
195. #2381C22semidirect
196. #2379C22semidirect
198. #2372C22semidirect
199. #2367C22semidirect
200. #2364C22semidirect
201. #2364C22semidirect
202. #2361C22semidirect
203. #2359C22semidirect
204. #2358C22semidirect
205. #2357C22semidirect
206. #2339C22semidirect
207. #2329C22semidirect
209. #2325C22semidirect
211. #2316C22semidirect
212. #2315C22semidirect
213. #2313C22semidirect
214. #2310C22semidirect

Maximal subgroups

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

subgroupindex
#549572
#549492
#545722
#520832
#518312
#510452
#495932
#487092
#480512
#478312
#464812
#442702
#441702
#429852
#421122
#420992
#379402
#377692
#367072
#359072
#357042
#356332
#353772