Finite Group Databasebeta

← #7898357

Subgroups — #7898357

Order 512.

4185 conjugacy classes of subgroups.

The subgroup lattice has 1369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59828C211yesmaximal, characteristic, complemented
2#59714C212yesmaximal, complemented
3#52272C211yesmaximal, characteristic, complemented
4#50513C214yesmaximal, complemented
5#50030C214yesmaximal, complemented
6#48653C214yesmaximal, complemented
7#47534C214yesmaximal, complemented
8#46295C212yesmaximal, complemented
9#45270C212yesmaximal
10#45197C212yesmaximal, complemented
11#45183C212yesmaximal, complemented
12#45021C214yesmaximal, complemented
13#42561C212yesmaximal, complemented
14#42512C212yesmaximal, complemented
15#41543C214yesmaximal, complemented
16#39801C212yesmaximal, complemented
17#39621C211yesmaximal, characteristic, complemented
18#39583C212yesmaximal, complemented
19#39501C211yesmaximal, characteristic, complemented
20#39010C212yesmaximal, complemented
21#38801C212yesmaximal, complemented
22#38291C212yesmaximal, complemented
23#37210C212yesmaximal, complemented
24#36476C211yesmaximal, characteristic, complemented
25#35818C212yesmaximal, complemented
26#35579C212yesmaximal, complemented
27#35206C211yesmaximal, characteristic, complemented
28#34490C212yesmaximal, complemented
29#34321C211yesmaximal, characteristic
30C2×#557C2212yes—
31C2×#555C2211yescharacteristic
32#2862C2211yescharacteristic
33#2861C2212yes—
34#2855C2212yes—
35#2855C2212yes—
36#2851C2212yes—
37#2839C2214yes—
38#2838C2214yes—
39#2811C2212yes—
40#2810C2211yescharacteristic
41#2809C2212yes—
42#2809C2212yes—
43#2808C2212yes—
44#2808C2214yes—
45#2808C2211yescharacteristic
46#2808C2212yes—
47#2806C2212yes—
48#2806C2212yes—
49#2805C2211yescharacteristic
50#2800C2212yes—
51#2800C2214yes—
52#2798C2214yes—
53#2798C2212yes—
54#2796C2214yes—
55#2793C2212yes—
56#2793C2214yes—
57#2788C2214yes—
58#2787C2214yes—
59#2783C2214yes—
60#2777C2214yes—
61#2777C2214yes—
62#2776C2212yes—
63#2775C2214yes—
64#2770C2214yes—
65#2770C2214yes—
66#2764C2214yes—
67#2763C2214yes—
68#2759C2212yes—
69#2759C2214yes—
70#2758C2214yes—
71#2758C2214yes—
72#2751C2214yes—
73#2744C2214yes—
74#2740C2214yes—
75#2739C2214yes—
76#2737C2214yes—
77#2737C2214yes—
78#2734C2212yes—
79#2731C2214yes—
80#2731C2214yes—
81#2729C2214yes—
82#2727C2211yescharacteristic
83#2726C2212yes—
84#2726C2212yes—
85#2723C2214yes—
86#2716C2212yes—
87#2716C2214yes—
88#2711C2214yes—
89#2711C2214yes—
90#2698C2214yes—
91#2698C2214yes—
92#2689C2214yes—
93#2666C2214yes—
94#2660C2212yes—
95#2655C2214yes—
96#2654C2214yes—
97#2652C2214yes—
98#2650C2214yes—
99#2640C2212yes—
100#2638C2214yes—
101#2638C2214yes—
102#2621C2212yes—
103#2607C2214yes—
104#2604C2214yes—
105#2604C2214yes—
106#2599C2214yes—
107#2596C2214yes—
108#2594C2214yes—
109#2589C2214yes—
110#2588C2214yes—
111#2588C2214yes—
112#2587C2214yes—
113#2586C2214yes—
114#2585C2214yes—
115#2582C2212yes—
116#2580C2212yes—
117#2577C2214yes—
118#2575C2214yes—
119#2574C2214yes—
120#2573C2214yes—
121#2570C2212yes—
122#2568C2211yescharacteristic
123#2563C2211yescharacteristic
124#2560C2214yes—
125#2556C2214yes—
126#2552C2211yescharacteristic
127#2552C2212yes—
128#2551C2212yes—
129#2550C2212yes—
130#2550C2212yes—
131#2547C2211yescharacteristic
132#2546C2212yes—
133#2542C2211yescharacteristic
134#2538C2211yescharacteristic
135#2536C2212yes—
136#2533C2214yes—
137#2532C2214yes—
138#2532C2214yes—
139#2532C2214yes—
140#2532C2214yes—
141#2532C2214yes—
142#2531C2214yes—
143#2527C2214yes—
144#2525C2214yes—
145#2524C2214yes—
146#2524C2214yes—
147#2522C2214yes—
148#2520C2214yes—
149#2515C2214yes—
150#2515C2214yes—
151#2514C2214yes—
152#2514C2212yes—
153#2513C2214yes—
154#2513C2212yes—
155#2512C2214yes—
156#2512C2212yes—
157#2511C2212yes—
158#2511C2212yes—
159#2509C2214yes—
160#2507C2214yes—
161#2506C2214yes—
162#2503C2212yes—
163#2502C2212yes—
164#2496C2212yes—
165#2495C2212yes—
166#2495C2212yes—
167#2492C2212yes—
168#2492C2212yes—
169#2492C2212yes—
170#2492C2212yes—
171#2490C2212yes—
172#2490C2212yes—
173#2489C2212yes—
174#2489C2212yes—
175#2478C2214yes—
176#2475C2214yes—
177#2475C2214yes—
178#2469C2214yes—
179#2468C2214yes—
180#2468C2214yes—
181#2462C2214yes—
182#2453C2212yes—
183#2453C2212yes—
184#2452C2214yes—
185#2451C2214yes—
186#2448C2214yes—
187#2448C2214yes—
188#2447C2212yes—
189#2446C2214yes—
190#2442C2212yes—
191#2441C2212yes—
192#2441C2212yes—
193#2440C2212yes—
194#2426C2212yes—
195#2426C2212yes—
196#2423C2214yes—
197#2423C2212yes—
198#2402C2214yes—
199#2401C2212yes—
200#2398C2212yes—
201#2396C2212yes—
202#2382C2214yes—
203#2381C2214yes—
204#2371C2214yes—
205#2370C2212yes—
206#2370C2212yes—
207#2369C2211yescharacteristic
208#2369C2211yescharacteristic
209#2367C2214yes—
210#2365C2211yescharacteristic
211#2365C2214yes—
212#2365C2212yes—
213#2363C2212yes—
214#2362C2212yes—
215#2362C2212yes—
216#2361C2212yes—
217#2357C2212yes—
218#2356C2212yes—
219#2356C2214yes—
220#2356C2212yes—
221#2355C2212yes—
222#2355C2212yes—
223#2355C2212yes—
224#2354C2211yescharacteristic
225Q8×C4⋊C4C2212yes—
226D4×C4⋊C4C2211yescharacteristic
227#2347C2212yes—
228#2347C2212yes—
229#2337C2214yes—
230#2336C2214yes—
231#2336C2214yes—
232#2331C2214yes—
233#2331C2212yes—
234#2330C2212yes—
235#2330C2212yes—
236#2326C2212yes—
237#2324C2212yes—
238#2320C2212yes—
239#2320C2212yes—
240#2320C2214yes—
241#2319C2214yes—
242#2314C2212yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2212yes—
246C4×C4⋊Q8C2211yescharacteristic
247C4×#125C2212yes—
248C4×#126C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×#121C2212yes—
251#2298C2212yes—
252#2296C2212yes—
253#2295C2212yes—
254#2295C2211yescharacteristic
255#2295C2212yes—
256#2293C2211yescharacteristic
257#2274C2212yes—
258C42×D4C2211yescharacteristic
259#557—216no—
260#555—28no—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2314yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×#126C2312yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#125C2314yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#124C2314yes—
279C2×#124C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×#121C2312yes—
287C2×#121C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2314yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2314yes—
296C2×C4×Q8C2312yes—
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2311yescharacteristic
299C2×C4×D4C2311yescharacteristic
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2314yes—
302C2×C4×D4C2312yes—
303C2×#117C2312yes—
304C2×#117C2312yes—
305C2×#117C2312yes—
306C2×#117C2312yes—
307C22×C4⋊C4C2312yes—
308C22×C42C2312yes—
309#401C2312yes—
310#401C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2312yes—
316#400C2314yes—
317#400C2314yes—
318#400C2312yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2312yes—
331#400C2312yes—
332#400C2312yes—
333#400C2312yes—
334#400C2314yes—
335#399C2312yes—
336#399C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2312yes—
356#398C2312yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2312yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2312yes—
377#397C2312yes—
378#397C2312yes—
379#397C2312yes—
380#397C2314yes—
381#396C2312yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2312yes—
387#396C2314yes—
388#396C2314yes—
389#396C2312yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2312yes—
398#394C2314yes—
399#394C2312yes—
400#394C2314yes—
401#394C2314yes—
402#394C2312yes—
403#394C2314yes—
404#394C2314yes—
405#393C2312yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2312yes—
413#393C2312yes—
414#393C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2314yes—
424#391C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2312yes—
432#391C2314yes—
433#391C2314yes—
434#391C2312yes—
435#391C2314yes—
436#391C2314yes—
437#391C2312yes—
438#391C2314yes—
439#391C2314yes—
440#391C2311yescharacteristic
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2314yes—
447#391C2311yescharacteristic
448#390C2314yes—
449#390C2312yes—
450#390C2314yes—
451#390C2312yes—
452#390C2314yes—
453#390C2312yes—
454#390C2312yes—
455#390C2311yescharacteristic
456#390C2314yes—
457#390C2314yes—
458#390C2311yescharacteristic
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2311yescharacteristic
466#389C2312yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2311yescharacteristic
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2314yes—
477#389C2312yes—
478#389C2314yes—
479#389C2312yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2312yes—
494#389C2311yescharacteristic
495#389C2312yes—
496#389C2311yescharacteristic
497#389C2314yes—
498#389C2314yes—
499#389C2312yes—
500#389C2311yescharacteristic
501#389C2311yescharacteristic
502#388C2312yes—
503#388C2312yes—
504#388C2312yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
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#388C2312yes—
523#388C2314yes—
524#388C2314yes—
525#388C2312yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2312yes—
536#388C2314yes—
537#388C2314yes—
538#388C2312yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2312yes—
543#388C2312yes—
544#387C2312yes—
545#387C2312yes—
546#387C2312yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2312yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2312yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2312yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2312yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2312yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2312yes—
598#387C2314yes—
599#387C2312yes—
600#387C2314yes—
601#387C2314yes—
602#387C2312yes—
603#387C2312yes—
604#386C2314yes—
605#386C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#384C2311yescharacteristic
619#384C2312yes—
620#384C2311yescharacteristic
621#384C2311yescharacteristic
622#384C2312yes—
623#384C2314yes—
624#384C2312yes—
625#383C2312yes—
626#383C2314yes—
627#383C2314yes—
628#383C2314yes—
629#383C2314yes—
630#383C2314yes—
631#383C2314yes—
632#383C2314yes—
633#382C2312yes—
634#382C2312yes—
635#382C2312yes—
636#382C2314yes—
637#382C2314yes—
638#382C2314yes—
639#382C2314yes—
640#382C2312yes—
641#382C2312yes—
642#381C2314yes—
643#381C2314yes—
644#381C2314yes—
645#381C2314yes—
646#380C2312yes—
647#380C2312yes—
648#380C2312yes—
649#380C2312yes—
650#380C2312yes—
651#380C2314yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2312yes—
656C4×C4⋊C4C2311yescharacteristic
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2311yescharacteristic
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707#376C2314yes—
708#376C2312yes—
709#376C2312yes—
710#376C2314yes—
711#376C2314yes—
712C43C2312yes—
713C43C2311yescharacteristic
714C22×Q8C2412yes—
715C22×Q8C2412yes—
716C22×Q8C2411yescharacteristic
717C22×Q8C2412yes—
718C22×Q8C2414yes—
719C22×Q8C2412yes—
720C22×Q8C2412yes—
721C22×D4C2411yescharacteristic
722C22×D4C2411yescharacteristic
723C22×D4C2414yes—
724C23×C4C2412yes—
725C23×C4C2412yes—
726C23×C4C2412yes—
727C23×C4C2412yes—
728C23×C4C2414yes—
729C4⋊Q8—216no—
730C4⋊Q8—24no—
731C4⋊Q8—42no—
732C4⋊Q8—42no—
733C4⋊Q8—42no—
734C4⋊Q8—44no—
735C4⋊Q8—48no—
736C4⋊Q8#4118yes—
737#126—44no—
738#126—84no—
739#126—84no—
740#125—216no—
741#125—216no—
742#125—28no—
743#125—28no—
744#125—44no—
745#125—82no—
746#124—216no—
747#124—44no—
748C22⋊Q8—44no—
749C22⋊Q8—44no—
750C22⋊Q8—44no—
751C22⋊Q8—84no—
752C22⋊Q8—82no—
753C22⋊Q8—82no—
754#121—28no—
755#121—28no—
756C4×Q8—216no—
757C4×Q8—28no—
758C4×Q8—28no—
759C4×Q8—28no—
760C4×Q8—28no—
761C4×Q8—24no—
762C4×Q8—44no—
763C4×Q8—82no—
764C4×Q8—84no—
765C4×D4—24no—
766C4×D4—24no—
767C4×D4—24no—
768C4×D4—42no—
769C4×D4—48no—
770C4×D4—82no—
771#117—28no—
772#117—28no—
773#117—28no—
774#117—82no—
775C2×C4⋊C4—44no—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C42—82no—
880C2×C42C2414yes—
881C2×C42C2412yes—
882C2×C42C2411yescharacteristic
883C2×C42C2412yes—
884C2×C42C2414yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2411yescharacteristic
888C2×C42C2414yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2414yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2412yes—
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2412yes—
906C2×C42C2411yescharacteristic
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912#95C2412yes—
913#95C2412yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2412yes—
920#95C2412yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2414yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991C24C2512yes—
992C24C2512yes—
993C2×Q8—24no—
994C2×Q8—24no—
995C2×Q8—24no—
996C2×Q8—22no—
997C2×Q8—24no—
998C2×Q8—24no—
999C2×Q8—42no—
1000C2×Q8—42no—
1001C2×Q8—42no—
1002C2×Q8—44no—
1003C2×Q8—41no—
1004C2×Q8—42no—
1005C2×Q8—42no—
1006C2×Q8—44no—
1007C2×Q8—44no—
1008C2×Q8—41no—
1009C2×Q8—42no—
1010C2×Q8—42no—
1011C2×Q8—42no—
1012C2×Q8—42no—
1013C2×Q8C2×#4118yes—
1014C2×D4—22no—
1015C2×D4—22no—
1016C2×D4—28no—
1017C2×D4—22no—
1018C2×D4—22no—
1019C2×D4—41no—
1020C2×D4—41no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4C2511yescharacteristic
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2514yes—
1043C22×C4C2512yes—
1044C22×C4C2514yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2514yes—
1054C22×C4C2514yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2514yes—
1058C22×C4C2511yescharacteristic
1059C22×C4C2514yes—
1060C22×C4C2511yescharacteristic
1061C22×C4C2511yescharacteristic
1062C22×C4C2511yescharacteristic
1063C22×C4C2511yescharacteristic
1064C22×C4C2511yescharacteristic
1065C4⋊C4—22no—
1066C4⋊C4—22no—
1067C4⋊C4—24no—
1068C4⋊C4—28no—
1069C4⋊C4—28no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—28no—
1073C4⋊C4—24no—
1074C4⋊C4—28no—
1075C4⋊C4—28no—
1076C4⋊C4—28no—
1077C4⋊C4—28no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—22no—
1081C4⋊C4—22no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—22no—
1086C4⋊C4—24no—
1087C4⋊C4—28no—
1088C4⋊C4—22no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—22no—
1092C4⋊C4—24no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—41no—
1099C4⋊C4—41no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—42no—
1105C4⋊C4—41no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—41no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—41no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—41no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4C2×#4118yes—
1134C4⋊C4C2×#4118yes—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—24no—
1138C22⋊C4—24no—
1139C22⋊C4—24no—
1140C22⋊C4—24no—
1141C22⋊C4—24no—
1142C22⋊C4—24no—
1143C22⋊C4—42no—
1144C22⋊C4—42no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—42no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—42no—
1151C22⋊C4—42no—
1152C22⋊C4—44no—
1153C22⋊C4—42no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—42no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—42no—
1166C22⋊C4—42no—
1167C22⋊C4—42no—
1168C42—28no—
1169C42—28no—
1170C42—28no—
1171C42—24no—
1172C42—24no—
1173C42—28no—
1174C42—24no—
1175C42—24no—
1176C42—22no—
1177C42—22no—
1178C42—24no—
1179C42—41no—
1180C42—42no—
1181C42—42no—
1182C42—42no—
1183C42—41no—
1184C42—44no—
1185C42—41no—
1186C42—42no—
1187C42—44no—
1188C42—44no—
1189C42—42no—
1190C42—44no—
1191C42—44no—
1192C42—44no—
1193C42—42no—
1194C42—44no—
1195C42—44no—
1196C42—42no—
1197C42—44no—
1198C42C2×#4114yes—
1199C422−1+414yes—
1200C23—22no—
1201C23—22no—
1202C23—22no—
1203C23—22no—
1204C23—22no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23C2611yescharacteristic
1215Q8—48no—
1216Q8—48no—
1217Q8—84no—
1218Q8—82no—
1219Q8—84no—
1220Q8—88no—
1221Q8—162no—
1222D4—44no—
1223D4—44no—
1224D4—88no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—24no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—24no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—21no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—21no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—48no—
1298C2×C4—48no—
1299C2×C4—84no—
1300C2×C4—84no—
1301C2×C4—164no—
1302C2×C4C22×#4112yes—
1303C2×C4C22×#4118yes—
1304C2×C4C22×#4112yes—
1305C2×C4C22×#4112yes—
1306C2×C4C2×2−1+412yes—
1307C2×C4C2×2−1+412yes—
1308C2×C4C2×2−1+412yes—
1309C2×C4#58512yes—
1310C2×C4#58512yes—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22C23×#4111yescharacteristic
1326C22C22×2−1+411yescharacteristic
1327C22C2×#58511yescharacteristic
1328C22C2×#58511yescharacteristic
1329C22H(7,𝔽2)11yescharacteristic
1330C222−1+611yescharacteristic
1331C222−1+611yescharacteristic
1332C4—28no—
1333C4—22no—
1334C4—22no—
1335C4—22no—
1336C4—22no—
1337C4—22no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—44no—
1342C4—42no—
1343C4—44no—
1344C4—41no—
1345C4—42no—
1346C4—42no—
1347C4—44no—
1348C4—42no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—42no—
1353C4—42no—
1354C4—42no—
1355C4—44no—
1356C4—42no—
1357C4—44no—
1358C4#351814yes—
1359C2—82no—
1360C2—82no—
1361C2C2×#351811yescharacteristic
1362C2#6285111yescharacteristic
1363C2#6287911yescharacteristic
1364C2#6295611yescharacteristic
1365C2#6296511yescharacteristic
1366C2#6299111yescharacteristic
1367C2#6306211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#555C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59828C2semidirect
2. #59714C2semidirect
3. #52272C2semidirect
4. #50513C2semidirect
5. #50030C2semidirect
6. #48653C2semidirect
7. #47534C2semidirect
8. #46295C2semidirect
10. #45197C2semidirect
11. #45183C2semidirect
12. #45021C2semidirect
13. #42561C2semidirect
14. #42512C2semidirect
15. #41543C2semidirect
16. #39801C2semidirect
17. #39621C2semidirect
18. #39583C2semidirect
19. #39501C2semidirect
20. #39010C2semidirect
21. #38801C2semidirect
22. #38291C2semidirect
23. #37210C2semidirect
24. #36476C2semidirect
25. #35818C2semidirect
26. #35579C2semidirect
27. #35206C2semidirect
28. #34490C2semidirect

Maximal subgroups

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

subgroupindex
#598282
#597142
#522722
#505132
#500302
#486532
#475342
#462952
#452702
#451972
#451832
#450212
#425612
#425122
#415432
#398012
#396212
#395832
#395012
#390102
#388012
#382912
#372102
#364762
#358182
#355792
#352062
#344902
#343212