Finite Group Databasebeta

← #8508894

Subgroups — #8508894

Order 512.

4449 conjugacy classes of subgroups.

The subgroup lattice has 1457 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59821C211yesmaximal, characteristic, complemented
2#58422C214yesmaximal, complemented
3#57572C214yesmaximal, complemented
4#57493C214yesmaximal, complemented
5#57359C214yesmaximal, complemented
6#57240C214yesmaximal, complemented
7#53374C212yesmaximal, complemented
8#53365C212yesmaximal, complemented
9#53122C212yesmaximal, complemented
10#52160C211yesmaximal, characteristic
11#50058C214yesmaximal, complemented
12#46158C212yesmaximal, complemented
13#45717C212yesmaximal, complemented
14#45432C212yesmaximal, complemented
15#45264C212yesmaximal, complemented
16#42878C212yesmaximal, complemented
17#42690C212yesmaximal, complemented
18#42675C212yesmaximal, complemented
19#39959C212yesmaximal, complemented
20#39629C211yesmaximal, characteristic, complemented
21#39493C211yesmaximal, characteristic, complemented
22#38107C212yesmaximal, complemented
23#38051C212yesmaximal, complemented
24#37399C212yesmaximal, complemented
25#37378C212yesmaximal, complemented
26#37207C212yesmaximal, complemented
27#36534C211yesmaximal, characteristic, complemented
28#35209C211yesmaximal, characteristic, complemented
29#35208C211yesmaximal, characteristic, complemented
30C2×#556C2211yescharacteristic
31C2×#556C2212yes—
32C2×#554C2211yescharacteristic
33C2×#552C2212yes—
34C2×#552C2212yes—
35C2×#541C2212yes—
36C2×#529C2212yes—
37#2863C2212yes—
38#2862C2211yescharacteristic
39#2861C2212yes—
40#2860C2212yes—
41#2859C2212yes—
42#2859C2212yes—
43#2857C2212yes—
44#2855C2212yes—
45#2851C2212yes—
46#2836C2214yes—
47#2836C2214yes—
48#2830C2214yes—
49#2829C2214yes—
50#2827C2214yes—
51#2820C2214yes—
52#2820C2214yes—
53#2814C2214yes—
54#2807C2214yes—
55#2806C2212yes—
56#2806C2212yes—
57#2806C2212yes—
58#2805C2212yes—
59#2805C2212yes—
60#2805C2212yes—
61#2804C2212yes—
62#2798C2214yes—
63#2791C2214yes—
64#2791C2214yes—
65#2790C2214yes—
66#2788C2214yes—
67#2786C2214yes—
68#2786C2214yes—
69#2783C2214yes—
70#2780C2214yes—
71#2777C2214yes—
72#2777C2214yes—
73#2773C2214yes—
74#2773C2214yes—
75#2768C2214yes—
76#2761C2214yes—
77#2756C2214yes—
78#2755C2214yes—
79#2753C2214yes—
80#2751C2214yes—
81#2748C2214yes—
82#2740C2214yes—
83#2738C2214yes—
84#2733C2211yescharacteristic
85#2732C2212yes—
86#2732C2211yescharacteristic
87#2730C2212yes—
88#2730C2214yes—
89#2727C2214yes—
90#2727C2211yescharacteristic
91#2727C2212yes—
92#2727C2214yes—
93#2727C2212yes—
94#2726C2214yes—
95#2726C2214yes—
96#2725C2214yes—
97#2725C2214yes—
98#2725C2214yes—
99#2725C2214yes—
100#2725C2214yes—
101#2722C2214yes—
102#2722C2214yes—
103#2721C2214yes—
104#2721C2214yes—
105#2721C2212yes—
106#2719C2214yes—
107#2718C2214yes—
108#2718C2214yes—
109#2717C2214yes—
110#2715C2214yes—
111#2715C2214yes—
112#2714C2212yes—
113#2711C2214yes—
114#2707C2214yes—
115#2706C2214yes—
116#2705C2214yes—
117#2705C2214yes—
118#2705C2212yes—
119#2704C2214yes—
120#2704C2214yes—
121#2704C2214yes—
122#2702C2214yes—
123#2695C2214yes—
124#2695C2214yes—
125#2694C2212yes—
126#2691C2214yes—
127#2689C2214yes—
128#2686C2214yes—
129#2682C2211yescharacteristic
130#2673C2212yes—
131#2672C2214yes—
132#2666C2214yes—
133#2664C2214yes—
134#2664C2214yes—
135#2662C2214yes—
136#2654C2214yes—
137#2648C2214yes—
138#2647C2212yes—
139#2637C2214yes—
140#2630C2214yes—
141#2629C2212yes—
142#2628C2212yes—
143#2625C2214yes—
144#2625C2212yes—
145#2621C2212yes—
146#2601C2214yes—
147#2590C2214yes—
148#2589C2214yes—
149#2585C2214yes—
150#2584C2214yes—
151#2584C2214yes—
152#2582C2211yescharacteristic
153#2581C2212yes—
154#2570C2212yes—
155#2567C2211yescharacteristic
156#2567C2211yescharacteristic
157#2565C2212yes—
158#2563C2211yescharacteristic
159#2560C2214yes—
160#2560C2214yes—
161#2552C2211yescharacteristic
162#2552C2211yescharacteristic
163#2548C2212yes—
164#2547C2211yescharacteristic
165#2546C2211yescharacteristic
166#2544C2212yes—
167#2542C2212yes—
168#2542C2211yescharacteristic
169#2538C2212yes—
170#2538C2212yes—
171#2538C2212yes—
172#2538C2211yescharacteristic
173#2536C2212yes—
174#2536C2212yes—
175#2522C2214yes—
176#2522C2214yes—
177#2521C2214yes—
178#2520C2214yes—
179#2520C2214yes—
180#2519C2214yes—
181#2512C2214yes—
182#2512C2212yes—
183#2511C2212yes—
184#2507C2212yes—
185#2506C2212yes—
186#2506C2212yes—
187#2497C2214yes—
188#2496C2214yes—
189#2489C2212yes—
190#2487C2212yes—
191#2485C2214yes—
192#2485C2212yes—
193#2485C2212yes—
194#2485C2212yes—
195#2479C2214yes—
196#2478C2214yes—
197#2471C2214yes—
198#2471C2214yes—
199#2470C2214yes—
200#2469C2214yes—
201#2465C2214yes—
202#2462C2214yes—
203#2462C2214yes—
204#2453C2212yes—
205#2451C2212yes—
206#2451C2212yes—
207#2448C2214yes—
208#2442C2212yes—
209#2441C2214yes—
210#2441C2212yes—
211#2441C2214yes—
212#2441C2214yes—
213#2441C2212yes—
214#2441C2212yes—
215#2440C2212yes—
216#2439C2212yes—
217#2429C2212yes—
218#2429C2212yes—
219#2429C2212yes—
220#2423C2212yes—
221#2421C2212yes—
222#2417C2212yes—
223#2417C2212yes—
224#2417C2212yes—
225#2415C2212yes—
226#2415C2212yes—
227#2415C2212yes—
228#2415C2212yes—
229#2415C2212yes—
230#2415C2212yes—
231#2415C2212yes—
232#2397C2212yes—
233#2392C2212yes—
234#2392C2212yes—
235#2382C2214yes—
236#2354C2212yes—
237#2352C2212yes—
238#2352C2212yes—
239#2352C2212yes—
240#2351C2212yes—
241Q8×C4⋊C4C2212yes—
242#2330C2212yes—
243#2327C2212yes—
244#2323C2214yes—
245#2323C2212yes—
246#2320C2212yes—
247#2317C2212yes—
248#2316C2212yes—
249C4×C4⋊Q8C2211yescharacteristic
250C4×C4⋊Q8C2211yescharacteristic
251C4×#127C2211yescharacteristic
252C4×#124C2212yes—
253C4×#121C2212yes—
254#2296C2212yes—
255#2295C2211yescharacteristic
256#2293C2211yescharacteristic
257#2290C2212yes—
258C42×Q8C2211yescharacteristic
259#556—44no—
260#556—48no—
261#554—44no—
262#552—48no—
263#552—48no—
264#541—48no—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×#127C2311yescharacteristic
271#529—48no—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2312yes—
276C2×#126C2312yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#125C2312yes—
285C2×#125C2314yes—
286C2×#125C2312yes—
287C2×#125C2314yes—
288C2×#125C2312yes—
289C2×#125C2314yes—
290C2×#124C2312yes—
291C2×#124C2314yes—
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#123C2314yes—
295C2×#123C2312yes—
296C2×#123C2312yes—
297C2×#123C2314yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×#121C2312yes—
311C2×#121C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2314yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×#117C2312yes—
333C2×#117C2312yes—
334C2×#117C2312yes—
335C2×#117C2312yes—
336C2×#117C2312yes—
337C2×#117C2314yes—
338C2×#117C2312yes—
339C2×#117C2314yes—
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2312yes—
342C22×C42C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2312yes—
361#399C2312yes—
362#399C2312yes—
363#399C2312yes—
364#399C2314yes—
365#399C2314yes—
366#399C2314yes—
367#399C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2312yes—
395#398C2314yes—
396#398C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2312yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2312yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2312yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2312yes—
434#396C2312yes—
435#396C2312yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#395C2314yes—
445#395C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2312yes—
449#394C2312yes—
450#394C2314yes—
451#394C2312yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2312yes—
461#394C2312yes—
462#394C2312yes—
463#394C2314yes—
464#393C2314yes—
465#393C2314yes—
466#393C2314yes—
467#392C2312yes—
468#392C2312yes—
469#392C2312yes—
470#392C2312yes—
471#392C2312yes—
472#392C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2314yes—
484#391C2312yes—
485#391C2312yes—
486#391C2312yes—
487#391C2314yes—
488#391C2312yes—
489#391C2311yescharacteristic
490#391C2314yes—
491#391C2311yescharacteristic
492#390C2312yes—
493#390C2312yes—
494#390C2311yescharacteristic
495#390C2311yescharacteristic
496#390C2312yes—
497#390C2314yes—
498#390C2312yes—
499#390C2311yescharacteristic
500#390C2312yes—
501#390C2312yes—
502#390C2314yes—
503#390C2314yes—
504#390C2314yes—
505#390C2314yes—
506#390C2311yescharacteristic
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2311yescharacteristic
547#389C2311yescharacteristic
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2314yes—
553#389C2314yes—
554#389C2312yes—
555#389C2312yes—
556#389C2314yes—
557#389C2314yes—
558#389C2312yes—
559#389C2314yes—
560#389C2314yes—
561#389C2311yescharacteristic
562#389C2311yescharacteristic
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2312yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2312yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2312yes—
590#388C2314yes—
591#388C2312yes—
592#388C2314yes—
593#388C2312yes—
594#388C2312yes—
595#388C2314yes—
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#387C2312yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2312yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2312yes—
631#387C2312yes—
632#387C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2312yes—
641#386C2312yes—
642#386C2312yes—
643#386C2312yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2312yes—
654#385C2314yes—
655#385C2312yes—
656#384C2311yescharacteristic
657#384C2311yescharacteristic
658#384C2311yescharacteristic
659#384C2312yes—
660#384C2312yes—
661#384C2312yes—
662#384C2312yes—
663#384C2312yes—
664#384C2312yes—
665#384C2314yes—
666#383C2314yes—
667#382C2312yes—
668#382C2314yes—
669#382C2314yes—
670#382C2312yes—
671#382C2312yes—
672#382C2312yes—
673#382C2314yes—
674#381C2314yes—
675#380C2312yes—
676#380C2312yes—
677#380C2314yes—
678#380C2314yes—
679#380C2314yes—
680#380C2312yes—
681#380C2312yes—
682#380C2314yes—
683#380C2314yes—
684#380C2312yes—
685#380C2312yes—
686#380C2312yes—
687#380C2312yes—
688#380C2312yes—
689#380C2314yes—
690#380C2314yes—
691#380C2312yes—
692#380C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2311yescharacteristic
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2311yescharacteristic
702C4×C4⋊C4C2311yescharacteristic
703C4×C4⋊C4C2311yescharacteristic
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2314yes—
706C4×C4⋊C4C2314yes—
707C4×C4⋊C4C2314yes—
708C4×C4⋊C4C2311yescharacteristic
709C4×C4⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716#376C2312yes—
717C43C2311yescharacteristic
718C43C2312yes—
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×D4C2411yescharacteristic
726C22×D4C2411yescharacteristic
727C22×D4C2412yes—
728C22×D4C2412yes—
729C22×D4C2411yescharacteristic
730C22×D4C2412yes—
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2412yes—
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2412yes—
737C23×C4C2414yes—
738C23×C4C2414yes—
739C23×C4C2412yes—
740C23×C4C2412yes—
741C4⋊Q8—24no—
742C4⋊Q8—24no—
743C4⋊Q8—42no—
744C4⋊Q8—42no—
745C4⋊Q8—44no—
746#127—42no—
747#126—48no—
748#126—48no—
749#126—48no—
750#126—44no—
751#126—44no—
752#126—48no—
753#126—48no—
754#126—48no—
755#126—48no—
756#125—28no—
757#125—48no—
758#125—44no—
759#125—48no—
760#125—48no—
761#125—48no—
762#125—44no—
763#125—44no—
764#125—48no—
765#124—44no—
766#124—44no—
767#124—48no—
768#124—44no—
769#123—44no—
770#123—48no—
771#123—48no—
772#123—44no—
773C22⋊Q8—28no—
774C22⋊Q8—48no—
775C22⋊Q8—44no—
776C22⋊Q8—48no—
777C22⋊Q8—44no—
778C22⋊Q8—44no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781C22⋊Q8—44no—
782C22⋊Q8—44no—
783C22⋊Q8—44no—
784C22⋊Q8—44no—
785#121—44no—
786#121—44no—
787C4×Q8—24no—
788C4×Q8—24no—
789C4×Q8—24no—
790C4×Q8—28no—
791C4×Q8—24no—
792C4×Q8—44no—
793C4×Q8—44no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×Q8—48no—
797C4×D4—28no—
798C4×D4—28no—
799C4×D4—24no—
800C4×D4—44no—
801C4×D4—44no—
802C4×D4—44no—
803C4×D4—44no—
804C4×D4—42no—
805C4×D4—44no—
806C4×D4—42no—
807#117—28no—
808#117—28no—
809#117—44no—
810#117—48no—
811#117—44no—
812#117—48no—
813#117—44no—
814#117—44no—
815C2×C4⋊C4—28no—
816C2×C4⋊C4—44no—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊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⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2411yescharacteristic
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C42—44no—
942C2×C42C2414yes—
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2411yescharacteristic
947C2×C42C2412yes—
948C2×C42C2414yes—
949C2×C42C2411yescharacteristic
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2411yescharacteristic
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025C24C2512yes—
1026C24C2512yes—
1027C24C2512yes—
1028C2×Q8—22no—
1029C2×Q8—24no—
1030C2×Q8—22no—
1031C2×Q8—24no—
1032C2×Q8—24no—
1033C2×Q8—22no—
1034C2×Q8—22no—
1035C2×Q8—24no—
1036C2×Q8—24no—
1037C2×Q8—42no—
1038C2×Q8—42no—
1039C2×Q8—42no—
1040C2×Q8—41no—
1041C2×Q8—41no—
1042C2×Q8—42no—
1043C2×Q8—42no—
1044C2×Q8—42no—
1045C2×Q8—42no—
1046C2×D4—24no—
1047C2×D4—22no—
1048C2×D4—24no—
1049C2×D4—22no—
1050C2×D4—22no—
1051C2×D4—41no—
1052C2×D4—41no—
1053C2×D4—42no—
1054C2×D4—42no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—41no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—42no—
1062C2×D4—41no—
1063C2×D4—41no—
1064C2×D4—42no—
1065C2×D4—41no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C2×D4—42no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—42no—
1072C2×D4—42no—
1073C22×C4—24no—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—24no—
1082C22×C4—28no—
1083C22×C4—42no—
1084C22×C4—42no—
1085C22×C4—44no—
1086C22×C4—42no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2511yescharacteristic
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2514yes—
1101C22×C4C2512yes—
1102C22×C4C2514yes—
1103C22×C4C2514yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2514yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2514yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2512yes—
1115C22×C4C2511yescharacteristic
1116C22×C4C2511yescharacteristic
1117C22×C4C2511yescharacteristic
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—28no—
1129C4⋊C4—28no—
1130C4⋊C4—28no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—22no—
1134C4⋊C4—24no—
1135C4⋊C4—22no—
1136C4⋊C4—24no—
1137C4⋊C4—28no—
1138C4⋊C4—24no—
1139C4⋊C4—22no—
1140C4⋊C4—24no—
1141C4⋊C4—22no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—28no—
1146C4⋊C4—24no—
1147C4⋊C4—44no—
1148C4⋊C4—41no—
1149C4⋊C4—41no—
1150C4⋊C4—42no—
1151C4⋊C4—41no—
1152C4⋊C4—42no—
1153C4⋊C4—41no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—41no—
1169C4⋊C4—42no—
1170C4⋊C4—41no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
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—44no—
1194C4⋊C4—44no—
1195C4⋊C4—42no—
1196C4⋊C4H(5,𝔽2)14yes—
1197C22⋊C4—24no—
1198C22⋊C4—24no—
1199C22⋊C4—28no—
1200C22⋊C4—28no—
1201C22⋊C4—24no—
1202C22⋊C4—24no—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—24no—
1206C22⋊C4—24no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—42no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—42no—
1214C22⋊C4—44no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—44no—
1221C22⋊C4—42no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—42no—
1226C22⋊C4—44no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
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—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C42—24no—
1245C42—24no—
1246C42—28no—
1247C42—22no—
1248C42—24no—
1249C42—24no—
1250C42—28no—
1251C42—24no—
1252C42—24no—
1253C42—22no—
1254C42—24no—
1255C42—42no—
1256C42—42no—
1257C42—42no—
1258C42—41no—
1259C42—42no—
1260C42—41no—
1261C42—41no—
1262C42—44no—
1263C42—44no—
1264C42—44no—
1265C42—44no—
1266C42—44no—
1267C42—44no—
1268C42H(5,𝔽2)14yes—
1269C422−1+414yes—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—22no—
1275C23—22no—
1276C23—22no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—22no—
1282C23—22no—
1283C23—22no—
1284C23—22no—
1285C23—22no—
1286C23—22no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23C2611yescharacteristic
1292Q8—48no—
1293Q8—44no—
1294Q8—48no—
1295Q8—82no—
1296Q8—84no—
1297Q8—162no—
1298D4—44no—
1299D4—82no—
1300D4—82no—
1301D4—84no—
1302D4—84no—
1303D4—84no—
1304D4—84no—
1305D4—84no—
1306D4—84no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—21no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—22no—
1373C2×C4—24no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—48no—
1377C2×C4—48no—
1378C2×C4—48no—
1379C2×C4—88no—
1380C2×C4—84no—
1381C2×C4—88no—
1382C2×C4—84no—
1383C2×C4C2×H(5,𝔽2)12yes—
1384C2×C4C2×H(5,𝔽2)14yes—
1385C2×C4C2×H(5,𝔽2)12yes—
1386C2×C4C2×H(5,𝔽2)12yes—
1387C2×C4C2×H(5,𝔽2)12yes—
1388C2×C4C2×2−1+412yes—
1389C2×C4C2×2−1+412yes—
1390C2×C4C2×2−1+412yes—
1391C2×C4#58512yes—
1392C22—42no—
1393C22—42no—
1394C22—42no—
1395C22—42no—
1396C22—42no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—42no—
1408C22—42no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22C22×H(5,𝔽2)11yescharacteristic
1414C22C22×H(5,𝔽2)11yescharacteristic
1415C22C22×2−1+411yescharacteristic
1416C22C2×#58511yescharacteristic
1417C222−1+611yescharacteristic
1418C222−1+611yescharacteristic
1419C222−1+611yescharacteristic
1420C4—24no—
1421C4—22no—
1422C4—22no—
1423C4—22no—
1424C4—22no—
1425C4—22no—
1426C4—42no—
1427C4—42no—
1428C4—42no—
1429C4—42no—
1430C4—44no—
1431C4—44no—
1432C4—42no—
1433C4—41no—
1434C4—44no—
1435C4—42no—
1436C4—42no—
1437C4—44no—
1438C4—44no—
1439C4—42no—
1440C4—42no—
1441C4—42no—
1442C4—42no—
1443C4—44no—
1444C4—42no—
1445C4#354814yes—
1446C2—82no—
1447C2—82no—
1448C2—82no—
1449C2C2×#354811yescharacteristic
1450C2#6288811yescharacteristic
1451C2#6288911yescharacteristic
1452C2#6289711yescharacteristic
1453C2#6292511yescharacteristic
1454C2#6295911yescharacteristic
1455C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#52160C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59821C2semidirect
2. #58422C2semidirect
3. #57572C2semidirect
4. #57493C2semidirect
5. #57359C2semidirect
6. #57240C2semidirect
7. #53374C2semidirect
8. #53365C2semidirect
9. #53122C2semidirect
11. #50058C2semidirect
12. #46158C2semidirect
13. #45717C2semidirect
14. #45432C2semidirect
15. #45264C2semidirect
16. #42878C2semidirect
17. #42690C2semidirect
18. #42675C2semidirect
19. #39959C2semidirect
20. #39629C2semidirect
21. #39493C2semidirect
22. #38107C2semidirect
23. #38051C2semidirect
24. #37399C2semidirect
25. #37378C2semidirect
26. #37207C2semidirect
27. #36534C2semidirect
28. #35209C2semidirect
29. #35208C2semidirect

Maximal subgroups

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

subgroupindex
#598212
#584222
#575722
#574932
#573592
#572402
#533742
#533652
#531222
#521602
#500582
#461582
#457172
#454322
#452642
#428782
#426902
#426752
#399592
#396292
#394932
#381072
#380512
#373992
#373782
#372072
#365342
#352092
#352082