Finite Group Databasebeta

← #8751563

Subgroups — #8751563

Order 512.

5069 conjugacy classes of subgroups.

The subgroup lattice has 1544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#59694C212yesmaximal, complemented
3#58905C214yesmaximal, complemented
4#58804C212yesmaximal, complemented
5#58729C214yesmaximal, complemented
6#58006C214yesmaximal, complemented
7#53716C214yesmaximal, complemented
8#53099C212yesmaximal, complemented
9#53095C212yesmaximal, complemented
10#52960C211yesmaximal, characteristic, complemented
11#52485C214yesmaximal, complemented
12#47726C212yesmaximal, complemented
13#45332C212yesmaximal, complemented
14#45314C212yesmaximal, complemented
15#45245C212yesmaximal, complemented
16#45244C211yesmaximal, characteristic, complemented
17#45241C212yesmaximal, complemented
18#42916C212yesmaximal, complemented
19#42911C211yesmaximal, characteristic, complemented
20#42862C212yesmaximal, complemented
21#42787C212yesmaximal, complemented
22#42746C212yesmaximal, complemented
23#42341C212yesmaximal, complemented
24#41021C214yesmaximal, complemented
25#39790C212yesmaximal, complemented
26#39747C211yesmaximal, characteristic, complemented
27#36696C211yesmaximal, characteristic, complemented
28#36007C211yesmaximal, characteristic, complemented
29#35771C212yesmaximal, complemented
30C2×#556C2211yescharacteristic
31C2×#550C2211yescharacteristic
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2212yes—
34C2×#548C2212yes—
35C2×#548C2212yes—
36C2×#547C2212yes—
37C2×#537C2212yes—
38C2×#536C2212yes—
39C2×#536C2211yescharacteristic
40C2×#519C2211yescharacteristic
41#2858C2211yescharacteristic
42#2843C2211yescharacteristic
43#2837C2214yes—
44#2831C2214yes—
45#2830C2212yes—
46#2830C2211yescharacteristic
47#2830C2212yes—
48#2829C2214yes—
49#2829C2212yes—
50#2829C2212yes—
51#2829C2212yes—
52#2828C2212yes—
53#2828C2211yescharacteristic
54#2827C2214yes—
55#2826C2212yes—
56#2826C2214yes—
57#2824C2214yes—
58#2823C2211yescharacteristic
59#2823C2214yes—
60#2821C2212yes—
61#2818C2212yes—
62#2814C2214yes—
63#2814C2214yes—
64#2806C2214yes—
65#2803C2214yes—
66#2803C2214yes—
67#2802C2214yes—
68#2800C2214yes—
69#2797C2214yes—
70#2790C2214yes—
71#2790C2214yes—
72#2784C2212yes—
73#2780C2214yes—
74#2780C2214yes—
75#2768C2214yes—
76#2757C2214yes—
77#2751C2214yes—
78#2732C2214yes—
79#2729C2214yes—
80#2729C2214yes—
81#2728C2214yes—
82#2718C2214yes—
83#2718C2214yes—
84#2715C2214yes—
85#2715C2214yes—
86#2714C2214yes—
87#2714C2214yes—
88#2714C2214yes—
89#2710C2214yes—
90#2710C2214yes—
91#2709C2214yes—
92#2706C2214yes—
93#2701C2214yes—
94#2701C2214yes—
95#2701C2214yes—
96#2695C2214yes—
97#2693C2212yes—
98#2691C2214yes—
99#2683C2212yes—
100#2683C2212yes—
101#2683C2212yes—
102#2682C2214yes—
103#2682C2214yes—
104#2682C2214yes—
105#2681C2214yes—
106#2681C2214yes—
107#2681C2214yes—
108#2680C2214yes—
109#2677C2214yes—
110#2676C2214yes—
111#2676C2214yes—
112#2676C2214yes—
113#2675C2212yes—
114#2674C2214yes—
115#2673C2214yes—
116#2672C2214yes—
117#2672C2214yes—
118#2665C2214yes—
119#2663C2214yes—
120#2662C2214yes—
121#2662C2212yes—
122#2661C2214yes—
123#2661C2214yes—
124#2657C2212yes—
125#2652C2214yes—
126#2644C2214yes—
127#2637C2212yes—
128#2632C2212yes—
129#2630C2214yes—
130#2625C2212yes—
131#2625C2211yescharacteristic
132#2620C2212yes—
133#2620C2214yes—
134#2618C2214yes—
135#2616C2211yescharacteristic
136#2606C2214yes—
137#2604C2212yes—
138#2602C2214yes—
139#2597C2214yes—
140#2587C2214yes—
141#2587C2214yes—
142#2587C2214yes—
143#2585C2214yes—
144#2583C2214yes—
145#2581C2212yes—
146#2567C2212yes—
147#2557C2214yes—
148#2555C2212yes—
149#2554C2214yes—
150#2554C2214yes—
151#2551C2212yes—
152#2548C2212yes—
153#2547C2211yescharacteristic
154#2546C2212yes—
155#2545C2212yes—
156#2545C2214yes—
157#2544C2212yes—
158#2544C2212yes—
159#2542C2212yes—
160#2541C2211yescharacteristic
161#2540C2212yes—
162#2538C2212yes—
163#2538C2212yes—
164#2538C2214yes—
165#2538C2212yes—
166#2526C2214yes—
167#2525C2214yes—
168#2512C2212yes—
169#2512C2214yes—
170#2511C2212yes—
171#2507C2212yes—
172#2507C2214yes—
173#2502C2212yes—
174#2496C2212yes—
175#2492C2212yes—
176#2491C2214yes—
177#2486C2212yes—
178#2478C2214yes—
179#2474C2214yes—
180#2464C2214yes—
181#2464C2214yes—
182#2463C2212yes—
183#2461C2214yes—
184#2456C2214yes—
185#2455C2214yes—
186#2452C2214yes—
187#2452C2214yes—
188#2452C2214yes—
189#2451C2212yes—
190#2449C2214yes—
191#2449C2214yes—
192#2448C2212yes—
193#2446C2212yes—
194#2445C2214yes—
195#2443C2214yes—
196#2440C2214yes—
197#2436C2212yes—
198#2434C2211yescharacteristic
199#2434C2211yescharacteristic
200#2432C2212yes—
201#2432C2212yes—
202#2431C2212yes—
203#2429C2212yes—
204#2429C2214yes—
205#2429C2212yes—
206#2429C2212yes—
207#2429C2212yes—
208#2428C2214yes—
209#2427C2212yes—
210#2426C2212yes—
211#2426C2212yes—
212#2426C2214yes—
213#2426C2212yes—
214#2422C2212yes—
215#2422C2212yes—
216#2417C2212yes—
217#2416C2212yes—
218#2415C2214yes—
219#2415C2212yes—
220#2414C2212yes—
221#2414C2214yes—
222#2414C2212yes—
223#2409C2212yes—
224#2409C2212yes—
225#2409C2211yescharacteristic
226#2409C2211yescharacteristic
227#2407C2212yes—
228#2407C2212yes—
229#2407C2212yes—
230#2399C2212yes—
231#2395C2212yes—
232#2395C2211yescharacteristic
233#2392C2214yes—
234#2392C2212yes—
235#2392C2212yes—
236#2392C2212yes—
237#2388C2211yescharacteristic
238#2388C2212yes—
239#2373C2214yes—
240#2367C2212yes—
241#2366C2212yes—
242#2365C2212yes—
243#2362C2212yes—
244#2360C2212yes—
245#2360C2212yes—
246Q8×C4⋊C4C2212yes—
247#2347C2211yescharacteristic
248#2346C2211yescharacteristic
249#2341C2212yes—
250Q8×C22⋊C4C2212yes—
251#2337C2214yes—
252#2326C2212yes—
253#2324C2212yes—
254#2323C2212yes—
255C4×C4⋊Q8C2212yes—
256C4×#127C2211yescharacteristic
257C4×#126C2212yes—
258#2295C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2311yescharacteristic
261C22×#41C2312yes—
262C23×Q8C2311yescharacteristic
263C23×Q8C2312yes—
264C23×Q8C2311yescharacteristic
265#556—44no—
266#550—44no—
267D4×Q8—48no—
268D4×Q8—48no—
269#548—48no—
270#548—48no—
271#547—48no—
272#537—48no—
273#536—44no—
274#536—48no—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2314yes—
280C2×C4⋊Q8C2314yes—
281C2×C4⋊Q8C2312yes—
282C2×#127C2311yescharacteristic
283C2×#127C2311yescharacteristic
284C2×#127C2312yes—
285C2×#127C2312yes—
286C2×#126C2312yes—
287C2×#126C2312yes—
288C2×#126C2312yes—
289C2×#126C2314yes—
290C2×#126C2314yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2314yes—
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#124C2312yes—
297C2×#124C2314yes—
298C2×#124C2312yes—
299C2×#124C2312yes—
300C2×#124C2312yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2311yescharacteristic
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2311yescharacteristic
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2312yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×#121C2312yes—
329C2×#121C2314yes—
330C2×#121C2312yes—
331C2×#121C2314yes—
332C2×#121C2312yes—
333C2×#121C2312yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#121C2314yes—
337C2×#121C2314yes—
338C2×#121C2314yes—
339C2×#121C2314yes—
340#519—44no—
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2312yes—
346C2×C4×Q8C2312yes—
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2312yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2311yescharacteristic
352C2×C4×D4C2312yes—
353C2×C4×D4C2311yescharacteristic
354C2×C4×D4C2312yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2314yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2314yes—
363C2×#117C2311yescharacteristic
364C2×#117C2311yescharacteristic
365C2×#117C2312yes—
366C2×#117C2311yescharacteristic
367C2×#117C2314yes—
368C22×C4⋊C4C2314yes—
369C22×C4⋊C4C2312yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2312yes—
374#400C2314yes—
375#400C2314yes—
376#400C2311yescharacteristic
377#400C2312yes—
378#400C2314yes—
379#399C2314yes—
380#399C2311yescharacteristic
381#399C2314yes—
382#399C2312yes—
383#399C2314yes—
384#399C2314yes—
385#398C2314yes—
386#398C2312yes—
387#398C2314yes—
388#398C2311yescharacteristic
389#398C2312yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2312yes—
394#398C2312yes—
395#398C2312yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#397C2314yes—
407#397C2312yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2312yes—
413#397C2314yes—
414#397C2312yes—
415#397C2312yes—
416#397C2311yescharacteristic
417#397C2312yes—
418#397C2312yes—
419#397C2312yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#396C2312yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2312yes—
431#396C2312yes—
432#396C2312yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2312yes—
438#396C2312yes—
439#396C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#395C2312yes—
453#395C2312yes—
454#395C2311yescharacteristic
455#395C2312yes—
456#395C2312yes—
457#395C2312yes—
458#395C2314yes—
459#395C2312yes—
460#395C2312yes—
461#395C2312yes—
462#395C2314yes—
463#395C2314yes—
464#394C2312yes—
465#394C2312yes—
466#394C2312yes—
467#394C2312yes—
468#394C2312yes—
469#394C2312yes—
470#394C2314yes—
471#394C2311yescharacteristic
472#394C2312yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2312yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2312yes—
485#394C2312yes—
486#394C2312yes—
487#394C2312yes—
488#394C2312yes—
489#394C2312yes—
490#394C2312yes—
491#394C2312yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2312yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#393C2311yescharacteristic
505#393C2312yes—
506#393C2314yes—
507#393C2314yes—
508#393C2312yes—
509#393C2314yes—
510#393C2312yes—
511#393C2314yes—
512#393C2314yes—
513#392C2312yes—
514#392C2312yes—
515#392C2312yes—
516#392C2312yes—
517#392C2312yes—
518#392C2312yes—
519#392C2312yes—
520#392C2314yes—
521#392C2312yes—
522#392C2311yescharacteristic
523#392C2312yes—
524#392C2314yes—
525#392C2314yes—
526#392C2314yes—
527#392C2314yes—
528#392C2314yes—
529#392C2314yes—
530#392C2314yes—
531#391C2312yes—
532#391C2312yes—
533#391C2314yes—
534#391C2314yes—
535#391C2312yes—
536#391C2314yes—
537#391C2312yes—
538#391C2312yes—
539#391C2314yes—
540#391C2312yes—
541#391C2312yes—
542#391C2312yes—
543#391C2312yes—
544#390C2311yescharacteristic
545#390C2312yes—
546#390C2311yescharacteristic
547#390C2312yes—
548#390C2314yes—
549#390C2312yes—
550#390C2314yes—
551#390C2312yes—
552#390C2312yes—
553#390C2312yes—
554#390C2314yes—
555#390C2314yes—
556#390C2314yes—
557#390C2314yes—
558#390C2312yes—
559#390C2314yes—
560#390C2314yes—
561#390C2314yes—
562#390C2314yes—
563#390C2314yes—
564#390C2314yes—
565#390C2314yes—
566#390C2314yes—
567#390C2314yes—
568#389C2314yes—
569#389C2314yes—
570#389C2314yes—
571#389C2314yes—
572#389C2314yes—
573#389C2312yes—
574#389C2312yes—
575#389C2314yes—
576#389C2314yes—
577#389C2314yes—
578#389C2314yes—
579#389C2314yes—
580#389C2314yes—
581#389C2314yes—
582#389C2314yes—
583#389C2314yes—
584#389C2314yes—
585#389C2314yes—
586#389C2312yes—
587#389C2314yes—
588#389C2312yes—
589#389C2314yes—
590#389C2312yes—
591#389C2312yes—
592#389C2314yes—
593#388C2312yes—
594#388C2312yes—
595#388C2312yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#387C2312yes—
622#387C2312yes—
623#387C2312yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2312yes—
652#386C2312yes—
653#386C2314yes—
654#386C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2312yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2312yes—
674#385C2314yes—
675#385C2314yes—
676#384C2311yescharacteristic
677#384C2312yes—
678#384C2314yes—
679#384C2312yes—
680#384C2314yes—
681#383C2312yes—
682#383C2312yes—
683#382C2312yes—
684#381C2314yes—
685#380C2312yes—
686#380C2312yes—
687#380C2312yes—
688#380C2314yes—
689#380C2312yes—
690#380C2314yes—
691#380C2311yescharacteristic
692#380C2311yescharacteristic
693#380C2314yes—
694#380C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2311yescharacteristic
706C4×C4⋊C4C2314yes—
707C4×C4⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2311yescharacteristic
718C4×C22⋊C4C2311yescharacteristic
719C4×C22⋊C4C2312yes—
720#376C2312yes—
721#376C2312yes—
722C43C2311yescharacteristic
723C2×#41—28no—
724C2×#41—42no—
725C2×#41—44no—
726C2×#41—44no—
727C2×#41—44no—
728C2×#41—44no—
729C2×#41—44no—
730C2×#41—44no—
731C22×Q8—28no—
732C22×Q8—28no—
733C22×Q8—42no—
734C22×Q8—42no—
735C22×Q8—44no—
736C22×Q8—44no—
737C22×Q8—44no—
738C22×Q8C2412yes—
739C22×Q8C2411yescharacteristic
740C22×Q8C2412yes—
741C22×Q8C2412yes—
742C22×Q8C2412yes—
743C22×Q8C2414yes—
744C22×Q8C2411yescharacteristic
745C22×Q8C2412yes—
746C22×D4C2412yes—
747C22×D4C2412yes—
748C22×D4C2412yes—
749C22×D4C2414yes—
750C22×D4C2412yes—
751C22×D4C2411yescharacteristic
752C22×D4C2411yescharacteristic
753C22×D4C2414yes—
754C22×D4C2412yes—
755C22×D4C2414yes—
756C22×D4C2412yes—
757C22×D4C2412yes—
758C22×D4C2412yes—
759C22×D4C2414yes—
760C22×D4C2411yescharacteristic
761C22×D4C2414yes—
762C22×D4C2414yes—
763C22×D4C2412yes—
764C23×C4C2412yes—
765C23×C4C2411yescharacteristic
766C23×C4C2412yes—
767C23×C4C2411yescharacteristic
768C23×C4C2412yes—
769C23×C4C2414yes—
770C23×C4C2414yes—
771C23×C4C2414yes—
772C23×C4C2414yes—
773C23×C4C2414yes—
774C23×C4C2412yes—
775C4⋊Q8—28no—
776C4⋊Q8—28no—
777C4⋊Q8—44no—
778C4⋊Q8—42no—
779C4⋊Q8—44no—
780C4⋊Q8—48no—
781C4⋊Q8—48no—
782#127—24no—
783#127—42no—
784#127—44no—
785#127—82no—
786#126—28no—
787#126—44no—
788#126—44no—
789#126—84no—
790#126—84no—
791#124—28no—
792#124—28no—
793#124—44no—
794#124—48no—
795#124—44no—
796#124—44no—
797#124—44no—
798#124—48no—
799#124—82no—
800#124—82no—
801#123—48no—
802#123—48no—
803#123—48no—
804#123—48no—
805#123—48no—
806#123—84no—
807#123—84no—
808#123—84no—
809C22⋊Q8—28no—
810C22⋊Q8—28no—
811C22⋊Q8—28no—
812C22⋊Q8—28no—
813C22⋊Q8—48no—
814C22⋊Q8—48no—
815C22⋊Q8—48no—
816C22⋊Q8—48no—
817C22⋊Q8—48no—
818C22⋊Q8—48no—
819C22⋊Q8—48no—
820C22⋊Q8—48no—
821C22⋊Q8—48no—
822C22⋊Q8—44no—
823C22⋊Q8—44no—
824C22⋊Q8—44no—
825C22⋊Q8—44no—
826C22⋊Q8—42no—
827C22⋊Q8—42no—
828#121—28no—
829#121—48no—
830#121—48no—
831#121—48no—
832#121—48no—
833#121—48no—
834#121—48no—
835#121—48no—
836#121—44no—
837#121—44no—
838#121—44no—
839#121—84no—
840C4×Q8—28no—
841C4×Q8—24no—
842C4×Q8—44no—
843C4×Q8—44no—
844C4×Q8—44no—
845C4×Q8—44no—
846C4×Q8—44no—
847C4×Q8—44no—
848C4×Q8—44no—
849C4×D4—44no—
850C4×D4—44no—
851C4×D4—48no—
852C4×D4—44no—
853C4×D4—44no—
854C4×D4—44no—
855C4×D4—44no—
856C4×D4—44no—
857C4×D4—42no—
858C4×D4—42no—
859C4×D4—48no—
860C4×D4—48no—
861C4×D4—48no—
862#117—24no—
863#117—24no—
864#117—42no—
865#117—44no—
866#117—48no—
867C2×C4⋊C4—44no—
868C2×C4⋊C4—48no—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2411yescharacteristic
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2411yescharacteristic
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2411yescharacteristic
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2411yescharacteristic
959C2×C22⋊C4C2411yescharacteristic
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2414yes—
979C2×C22⋊C4C2414yes—
980C2×C22⋊C4C2414yes—
981C2×C22⋊C4C2414yes—
982C2×C22⋊C4C2412yes—
983C2×C22⋊C4C2412yes—
984C2×C22⋊C4C2412yes—
985C2×C22⋊C4C2414yes—
986C2×C22⋊C4C2412yes—
987C2×C22⋊C4C2412yes—
988C2×C22⋊C4C2412yes—
989C2×C22⋊C4C2412yes—
990C2×C22⋊C4C2414yes—
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2414yes—
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2411yescharacteristic
999C2×C42C2412yes—
1000C2×C42C2414yes—
1001C2×C42C2414yes—
1002C2×C42C2414yes—
1003C2×C42C2414yes—
1004C2×C42C2411yescharacteristic
1005C2×C42C2412yes—
1006C2×C42C2414yes—
1007C2×C42C2412yes—
1008C2×C42C2414yes—
1009C2×C42C2411yescharacteristic
1010#95C2411yescharacteristic
1011#95C2414yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2411yescharacteristic
1019#95C2412yes—
1020#95C2411yescharacteristic
1021#95C2414yes—
1022#95C2412yes—
1023#95C2411yescharacteristic
1024#95C2412yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2412yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2412yes—
1040#95C2414yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2412yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061C24C2511yescharacteristic
1062C24C2511yescharacteristic
1063C24C2512yes—
1064C24C2514yes—
1065C24C2512yes—
1066#41—88no—
1067#41—816no—
1068#41—816no—
1069C2×Q8—24no—
1070C2×Q8—24no—
1071C2×Q8—22no—
1072C2×Q8—24no—
1073C2×Q8—24no—
1074C2×Q8—28no—
1075C2×Q8—24no—
1076C2×Q8—24no—
1077C2×Q8—28no—
1078C2×Q8—24no—
1079C2×Q8—42no—
1080C2×Q8—42no—
1081C2×Q8—42no—
1082C2×Q8—44no—
1083C2×Q8—44no—
1084C2×Q8—44no—
1085C2×Q8—42no—
1086C2×Q8—42no—
1087C2×Q8—41no—
1088C2×Q8—416no—
1089C2×Q8—816no—
1090C2×Q8—88no—
1091C2×Q8H(5,𝔽2)18yes—
1092C2×D4—24no—
1093C2×D4—24no—
1094C2×D4—24no—
1095C2×D4—28no—
1096C2×D4—28no—
1097C2×D4—24no—
1098C2×D4—24no—
1099C2×D4—24no—
1100C2×D4—22no—
1101C2×D4—22no—
1102C2×D4—42no—
1103C2×D4—42no—
1104C2×D4—42no—
1105C2×D4—42no—
1106C2×D4—42no—
1107C2×D4—42no—
1108C2×D4—42no—
1109C2×D4—44no—
1110C2×D4—41no—
1111C2×D4—42no—
1112C2×D4—41no—
1113C2×D4—42no—
1114C2×D4—42no—
1115C2×D4—42no—
1116C2×D4—44no—
1117C2×D4—44no—
1118C2×D4—44no—
1119C2×D4—44no—
1120C2×D4—42no—
1121C2×D4—44no—
1122C2×D4—42no—
1123C2×D4—44no—
1124C2×D4—42no—
1125C2×D4—41no—
1126C2×D4—41no—
1127C2×D4—42no—
1128C2×D4—41no—
1129C2×D4—44no—
1130C2×D4—44no—
1131C2×D4—42no—
1132C2×D4—42no—
1133C2×D4—42no—
1134C2×D4—42no—
1135C2×D4—44no—
1136C2×D4—44no—
1137C2×D4—44no—
1138C2×D4—42no—
1139C2×D4—44no—
1140C2×D4—44no—
1141C2×D4—44no—
1142C2×D4—44no—
1143C2×D4—44no—
1144C22×C4—24no—
1145C22×C4—22no—
1146C22×C4—22no—
1147C22×C4—24no—
1148C22×C4—24no—
1149C22×C4—28no—
1150C22×C4—24no—
1151C22×C4—24no—
1152C22×C4—24no—
1153C22×C4—24no—
1154C22×C4—24no—
1155C22×C4—28no—
1156C22×C4—28no—
1157C22×C4—42no—
1158C22×C4—44no—
1159C22×C4—44no—
1160C22×C4—44no—
1161C22×C4—44no—
1162C22×C4—44no—
1163C22×C4—44no—
1164C22×C4—44no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4—42no—
1168C22×C4—44no—
1169C22×C4—44no—
1170C22×C4—44no—
1171C22×C4—44no—
1172C22×C4—44no—
1173C22×C4C2511yescharacteristic
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2514yes—
1178C22×C4C2512yes—
1179C22×C4C2512yes—
1180C22×C4C2512yes—
1181C22×C4C2514yes—
1182C22×C4C2512yes—
1183C22×C4C2512yes—
1184C22×C4C2514yes—
1185C22×C4C2511yescharacteristic
1186C22×C4C2514yes—
1187C22×C4C2512yes—
1188C22×C4C2512yes—
1189C22×C4C2512yes—
1190C22×C4C2512yes—
1191C22×C4C2511yescharacteristic
1192C22×C4C2512yes—
1193C22×C4C2514yes—
1194C22×C4C2511yescharacteristic
1195C22×C4C2512yes—
1196C22×C4C2511yescharacteristic
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—28no—
1200C4⋊C4—28no—
1201C4⋊C4—22no—
1202C4⋊C4—22no—
1203C4⋊C4—28no—
1204C4⋊C4—28no—
1205C4⋊C4—24no—
1206C4⋊C4—28no—
1207C4⋊C4—28no—
1208C4⋊C4—24no—
1209C4⋊C4—28no—
1210C4⋊C4—28no—
1211C4⋊C4—28no—
1212C4⋊C4—24no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—42no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C4⋊C4—44no—
1221C4⋊C4—42no—
1222C4⋊C4—42no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—41no—
1226C4⋊C4—41no—
1227C4⋊C4—42no—
1228C4⋊C4—42no—
1229C4⋊C4—41no—
1230C4⋊C4—41no—
1231C4⋊C4—42no—
1232C4⋊C4—42no—
1233C4⋊C4—42no—
1234C4⋊C4—42no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—42no—
1239C4⋊C4—42no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—42no—
1251C4⋊C4—44no—
1252C4⋊C4—42no—
1253C4⋊C4H(5,𝔽2)14yes—
1254C22⋊C4—24no—
1255C22⋊C4—24no—
1256C22⋊C4—28no—
1257C22⋊C4—28no—
1258C22⋊C4—28no—
1259C22⋊C4—28no—
1260C22⋊C4—28no—
1261C22⋊C4—28no—
1262C22⋊C4—28no—
1263C22⋊C4—28no—
1264C22⋊C4—28no—
1265C22⋊C4—24no—
1266C22⋊C4—24no—
1267C22⋊C4—24no—
1268C22⋊C4—42no—
1269C22⋊C4—42no—
1270C22⋊C4—42no—
1271C22⋊C4—44no—
1272C22⋊C4—42no—
1273C22⋊C4—42no—
1274C22⋊C4—42no—
1275C22⋊C4—44no—
1276C22⋊C4—42no—
1277C22⋊C4—42no—
1278C22⋊C4—42no—
1279C22⋊C4—42no—
1280C22⋊C4—42no—
1281C22⋊C4—42no—
1282C22⋊C4—42no—
1283C22⋊C4—42no—
1284C22⋊C4—42no—
1285C22⋊C4—42no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—42no—
1290C22⋊C4—42no—
1291C22⋊C4—42no—
1292C22⋊C4—44no—
1293C22⋊C4—42no—
1294C22⋊C4—41no—
1295C22⋊C4—41no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—42no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—44no—
1305C22⋊C4—44no—
1306C22⋊C4—42no—
1307C22⋊C4—42no—
1308C22⋊C4—42no—
1309C22⋊C4—42no—
1310C22⋊C4—44no—
1311C22⋊C4—42no—
1312C22⋊C4—44no—
1313C22⋊C4—44no—
1314C22⋊C4—44no—
1315C22⋊C4—44no—
1316C22⋊C4—44no—
1317C22⋊C4—44no—
1318C22⋊C4—42no—
1319C42—24no—
1320C42—24no—
1321C42—24no—
1322C42—28no—
1323C42—24no—
1324C42—24no—
1325C42—22no—
1326C42—24no—
1327C42—24no—
1328C42—44no—
1329C42—42no—
1330C42—44no—
1331C42—44no—
1332C42—44no—
1333C42—44no—
1334C42—41no—
1335C42—42no—
1336C42—44no—
1337C422−1+414yes—
1338C23—21no—
1339C23—21no—
1340C23—22no—
1341C23—24no—
1342C23—22no—
1343C23—22no—
1344C23—22no—
1345C23—24no—
1346C23—22no—
1347C23—22no—
1348C23—22no—
1349C23—24no—
1350C23—22no—
1351C23—22no—
1352C23—24no—
1353C23—22no—
1354C23—21no—
1355C23—21no—
1356C23—22no—
1357C23—24no—
1358C23—21no—
1359C23—22no—
1360C23—21no—
1361C23—24no—
1362C23—22no—
1363C23—22no—
1364C23—22no—
1365C23—22no—
1366C23—22no—
1367C23—24no—
1368C23—22no—
1369C23C2611yescharacteristic
1370Q8—216no—
1371Q8—48no—
1372Q8—48no—
1373Q8—44no—
1374Q8—84no—
1375Q8—88no—
1376Q8—84no—
1377Q8—82no—
1378D4—48no—
1379D4—48no—
1380D4—48no—
1381D4—88no—
1382D4—84no—
1383D4—82no—
1384D4—82no—
1385D4—88no—
1386D4—84no—
1387D4—88no—
1388D4—84no—
1389D4—84no—
1390D4—84no—
1391D4—82no—
1392D4—88no—
1393D4—164no—
1394D4—164no—
1395D4—162no—
1396C2×C4—21no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—24no—
1400C2×C4—21no—
1401C2×C4—24no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—21no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—24no—
1418C2×C4—24no—
1419C2×C4—24no—
1420C2×C4—22no—
1421C2×C4—24no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—24no—
1427C2×C4—22no—
1428C2×C4—24no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—24no—
1440C2×C4—24no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—24no—
1444C2×C4—22no—
1445C2×C4—22no—
1446C2×C4—22no—
1447C2×C4—24no—
1448C2×C4—22no—
1449C2×C4—22no—
1450C2×C4—22no—
1451C2×C4—22no—
1452C2×C4—24no—
1453C2×C4—22no—
1454C2×C4—22no—
1455C2×C4—24no—
1456C2×C4—48no—
1457C2×C4—44no—
1458C2×C4—48no—
1459C2×C4—44no—
1460C2×C4—48no—
1461C2×C4—88no—
1462C2×C4—88no—
1463C2×C4—88no—
1464C2×C4—84no—
1465C2×C4—88no—
1466C2×C4—164no—
1467C2×C4C2×H(5,𝔽2)14yes—
1468C2×C4C2×H(5,𝔽2)18yes—
1469C2×C4C2×H(5,𝔽2)14yes—
1470C2×C4C2×H(5,𝔽2)12yes—
1471C2×C4C2×2−1+414yes—
1472C2×C4C2×2−1+412yes—
1473C22—41no—
1474C22—42no—
1475C22—41no—
1476C22—42no—
1477C22—44no—
1478C22—44no—
1479C22—42no—
1480C22—42no—
1481C22—42no—
1482C22—44no—
1483C22—42no—
1484C22—42no—
1485C22—42no—
1486C22—42no—
1487C22—44no—
1488C22—42no—
1489C22—41no—
1490C22—41no—
1491C22—42no—
1492C22—42no—
1493C22—42no—
1494C22—42no—
1495C22—44no—
1496C22—42no—
1497C22—42no—
1498C22—44no—
1499C22—41no—
1500C22—41no—
1501C22—44no—
1502C22—42no—
1503C22—42no—
1504C22C22×H(5,𝔽2)12yes—
1505C22C22×H(5,𝔽2)11yescharacteristic
1506C22C22×2−1+411yescharacteristic
1507C22H(7,𝔽2)11yescharacteristic
1508C222−1+612yes—
1509C4—28no—
1510C4—24no—
1511C4—24no—
1512C4—22no—
1513C4—42no—
1514C4—42no—
1515C4—41no—
1516C4—41no—
1517C4—42no—
1518C4—44no—
1519C4—42no—
1520C4—44no—
1521C4—42no—
1522C4—44no—
1523C4—44no—
1524C4—42no—
1525C4—42no—
1526C4—41no—
1527C4—42no—
1528C4—42no—
1529C4—42no—
1530C4—42no—
1531C4—42no—
1532C4#353714yes—
1533C2—81no—
1534C2—82no—
1535C2—81no—
1536C2—82no—
1537C2—84no—
1538C2C2×#353711yescharacteristic
1539C2#6291312yes—
1540C2#6291711yescharacteristic
1541C2#6305212yes—
1542C2#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. #59817C2semidirect
2. #59694C2semidirect
3. #58905C2semidirect
4. #58804C2semidirect
5. #58729C2semidirect
6. #58006C2semidirect
7. #53716C2semidirect
8. #53099C2semidirect
9. #53095C2semidirect
10. #52960C2semidirect
11. #52485C2semidirect
12. #47726C2semidirect
13. #45332C2semidirect
14. #45314C2semidirect
15. #45245C2semidirect
16. #45244C2semidirect
17. #45241C2semidirect
18. #42916C2semidirect
19. #42911C2semidirect
20. #42862C2semidirect
21. #42787C2semidirect
22. #42746C2semidirect
23. #42341C2semidirect
24. #41021C2semidirect
25. #39790C2semidirect
26. #39747C2semidirect
27. #36696C2semidirect
28. #36007C2semidirect
29. #35771C2semidirect

Maximal subgroups

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

subgroupindex
#598172
#596942
#589052
#588042
#587292
#580062
#537162
#530992
#530952
#529602
#524852
#477262
#453322
#453142
#452452
#452442
#452412
#429162
#429112
#428622
#427872
#427462
#423412
#410212
#397902
#397472
#366962
#360072
#357712