Finite Group Databasebeta

← #8757155

Subgroups — #8757155

Order 512.

4653 conjugacy classes of subgroups.

The subgroup lattice has 1423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58889C212yesmaximal, complemented
2#58384C212yesmaximal, complemented
3#57985C214yesmaximal, complemented
4#57056C212yesmaximal, complemented
5#55043C212yesmaximal, complemented
6#54006C214yesmaximal, complemented
7#53948C214yesmaximal, complemented
8#53446C214yesmaximal, complemented
9#52035C212yesmaximal, complemented
10#51966C212yesmaximal, complemented
11#49793C212yesmaximal, complemented
12#49681C212yesmaximal, complemented
13#49638C212yesmaximal, complemented
14#47962C212yesmaximal, complemented
15#47809C212yesmaximal, complemented
16#47700C212yesmaximal, complemented
17#47082C214yesmaximal, complemented
18#46487C214yesmaximal, complemented
19#46232C212yesmaximal, complemented
20#46224C212yesmaximal, complemented
21#46141C212yesmaximal, complemented
22#45984C212yesmaximal, complemented
23#45978C212yesmaximal, complemented
24#45976C212yesmaximal, complemented
25#35333C211yesmaximal, characteristic, complemented
26#35190C211yesmaximal, characteristic, complemented
27#35129C211yesmaximal, characteristic, complemented
28C2×#562C2212yes—
29C2×#532C2211yescharacteristic, complemented
30C22×#125C2211yescharacteristic, complemented
31C22×#124C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33#2851C2212yes—
34#2851C2212yescomplemented
35#2850C2212yes—
36#2850C2212yes—
37#2850C2212yes—
38#2850C2212yescomplemented
39#2844C2212yescomplemented
40#2843C2212yescomplemented
41#2836C2214yescomplemented
42#2830C2214yescomplemented
43#2829C2214yescomplemented
44#2827C2214yescomplemented
45#2820C2212yes—
46#2820C2212yescomplemented
47#2819C2212yes—
48#2819C2212yes—
49#2816C2214yescomplemented
50#2813C2214yes—
51#2804C2212yes—
52#2804C2214yescomplemented
53#2795C2212yes—
54#2795C2214yescomplemented
55#2790C2214yescomplemented
56#2785C2212yescomplemented
57#2784C2214yes—
58#2782C2212yes—
59#2781C2214yes—
60#2781C2214yescomplemented
61#2780C2214yes—
62#2779C2214yes—
63#2775C2214yescomplemented
64#2768C2214yes—
65#2764C2214yescomplemented
66#2758C2214yescomplemented
67#2757C2214yescomplemented
68#2756C2214yes—
69#2756C2214yescomplemented
70#2750C2214yescomplemented
71#2748C2212yes—
72#2748C2214yescomplemented
73#2743C2214yes—
74#2738C2214yescomplemented
75#2738C2214yescomplemented
76#2737C2214yes—
77#2737C2214yescomplemented
78#2730C2214yes—
79#2729C2214yescomplemented
80#2718C2214yescomplemented
81#2715C2214yescomplemented
82#2714C2214yescomplemented
83#2714C2214yescomplemented
84#2712C2214yescomplemented
85#2711C2214yes—
86#2711C2214yescomplemented
87#2710C2214yes—
88#2706C2214yescomplemented
89#2705C2214yescomplemented
90#2704C2214yescomplemented
91#2704C2214yescomplemented
92#2703C2214yes—
93#2703C2214yescomplemented
94#2703C2214yescomplemented
95#2702C2214yescomplemented
96#2700C2214yes—
97#2698C2214yescomplemented
98#2697C2214yes—
99#2694C2214yescomplemented
100#2694C2214yescomplemented
101#2692C2214yescomplemented
102#2692C2214yescomplemented
103#2692C2214yescomplemented
104#2691C2214yescomplemented
105#2688C2214yes—
106#2688C2214yescomplemented
107#2687C2214yescomplemented
108#2686C2214yes—
109#2686C2214yes—
110#2681C2214yescomplemented
111#2680C2212yescomplemented
112#2680C2214yescomplemented
113#2678C2214yes—
114#2676C2214yes—
115#2676C2214yes—
116#2675C2214yes—
117#2673C2214yescomplemented
118#2672C2214yes—
119#2671C2214yescomplemented
120#2670C2214yes—
121#2669C2212yes—
122#2669C2212yes—
123#2666C2214yescomplemented
124#2661C2214yes—
125#2635C2212yes—
126#2635C2214yescomplemented
127#2635C2212yescomplemented
128#2632C2212yes—
129#2631C2212yes—
130#2631C2214yescomplemented
131#2630C2214yes—
132#2629C2212yes—
133#2629C2212yescomplemented
134#2626C2214yes—
135#2612C2212yescomplemented
136#2610C2212yes—
137#2610C2212yes—
138#2610C2214yescomplemented
139#2605C2214yescomplemented
140#2604C2214yescomplemented
141#2603C2214yes—
142#2598C2212yes—
143#2598C2214yescomplemented
144#2598C2212yescomplemented
145#2592C2212yes—
146#2580C2214yescomplemented
147#2579C2212yes—
148#2579C2212yes—
149#2579C2212yescomplemented
150#2579C2212yescomplemented
151#2578C2214yescomplemented
152#2574C2214yescomplemented
153#2573C2214yescomplemented
154#2568C2211yescharacteristic, complemented
155#2566C2212yes—
156#2566C2212yes—
157#2565C2212yescomplemented
158#2565C2212yescomplemented
159#2564C2214yescomplemented
160#2559C2214yes—
161#2554C2214yescomplemented
162#2548C2211yescharacteristic, complemented
163#2542C2211yescharacteristic
164#2541C2211yescharacteristic
165#2540C2212yes—
166#2537C2212yes—
167#2534C2214yes—
168#2532C2214yescomplemented
169#2532C2214yescomplemented
170#2532C2214yescomplemented
171#2530C2214yescomplemented
172#2526C2214yes—
173#2525C2214yescomplemented
174#2521C2214yescomplemented
175#2500C2212yescomplemented
176#2482C2212yes—
177#2469C2214yescomplemented
178#2465C2214yes—
179#2464C2214yescomplemented
180#2461C2214yes—
181#2461C2214yescomplemented
182#2459C2214yescomplemented
183#2456C2214yes—
184#2456C2214yes—
185#2455C2214yescomplemented
186#2450C2214yes—
187#2450C2214yescomplemented
188#2449C2214yescomplemented
189#2449C2214yescomplemented
190#2443C2214yescomplemented
191#2443C2214yescomplemented
192#2437C2214yes—
193#2431C2212yes—
194#2430C2214yescomplemented
195#2426C2214yescomplemented
196#2425C2214yescomplemented
197#2424C2214yes—
198#2424C2214yes—
199#2423C2214yescomplemented
200#2419C2214yescomplemented
201#2418C2214yes—
202#2416C2214yes—
203#2416C2214yescomplemented
204#2412C2214yes—
205#2410C2214yes—
206#2409C2211yescharacteristic
207#2409C2214yes—
208#2409C2211yescharacteristic
209#2408C2211yescharacteristic
210#2408C2211yescharacteristic
211#2407C2212yes—
212#2407C2212yescomplemented
213#2407C2214yescomplemented
214#2404C2212yes—
215#2382C2212yescomplemented
216#2380C2212yes—
217#2379C2212yes—
218#2379C2212yescomplemented
219#2375C2212yes—
220#2366C2212yes—
221#2358C2212yes—
222#2328C2212yes—
223#2326C2212yescomplemented
224#2326C2214yescomplemented
225#2321C2212yes—
226#2321C2212yes—
227#2318C2214yescomplemented
228#2317C2211yescharacteristic, complemented
229#2317C2211yescharacteristic, complemented
230#2311C2211yescharacteristic
231#2311C2211yescharacteristic
232#2285C2211yescharacteristic, complemented
233#2283C2211yescharacteristic
234#2283C2211yescharacteristic, complemented
235C22×#41C2311yescharacteristic
236C22×#41C2312yes—
237C23×Q8C2311yescharacteristic
238C23×D4C2311yescharacteristic
239#562—48no—
240#532—44no—
241C2×C4⋊Q8C2311yescharacteristic
242C2×#127C2312yes—
243C2×#127C2311yescharacteristic
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#125—44no—
247C2×#125C2312yes—
248C2×#125C2312yes—
249C2×#125C2312yes—
250C2×#125C2312yes—
251C2×#124—44no—
252C2×#124C2312yes—
253C2×#124C2312yes—
254C2×#124C2314yes—
255C2×#124C2312yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×#121C2312yes—
276C2×#121C2314yes—
277C2×#121C2312yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2312yes—
281C2×#121C2312yes—
282C2×#121C2312yes—
283C2×#121C2312yes—
284C2×#121C2314yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#120C2312yes—
290C2×#120C2312yes—
291C2×#120C2314yes—
292C2×#120C2314yes—
293C4×#41—44no—
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2314yes—
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2311yescharacteristic
299C2×C4×D4C2314yes—
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2311yescharacteristic
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2314yes—
310C2×#117C2311yescharacteristic
311C2×#117C2311yescharacteristic
312C2×#117C2311yescharacteristic
313C2×#117C2311yescharacteristic
314C2×#117C2311yescharacteristic
315C22×C4⋊C4C2311yescharacteristic
316C22×C4⋊C4C2311yescharacteristic
317C22×C4⋊C4C2312yes—
318C22×C4⋊C4C2312yes—
319C22×C22⋊C4C2312yes—
320C22×C22⋊C4C2312yes—
321C22×C22⋊C4C2314yes—
322C22×C42C2311yescharacteristic
323C22×C42C2311yescharacteristic
324C22×C42C2311yescharacteristic
325#400C2314yes—
326#400C2312yes—
327#400C2312yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2312yes—
345#399C2312yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2312yes—
394#395C2314yes—
395#395C2314yes—
396#395C2312yes—
397#394C2312yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2312yes—
404#394C2314yes—
405#394C2312yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2312yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2312yes—
431#393C2312yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#392C2314yes—
437#392C2314yes—
438#392C2314yes—
439#392C2314yes—
440#392C2314yes—
441#392C2312yes—
442#392C2314yes—
443#392C2312yes—
444#392C2314yes—
445#392C2312yes—
446#392C2312yes—
447#392C2314yes—
448#392C2314yes—
449#392C2314yes—
450#392C2314yes—
451#392C2314yes—
452#392C2314yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2314yes—
459#391C2314yes—
460#391C2312yes—
461#391C2312yes—
462#391C2314yes—
463#391C2314yes—
464#391C2314yes—
465#390C2312yes—
466#390C2312yes—
467#390C2314yes—
468#390C2314yes—
469#390C2314yes—
470#390C2314yes—
471#390C2314yes—
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2314yes—
480#390C2314yes—
481#390C2314yes—
482#390C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2312yes—
550#386C2312yes—
551#386C2312yes—
552#386C2312yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2312yes—
558#386C2312yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#385C2312yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2312yes—
590#385C2312yes—
591#385C2312yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2312yes—
597#385C2312yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#384C2312yes—
610#384C2312yes—
611#384C2312yes—
612#384C2312yes—
613#383C2314yes—
614#383C2314yes—
615#383C2314yes—
616#383C2312yes—
617#383C2312yes—
618#382C2312yes—
619#382C2312yes—
620#382C2312yes—
621#382C2312yes—
622#382C2312yes—
623#382C2312yes—
624#382C2314yes—
625#381C2314yes—
626#381C2314yes—
627#381C2312yes—
628#381C2314yes—
629#381C2312yes—
630#380C2314yes—
631#380C2314yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2314yes—
637#380C2314yes—
638#380C2312yes—
639#380C2312yes—
640#380C2314yes—
641#380C2312yes—
642#380C2311yescharacteristic
643#380C2311yescharacteristic
644#380C2314yes—
645#380C2314yes—
646#379C2312yes—
647#379C2312yes—
648#379C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2311yescharacteristic
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2311yescharacteristic
654C4×C4⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2312yes—
659#376C2312yes—
660#376C2314yes—
661#376C2312yes—
662C2×#95C2314yes—
663C25C2412yes—
664C2×#41—24no—
665C2×#41—42no—
666C2×#41—42no—
667C2×#41—44no—
668C2×#41—82no—
669C2×#41—82no—
670C22×Q8—42no—
671C22×Q8—82no—
672C22×Q8C2411yescharacteristic
673C22×Q8C2412yes—
674C22×Q8C2412yes—
675C22×Q8C2414yes—
676C22×Q8C2412yes—
677C22×D4—42no—
678C22×D4—82no—
679C22×D4C2411yescharacteristic
680C22×D4C2411yescharacteristic
681C22×D4C2414yes—
682C22×D4C2414yes—
683C22×D4C2414yes—
684C22×D4C2412yes—
685C22×D4C2412yes—
686C22×D4C2412yes—
687C22×D4C2414yes—
688C22×D4C2414yes—
689C22×D4C2412yes—
690C22×D4C2414yes—
691C22×D4C2414yes—
692C22×D4C2414yes—
693C22×D4C2414yes—
694C22×D4C2412yes—
695C22×D4C2411yescharacteristic
696C23×C4C2411yescharacteristic
697C23×C4C2411yescharacteristic
698C23×C4C2411yescharacteristic
699C23×C4C2411yescharacteristic
700C23×C4C2411yescharacteristic
701C23×C4C2411yescharacteristic
702C23×C4C2411yescharacteristic
703C23×C4C2411yescharacteristic
704C23×C4C2411yescharacteristic
705C23×C4C2412yes—
706C23×C4C2414yes—
707C23×C4C2414yes—
708C23×C4C2412yes—
709C23×C4C2412yes—
710C23×C4C2414yes—
711C23×C4C2414yes—
712C23×C4C2414yes—
713C4⋊Q8—42no—
714#127—28no—
715#127—42no—
716#126—84no—
717#126—84no—
718#125—28no—
719#125—44no—
720#125—44no—
721#125—44no—
722#124—28no—
723#124—28no—
724#124—44no—
725#124—44no—
726#124—48no—
727#124—44no—
728#124—44no—
729#124—84no—
730#123—48no—
731#123—48no—
732#123—84no—
733#123—84no—
734#123—84no—
735#123—84no—
736C22⋊Q8—48no—
737C22⋊Q8—48no—
738C22⋊Q8—82no—
739C22⋊Q8—82no—
740C22⋊Q8—82no—
741C22⋊Q8—84no—
742C22⋊Q8—84no—
743C22⋊Q8—84no—
744C22⋊Q8—82no—
745#121—44no—
746#121—44no—
747#121—48no—
748#121—48no—
749#121—84no—
750#121—84no—
751#121—84no—
752#121—84no—
753#121—82no—
754#121—84no—
755#121—84no—
756#121—82no—
757#121—82no—
758#121—82no—
759#120—28no—
760#120—44no—
761#120—84no—
762#120—84no—
763C4×Q8—42no—
764C4×Q8—42no—
765C4×Q8—84no—
766C4×D4—48no—
767C4×D4—44no—
768C4×D4—44no—
769C4×D4—42no—
770C4×D4—42no—
771C4×D4—42no—
772C4×D4—42no—
773C4×D4—42no—
774C4×D4—42no—
775C4×D4—84no—
776C4×D4—84no—
777C4×D4—84no—
778C4×D4—84no—
779#117—42no—
780#117—42no—
781#117—42no—
782#117—42no—
783#117—42no—
784C2×C4⋊C4—44no—
785C2×C4⋊C4—44no—
786C2×C4⋊C4—42no—
787C2×C4⋊C4—42no—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C22⋊C4—44no—
834C2×C22⋊C4—44no—
835C2×C22⋊C4—84no—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2411yescharacteristic
851C2×C22⋊C4C2411yescharacteristic
852C2×C22⋊C4C2411yescharacteristic
853C2×C22⋊C4C2411yescharacteristic
854C2×C22⋊C4C2411yescharacteristic
855C2×C22⋊C4C2411yescharacteristic
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C42—24no—
894C2×C42—24no—
895C2×C42—24no—
896C2×C42C2411yescharacteristic
897C2×C42C2411yescharacteristic
898C2×C42C2411yescharacteristic
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2412yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2411yescharacteristic
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2412yes—
920#95C2414yes—
921#95C2412yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961C24—24no—
962C24—42no—
963C24—44no—
964C24—44no—
965C24—42no—
966C24C2514yes—
967C24C2514yes—
968C24C2511yescharacteristic
969C24C2511yescharacteristic
970C24C2511yescharacteristic
971#41—416no—
972#41—816no—
973C2×Q8—24no—
974C2×Q8—24no—
975C2×Q8—22no—
976C2×Q8—22no—
977C2×Q8—41no—
978C2×Q8—44no—
979C2×Q8—44no—
980C2×Q8—42no—
981C2×Q8—42no—
982C2×Q8—44no—
983C2×Q8—42no—
984C2×Q8—42no—
985C2×Q8—42no—
986C2×Q8—44no—
987C2×Q8—88no—
988C2×D4—22no—
989C2×D4—22no—
990C2×D4—28no—
991C2×D4—28no—
992C2×D4—28no—
993C2×D4—24no—
994C2×D4—24no—
995C2×D4—24no—
996C2×D4—22no—
997C2×D4—41no—
998C2×D4—41no—
999C2×D4—41no—
1000C2×D4—41no—
1001C2×D4—41no—
1002C2×D4—42no—
1003C2×D4—42no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—42no—
1018C2×D4—42no—
1019C2×D4—44no—
1020C2×D4—42no—
1021C2×D4—42no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—42no—
1025C2×D4—42no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—88no—
1037C2×D42−1+414yes—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—22no—
1041C22×C4—22no—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—22no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—22no—
1049C22×C4—22no—
1050C22×C4—22no—
1051C22×C4—42no—
1052C22×C4—41no—
1053C22×C4—41no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—42no—
1057C22×C4—42no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4C2511yescharacteristic
1081C22×C4C2514yes—
1082C22×C4C2514yes—
1083C22×C4C2514yes—
1084C22×C4C2511yescharacteristic
1085C22×C4C2511yescharacteristic
1086C22×C4C2514yes—
1087C22×C4C2514yes—
1088C22×C4C2514yes—
1089C22×C4C2514yes—
1090C22×C4C2514yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2514yes—
1093C22×C4C2514yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2511yescharacteristic
1096C22×C4C2511yescharacteristic
1097C22×C4C2511yescharacteristic
1098C22×C4C2511yescharacteristic
1099C22×C4C2511yescharacteristic
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C4⋊C4—28no—
1103C4⋊C4—28no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—41no—
1113C4⋊C4—41no—
1114C4⋊C4—41no—
1115C4⋊C4—41no—
1116C4⋊C4—41no—
1117C4⋊C4—41no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C22⋊C4—24no—
1148C22⋊C4—28no—
1149C22⋊C4—28no—
1150C22⋊C4—28no—
1151C22⋊C4—28no—
1152C22⋊C4—28no—
1153C22⋊C4—28no—
1154C22⋊C4—28no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—42no—
1162C22⋊C4—42no—
1163C22⋊C4—41no—
1164C22⋊C4—41no—
1165C22⋊C4—41no—
1166C22⋊C4—41no—
1167C22⋊C4—41no—
1168C22⋊C4—41no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—42no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C42—22no—
1205C42—22no—
1206C42—22no—
1207C42—22no—
1208C42—22no—
1209C42—22no—
1210C42—22no—
1211C42—22no—
1212C42—22no—
1213C42—24no—
1214C42—24no—
1215C42—24no—
1216C42—44no—
1217C42—44no—
1218C42—44no—
1219C42—44no—
1220C42—44no—
1221C42—42no—
1222C42H(5,𝔽2)14yes—
1223C23—21no—
1224C23—21no—
1225C23—21no—
1226C23—21no—
1227C23—22no—
1228C23—22no—
1229C23—22no—
1230C23—22no—
1231C23—24no—
1232C23—24no—
1233C23—21no—
1234C23—24no—
1235C23—21no—
1236C23—24no—
1237C23—24no—
1238C23—24no—
1239C23—21no—
1240C23—22no—
1241C23—24no—
1242C23—24no—
1243C23—24no—
1244C23—24no—
1245C23—24no—
1246C23—24no—
1247C23—24no—
1248C23—22no—
1249C23—24no—
1250C23—88no—
1251C23—84no—
1252C23—84no—
1253C23—84no—
1254C23—164no—
1255C23C2×2−1+412yes—
1256C23C2×2−1+412yes—
1257C23C2611yescharacteristic
1258Q8—44no—
1259Q8—84no—
1260Q8—84no—
1261Q8—88no—
1262Q8—84no—
1263D4—44no—
1264D4—44no—
1265D4—44no—
1266D4—84no—
1267D4—84no—
1268D4—84no—
1269D4—88no—
1270D4—88no—
1271D4—88no—
1272D4—88no—
1273D4—88no—
1274D4—84no—
1275D4—84no—
1276D4—88no—
1277D4—164no—
1278D4—164no—
1279D4—164no—
1280C2×C4—28no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—21no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—21no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—44no—
1335C2×C4—44no—
1336C2×C4—44no—
1337C2×C4—44no—
1338C2×C4—82no—
1339C2×C4—82no—
1340C2×C4—82no—
1341C2×C4—82no—
1342C2×C4—84no—
1343C2×C4—84no—
1344C2×C4—84no—
1345C2×C4—88no—
1346C2×C4—164no—
1347C2×C4—164no—
1348C2×C4—164no—
1349C2×C4—164no—
1350C2×C4C2×H(5,𝔽2)12yes—
1351C2×C4C2×H(5,𝔽2)12yes—
1352C2×C4C2×H(5,𝔽2)12yes—
1353C2×C4C2×2−1+412yes—
1354C2×C4#58512yes—
1355C22—24no—
1356C22—24no—
1357C22—22no—
1358C22—22no—
1359C22—42no—
1360C22—42no—
1361C22—41no—
1362C22—41no—
1363C22—41no—
1364C22—41no—
1365C22—44no—
1366C22—44no—
1367C22—44no—
1368C22—44no—
1369C22—42no—
1370C22—44no—
1371C22—44no—
1372C22—44no—
1373C22—42no—
1374C22—44no—
1375C22—41no—
1376C22—44no—
1377C22—44no—
1378C22—41no—
1379C22—44no—
1380C22—41no—
1381C22—44no—
1382C22—44no—
1383C22—44no—
1384C22—168no—
1385C22C22×H(5,𝔽2)11yescharacteristic
1386C22C22×2−1+411yescharacteristic
1387C22C2×#58511yescharacteristic
1388C22H(7,𝔽2)12yes—
1389C22H(7,𝔽2)12yes—
1390C4—22no—
1391C4—22no—
1392C4—22no—
1393C4—22no—
1394C4—22no—
1395C4—44no—
1396C4—44no—
1397C4—44no—
1398C4—44no—
1399C4—44no—
1400C4—44no—
1401C4—41no—
1402C4—41no—
1403C4—41no—
1404C4—41no—
1405C4—41no—
1406C4—41no—
1407C4—44no—
1408C4—44no—
1409C4—44no—
1410C4—44no—
1411C4—41no—
1412C2—42no—
1413C2—42no—
1414C2—84no—
1415C2—81no—
1416C2—84no—
1417C2#6281911yescharacteristic
1418C2#6287411yescharacteristic
1419C2#6287411yescharacteristic
1420C2#6305112yes—
1421C2#6305412yes—
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. #58889C2semidirect
2. #58384C2semidirect
3. #57985C2semidirect
4. #57056C2semidirect
5. #55043C2semidirect
6. #54006C2semidirect
7. #53948C2semidirect
8. #53446C2semidirect
9. #52035C2semidirect
10. #51966C2semidirect
11. #49793C2semidirect
12. #49681C2semidirect
13. #49638C2semidirect
14. #47962C2semidirect
15. #47809C2semidirect
16. #47700C2semidirect
17. #47082C2semidirect
18. #46487C2semidirect
19. #46232C2semidirect
20. #46224C2semidirect
21. #46141C2semidirect
22. #45984C2semidirect
23. #45978C2semidirect
24. #45976C2semidirect
25. #35333C2semidirect
26. #35190C2semidirect
27. #35129C2semidirect
29. C2×#532C22semidirect
30. C22×#125C22semidirect
34. #2851C22semidirect
38. #2850C22semidirect
39. #2844C22semidirect
40. #2843C22semidirect
41. #2836C22semidirect
42. #2830C22semidirect
43. #2829C22semidirect
44. #2827C22semidirect
46. #2820C22semidirect
49. #2816C22semidirect
52. #2804C22semidirect
54. #2795C22semidirect
55. #2790C22semidirect
56. #2785C22semidirect
60. #2781C22semidirect
63. #2775C22semidirect
65. #2764C22semidirect
66. #2758C22semidirect
67. #2757C22semidirect
69. #2756C22semidirect
70. #2750C22semidirect
72. #2748C22semidirect
74. #2738C22semidirect
75. #2738C22semidirect
77. #2737C22semidirect
79. #2729C22semidirect
80. #2718C22semidirect
81. #2715C22semidirect
82. #2714C22semidirect
83. #2714C22semidirect
84. #2712C22semidirect
86. #2711C22semidirect
88. #2706C22semidirect
89. #2705C22semidirect
90. #2704C22semidirect
91. #2704C22semidirect
93. #2703C22semidirect
94. #2703C22semidirect
95. #2702C22semidirect
97. #2698C22semidirect
99. #2694C22semidirect
100. #2694C22semidirect
101. #2692C22semidirect
102. #2692C22semidirect
103. #2692C22semidirect
104. #2691C22semidirect
106. #2688C22semidirect
107. #2687C22semidirect
110. #2681C22semidirect
111. #2680C22semidirect
112. #2680C22semidirect
117. #2673C22semidirect
119. #2671C22semidirect
123. #2666C22semidirect
126. #2635C22semidirect
127. #2635C22semidirect
130. #2631C22semidirect
133. #2629C22semidirect
135. #2612C22semidirect
138. #2610C22semidirect
139. #2605C22semidirect
140. #2604C22semidirect
143. #2598C22semidirect
144. #2598C22semidirect
146. #2580C22semidirect
149. #2579C22semidirect
150. #2579C22semidirect
151. #2578C22semidirect
152. #2574C22semidirect
153. #2573C22semidirect
154. #2568C22semidirect
157. #2565C22semidirect
158. #2565C22semidirect
159. #2564C22semidirect
161. #2554C22semidirect
162. #2548C22semidirect
168. #2532C22semidirect
169. #2532C22semidirect
170. #2532C22semidirect
171. #2530C22semidirect
173. #2525C22semidirect
174. #2521C22semidirect
175. #2500C22semidirect
177. #2469C22semidirect
179. #2464C22semidirect
181. #2461C22semidirect
182. #2459C22semidirect
185. #2455C22semidirect
187. #2450C22semidirect
188. #2449C22semidirect
189. #2449C22semidirect
190. #2443C22semidirect
191. #2443C22semidirect
194. #2430C22semidirect
195. #2426C22semidirect
196. #2425C22semidirect
199. #2423C22semidirect
200. #2419C22semidirect
203. #2416C22semidirect
212. #2407C22semidirect
213. #2407C22semidirect
215. #2382C22semidirect
218. #2379C22semidirect
223. #2326C22semidirect
224. #2326C22semidirect
227. #2318C22semidirect
228. #2317C22semidirect
229. #2317C22semidirect
232. #2285C22semidirect
234. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#588892
#583842
#579852
#570562
#550432
#540062
#539482
#534462
#520352
#519662
#497932
#496812
#496382
#479622
#478092
#477002
#470822
#464872
#462322
#462242
#461412
#459842
#459782
#459762
#353332
#351902
#351292