Finite Group Databasebeta

← #8688203

Subgroups — #8688203

Order 512.

4031 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58976C214yesmaximal, complemented
2#58752C212yesmaximal, complemented
3#58575C214yesmaximal, complemented
4#58382C212yesmaximal
5#57322C214yesmaximal, complemented
6#54910C214yesmaximal, complemented
7#54561C214yesmaximal
8#46346C211yesmaximal, characteristic, complemented
9#46268C212yesmaximal
10#46060C212yesmaximal, complemented
11#45827C214yesmaximal, complemented
12#45414C212yesmaximal, complemented
13#45410C211yesmaximal, characteristic
14#45364C211yesmaximal, characteristic, complemented
15#45324C212yesmaximal, complemented
16#45284C212yesmaximal, complemented
17#45177C212yesmaximal
18#44997C212yesmaximal, complemented
19#42981C212yesmaximal, complemented
20#42824C212yesmaximal, complemented
21#42814C211yesmaximal, characteristic
22#42811C211yesmaximal, characteristic, complemented
23#42793C212yesmaximal, complemented
24#42785C212yesmaximal
25#42747C212yesmaximal, complemented
26#37638C212yesmaximal, complemented
27#36697C211yesmaximal, characteristic
28#36474C211yesmaximal, characteristic, complemented
29#36311C212yesmaximal, complemented
30C2×Q82C2211yescharacteristic
31C2×#557C2211yescharacteristic
32C2×#557C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#541C2212yes—
35#2865C2214yes—
36#2863C2212yes—
37#2862C2212yes—
38#2862C2211yescharacteristic
39#2844C2214yes—
40#2843C2214yes—
41#2843C2211yescharacteristic
42#2839C2212yes—
43#2839C2214yes—
44#2838C2212yes—
45#2837C2212yes—
46#2836C2212yes—
47#2833C2214yes—
48#2833C2211yescharacteristic
49#2833C2212yes—
50#2832C2214yes—
51#2832C2211yescharacteristic
52#2831C2212yes—
53#2823C2211yescharacteristic
54#2822C2212yes—
55#2822C2212yes—
56#2821C2214yes—
57#2821C2212yes—
58#2811C2212yes—
59#2809C2214yes—
60#2807C2214yes—
61#2806C2214yes—
62#2806C2214yes—
63#2802C2214yes—
64#2801C2214yes—
65#2799C2214yes—
66#2795C2212yes—
67#2794C2212yes—
68#2792C2212yes—
69#2791C2214yes—
70#2790C2214yes—
71#2788C2214yes—
72#2788C2214yes—
73#2785C2212yes—
74#2777C2214yes—
75#2775C2214yes—
76#2775C2214yes—
77#2774C2214yes—
78#2774C2214yes—
79#2774C2214yes—
80#2769C2214yes—
81#2767C2214yes—
82#2766C2214yes—
83#2764C2214yes—
84#2764C2214yes—
85#2762C2214yes—
86#2762C2214yes—
87#2759C2214yes—
88#2758C2214yes—
89#2758C2214yes—
90#2758C2214yes—
91#2758C2214yes—
92#2755C2214yes—
93#2755C2214yes—
94#2754C2214yes—
95#2754C2214yes—
96#2745C2214yes—
97#2742C2214yes—
98#2739C2214yes—
99#2734C2212yes—
100#2729C2214yes—
101#2726C2214yes—
102#2725C2214yes—
103#2721C2214yes—
104#2720C2214yes—
105#2719C2214yes—
106#2719C2214yes—
107#2719C2214yes—
108#2716C2214yes—
109#2716C2214yes—
110#2713C2214yes—
111#2713C2214yes—
112#2713C2214yes—
113#2698C2214yes—
114#2698C2214yes—
115#2690C2214yes—
116#2689C2214yes—
117#2677C2214yes—
118#2666C2214yes—
119#2665C2214yes—
120#2660C2211yescharacteristic
121#2654C2214yes—
122#2647C2214yes—
123#2647C2214yes—
124#2647C2214yes—
125#2645C2214yes—
126#2645C2214yes—
127#2642C2214yes—
128#2642C2211yescharacteristic
129#2634C2212yes—
130#2634C2214yes—
131#2634C2212yes—
132#2634C2212yes—
133#2633C2212yes—
134#2628C2212yes—
135#2612C2214yes—
136#2612C2212yes—
137#2612C2214yes—
138#2606C2214yes—
139#2605C2214yes—
140#2604C2214yes—
141#2589C2214yes—
142#2586C2212yes—
143#2584C2212yes—
144#2584C2211yescharacteristic
145#2582C2212yes—
146#2581C2212yes—
147#2581C2212yes—
148#2571C2212yes—
149#2571C2212yes—
150#2568C2211yescharacteristic
151#2568C2212yes—
152#2567C2214yes—
153#2567C2212yes—
154#2567C2211yescharacteristic
155#2565C2212yes—
156#2562C2211yescharacteristic
157#2550C2212yes—
158#2550C2214yes—
159#2550C2212yes—
160#2550C2212yes—
161#2550C2212yes—
162#2550C2214yes—
163#2550C2212yes—
164#2546C2211yescharacteristic
165#2546C2211yescharacteristic
166#2546C2212yes—
167#2536C2212yes—
168#2533C2214yes—
169#2532C2214yes—
170#2532C2214yes—
171#2532C2214yes—
172#2529C2214yes—
173#2528C2214yes—
174#2528C2214yes—
175#2527C2214yes—
176#2525C2214yes—
177#2524C2214yes—
178#2524C2214yes—
179#2520C2214yes—
180#2520C2214yes—
181#2519C2214yes—
182#2514C2214yes—
183#2514C2214yes—
184#2514C2212yes—
185#2514C2212yes—
186#2509C2212yes—
187#2509C2212yes—
188#2509C2212yes—
189#2509C2212yes—
190#2507C2212yes—
191#2506C2214yes—
192#2506C2214yes—
193#2503C2212yes—
194#2494C2212yes—
195#2492C2212yes—
196#2492C2212yes—
197#2492C2212yes—
198#2489C2214yes—
199#2469C2214yes—
200#2469C2214yes—
201#2468C2214yes—
202#2466C2214yes—
203#2465C2214yes—
204#2462C2214yes—
205#2453C2212yes—
206#2451C2214yes—
207#2451C2212yes—
208#2451C2212yes—
209#2451C2212yes—
210#2451C2212yes—
211#2446C2212yes—
212#2446C2212yes—
213#2446C2212yes—
214#2446C2212yes—
215#2442C2212yes—
216#2442C2212yes—
217#2440C2212yes—
218#2439C2212yes—
219#2429C2212yes—
220#2429C2212yes—
221#2423C2212yes—
222#2421C2212yes—
223#2421C2212yes—
224#2421C2212yes—
225#2415C2212yes—
226#2402C2212yes—
227#2401C2212yes—
228#2399C2211yescharacteristic
229#2398C2211yescharacteristic
230#2396C2212yes—
231#2396C2212yes—
232#2395C2212yes—
233#2381C2212yes—
234#2378C2214yes—
235#2369C2212yes—
236#2365C2212yes—
237#2365C2212yes—
238#2362C2212yes—
239#2362C2212yes—
240#2360C2212yes—
241#2356C2212yes—
242#2356C2212yes—
243#2351C2212yes—
244#2351C2212yes—
245Q8×C4⋊C4C2212yes—
246#2346C2212yes—
247#2346C2212yes—
248#2331C2212yes—
249#2323C2212yes—
250#2320C2211yescharacteristic
251#2320C2211yescharacteristic
252#2320C2212yes—
253#2317C2212yes—
254C4×C4⋊Q8C2212yes—
255C4×C4⋊Q8C2211yescharacteristic
256C4×#126C2212yes—
257#2295C2214yes—
258C42×Q8C2211yescharacteristic
259Q82—44no—
260#557—44no—
261#557—44no—
262#554—44no—
263#541—48no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2311yescharacteristic
277C2×#126C2312yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#125C2311yescharacteristic
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2312yes—
286C2×#125C2311yescharacteristic
287C2×#125C2314yes—
288C2×#125C2314yes—
289C2×#125C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2314yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×D4C2311yescharacteristic
311C2×C4×D4C2312yes—
312C2×#117C2312yes—
313C2×#117C2312yes—
314C22×C4⋊C4C2312yes—
315#401C2312yes—
316#401C2314yes—
317#401C2314yes—
318#401C2314yes—
319#400C2312yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2312yes—
324#400C2311yescharacteristic
325#400C2312yes—
326#400C2312yes—
327#400C2314yes—
328#400C2314yes—
329#400C2312yes—
330#400C2314yes—
331#400C2311yescharacteristic
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2312yes—
336#400C2312yes—
337#400C2312yes—
338#400C2312yes—
339#400C2314yes—
340#400C2314yes—
341#400C2312yes—
342#400C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2312yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#399C2312yes—
369#399C2312yes—
370#399C2312yes—
371#399C2314yes—
372#399C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2312yes—
376#398C2312yes—
377#398C2314yes—
378#398C2314yes—
379#398C2311yescharacteristic
380#398C2314yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2312yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2311yescharacteristic
390#398C2312yes—
391#398C2312yes—
392#398C2312yes—
393#398C2312yes—
394#398C2314yes—
395#398C2312yes—
396#398C2314yes—
397#398C2314yes—
398#398C2312yes—
399#398C2312yes—
400#398C2312yes—
401#398C2312yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2312yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#397C2312yes—
417#397C2312yes—
418#397C2314yes—
419#397C2314yes—
420#397C2312yes—
421#397C2312yes—
422#397C2312yes—
423#397C2312yes—
424#397C2314yes—
425#397C2314yes—
426#397C2312yes—
427#397C2314yes—
428#396C2312yes—
429#396C2312yes—
430#396C2312yes—
431#396C2312yes—
432#396C2312yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#395C2312yes—
437#395C2312yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#395C2312yes—
445#395C2314yes—
446#395C2312yes—
447#395C2311yescharacteristic
448#395C2312yes—
449#395C2311yescharacteristic
450#395C2312yes—
451#395C2314yes—
452#395C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2314yes—
456#395C2314yes—
457#395C2314yes—
458#394C2312yes—
459#394C2312yes—
460#394C2311yescharacteristic
461#394C2312yes—
462#394C2314yes—
463#394C2311yescharacteristic
464#393C2312yes—
465#393C2312yes—
466#393C2314yes—
467#393C2314yes—
468#393C2312yes—
469#393C2314yes—
470#393C2314yes—
471#393C2314yes—
472#391C2311yescharacteristic
473#391C2311yescharacteristic
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2314yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2314yes—
482#391C2312yes—
483#391C2312yes—
484#391C2314yes—
485#391C2312yes—
486#391C2312yes—
487#391C2314yes—
488#391C2312yes—
489#391C2312yes—
490#391C2314yes—
491#391C2312yes—
492#391C2314yes—
493#391C2314yes—
494#391C2314yes—
495#391C2312yes—
496#391C2314yes—
497#391C2314yes—
498#391C2314yes—
499#391C2314yes—
500#391C2314yes—
501#391C2314yes—
502#391C2314yes—
503#391C2312yes—
504#391C2314yes—
505#391C2314yes—
506#391C2312yes—
507#391C2314yes—
508#391C2314yes—
509#391C2314yes—
510#391C2314yes—
511#389C2312yes—
512#389C2312yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2314yes—
517#389C2314yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2312yes—
540#389C2312yes—
541#389C2314yes—
542#389C2314yes—
543#389C2312yes—
544#389C2312yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#388C2312yes—
558#388C2312yes—
559#388C2312yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#387C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#384C2311yescharacteristic
643#384C2312yes—
644#384C2312yes—
645#384C2314yes—
646#384C2314yes—
647#383C2312yes—
648#383C2314yes—
649#383C2314yes—
650#383C2312yes—
651#383C2312yes—
652#383C2314yes—
653#383C2314yes—
654#383C2314yes—
655#383C2314yes—
656#382C2312yes—
657#382C2312yes—
658#382C2312yes—
659#382C2312yes—
660#382C2312yes—
661#382C2312yes—
662#382C2314yes—
663#382C2314yes—
664#382C2314yes—
665#382C2314yes—
666#382C2312yes—
667#382C2314yes—
668#382C2312yes—
669#382C2314yes—
670#382C2314yes—
671#381C2314yes—
672#381C2314yes—
673#380C2312yes—
674#380C2312yes—
675#380C2312yes—
676#380C2314yes—
677#380C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709#376C2311yescharacteristic
710#376C2311yescharacteristic
711#376C2314yes—
712#376C2314yes—
713#376C2314yes—
714#376C2314yes—
715C43C2311yescharacteristic
716C43C2312yes—
717C22×Q8C2412yes—
718C22×Q8C2411yescharacteristic
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×Q8C2411yescharacteristic
722C22×Q8C2414yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×Q8C2414yes—
727C22×D4C2411yescharacteristic
728C23×C4C2412yes—
729C23×C4C2414yes—
730C4⋊Q8—28no—
731C4⋊Q8—28no—
732C4⋊Q8—42no—
733C4⋊Q8—42no—
734C4⋊Q8—44no—
735C4⋊Q8—44no—
736C4⋊Q8—42no—
737C4⋊Q8—44no—
738C4⋊Q8—48no—
739C4⋊Q8—44no—
740C4⋊Q8—42no—
741C4⋊Q8—42no—
742C4⋊Q8—44no—
743#126—44no—
744#126—48no—
745#126—48no—
746#125—44no—
747#125—48no—
748#125—44no—
749#125—44no—
750#125—42no—
751#125—44no—
752#125—44no—
753#125—42no—
754#125—48no—
755#125—48no—
756C22⋊Q8—28no—
757C22⋊Q8—28no—
758C22⋊Q8—48no—
759C22⋊Q8—48no—
760C22⋊Q8—44no—
761C4×Q8—28no—
762C4×Q8—24no—
763C4×Q8—24no—
764C4×Q8—24no—
765C4×Q8—28no—
766C4×Q8—28no—
767C4×Q8—42no—
768C4×Q8—44no—
769C4×Q8—42no—
770C4×Q8—42no—
771C4×Q8—44no—
772C4×Q8—48no—
773C4×Q8—44no—
774C4×Q8—44no—
775C4×Q8—44no—
776C4×D4—44no—
777C4×D4—42no—
778#117—28no—
779#117—44no—
780C2×C4⋊C4—44no—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C42C2412yes—
881C2×C42C2412yes—
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2411yescharacteristic
885C2×C42C2412yes—
886C2×C42C2411yescharacteristic
887C2×C42C2411yescharacteristic
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2414yes—
893C2×C42C2412yes—
894C2×C42C2414yes—
895C2×C42C2411yescharacteristic
896C2×C42C2412yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2411yescharacteristic
903C2×C42C2414yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2411yescharacteristic
916#95C2411yescharacteristic
917#95C2411yescharacteristic
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2412yes—
925#95C2411yescharacteristic
926#95C2414yes—
927#95C2412yes—
928#95C2414yes—
929#95C2414yes—
930#95C2412yes—
931#95C2412yes—
932#95C2414yes—
933#95C2412yes—
934#95C2414yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2414yes—
945#95C2412yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997C24C2512yes—
998C2×Q8—24no—
999C2×Q8—24no—
1000C2×Q8—24no—
1001C2×Q8—24no—
1002C2×Q8—28no—
1003C2×Q8—22no—
1004C2×Q8—24no—
1005C2×Q8—22no—
1006C2×Q8—41no—
1007C2×Q8—41no—
1008C2×Q8—41no—
1009C2×Q8—42no—
1010C2×Q8—42no—
1011C2×Q8—41no—
1012C2×Q8—44no—
1013C2×Q8—44no—
1014C2×Q8—41no—
1015C2×Q8—42no—
1016C2×Q8—42no—
1017C2×Q8—44no—
1018C2×Q8—42no—
1019C2×Q8—42no—
1020C2×Q8—44no—
1021C2×Q8—44no—
1022C2×Q8—44no—
1023C2×Q8—42no—
1024C2×Q8H(5,𝔽2)14yes—
1025C2×D4—41no—
1026C2×D4—42no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2514yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2514yes—
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2514yes—
1045C22×C4C2512yes—
1046C22×C4C2511yescharacteristic
1047C22×C4C2511yescharacteristic
1048C22×C4C2512yes—
1049C22×C4C2511yescharacteristic
1050C22×C4C2512yes—
1051C22×C4C2511yescharacteristic
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2511yescharacteristic
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2514yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2511yescharacteristic
1061C4⋊C4—22no—
1062C4⋊C4—24no—
1063C4⋊C4—22no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—22no—
1069C4⋊C4—28no—
1070C4⋊C4—28no—
1071C4⋊C4—28no—
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—28no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—42no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—44no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—41no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—41no—
1110C4⋊C4—42no—
1111C4⋊C4—41no—
1112C4⋊C4—41no—
1113C4⋊C4—41no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—41no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C42−1+418yes—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—28no—
1143C22⋊C4—24no—
1144C22⋊C4—42no—
1145C22⋊C4—42no—
1146C22⋊C4—42no—
1147C22⋊C4—44no—
1148C22⋊C4—42no—
1149C22⋊C4—44no—
1150C22⋊C4—42no—
1151C22⋊C4—42no—
1152C22⋊C4—42no—
1153C22⋊C4—42no—
1154C22⋊C4—42no—
1155C22⋊C4—42no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—42no—
1159C22⋊C4—42no—
1160C42—24no—
1161C42—24no—
1162C42—24no—
1163C42—22no—
1164C42—24no—
1165C42—22no—
1166C42—24no—
1167C42—22no—
1168C42—28no—
1169C42—28no—
1170C42—28no—
1171C42—24no—
1172C42—24no—
1173C42—28no—
1174C42—24no—
1175C42—24no—
1176C42—22no—
1177C42—44no—
1178C42—41no—
1179C42—42no—
1180C42—42no—
1181C42—44no—
1182C42—44no—
1183C42—44no—
1184C42—44no—
1185C42—44no—
1186C42—44no—
1187C42—42no—
1188C23—22no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
1194C23—22no—
1195C23C2611yescharacteristic
1196Q8—28no—
1197Q8—44no—
1198Q8—44no—
1199Q8—48no—
1200Q8—84no—
1201Q8—82no—
1202Q8—88no—
1203Q8—164no—
1204Q8—162no—
1205Q8—162no—
1206D4—44no—
1207C2×C4—21no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—21no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—21no—
1222C2×C4—22no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—21no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—21no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—21no—
1280C2×C4—48no—
1281C2×C4—164no—
1282C2×C4C2×H(5,𝔽2)14yes—
1283C2×C4C2×H(5,𝔽2)12yes—
1284C2×C4C2×2−1+418yes—
1285C2×C4C2×2−1+414yes—
1286C2×C4#58512yes—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22C22×H(5,𝔽2)11yescharacteristic
1295C22C22×2−1+412yes—
1296C22C2×#58511yescharacteristic
1297C222−1+612yes—
1298C222−1+611yescharacteristic
1299C4—24no—
1300C4—22no—
1301C4—28no—
1302C4—42no—
1303C4—44no—
1304C4—41no—
1305C4—41no—
1306C4—42no—
1307C4—42no—
1308C4—44no—
1309C4—42no—
1310C4—41no—
1311C4—42no—
1312C4—42no—
1313C4—44no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—44no—
1318C4—42no—
1319C4—42no—
1320C4—41no—
1321C4—41no—
1322C4—42no—
1323C4—42no—
1324C4—44no—
1325C4—42no—
1326C4#354414yes—
1327C2—82no—
1328C2C2×#354411yescharacteristic
1329C2#6291911yescharacteristic
1330C2#6295012yes—
1331C2#6304811yescharacteristic
1332C2#6305712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58976C2semidirect
2. #58752C2semidirect
3. #58575C2semidirect
5. #57322C2semidirect
6. #54910C2semidirect
8. #46346C2semidirect
10. #46060C2semidirect
11. #45827C2semidirect
12. #45414C2semidirect
14. #45364C2semidirect
15. #45324C2semidirect
16. #45284C2semidirect
18. #44997C2semidirect
19. #42981C2semidirect
20. #42824C2semidirect
22. #42811C2semidirect
23. #42793C2semidirect
25. #42747C2semidirect
26. #37638C2semidirect
28. #36474C2semidirect
29. #36311C2semidirect

Maximal subgroups

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

subgroupindex
#589762
#587522
#585752
#583822
#573222
#549102
#545612
#463462
#462682
#460602
#458272
#454142
#454102
#453642
#453242
#452842
#451772
#449972
#429812
#428242
#428142
#428112
#427932
#427852
#427472
#376382
#366972
#364742
#363112