Finite Group Databasebeta

← #7895519

Subgroups — #7895519

Order 512.

4181 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59963C212yesmaximal, complemented
2#59870C211yesmaximal, characteristic, complemented
3#52274C211yesmaximal, characteristic, complemented
4#52026C214yesmaximal, complemented
5#51850C214yesmaximal, complemented
6#49536C214yesmaximal, complemented
7#47345C214yesmaximal, complemented
8#46285C212yesmaximal, complemented
9#45370C212yesmaximal, complemented
10#45233C212yesmaximal, complemented
11#45007C212yesmaximal
12#44304C214yesmaximal, complemented
13#42884C212yesmaximal, complemented
14#42850C212yesmaximal, complemented
15#41760C214yesmaximal, complemented
16#39765C211yesmaximal, characteristic
17#39765C211yesmaximal, characteristic
18#39509C212yesmaximal, complemented
19#39243C212yesmaximal
20#38472C212yesmaximal, complemented
21#38237C212yesmaximal, complemented
22#38237C212yesmaximal, complemented
23#37143C212yesmaximal, complemented
24#36271C211yesmaximal, characteristic
25#35869C212yesmaximal, complemented
26#35658C212yesmaximal, complemented
27#35208C211yesmaximal, characteristic, complemented
28#34499C212yesmaximal, complemented
29#34337C211yesmaximal, characteristic, complemented
30C2×#557C2211yescharacteristic
31C2×#556C2212yes—
32#2863C2212yes—
33#2860C2212yes—
34#2860C2212yes—
35#2859C2212yes—
36#2858C2211yescharacteristic
37#2839C2214yes—
38#2821C2214yes—
39#2810C2214yes—
40#2809C2211yescharacteristic
41#2808C2212yes—
42#2808C2212yes—
43#2808C2212yes—
44#2808C2212yes—
45#2807C2214yes—
46#2806C2211yescharacteristic
47#2805C2212yes—
48#2805C2211yescharacteristic
49#2805C2212yes—
50#2804C2212yes—
51#2804C2212yes—
52#2802C2214yes—
53#2802C2212yes—
54#2799C2212yes—
55#2798C2214yes—
56#2798C2214yes—
57#2796C2214yes—
58#2795C2214yes—
59#2794C2214yes—
60#2793C2214yes—
61#2793C2214yes—
62#2791C2212yes—
63#2791C2214yes—
64#2790C2214yes—
65#2788C2214yes—
66#2788C2214yes—
67#2788C2214yes—
68#2787C2214yes—
69#2783C2214yes—
70#2779C2214yes—
71#2775C2214yes—
72#2774C2212yes—
73#2768C2214yes—
74#2768C2214yes—
75#2767C2214yes—
76#2755C2212yes—
77#2745C2214yes—
78#2745C2214yes—
79#2743C2214yes—
80#2727C2214yes—
81#2726C2211yescharacteristic
82#2724C2212yes—
83#2724C2212yes—
84#2721C2214yes—
85#2721C2214yes—
86#2719C2214yes—
87#2718C2214yes—
88#2713C2212yes—
89#2707C2214yes—
90#2695C2214yes—
91#2690C2214yes—
92#2690C2214yes—
93#2666C2214yes—
94#2655C2214yes—
95#2655C2214yes—
96#2650C2214yes—
97#2649C2214yes—
98#2645C2212yes—
99#2640C2212yes—
100#2640C2212yes—
101#2637C2214yes—
102#2628C2214yes—
103#2604C2214yes—
104#2604C2214yes—
105#2601C2214yes—
106#2599C2214yes—
107#2599C2214yes—
108#2597C2214yes—
109#2597C2214yes—
110#2596C2214yes—
111#2596C2214yes—
112#2594C2214yes—
113#2594C2214yes—
114#2592C2212yes—
115#2592C2212yes—
116#2592C2212yes—
117#2590C2214yes—
118#2587C2214yes—
119#2585C2214yes—
120#2582C2211yescharacteristic
121#2581C2214yes—
122#2574C2214yes—
123#2571C2212yes—
124#2568C2212yes—
125#2567C2211yescharacteristic
126#2567C2211yescharacteristic
127#2567C2212yes—
128#2566C2212yes—
129#2565C2212yes—
130#2562C2214yes—
131#2560C2214yes—
132#2558C2214yes—
133#2553C2214yes—
134#2552C2211yescharacteristic
135#2548C2211yescharacteristic
136#2546C2211yescharacteristic
137#2545C2212yes—
138#2533C2214yes—
139#2533C2214yes—
140#2532C2214yes—
141#2530C2214yes—
142#2530C2214yes—
143#2529C2214yes—
144#2529C2214yes—
145#2528C2214yes—
146#2528C2214yes—
147#2527C2214yes—
148#2527C2214yes—
149#2527C2214yes—
150#2522C2214yes—
151#2515C2214yes—
152#2514C2212yes—
153#2513C2212yes—
154#2512C2212yes—
155#2512C2212yes—
156#2512C2212yes—
157#2511C2212yes—
158#2511C2212yes—
159#2511C2212yes—
160#2511C2214yes—
161#2509C2212yes—
162#2509C2212yes—
163#2507C2212yes—
164#2506C2212yes—
165#2505C2214yes—
166#2505C2214yes—
167#2498C2214yes—
168#2497C2214yes—
169#2496C2214yes—
170#2496C2214yes—
171#2479C2214yes—
172#2478C2214yes—
173#2478C2214yes—
174#2469C2214yes—
175#2469C2214yes—
176#2469C2214yes—
177#2469C2214yes—
178#2462C2214yes—
179#2458C2214yes—
180#2458C2214yes—
181#2454C2212yes—
182#2454C2212yes—
183#2454C2212yes—
184#2453C2212yes—
185#2453C2212yes—
186#2453C2212yes—
187#2453C2212yes—
188#2452C2212yes—
189#2448C2212yes—
190#2448C2212yes—
191#2446C2212yes—
192#2446C2212yes—
193#2446C2212yes—
194#2446C2212yes—
195#2445C2212yes—
196#2445C2212yes—
197#2419C2214yes—
198#2402C2212yes—
199#2402C2212yes—
200#2399C2212yes—
201#2396C2214yes—
202#2383C2214yes—
203#2378C2214yes—
204#2373C2214yes—
205#2370C2214yes—
206#2370C2214yes—
207#2370C2212yes—
208#2367C2212yes—
209#2367C2212yes—
210#2367C2212yes—
211#2367C2212yes—
212#2366C2211yescharacteristic
213#2365C2212yes—
214#2365C2212yes—
215#2365C2212yes—
216#2365C2211yescharacteristic
217#2365C2211yescharacteristic
218#2355C2212yes—
219#2355C2212yes—
220#2354C2212yes—
221#2351C2212yes—
222Q8×C4⋊C4C2212yes—
223Q8×C4⋊C4C2211yescharacteristic
224Q8×C4⋊C4C2212yes—
225Q8×C4⋊C4C2212yes—
226Q8×C4⋊C4C2211yescharacteristic
227#2349C2212yes—
228#2343C2214yes—
229#2335C2214yes—
230#2334C2214yes—
231#2334C2214yes—
232#2330C2212yes—
233#2330C2214yes—
234#2330C2212yes—
235#2329C2214yes—
236#2327C2212yes—
237#2326C2212yes—
238#2326C2212yes—
239#2320C2212yes—
240#2319C2212yes—
241#2319C2212yes—
242#2314C2214yes—
243C4×C4⋊Q8C2212yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2211yescharacteristic
247C4×#125C2212yes—
248C4×#124C2212yes—
249#2295C2212yes—
250#2295C2211yescharacteristic
251#2295C2212yes—
252#2295C2211yescharacteristic
253#2295C2212yes—
254#2295C2212yes—
255#2295C2212yes—
256#2293C2212yes—
257#2276C2212yes—
258C42×Q8C2211yescharacteristic
259#557—28no—
260#556—216no—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×#127C2311yescharacteristic
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#125C2314yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#125C2312yes—
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2314yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×#117C2314yes—
306C2×#117C2314yes—
307#401C2314yes—
308#401C2314yes—
309#400C2312yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2312yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2312yes—
326#400C2312yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2312yes—
333#400C2314yes—
334#400C2314yes—
335#400C2312yes—
336#400C2314yes—
337#400C2312yes—
338#400C2312yes—
339#400C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2312yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2312yes—
358#398C2314yes—
359#398C2314yes—
360#398C2312yes—
361#398C2312yes—
362#398C2312yes—
363#398C2314yes—
364#398C2312yes—
365#398C2312yes—
366#398C2312yes—
367#398C2312yes—
368#398C2312yes—
369#398C2312yes—
370#398C2312yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#395C2312yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2312yes—
399#395C2312yes—
400#395C2312yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#391C2312yes—
414#391C2312yes—
415#391C2311yescharacteristic
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2314yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2314yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2311yescharacteristic
432#391C2312yes—
433#391C2311yescharacteristic
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2311yescharacteristic
438#391C2312yes—
439#391C2312yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#390C2312yes—
447#390C2312yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2312yes—
461#389C2311yescharacteristic
462#389C2312yes—
463#389C2314yes—
464#389C2312yes—
465#389C2311yescharacteristic
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2311yescharacteristic
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2311yescharacteristic
503#389C2312yes—
504#389C2314yes—
505#389C2312yes—
506#389C2312yes—
507#389C2311yescharacteristic
508#389C2311yescharacteristic
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#387C2314yes—
549#387C2312yes—
550#387C2312yes—
551#387C2312yes—
552#387C2312yes—
553#387C2314yes—
554#387C2314yes—
555#387C2312yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2312yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2312yes—
588#387C2314yes—
589#387C2312yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2312yes—
594#387C2312yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2312yes—
602#387C2314yes—
603#387C2312yes—
604#387C2314yes—
605#387C2314yes—
606#387C2312yes—
607#387C2314yes—
608#387C2312yes—
609#387C2314yes—
610#387C2312yes—
611#387C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#384C2312yes—
631#384C2311yescharacteristic
632#384C2311yescharacteristic
633#384C2311yescharacteristic
634#384C2312yes—
635#384C2312yes—
636#384C2312yes—
637#384C2314yes—
638#384C2314yes—
639#384C2312yes—
640#383C2314yes—
641#383C2314yes—
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2314yes—
646#382C2314yes—
647#382C2314yes—
648#382C2314yes—
649#381C2314yes—
650#381C2314yes—
651#380C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2314yes—
655#380C2314yes—
656#380C2314yes—
657#380C2314yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2311yescharacteristic
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704#376C2312yes—
705#376C2312yes—
706#376C2312yes—
707#376C2314yes—
708#376C2314yes—
709#376C2314yes—
710C2×#95C2314yes—
711C43C2312yes—
712C43C2311yescharacteristic
713C43C2312yes—
714C22×Q8C2412yes—
715C22×Q8C2411yescharacteristic
716C22×Q8C2411yescharacteristic
717C22×Q8C2412yes—
718C22×Q8C2412yes—
719C22×Q8C2412yes—
720C22×Q8C2411yescharacteristic
721C22×D4C2412yes—
722C22×D4C2412yes—
723C22×D4C2412yes—
724C23×C4C2414yes—
725C23×C4C2414yes—
726C23×C4C2414yes—
727C4⋊Q8—28no—
728C4⋊Q8—28no—
729C4⋊Q8—24no—
730C4⋊Q8—24no—
731C4⋊Q8—42no—
732C4⋊Q8—42no—
733#127—42no—
734#126—216no—
735#126—216no—
736#126—84no—
737#126—84no—
738#126—84no—
739#125—28no—
740#125—216no—
741#125—44no—
742#125—48no—
743#125—44no—
744#124—28no—
745#124—28no—
746#124—28no—
747#123—48no—
748#123—84no—
749C22⋊Q8—216no—
750C4×Q8—28no—
751C4×Q8—28no—
752C4×Q8—28no—
753C4×Q8—28no—
754C4×Q8—24no—
755C4×Q8—24no—
756C4×Q8—24no—
757C4×Q8—44no—
758C4×Q8—44no—
759C4×Q8—44no—
760C4×Q8—44no—
761C4×Q8—42no—
762C4×Q8—82no—
763C4×Q8—84no—
764C4×Q8—82no—
765C4×Q8—82no—
766C4×Q8#4118yes—
767C4×D4—28no—
768C4×D4—44no—
769C4×D4—44no—
770C4×D4—44no—
771#117—216no—
772#117—84no—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2412yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C42C2414yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2412yes—
880C2×C42C2412yes—
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2414yes—
884C2×C42C2411yescharacteristic
885C2×C42C2411yescharacteristic
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2412yes—
891C2×C42C2411yescharacteristic
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2411yescharacteristic
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2411yescharacteristic
907C2×C42C2412yes—
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2412yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2412yes—
919#95C2414yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2412yes—
928#95C2414yes—
929#95C2414yes—
930#95C2412yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2412yes—
951#95C2414yes—
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989C24C2514yes—
990C2×Q8—24no—
991C2×Q8—24no—
992C2×Q8—22no—
993C2×Q8—24no—
994C2×Q8—22no—
995C2×Q8—24no—
996C2×Q8—24no—
997C2×Q8—22no—
998C2×Q8—22no—
999C2×Q8—24no—
1000C2×Q8—42no—
1001C2×Q8—42no—
1002C2×Q8—41no—
1003C2×Q8—42no—
1004C2×Q8—41no—
1005C2×Q8—42no—
1006C2×Q8—42no—
1007C2×Q8—41no—
1008C2×Q8—41no—
1009C2×Q8—42no—
1010C2×Q8C2×#4114yes—
1011C2×D4—24no—
1012C2×D4—24no—
1013C2×D4—24no—
1014C2×D4—24no—
1015C2×D4—42no—
1016C2×D4—42no—
1017C2×D4—42no—
1018C2×D4—42no—
1019C2×D4—42no—
1020C22×C4—28no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C22×C4C2512yes—
1032C22×C4C2514yes—
1033C22×C4C2512yes—
1034C22×C4C2514yes—
1035C22×C4C2511yescharacteristic
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2514yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2511yescharacteristic
1051C22×C4C2511yescharacteristic
1052C22×C4C2512yes—
1053C22×C4C2511yescharacteristic
1054C22×C4C2511yescharacteristic
1055C22×C4C2511yescharacteristic
1056C22×C4C2511yescharacteristic
1057C4⋊C4—24no—
1058C4⋊C4—28no—
1059C4⋊C4—22no—
1060C4⋊C4—28no—
1061C4⋊C4—28no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—28no—
1068C4⋊C4—24no—
1069C4⋊C4—28no—
1070C4⋊C4—24no—
1071C4⋊C4—22no—
1072C4⋊C4—22no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—22no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—28no—
1080C4⋊C4—22no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—22no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—42no—
1087C4⋊C4—44no—
1088C4⋊C4—41no—
1089C4⋊C4—41no—
1090C4⋊C4—42no—
1091C4⋊C4—41no—
1092C4⋊C4—44no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—44no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—44no—
1104C4⋊C4—42no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—41no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4C2×#4114yes—
1134C4⋊C4C2×#4118yes—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C42—28no—
1161C42—24no—
1162C42—24no—
1163C42—28no—
1164C42—24no—
1165C42—24no—
1166C42—24no—
1167C42—24no—
1168C42—24no—
1169C42—24no—
1170C42—22no—
1171C42—22no—
1172C42—42no—
1173C42—41no—
1174C42—41no—
1175C42—42no—
1176C42—42no—
1177C42—44no—
1178C42—44no—
1179C42—44no—
1180C42—42no—
1181C42—44no—
1182C42—44no—
1183C42—44no—
1184C42—41no—
1185C42—44no—
1186C42—42no—
1187C42—44no—
1188C42—44no—
1189C42—42no—
1190C42—42no—
1191C42C2×#4118yes—
1192C42C2×#4114yes—
1193C422−1+414yes—
1194C23—24no—
1195C23—24no—
1196C23—24no—
1197C23—24no—
1198C23—24no—
1199C23—24no—
1200C23—24no—
1201C23C2611yescharacteristic
1202Q8—28no—
1203Q8—44no—
1204Q8—48no—
1205Q8—48no—
1206Q8—48no—
1207Q8—84no—
1208Q8—82no—
1209D4—48no—
1210D4—84no—
1211D4—162no—
1212C2×C4—22no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—21no—
1217C2×C4—22no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—22no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—21no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—21no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—88no—
1287C2×C4—88no—
1288C2×C4—164no—
1289C2×C4C22×#4114yes—
1290C2×C4C22×#4114yes—
1291C2×C4C22×#4112yes—
1292C2×C4C22×#4112yes—
1293C2×C4C22×#4112yes—
1294C2×C4C2×2−1+412yes—
1295C2×C4C2×2−1+412yes—
1296C2×C4C2×2−1+412yes—
1297C2×C4#58512yes—
1298C2×C4#58512yes—
1299C22—44no—
1300C22—44no—
1301C22—44no—
1302C22—44no—
1303C22—44no—
1304C22—44no—
1305C22—44no—
1306C22C23×#4111yescharacteristic
1307C22C22×2−1+411yescharacteristic
1308C22C2×#58511yescharacteristic
1309C22C2×#58511yescharacteristic
1310C22H(7,𝔽2)11yescharacteristic
1311C222−1+611yescharacteristic
1312C222−1+611yescharacteristic
1313C4—24no—
1314C4—22no—
1315C4—24no—
1316C4—22no—
1317C4—22no—
1318C4—22no—
1319C4—22no—
1320C4—42no—
1321C4—42no—
1322C4—42no—
1323C4—44no—
1324C4—42no—
1325C4—42no—
1326C4—44no—
1327C4—42no—
1328C4—41no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—44no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—44no—
1337C4—42no—
1338C4—44no—
1339C4—42no—
1340C4#350714yes—
1341C2—84no—
1342C2C2×#350711yescharacteristic
1343C2#6285111yescharacteristic
1344C2#6288911yescharacteristic
1345C2#6292611yescharacteristic
1346C2#6296411yescharacteristic
1347C2#6300911yescharacteristic
1348C2#6305611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59963C2semidirect
2. #59870C2semidirect
3. #52274C2semidirect
4. #52026C2semidirect
5. #51850C2semidirect
6. #49536C2semidirect
7. #47345C2semidirect
8. #46285C2semidirect
9. #45370C2semidirect
10. #45233C2semidirect
12. #44304C2semidirect
13. #42884C2semidirect
14. #42850C2semidirect
15. #41760C2semidirect
18. #39509C2semidirect
20. #38472C2semidirect
21. #38237C2semidirect
22. #38237C2semidirect
23. #37143C2semidirect
25. #35869C2semidirect
26. #35658C2semidirect
27. #35208C2semidirect
28. #34499C2semidirect
29. #34337C2semidirect

Maximal subgroups

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

subgroupindex
#599632
#598702
#522742
#520262
#518502
#495362
#473452
#462852
#453702
#452332
#450072
#443042
#428842
#428502
#417602
#397652
#395092
#392432
#384722
#382372
#371432
#362712
#358692
#356582
#352082
#344992
#343372