Finite Group Databasebeta

← #7898321

Subgroups — #7898321

Order 512.

4289 conjugacy classes of subgroups.

The subgroup lattice has 1385 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59321C212yesmaximal, complemented
3#52267C211yesmaximal, characteristic, complemented
4#51020C214yesmaximal, complemented
5#50239C214yesmaximal, complemented
6#48676C214yesmaximal, complemented
7#47425C214yesmaximal, complemented
8#46293C212yesmaximal, complemented
9#45147C212yesmaximal, complemented
10#45145C212yesmaximal, complemented
11#44967C212yesmaximal, complemented
12#43841C214yesmaximal, complemented
13#42939C212yesmaximal, complemented
14#42527C212yesmaximal, complemented
15#41779C214yesmaximal, complemented
16#40035C212yesmaximal, complemented
17#39822C212yesmaximal, complemented
18#39749C211yesmaximal, characteristic, complemented
19#39709C212yesmaximal, complemented
20#39484C211yesmaximal, characteristic, complemented
21#38800C212yesmaximal, complemented
22#37863C212yesmaximal
23#37168C212yesmaximal, complemented
24#36477C211yesmaximal, characteristic, complemented
25#35818C212yesmaximal, complemented
26#35555C212yesmaximal, complemented
27#35206C211yesmaximal, characteristic, complemented
28#34462C212yesmaximal, complemented
29#34316C211yesmaximal, characteristic
30C2×#552C2212yes—
31C2×#547C2211yescharacteristic
32#2859C2211yescharacteristic
33#2855C2212yes—
34#2855C2212yes—
35#2851C2212yes—
36#2850C2212yes—
37#2836C2214yes—
38#2833C2214yes—
39#2809C2212yes—
40#2807C2212yes—
41#2806C2211yescharacteristic
42#2806C2212yes—
43#2806C2212yes—
44#2806C2212yes—
45#2805C2211yescharacteristic
46#2805C2212yes—
47#2804C2211yescharacteristic
48#2802C2212yes—
49#2796C2214yes—
50#2793C2214yes—
51#2791C2214yes—
52#2791C2214yes—
53#2790C2212yes—
54#2788C2212yes—
55#2786C2214yes—
56#2780C2212yes—
57#2777C2214yes—
58#2777C2214yes—
59#2776C2214yes—
60#2770C2214yes—
61#2769C2214yes—
62#2768C2214yes—
63#2766C2214yes—
64#2766C2214yes—
65#2758C2214yes—
66#2757C2214yes—
67#2746C2214yes—
68#2746C2214yes—
69#2739C2214yes—
70#2739C2214yes—
71#2738C2214yes—
72#2738C2214yes—
73#2732C2211yescharacteristic
74#2729C2212yes—
75#2728C2214yes—
76#2726C2212yes—
77#2726C2212yes—
78#2726C2212yes—
79#2724C2212yes—
80#2724C2212yes—
81#2721C2214yes—
82#2720C2214yes—
83#2720C2214yes—
84#2719C2214yes—
85#2718C2214yes—
86#2718C2214yes—
87#2707C2214yes—
88#2707C2214yes—
89#2695C2214yes—
90#2694C2214yes—
91#2687C2214yes—
92#2687C2214yes—
93#2667C2214yes—
94#2666C2214yes—
95#2664C2214yes—
96#2660C2212yes—
97#2655C2214yes—
98#2654C2214yes—
99#2652C2214yes—
100#2634C2214yes—
101#2621C2212yes—
102#2620C2212yes—
103#2611C2214yes—
104#2608C2214yes—
105#2597C2214yes—
106#2594C2214yes—
107#2594C2214yes—
108#2590C2214yes—
109#2590C2214yes—
110#2587C2214yes—
111#2584C2214yes—
112#2582C2212yes—
113#2582C2212yes—
114#2578C2214yes—
115#2577C2214yes—
116#2575C2214yes—
117#2573C2214yes—
118#2571C2212yes—
119#2570C2212yes—
120#2570C2212yes—
121#2570C2212yes—
122#2570C2212yes—
123#2570C2212yes—
124#2568C2211yescharacteristic
125#2567C2212yes—
126#2566C2212yes—
127#2565C2214yes—
128#2565C2212yes—
129#2558C2214yes—
130#2556C2214yes—
131#2556C2214yes—
132#2553C2214yes—
133#2552C2212yes—
134#2552C2212yes—
135#2552C2212yes—
136#2552C2212yes—
137#2552C2212yes—
138#2552C2211yescharacteristic
139#2552C2212yes—
140#2547C2211yescharacteristic
141#2538C2211yescharacteristic
142#2538C2211yescharacteristic
143#2538C2211yescharacteristic
144#2533C2214yes—
145#2529C2214yes—
146#2527C2214yes—
147#2527C2214yes—
148#2525C2214yes—
149#2524C2214yes—
150#2522C2214yes—
151#2520C2214yes—
152#2519C2214yes—
153#2515C2214yes—
154#2515C2214yes—
155#2515C2214yes—
156#2514C2212yes—
157#2514C2212yes—
158#2513C2212yes—
159#2512C2212yes—
160#2511C2212yes—
161#2511C2212yes—
162#2511C2212yes—
163#2507C2214yes—
164#2507C2214yes—
165#2507C2214yes—
166#2506C2214yes—
167#2506C2214yes—
168#2506C2214yes—
169#2503C2212yes—
170#2502C2212yes—
171#2502C2212yes—
172#2501C2212yes—
173#2500C2212yes—
174#2499C2212yes—
175#2497C2212yes—
176#2495C2212yes—
177#2489C2212yes—
178#2478C2214yes—
179#2478C2214yes—
180#2478C2214yes—
181#2473C2214yes—
182#2473C2214yes—
183#2473C2214yes—
184#2473C2214yes—
185#2473C2214yes—
186#2473C2214yes—
187#2462C2214yes—
188#2462C2214yes—
189#2448C2212yes—
190#2448C2212yes—
191#2447C2212yes—
192#2442C2214yes—
193#2429C2212yes—
194#2413C2214yes—
195#2413C2214yes—
196#2406C2214yes—
197#2406C2214yes—
198#2402C2212yes—
199#2402C2214yes—
200#2396C2212yes—
201#2396C2212yes—
202#2383C2214yes—
203#2376C2214yes—
204#2374C2214yes—
205#2370C2214yes—
206#2370C2212yes—
207#2369C2212yes—
208#2365C2211yescharacteristic
209#2365C2212yes—
210#2363C2212yes—
211#2362C2212yes—
212#2362C2212yes—
213#2362C2212yes—
214#2360C2214yes—
215#2357C2212yes—
216#2356C2212yes—
217#2355C2212yes—
218#2355C2211yescharacteristic
219#2355C2212yes—
220#2354C2211yescharacteristic
221#2354C2211yescharacteristic
222Q8×C4⋊C4C2211yescharacteristic
223Q8×C4⋊C4C2212yes—
224#2347C2214yes—
225#2347C2212yes—
226#2345C2212yes—
227#2345C2212yes—
228#2341C2212yes—
229#2336C2214yes—
230#2335C2214yes—
231#2335C2214yes—
232#2334C2214yes—
233#2332C2214yes—
234#2330C2212yes—
235#2326C2212yes—
236#2324C2212yes—
237#2323C2212yes—
238#2320C2212yes—
239#2317C2212yes—
240#2317C2212yes—
241#2316C2212yes—
242#2314C2214yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×C22⋊Q8C2212yes—
247C4×C22⋊Q8C2212yes—
248C4×C22⋊Q8C2212yes—
249C4×C22⋊Q8C2212yes—
250#2297C2212yes—
251#2296C2212yes—
252#2296C2212yes—
253#2295C2211yescharacteristic
254#2293C2211yescharacteristic
255#2290C2212yes—
256C2×#384C2212yes—
257#2274C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260#552—216no—
261#547—28no—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×#126C2314yes—
266C2×#126C2314yes—
267C2×#125C2312yes—
268C2×#125C2314yes—
269C2×#125C2314yes—
270C2×#125C2314yes—
271C2×#125C2312yes—
272C2×#125C2314yes—
273C2×#125C2314yes—
274C2×#125C2314yes—
275C2×#124C2312yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×#121C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2311yescharacteristic
299C2×C4×D4C2311yescharacteristic
300C2×C4×D4C2311yescharacteristic
301C2×#117C2314yes—
302C2×#117C2312yes—
303C2×#117C2312yes—
304C2×#117C2312yes—
305C2×#117C2312yes—
306C2×#117C2312yes—
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2314yes—
310C22×C4⋊C4C2314yes—
311C22×C42C2312yes—
312C22×C42C2312yes—
313#401C2314yes—
314#401C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2312yes—
326#400C2314yes—
327#400C2314yes—
328#400C2312yes—
329#400C2314yes—
330#400C2314yes—
331#400C2312yes—
332#400C2314yes—
333#400C2312yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2312yes—
338#400C2312yes—
339#399C2312yes—
340#399C2314yes—
341#399C2314yes—
342#399C2312yes—
343#399C2314yes—
344#399C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2312yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2312yes—
377#398C2312yes—
378#398C2312yes—
379#398C2312yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2312yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2312yes—
403#396C2312yes—
404#396C2312yes—
405#396C2314yes—
406#396C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2312yes—
412#395C2312yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#393C2312yes—
418#393C2312yes—
419#391C2312yes—
420#391C2311yescharacteristic
421#391C2311yescharacteristic
422#391C2312yes—
423#391C2312yes—
424#391C2314yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2314yes—
435#391C2311yescharacteristic
436#391C2312yes—
437#391C2314yes—
438#391C2311yescharacteristic
439#390C2312yes—
440#390C2312yes—
441#390C2314yes—
442#390C2312yes—
443#390C2312yes—
444#390C2312yes—
445#390C2314yes—
446#390C2311yescharacteristic
447#390C2311yescharacteristic
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2314yes—
486#389C2312yes—
487#389C2311yescharacteristic
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2311yescharacteristic
495#389C2312yes—
496#389C2314yes—
497#389C2311yescharacteristic
498#389C2311yescharacteristic
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#388C2312yes—
503#388C2314yes—
504#388C2314yes—
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#388C2314yes—
523#388C2314yes—
524#388C2312yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2312yes—
531#388C2312yes—
532#388C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2312yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2312yes—
576#387C2314yes—
577#387C2312yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
583#387C2314yes—
584#387C2312yes—
585#386C2314yes—
586#386C2314yes—
587#386C2312yes—
588#386C2314yes—
589#386C2314yes—
590#386C2312yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2312yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2312yes—
605#385C2314yes—
606#385C2312yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2312yes—
611#385C2314yes—
612#385C2312yes—
613#385C2312yes—
614#385C2312yes—
615#385C2312yes—
616#384C2311yescharacteristic
617#384C2311yescharacteristic
618#384C2311yescharacteristic
619#384C2312yes—
620#384C2314yes—
621#384C2312yes—
622#384C2312yes—
623#384C2312yes—
624#384C2314yes—
625#384C2311yescharacteristic
626#384C2312yes—
627#384C2312yes—
628#384C2311yescharacteristic
629#384C2312yes—
630#384C2314yes—
631#383C2314yes—
632#383C2314yes—
633#383C2314yes—
634#383C2314yes—
635#383C2314yes—
636#382C2312yes—
637#382C2314yes—
638#382C2312yes—
639#382C2312yes—
640#382C2314yes—
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2314yes—
645#381C2314yes—
646#381C2314yes—
647#381C2314yes—
648#381C2314yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711#376C2312yes—
712#376C2314yes—
713C43C2311yescharacteristic
714C2×#41—28no—
715C2×#41—82no—
716C2×#41—82no—
717C22×Q8C2412yes—
718C22×Q8C2412yes—
719C22×Q8C2411yescharacteristic
720C22×Q8C2411yescharacteristic
721C22×Q8C2411yescharacteristic
722C22×D4C2411yescharacteristic
723C22×D4C2414yes—
724C22×D4C2411yescharacteristic
725C23×C4C2412yes—
726C23×C4C2414yes—
727C23×C4C2414yes—
728C23×C4C2412yes—
729C23×C4C2412yes—
730C23×C4C2412yes—
731C23×C4C2412yes—
732C23×C4C2412yes—
733C4⋊Q8—24no—
734C4⋊Q8—24no—
735C4⋊Q8—24no—
736#126—216no—
737#126—84no—
738#125—216no—
739#125—28no—
740#125—82no—
741#125—84no—
742#125—84no—
743#125—84no—
744#125—84no—
745#125—84no—
746#124—44no—
747#123—216no—
748#123—216no—
749#123—84no—
750#123—84no—
751C22⋊Q8—28no—
752C22⋊Q8—28no—
753C22⋊Q8—28no—
754C22⋊Q8—28no—
755C22⋊Q8—28no—
756C22⋊Q8—82no—
757C22⋊Q8—82no—
758#121—28no—
759C4×Q8—28no—
760C4×Q8—24no—
761C4×Q8—42no—
762C4×Q8—42no—
763C4×Q8—44no—
764C4×Q8—44no—
765C4×Q8—82no—
766C4×Q8—82no—
767C4×Q8—82no—
768C4×D4—24no—
769C4×D4—24no—
770C4×D4—42no—
771C4×D4#4118yes—
772#117—28no—
773#117—216no—
774#117—28no—
775#117—44no—
776#117—44no—
777#117—82no—
778C2×C4⋊C4—28no—
779C2×C4⋊C4—28no—
780C2×C4⋊C4—84no—
781C2×C4⋊C4—84no—
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C42—44no—
894C2×C42—82no—
895C2×C42C2414yes—
896C2×C42C2412yes—
897C2×C42C2414yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2411yescharacteristic
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2411yescharacteristic
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2411yescharacteristic
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2414yes—
915C2×C42C2412yes—
916C2×C42C2411yescharacteristic
917C2×C42C2411yescharacteristic
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2411yescharacteristic
923C2×C42C2411yescharacteristic
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2412yes—
928#95C2412yes—
929#95C2414yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2414yes—
938#95C2414yes—
939#95C2412yes—
940#95C2414yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997C24C2512yes—
998C24C2512yes—
999#41—816no—
1000C2×Q8—24no—
1001C2×Q8—24no—
1002C2×Q8—24no—
1003C2×Q8—22no—
1004C2×Q8—22no—
1005C2×Q8—24no—
1006C2×Q8—41no—
1007C2×Q8—41no—
1008C2×Q8—42no—
1009C2×Q8—42no—
1010C2×Q8—41no—
1011C2×Q8—41no—
1012C2×Q8—41no—
1013C2×Q8—41no—
1014C2×Q82−1+414yes—
1015C2×D4—28no—
1016C2×D4—22no—
1017C2×D4—22no—
1018C2×D4—22no—
1019C2×D4—41no—
1020C2×D4—41no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4C2×#4114yes—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—28no—
1027C22×C4—28no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—42no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4C2×#4118yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2514yes—
1062C22×C4C2514yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2512yes—
1065C22×C4C2514yes—
1066C22×C4C2514yes—
1067C22×C4C2511yescharacteristic
1068C22×C4C2512yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2511yescharacteristic
1071C22×C4C2511yescharacteristic
1072C22×C4C2511yescharacteristic
1073C22×C4C2512yes—
1074C22×C4C2511yescharacteristic
1075C4⋊C4—22no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—28no—
1079C4⋊C4—24no—
1080C4⋊C4—28no—
1081C4⋊C4—24no—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—24no—
1087C4⋊C4—28no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—22no—
1091C4⋊C4—22no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—28no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—22no—
1103C4⋊C4—24no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—41no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—41no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—41no—
1125C4⋊C4—41no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—41no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—41no—
1143C4⋊C4—42no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4C2×#4114yes—
1156C22⋊C4—28no—
1157C22⋊C4—28no—
1158C22⋊C4—28no—
1159C22⋊C4—24no—
1160C22⋊C4—28no—
1161C22⋊C4—24no—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—24no—
1166C22⋊C4—28no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—42no—
1170C22⋊C4—42no—
1171C22⋊C4—44no—
1172C22⋊C4—42no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—42no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—42no—
1180C22⋊C4—42no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4C2×#4118yes—
1186C42—28no—
1187C42—28no—
1188C42—24no—
1189C42—24no—
1190C42—22no—
1191C42—24no—
1192C42—24no—
1193C42—24no—
1194C42—22no—
1195C42—42no—
1196C42—42no—
1197C42—41no—
1198C42—42no—
1199C42—42no—
1200C42—42no—
1201C42—41no—
1202C42—44no—
1203C42—44no—
1204C42—44no—
1205C42—44no—
1206C42—44no—
1207C42—44no—
1208C42—41no—
1209C42—44no—
1210C42—44no—
1211C42—44no—
1212C42—44no—
1213C42C2×#4114yes—
1214C422−1+414yes—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23—22no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—22no—
1228C23C22×#4114yes—
1229C23C2611yescharacteristic
1230Q8—44no—
1231Q8—48no—
1232Q8—48no—
1233Q8—82no—
1234Q8—82no—
1235D4—44no—
1236D4—44no—
1237D4—88no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—22no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—216no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—21no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—21no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—48no—
1311C2×C4—48no—
1312C2×C4—48no—
1313C2×C4—84no—
1314C2×C4—84no—
1315C2×C4—88no—
1316C2×C4—88no—
1317C2×C4C22×#4112yes—
1318C2×C4C22×#4114yes—
1319C2×C4C22×#4112yes—
1320C2×C4C22×#4112yes—
1321C2×C4C2×2−1+412yes—
1322C2×C4C2×2−1+412yes—
1323C2×C4C2×2−1+412yes—
1324C2×C4C2×2−1+414yes—
1325C2×C4C2×2−1+412yes—
1326C2×C4#58512yes—
1327C22—24no—
1328C22—24no—
1329C22—24no—
1330C22—42no—
1331C22—42no—
1332C22—42no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22C23×#4111yescharacteristic
1342C22C22×2−1+411yescharacteristic
1343C22C22×2−1+411yescharacteristic
1344C22C2×#58511yescharacteristic
1345C22H(7,𝔽2)11yescharacteristic
1346C22H(7,𝔽2)11yescharacteristic
1347C222−1+611yescharacteristic
1348C4—22no—
1349C4—24no—
1350C4—22no—
1351C4—22no—
1352C4—24no—
1353C4—22no—
1354C4—22no—
1355C4—44no—
1356C4—44no—
1357C4—41no—
1358C4—42no—
1359C4—44no—
1360C4—42no—
1361C4—42no—
1362C4—42no—
1363C4—44no—
1364C4—44no—
1365C4—44no—
1366C4—42no—
1367C4—42no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—42no—
1374C4#351514yes—
1375C2—44no—
1376C2—82no—
1377C2C2×#351511yescharacteristic
1378C2#6285511yescharacteristic
1379C2#6287911yescharacteristic
1380C2#6290211yescharacteristic
1381C2#6294311yescharacteristic
1382C2#6300111yescharacteristic
1383C2#6304711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#547C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59871C2semidirect
2. #59321C2semidirect
3. #52267C2semidirect
4. #51020C2semidirect
5. #50239C2semidirect
6. #48676C2semidirect
7. #47425C2semidirect
8. #46293C2semidirect
9. #45147C2semidirect
10. #45145C2semidirect
11. #44967C2semidirect
12. #43841C2semidirect
13. #42939C2semidirect
14. #42527C2semidirect
15. #41779C2semidirect
16. #40035C2semidirect
17. #39822C2semidirect
18. #39749C2semidirect
19. #39709C2semidirect
20. #39484C2semidirect
21. #38800C2semidirect
23. #37168C2semidirect
24. #36477C2semidirect
25. #35818C2semidirect
26. #35555C2semidirect
27. #35206C2semidirect
28. #34462C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#593212
#522672
#510202
#502392
#486762
#474252
#462932
#451472
#451452
#449672
#438412
#429392
#425272
#417792
#400352
#398222
#397492
#397092
#394842
#388002
#378632
#371682
#364772
#358182
#355552
#352062
#344622
#343162