Finite Group Databasebeta

← #7660806

Subgroups — #7660806

Order 512.

4760 conjugacy classes of subgroups.

The subgroup lattice has 1508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52278C212yesmaximal, complemented
2#52169C211yesmaximal, characteristic, complemented
3#42668C212yesmaximal, complemented
4#42661C212yesmaximal, complemented
5#42505C212yesmaximal, complemented
6#42413C214yesmaximal, complemented
7#41911C214yesmaximal, complemented
8#41180C214yesmaximal, complemented
9#40368C214yesmaximal, complemented
10#39906C212yesmaximal, complemented
11#39760C211yesmaximal, characteristic, complemented
12#39708C212yesmaximal, complemented
13#39632C211yesmaximal, characteristic, complemented
14#39159C212yesmaximal, complemented
15#38792C214yesmaximal, complemented
16#38782C212yesmaximal, complemented
17#37379C212yesmaximal, complemented
18#37308C211yesmaximal, characteristic, complemented
19#37168C212yesmaximal, complemented
20#36950C214yesmaximal, complemented
21#36561C212yesmaximal, complemented
22#36492C211yesmaximal, characteristic, complemented
23#36404C211yesmaximal, characteristic, complemented
24#36255C212yesmaximal, complemented
25#35789C212yesmaximal, complemented
26#35738C212yesmaximal, complemented
27#35697C212yesmaximal, complemented
28#34268C211yesmaximal, characteristic, complemented
29#34241C212yesmaximal, complemented
30C2×#554C2212yes—
31C2×#554C2211yescharacteristic
32C2×#547C2211yescharacteristic
33C2×#536C2211yescharacteristic
34C2×#529C2212yes—
35C2×#519C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37#2857C2212yes—
38#2857C2211yescharacteristic
39#2857C2211yescharacteristic
40#2857C2214yes—
41#2855C2212yes—
42#2852C2214yes—
43#2851C2212yes—
44#2850C2212yes—
45#2836C2214yes—
46#2832C2214yes—
47#2826C2214yes—
48#2808C2212yes—
49#2806C2212yes—
50#2805C2212yes—
51#2805C2212yes—
52#2805C2212yes—
53#2804C2212yes—
54#2797C2214yes—
55#2793C2214yes—
56#2791C2214yes—
57#2788C2214yes—
58#2786C2214yes—
59#2784C2214yes—
60#2779C2214yes—
61#2778C2214yes—
62#2770C2214yes—
63#2759C2214yes—
64#2758C2214yes—
65#2758C2214yes—
66#2756C2214yes—
67#2745C2214yes—
68#2745C2214yes—
69#2742C2214yes—
70#2740C2214yes—
71#2739C2214yes—
72#2738C2214yes—
73#2734C2212yes—
74#2734C2212yes—
75#2731C2214yes—
76#2727C2211yescharacteristic
77#2726C2211yescharacteristic
78#2723C2214yes—
79#2720C2214yes—
80#2718C2214yes—
81#2716C2214yes—
82#2715C2214yes—
83#2715C2212yes—
84#2710C2214yes—
85#2707C2212yes—
86#2706C2214yes—
87#2703C2214yes—
88#2702C2212yes—
89#2696C2214yes—
90#2695C2212yes—
91#2692C2214yes—
92#2688C2214yes—
93#2683C2211yescharacteristic
94#2682C2211yescharacteristic
95#2677C2214yes—
96#2676C2212yes—
97#2671C2212yes—
98#2665C2214yes—
99#2663C2214yes—
100#2653C2214yes—
101#2652C2214yes—
102#2651C2214yes—
103#2650C2214yes—
104#2649C2214yes—
105#2648C2214yes—
106#2646C2212yes—
107#2645C2214yes—
108#2639C2212yes—
109#2634C2214yes—
110#2631C2214yes—
111#2628C2212yes—
112#2621C2212yes—
113#2620C2212yes—
114#2611C2214yes—
115#2602C2214yes—
116#2598C2214yes—
117#2594C2214yes—
118#2592C2212yes—
119#2588C2214yes—
120#2585C2214yes—
121#2577C2214yes—
122#2570C2212yes—
123#2570C2212yes—
124#2568C2212yes—
125#2568C2211yescharacteristic
126#2568C2212yes—
127#2564C2214yes—
128#2564C2214yes—
129#2563C2211yescharacteristic
130#2562C2212yes—
131#2558C2214yes—
132#2556C2214yes—
133#2556C2214yes—
134#2556C2214yes—
135#2551C2212yes—
136#2551C2212yes—
137#2542C2212yes—
138#2540C2212yes—
139#2538C2211yescharacteristic
140#2537C2211yescharacteristic
141#2536C2212yes—
142#2535C2212yes—
143#2532C2214yes—
144#2531C2214yes—
145#2531C2214yes—
146#2528C2214yes—
147#2524C2214yes—
148#2523C2214yes—
149#2522C2214yes—
150#2521C2214yes—
151#2517C2214yes—
152#2514C2212yes—
153#2514C2212yes—
154#2512C2212yes—
155#2511C2212yes—
156#2510C2214yes—
157#2510C2214yes—
158#2506C2214yes—
159#2504C2212yes—
160#2502C2212yes—
161#2499C2212yes—
162#2499C2212yes—
163#2495C2214yes—
164#2492C2212yes—
165#2492C2214yes—
166#2492C2212yes—
167#2492C2212yes—
168#2491C2212yes—
169#2478C2214yes—
170#2477C2214yes—
171#2477C2214yes—
172#2477C2214yes—
173#2470C2214yes—
174#2467C2214yes—
175#2465C2214yes—
176#2465C2214yes—
177#2463C2214yes—
178#2461C2214yes—
179#2457C2214yes—
180#2452C2214yes—
181#2452C2214yes—
182#2450C2214yes—
183#2450C2214yes—
184#2432C2214yes—
185#2421C2212yes—
186#2421C2212yes—
187#2421C2212yes—
188#2420C2212yes—
189#2417C2212yes—
190#2417C2212yes—
191#2415C2212yes—
192#2415C2212yes—
193#2414C2212yes—
194#2409C2212yes—
195#2409C2212yes—
196#2407C2212yes—
197#2407C2212yes—
198#2407C2212yes—
199#2401C2214yes—
200#2398C2214yes—
201#2396C2212yes—
202#2392C2212yes—
203#2392C2212yes—
204#2388C2214yes—
205#2373C2214yes—
206#2373C2214yes—
207#2368C2214yes—
208#2367C2212yes—
209#2367C2212yes—
210#2365C2212yes—
211#2365C2212yes—
212#2364C2214yes—
213#2361C2212yes—
214#2360C2212yes—
215#2360C2212yes—
216#2360C2212yes—
217#2359C2214yes—
218#2359C2214yes—
219#2356C2212yes—
220#2355C2211yescharacteristic
221#2355C2212yes—
222#2355C2212yes—
223#2354C2211yescharacteristic
224#2352C2212yes—
225#2352C2212yes—
226#2352C2212yes—
227#2352C2212yes—
228D4×C4⋊C4C2212yes—
229D4×C4⋊C4C2212yes—
230#2337C2214yes—
231#2336C2214yes—
232#2333C2214yes—
233#2331C2214yes—
234#2329C2212yes—
235#2325C2212yes—
236#2323C2212yes—
237#2323C2212yes—
238#2314C2212yes—
239#2314C2212yes—
240#2311C2211yescharacteristic
241C4×C22⋊Q8C2212yes—
242C4×C22⋊Q8C2212yes—
243C4×C22⋊Q8C2212yes—
244C4×#123C2214yes—
245C4×#123C2214yes—
246C4×#121C2212yes—
247C4×#121C2211yescharacteristic
248C4×#121C2214yes—
249C4×#121C2211yescharacteristic
250C4×#121C2212yes—
251#2297C2212yes—
252#2296C2211yescharacteristic
253C2×#391C2211yescharacteristic
254#2290C2214yes—
255#2283C2212yes—
256#2274C2212yes—
257#2274C2211yescharacteristic
258C2×C4×C4⋊C4C2212yes—
259C22×#41C2311yescharacteristic
260C22×#41C2312yes—
261C23×Q8C2311yescharacteristic
262#554—48no—
263#554—44no—
264#547—44no—
265#536—28no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2314yes—
272#529—216no—
273C2×#126C2312yes—
274C2×#126C2312yes—
275C2×#126C2314yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#124C2314yes—
282C2×#123C2314yes—
283C2×#123C2312yes—
284C2×#123C2312yes—
285C2×#123C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×#121C2311yescharacteristic
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2312yes—
308C2×#121C2311yescharacteristic
309#519—44no—
310C4×#41—44no—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2312yes—
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2311yescharacteristic
331C2×C4×D4C2314yes—
332C2×C4×D4C2314yes—
333C2×#117C2312yes—
334C2×#117C2311yescharacteristic
335C2×#117C2311yescharacteristic
336C2×#117C2312yes—
337C2×#117C2314yes—
338C2×#117C2312yes—
339C2×#117C2312yes—
340C2×#117C2311yescharacteristic
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C4⋊C4C2311yescharacteristic
344C22×C4⋊C4C2312yes—
345C22×C42C2312yes—
346C22×C42C2312yes—
347C22×C42C2311yescharacteristic
348C22×C42C2314yes—
349#401C2314yes—
350#401C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2312yes—
370#399C2314yes—
371#399C2314yes—
372#399C2314yes—
373#399C2312yes—
374#399C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2312yes—
383#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#398C2312yes—
387#398C2312yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2312yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2312yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2312yes—
412#396C2312yes—
413#396C2312yes—
414#396C2314yes—
415#396C2312yes—
416#396C2312yes—
417#395C2314yes—
418#395C2314yes—
419#395C2312yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#394C2314yes—
426#394C2312yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2312yes—
433#394C2314yes—
434#394C2314yes—
435#394C2312yes—
436#394C2312yes—
437#394C2312yes—
438#394C2312yes—
439#394C2314yes—
440#394C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2314yes—
444#393C2312yes—
445#393C2314yes—
446#393C2314yes—
447#393C2314yes—
448#393C2314yes—
449#393C2314yes—
450#393C2314yes—
451#392C2314yes—
452#392C2312yes—
453#392C2314yes—
454#392C2314yes—
455#392C2312yes—
456#392C2314yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2314yes—
462#391C2314yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2314yes—
468#391C2314yes—
469#391C2312yes—
470#391C2314yes—
471#391C2314yes—
472#391C2314yes—
473#391C2314yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#390C2312yes—
482#390C2312yes—
483#390C2314yes—
484#390C2314yes—
485#390C2312yes—
486#390C2314yes—
487#390C2312yes—
488#390C2312yes—
489#390C2311yescharacteristic
490#390C2311yescharacteristic
491#390C2314yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2311yescharacteristic
497#389C2311yescharacteristic
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2312yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2311yescharacteristic
509#389C2312yes—
510#389C2311yescharacteristic
511#389C2312yes—
512#389C2314yes—
513#389C2312yes—
514#389C2314yes—
515#389C2311yescharacteristic
516#389C2311yescharacteristic
517#389C2312yes—
518#389C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2312yes—
548#388C2312yes—
549#388C2312yes—
550#388C2312yes—
551#388C2314yes—
552#388C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2312yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#386C2312yes—
593#386C2312yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2312yes—
610#386C2314yes—
611#386C2312yes—
612#386C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2312yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2312yes—
628#385C2312yes—
629#385C2314yes—
630#385C2314yes—
631#385C2312yes—
632#385C2314yes—
633#384C2312yes—
634#384C2312yes—
635#384C2311yescharacteristic
636#384C2311yescharacteristic
637#384C2314yes—
638#383C2314yes—
639#383C2314yes—
640#383C2314yes—
641#383C2314yes—
642#382C2312yes—
643#382C2312yes—
644#382C2314yes—
645#382C2312yes—
646#382C2312yes—
647#382C2312yes—
648#382C2312yes—
649#381C2314yes—
650#381C2314yes—
651#380C2311yescharacteristic
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2312yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2311yescharacteristic
668#380C2312yes—
669#380C2314yes—
670#380C2312yes—
671#380C2312yes—
672#380C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714#376C2314yes—
715#376C2314yes—
716C2×#95C2314yes—
717C2×#95C2312yes—
718C2×#95C2312yes—
719C2×#41—24no—
720C2×#41—44no—
721C2×#41—42no—
722C2×#41—42no—
723C2×#41—44no—
724C2×#41—82no—
725C22×Q8—24no—
726C22×Q8—42no—
727C22×Q8—42no—
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2412yes—
731C22×Q8C2412yes—
732C22×Q8C2412yes—
733C22×Q8C2412yes—
734C22×Q8C2414yes—
735C22×D4C2411yescharacteristic
736C22×D4C2412yes—
737C22×D4C2412yes—
738C22×D4C2412yes—
739C22×D4C2412yes—
740C22×D4C2412yes—
741C22×D4C2414yes—
742C22×D4C2411yescharacteristic
743C22×D4C2414yes—
744C22×D4C2411yescharacteristic
745C23×C4C2412yes—
746C23×C4C2412yes—
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2411yescharacteristic
750C23×C4C2414yes—
751C23×C4C2414yes—
752C23×C4C2412yes—
753C23×C4C2412yes—
754C23×C4C2411yescharacteristic
755C23×C4C2411yescharacteristic
756C23×C4C2412yes—
757C23×C4C2412yes—
758C23×C4C2412yes—
759C23×C4C2414yes—
760C4⋊Q8—28no—
761C4⋊Q8—42no—
762C4⋊Q8—42no—
763C4⋊Q8—44no—
764C4⋊Q8—48no—
765C4⋊Q8—84no—
766#126—28no—
767#126—28no—
768#126—84no—
769#125—28no—
770#125—44no—
771#125—48no—
772#124—28no—
773#124—28no—
774#124—84no—
775#123—28no—
776#123—28no—
777#123—216no—
778#123—48no—
779C22⋊Q8—28no—
780C22⋊Q8—28no—
781C22⋊Q8—28no—
782C22⋊Q8—44no—
783C22⋊Q8—44no—
784C22⋊Q8—44no—
785C22⋊Q8—48no—
786C22⋊Q8—48no—
787C22⋊Q8—48no—
788C22⋊Q8—44no—
789C22⋊Q8—44no—
790C22⋊Q8—44no—
791C22⋊Q8—44no—
792C22⋊Q8—44no—
793C22⋊Q8—44no—
794C22⋊Q8—82no—
795#121—24no—
796#121—28no—
797#121—28no—
798#121—28no—
799#121—44no—
800#121—42no—
801#121—44no—
802C4×Q8—24no—
803C4×Q8—28no—
804C4×Q8—28no—
805C4×Q8—44no—
806C4×Q8—44no—
807C4×Q8—42no—
808C4×Q8—44no—
809C4×D4—28no—
810C4×D4—28no—
811C4×D4—24no—
812C4×D4—28no—
813C4×D4—44no—
814C4×D4—42no—
815C4×D4—42no—
816C4×D4—44no—
817C4×D4—42no—
818C4×D4—48no—
819C4×D4—44no—
820C4×D4—48no—
821C4×D4—44no—
822C4×D4—84no—
823C4×D4—84no—
824#117—24no—
825#117—28no—
826#117—42no—
827#117—44no—
828#117—48no—
829#117—44no—
830#117—82no—
831#117#4118yescomplemented
832C2×C4⋊C4—28no—
833C2×C4⋊C4—28no—
834C2×C4⋊C4—42no—
835C2×C4⋊C4—44no—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2411yescharacteristic
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2412yes—
947C2×C42—28no—
948C2×C42—44no—
949C2×C42—42no—
950C2×C42—84no—
951C2×C42C2412yes—
952C2×C42C2414yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2412yes—
956C2×C42C2411yescharacteristic
957C2×C42C2411yescharacteristic
958C2×C42C2412yes—
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2411yescharacteristic
962C2×C42C2414yes—
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2412yes—
966C2×C42C2414yes—
967C2×C42C2414yes—
968C2×C42C2414yes—
969C2×C42C2414yes—
970C2×C42C2414yes—
971C2×C42C2414yes—
972C2×C42C2414yes—
973C2×C42C2411yescharacteristic
974C2×C42C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037C24C2512yes—
1038C24C2512yes—
1039C24C2511yescharacteristic
1040C24C2512yes—
1041#41—416no—
1042#41—816no—
1043C2×Q8—24no—
1044C2×Q8—24no—
1045C2×Q8—22no—
1046C2×Q8—24no—
1047C2×Q8—24no—
1048C2×Q8—22no—
1049C2×Q8—24no—
1050C2×Q8—22no—
1051C2×Q8—24no—
1052C2×Q8—42no—
1053C2×Q8—42no—
1054C2×Q8—42no—
1055C2×Q8—42no—
1056C2×Q8—42no—
1057C2×Q8—42no—
1058C2×Q8—44no—
1059C2×Q8—42no—
1060C2×Q8—42no—
1061C2×Q8—44no—
1062C2×Q8—44no—
1063C2×Q8—42no—
1064C2×Q8—416no—
1065C2×D4—24no—
1066C2×D4—24no—
1067C2×D4—24no—
1068C2×D4—24no—
1069C2×D4—24no—
1070C2×D4—24no—
1071C2×D4—28no—
1072C2×D4—24no—
1073C2×D4—22no—
1074C2×D4—22no—
1075C2×D4—22no—
1076C2×D4—22no—
1077C2×D4—41no—
1078C2×D4—42no—
1079C2×D4—42no—
1080C2×D4—41no—
1081C2×D4—42no—
1082C2×D4—42no—
1083C2×D4—41no—
1084C2×D4—42no—
1085C2×D4—42no—
1086C2×D4—41no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4—44no—
1090C2×D4—42no—
1091C2×D4—44no—
1092C2×D4—42no—
1093C2×D4—44no—
1094C2×D42−1+414yes—
1095C22×C4—22no—
1096C22×C4—22no—
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—24no—
1106C22×C4—24no—
1107C22×C4—24no—
1108C22×C4—24no—
1109C22×C4—24no—
1110C22×C4—28no—
1111C22×C4—28no—
1112C22×C4—22no—
1113C22×C4—24no—
1114C22×C4—22no—
1115C22×C4—42no—
1116C22×C4—42no—
1117C22×C4—42no—
1118C22×C4—42no—
1119C22×C4—42no—
1120C22×C4—42no—
1121C22×C4—42no—
1122C22×C4—41no—
1123C22×C4—41no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—44no—
1129C22×C4—42no—
1130C22×C4—41no—
1131C22×C4—42no—
1132C22×C4—42no—
1133C22×C4—41no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4—42no—
1137C22×C4—42no—
1138C22×C4—42no—
1139C22×C4C2×#4114yes—
1140C22×C4C2512yes—
1141C22×C4C2514yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2514yes—
1145C22×C4C2512yes—
1146C22×C4C2512yes—
1147C22×C4C2512yes—
1148C22×C4C2511yescharacteristic
1149C22×C4C2514yes—
1150C22×C4C2514yes—
1151C22×C4C2512yes—
1152C22×C4C2514yes—
1153C22×C4C2511yescharacteristic
1154C22×C4C2514yes—
1155C22×C4C2512yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2511yescharacteristic
1161C22×C4C2512yes—
1162C22×C4C2511yescharacteristic
1163C22×C4C2511yescharacteristic
1164C22×C4C2511yescharacteristic
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—28no—
1174C4⋊C4—28no—
1175C4⋊C4—24no—
1176C4⋊C4—28no—
1177C4⋊C4—28no—
1178C4⋊C4—24no—
1179C4⋊C4—22no—
1180C4⋊C4—24no—
1181C4⋊C4—28no—
1182C4⋊C4—24no—
1183C4⋊C4—22no—
1184C4⋊C4—24no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—28no—
1189C4⋊C4—22no—
1190C4⋊C4—24no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—42no—
1194C4⋊C4—41no—
1195C4⋊C4—44no—
1196C4⋊C4—42no—
1197C4⋊C4—42no—
1198C4⋊C4—41no—
1199C4⋊C4—41no—
1200C4⋊C4—44no—
1201C4⋊C4—41no—
1202C4⋊C4—42no—
1203C4⋊C4—41no—
1204C4⋊C4—41no—
1205C4⋊C4—42no—
1206C4⋊C4—42no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—42no—
1211C4⋊C4—42no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—42no—
1220C4⋊C4—42no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—42no—
1225C4⋊C4C2×#4114yes—
1226C4⋊C4C2×#4114yes—
1227C4⋊C4H(5,𝔽2)14yes—
1228C22⋊C4—24no—
1229C22⋊C4—24no—
1230C22⋊C4—28no—
1231C22⋊C4—24no—
1232C22⋊C4—24no—
1233C22⋊C4—24no—
1234C22⋊C4—24no—
1235C22⋊C4—24no—
1236C22⋊C4—24no—
1237C22⋊C4—24no—
1238C22⋊C4—24no—
1239C22⋊C4—28no—
1240C22⋊C4—28no—
1241C22⋊C4—24no—
1242C22⋊C4—24no—
1243C22⋊C4—24no—
1244C22⋊C4—24no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—42no—
1251C22⋊C4—42no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—42no—
1255C22⋊C4—42no—
1256C22⋊C4—42no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—42no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—42no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—42no—
1272C22⋊C4—42no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4C2×#4118yes—
1276C42—24no—
1277C42—24no—
1278C42—24no—
1279C42—24no—
1280C42—24no—
1281C42—22no—
1282C42—24no—
1283C42—22no—
1284C42—28no—
1285C42—24no—
1286C42—41no—
1287C42—41no—
1288C42—42no—
1289C42—44no—
1290C42—44no—
1291C42—44no—
1292C42—44no—
1293C42—44no—
1294C42—44no—
1295C42—44no—
1296C42—44no—
1297C42—44no—
1298C42—44no—
1299C42C2×#4118yes—
1300C23—22no—
1301C23—21no—
1302C23—22no—
1303C23—21no—
1304C23—22no—
1305C23—21no—
1306C23—22no—
1307C23—21no—
1308C23—21no—
1309C23—22no—
1310C23—21no—
1311C23—22no—
1312C23—22no—
1313C23—22no—
1314C23—22no—
1315C23—22no—
1316C23—22no—
1317C23—22no—
1318C23—22no—
1319C23—22no—
1320C23—22no—
1321C23—22no—
1322C23—22no—
1323C23—22no—
1324C23—22no—
1325C23—22no—
1326C23C22×#4112yes—
1327C23C2×2−1+414yes—
1328C23C2611yescharacteristic
1329Q8—48no—
1330Q8—48no—
1331Q8—44no—
1332Q8—84no—
1333Q8—84no—
1334Q8—164no—
1335Q8—162no—
1336D4—44no—
1337D4—48no—
1338D4—44no—
1339D4—48no—
1340D4—48no—
1341D4—48no—
1342D4—44no—
1343D4—84no—
1344D4—88no—
1345D4—88no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—21no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—21no—
1356C2×C4—22no—
1357C2×C4—21no—
1358C2×C4—28no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—22no—
1373C2×C4—24no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—21no—
1381C2×C4—22no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—21no—
1395C2×C4—22no—
1396C2×C4—24no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—24no—
1400C2×C4—22no—
1401C2×C4—24no—
1402C2×C4—24no—
1403C2×C4—24no—
1404C2×C4—22no—
1405C2×C4—21no—
1406C2×C4—22no—
1407C2×C4—24no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—21no—
1413C2×C4—48no—
1414C2×C4—48no—
1415C2×C4—48no—
1416C2×C4—48no—
1417C2×C4—48no—
1418C2×C4—48no—
1419C2×C4—84no—
1420C2×C4—82no—
1421C2×C4—84no—
1422C2×C4—82no—
1423C2×C4—88no—
1424C2×C4—88no—
1425C2×C4—88no—
1426C2×C4—162no—
1427C2×C4C22×#4114yes—
1428C2×C4C22×#4114yes—
1429C2×C4C22×#4112yes—
1430C2×C4C22×#4112yes—
1431C2×C4C2×H(5,𝔽2)14yes—
1432C2×C4C2×H(5,𝔽2)12yes—
1433C2×C4C2×2−1+412yes—
1434C2×C4#58512yes—
1435C2×C4#58512yes—
1436C22—24no—
1437C22—22no—
1438C22—22no—
1439C22—24no—
1440C22—24no—
1441C22—22no—
1442C22—42no—
1443C22—41no—
1444C22—42no—
1445C22—41no—
1446C22—41no—
1447C22—42no—
1448C22—41no—
1449C22—42no—
1450C22—42no—
1451C22—42no—
1452C22—42no—
1453C22—42no—
1454C22—42no—
1455C22—42no—
1456C22—42no—
1457C22—42no—
1458C22—42no—
1459C22—42no—
1460C22—42no—
1461C22—42no—
1462C22—42no—
1463C22—42no—
1464C22C23×#4111yescharacteristic
1465C22C22×H(5,𝔽2)11yescharacteristic
1466C22C22×2−1+411yescharacteristic
1467C22C2×#58511yescharacteristic
1468C22C2×#58511yescharacteristic
1469C22H(7,𝔽2)11yescharacteristic
1470C222−1+611yescharacteristic
1471C4—24no—
1472C4—24no—
1473C4—22no—
1474C4—22no—
1475C4—24no—
1476C4—22no—
1477C4—42no—
1478C4—42no—
1479C4—42no—
1480C4—42no—
1481C4—44no—
1482C4—44no—
1483C4—44no—
1484C4—42no—
1485C4—41no—
1486C4—42no—
1487C4—44no—
1488C4—41no—
1489C4—44no—
1490C4—42no—
1491C4—42no—
1492C4—42no—
1493C4—42no—
1494C4—44no—
1495C4#346014yes—
1496C2—44no—
1497C2—42no—
1498C2—82no—
1499C2—82no—
1500C2C2×#346011yescharacteristic
1501C2#6289311yescharacteristic
1502C2#6291811yescharacteristic
1503C2#6300011yescharacteristic
1504C2#6300911yescharacteristic
1505C2#6302511yescharacteristic
1506C2#6305611yescharacteristic
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. #52278C2semidirect
2. #52169C2semidirect
3. #42668C2semidirect
4. #42661C2semidirect
5. #42505C2semidirect
6. #42413C2semidirect
7. #41911C2semidirect
8. #41180C2semidirect
9. #40368C2semidirect
10. #39906C2semidirect
11. #39760C2semidirect
12. #39708C2semidirect
13. #39632C2semidirect
14. #39159C2semidirect
15. #38792C2semidirect
16. #38782C2semidirect
17. #37379C2semidirect
18. #37308C2semidirect
19. #37168C2semidirect
20. #36950C2semidirect
21. #36561C2semidirect
22. #36492C2semidirect
23. #36404C2semidirect
24. #36255C2semidirect
25. #35789C2semidirect
26. #35738C2semidirect
27. #35697C2semidirect
28. #34268C2semidirect
29. #34241C2semidirect
831. #117#41semidirect

Maximal subgroups

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

subgroupindex
#522782
#521692
#426682
#426612
#425052
#424132
#419112
#411802
#403682
#399062
#397602
#397082
#396322
#391592
#387922
#387822
#373792
#373082
#371682
#369502
#365612
#364922
#364042
#362552
#357892
#357382
#356972
#342682
#342412