Finite Group Databasebeta

← #7895522

Subgroups — #7895522

Order 512.

4245 conjugacy classes of subgroups.

The subgroup lattice has 1355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59961C212yesmaximal, complemented
2#59863C211yesmaximal, characteristic
3#52274C211yesmaximal, characteristic, complemented
4#51485C214yesmaximal, complemented
5#50279C214yesmaximal, complemented
6#50002C214yesmaximal, complemented
7#47506C214yesmaximal, complemented
8#46023C212yesmaximal, complemented
9#45363C212yesmaximal, complemented
10#45318C212yesmaximal, complemented
11#45021C212yesmaximal, complemented
12#44054C214yesmaximal, complemented
13#42886C212yesmaximal
14#42582C212yesmaximal, complemented
15#41747C214yesmaximal, complemented
16#39756C211yesmaximal, characteristic
17#39637C211yesmaximal, characteristic, complemented
18#39574C212yesmaximal, complemented
19#39501C212yesmaximal, complemented
20#39027C212yesmaximal, complemented
21#38238C212yesmaximal
22#38225C212yesmaximal, complemented
23#37203C212yesmaximal, complemented
24#36466C211yesmaximal, characteristic, complemented
25#35871C212yesmaximal, complemented
26#35602C212yesmaximal, complemented
27#35199C211yesmaximal, characteristic, complemented
28#34490C212yesmaximal, complemented
29#34331C211yesmaximal, characteristic
30C2×#559C2211yescharacteristic
31C2×#557C2212yes—
32#2863C2212yes—
33#2862C2212yes—
34#2860C2212yes—
35#2859C2211yescharacteristic
36#2859C2212yes—
37#2831C2214yes—
38#2820C2214yes—
39#2809C2214yes—
40#2809C2211yescharacteristic
41#2809C2212yes—
42#2808C2214yes—
43#2808C2212yes—
44#2808C2212yes—
45#2808C2212yes—
46#2808C2212yes—
47#2806C2211yescharacteristic
48#2806C2214yes—
49#2806C2212yes—
50#2805C2212yes—
51#2805C2211yescharacteristic
52#2802C2212yes—
53#2802C2214yes—
54#2800C2214yes—
55#2799C2212yes—
56#2793C2214yes—
57#2791C2212yes—
58#2786C2214yes—
59#2777C2214yes—
60#2775C2214yes—
61#2774C2212yes—
62#2774C2214yes—
63#2773C2214yes—
64#2772C2214yes—
65#2772C2214yes—
66#2770C2214yes—
67#2770C2214yes—
68#2768C2214yes—
69#2755C2212yes—
70#2754C2214yes—
71#2754C2214yes—
72#2754C2214yes—
73#2747C2214yes—
74#2738C2214yes—
75#2738C2214yes—
76#2727C2212yes—
77#2727C2212yes—
78#2726C2212yes—
79#2726C2211yescharacteristic
80#2722C2214yes—
81#2721C2214yes—
82#2721C2214yes—
83#2716C2214yes—
84#2713C2212yes—
85#2704C2214yes—
86#2700C2214yes—
87#2698C2214yes—
88#2694C2214yes—
89#2694C2214yes—
90#2690C2214yes—
91#2674C2214yes—
92#2674C2214yes—
93#2666C2214yes—
94#2665C2214yes—
95#2654C2214yes—
96#2650C2214yes—
97#2647C2212yes—
98#2644C2212yes—
99#2641C2212yes—
100#2633C2214yes—
101#2632C2214yes—
102#2621C2214yes—
103#2611C2214yes—
104#2611C2214yes—
105#2607C2214yes—
106#2604C2214yes—
107#2592C2214yes—
108#2590C2214yes—
109#2589C2214yes—
110#2589C2214yes—
111#2587C2214yes—
112#2585C2214yes—
113#2584C2214yes—
114#2584C2212yes—
115#2584C2212yes—
116#2582C2211yescharacteristic
117#2581C2214yes—
118#2580C2212yes—
119#2574C2214yes—
120#2570C2212yes—
121#2570C2212yes—
122#2569C2214yes—
123#2568C2211yescharacteristic
124#2563C2212yes—
125#2560C2214yes—
126#2556C2214yes—
127#2552C2212yes—
128#2552C2211yescharacteristic
129#2551C2211yescharacteristic
130#2551C2212yes—
131#2551C2211yescharacteristic
132#2550C2212yes—
133#2550C2214yes—
134#2549C2214yes—
135#2548C2212yes—
136#2547C2212yes—
137#2546C2211yescharacteristic
138#2536C2214yes—
139#2532C2214yes—
140#2532C2214yes—
141#2532C2214yes—
142#2532C2214yes—
143#2532C2214yes—
144#2530C2214yes—
145#2530C2214yes—
146#2529C2214yes—
147#2522C2214yes—
148#2520C2214yes—
149#2519C2214yes—
150#2519C2214yes—
151#2515C2214yes—
152#2513C2212yes—
153#2513C2212yes—
154#2513C2212yes—
155#2513C2212yes—
156#2512C2212yes—
157#2512C2212yes—
158#2509C2212yes—
159#2508C2212yes—
160#2508C2212yes—
161#2507C2212yes—
162#2507C2212yes—
163#2506C2212yes—
164#2506C2212yes—
165#2499C2214yes—
166#2492C2214yes—
167#2492C2214yes—
168#2485C2214yes—
169#2478C2214yes—
170#2478C2214yes—
171#2475C2214yes—
172#2474C2214yes—
173#2466C2214yes—
174#2466C2214yes—
175#2466C2214yes—
176#2462C2214yes—
177#2454C2212yes—
178#2454C2212yes—
179#2453C2214yes—
180#2453C2214yes—
181#2452C2212yes—
182#2452C2212yes—
183#2452C2212yes—
184#2452C2212yes—
185#2451C2212yes—
186#2451C2212yes—
187#2448C2212yes—
188#2448C2212yes—
189#2448C2212yes—
190#2448C2212yes—
191#2446C2212yes—
192#2439C2214yes—
193#2438C2214yes—
194#2438C2214yes—
195#2429C2214yes—
196#2423C2214yes—
197#2415C2214yes—
198#2402C2212yes—
199#2402C2212yes—
200#2399C2212yes—
201#2396C2214yes—
202#2382C2214yes—
203#2381C2214yes—
204#2373C2214yes—
205#2371C2214yes—
206#2370C2212yes—
207#2370C2212yes—
208#2369C2212yes—
209#2369C2212yes—
210#2367C2212yes—
211#2367C2212yes—
212#2366C2211yescharacteristic
213#2365C2212yes—
214#2359C2214yes—
215#2357C2212yes—
216#2356C2212yes—
217#2356C2212yes—
218#2356C2214yes—
219#2355C2211yescharacteristic
220#2355C2212yes—
221#2354C2212yes—
222#2354C2212yes—
223#2354C2212yes—
224#2351C2212yes—
225Q8×C4⋊C4C2211yescharacteristic
226Q8×C4⋊C4C2211yescharacteristic
227Q8×C4⋊C4C2211yescharacteristic
228#2349C2212yes—
229#2336C2214yes—
230#2336C2214yes—
231#2335C2214yes—
232#2331C2212yes—
233#2331C2212yes—
234#2331C2212yes—
235#2331C2214yes—
236#2330C2212yes—
237#2326C2212yes—
238#2320C2214yes—
239#2320C2212yes—
240#2320C2212yes—
241#2319C2212yes—
242#2314C2214yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×C4⋊Q8C2212yes—
245C4×C4⋊Q8C2211yescharacteristic
246C4×#127C2211yescharacteristic
247C4×#125C2212yes—
248C4×#125C2212yes—
249C4×#124C2212yes—
250#2295C2212yes—
251#2295C2211yescharacteristic
252#2295C2211yescharacteristic
253#2295C2212yes—
254#2295C2212yes—
255#2293C2212yes—
256#2293C2212yes—
257#2275C2212yes—
258C42×Q8C2211yescharacteristic
259#559—28no—
260#557—216no—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×#127C2311yescharacteristic
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#125C2314yes—
280C2×#124C2312yes—
281C2×#124C2312yes—
282C2×#124C2314yes—
283C2×#123C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C4×Q8C2314yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2314yes—
299C2×C4×Q8C2311yescharacteristic
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×#117C2314yes—
308C2×#117C2314yes—
309C2×#117C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2312yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2312yes—
321#400C2312yes—
322#400C2314yes—
323#400C2312yes—
324#400C2312yes—
325#400C2312yes—
326#400C2312yes—
327#400C2312yes—
328#400C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2312yes—
350#398C2314yes—
351#398C2314yes—
352#398C2312yes—
353#398C2314yes—
354#398C2312yes—
355#398C2314yes—
356#398C2312yes—
357#398C2312yes—
358#398C2312yes—
359#398C2312yes—
360#398C2312yes—
361#398C2312yes—
362#398C2312yes—
363#398C2312yes—
364#398C2312yes—
365#398C2314yes—
366#398C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
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#395C2314yes—
399#395C2312yes—
400#395C2314yes—
401#395C2312yes—
402#395C2312yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2314yes—
424#391C2314yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#391C2311yescharacteristic
438#391C2314yes—
439#391C2314yes—
440#391C2311yescharacteristic
441#391C2314yes—
442#391C2312yes—
443#391C2312yes—
444#391C2311yescharacteristic
445#391C2312yes—
446#391C2311yescharacteristic
447#390C2314yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2312yes—
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2311yescharacteristic
466#389C2314yes—
467#389C2312yes—
468#389C2311yescharacteristic
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2314yes—
510#389C2311yescharacteristic
511#389C2312yes—
512#389C2311yescharacteristic
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2311yescharacteristic
519#389C2311yescharacteristic
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#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#387C2312yes—
556#387C2314yes—
557#387C2312yes—
558#387C2312yes—
559#387C2314yes—
560#387C2312yes—
561#387C2312yes—
562#387C2312yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2312yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2312yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2312yes—
597#387C2314yes—
598#387C2312yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2312yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2312yes—
609#387C2312yes—
610#387C2312yes—
611#387C2312yes—
612#386C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#384C2311yescharacteristic
625#384C2312yes—
626#384C2311yescharacteristic
627#384C2311yescharacteristic
628#384C2312yes—
629#384C2312yes—
630#384C2312yes—
631#384C2311yescharacteristic
632#384C2311yescharacteristic
633#383C2314yes—
634#383C2314yes—
635#383C2314yes—
636#383C2314yes—
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2314yes—
641#382C2312yes—
642#382C2314yes—
643#382C2314yes—
644#382C2314yes—
645#382C2312yes—
646#382C2312yes—
647#382C2314yes—
648#381C2314yes—
649#381C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2314yes—
655#380C2314yes—
656#380C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
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⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2311yescharacteristic
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704#376C2312yes—
705#376C2312yes—
706#376C2314yes—
707#376C2312yes—
708#376C2314yes—
709#376C2314yes—
710C2×#95C2314yes—
711C43C2312yes—
712C43C2311yescharacteristic
713C43C2312yes—
714C22×Q8C2411yescharacteristic
715C22×Q8C2411yescharacteristic
716C22×Q8C2414yes—
717C22×Q8C2414yes—
718C22×Q8C2412yes—
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×D4C2412yes—
722C22×D4C2412yes—
723C22×D4C2412yes—
724C23×C4C2414yes—
725C23×C4C2414yes—
726C23×C4C2414yes—
727C4⋊Q8—28no—
728C4⋊Q8—216no—
729C4⋊Q8—28no—
730C4⋊Q8—24no—
731C4⋊Q8—44no—
732C4⋊Q8—42no—
733C4⋊Q8—82no—
734C4⋊Q8—82no—
735#127—24no—
736#126—48no—
737#126—84no—
738#126—84no—
739#125—28no—
740#125—216no—
741#125—216no—
742#125—28no—
743#125—44no—
744#125—84no—
745#125—84no—
746#124—28no—
747#124—28no—
748#124—84no—
749#123—216no—
750C22⋊Q8—84no—
751C22⋊Q8—84no—
752C22⋊Q8—84no—
753C22⋊Q8—84no—
754C4×Q8—28no—
755C4×Q8—28no—
756C4×Q8—24no—
757C4×Q8—216no—
758C4×Q8—28no—
759C4×Q8—24no—
760C4×Q8—24no—
761C4×Q8—24no—
762C4×Q8—84no—
763C4×Q8—82no—
764C4×Q8—82no—
765C4×Q8#4118yes—
766C4×D4—28no—
767C4×D4—28no—
768C4×D4—28no—
769C4×D4—28no—
770C4×D4—44no—
771C4×D4—82no—
772C4×D4—82no—
773#117—48no—
774#117—84no—
775#117—84no—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C42C2412yes—
882C2×C42C2411yescharacteristic
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2412yes—
888C2×C42C2414yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2411yescharacteristic
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2414yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2411yescharacteristic
900C2×C42C2412yes—
901C2×C42C2411yescharacteristic
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2412yes—
909C2×C42C2411yescharacteristic
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915#95C2412yes—
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2412yes—
929#95C2414yes—
930#95C2412yes—
931#95C2412yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992C24C2514yes—
993C2×Q8—22no—
994C2×Q8—28no—
995C2×Q8—24no—
996C2×Q8—22no—
997C2×Q8—22no—
998C2×Q8—22no—
999C2×Q8—28no—
1000C2×Q8—24no—
1001C2×Q8—41no—
1002C2×Q8—41no—
1003C2×Q8—44no—
1004C2×Q8—42no—
1005C2×Q8—44no—
1006C2×Q8—44no—
1007C2×Q8—42no—
1008C2×Q8—44no—
1009C2×Q8—42no—
1010C2×Q8—41no—
1011C2×Q8—41no—
1012C2×Q8—42no—
1013C2×Q8C2×#4114yes—
1014C2×D4—24no—
1015C2×D4—24no—
1016C2×D4—24no—
1017C2×D4—24no—
1018C2×D4—24no—
1019C2×D4—42no—
1020C2×D4—42no—
1021C2×D4—42no—
1022C2×D4—42no—
1023C22×C4—28no—
1024C22×C4—28no—
1025C22×C4—28no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4—44no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2514yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2514yes—
1048C22×C4C2511yescharacteristic
1049C22×C4C2514yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2511yescharacteristic
1053C22×C4C2511yescharacteristic
1054C22×C4C2512yes—
1055C22×C4C2511yescharacteristic
1056C22×C4C2511yescharacteristic
1057C22×C4C2512yes—
1058C22×C4C2511yescharacteristic
1059C22×C4C2511yescharacteristic
1060C4⋊C4—22no—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—24no—
1065C4⋊C4—28no—
1066C4⋊C4—24no—
1067C4⋊C4—28no—
1068C4⋊C4—24no—
1069C4⋊C4—28no—
1070C4⋊C4—24no—
1071C4⋊C4—28no—
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—22no—
1078C4⋊C4—22no—
1079C4⋊C4—24no—
1080C4⋊C4—28no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—22no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—22no—
1089C4⋊C4—41no—
1090C4⋊C4—42no—
1091C4⋊C4—41no—
1092C4⋊C4—41no—
1093C4⋊C4—41no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—41no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—41no—
1137C4⋊C4C2×#4114yes—
1138C4⋊C4C2×#4118yes—
1139C4⋊C42−1+414yes—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—28no—
1143C22⋊C4—28no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
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—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C42—24no—
1166C42—28no—
1167C42—24no—
1168C42—28no—
1169C42—24no—
1170C42—24no—
1171C42—24no—
1172C42—22no—
1173C42—24no—
1174C42—24no—
1175C42—24no—
1176C42—24no—
1177C42—22no—
1178C42—41no—
1179C42—42no—
1180C42—44no—
1181C42—44no—
1182C42—42no—
1183C42—44no—
1184C42—44no—
1185C42—44no—
1186C42—41no—
1187C42—42no—
1188C42—41no—
1189C42—44no—
1190C42—44no—
1191C42—44no—
1192C42—42no—
1193C42—44no—
1194C42—42no—
1195C42—42no—
1196C42C2×#4118yes—
1197C42C2×#4114yes—
1198C422−1+414yes—
1199C23—24no—
1200C23—24no—
1201C23—24no—
1202C23—24no—
1203C23—24no—
1204C23—24no—
1205C23—24no—
1206C23C2611yescharacteristic
1207Q8—28no—
1208Q8—44no—
1209Q8—88no—
1210Q8—84no—
1211Q8—88no—
1212Q8—82no—
1213Q8—84no—
1214D4—48no—
1215D4—48no—
1216D4—84no—
1217C2×C4—21no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—21no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—21no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—88no—
1291C2×C4—88no—
1292C2×C4—88no—
1293C2×C4C22×#4114yes—
1294C2×C4C22×#4112yes—
1295C2×C4C22×#4114yes—
1296C2×C4C22×#4112yes—
1297C2×C4C22×#4112yes—
1298C2×C4C2×2−1+412yes—
1299C2×C4C2×2−1+414yes—
1300C2×C4C2×2−1+412yes—
1301C2×C4C2×2−1+412yes—
1302C2×C4C2×2−1+412yes—
1303C2×C4#58512yes—
1304C22—44no—
1305C22—44no—
1306C22—44no—
1307C22—44no—
1308C22—44no—
1309C22—44no—
1310C22—44no—
1311C22C23×#4111yescharacteristic
1312C22C22×2−1+411yescharacteristic
1313C22C22×2−1+411yescharacteristic
1314C22C2×#58511yescharacteristic
1315C22H(7,𝔽2)11yescharacteristic
1316C22H(7,𝔽2)11yescharacteristic
1317C222−1+611yescharacteristic
1318C4—24no—
1319C4—22no—
1320C4—24no—
1321C4—24no—
1322C4—22no—
1323C4—22no—
1324C4—22no—
1325C4—22no—
1326C4—42no—
1327C4—44no—
1328C4—42no—
1329C4—42no—
1330C4—41no—
1331C4—42no—
1332C4—44no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—44no—
1337C4—42no—
1338C4—42no—
1339C4—44no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—42no—
1344C4—44no—
1345C4#350914yes—
1346C2—84no—
1347C2C2×#350911yescharacteristic
1348C2#6285111yescharacteristic
1349C2#6287911yescharacteristic
1350C2#6294911yescharacteristic
1351C2#6296211yescharacteristic
1352C2#6299411yescharacteristic
1353C2#6305411yescharacteristic
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. #59961C2semidirect
3. #52274C2semidirect
4. #51485C2semidirect
5. #50279C2semidirect
6. #50002C2semidirect
7. #47506C2semidirect
8. #46023C2semidirect
9. #45363C2semidirect
10. #45318C2semidirect
11. #45021C2semidirect
12. #44054C2semidirect
14. #42582C2semidirect
15. #41747C2semidirect
17. #39637C2semidirect
18. #39574C2semidirect
19. #39501C2semidirect
20. #39027C2semidirect
22. #38225C2semidirect
23. #37203C2semidirect
24. #36466C2semidirect
25. #35871C2semidirect
26. #35602C2semidirect
27. #35199C2semidirect
28. #34490C2semidirect

Maximal subgroups

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

subgroupindex
#599612
#598632
#522742
#514852
#502792
#500022
#475062
#460232
#453632
#453182
#450212
#440542
#428862
#425822
#417472
#397562
#396372
#395742
#395012
#390272
#382382
#382252
#372032
#364662
#358712
#356022
#351992
#344902
#343312