Finite Group Databasebeta

← #8581526

Subgroups — #8581526

Order 512.

4339 conjugacy classes of subgroups.

The subgroup lattice has 1415 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59229C212yesmaximal, complemented
2#58241C214yesmaximal, complemented
3#55512C214yesmaximal, complemented
4#55175C214yesmaximal, complemented
5#54849C212yesmaximal, complemented
6#54258C214yesmaximal, complemented
7#53510C214yesmaximal, complemented
8#53119C212yesmaximal, complemented
9#53081C211yesmaximal, characteristic, complemented
10#52549C212yesmaximal, complemented
11#52228C211yesmaximal, characteristic, complemented
12#49871C214yesmaximal, complemented
13#47750C212yesmaximal, complemented
14#46196C211yesmaximal, characteristic, complemented
15#45435C211yesmaximal, characteristic, complemented
16#44928C212yesmaximal, complemented
17#42681C212yesmaximal, complemented
18#42662C212yesmaximal, complemented
19#42482C211yesmaximal, characteristic, complemented
20#42190C212yesmaximal, complemented
21#39902C212yesmaximal, complemented
22#39489C211yesmaximal, characteristic, complemented
23#38926C212yesmaximal, complemented
24#38278C212yesmaximal, complemented
25#37879C212yesmaximal, complemented
26#37624C212yesmaximal, complemented
27#37312C212yesmaximal, complemented
28#35950C211yesmaximal, characteristic, complemented
29#35551C212yesmaximal, complemented
30C2×#555C2211yescharacteristic
31C2×#555C2212yes—
32C2×#554C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#547C2211yescharacteristic
35#2868C2211yescharacteristic
36#2864C2212yes—
37#2851C2212yes—
38#2841C2214yes—
39#2841C2214yes—
40#2839C2214yes—
41#2836C2214yes—
42#2832C2212yes—
43#2831C2214yes—
44#2830C2212yes—
45#2829C2214yes—
46#2827C2214yes—
47#2823C2212yes—
48#2821C2214yes—
49#2817C2212yes—
50#2816C2214yes—
51#2801C2214yes—
52#2799C2212yes—
53#2795C2214yes—
54#2794C2212yes—
55#2793C2214yes—
56#2793C2214yes—
57#2792C2214yes—
58#2792C2212yes—
59#2792C2212yes—
60#2791C2214yes—
61#2790C2214yes—
62#2789C2212yes—
63#2788C2214yes—
64#2785C2211yescharacteristic
65#2784C2211yescharacteristic
66#2784C2214yes—
67#2781C2212yes—
68#2780C2214yes—
69#2779C2214yes—
70#2777C2214yes—
71#2775C2212yes—
72#2770C2214yes—
73#2770C2214yes—
74#2769C2211yescharacteristic
75#2768C2214yes—
76#2767C2214yes—
77#2765C2214yes—
78#2761C2214yes—
79#2759C2214yes—
80#2758C2214yes—
81#2756C2212yes—
82#2750C2214yes—
83#2744C2212yes—
84#2744C2214yes—
85#2742C2214yes—
86#2739C2214yes—
87#2737C2212yes—
88#2734C2214yes—
89#2734C2214yes—
90#2731C2212yes—
91#2729C2214yes—
92#2729C2214yes—
93#2723C2214yes—
94#2720C2214yes—
95#2717C2214yes—
96#2716C2214yes—
97#2713C2214yes—
98#2702C2214yes—
99#2701C2214yes—
100#2700C2214yes—
101#2700C2214yes—
102#2699C2211yescharacteristic
103#2695C2214yes—
104#2691C2214yes—
105#2687C2214yes—
106#2686C2212yes—
107#2686C2214yes—
108#2686C2214yes—
109#2680C2214yes—
110#2677C2214yes—
111#2674C2214yes—
112#2674C2214yes—
113#2674C2214yes—
114#2674C2214yes—
115#2674C2214yes—
116#2672C2214yes—
117#2666C2214yes—
118#2666C2214yes—
119#2660C2211yescharacteristic
120#2660C2212yes—
121#2660C2211yescharacteristic
122#2659C2212yes—
123#2655C2214yes—
124#2651C2214yes—
125#2650C2214yes—
126#2647C2212yes—
127#2647C2212yes—
128#2647C2212yes—
129#2629C2214yes—
130#2629C2212yes—
131#2628C2214yes—
132#2627C2212yes—
133#2625C2214yes—
134#2620C2212yes—
135#2618C2214yes—
136#2616C2212yes—
137#2601C2214yes—
138#2588C2214yes—
139#2587C2214yes—
140#2586C2214yes—
141#2585C2214yes—
142#2584C2211yescharacteristic
143#2583C2212yes—
144#2577C2214yes—
145#2577C2214yes—
146#2574C2214yes—
147#2571C2212yes—
148#2570C2212yes—
149#2570C2214yes—
150#2567C2211yescharacteristic
151#2567C2211yescharacteristic
152#2566C2212yes—
153#2563C2211yescharacteristic
154#2562C2211yescharacteristic
155#2562C2212yes—
156#2562C2212yes—
157#2558C2214yes—
158#2552C2212yes—
159#2552C2212yes—
160#2551C2212yes—
161#2551C2212yes—
162#2551C2212yes—
163#2551C2212yes—
164#2550C2212yes—
165#2550C2214yes—
166#2549C2214yes—
167#2547C2214yes—
168#2546C2211yescharacteristic
169#2546C2212yes—
170#2537C2212yes—
171#2525C2214yes—
172#2518C2214yes—
173#2515C2214yes—
174#2505C2214yes—
175#2502C2212yes—
176#2501C2212yes—
177#2499C2212yes—
178#2497C2212yes—
179#2496C2212yes—
180#2496C2212yes—
181#2495C2212yes—
182#2495C2212yes—
183#2494C2212yes—
184#2493C2214yes—
185#2491C2214yes—
186#2487C2212yes—
187#2485C2212yes—
188#2485C2212yes—
189#2485C2212yes—
190#2484C2214yes—
191#2484C2214yes—
192#2481C2214yes—
193#2479C2214yes—
194#2477C2214yes—
195#2476C2214yes—
196#2474C2214yes—
197#2474C2214yes—
198#2470C2214yes—
199#2470C2214yes—
200#2468C2214yes—
201#2460C2214yes—
202#2442C2212yes—
203#2441C2212yes—
204#2441C2212yes—
205#2441C2212yes—
206#2441C2212yes—
207#2440C2214yes—
208#2440C2212yes—
209#2440C2212yes—
210#2439C2212yes—
211#2439C2212yes—
212#2439C2212yes—
213#2439C2212yes—
214#2439C2212yes—
215#2438C2214yes—
216#2432C2214yes—
217#2430C2214yes—
218#2425C2214yes—
219#2422C2212yes—
220#2422C2212yes—
221#2422C2212yes—
222#2420C2212yes—
223#2420C2212yes—
224#2420C2212yes—
225#2419C2214yes—
226#2416C2214yes—
227#2406C2212yes—
228#2399C2211yescharacteristic
229#2398C2211yescharacteristic
230#2398C2212yes—
231#2392C2212yes—
232C2×#398C2212yes—
233#2381C2212yes—
234#2370C2212yes—
235#2370C2212yes—
236#2354C2212yes—
237#2352C2212yes—
238#2349C2212yes—
239D4×C4⋊C4C2212yes—
240#2344C2214yes—
241#2334C2214yes—
242#2330C2212yes—
243#2324C2212yes—
244#2319C2211yescharacteristic
245#2319C2212yes—
246#2317C2212yes—
247#2317C2212yes—
248#2314C2212yes—
249C4×#124C2211yescharacteristic
250C4×#121C2212yes—
251C4×#121C2212yes—
252#2298C2212yes—
253#2293C2211yescharacteristic
254#2290C2212yes—
255#2285C2212yes—
256#2285C2212yes—
257#2283C2212yes—
258#2275C2211yescharacteristic
259C22×#41C2312yes—
260#555—48no—
261#555—44no—
262#554—44no—
263#554—44no—
264#547—44no—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2314yes—
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2311yescharacteristic
280C2×#125C2311yescharacteristic
281C2×#125C2314yes—
282C2×#124C2311yescharacteristic
283C2×#124C2314yes—
284C2×#124C2314yes—
285C2×#124C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2314yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2311yescharacteristic
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2312yes—
314C2×C4×D4C2311yescharacteristic
315C2×C4×D4C2314yes—
316C2×#117C2312yes—
317C2×#117C2312yes—
318C2×#117C2312yes—
319C2×#117C2312yes—
320C2×#117C2314yes—
321C2×#117C2312yes—
322C2×#117C2312yes—
323C2×#117C2314yes—
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2314yes—
327C22×C4⋊C4C2312yes—
328C22×C42C2312yes—
329#401C2314yes—
330#400C2311yescharacteristic
331#400C2312yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2311yescharacteristic
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2312yes—
377#398C2314yes—
378#398C2312yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2311yescharacteristic
385#398C2314yes—
386#398C2312yes—
387#398C2312yes—
388#398C2311yescharacteristic
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2312yes—
403#397C2314yes—
404#397C2312yes—
405#397C2314yes—
406#397C2312yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2312yes—
422#396C2312yes—
423#395C2312yes—
424#395C2312yes—
425#395C2314yes—
426#395C2312yes—
427#395C2314yes—
428#395C2312yes—
429#395C2312yes—
430#395C2312yes—
431#395C2314yes—
432#395C2311yescharacteristic
433#395C2314yes—
434#395C2314yes—
435#395C2314yes—
436#395C2312yes—
437#395C2314yes—
438#395C2312yes—
439#395C2314yes—
440#395C2311yescharacteristic
441#395C2314yes—
442#395C2314yes—
443#394C2312yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2312yes—
450#394C2314yes—
451#394C2311yescharacteristic
452#394C2314yes—
453#394C2312yes—
454#394C2314yes—
455#394C2314yes—
456#394C2311yescharacteristic
457#394C2314yes—
458#394C2314yes—
459#394C2312yes—
460#394C2312yes—
461#394C2312yes—
462#394C2314yes—
463#394C2314yes—
464#393C2314yes—
465#393C2314yes—
466#393C2314yes—
467#393C2312yes—
468#393C2314yes—
469#393C2314yes—
470#393C2314yes—
471#393C2312yes—
472#393C2312yes—
473#392C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2314yes—
477#391C2314yes—
478#391C2312yes—
479#391C2314yes—
480#391C2314yes—
481#391C2311yescharacteristic
482#391C2314yes—
483#391C2314yes—
484#391C2314yes—
485#390C2312yes—
486#390C2312yes—
487#390C2312yes—
488#390C2314yes—
489#390C2311yescharacteristic
490#390C2314yes—
491#390C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2314yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2312yes—
512#389C2312yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2314yes—
521#389C2312yes—
522#389C2312yes—
523#389C2314yes—
524#389C2314yes—
525#389C2312yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2312yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2312yes—
544#388C2312yes—
545#388C2312yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2312yes—
550#388C2314yes—
551#388C2312yes—
552#388C2314yes—
553#388C2312yes—
554#388C2312yes—
555#388C2312yes—
556#388C2312yes—
557#388C2314yes—
558#388C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2312yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2312yes—
594#387C2312yes—
595#387C2314yes—
596#387C2312yes—
597#387C2312yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2312yes—
605#386C2312yes—
606#386C2314yes—
607#386C2312yes—
608#386C2312yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2312yes—
628#385C2312yes—
629#384C2312yes—
630#384C2312yes—
631#384C2312yes—
632#384C2312yes—
633#384C2312yes—
634#384C2314yes—
635#384C2312yes—
636#384C2312yes—
637#384C2312yes—
638#384C2312yes—
639#384C2312yes—
640#383C2314yes—
641#383C2312yes—
642#383C2314yes—
643#383C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2314yes—
648#382C2312yes—
649#382C2312yes—
650#382C2312yes—
651#382C2312yes—
652#382C2311yescharacteristic
653#382C2314yes—
654#382C2312yes—
655#381C2314yes—
656#381C2312yes—
657#381C2312yes—
658#381C2312yes—
659#381C2314yes—
660#381C2314yes—
661#381C2314yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2314yes—
672#380C2312yes—
673#380C2314yes—
674#380C2314yes—
675#380C2314yes—
676#380C2314yes—
677#380C2314yes—
678#380C2314yes—
679#380C2312yes—
680#380C2314yes—
681#380C2312yes—
682#380C2312yes—
683#380C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711#376C2311yescharacteristic
712#376C2312yes—
713#376C2311yescharacteristic
714C2×#95C2314yes—
715C2×#95C2312yes—
716C43C2311yescharacteristic
717C2×#41—44no—
718C2×#41—84no—
719C22×Q8C2411yescharacteristic
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C22×Q8C2414yes—
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×D4C2411yescharacteristic
727C22×D4C2414yes—
728C22×D4C2411yescharacteristic
729C22×D4C2412yes—
730C22×D4C2414yes—
731C22×D4C2412yes—
732C22×D4C2411yescharacteristic
733C23×C4C2412yes—
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2414yes—
737C23×C4C2412yes—
738C23×C4C2414yes—
739C23×C4C2412yes—
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2414yes—
743C4⋊Q8—42no—
744C4⋊Q8—42no—
745C4⋊Q8—42no—
746C4⋊Q8—44no—
747C4⋊Q8—42no—
748C4⋊Q8—44no—
749C4⋊Q8—84no—
750C4⋊Q8—84no—
751C4⋊Q8—84no—
752C4⋊Q8—84no—
753#126—48no—
754#126—84no—
755#125—28no—
756#125—42no—
757#125—44no—
758#125—42no—
759#125—84no—
760#124—42no—
761#124—48no—
762#124—48no—
763#124—48no—
764#123—48no—
765#123—84no—
766#123—84no—
767#123—84no—
768C22⋊Q8—44no—
769C22⋊Q8—44no—
770C22⋊Q8—48no—
771C22⋊Q8—44no—
772C22⋊Q8—44no—
773C22⋊Q8—44no—
774C22⋊Q8—84no—
775C22⋊Q8—84no—
776#121—28no—
777#121—28no—
778#121—44no—
779#121—44no—
780#121—48no—
781#121—84no—
782C4×Q8—42no—
783C4×Q8—42no—
784C4×D4—24no—
785C4×D4—24no—
786C4×D4—28no—
787C4×D4—24no—
788C4×D4—28no—
789C4×D4—28no—
790C4×D4—42no—
791C4×D4—44no—
792C4×D4—42no—
793C4×D4—84no—
794#117—28no—
795#117—44no—
796#117—44no—
797#117—48no—
798#117—44no—
799#117—44no—
800#117—44no—
801#117—84no—
802C2×C4⋊C4—48no—
803C2×C4⋊C4—44no—
804C2×C4⋊C4—44no—
805C2×C4⋊C4—44no—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C42—28no—
919C2×C42C2411yescharacteristic
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2411yescharacteristic
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2411yescharacteristic
939C2×C42C2412yes—
940C2×C42C2412yes—
941#95C2411yescharacteristic
942#95C2412yes—
943#95C2414yes—
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2411yescharacteristic
949#95C2412yes—
950#95C2411yescharacteristic
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2411yescharacteristic
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012C24C2512yes—
1013C24C2512yes—
1014C24C2512yes—
1015#41—816no—
1016C2×Q8—22no—
1017C2×Q8—41no—
1018C2×Q8—41no—
1019C2×Q8—42no—
1020C2×Q8—42no—
1021C2×Q8—44no—
1022C2×Q8—41no—
1023C2×Q8—42no—
1024C2×Q8—42no—
1025C2×Q8—44no—
1026C2×Q8—44no—
1027C2×Q8—44no—
1028C2×Q8—42no—
1029C2×Q8—42no—
1030C2×Q8—44no—
1031C2×Q8—44no—
1032C2×Q8—42no—
1033C2×D4—28no—
1034C2×D4—28no—
1035C2×D4—24no—
1036C2×D4—24no—
1037C2×D4—22no—
1038C2×D4—41no—
1039C2×D4—42no—
1040C2×D4—41no—
1041C2×D4—42no—
1042C2×D4—44no—
1043C2×D4—42no—
1044C2×D4—42no—
1045C2×D4—42no—
1046C2×D4—44no—
1047C2×D4—44no—
1048C2×D4—44no—
1049C2×D4—41no—
1050C2×D4—42no—
1051C2×D4H(5,𝔽2)14yes—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—28no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—28no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—42no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2514yes—
1085C22×C4C2511yescharacteristic
1086C22×C4C2512yes—
1087C22×C4C2514yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2511yescharacteristic
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2514yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2514yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2511yescharacteristic
1105C22×C4C2511yescharacteristic
1106C4⋊C4—22no—
1107C4⋊C4—24no—
1108C4⋊C4—22no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—22no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—28no—
1117C4⋊C4—28no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—41no—
1123C4⋊C4—41no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—41no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—41no—
1144C4⋊C4—44no—
1145C4⋊C4—41no—
1146C4⋊C4—42no—
1147C4⋊C4—41no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C22⋊C4—28no—
1175C22⋊C4—28no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—28no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—28no—
1183C22⋊C4—24no—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—42no—
1190C22⋊C4—42no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—42no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—42no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—42no—
1214C22⋊C4—42no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—42no—
1218C42—22no—
1219C42—24no—
1220C42—22no—
1221C42—22no—
1222C42—24no—
1223C42—24no—
1224C42—24no—
1225C42—24no—
1226C42—22no—
1227C42—24no—
1228C42—41no—
1229C42—42no—
1230C42—44no—
1231C42—44no—
1232C42—44no—
1233C42—44no—
1234C42—44no—
1235C42—44no—
1236C42—44no—
1237C42—42no—
1238C42—42no—
1239C422−1+418yes—
1240C23—24no—
1241C23—22no—
1242C23—24no—
1243C23—22no—
1244C23—22no—
1245C23—22no—
1246C23—22no—
1247C23—22no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23—22no—
1258C23C2×H(5,𝔽2)14yes—
1259C23C2611yescharacteristic
1260Q8—82no—
1261Q8—82no—
1262Q8—84no—
1263Q8—162no—
1264Q8—164no—
1265Q8—162no—
1266Q8—162no—
1267D4—28no—
1268D4—44no—
1269D4—82no—
1270D4—84no—
1271D4—88no—
1272D4—88no—
1273D4—84no—
1274C2×C4—21no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—21no—
1279C2×C4—22no—
1280C2×C4—21no—
1281C2×C4—22no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—22no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—21no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—21no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—21no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—21no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—48no—
1342C2×C4—48no—
1343C2×C4—48no—
1344C2×C4—48no—
1345C2×C4—88no—
1346C2×C4—84no—
1347C2×C4—84no—
1348C2×C4—88no—
1349C2×C4—84no—
1350C2×C4—88no—
1351C2×C4C2×H(5,𝔽2)12yes—
1352C2×C4C2×2−1+414yes—
1353C2×C4C2×2−1+414yes—
1354C2×C4C2×2−1+414yes—
1355C2×C4#58512yes—
1356C22—24no—
1357C22—24no—
1358C22—24no—
1359C22—44no—
1360C22—44no—
1361C22—42no—
1362C22—42no—
1363C22—42no—
1364C22—42no—
1365C22—42no—
1366C22—42no—
1367C22—42no—
1368C22—42no—
1369C22—42no—
1370C22—42no—
1371C22—42no—
1372C22—42no—
1373C22—42no—
1374C22—42no—
1375C22C22×H(5,𝔽2)11yescharacteristic
1376C22C22×2−1+412yes—
1377C22C2×#58511yescharacteristic
1378C22H(7,𝔽2)12yes—
1379C222−1+611yescharacteristic
1380C4—24no—
1381C4—22no—
1382C4—24no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4—41no—
1387C4—41no—
1388C4—44no—
1389C4—42no—
1390C4—44no—
1391C4—42no—
1392C4—41no—
1393C4—42no—
1394C4—44no—
1395C4—42no—
1396C4—42no—
1397C4—42no—
1398C4—44no—
1399C4—41no—
1400C4—41no—
1401C4—42no—
1402C4—44no—
1403C4—42no—
1404C4—44no—
1405C4#354414yes—
1406C2—44no—
1407C2—82no—
1408C2—82no—
1409C2C2×#354411yescharacteristic
1410C2#6287712yes—
1411C2#6289811yescharacteristic
1412C2#6292912yes—
1413C2#6304111yescharacteristic
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. #59229C2semidirect
2. #58241C2semidirect
3. #55512C2semidirect
4. #55175C2semidirect
5. #54849C2semidirect
6. #54258C2semidirect
7. #53510C2semidirect
8. #53119C2semidirect
9. #53081C2semidirect
10. #52549C2semidirect
11. #52228C2semidirect
12. #49871C2semidirect
13. #47750C2semidirect
14. #46196C2semidirect
15. #45435C2semidirect
16. #44928C2semidirect
17. #42681C2semidirect
18. #42662C2semidirect
19. #42482C2semidirect
20. #42190C2semidirect
21. #39902C2semidirect
22. #39489C2semidirect
23. #38926C2semidirect
24. #38278C2semidirect
25. #37879C2semidirect
26. #37624C2semidirect
27. #37312C2semidirect
28. #35950C2semidirect
29. #35551C2semidirect

Maximal subgroups

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

subgroupindex
#592292
#582412
#555122
#551752
#548492
#542582
#535102
#531192
#530812
#525492
#522282
#498712
#477502
#461962
#454352
#449282
#426812
#426622
#424822
#421902
#399022
#394892
#389262
#382782
#378792
#376242
#373122
#359502
#355512