Finite Group Databasebeta

← #8726269

Subgroups — #8726269

Order 512.

4536 conjugacy classes of subgroups.

The subgroup lattice has 1478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59953C212yesmaximal, complemented
2#59933C212yesmaximal, complemented
3#59765C212yesmaximal, complemented
4#59199C211yesmaximal, characteristic, complemented
5#59014C212yesmaximal, complemented
6#57509C212yesmaximal, complemented
7#54430C214yesmaximal, complemented
8#54298C214yesmaximal, complemented
9#54268C214yesmaximal, complemented
10#53127C212yesmaximal, complemented
11#52991C211yesmaximal, characteristic, complemented
12#52294C211yesmaximal, characteristic, complemented
13#47227C214yesmaximal, complemented
14#46849C212yesmaximal, complemented
15#45251C211yesmaximal, characteristic, complemented
16#44913C212yesmaximal, complemented
17#44823C212yesmaximal, complemented
18#44038C214yesmaximal, complemented
19#42908C211yesmaximal, characteristic, complemented
20#42449C212yesmaximal, complemented
21#41931C212yesmaximal, complemented
22#41768C214yesmaximal, complemented
23#40003C212yesmaximal, complemented
24#39955C212yesmaximal, complemented
25#39144C212yesmaximal, complemented
26#39133C211yesmaximal, characteristic, complemented
27#38977C212yesmaximal, complemented
28#35911C212yesmaximal, complemented
29#35854C211yesmaximal, characteristic, complemented
30C2×#557C2211yescharacteristic, complemented
31C2×#552C2212yes—
32C2×#548C2211yescharacteristic
33C2×#537C2211yescharacteristic, complemented
34C22×C22⋊Q8C2211yescharacteristic
35#2859C2212yescomplemented
36#2847C2211yescharacteristic
37#2841C2212yes—
38#2839C2214yescomplemented
39#2836C2214yescomplemented
40#2835C2212yescomplemented
41#2832C2214yescomplemented
42#2827C2214yescomplemented
43#2827C2214yescomplemented
44#2817C2212yescomplemented
45#2816C2214yes—
46#2799C2214yescomplemented
47#2798C2214yescomplemented
48#2797C2214yes—
49#2796C2214yescomplemented
50#2789C2212yescomplemented
51#2788C2214yes—
52#2788C2214yescomplemented
53#2783C2214yescomplemented
54#2780C2214yes—
55#2779C2214yes—
56#2778C2214yes—
57#2774C2214yescomplemented
58#2773C2214yescomplemented
59#2771C2212yes—
60#2765C2214yes—
61#2765C2214yescomplemented
62#2763C2211yescharacteristic
63#2763C2212yes—
64#2760C2212yes—
65#2753C2212yes—
66#2753C2212yes—
67#2753C2212yes—
68#2751C2214yes—
69#2751C2214yescomplemented
70#2748C2212yes—
71#2748C2214yes—
72#2746C2214yes—
73#2742C2212yes—
74#2739C2214yes—
75#2739C2214yescomplemented
76#2736C2211yescharacteristic
77#2732C2214yes—
78#2730C2214yes—
79#2727C2214yescomplemented
80#2722C2212yescomplemented
81#2719C2214yescomplemented
82#2713C2214yescomplemented
83#2712C2211yescharacteristic
84#2712C2212yes—
85#2711C2214yescomplemented
86#2710C2214yes—
87#2708C2214yes—
88#2705C2214yes—
89#2704C2214yescomplemented
90#2702C2214yes—
91#2701C2214yes—
92#2695C2214yes—
93#2694C2214yes—
94#2691C2214yescomplemented
95#2690C2214yes—
96#2688C2214yes—
97#2687C2214yes—
98#2686C2214yes—
99#2686C2214yescomplemented
100#2674C2214yes—
101#2671C2214yes—
102#2670C2212yes—
103#2670C2211yescharacteristic
104#2664C2214yescomplemented
105#2655C2214yescomplemented
106#2649C2214yescomplemented
107#2649C2214yescomplemented
108#2647C2212yescomplemented
109#2645C2214yescomplemented
110#2643C2214yes—
111#2640C2211yescharacteristic, complemented
112#2640C2212yescomplemented
113#2639C2212yescomplemented
114#2636C2214yes—
115#2635C2212yes—
116#2618C2212yes—
117#2616C2211yescharacteristic, complemented
118#2612C2214yescomplemented
119#2611C2214yes—
120#2609C2214yescomplemented
121#2609C2212yescomplemented
122#2607C2212yes—
123#2604C2214yescomplemented
124#2603C2214yes—
125#2592C2211yescharacteristic, complemented
126#2592C2212yescomplemented
127#2589C2214yes—
128#2589C2214yescomplemented
129#2589C2214yescomplemented
130#2585C2214yescomplemented
131#2584C2212yescomplemented
132#2582C2212yescomplemented
133#2582C2212yescomplemented
134#2580C2212yescomplemented
135#2574C2214yescomplemented
136#2564C2212yes—
137#2564C2214yes—
138#2563C2212yes—
139#2563C2211yescharacteristic
140#2562C2212yes—
141#2559C2214yescomplemented
142#2557C2214yes—
143#2539C2212yes—
144#2538C2212yes—
145#2536C2212yes—
146#2535C2212yes—
147#2534C2212yes—
148#2531C2214yes—
149#2530C2214yes—
150#2527C2214yescomplemented
151#2527C2214yescomplemented
152#2526C2214yescomplemented
153#2522C2214yes—
154#2522C2214yes—
155#2508C2214yescomplemented
156#2505C2214yes—
157#2505C2214yescomplemented
158#2503C2212yes—
159#2503C2211yescharacteristic, complemented
160#2501C2211yescharacteristic
161#2500C2212yescomplemented
162#2497C2212yes—
163#2497C2212yes—
164#2496C2212yescomplemented
165#2496C2212yescomplemented
166#2494C2212yes—
167#2494C2212yescomplemented
168#2490C2214yes—
169#2490C2212yes—
170#2490C2212yescomplemented
171#2489C2212yes—
172#2489C2214yescomplemented
173#2489C2212yescomplemented
174#2488C2214yes—
175#2487C2212yes—
176#2487C2212yes—
177#2487C2211yescharacteristic
178#2486C2211yescharacteristic
179#2485C2214yes—
180#2481C2214yes—
181#2479C2214yescomplemented
182#2479C2214yescomplemented
183#2478C2214yescomplemented
184#2477C2214yes—
185#2471C2214yes—
186#2470C2214yes—
187#2468C2214yes—
188#2467C2214yes—
189#2464C2214yes—
190#2447C2214yes—
191#2442C2214yes—
192#2442C2212yes—
193#2442C2212yes—
194#2442C2212yescomplemented
195#2441C2212yescomplemented
196#2440C2212yes—
197#2439C2212yescomplemented
198#2438C2214yes—
199#2437C2212yes—
200#2427C2212yescomplemented
201#2426C2212yes—
202#2424C2214yes—
203#2423C2212yes—
204#2423C2212yescomplemented
205#2423C2212yescomplemented
206#2422C2212yes—
207#2421C2212yes—
208#2421C2212yescomplemented
209#2418C2214yes—
210#2417C2212yes—
211#2416C2212yes—
212#2416C2212yes—
213#2415C2212yes—
214#2414C2214yes—
215#2412C2214yes—
216#2409C2212yes—
217#2407C2212yes—
218#2398C2212yes—
219#2398C2211yescharacteristic
220#2398C2212yes—
221#2395C2214yes—
222#2388C2212yes—
223#2388C2211yescharacteristic
224#2372C2214yes—
225#2363C2214yes—
226#2361C2212yes—
227#2360C2212yes—
228#2360C2212yescomplemented
229#2360C2212yescomplemented
230#2359C2214yes—
231#2358C2212yes—
232#2355C2212yescomplemented
233#2352C2212yes—
234D4×C4⋊C4C2212yes—
235D4×C4⋊C4C2212yes—
236#2345C2212yes—
237#2344C2212yescomplemented
238#2342C2214yes—
239#2341C2212yescomplemented
240Q8×C22⋊C4C2212yes—
241Q8×C22⋊C4C2211yescharacteristic
242#2339C2211yescharacteristic, complemented
243#2335C2214yes—
244#2325C2214yes—
245#2323C2214yes—
246#2322C2212yes—
247#2319C2214yes—
248#2311C2212yescomplemented
249C4×#124C2212yes—
250C4×#124C2212yes—
251C4×#124C2212yes—
252C4×#120C2211yescharacteristic
253C4×#120C2212yes—
254#2295C2212yescomplemented
255#2295C2212yescomplemented
256#2293C2212yescomplemented
257C2×#380C2212yes—
258#2276C2211yescharacteristic, complemented
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C23×Q8C2311yescharacteristic
262C24×C4C2311yescharacteristic
263#557—44no—
264#552—48no—
265#548—44no—
266#537—44no—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#125C2314yes—
276C2×#124C2312yes—
277C2×#124C2311yescharacteristic
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#123C2312yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2312yes—
285C2×#123C2312yes—
286C2×C22⋊Q8—44no—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2311yescharacteristic
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×#121C2314yes—
297C2×#121C2312yes—
298C2×#121C2311yescharacteristic
299C2×#121C2312yes—
300C2×#121C2314yes—
301C2×#121C2312yes—
302C2×#121C2314yes—
303C2×#121C2312yes—
304C2×#120C2311yescharacteristic
305C2×#120C2312yes—
306C2×#120C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2314yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2314yes—
324C2×#117C2312yes—
325C2×#117C2314yes—
326C2×#117C2314yes—
327C2×#117C2314yes—
328C22×C4⋊C4C2312yes—
329C22×C4⋊C4C2312yes—
330C22×C4⋊C4C2312yes—
331C22×C4⋊C4C2311yescharacteristic
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2311yescharacteristic
334C22×C22⋊C4C2312yes—
335C22×C22⋊C4C2314yes—
336#401C2314yes—
337#401C2314yes—
338#400C2312yes—
339#400C2314yes—
340#400C2312yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2312yes—
353#400C2314yes—
354#400C2314yes—
355#400C2312yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#399C2314yes—
363#399C2314yes—
364#399C2314yes—
365#399C2312yes—
366#399C2314yes—
367#399C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2312yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2312yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2312yes—
397#397C2311yescharacteristic
398#397C2312yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2311yescharacteristic
406#397C2312yes—
407#397C2314yes—
408#397C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#395C2311yescharacteristic
420#395C2312yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2312yes—
425#394C2312yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2312yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2311yescharacteristic
437#394C2314yes—
438#394C2312yes—
439#394C2314yes—
440#394C2312yes—
441#394C2312yes—
442#394C2312yes—
443#394C2312yes—
444#394C2314yes—
445#394C2312yes—
446#394C2314yes—
447#394C2314yes—
448#393C2312yes—
449#393C2314yes—
450#393C2311yescharacteristic
451#393C2312yes—
452#393C2312yes—
453#393C2312yes—
454#393C2311yescharacteristic
455#393C2312yes—
456#393C2312yes—
457#393C2314yes—
458#393C2311yescharacteristic
459#393C2312yes—
460#393C2314yes—
461#393C2312yes—
462#392C2314yes—
463#392C2311yescharacteristic
464#392C2314yes—
465#392C2312yes—
466#392C2312yes—
467#392C2312yes—
468#392C2312yes—
469#391C2314yes—
470#391C2312yes—
471#391C2314yes—
472#391C2314yes—
473#391C2314yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2314yes—
479#391C2314yes—
480#391C2314yes—
481#391C2314yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#390C2314yes—
486#390C2312yes—
487#390C2314yes—
488#390C2312yes—
489#390C2314yes—
490#390C2312yes—
491#390C2312yes—
492#390C2314yes—
493#390C2312yes—
494#390C2314yes—
495#390C2312yes—
496#390C2314yes—
497#390C2314yes—
498#390C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2314yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2312yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2312yes—
541#388C2312yes—
542#388C2314yes—
543#388C2312yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2312yes—
550#388C2314yes—
551#388C2314yes—
552#388C2312yes—
553#388C2312yes—
554#388C2312yes—
555#388C2314yes—
556#388C2314yes—
557#388C2312yes—
558#388C2314yes—
559#388C2314yes—
560#388C2312yes—
561#388C2312yes—
562#388C2312yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
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#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#386C2312yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2312yes—
597#386C2312yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2312yes—
604#386C2314yes—
605#386C2314yes—
606#386C2311yescharacteristic
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2312yes—
612#386C2312yes—
613#385C2312yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2311yescharacteristic
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2312yes—
635#385C2312yes—
636#385C2312yes—
637#385C2312yes—
638#384C2312yes—
639#384C2312yes—
640#384C2312yes—
641#382C2312yes—
642#382C2314yes—
643#382C2314yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2312yes—
648#382C2312yes—
649#382C2312yes—
650#381C2314yes—
651#381C2312yes—
652#381C2314yes—
653#381C2312yes—
654#381C2314yes—
655#381C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2314yes—
663#380C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2312yes—
668#380C2312yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2311yescharacteristic
673#380C2311yescharacteristic
674#380C2312yes—
675#380C2314yes—
676#380C2312yes—
677#380C2312yes—
678#380C2314yes—
679#379C2312yes—
680#379C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2311yescharacteristic
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2311yescharacteristic
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710#376C2314yes—
711#376C2314yes—
712#376C2311yescharacteristic
713#376C2312yes—
714C2×#95C2314yes—
715C2×#95C2312yes—
716C43C2312yes—
717C25C2411yescharacteristic
718C2×#41—24no—
719C2×#41—42no—
720C2×#41—44no—
721C2×#41—44no—
722C22×Q8—24no—
723C22×Q8—44no—
724C22×Q8C2411yescharacteristic
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2411yescharacteristic
731C22×D4C2411yescharacteristic
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2412yes—
736C22×D4C2411yescharacteristic
737C22×D4C2412yes—
738C22×D4C2412yes—
739C22×D4C2412yes—
740C22×D4C2414yes—
741C22×D4C2411yescharacteristic
742C22×D4C2412yes—
743C23×C4—42no—
744C23×C4—44no—
745C23×C4C2412yes—
746C23×C4C2412yes—
747C23×C4C2411yescharacteristic
748C23×C4C2411yescharacteristic
749C23×C4C2412yes—
750C23×C4C2414yes—
751C23×C4C2412yes—
752C23×C4C2412yes—
753C23×C4C2414yes—
754C23×C4C2411yescharacteristic
755C23×C4C2414yes—
756C23×C4C2412yes—
757C23×C4C2414yes—
758C23×C4C2412yes—
759C4⋊Q8—42no—
760C4⋊Q8—44no—
761#126—48no—
762#126—84no—
763#126—84no—
764#125—44no—
765#125—48no—
766#125—44no—
767#125—48no—
768#124—28no—
769#124—42no—
770#124—44no—
771#124—44no—
772#124—44no—
773#123—28no—
774#123—48no—
775#123—48no—
776#123—82no—
777#123—82no—
778C22⋊Q8—28no—
779C22⋊Q8—28no—
780C22⋊Q8—48no—
781C22⋊Q8—48no—
782C22⋊Q8—44no—
783C22⋊Q8—44no—
784C22⋊Q8—44no—
785C22⋊Q8—42no—
786C22⋊Q8—44no—
787#121—44no—
788#121—48no—
789#121—48no—
790#121—44no—
791#121—44no—
792#121—42no—
793#121—44no—
794#121—48no—
795#120—24no—
796#120—44no—
797#120—82no—
798C4×Q8—24no—
799C4×Q8—28no—
800C4×Q8—44no—
801C4×Q8—44no—
802C4×Q8—42no—
803C4×Q8—44no—
804C4×Q8—44no—
805C4×D4—44no—
806C4×D4—44no—
807C4×D4—44no—
808C4×D4—44no—
809C4×D4—42no—
810C4×D4—44no—
811C4×D4—44no—
812C4×D4—48no—
813C4×D4—84no—
814C4×D4—84no—
815#117—48no—
816#117—44no—
817#117—84no—
818#117—84no—
819C2×C4⋊C4—44no—
820C2×C4⋊C4—44no—
821C2×C4⋊C4—42no—
822C2×C4⋊C4—44no—
823C2×C4⋊C4—42no—
824C2×C4⋊C4—44no—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C22⋊C4—44no—
878C2×C22⋊C4—48no—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2411yescharacteristic
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2411yescharacteristic
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2411yescharacteristic
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2411yescharacteristic
938C2×C42C2414yes—
939C2×C42C2412yes—
940C2×C42C2411yescharacteristic
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2414yes—
947C2×C42C2412yes—
948C2×C42C2414yes—
949C2×C42C2412yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2412yes—
956C2×C42C2412yes—
957#95C2411yescharacteristic
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2411yescharacteristic
965#95C2414yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2411yescharacteristic
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2411yescharacteristic
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022C24—22no—
1023C24—24no—
1024C24—41no—
1025C24—42no—
1026C24—41no—
1027C24C2512yes—
1028C24C2512yes—
1029C24C2511yescharacteristic
1030C24C2511yescharacteristic
1031C24C2512yes—
1032#41—88no—
1033#41—88no—
1034C2×Q8—22no—
1035C2×Q8—24no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—24no—
1039C2×Q8—42no—
1040C2×Q8—41no—
1041C2×Q8—42no—
1042C2×Q8—41no—
1043C2×Q8—44no—
1044C2×Q8—42no—
1045C2×Q8—42no—
1046C2×Q8—44no—
1047C2×Q8—42no—
1048C2×Q8—88no—
1049C2×Q8H(5,𝔽2)14yes—
1050C2×D4—24no—
1051C2×D4—24no—
1052C2×D4—22no—
1053C2×D4—24no—
1054C2×D4—24no—
1055C2×D4—28no—
1056C2×D4—24no—
1057C2×D4—22no—
1058C2×D4—24no—
1059C2×D4—24no—
1060C2×D4—24no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—41no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C2×D4—44no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—42no—
1072C2×D4—42no—
1073C2×D4—41no—
1074C2×D4—44no—
1075C2×D4—41no—
1076C2×D4—44no—
1077C2×D4—42no—
1078C2×D4—42no—
1079C2×D4—42no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C22×C4—24no—
1084C22×C4—28no—
1085C22×C4—22no—
1086C22×C4—24no—
1087C22×C4—22no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—24no—
1095C22×C4—24no—
1096C22×C4—24no—
1097C22×C4—42no—
1098C22×C4—44no—
1099C22×C4—41no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—42no—
1107C22×C4—44no—
1108C22×C4—42no—
1109C22×C4—42no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—42no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—88no—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2511yescharacteristic
1123C22×C4C2511yescharacteristic
1124C22×C4C2512yes—
1125C22×C4C2514yes—
1126C22×C4C2511yescharacteristic
1127C22×C4C2512yes—
1128C22×C4C2514yes—
1129C22×C4C2512yes—
1130C22×C4C2514yes—
1131C22×C4C2514yes—
1132C22×C4C2512yes—
1133C22×C4C2511yescharacteristic
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2514yes—
1138C22×C4C2514yes—
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2511yescharacteristic
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—28no—
1148C4⋊C4—28no—
1149C4⋊C4—24no—
1150C4⋊C4—22no—
1151C4⋊C4—28no—
1152C4⋊C4—28no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—41no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—41no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—42no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C22⋊C4—24no—
1197C22⋊C4—28no—
1198C22⋊C4—28no—
1199C22⋊C4—24no—
1200C22⋊C4—24no—
1201C22⋊C4—24no—
1202C22⋊C4—28no—
1203C22⋊C4—28no—
1204C22⋊C4—24no—
1205C22⋊C4—28no—
1206C22⋊C4—24no—
1207C22⋊C4—24no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—42no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—41no—
1226C22⋊C4—42no—
1227C22⋊C4—41no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—42no—
1241C22⋊C4—42no—
1242C22⋊C4—42no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—41no—
1246C22⋊C4—44no—
1247C22⋊C4—42no—
1248C22⋊C4—42no—
1249C22⋊C4—42no—
1250C22⋊C4—42no—
1251C22⋊C4—42no—
1252C22⋊C4—42no—
1253C22⋊C4—42no—
1254C22⋊C42−1+414yes—
1255C42—28no—
1256C42—24no—
1257C42—22no—
1258C42—24no—
1259C42—24no—
1260C42—24no—
1261C42—24no—
1262C42—24no—
1263C42—44no—
1264C42—42no—
1265C42—42no—
1266C42—44no—
1267C42—44no—
1268C42—44no—
1269C42—44no—
1270C42—44no—
1271C42—44no—
1272C42—42no—
1273C42—42no—
1274C23—22no—
1275C23—21no—
1276C23—22no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—22no—
1282C23—21no—
1283C23—22no—
1284C23—22no—
1285C23—22no—
1286C23—21no—
1287C23—22no—
1288C23—22no—
1289C23—21no—
1290C23—22no—
1291C23—22no—
1292C23—24no—
1293C23—24no—
1294C23—22no—
1295C23—22no—
1296C23—22no—
1297C23—22no—
1298C23—21no—
1299C23—22no—
1300C23—22no—
1301C23—44no—
1302C23—48no—
1303C23—82no—
1304C23—84no—
1305C23—82no—
1306C23C2×2−1+412yes—
1307C23#58514yes—
1308C23C2611yescharacteristic
1309Q8—28no—
1310Q8—44no—
1311Q8—84no—
1312Q8—84no—
1313Q8—84no—
1314Q8—82no—
1315Q8—82no—
1316D4—48no—
1317D4—48no—
1318D4—44no—
1319D4—84no—
1320D4—84no—
1321D4—84no—
1322D4—82no—
1323D4—84no—
1324D4—88no—
1325D4—82no—
1326D4—84no—
1327D4—164no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—21no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—21no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—21no—
1342C2×C4—22no—
1343C2×C4—21no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—21no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—24no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—24no—
1368C2×C4—24no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—24no—
1372C2×C4—22no—
1373C2×C4—24no—
1374C2×C4—24no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—21no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—24no—
1390C2×C4—48no—
1391C2×C4—44no—
1392C2×C4—48no—
1393C2×C4—44no—
1394C2×C4—84no—
1395C2×C4—84no—
1396C2×C4—88no—
1397C2×C4—84no—
1398C2×C4—88no—
1399C2×C4—88no—
1400C2×C4—82no—
1401C2×C4—84no—
1402C2×C4—162no—
1403C2×C4—164no—
1404C2×C4C2×H(5,𝔽2)14yes—
1405C2×C4C2×H(5,𝔽2)12yes—
1406C2×C4C2×2−1+414yes—
1407C2×C4#58514yes—
1408C22—24no—
1409C22—24no—
1410C22—24no—
1411C22—22no—
1412C22—24no—
1413C22—41no—
1414C22—42no—
1415C22—41no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—41no—
1421C22—42no—
1422C22—42no—
1423C22—41no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22—42no—
1429C22—44no—
1430C22—42no—
1431C22—41no—
1432C22—42no—
1433C22—42no—
1434C22—44no—
1435C22—42no—
1436C22—42no—
1437C22—88no—
1438C22C22×H(5,𝔽2)11yescharacteristic
1439C22C22×2−1+411yescharacteristic
1440C22C2×#58512yes—
1441C22C2×#58512yes—
1442C22H(7,𝔽2)11yescharacteristic
1443C4—24no—
1444C4—24no—
1445C4—42no—
1446C4—41no—
1447C4—41no—
1448C4—42no—
1449C4—42no—
1450C4—44no—
1451C4—44no—
1452C4—42no—
1453C4—41no—
1454C4—42no—
1455C4—42no—
1456C4—42no—
1457C4—44no—
1458C4—41no—
1459C4—42no—
1460C4—42no—
1461C4—42no—
1462C4—44no—
1463C4—44no—
1464C4—44no—
1465C4—42no—
1466C4#354514yes—
1467C2—44no—
1468C2—42no—
1469C2—81no—
1470C2—82no—
1471C2—82no—
1472C2C2×#354511yescharacteristic
1473C2#6291711yescharacteristic
1474C2#6293512yes—
1475C2#6302011yescharacteristic
1476C2#6302312yes—
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. #59953C2semidirect
2. #59933C2semidirect
3. #59765C2semidirect
4. #59199C2semidirect
5. #59014C2semidirect
6. #57509C2semidirect
7. #54430C2semidirect
8. #54298C2semidirect
9. #54268C2semidirect
10. #53127C2semidirect
11. #52991C2semidirect
12. #52294C2semidirect
13. #47227C2semidirect
14. #46849C2semidirect
15. #45251C2semidirect
16. #44913C2semidirect
17. #44823C2semidirect
18. #44038C2semidirect
19. #42908C2semidirect
20. #42449C2semidirect
21. #41931C2semidirect
22. #41768C2semidirect
23. #40003C2semidirect
24. #39955C2semidirect
25. #39144C2semidirect
26. #39133C2semidirect
27. #38977C2semidirect
28. #35911C2semidirect
29. #35854C2semidirect
30. C2×#557C22semidirect
33. C2×#537C22semidirect
35. #2859C22semidirect
38. #2839C22semidirect
39. #2836C22semidirect
40. #2835C22semidirect
41. #2832C22semidirect
42. #2827C22semidirect
43. #2827C22semidirect
44. #2817C22semidirect
46. #2799C22semidirect
47. #2798C22semidirect
49. #2796C22semidirect
50. #2789C22semidirect
52. #2788C22semidirect
53. #2783C22semidirect
57. #2774C22semidirect
58. #2773C22semidirect
61. #2765C22semidirect
69. #2751C22semidirect
75. #2739C22semidirect
79. #2727C22semidirect
80. #2722C22semidirect
81. #2719C22semidirect
82. #2713C22semidirect
85. #2711C22semidirect
89. #2704C22semidirect
94. #2691C22semidirect
99. #2686C22semidirect
104. #2664C22semidirect
105. #2655C22semidirect
106. #2649C22semidirect
107. #2649C22semidirect
108. #2647C22semidirect
109. #2645C22semidirect
111. #2640C22semidirect
112. #2640C22semidirect
113. #2639C22semidirect
117. #2616C22semidirect
118. #2612C22semidirect
120. #2609C22semidirect
121. #2609C22semidirect
123. #2604C22semidirect
125. #2592C22semidirect
126. #2592C22semidirect
128. #2589C22semidirect
129. #2589C22semidirect
130. #2585C22semidirect
131. #2584C22semidirect
132. #2582C22semidirect
133. #2582C22semidirect
134. #2580C22semidirect
135. #2574C22semidirect
141. #2559C22semidirect
150. #2527C22semidirect
151. #2527C22semidirect
152. #2526C22semidirect
155. #2508C22semidirect
157. #2505C22semidirect
159. #2503C22semidirect
161. #2500C22semidirect
164. #2496C22semidirect
165. #2496C22semidirect
167. #2494C22semidirect
170. #2490C22semidirect
172. #2489C22semidirect
173. #2489C22semidirect
181. #2479C22semidirect
182. #2479C22semidirect
183. #2478C22semidirect
194. #2442C22semidirect
195. #2441C22semidirect
197. #2439C22semidirect
200. #2427C22semidirect
204. #2423C22semidirect
205. #2423C22semidirect
208. #2421C22semidirect
228. #2360C22semidirect
229. #2360C22semidirect
232. #2355C22semidirect
237. #2344C22semidirect
239. #2341C22semidirect
242. #2339C22semidirect
248. #2311C22semidirect
254. #2295C22semidirect
255. #2295C22semidirect
256. #2293C22semidirect
258. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#599532
#599332
#597652
#591992
#590142
#575092
#544302
#542982
#542682
#531272
#529912
#522942
#472272
#468492
#452512
#449132
#448232
#440382
#429082
#424492
#419312
#417682
#400032
#399552
#391442
#391332
#389772
#359112
#358542