Finite Group Databasebeta

← #7656000

Subgroups — #7656000

Order 512.

4292 conjugacy classes of subgroups.

The subgroup lattice has 1399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42692C212yesmaximal, complemented
2#42665C212yesmaximal, complemented
3#42511C212yesmaximal, complemented
4#42469C212yesmaximal, complemented
5#41763C214yesmaximal, complemented
6#41664C214yesmaximal, complemented
7#41124C214yesmaximal, complemented
8#40981C214yesmaximal, complemented
9#39559C214yesmaximal, complemented
10#39476C212yesmaximal, complemented
11#39155C212yesmaximal, complemented
12#38257C214yesmaximal, complemented
13#37561C211yesmaximal, characteristic, complemented
14#37555C211yesmaximal, characteristic
15#37466C212yesmaximal, complemented
16#37464C212yesmaximal
17#36553C212yesmaximal, complemented
18#36256C212yesmaximal, complemented
19#35958C212yesmaximal, complemented
20#35911C212yesmaximal, complemented
21#35789C212yesmaximal, complemented
22#35783C212yesmaximal, complemented
23#35179C211yesmaximal, characteristic, complemented
24#35013C212yesmaximal, complemented
25#34602C211yesmaximal, characteristic
26#34584C212yesmaximal
27#34243C211yesmaximal, characteristic
28#34235C211yesmaximal, characteristic, complemented
29C2×#2355C211yesmaximal, characteristic, complemented
30C2×#533C2211yescharacteristic
31C2×#529C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33#2855C2212yes—
34#2855C2212yes—
35#2855C2214yes—
36#2851C2214yes—
37#2845C2212yes—
38#2844C2212yes—
39#2839C2214yes—
40#2839C2214yes—
41#2833C2214yes—
42#2830C2214yes—
43#2822C2212yes—
44#2820C2212yes—
45#2799C2214yes—
46#2798C2214yes—
47#2798C2214yes—
48#2794C2214yes—
49#2794C2214yes—
50#2793C2214yes—
51#2791C2214yes—
52#2789C2214yes—
53#2789C2214yes—
54#2783C2214yes—
55#2776C2214yes—
56#2775C2214yes—
57#2775C2214yes—
58#2772C2214yes—
59#2767C2214yes—
60#2767C2214yes—
61#2759C2214yes—
62#2758C2214yes—
63#2755C2214yes—
64#2754C2214yes—
65#2754C2214yes—
66#2721C2214yes—
67#2721C2214yes—
68#2719C2214yes—
69#2666C2214yes—
70#2666C2214yes—
71#2665C2214yes—
72#2660C2212yes—
73#2659C2212yes—
74#2659C2212yes—
75#2655C2214yes—
76#2655C2214yes—
77#2655C2214yes—
78#2654C2214yes—
79#2652C2214yes—
80#2651C2214yes—
81#2650C2214yes—
82#2650C2214yes—
83#2647C2212yes—
84#2646C2212yes—
85#2643C2214yes—
86#2639C2212yes—
87#2637C2212yes—
88#2637C2214yes—
89#2637C2214yes—
90#2637C2212yes—
91#2634C2214yes—
92#2634C2212yes—
93#2632C2212yes—
94#2628C2212yes—
95#2627C2212yes—
96#2627C2211yescharacteristic
97#2627C2211yescharacteristic
98#2627C2212yes—
99#2623C2214yes—
100#2623C2212yes—
101#2621C2212yes—
102#2618C2211yescharacteristic
103#2618C2211yescharacteristic
104#2614C2212yes—
105#2612C2214yes—
106#2607C2214yes—
107#2605C2214yes—
108#2589C2214yes—
109#2588C2214yes—
110#2588C2214yes—
111#2588C2214yes—
112#2587C2214yes—
113#2586C2214yes—
114#2586C2214yes—
115#2585C2214yes—
116#2585C2214yes—
117#2585C2214yes—
118#2585C2214yes—
119#2585C2214yes—
120#2582C2212yes—
121#2582C2212yes—
122#2581C2212yes—
123#2581C2214yes—
124#2574C2214yes—
125#2573C2214yes—
126#2571C2212yes—
127#2570C2212yes—
128#2570C2212yes—
129#2568C2212yes—
130#2568C2212yes—
131#2567C2212yes—
132#2565C2214yes—
133#2565C2212yes—
134#2550C2212yes—
135#2536C2212yes—
136#2530C2214yes—
137#2528C2214yes—
138#2528C2214yes—
139#2527C2214yes—
140#2524C2214yes—
141#2523C2214yes—
142#2520C2214yes—
143#2520C2214yes—
144#2520C2214yes—
145#2520C2214yes—
146#2517C2214yes—
147#2514C2212yes—
148#2511C2212yes—
149#2511C2212yes—
150#2511C2212yes—
151#2511C2214yes—
152#2509C2212yes—
153#2507C2212yes—
154#2506C2212yes—
155#2506C2212yes—
156#2505C2214yes—
157#2499C2212yes—
158#2499C2212yes—
159#2498C2214yes—
160#2497C2212yes—
161#2496C2212yes—
162#2494C2212yes—
163#2494C2212yes—
164#2493C2214yes—
165#2493C2214yes—
166#2492C2212yes—
167#2489C2212yes—
168#2488C2214yes—
169#2481C2214yes—
170#2478C2214yes—
171#2475C2214yes—
172#2473C2214yes—
173#2468C2214yes—
174#2462C2214yes—
175#2462C2214yes—
176#2462C2214yes—
177#2450C2214yes—
178#2442C2212yes—
179#2441C2212yes—
180#2441C2214yes—
181#2440C2212yes—
182#2439C2212yes—
183#2438C2214yes—
184#2423C2212yes—
185#2421C2212yes—
186#2419C2214yes—
187#2417C2212yes—
188#2417C2212yes—
189#2402C2214yes—
190#2401C2214yes—
191#2399C2212yes—
192#2398C2212yes—
193#2396C2214yes—
194#2396C2212yes—
195#2396C2212yes—
196#2395C2214yes—
197#2370C2212yes—
198#2370C2212yes—
199#2369C2212yes—
200#2367C2212yes—
201#2365C2211yescharacteristic
202#2365C2211yescharacteristic
203#2365C2211yescharacteristic
204#2365C2211yescharacteristic
205#2360C2212yes—
206#2360C2212yes—
207#2360C2212yes—
208#2360C2212yes—
209#2359C2214yes—
210#2356C2212yes—
211#2356C2212yes—
212#2355C2212yes—
213#2355C2214yes—
214#2355C2214yes—
215#2355C2212yes—
216#2355C2212yes—
217#2355C2212yes—
218#2355C2211yescharacteristic
219#2355C2212yes—
220#2354C2211yescharacteristic
221#2352C2212yes—
222#2351C2212yes—
223Q8×C4⋊C4C2211yescharacteristic
224D4×C4⋊C4C2211yescharacteristic
225D4×C4⋊C4C2212yes—
226#2345C2212yes—
227#2344C2212yes—
228#2343C2214yes—
229#2336C2214yes—
230#2334C2214yes—
231#2329C2214yes—
232#2320C2212yes—
233#2317C2212yes—
234#2314C2212yes—
235#2313C2214yes—
236#2310C2212yes—
237C4×C22⋊Q8C2212yes—
238C4×C22⋊Q8C2212yes—
239C4×C22⋊Q8C2212yes—
240C4×#123C2214yes—
241C4×#123C2212yes—
242C4×#123C2212yes—
243C4×#121C2212yes—
244C2×#391C2212yes—
245#2290C2214yes—
246C2×#387C2212yes—
247C2×#387C2212yes—
248#2285C2211yescharacteristic
249C2×#384C2211yescharacteristic
250#2283C2211yescharacteristic
251C2×#382C2211yescharacteristic
252C2×#382C2211yescharacteristic
253#2276C2212yes—
254#2274C2212yes—
255C2×C4×C4⋊C4C2212yes—
256C2×C4×C4⋊C4C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C23×Q8C2311yescharacteristic
260#533—28no—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264#529—28no—
265C2×#126C2312yes—
266C2×#126C2314yes—
267C2×#125C2312yes—
268C2×#125C2311yescharacteristic
269C2×#125C2312yes—
270C2×#125C2314yes—
271C2×#125C2314yes—
272C2×#124C2311yescharacteristic
273C2×#123C2312yes—
274C2×#123C2312yes—
275C2×#123C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2311yescharacteristic
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×#121C2311yescharacteristic
283C2×C4×Q8—28no—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
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×Q8C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2314yes—
299C2×C4×D4C2312yes—
300C2×#117C2312yes—
301C2×#117C2312yes—
302C2×#117C2312yes—
303C2×#117C2312yes—
304C2×#117C2314yes—
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2311yescharacteristic
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2311yescharacteristic
311C22×C4⋊C4C2311yescharacteristic
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2311yescharacteristic
314C22×C4⋊C4C2312yes—
315C22×C42C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2312yes—
318C22×C42C2312yes—
319C22×C42C2312yes—
320C22×C42C2311yescharacteristic
321#401C2314yes—
322#401C2314yes—
323#401C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#400C2312yes—
353#400C2312yes—
354#400C2312yes—
355#400C2314yes—
356#400C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2312yes—
361#399C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2312yes—
376#398C2312yes—
377#398C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2312yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2312yes—
390#398C2314yes—
391#398C2314yes—
392#398C2312yes—
393#398C2312yes—
394#398C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2312yes—
402#397C2312yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2312yes—
413#396C2312yes—
414#396C2312yes—
415#396C2312yes—
416#396C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2312yes—
424#395C2314yes—
425#395C2312yes—
426#395C2312yes—
427#395C2314yes—
428#395C2312yes—
429#395C2312yes—
430#395C2312yes—
431#394C2314yes—
432#394C2312yes—
433#394C2312yes—
434#393C2314yes—
435#393C2314yes—
436#393C2312yes—
437#393C2312yes—
438#393C2312yes—
439#393C2312yes—
440#393C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2314yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2314yes—
458#391C2312yes—
459#391C2312yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2314yes—
467#390C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2312yes—
502#388C2314yes—
503#388C2312yes—
504#388C2314yes—
505#388C2312yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2312yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
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#387C2312yes—
550#387C2312yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
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#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2312yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#386C2314yes—
588#386C2312yes—
589#386C2312yes—
590#386C2314yes—
591#386C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2312yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2312yes—
603#385C2314yes—
604#385C2314yes—
605#384C2314yes—
606#384C2312yes—
607#384C2312yes—
608#384C2312yes—
609#384C2311yescharacteristic
610#384C2311yescharacteristic
611#384C2312yes—
612#384C2314yes—
613#383C2314yes—
614#383C2314yes—
615#383C2312yes—
616#383C2314yes—
617#382C2312yes—
618#382C2312yes—
619#382C2314yes—
620#382C2312yes—
621#382C2312yes—
622#382C2312yes—
623#382C2314yes—
624#382C2314yes—
625#382C2314yes—
626#382C2312yes—
627#382C2312yes—
628#382C2311yescharacteristic
629#382C2312yes—
630#382C2311yescharacteristic
631#382C2314yes—
632#382C2312yes—
633#382C2314yes—
634#381C2314yes—
635#381C2314yes—
636#381C2312yes—
637#381C2314yes—
638#381C2312yes—
639#381C2312yes—
640#380C2314yes—
641#380C2314yes—
642#380C2312yes—
643#380C2312yes—
644#380C2314yes—
645#380C2314yes—
646#380C2312yes—
647#380C2312yes—
648#380C2312yes—
649#380C2311yescharacteristic
650#380C2311yescharacteristic
651#380C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2311yescharacteristic
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2311yescharacteristic
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705#376C2312yes—
706#376C2314yes—
707#376C2314yes—
708C2×#95C2312yes—
709C2×#95C2312yes—
710C2×#95C2312yes—
711C2×#95C2312yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C2×#95C2312yes—
715C22×Q8—24no—
716C22×Q8—24no—
717C22×Q8—42no—
718C22×Q8C2412yes—
719C22×Q8C2412yes—
720C22×Q8C2412yes—
721C22×Q8C2411yescharacteristic
722C22×Q8C2412yes—
723C22×Q8C2414yes—
724C22×D4C2412yes—
725C22×D4C2411yescharacteristic
726C23×C4C2412yes—
727C23×C4C2411yescharacteristic
728C23×C4C2412yes—
729C23×C4C2411yescharacteristic
730C23×C4C2411yescharacteristic
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2412yes—
734C23×C4C2412yes—
735C23×C4C2411yescharacteristic
736C23×C4C2414yes—
737C23×C4C2412yes—
738C23×C4C2411yescharacteristic
739C4⋊Q8—24no—
740C4⋊Q8—24no—
741C4⋊Q8—44no—
742#126—28no—
743#126—84no—
744#125—24no—
745#125—28no—
746#125—44no—
747#125—84no—
748#125—84no—
749#124—24no—
750#123—28no—
751#123—28no—
752#123—44no—
753C22⋊Q8—24no—
754C22⋊Q8—28no—
755C22⋊Q8—28no—
756C22⋊Q8—48no—
757C22⋊Q8—44no—
758C22⋊Q8—44no—
759#121—24no—
760C4×Q8—28no—
761C4×Q8—28no—
762C4×Q8—28no—
763C4×Q8—28no—
764C4×Q8—28no—
765C4×Q8—24no—
766C4×Q8—28no—
767C4×Q8—28no—
768C4×Q8—44no—
769C4×Q8—82no—
770C4×Q8—82no—
771C4×Q8—82no—
772C4×D4—28no—
773C4×D4—24no—
774C4×D4—48no—
775C4×D4—82no—
776#117—28no—
777#117—28no—
778#117—44no—
779#117—44no—
780#117—84no—
781C2×C4⋊C4—24no—
782C2×C4⋊C4—24no—
783C2×C4⋊C4—24no—
784C2×C4⋊C4—28no—
785C2×C4⋊C4—24no—
786C2×C4⋊C4—28no—
787C2×C4⋊C4—42no—
788C2×C4⋊C4—42no—
789C2×C4⋊C4—42no—
790C2×C4⋊C4—82no—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C42—24no—
890C2×C42—24no—
891C2×C42—44no—
892C2×C42—82no—
893C2×C42—82no—
894C2×C42#4118yes—
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2412yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2412yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923#95C2412yes—
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2412yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2412yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005C24C2512yes—
1006C24C2511yescharacteristic
1007C2×Q8—24no—
1008C2×Q8—24no—
1009C2×Q8—22no—
1010C2×Q8—24no—
1011C2×Q8—24no—
1012C2×Q8—24no—
1013C2×Q8—24no—
1014C2×Q8—24no—
1015C2×Q8—24no—
1016C2×Q8—41no—
1017C2×Q8—42no—
1018C2×Q8—42no—
1019C2×Q8—42no—
1020C2×Q8—41no—
1021C2×Q8—42no—
1022C2×Q8—44no—
1023C2×Q8—44no—
1024C2×Q8—44no—
1025C2×Q8—416no—
1026C2×D4—24no—
1027C2×D4—24no—
1028C2×D4—24no—
1029C2×D4—22no—
1030C2×D4—41no—
1031C2×D4—41no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—22no—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—22no—
1041C22×C4—22no—
1042C22×C4—24no—
1043C22×C4—22no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—28no—
1052C22×C4—42no—
1053C22×C4—41no—
1054C22×C4—41no—
1055C22×C4—41no—
1056C22×C4—41no—
1057C22×C4—41no—
1058C22×C4—41no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—42no—
1067C22×C4C2×#4114yes—
1068C22×C4C2×#4114yes—
1069C22×C4C2×#4114yes—
1070C22×C42−1+414yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2514yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2514yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2514yes—
1082C22×C4C2514yes—
1083C22×C4C2514yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2511yescharacteristic
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2511yescharacteristic
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—22no—
1109C4⋊C4—24no—
1110C4⋊C4—22no—
1111C4⋊C4—28no—
1112C4⋊C4—28no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—28no—
1119C4⋊C4—28no—
1120C4⋊C4—22no—
1121C4⋊C4—24no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—22no—
1126C4⋊C4—22no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—41no—
1137C4⋊C4—41no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—41no—
1152C4⋊C4—41no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C42−1+414yes—
1172C22⋊C4—28no—
1173C22⋊C4—24no—
1174C22⋊C4—24no—
1175C22⋊C4—28no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—42no—
1184C22⋊C4—42no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—42no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—42no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C42—24no—
1197C42—24no—
1198C42—24no—
1199C42—24no—
1200C42—24no—
1201C42—28no—
1202C42—24no—
1203C42—28no—
1204C42—24no—
1205C42—44no—
1206C42—44no—
1207C42—44no—
1208C42—42no—
1209C42—42no—
1210C42—42no—
1211C42—42no—
1212C42—44no—
1213C42—44no—
1214C42—44no—
1215C42—44no—
1216C42—44no—
1217C42—44no—
1218C42—44no—
1219C42—44no—
1220C42C2×#4114yes—
1221C42C2×#4114yes—
1222C42C2×#4114yes—
1223C42C2×#4114yes—
1224C23—21no—
1225C23—21no—
1226C23—21no—
1227C23—21no—
1228C23—22no—
1229C23—22no—
1230C23—22no—
1231C23—22no—
1232C23—22no—
1233C23—22no—
1234C23—22no—
1235C23C22×#4112yes—
1236C23C2×2−1+412yes—
1237C23#58512yes—
1238C23C2611yescharacteristic
1239Q8—48no—
1240Q8—48no—
1241Q8—44no—
1242Q8—48no—
1243Q8—48no—
1244Q8—164no—
1245D4—44no—
1246D4—48no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—22no—
1252C2×C4—21no—
1253C2×C4—22no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—28no—
1262C2×C4—28no—
1263C2×C4—28no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
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—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—44no—
1322C2×C4—48no—
1323C2×C4—44no—
1324C2×C4—44no—
1325C2×C4—44no—
1326C2×C4—48no—
1327C2×C4—88no—
1328C2×C4—84no—
1329C2×C4—84no—
1330C2×C4—84no—
1331C2×C4C22×#4112yes—
1332C2×C4C22×#4112yes—
1333C2×C4C22×#4112yes—
1334C2×C4C22×#4112yes—
1335C2×C4C22×#4112yes—
1336C2×C4C22×#4112yes—
1337C2×C4C2×2−1+414yes—
1338C2×C4C2×2−1+414yes—
1339C2×C4C2×2−1+412yes—
1340C2×C4#58512yes—
1341C22—22no—
1342C22—22no—
1343C22—22no—
1344C22—22no—
1345C22—22no—
1346C22—22no—
1347C22—42no—
1348C22—42no—
1349C22—42no—
1350C22—42no—
1351C22—42no—
1352C22—42no—
1353C22—42no—
1354C22#349514yes—
1355C22C23×#4111yescharacteristic
1356C22C22×2−1+411yescharacteristic
1357C22C22×2−1+411yescharacteristic
1358C22C2×#58511yescharacteristic
1359C22C2×#58511yescharacteristic
1360C22H(7,𝔽2)11yescharacteristic
1361C222−1+611yescharacteristic
1362C4—22no—
1363C4—22no—
1364C4—24no—
1365C4—22no—
1366C4—22no—
1367C4—22no—
1368C4—24no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—42no—
1374C4—44no—
1375C4—42no—
1376C4—44no—
1377C4—42no—
1378C4—42no—
1379C4—42no—
1380C4—44no—
1381C4—42no—
1382C4—42no—
1383C4—42no—
1384C4—44no—
1385C4—44no—
1386C4—44no—
1387C4—42no—
1388C4#346114yes—
1389C2—24no—
1390C2—82no—
1391C2C2×#346111yescharacteristic
1392C2C2×#349511yescharacteristic
1393C2#6284511yescharacteristic
1394C2#6294711yescharacteristic
1395C2#6294811yescharacteristic
1396C2#6296211yescharacteristic
1397C2#6296411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42692C2semidirect
2. #42665C2semidirect
3. #42511C2semidirect
4. #42469C2semidirect
5. #41763C2semidirect
6. #41664C2semidirect
7. #41124C2semidirect
8. #40981C2semidirect
9. #39559C2semidirect
10. #39476C2semidirect
11. #39155C2semidirect
12. #38257C2semidirect
13. #37561C2semidirect
15. #37466C2semidirect
17. #36553C2semidirect
18. #36256C2semidirect
19. #35958C2semidirect
20. #35911C2semidirect
21. #35789C2semidirect
22. #35783C2semidirect
23. #35179C2semidirect
24. #35013C2semidirect
28. #34235C2semidirect
29. C2×#2355C2semidirect

Maximal subgroups

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

subgroupindex
#426922
#426652
#425112
#424692
#417632
#416642
#411242
#409812
#395592
#394762
#391552
#382572
#375612
#375552
#374662
#374642
#365532
#362562
#359582
#359112
#357892
#357832
#351792
#350132
#346022
#345842
#342432
#342352
C2×#23552