Finite Group Databasebeta

← #8751531

Subgroups — #8751531

Order 512.

5513 conjugacy classes of subgroups.

The subgroup lattice has 1586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59946C211yesmaximal, characteristic, complemented
2#59765C212yesmaximal, complemented
3#58801C212yesmaximal, complemented
4#58177C214yesmaximal, complemented
5#57609C214yesmaximal, complemented
6#57297C214yesmaximal, complemented
7#57184C214yesmaximal, complemented
8#52966C211yesmaximal, characteristic, complemented
9#52956C212yesmaximal, complemented
10#52415C214yesmaximal, complemented
11#52414C212yesmaximal, complemented
12#47663C212yesmaximal, complemented
13#45307C212yesmaximal, complemented
14#45269C212yesmaximal, complemented
15#45244C211yesmaximal, characteristic, complemented
16#44935C212yesmaximal, complemented
17#44884C212yesmaximal, complemented
18#42916C211yesmaximal, characteristic, complemented
19#42908C212yesmaximal, complemented
20#42844C212yesmaximal, complemented
21#42829C212yesmaximal, complemented
22#42598C212yesmaximal, complemented
23#42101C214yesmaximal, complemented
24#42023C212yesmaximal, complemented
25#39954C212yesmaximal, complemented
26#38956C211yesmaximal, characteristic, complemented
27#36694C211yesmaximal, characteristic, complemented
28#36085C211yesmaximal, characteristic, complemented
29#35757C212yesmaximal, complemented
30C22×2−1+4C2211yescharacteristic
31C2×#556C2212yes—
32C2×#550C2211yescharacteristic
33C2×#550C2212yes—
34C2×#548C2212yes—
35C2×#548C2212yes—
36C2×#547C2211yescharacteristic
37C2×#547C2212yes—
38C2×#537C2211yescharacteristic
39C2×#537C2212yes—
40#2858C2211yescharacteristic
41#2844C2211yescharacteristic
42#2838C2214yes—
43#2833C2214yes—
44#2832C2212yes—
45#2832C2211yescharacteristic
46#2832C2211yescharacteristic
47#2832C2212yes—
48#2831C2214yes—
49#2830C2212yes—
50#2829C2214yes—
51#2828C2212yes—
52#2828C2212yes—
53#2828C2212yes—
54#2826C2214yes—
55#2825C2214yes—
56#2825C2214yes—
57#2824C2214yes—
58#2819C2212yes—
59#2819C2211yescharacteristic
60#2817C2214yes—
61#2815C2212yes—
62#2814C2212yes—
63#2804C2214yes—
64#2796C2214yes—
65#2789C2212yes—
66#2788C2214yes—
67#2788C2214yes—
68#2784C2214yes—
69#2778C2214yes—
70#2774C2214yes—
71#2760C2212yes—
72#2760C2214yes—
73#2750C2214yes—
74#2746C2214yes—
75#2745C2214yes—
76#2743C2214yes—
77#2723C2214yes—
78#2717C2212yes—
79#2715C2214yes—
80#2714C2214yes—
81#2714C2214yes—
82#2714C2214yes—
83#2714C2214yes—
84#2708C2214yes—
85#2705C2214yes—
86#2703C2214yes—
87#2703C2214yes—
88#2703C2214yes—
89#2701C2214yes—
90#2700C2214yes—
91#2699C2212yes—
92#2696C2214yes—
93#2696C2214yes—
94#2695C2214yes—
95#2692C2214yes—
96#2691C2214yes—
97#2689C2214yes—
98#2688C2214yes—
99#2688C2214yes—
100#2688C2214yes—
101#2688C2214yes—
102#2688C2214yes—
103#2686C2214yes—
104#2686C2214yes—
105#2683C2212yes—
106#2682C2214yes—
107#2681C2214yes—
108#2676C2214yes—
109#2676C2214yes—
110#2675C2212yes—
111#2675C2214yes—
112#2673C2214yes—
113#2673C2214yes—
114#2673C2214yes—
115#2673C2214yes—
116#2671C2214yes—
117#2665C2214yes—
118#2662C2214yes—
119#2661C2212yes—
120#2653C2214yes—
121#2653C2214yes—
122#2652C2214yes—
123#2645C2212yes—
124#2643C2214yes—
125#2639C2214yes—
126#2635C2214yes—
127#2635C2214yes—
128#2619C2212yes—
129#2618C2212yes—
130#2616C2211yescharacteristic
131#2616C2211yescharacteristic
132#2615C2214yes—
133#2615C2212yes—
134#2614C2212yes—
135#2610C2214yes—
136#2603C2214yes—
137#2603C2214yes—
138#2592C2212yes—
139#2586C2212yes—
140#2583C2212yes—
141#2582C2212yes—
142#2581C2212yes—
143#2580C2212yes—
144#2576C2214yes—
145#2568C2211yescharacteristic
146#2564C2214yes—
147#2559C2214yes—
148#2557C2214yes—
149#2555C2212yes—
150#2541C2211yescharacteristic
151#2540C2212yes—
152#2538C2212yes—
153#2535C2212yes—
154#2535C2212yes—
155#2530C2214yes—
156#2527C2214yes—
157#2527C2214yes—
158#2505C2214yes—
159#2504C2212yes—
160#2503C2212yes—
161#2502C2211yescharacteristic
162#2496C2212yes—
163#2494C2212yes—
164#2494C2212yes—
165#2487C2212yes—
166#2486C2211yescharacteristic
167#2481C2214yes—
168#2481C2214yes—
169#2479C2214yes—
170#2476C2214yes—
171#2471C2214yes—
172#2471C2214yes—
173#2466C2214yes—
174#2464C2214yes—
175#2463C2212yes—
176#2450C2214yes—
177#2449C2214yes—
178#2444C2214yes—
179#2444C2214yes—
180#2444C2214yes—
181#2438C2214yes—
182#2436C2214yes—
183#2436C2212yes—
184#2434C2212yes—
185#2434C2211yescharacteristic
186#2432C2212yes—
187#2431C2212yes—
188#2431C2212yes—
189#2431C2212yes—
190#2431C2212yes—
191#2431C2214yes—
192#2431C2212yes—
193#2431C2214yes—
194#2430C2214yes—
195#2430C2214yes—
196#2430C2214yes—
197#2430C2212yes—
198#2429C2212yes—
199#2429C2212yes—
200#2428C2212yes—
201#2428C2212yes—
202#2428C2214yes—
203#2428C2214yes—
204#2427C2212yes—
205#2427C2212yes—
206#2427C2212yes—
207#2426C2212yes—
208#2426C2212yes—
209#2422C2212yes—
210#2422C2212yes—
211#2421C2212yes—
212#2421C2212yes—
213#2421C2212yes—
214#2420C2212yes—
215#2417C2212yes—
216#2416C2214yes—
217#2416C2212yes—
218#2416C2212yes—
219#2409C2214yes—
220#2409C2211yescharacteristic
221#2409C2212yes—
222#2409C2212yes—
223#2407C2214yes—
224#2407C2212yes—
225#2407C2214yes—
226#2407C2212yes—
227#2406C2212yes—
228#2406C2214yes—
229#2398C2212yes—
230#2398C2212yes—
231#2398C2212yes—
232#2388C2212yes—
233#2388C2211yescharacteristic
234#2388C2212yes—
235#2388C2211yescharacteristic
236#2388C2214yes—
237C2×#395C2212yes—
238#2374C2212yes—
239#2361C2212yes—
240#2360C2212yes—
241#2360C2212yes—
242#2359C2214yes—
243#2341C2212yes—
244#2341C2211yescharacteristic
245Q8×C22⋊C4C2212yes—
246Q8×C22⋊C4C2212yes—
247#2339C2211yescharacteristic
248#2339C2212yes—
249#2339C2212yes—
250#2328C2212yes—
251#2327C2212yes—
252#2326C2212yes—
253#2324C2214yes—
254#2311C2212yes—
255C4×#124C2212yes—
256C4×#124C2211yescharacteristic
257#2295C2212yes—
258#2293C2211yescharacteristic
259C2×2−1+4—48no—
260C2×2−1+4—44no—
261C22×#41C2312yes—
262C22×#41C2311yescharacteristic
263C22×#41C2312yes—
264C22×#41C2311yescharacteristic
265C22×#41C2311yescharacteristic
266C22×#41C2314yes—
267C22×#41C2312yes—
268C22×#41C2311yescharacteristic
269C22×#41C2312yes—
270C23×Q8C2311yescharacteristic
271C23×Q8C2312yes—
272C23×Q8C2312yes—
273#556—48no—
274#550—44no—
275#550—48no—
276#548—48no—
277#548—48no—
278#547—44no—
279#547—48no—
280#537—44no—
281#537—48no—
282C2×C4⋊Q8C2312yes—
283C2×C4⋊Q8C2311yescharacteristic
284C2×#127C2312yes—
285C2×#127C2311yescharacteristic
286C2×#127C2314yes—
287C2×#127C2312yes—
288C2×#126C2314yes—
289C2×#126C2314yes—
290C2×#126C2314yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2311yescharacteristic
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#124C2314yes—
297C2×#124C2314yes—
298C2×#123C2314yes—
299C2×#123C2312yes—
300C2×#123C2314yes—
301C2×#123C2312yes—
302C2×#123C2312yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2311yescharacteristic
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2311yescharacteristic
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2314yes—
317C2×#121C2312yes—
318C2×#121C2314yes—
319C2×#121C2314yes—
320C2×#121C2312yes—
321C2×#121C2312yes—
322C2×#121C2314yes—
323C2×#121C2314yes—
324C2×#121C2312yes—
325C2×#121C2312yes—
326C2×#121C2312yes—
327C2×#121C2312yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331C2×#121C2314yes—
332C2×#121C2314yes—
333C2×#121C2312yes—
334C2×#121C2312yes—
335C2×#121C2314yes—
336C2×#121C2314yes—
337C2×#121C2314yes—
338C2×#121C2314yes—
339C2×#121C2314yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2311yescharacteristic
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2312yes—
346C2×C4×D4C2311yescharacteristic
347C2×C4×D4C2314yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2312yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2311yescharacteristic
356C2×C4×D4C2314yes—
357C2×C4×D4C2314yes—
358C2×C4×D4C2314yes—
359C2×#117C2314yes—
360C2×#117C2312yes—
361C22×C4⋊C4C2312yes—
362C22×C4⋊C4C2311yescharacteristic
363C22×C4⋊C4C2312yes—
364C22×C4⋊C4C2314yes—
365#401C2314yes—
366#401C2314yes—
367#401C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2312yes—
377#400C2312yes—
378#400C2312yes—
379#400C2314yes—
380#400C2314yes—
381#400C2312yes—
382#400C2312yes—
383#400C2312yes—
384#400C2314yes—
385#400C2314yes—
386#399C2314yes—
387#399C2314yes—
388#399C2314yes—
389#398C2314yes—
390#398C2312yes—
391#398C2312yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2312yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2312yes—
408#397C2312yes—
409#397C2312yes—
410#397C2312yes—
411#397C2312yes—
412#397C2312yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#395C2312yes—
429#395C2312yes—
430#395C2314yes—
431#395C2314yes—
432#395C2311yescharacteristic
433#395C2312yes—
434#395C2311yescharacteristic
435#395C2314yes—
436#395C2314yes—
437#395C2312yes—
438#395C2312yes—
439#395C2312yes—
440#395C2314yes—
441#395C2312yes—
442#394C2312yes—
443#394C2312yes—
444#394C2312yes—
445#394C2312yes—
446#394C2311yescharacteristic
447#394C2312yes—
448#394C2311yescharacteristic
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2312yes—
454#394C2312yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2312yes—
460#394C2312yes—
461#394C2312yes—
462#394C2312yes—
463#394C2312yes—
464#394C2312yes—
465#394C2312yes—
466#394C2312yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2312yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#393C2312yes—
479#393C2312yes—
480#393C2312yes—
481#393C2312yes—
482#393C2312yes—
483#393C2312yes—
484#393C2312yes—
485#393C2314yes—
486#393C2314yes—
487#393C2314yes—
488#393C2314yes—
489#393C2311yescharacteristic
490#393C2312yes—
491#393C2311yescharacteristic
492#393C2314yes—
493#393C2312yes—
494#393C2314yes—
495#393C2314yes—
496#392C2312yes—
497#392C2312yes—
498#392C2312yes—
499#392C2312yes—
500#392C2312yes—
501#392C2312yes—
502#392C2314yes—
503#392C2312yes—
504#392C2314yes—
505#392C2314yes—
506#392C2314yes—
507#392C2314yes—
508#392C2314yes—
509#392C2314yes—
510#392C2312yes—
511#392C2311yescharacteristic
512#392C2311yescharacteristic
513#392C2312yes—
514#392C2314yes—
515#392C2314yes—
516#392C2314yes—
517#392C2314yes—
518#392C2314yes—
519#392C2314yes—
520#392C2314yes—
521#392C2314yes—
522#392C2314yes—
523#392C2314yes—
524#392C2314yes—
525#392C2312yes—
526#391C2311yescharacteristic
527#391C2312yes—
528#391C2312yes—
529#391C2312yes—
530#391C2314yes—
531#391C2312yes—
532#391C2314yes—
533#391C2312yes—
534#391C2312yes—
535#391C2312yes—
536#391C2312yes—
537#391C2314yes—
538#391C2314yes—
539#391C2312yes—
540#391C2312yes—
541#391C2314yes—
542#390C2312yes—
543#390C2312yes—
544#390C2312yes—
545#390C2311yescharacteristic
546#390C2314yes—
547#390C2314yes—
548#390C2312yes—
549#390C2312yes—
550#390C2312yes—
551#390C2312yes—
552#390C2314yes—
553#390C2314yes—
554#390C2314yes—
555#390C2314yes—
556#390C2312yes—
557#390C2314yes—
558#390C2314yes—
559#390C2314yes—
560#389C2314yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2314yes—
566#389C2312yes—
567#389C2312yes—
568#389C2314yes—
569#389C2314yes—
570#389C2314yes—
571#389C2314yes—
572#388C2312yes—
573#388C2312yes—
574#388C2312yes—
575#388C2312yes—
576#388C2312yes—
577#388C2312yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
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#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2312yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2312yes—
667#385C2314yes—
668#385C2314yes—
669#384C2312yes—
670#382C2312yes—
671#382C2311yescharacteristic
672#382C2312yes—
673#382C2312yes—
674#382C2312yes—
675#381C2314yes—
676#381C2314yes—
677#381C2314yes—
678#381C2312yes—
679#381C2314yes—
680#381C2314yes—
681#381C2312yes—
682#380C2314yes—
683#380C2314yes—
684#380C2314yes—
685#380C2311yescharacteristic
686#380C2312yes—
687#380C2312yes—
688#380C2312yes—
689#380C2312yes—
690#380C2314yes—
691#380C2314yes—
692#380C2312yes—
693#380C2314yes—
694#380C2311yescharacteristic
695#380C2312yes—
696#380C2314yes—
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2311yescharacteristic
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2311yescharacteristic
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717#376C2312yes—
718#376C2314yes—
719C2×#95C2314yes—
720C2×#95C2314yes—
721C2×#95C2312yes—
722C43C2311yescharacteristic
7232−1+4—464no—
724C2×#41—28no—
725C2×#41—28no—
726C2×#41—24no—
727C2×#41—28no—
728C2×#41—24no—
729C2×#41—48no—
730C2×#41—44no—
731C2×#41—42no—
732C2×#41—42no—
733C2×#41—44no—
734C2×#41—44no—
735C2×#41—48no—
736C2×#41—44no—
737C2×#41—44no—
738C2×#41—44no—
739C2×#41—48no—
740C2×#41—48no—
741C2×#41—44no—
742C2×#41—44no—
743C2×#41—44no—
744C2×#41—44no—
745C2×#41—82no—
746C22×Q8—28no—
747C22×Q8—28no—
748C22×Q8—44no—
749C22×Q8—48no—
750C22×Q8—44no—
751C22×Q8—44no—
752C22×Q8—42no—
753C22×Q8C2411yescharacteristic
754C22×Q8C2411yescharacteristic
755C22×Q8C2412yes—
756C22×Q8C2412yes—
757C22×Q8C2411yescharacteristic
758C22×Q8C2414yes—
759C22×Q8C2412yes—
760C22×Q8C2411yescharacteristic
761C22×Q8C2411yescharacteristic
762C22×D4C2412yes—
763C22×D4C2414yes—
764C22×D4C2411yescharacteristic
765C22×D4C2414yes—
766C22×D4C2411yescharacteristic
767C22×D4C2414yes—
768C22×D4C2412yes—
769C22×D4C2414yes—
770C22×D4C2414yes—
771C22×D4C2412yes—
772C22×D4C2412yes—
773C22×D4C2412yes—
774C22×D4C2412yes—
775C22×D4C2414yes—
776C22×D4C2414yes—
777C22×D4C2412yes—
778C22×D4C2412yes—
779C22×D4C2411yescharacteristic
780C22×D4C2412yes—
781C22×D4C2414yes—
782C22×D4C2414yes—
783C22×D4C2414yes—
784C22×D4C2412yes—
785C22×D4C2412yes—
786C22×D4C2411yescharacteristic
787C23×C4C2412yes—
788C23×C4C2411yescharacteristic
789C23×C4C2411yescharacteristic
790C23×C4C2412yes—
791C23×C4C2412yes—
792C23×C4C2414yes—
793C23×C4C2412yes—
794C23×C4C2412yes—
795C23×C4C2412yes—
796C23×C4C2414yes—
797C23×C4C2414yes—
798C23×C4C2414yes—
799C23×C4C2414yes—
800C23×C4C2412yes—
801C23×C4C2414yes—
802C23×C4C2414yes—
803C4⋊Q8—28no—
804C4⋊Q8—42no—
805#127—28no—
806#127—42no—
807#127—48no—
808#127—82no—
809#126—48no—
810#126—48no—
811#126—84no—
812#124—28no—
813#124—44no—
814#124—42no—
815#124—48no—
816#124—44no—
817#124—44no—
818#124—48no—
819#123—48no—
820#123—48no—
821#123—44no—
822#123—44no—
823#123—44no—
824#123—48no—
825#123—84no—
826C22⋊Q8—28no—
827C22⋊Q8—28no—
828C22⋊Q8—44no—
829C22⋊Q8—48no—
830C22⋊Q8—48no—
831C22⋊Q8—48no—
832C22⋊Q8—44no—
833C22⋊Q8—44no—
834C22⋊Q8—42no—
835C22⋊Q8—42no—
836C22⋊Q8—44no—
837C22⋊Q8—48no—
838#121—28no—
839#121—48no—
840#121—48no—
841#121—48no—
842#121—48no—
843#121—48no—
844#121—48no—
845#121—48no—
846#121—48no—
847#121—48no—
848#121—44no—
849#121—44no—
850#121—44no—
851#121—44no—
852#121—48no—
853#121—44no—
854#121—44no—
855#121—44no—
856#121—44no—
857#121—48no—
858#121—84no—
859#121—84no—
860#121—84no—
861C4×Q8—28no—
862C4×Q8—42no—
863C4×Q8—44no—
864C4×Q8—44no—
865C4×Q8—44no—
866C4×Q8—44no—
867C4×D4—24no—
868C4×D4—44no—
869C4×D4—44no—
870C4×D4—44no—
871C4×D4—42no—
872C4×D4—44no—
873C4×D4—48no—
874C4×D4—44no—
875C4×D4—44no—
876C4×D4—44no—
877C4×D4—48no—
878C4×D4—48no—
879C4×D4—84no—
880#117—48no—
881#117—82no—
882C2×C4⋊C4—44no—
883C2×C4⋊C4—42no—
884C2×C4⋊C4—48no—
885C2×C4⋊C4—44no—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2411yescharacteristic
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2411yescharacteristic
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2411yescharacteristic
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2412yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2412yes—
980C2×C22⋊C4C2412yes—
981C2×C22⋊C4C2412yes—
982C2×C22⋊C4C2412yes—
983C2×C22⋊C4C2414yes—
984C2×C22⋊C4C2414yes—
985C2×C22⋊C4C2412yes—
986C2×C22⋊C4C2412yes—
987C2×C22⋊C4C2412yes—
988C2×C22⋊C4C2412yes—
989C2×C22⋊C4C2412yes—
990C2×C22⋊C4C2414yes—
991C2×C22⋊C4C2414yes—
992C2×C42C2414yes—
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2411yescharacteristic
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2411yescharacteristic
999C2×C42C2411yescharacteristic
1000C2×C42C2414yes—
1001C2×C42C2412yes—
1002C2×C42C2414yes—
1003C2×C42C2414yes—
1004C2×C42C2414yes—
1005C2×C42C2412yes—
1006#95C2412yes—
1007#95C2411yescharacteristic
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2411yescharacteristic
1027#95C2414yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2411yescharacteristic
1035#95C2411yescharacteristic
1036#95C2412yes—
1037#95C2412yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2414yes—
1052#95C2412yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2414yes—
1062#95C2414yes—
1063#95C2414yes—
1064#95C2414yes—
1065C24C2514yes—
1066C24C2511yescharacteristic
1067C24C2512yes—
1068C24C2511yescharacteristic
1069C24C2512yes—
1070C24C2512yes—
1071#41—432no—
1072#41—416no—
1073#41—464no—
1074#41—432no—
1075#41—416no—
1076#41—88no—
1077#41—88no—
1078#41—816no—
1079#41—816no—
1080C2×Q8—24no—
1081C2×Q8—24no—
1082C2×Q8—24no—
1083C2×Q8—22no—
1084C2×Q8—28no—
1085C2×Q8—28no—
1086C2×Q8—24no—
1087C2×Q8—22no—
1088C2×Q8—22no—
1089C2×Q8—41no—
1090C2×Q8—42no—
1091C2×Q8—44no—
1092C2×Q8—44no—
1093C2×Q8—41no—
1094C2×Q8—42no—
1095C2×Q8—41no—
1096C2×Q8—42no—
1097C2×Q8—41no—
1098C2×Q8—42no—
1099C2×Q8—42no—
1100C2×Q8—42no—
1101C2×Q8—416no—
1102C2×Q8—432no—
1103C2×Q8—432no—
1104C2×Q8H(5,𝔽2)18yes—
1105C2×D4—24no—
1106C2×D4—28no—
1107C2×D4—28no—
1108C2×D4—28no—
1109C2×D4—24no—
1110C2×D4—28no—
1111C2×D4—24no—
1112C2×D4—24no—
1113C2×D4—24no—
1114C2×D4—24no—
1115C2×D4—28no—
1116C2×D4—28no—
1117C2×D4—24no—
1118C2×D4—22no—
1119C2×D4—44no—
1120C2×D4—42no—
1121C2×D4—44no—
1122C2×D4—42no—
1123C2×D4—42no—
1124C2×D4—42no—
1125C2×D4—41no—
1126C2×D4—41no—
1127C2×D4—42no—
1128C2×D4—44no—
1129C2×D4—42no—
1130C2×D4—42no—
1131C2×D4—44no—
1132C2×D4—42no—
1133C2×D4—44no—
1134C2×D4—42no—
1135C2×D4—42no—
1136C2×D4—42no—
1137C2×D4—42no—
1138C2×D4—41no—
1139C2×D4—44no—
1140C2×D4—44no—
1141C2×D4—42no—
1142C2×D4—44no—
1143C2×D4—44no—
1144C2×D4—42no—
1145C2×D4—42no—
1146C2×D4—44no—
1147C2×D4—44no—
1148C2×D4—44no—
1149C2×D4—42no—
1150C2×D4—41no—
1151C2×D4—42no—
1152C2×D4—42no—
1153C2×D4—42no—
1154C2×D4—44no—
1155C2×D4—42no—
1156C2×D4—44no—
1157C2×D4—44no—
1158C2×D4—44no—
1159C2×D4—42no—
1160C2×D4—42no—
1161C2×D4—44no—
1162C2×D4—44no—
1163C2×D4—44no—
1164C2×D4—42no—
1165C2×D4—44no—
1166C2×D4—44no—
1167C2×D4—44no—
1168C2×D4—44no—
1169C2×D4—44no—
1170C2×D4—44no—
1171C2×D4—44no—
1172C2×D4—44no—
1173C2×D4H(5,𝔽2)14yes—
1174C22×C4—24no—
1175C22×C4—24no—
1176C22×C4—28no—
1177C22×C4—24no—
1178C22×C4—24no—
1179C22×C4—22no—
1180C22×C4—28no—
1181C22×C4—24no—
1182C22×C4—24no—
1183C22×C4—24no—
1184C22×C4—28no—
1185C22×C4—28no—
1186C22×C4—24no—
1187C22×C4—24no—
1188C22×C4—24no—
1189C22×C4—24no—
1190C22×C4—22no—
1191C22×C4—24no—
1192C22×C4—28no—
1193C22×C4—42no—
1194C22×C4—42no—
1195C22×C4—44no—
1196C22×C4—44no—
1197C22×C4—44no—
1198C22×C4—44no—
1199C22×C4—44no—
1200C22×C4—44no—
1201C22×C4—44no—
1202C22×C4—44no—
1203C22×C4—44no—
1204C22×C4—44no—
1205C22×C4—44no—
1206C22×C4—44no—
1207C22×C4—44no—
1208C22×C4—44no—
1209C22×C4—44no—
1210C22×C4—44no—
1211C22×C4—44no—
1212C22×C4—42no—
1213C22×C4—44no—
1214C22×C4—42no—
1215C22×C4—42no—
1216C22×C4—44no—
1217C22×C4C2512yes—
1218C22×C4C2511yescharacteristic
1219C22×C4C2512yes—
1220C22×C4C2512yes—
1221C22×C4C2512yes—
1222C22×C4C2514yes—
1223C22×C4C2514yes—
1224C22×C4C2512yes—
1225C22×C4C2514yes—
1226C22×C4C2512yes—
1227C22×C4C2511yescharacteristic
1228C22×C4C2512yes—
1229C22×C4C2512yes—
1230C22×C4C2514yes—
1231C22×C4C2512yes—
1232C22×C4C2512yes—
1233C22×C4C2512yes—
1234C22×C4C2511yescharacteristic
1235C22×C4C2512yes—
1236C22×C4C2512yes—
1237C22×C4C2514yes—
1238C22×C4C2511yescharacteristic
1239C22×C4C2511yescharacteristic
1240C4⋊C4—24no—
1241C4⋊C4—24no—
1242C4⋊C4—24no—
1243C4⋊C4—28no—
1244C4⋊C4—28no—
1245C4⋊C4—28no—
1246C4⋊C4—22no—
1247C4⋊C4—24no—
1248C4⋊C4—28no—
1249C4⋊C4—28no—
1250C4⋊C4—28no—
1251C4⋊C4—41no—
1252C4⋊C4—42no—
1253C4⋊C4—44no—
1254C4⋊C4—42no—
1255C4⋊C4—42no—
1256C4⋊C4—44no—
1257C4⋊C4—42no—
1258C4⋊C4—42no—
1259C4⋊C4—44no—
1260C4⋊C4—42no—
1261C4⋊C4—44no—
1262C4⋊C4—42no—
1263C4⋊C4—42no—
1264C4⋊C4—44no—
1265C4⋊C4—42no—
1266C4⋊C4—44no—
1267C4⋊C4—41no—
1268C4⋊C4—44no—
1269C4⋊C4—42no—
1270C4⋊C4—44no—
1271C4⋊C4—44no—
1272C4⋊C4—42no—
1273C4⋊C4—42no—
1274C4⋊C4—44no—
1275C4⋊C4—44no—
1276C4⋊C4—44no—
1277C4⋊C4—44no—
1278C4⋊C4—42no—
1279C4⋊C4—44no—
1280C22⋊C4—24no—
1281C22⋊C4—28no—
1282C22⋊C4—28no—
1283C22⋊C4—28no—
1284C22⋊C4—28no—
1285C22⋊C4—28no—
1286C22⋊C4—24no—
1287C22⋊C4—24no—
1288C22⋊C4—42no—
1289C22⋊C4—42no—
1290C22⋊C4—42no—
1291C22⋊C4—42no—
1292C22⋊C4—44no—
1293C22⋊C4—42no—
1294C22⋊C4—44no—
1295C22⋊C4—42no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—42no—
1299C22⋊C4—42no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—42no—
1303C22⋊C4—42no—
1304C22⋊C4—44no—
1305C22⋊C4—42no—
1306C22⋊C4—42no—
1307C22⋊C4—44no—
1308C22⋊C4—41no—
1309C22⋊C4—41no—
1310C22⋊C4—44no—
1311C22⋊C4—42no—
1312C22⋊C4—42no—
1313C22⋊C4—44no—
1314C22⋊C4—42no—
1315C22⋊C4—42no—
1316C22⋊C4—44no—
1317C22⋊C4—42no—
1318C22⋊C4—44no—
1319C22⋊C4—44no—
1320C22⋊C4—44no—
1321C22⋊C4—44no—
1322C22⋊C4—44no—
1323C22⋊C4—42no—
1324C22⋊C4—42no—
1325C22⋊C4—44no—
1326C22⋊C4—44no—
1327C22⋊C4—44no—
1328C22⋊C4—44no—
1329C22⋊C4—42no—
1330C22⋊C4—44no—
1331C22⋊C4—42no—
1332C22⋊C4—44no—
1333C22⋊C4—44no—
1334C22⋊C4—44no—
1335C22⋊C4—44no—
1336C22⋊C4—42no—
1337C22⋊C4—44no—
1338C22⋊C4—44no—
1339C22⋊C4—42no—
1340C22⋊C4—44no—
1341C22⋊C4—42no—
1342C22⋊C4—42no—
1343C22⋊C4—42no—
1344C22⋊C4—42no—
1345C22⋊C4—42no—
1346C42—28no—
1347C42—22no—
1348C42—24no—
1349C42—24no—
1350C42—24no—
1351C42—24no—
1352C42—22no—
1353C42—42no—
1354C42—44no—
1355C42—41no—
1356C42—42no—
1357C42—44no—
1358C42—44no—
1359C42—44no—
1360C23—24no—
1361C23—22no—
1362C23—22no—
1363C23—24no—
1364C23—24no—
1365C23—22no—
1366C23—22no—
1367C23—24no—
1368C23—22no—
1369C23—22no—
1370C23—21no—
1371C23—21no—
1372C23—22no—
1373C23—24no—
1374C23—22no—
1375C23—22no—
1376C23—22no—
1377C23—22no—
1378C23—22no—
1379C23—21no—
1380C23—21no—
1381C23—24no—
1382C23—22no—
1383C23—22no—
1384C23—24no—
1385C23—21no—
1386C23—21no—
1387C23—22no—
1388C23—22no—
1389C23—22no—
1390C23—22no—
1391C23—24no—
1392C23—24no—
1393C23—22no—
1394C23—22no—
1395C23C2×H(5,𝔽2)14yes—
1396C23C2611yescharacteristic
1397Q8—216no—
1398Q8—48no—
1399Q8—416no—
1400Q8—44no—
1401Q8—44no—
1402Q8—44no—
1403Q8—44no—
1404Q8—84no—
1405Q8—82no—
1406D4—28no—
1407D4—416no—
1408D4—48no—
1409D4—48no—
1410D4—44no—
1411D4—48no—
1412D4—82no—
1413D4—84no—
1414D4—88no—
1415D4—88no—
1416D4—88no—
1417D4—88no—
1418D4—84no—
1419D4—84no—
1420D4—88no—
1421D4—84no—
1422D4—84no—
1423D4—88no—
1424D4—84no—
1425D4—84no—
1426D4—82no—
1427D4—164no—
1428D4—164no—
1429D4—162no—
1430D4—164no—
1431C2×C4—21no—
1432C2×C4—24no—
1433C2×C4—24no—
1434C2×C4—21no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—24no—
1440C2×C4—21no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—22no—
1444C2×C4—22no—
1445C2×C4—24no—
1446C2×C4—24no—
1447C2×C4—24no—
1448C2×C4—22no—
1449C2×C4—22no—
1450C2×C4—24no—
1451C2×C4—22no—
1452C2×C4—22no—
1453C2×C4—22no—
1454C2×C4—22no—
1455C2×C4—22no—
1456C2×C4—22no—
1457C2×C4—24no—
1458C2×C4—22no—
1459C2×C4—21no—
1460C2×C4—22no—
1461C2×C4—21no—
1462C2×C4—22no—
1463C2×C4—22no—
1464C2×C4—22no—
1465C2×C4—22no—
1466C2×C4—24no—
1467C2×C4—24no—
1468C2×C4—22no—
1469C2×C4—22no—
1470C2×C4—22no—
1471C2×C4—24no—
1472C2×C4—24no—
1473C2×C4—24no—
1474C2×C4—22no—
1475C2×C4—22no—
1476C2×C4—22no—
1477C2×C4—22no—
1478C2×C4—22no—
1479C2×C4—22no—
1480C2×C4—22no—
1481C2×C4—22no—
1482C2×C4—22no—
1483C2×C4—24no—
1484C2×C4—22no—
1485C2×C4—22no—
1486C2×C4—24no—
1487C2×C4—22no—
1488C2×C4—22no—
1489C2×C4—24no—
1490C2×C4—48no—
1491C2×C4—416no—
1492C2×C4—48no—
1493C2×C4—416no—
1494C2×C4—48no—
1495C2×C4—44no—
1496C2×C4—48no—
1497C2×C4—48no—
1498C2×C4—44no—
1499C2×C4—88no—
1500C2×C4—84no—
1501C2×C4—88no—
1502C2×C4—88no—
1503C2×C4—88no—
1504C2×C4—164no—
1505C2×C4—162no—
1506C2×C4C2×H(5,𝔽2)18yes—
1507C2×C4C2×H(5,𝔽2)14yes—
1508C2×C4C2×H(5,𝔽2)12yes—
1509C2×C4#58512yes—
1510C22—24no—
1511C22—24no—
1512C22—24no—
1513C22—44no—
1514C22—44no—
1515C22—42no—
1516C22—42no—
1517C22—42no—
1518C22—42no—
1519C22—44no—
1520C22—42no—
1521C22—44no—
1522C22—42no—
1523C22—44no—
1524C22—42no—
1525C22—42no—
1526C22—41no—
1527C22—41no—
1528C22—44no—
1529C22—41no—
1530C22—42no—
1531C22—41no—
1532C22—42no—
1533C22—44no—
1534C22—42no—
1535C22—44no—
1536C22—42no—
1537C22—42no—
1538C22—42no—
1539C22—42no—
1540C22—42no—
1541C22—41no—
1542C22—42no—
1543C22—42no—
1544C22—41no—
1545C22—44no—
1546C22C22×H(5,𝔽2)12yes—
1547C22C22×H(5,𝔽2)11yescharacteristic
1548C22C2×#58511yescharacteristic
1549C22H(7,𝔽2)11yescharacteristic
1550C222−1+612yes—
1551C4—22no—
1552C4—28no—
1553C4—42no—
1554C4—42no—
1555C4—44no—
1556C4—44no—
1557C4—42no—
1558C4—42no—
1559C4—41no—
1560C4—42no—
1561C4—42no—
1562C4—44no—
1563C4—42no—
1564C4—44no—
1565C4—42no—
1566C4—42no—
1567C4—42no—
1568C4—41no—
1569C4—42no—
1570C4—42no—
1571C4—41no—
1572C4—42no—
1573C4#353214yes—
1574C2—44no—
1575C2—82no—
1576C2—81no—
1577C2—81no—
1578C2—84no—
1579C2—82no—
1580C2C2×#353211yescharacteristic
1581C2#6291811yescharacteristic
1582C2#6292212yes—
1583C2#6305212yes—
1584C2#6306311yescharacteristic
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. #59946C2semidirect
2. #59765C2semidirect
3. #58801C2semidirect
4. #58177C2semidirect
5. #57609C2semidirect
6. #57297C2semidirect
7. #57184C2semidirect
8. #52966C2semidirect
9. #52956C2semidirect
10. #52415C2semidirect
11. #52414C2semidirect
12. #47663C2semidirect
13. #45307C2semidirect
14. #45269C2semidirect
15. #45244C2semidirect
16. #44935C2semidirect
17. #44884C2semidirect
18. #42916C2semidirect
19. #42908C2semidirect
20. #42844C2semidirect
21. #42829C2semidirect
22. #42598C2semidirect
23. #42101C2semidirect
24. #42023C2semidirect
25. #39954C2semidirect
26. #38956C2semidirect
27. #36694C2semidirect
28. #36085C2semidirect
29. #35757C2semidirect

Maximal subgroups

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

subgroupindex
#599462
#597652
#588012
#581772
#576092
#572972
#571842
#529662
#529562
#524152
#524142
#476632
#453072
#452692
#452442
#449352
#448842
#429162
#429082
#428442
#428292
#425982
#421012
#420232
#399542
#389562
#366942
#360852
#357572