Finite Group Databasebeta

← #8346210

Subgroups — #8346210

Order 512.

4648 conjugacy classes of subgroups.

The subgroup lattice has 1477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59586C212yesmaximal, complemented
2#59027C212yesmaximal, complemented
3#59018C212yesmaximal, complemented
4#58390C212yesmaximal, complemented
5#56966C214yesmaximal, complemented
6#55315C214yesmaximal, complemented
7#54678C212yesmaximal, complemented
8#54354C214yesmaximal, complemented
9#53070C212yesmaximal, complemented
10#52673C212yesmaximal, complemented
11#52245C211yesmaximal, characteristic, complemented
12#49831C214yesmaximal, complemented
13#48382C214yesmaximal, complemented
14#46023C212yesmaximal, complemented
15#45433C212yesmaximal, complemented
16#44890C212yesmaximal, complemented
17#42937C211yesmaximal, characteristic, complemented
18#42817C211yesmaximal, characteristic, complemented
19#42675C212yesmaximal, complemented
20#42650C212yesmaximal, complemented
21#40761C214yesmaximal, complemented
22#40074C212yesmaximal, complemented
23#40072C212yesmaximal, complemented
24#39418C212yesmaximal, complemented
25#38967C212yesmaximal, complemented
26#37480C211yesmaximal, characteristic, complemented
27#36031C211yesmaximal, characteristic, complemented
28#35701C211yesmaximal, characteristic, complemented
29#35633C211yesmaximal, characteristic, complemented
30C2×#555C2212yes—
31C2×#554C2211yescharacteristic, complemented
32C2×#554C2211yescharacteristic, complemented
33C2×#552C2212yes—
34C2×#542C2212yescomplemented
35C2×#536C2211yescharacteristic
36C2×#525C2211yescharacteristic
37C22×C22⋊Q8C2211yescharacteristic
38C2×#520C2211yescharacteristic
39#2862C2212yescomplemented
40#2859C2212yescomplemented
41#2842C2212yes—
42#2841C2212yes—
43#2840C2212yes—
44#2839C2214yescomplemented
45#2837C2214yes—
46#2832C2214yes—
47#2832C2212yescomplemented
48#2831C2214yes—
49#2820C2214yes—
50#2814C2214yes—
51#2813C2214yes—
52#2811C2212yescomplemented
53#2808C2214yes—
54#2806C2214yescomplemented
55#2806C2214yescomplemented
56#2799C2212yescomplemented
57#2799C2214yescomplemented
58#2798C2214yescomplemented
59#2788C2214yes—
60#2788C2214yescomplemented
61#2779C2212yes—
62#2775C2214yes—
63#2772C2214yes—
64#2772C2214yescomplemented
65#2771C2212yes—
66#2768C2212yes—
67#2767C2214yescomplemented
68#2764C2211yescharacteristic
69#2761C2212yes—
70#2758C2214yescomplemented
71#2756C2212yes—
72#2754C2214yes—
73#2754C2214yes—
74#2754C2214yescomplemented
75#2754C2214yescomplemented
76#2752C2211yescharacteristic
77#2752C2212yes—
78#2751C2214yes—
79#2742C2214yes—
80#2742C2214yescomplemented
81#2738C2214yescomplemented
82#2735C2211yescharacteristic
83#2726C2214yescomplemented
84#2725C2214yes—
85#2723C2214yes—
86#2717C2214yescomplemented
87#2716C2214yes—
88#2715C2212yes—
89#2715C2214yes—
90#2715C2214yes—
91#2715C2214yescomplemented
92#2712C2214yes—
93#2712C2214yescomplemented
94#2706C2214yes—
95#2704C2214yescomplemented
96#2702C2214yes—
97#2700C2214yescomplemented
98#2698C2214yes—
99#2698C2214yescomplemented
100#2696C2214yes—
101#2694C2214yes—
102#2690C2214yescomplemented
103#2690C2214yescomplemented
104#2687C2214yes—
105#2687C2214yes—
106#2686C2214yes—
107#2685C2212yes—
108#2684C2214yes—
109#2678C2214yes—
110#2674C2214yes—
111#2670C2211yescharacteristic
112#2665C2214yes—
113#2665C2214yes—
114#2665C2214yes—
115#2650C2214yes—
116#2650C2214yescomplemented
117#2649C2214yes—
118#2639C2214yes—
119#2633C2212yes—
120#2630C2214yes—
121#2628C2212yes—
122#2628C2211yescharacteristic
123#2628C2211yescharacteristic
124#2628C2212yescomplemented
125#2627C2212yescomplemented
126#2625C2214yescomplemented
127#2625C2214yescomplemented
128#2621C2212yescomplemented
129#2611C2212yescomplemented
130#2607C2212yes—
131#2607C2212yes—
132#2607C2212yes—
133#2598C2212yescomplemented
134#2586C2212yescomplemented
135#2581C2212yescomplemented
136#2581C2211yescharacteristic, complemented
137#2571C2212yescomplemented
138#2568C2212yescomplemented
139#2568C2211yescharacteristic, complemented
140#2564C2212yes—
141#2563C2214yes—
142#2560C2214yes—
143#2557C2214yes—
144#2557C2214yes—
145#2556C2214yes—
146#2553C2214yes—
147#2551C2212yescomplemented
148#2550C2214yescomplemented
149#2549C2214yescomplemented
150#2547C2214yescomplemented
151#2542C2211yescharacteristic, complemented
152#2536C2212yes—
153#2535C2212yes—
154#2535C2211yescharacteristic, complemented
155#2534C2212yes—
156#2534C2212yes—
157#2529C2214yes—
158#2520C2214yescomplemented
159#2517C2214yescomplemented
160#2511C2212yescomplemented
161#2509C2214yescomplemented
162#2499C2212yes—
163#2499C2212yes—
164#2499C2212yescomplemented
165#2498C2214yescomplemented
166#2492C2212yes—
167#2492C2212yescomplemented
168#2489C2212yes—
169#2489C2214yescomplemented
170#2488C2214yes—
171#2488C2214yescomplemented
172#2487C2212yes—
173#2486C2212yes—
174#2486C2212yes—
175#2485C2214yescomplemented
176#2481C2214yes—
177#2480C2214yes—
178#2478C2214yescomplemented
179#2477C2214yes—
180#2477C2214yescomplemented
181#2473C2214yes—
182#2470C2214yes—
183#2463C2214yes—
184#2461C2214yes—
185#2459C2214yes—
186#2454C2214yes—
187#2453C2212yescomplemented
188#2451C2212yescomplemented
189#2451C2212yescomplemented
190#2450C2214yes—
191#2449C2214yescomplemented
192#2447C2214yes—
193#2447C2212yescomplemented
194#2446C2212yescomplemented
195#2444C2214yes—
196#2442C2212yes—
197#2442C2212yescomplemented
198#2439C2212yes—
199#2439C2212yes—
200#2439C2212yes—
201#2439C2212yes—
202#2439C2212yes—
203#2439C2212yescomplemented
204#2438C2214yescomplemented
205#2438C2214yescomplemented
206#2429C2212yes—
207#2429C2212yes—
208#2429C2212yescomplemented
209#2427C2212yes—
210#2427C2212yes—
211#2427C2212yescomplemented
212#2425C2214yes—
213#2423C2212yes—
214#2423C2212yescomplemented
215#2422C2212yes—
216#2418C2214yes—
217#2417C2214yes—
218#2417C2212yes—
219#2415C2214yes—
220#2415C2212yes—
221#2415C2212yes—
222#2415C2212yes—
223#2415C2212yescomplemented
224#2409C2212yes—
225#2407C2212yes—
226#2397C2212yes—
227#2396C2211yescharacteristic
228#2395C2212yes—
229C2×#400C2212yescomplemented
230#2392C2211yescharacteristic
231#2392C2212yes—
232#2382C2214yescomplemented
233#2363C2212yes—
234#2362C2212yes—
235#2361C2212yescomplemented
236#2359C2214yes—
237#2356C2211yescharacteristic, complemented
238#2354C2212yes—
239#2352C2214yes—
240#2352C2214yescomplemented
241#2349C2211yescharacteristic, complemented
242#2349C2212yescomplemented
243D4×C4⋊C4C2212yes—
244Q8×C22⋊C4C2212yes—
245#2339C2212yes—
246#2331C2214yescomplemented
247#2329C2214yescomplemented
248#2316C2211yescharacteristic
249#2316C2212yescomplemented
250#2310C2211yescharacteristic
251C4×#125C2212yescomplemented
252C4×#126C2212yes—
253C4×#124C2212yes—
254C4×#124C2212yescomplemented
255C4×#120C2212yes—
256#2293C2212yes—
257#2280C2211yescharacteristic
258#2280C2212yes—
259C22×#41C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261C24×C4C2311yescharacteristic
262#555—48no—
263#554—44no—
264#554—44no—
265#552—48no—
266#542—48no—
267#536—44no—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×#126C2312yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×#124C2314yes—
284C2×#124C2314yes—
285C2×#124C2314yes—
286#525—44no—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2312yes—
290C2×#123C2312yes—
291C2×#123C2312yes—
292C2×#123C2314yes—
293C2×C22⋊Q8—44no—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2314yes—
307C2×#121C2312yes—
308C2×#121C2312yes—
309C2×#121C2314yes—
310C2×#120C2312yes—
311C2×#120C2312yes—
312#520—44no—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2314yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×#117C2311yescharacteristic
333C2×#117C2311yescharacteristic
334C2×#117C2311yescharacteristic
335C2×#117C2312yes—
336C2×#117C2312yes—
337C2×#117C2312yes—
338C2×#117C2314yes—
339C2×#117C2314yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C22×C4⋊C4C2311yescharacteristic
343C22×C4⋊C4C2312yes—
344C22×C4⋊C4C2312yes—
345C22×C4⋊C4C2312yes—
346C22×C4⋊C4C2312yes—
347C22×C22⋊C4C2312yes—
348#400C2312yes—
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2314yes—
359#400C2312yes—
360#400C2314yes—
361#400C2314yes—
362#400C2312yes—
363#400C2314yes—
364#400C2314yes—
365#400C2312yes—
366#400C2314yes—
367#400C2311yescharacteristic
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#399C2312yes—
372#399C2314yes—
373#399C2314yes—
374#399C2314yes—
375#399C2312yes—
376#399C2314yes—
377#399C2312yes—
378#399C2311yescharacteristic
379#399C2312yes—
380#399C2312yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2311yescharacteristic
391#398C2312yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2312yes—
397#398C2312yes—
398#398C2314yes—
399#398C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2312yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2312yes—
411#397C2312yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2311yescharacteristic
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2312yes—
422#397C2312yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2314yes—
434#396C2312yes—
435#396C2312yes—
436#396C2312yes—
437#396C2314yes—
438#396C2312yes—
439#396C2314yes—
440#395C2312yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#395C2312yes—
445#395C2314yes—
446#395C2311yescharacteristic
447#395C2314yes—
448#395C2312yes—
449#395C2314yes—
450#395C2314yes—
451#395C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2312yes—
456#394C2314yes—
457#394C2314yes—
458#394C2311yescharacteristic
459#394C2314yes—
460#394C2312yes—
461#394C2314yes—
462#394C2312yes—
463#394C2312yes—
464#394C2312yes—
465#394C2312yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#393C2314yes—
470#393C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2314yes—
474#393C2311yescharacteristic
475#393C2314yes—
476#393C2314yes—
477#393C2314yes—
478#393C2312yes—
479#393C2312yes—
480#393C2314yes—
481#393C2314yes—
482#393C2314yes—
483#392C2312yes—
484#392C2312yes—
485#392C2311yescharacteristic
486#392C2314yes—
487#392C2314yes—
488#391C2314yes—
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#391C2314yes—
494#391C2312yes—
495#391C2314yes—
496#391C2312yes—
497#391C2314yes—
498#391C2314yes—
499#391C2312yes—
500#391C2314yes—
501#391C2314yes—
502#391C2314yes—
503#391C2314yes—
504#391C2314yes—
505#391C2312yes—
506#391C2314yes—
507#391C2314yes—
508#391C2312yes—
509#391C2312yes—
510#391C2314yes—
511#391C2314yes—
512#391C2314yes—
513#391C2314yes—
514#391C2312yes—
515#391C2312yes—
516#391C2314yes—
517#390C2314yes—
518#390C2312yes—
519#390C2314yes—
520#390C2312yes—
521#390C2312yes—
522#390C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2314yes—
528#389C2314yes—
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
532#389C2314yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2312yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2312yes—
550#389C2312yes—
551#388C2312yes—
552#388C2312yes—
553#388C2312yes—
554#388C2312yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2312yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2312yes—
577#388C2314yes—
578#388C2314yes—
579#388C2312yes—
580#388C2312yes—
581#388C2312yes—
582#388C2312yes—
583#388C2312yes—
584#387C2312yes—
585#387C2312yes—
586#387C2312yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2312yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2312yes—
630#386C2312yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2312yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2312yes—
645#385C2312yes—
646#384C2312yes—
647#384C2312yes—
648#383C2312yes—
649#383C2312yes—
650#382C2312yes—
651#382C2314yes—
652#382C2314yes—
653#382C2314yes—
654#382C2311yescharacteristic
655#382C2312yes—
656#382C2312yes—
657#382C2311yescharacteristic
658#382C2314yes—
659#382C2314yes—
660#382C2312yes—
661#381C2312yes—
662#381C2312yes—
663#381C2314yes—
664#381C2311yescharacteristic
665#381C2311yescharacteristic
666#381C2314yes—
667#381C2314yes—
668#380C2312yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2312yes—
674#380C2314yes—
675#380C2314yes—
676#380C2314yes—
677#380C2312yes—
678#380C2312yes—
679#380C2312yes—
680#380C2312yes—
681#380C2314yes—
682#380C2314yes—
683#380C2312yes—
684#380C2312yes—
685#380C2312yes—
686#380C2312yes—
687#380C2314yes—
688#380C2312yes—
689#379C2311yescharacteristic
690#379C2314yes—
691#379C2311yescharacteristic
692#379C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2311yescharacteristic
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716#376C2312yes—
717C2×#95C2312yes—
718C2×#95C2314yes—
719C2×#95C2314yes—
720C43C2312yes—
721C25C2411yescharacteristic
722C2×#41—24no—
723C2×#41—24no—
724C2×#41—42no—
725C22×Q8—24no—
726C22×Q8—42no—
727C22×Q8—42no—
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2412yes—
731C22×Q8C2411yescharacteristic
732C22×Q8C2412yes—
733C22×Q8C2412yes—
734C22×Q8C2414yes—
735C22×Q8C2414yes—
736C22×D4C2412yes—
737C22×D4C2412yes—
738C22×D4C2411yescharacteristic
739C22×D4C2414yes—
740C22×D4C2414yes—
741C22×D4C2411yescharacteristic
742C22×D4C2412yes—
743C22×D4C2412yes—
744C23×C4—24no—
745C23×C4—42no—
746C23×C4—42no—
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2412yes—
750C23×C4C2411yescharacteristic
751C23×C4C2412yes—
752C23×C4C2412yes—
753C23×C4C2412yes—
754C23×C4C2411yescharacteristic
755C23×C4C2414yes—
756C23×C4C2414yes—
757C23×C4C2412yes—
758C23×C4C2412yes—
759C23×C4C2414yes—
760C4⋊Q8—48no—
761C4⋊Q8—44no—
762C4⋊Q8—42no—
763C4⋊Q8—42no—
764C4⋊Q8—44no—
765C4⋊Q8—44no—
766#126—48no—
767#126—44no—
768#126—48no—
769#125—28no—
770#125—48no—
771#125—44no—
772#125—48no—
773#124—28no—
774#124—44no—
775#124—48no—
776#124—48no—
777#124—48no—
778#123—48no—
779#123—44no—
780#123—44no—
781#123—44no—
782#123—48no—
783#123—48no—
784C22⋊Q8—28no—
785C22⋊Q8—48no—
786C22⋊Q8—48no—
787C22⋊Q8—48no—
788C22⋊Q8—48no—
789C22⋊Q8—48no—
790C22⋊Q8—48no—
791C22⋊Q8—44no—
792C22⋊Q8—44no—
793C22⋊Q8—44no—
794C22⋊Q8—44no—
795C22⋊Q8—44no—
796C22⋊Q8—44no—
797#121—28no—
798#121—28no—
799#121—48no—
800#120—44no—
801#120—44no—
802C4×Q8—24no—
803C4×Q8—42no—
804C4×Q8—42no—
805C4×Q8—44no—
806C4×Q8—44no—
807C4×D4—28no—
808C4×D4—28no—
809C4×D4—24no—
810C4×D4—48no—
811C4×D4—48no—
812C4×D4—42no—
813C4×D4—44no—
814C4×D4—44no—
815C4×D4—44no—
816C4×D4—44no—
817C4×D4—42no—
818C4×D4—44no—
819C4×D4—44no—
820C4×D4—48no—
821#117—42no—
822#117—42no—
823#117—44no—
824#117—44no—
825#117—48no—
826#117—42no—
827#117—44no—
828#117—48no—
829#117—44no—
830#117—44no—
831C2×C4⋊C4—24no—
832C2×C4⋊C4—28no—
833C2×C4⋊C4—44no—
834C2×C4⋊C4—44no—
835C2×C4⋊C4—44no—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2411yescharacteristic
894C2×C22⋊C4—44no—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2411yescharacteristic
911C2×C22⋊C4C2411yescharacteristic
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2411yescharacteristic
918C2×C22⋊C4C2411yescharacteristic
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2414yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2411yescharacteristic
952C2×C42C2411yescharacteristic
953C2×C42C2412yes—
954C2×C42C2414yes—
955C2×C42C2412yes—
956C2×C42C2412yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2414yes—
963C2×C42C2414yes—
964C2×C42C2412yes—
965C2×C42C2412yes—
966C2×C42C2412yes—
967C2×C42C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2411yescharacteristic
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2411yescharacteristic
980#95C2412yes—
981#95C2414yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2411yescharacteristic
1008#95C2414yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2411yescharacteristic
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2414yes—
1036C24—22no—
1037C24—41no—
1038C24—42no—
1039C24—41no—
1040C24—42no—
1041C24C2512yes—
1042C24C2512yes—
1043C24C2512yes—
1044C24C2511yescharacteristic
1045#41—416no—
1046C2×Q8—22no—
1047C2×Q8—24no—
1048C2×Q8—24no—
1049C2×Q8—22no—
1050C2×Q8—24no—
1051C2×Q8—22no—
1052C2×Q8—24no—
1053C2×Q8—41no—
1054C2×Q8—42no—
1055C2×Q8—42no—
1056C2×Q8—42no—
1057C2×Q8—42no—
1058C2×Q8—42no—
1059C2×Q8—44no—
1060C2×Q8—44no—
1061C2×Q8—44no—
1062C2×Q8—44no—
1063C2×Q8—44no—
1064C2×Q8—44no—
1065C2×Q8—44no—
1066C2×Q8—44no—
1067C2×Q8—88no—
1068C2×D4—24no—
1069C2×D4—24no—
1070C2×D4—24no—
1071C2×D4—28no—
1072C2×D4—28no—
1073C2×D4—22no—
1074C2×D4—22no—
1075C2×D4—24no—
1076C2×D4—41no—
1077C2×D4—42no—
1078C2×D4—42no—
1079C2×D4—42no—
1080C2×D4—42no—
1081C2×D4—42no—
1082C2×D4—44no—
1083C2×D4—42no—
1084C2×D4—42no—
1085C2×D4—44no—
1086C2×D4—42no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4—42no—
1090C2×D4H(5,𝔽2)14yes—
1091C22×C4—22no—
1092C22×C4—22no—
1093C22×C4—24no—
1094C22×C4—28no—
1095C22×C4—22no—
1096C22×C4—24no—
1097C22×C4—24no—
1098C22×C4—24no—
1099C22×C4—24no—
1100C22×C4—24no—
1101C22×C4—24no—
1102C22×C4—24no—
1103C22×C4—24no—
1104C22×C4—24no—
1105C22×C4—28no—
1106C22×C4—24no—
1107C22×C4—24no—
1108C22×C4—42no—
1109C22×C4—42no—
1110C22×C4—41no—
1111C22×C4—42no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—42no—
1117C22×C4—41no—
1118C22×C4—42no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—42no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—88no—
1127C22×C42−1+414yes—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2511yescharacteristic
1131C22×C4C2514yes—
1132C22×C4C2514yes—
1133C22×C4C2511yescharacteristic
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2511yescharacteristic
1139C22×C4C2514yes—
1140C22×C4C2514yes—
1141C22×C4C2514yes—
1142C22×C4C2512yes—
1143C22×C4C2511yescharacteristic
1144C22×C4C2512yes—
1145C22×C4C2514yes—
1146C22×C4C2512yes—
1147C22×C4C2512yes—
1148C22×C4C2512yes—
1149C22×C4C2512yes—
1150C22×C4C2511yescharacteristic
1151C22×C4C2512yes—
1152C22×C4C2511yescharacteristic
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—22no—
1156C4⋊C4—28no—
1157C4⋊C4—28no—
1158C4⋊C4—28no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—28no—
1165C4⋊C4—24no—
1166C4⋊C4—28no—
1167C4⋊C4—24no—
1168C4⋊C4—28no—
1169C4⋊C4—24no—
1170C4⋊C4—41no—
1171C4⋊C4—41no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—41no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—41no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C4—42no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—42no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4H(5,𝔽2)14yes—
1211C22⋊C4—28no—
1212C22⋊C4—28no—
1213C22⋊C4—28no—
1214C22⋊C4—28no—
1215C22⋊C4—28no—
1216C22⋊C4—24no—
1217C22⋊C4—28no—
1218C22⋊C4—24no—
1219C22⋊C4—24no—
1220C22⋊C4—24no—
1221C22⋊C4—28no—
1222C22⋊C4—24no—
1223C22⋊C4—24no—
1224C22⋊C4—44no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—42no—
1235C22⋊C4—41no—
1236C22⋊C4—42no—
1237C22⋊C4—41no—
1238C22⋊C4—42no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—41no—
1243C22⋊C4—42no—
1244C22⋊C4—41no—
1245C22⋊C4—44no—
1246C22⋊C4—42no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—42no—
1252C22⋊C4—44no—
1253C22⋊C4—42no—
1254C22⋊C4—42no—
1255C22⋊C4—42no—
1256C22⋊C4—42no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—42no—
1261C22⋊C4—42no—
1262C22⋊C4—42no—
1263C22⋊C4—42no—
1264C42—24no—
1265C42—24no—
1266C42—22no—
1267C42—24no—
1268C42—22no—
1269C42—24no—
1270C42—24no—
1271C42—28no—
1272C42—24no—
1273C42—42no—
1274C42—44no—
1275C42—42no—
1276C42—44no—
1277C42—44no—
1278C42—44no—
1279C42—42no—
1280C42—42no—
1281C42—44no—
1282C42—44no—
1283C42—42no—
1284C23—22no—
1285C23—21no—
1286C23—21no—
1287C23—22no—
1288C23—24no—
1289C23—22no—
1290C23—22no—
1291C23—24no—
1292C23—22no—
1293C23—22no—
1294C23—22no—
1295C23—22no—
1296C23—22no—
1297C23—22no—
1298C23—22no—
1299C23—22no—
1300C23—22no—
1301C23—22no—
1302C23—22no—
1303C23—22no—
1304C23—22no—
1305C23—22no—
1306C23—44no—
1307C23—82no—
1308C23—84no—
1309C23—82no—
1310C23—84no—
1311C23C2×H(5,𝔽2)14yes—
1312C23C2×2−1+412yes—
1313C23C2611yescharacteristic
1314Q8—48no—
1315Q8—44no—
1316Q8—84no—
1317Q8—82no—
1318Q8—162no—
1319Q8—162no—
1320Q8—164no—
1321Q8—164no—
1322D4—28no—
1323D4—48no—
1324D4—48no—
1325D4—44no—
1326D4—88no—
1327D4—88no—
1328D4—84no—
1329D4—84no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—28no—
1336C2×C4—21no—
1337C2×C4—22no—
1338C2×C4—21no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—21no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—21no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—24no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—24no—
1376C2×C4—24no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—48no—
1395C2×C4—48no—
1396C2×C4—48no—
1397C2×C4—84no—
1398C2×C4—84no—
1399C2×C4—88no—
1400C2×C4—84no—
1401C2×C4—88no—
1402C2×C4—82no—
1403C2×C4—84no—
1404C2×C4—162no—
1405C2×C4—164no—
1406C2×C4C2×H(5,𝔽2)14yes—
1407C2×C4C2×H(5,𝔽2)12yes—
1408C2×C4C2×H(5,𝔽2)12yes—
1409C2×C4C2×2−1+412yes—
1410C2×C4C2×2−1+412yes—
1411C2×C4#58514yes—
1412C22—22no—
1413C22—24no—
1414C22—28no—
1415C22—24no—
1416C22—41no—
1417C22—42no—
1418C22—42no—
1419C22—41no—
1420C22—42no—
1421C22—44no—
1422C22—42no—
1423C22—42no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22—42no—
1429C22—42no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—42no—
1436C22—88no—
1437C22C22×H(5,𝔽2)11yescharacteristic
1438C22C22×H(5,𝔽2)11yescharacteristic
1439C22C22×2−1+411yescharacteristic
1440C22C2×#58512yes—
1441C222−1+612yes—
1442C4—22no—
1443C4—24no—
1444C4—24no—
1445C4—42no—
1446C4—42no—
1447C4—42no—
1448C4—44no—
1449C4—41no—
1450C4—42no—
1451C4—44no—
1452C4—41no—
1453C4—42no—
1454C4—42no—
1455C4—44no—
1456C4—41no—
1457C4—41no—
1458C4—42no—
1459C4—42no—
1460C4—44no—
1461C4—44no—
1462C4—44no—
1463C4—42no—
1464C4—42no—
1465C4—42no—
1466C4#353614yes—
1467C2—44no—
1468C2—42no—
1469C2—82no—
1470C2—82no—
1471C2C2×#353611yescharacteristic
1472C2#6292112yes—
1473C2#6292812yes—
1474C2#6302111yescharacteristic
1475C2#6304811yescharacteristic
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. #59586C2semidirect
2. #59027C2semidirect
3. #59018C2semidirect
4. #58390C2semidirect
5. #56966C2semidirect
6. #55315C2semidirect
7. #54678C2semidirect
8. #54354C2semidirect
9. #53070C2semidirect
10. #52673C2semidirect
11. #52245C2semidirect
12. #49831C2semidirect
13. #48382C2semidirect
14. #46023C2semidirect
15. #45433C2semidirect
16. #44890C2semidirect
17. #42937C2semidirect
18. #42817C2semidirect
19. #42675C2semidirect
20. #42650C2semidirect
21. #40761C2semidirect
22. #40074C2semidirect
23. #40072C2semidirect
24. #39418C2semidirect
25. #38967C2semidirect
26. #37480C2semidirect
27. #36031C2semidirect
28. #35701C2semidirect
29. #35633C2semidirect
31. C2×#554C22semidirect
32. C2×#554C22semidirect
34. C2×#542C22semidirect
39. #2862C22semidirect
40. #2859C22semidirect
44. #2839C22semidirect
47. #2832C22semidirect
52. #2811C22semidirect
54. #2806C22semidirect
55. #2806C22semidirect
56. #2799C22semidirect
57. #2799C22semidirect
58. #2798C22semidirect
60. #2788C22semidirect
64. #2772C22semidirect
67. #2767C22semidirect
70. #2758C22semidirect
74. #2754C22semidirect
75. #2754C22semidirect
80. #2742C22semidirect
81. #2738C22semidirect
83. #2726C22semidirect
86. #2717C22semidirect
91. #2715C22semidirect
93. #2712C22semidirect
95. #2704C22semidirect
97. #2700C22semidirect
99. #2698C22semidirect
102. #2690C22semidirect
103. #2690C22semidirect
116. #2650C22semidirect
124. #2628C22semidirect
125. #2627C22semidirect
126. #2625C22semidirect
127. #2625C22semidirect
128. #2621C22semidirect
129. #2611C22semidirect
133. #2598C22semidirect
134. #2586C22semidirect
135. #2581C22semidirect
136. #2581C22semidirect
137. #2571C22semidirect
138. #2568C22semidirect
139. #2568C22semidirect
147. #2551C22semidirect
148. #2550C22semidirect
149. #2549C22semidirect
150. #2547C22semidirect
151. #2542C22semidirect
154. #2535C22semidirect
158. #2520C22semidirect
159. #2517C22semidirect
160. #2511C22semidirect
161. #2509C22semidirect
164. #2499C22semidirect
165. #2498C22semidirect
167. #2492C22semidirect
169. #2489C22semidirect
171. #2488C22semidirect
175. #2485C22semidirect
178. #2478C22semidirect
180. #2477C22semidirect
187. #2453C22semidirect
188. #2451C22semidirect
189. #2451C22semidirect
191. #2449C22semidirect
193. #2447C22semidirect
194. #2446C22semidirect
197. #2442C22semidirect
203. #2439C22semidirect
204. #2438C22semidirect
205. #2438C22semidirect
208. #2429C22semidirect
211. #2427C22semidirect
214. #2423C22semidirect
223. #2415C22semidirect
229. C2×#400C22semidirect
232. #2382C22semidirect
235. #2361C22semidirect
237. #2356C22semidirect
240. #2352C22semidirect
241. #2349C22semidirect
242. #2349C22semidirect
246. #2331C22semidirect
247. #2329C22semidirect
249. #2316C22semidirect
251. C4×#125C22semidirect
254. C4×#124C22semidirect

Maximal subgroups

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

subgroupindex
#595862
#590272
#590182
#583902
#569662
#553152
#546782
#543542
#530702
#526732
#522452
#498312
#483822
#460232
#454332
#448902
#429372
#428172
#426752
#426502
#407612
#400742
#400722
#394182
#389672
#374802
#360312
#357012
#356332