Finite Group Databasebeta

← #8383484

Subgroups — #8383484

Order 512.

4163 conjugacy classes of subgroups.

The subgroup lattice has 1404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59479C212yesmaximal
2#58910C214yesmaximal, complemented
3#58289C214yesmaximal, complemented
4#57312C214yesmaximal, complemented
5#55884C214yesmaximal, complemented
6#53042C212yesmaximal, complemented
7#51121C214yesmaximal, complemented
8#49537C214yesmaximal, complemented
9#46116C212yesmaximal, complemented
10#45389C211yesmaximal, characteristic, complemented
11#45347C211yesmaximal, characteristic, complemented
12#45231C211yesmaximal, characteristic, complemented
13#45230C212yesmaximal
14#45139C211yesmaximal, characteristic, complemented
15#42879C211yesmaximal, characteristic, complemented
16#42826C212yesmaximal, complemented
17#42793C211yesmaximal, characteristic, complemented
18#42721C212yesmaximal, complemented
19#41494C214yesmaximal, complemented
20#41155C214yesmaximal, complemented
21#40215C212yesmaximal, complemented
22#39976C212yesmaximal, complemented
23#39617C211yesmaximal, characteristic, complemented
24#38970C211yesmaximal, characteristic, complemented
25#37320C211yesmaximal, characteristic, complemented
26#36560C211yesmaximal, characteristic, complemented
27#36394C211yesmaximal, characteristic, complemented
28#36040C211yesmaximal, characteristic
29#36031C211yesmaximal, characteristic
30#35622C211yesmaximal, characteristic
31#34604C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#554C2211yescharacteristic
36C2×#541C2211yescharacteristic
37C2×#520C2211yescharacteristic
38#2868C2211yescharacteristic
39#2864C2211yescharacteristic
40#2863C2212yes—
41#2859C2212yes—
42#2845C2214yes—
43#2841C2214yes—
44#2839C2214yes—
45#2839C2214yes—
46#2839C2214yes—
47#2834C2214yes—
48#2833C2214yes—
49#2821C2212yes—
50#2821C2212yes—
51#2807C2214yes—
52#2794C2214yes—
53#2792C2214yes—
54#2791C2214yes—
55#2791C2214yes—
56#2791C2214yes—
57#2787C2214yes—
58#2787C2214yes—
59#2786C2214yes—
60#2776C2214yes—
61#2776C2214yes—
62#2774C2214yes—
63#2770C2214yes—
64#2769C2214yes—
65#2769C2214yes—
66#2768C2214yes—
67#2767C2214yes—
68#2766C2214yes—
69#2766C2214yes—
70#2765C2214yes—
71#2764C2214yes—
72#2762C2214yes—
73#2762C2214yes—
74#2761C2214yes—
75#2757C2214yes—
76#2755C2214yes—
77#2747C2214yes—
78#2747C2214yes—
79#2745C2214yes—
80#2744C2214yes—
81#2739C2214yes—
82#2738C2214yes—
83#2738C2214yes—
84#2738C2214yes—
85#2734C2214yes—
86#2729C2214yes—
87#2726C2214yes—
88#2723C2214yes—
89#2722C2214yes—
90#2721C2214yes—
91#2721C2214yes—
92#2720C2214yes—
93#2720C2214yes—
94#2719C2214yes—
95#2716C2214yes—
96#2716C2214yes—
97#2713C2214yes—
98#2713C2214yes—
99#2713C2214yes—
100#2704C2214yes—
101#2677C2214yes—
102#2677C2214yes—
103#2667C2214yes—
104#2666C2214yes—
105#2666C2212yes—
106#2666C2214yes—
107#2664C2212yes—
108#2660C2212yes—
109#2660C2212yes—
110#2655C2212yes—
111#2655C2214yes—
112#2655C2212yes—
113#2654C2212yes—
114#2652C2214yes—
115#2650C2212yes—
116#2646C2214yes—
117#2645C2212yes—
118#2642C2212yes—
119#2637C2212yes—
120#2634C2212yes—
121#2634C2212yes—
122#2634C2212yes—
123#2628C2212yes—
124#2628C2211yescharacteristic
125#2628C2211yescharacteristic
126#2627C2212yes—
127#2604C2212yes—
128#2604C2212yes—
129#2599C2214yes—
130#2590C2214yes—
131#2585C2214yes—
132#2581C2211yescharacteristic
133#2581C2211yescharacteristic
134#2581C2211yescharacteristic
135#2580C2211yescharacteristic
136#2580C2212yes—
137#2577C2214yes—
138#2575C2214yes—
139#2575C2214yes—
140#2575C2214yes—
141#2570C2212yes—
142#2570C2212yes—
143#2570C2214yes—
144#2568C2211yescharacteristic
145#2568C2211yescharacteristic
146#2567C2211yescharacteristic
147#2566C2211yescharacteristic
148#2565C2212yes—
149#2565C2211yescharacteristic
150#2565C2212yes—
151#2565C2212yes—
152#2564C2212yes—
153#2563C2211yescharacteristic
154#2563C2212yes—
155#2560C2214yes—
156#2552C2212yes—
157#2552C2212yes—
158#2550C2212yes—
159#2550C2212yes—
160#2547C2211yescharacteristic
161#2546C2211yescharacteristic
162#2546C2214yes—
163#2542C2212yes—
164#2533C2214yes—
165#2528C2214yes—
166#2527C2214yes—
167#2524C2214yes—
168#2520C2214yes—
169#2516C2214yes—
170#2516C2214yes—
171#2514C2212yes—
172#2514C2212yes—
173#2508C2212yes—
174#2507C2212yes—
175#2507C2212yes—
176#2506C2214yes—
177#2506C2212yes—
178#2506C2214yes—
179#2505C2214yes—
180#2503C2211yescharacteristic
181#2502C2211yescharacteristic
182#2497C2212yes—
183#2496C2212yes—
184#2493C2214yes—
185#2493C2214yes—
186#2493C2214yes—
187#2492C2212yes—
188#2489C2212yes—
189#2487C2212yes—
190#2479C2214yes—
191#2475C2214yes—
192#2473C2214yes—
193#2473C2214yes—
194#2468C2214yes—
195#2466C2214yes—
196#2462C2214yes—
197#2454C2212yes—
198#2454C2212yes—
199#2454C2214yes—
200#2453C2212yes—
201#2453C2212yes—
202#2453C2212yes—
203#2451C2212yes—
204#2450C2214yes—
205#2447C2212yes—
206#2447C2212yes—
207#2446C2212yes—
208#2446C2212yes—
209#2446C2212yes—
210#2446C2212yes—
211#2446C2214yes—
212#2442C2214yes—
213#2442C2212yes—
214#2442C2212yes—
215#2441C2214yes—
216#2440C2214yes—
217#2438C2214yes—
218#2438C2214yes—
219#2438C2214yes—
220#2432C2211yescharacteristic
221#2432C2211yescharacteristic
222#2423C2212yes—
223#2423C2214yes—
224#2423C2214yes—
225#2421C2212yes—
226#2402C2211yescharacteristic
227#2402C2212yes—
228#2401C2212yes—
229#2399C2211yescharacteristic
230#2396C2211yescharacteristic
231#2396C2211yescharacteristic
232#2396C2212yes—
233C2×#400C2212yes—
234#2383C2214yes—
235#2368C2214yes—
236#2367C2212yes—
237#2365C2212yes—
238#2365C2214yes—
239#2357C2212yes—
240#2356C2211yescharacteristic
241#2356C2211yescharacteristic
242#2355C2212yes—
243#2351C2212yes—
244#2351C2211yescharacteristic
245#2349C2212yes—
246#2349C2211yescharacteristic
247#2343C2214yes—
248#2341C2212yes—
249#2339C2212yes—
250#2336C2214yes—
251#2331C2211yescharacteristic
252#2331C2211yescharacteristic
253#2329C2214yes—
254#2327C2211yescharacteristic
255#2326C2211yescharacteristic
256#2326C2212yes—
257#2320C2212yes—
258C4×C4⋊Q8C2212yes—
259C4×C4⋊Q8C2211yescharacteristic
260C4×#125C2212yes—
261C4×#126C2212yes—
262C4×#124C2211yescharacteristic
263#2298C2211yescharacteristic
264#2295C2211yescharacteristic
265#2293C2212yes—
266C42×Q8C2211yescharacteristic
267C22×#41C2311yescharacteristic
268Q82—44no—
269#557—44no—
270#557—44no—
271#554—44no—
272#541—44no—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2314yes—
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2314yes—
283C2×C4⋊Q8C2311yescharacteristic
284C2×#126C2312yes—
285C2×#126C2314yes—
286C2×#126C2312yes—
287C2×#126C2312yes—
288C2×#125C2312yes—
289C2×#125C2311yescharacteristic
290C2×#125C2312yes—
291C2×#125C2312yes—
292C2×#125C2312yes—
293C2×#125C2314yes—
294C2×#125C2312yes—
295C2×#125C2312yes—
296C2×#125C2314yes—
297C2×#125C2314yes—
298C2×#124C2311yescharacteristic
299C2×#124C2311yescharacteristic
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2311yescharacteristic
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2311yescharacteristic
306#520—44no—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2312yes—
327C2×#117C2311yescharacteristic
328C2×#117C2314yes—
329C2×#117C2312yes—
330C22×C4⋊C4C2312yes—
331C22×C4⋊C4C2312yes—
332C22×C4⋊C4C2311yescharacteristic
333#401C2314yes—
334#401C2314yes—
335#401C2314yes—
336#401C2312yes—
337#400C2312yes—
338#400C2312yes—
339#400C2312yes—
340#400C2314yes—
341#400C2312yes—
342#400C2312yes—
343#400C2314yes—
344#400C2312yes—
345#400C2314yes—
346#400C2312yes—
347#400C2312yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2312yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2312yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2312yes—
369#400C2312yes—
370#400C2311yescharacteristic
371#400C2312yes—
372#400C2312yes—
373#400C2311yescharacteristic
374#400C2314yes—
375#400C2314yes—
376#400C2312yes—
377#400C2312yes—
378#400C2312yes—
379#400C2314yes—
380#400C2314yes—
381#399C2312yes—
382#399C2311yescharacteristic
383#399C2314yes—
384#399C2312yes—
385#399C2312yes—
386#399C2314yes—
387#399C2314yes—
388#399C2314yes—
389#399C2311yescharacteristic
390#399C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2312yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2312yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2312yes—
429#398C2312yes—
430#398C2312yes—
431#398C2312yes—
432#398C2312yes—
433#398C2312yes—
434#398C2312yes—
435#398C2312yes—
436#398C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2312yes—
445#397C2312yes—
446#397C2312yes—
447#397C2314yes—
448#396C2314yes—
449#396C2312yes—
450#396C2314yes—
451#396C2312yes—
452#396C2312yes—
453#396C2314yes—
454#396C2314yes—
455#395C2312yes—
456#395C2312yes—
457#395C2312yes—
458#395C2314yes—
459#395C2312yes—
460#395C2314yes—
461#395C2314yes—
462#395C2312yes—
463#395C2314yes—
464#395C2311yescharacteristic
465#395C2311yescharacteristic
466#395C2312yes—
467#395C2312yes—
468#395C2312yes—
469#395C2312yes—
470#395C2314yes—
471#394C2314yes—
472#394C2314yes—
473#393C2314yes—
474#393C2311yescharacteristic
475#393C2312yes—
476#393C2312yes—
477#393C2312yes—
478#393C2312yes—
479#393C2311yescharacteristic
480#393C2312yes—
481#391C2314yes—
482#391C2311yescharacteristic
483#391C2311yescharacteristic
484#391C2312yes—
485#391C2312yes—
486#391C2311yescharacteristic
487#391C2312yes—
488#391C2311yescharacteristic
489#391C2314yes—
490#391C2314yes—
491#391C2312yes—
492#391C2314yes—
493#391C2312yes—
494#391C2312yes—
495#391C2311yescharacteristic
496#391C2311yescharacteristic
497#391C2314yes—
498#391C2314yes—
499#391C2314yes—
500#391C2314yes—
501#391C2312yes—
502#391C2312yes—
503#391C2312yes—
504#390C2314yes—
505#390C2312yes—
506#390C2314yes—
507#390C2311yescharacteristic
508#390C2311yescharacteristic
509#390C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2312yes—
517#389C2312yes—
518#389C2314yes—
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#389C2312yes—
523#389C2312yes—
524#389C2314yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2312yes—
538#389C2312yes—
539#389C2314yes—
540#389C2314yes—
541#389C2312yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2312yes—
546#389C2314yes—
547#388C2312yes—
548#388C2312yes—
549#388C2312yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2312yes—
565#388C2312yes—
566#388C2314yes—
567#387C2312yes—
568#387C2312yes—
569#387C2312yes—
570#387C2314yes—
571#387C2312yes—
572#387C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
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#387C2312yes—
625#387C2312yes—
626#387C2312yes—
627#387C2314yes—
628#387C2312yes—
629#387C2314yes—
630#387C2314yes—
631#386C2314yes—
632#386C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#384C2312yes—
652#384C2311yescharacteristic
653#384C2312yes—
654#384C2311yescharacteristic
655#384C2312yes—
656#384C2314yes—
657#384C2314yes—
658#384C2314yes—
659#383C2312yes—
660#383C2312yes—
661#383C2312yes—
662#383C2314yes—
663#383C2314yes—
664#383C2314yes—
665#383C2314yes—
666#382C2312yes—
667#382C2312yes—
668#382C2314yes—
669#382C2312yes—
670#382C2312yes—
671#382C2311yescharacteristic
672#382C2311yescharacteristic
673#382C2314yes—
674#382C2314yes—
675#382C2314yes—
676#382C2311yescharacteristic
677#382C2312yes—
678#382C2311yescharacteristic
679#382C2314yes—
680#381C2314yes—
681#381C2314yes—
682#381C2314yes—
683#381C2314yes—
684#381C2314yes—
685#380C2314yes—
686#380C2314yes—
687#380C2314yes—
688#380C2314yes—
689#380C2312yes—
690#380C2314yes—
691#380C2314yes—
692#380C2312yes—
693#380C2312yes—
694#380C2314yes—
695#380C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2311yescharacteristic
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2314yes—
706C4×C4⋊C4C2314yes—
707C4×C4⋊C4C2311yescharacteristic
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2311yescharacteristic
711C4×C4⋊C4C2311yescharacteristic
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2314yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2314yes—
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2314yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2312yes—
720C4×C4⋊C4C2312yes—
721C4×C4⋊C4C2312yes—
722C4×C22⋊C4C2311yescharacteristic
723C4×C22⋊C4C2312yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2314yes—
726C4×C22⋊C4C2314yes—
727C4×C22⋊C4C2314yes—
728C4×C22⋊C4C2314yes—
729C4×C22⋊C4C2314yes—
730C4×C22⋊C4C2311yescharacteristic
731#376C2312yes—
732#376C2311yescharacteristic
733#376C2312yes—
734#376C2312yes—
735C2×#95C2312yes—
736C2×#95C2314yes—
737C2×#95C2314yes—
738C43C2312yes—
739C43C2311yescharacteristic
740C2×#41—24no—
741C2×#41—24no—
742C2×#41—42no—
743C22×Q8C2411yescharacteristic
744C22×Q8C2411yescharacteristic
745C22×Q8C2411yescharacteristic
746C22×Q8C2411yescharacteristic
747C22×Q8C2411yescharacteristic
748C22×Q8C2412yes—
749C22×Q8C2412yes—
750C22×Q8C2414yes—
751C22×D4C2412yes—
752C22×D4C2411yescharacteristic
753C23×C4C2411yescharacteristic
754C23×C4C2412yes—
755C23×C4C2412yes—
756C23×C4C2414yes—
757C23×C4C2412yes—
758C23×C4C2412yes—
759C23×C4C2414yes—
760C4⋊Q8—24no—
761C4⋊Q8—24no—
762C4⋊Q8—24no—
763C4⋊Q8—24no—
764C4⋊Q8—48no—
765C4⋊Q8—44no—
766C4⋊Q8—44no—
767C4⋊Q8—42no—
768C4⋊Q8—44no—
769C4⋊Q8—44no—
770C4⋊Q8—48no—
771#126—44no—
772#126—44no—
773#126—44no—
774#126—48no—
775#125—44no—
776#125—42no—
777#125—44no—
778#125—44no—
779#125—44no—
780#125—44no—
781#125—44no—
782#125—48no—
783#125—48no—
784#125—48no—
785#124—24no—
786#124—24no—
787C22⋊Q8—48no—
788C22⋊Q8—48no—
789C22⋊Q8—48no—
790C22⋊Q8—42no—
791C22⋊Q8—42no—
792C22⋊Q8—44no—
793C4×Q8—28no—
794C4×Q8—24no—
795C4×Q8—24no—
796C4×Q8—24no—
797C4×Q8—24no—
798C4×Q8—24no—
799C4×Q8—44no—
800C4×Q8—42no—
801C4×Q8—44no—
802C4×Q8—44no—
803C4×Q8—44no—
804C4×Q8—44no—
805C4×Q8—44no—
806C4×Q8—44no—
807C4×D4—28no—
808C4×D4—24no—
809C4×D4—44no—
810C4×D4—42no—
811C4×D4—44no—
812C4×D4—44no—
813#117—24no—
814#117—48no—
815#117—44no—
816C2×C4⋊C4—44no—
817C2×C4⋊C4—42no—
818C2×C4⋊C4—44no—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2411yescharacteristic
901C2×C22⋊C4C2411yescharacteristic
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2414yes—
935C2×C42C2411yescharacteristic
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2412yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2414yes—
950C2×C42C2411yescharacteristic
951#95C2411yescharacteristic
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2411yescharacteristic
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2414yes—
987#95C2411yescharacteristic
988#95C2412yes—
989#95C2411yescharacteristic
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037C24C2511yescharacteristic
1038C24C2512yes—
1039#41—416no—
1040C2×Q8—22no—
1041C2×Q8—22no—
1042C2×Q8—22no—
1043C2×Q8—22no—
1044C2×Q8—22no—
1045C2×Q8—24no—
1046C2×Q8—24no—
1047C2×Q8—22no—
1048C2×Q8—22no—
1049C2×Q8—22no—
1050C2×Q8—22no—
1051C2×Q8—22no—
1052C2×Q8—42no—
1053C2×Q8—42no—
1054C2×Q8—44no—
1055C2×Q8—44no—
1056C2×Q8—44no—
1057C2×Q8—44no—
1058C2×Q8—44no—
1059C2×Q82−1+414yes—
1060C2×D4—24no—
1061C2×D4—22no—
1062C2×D4—22no—
1063C2×D4—24no—
1064C2×D4—42no—
1065C2×D42−1+414yes—
1066C22×C4—24no—
1067C22×C4—28no—
1068C22×C4—22no—
1069C22×C4—24no—
1070C22×C4—22no—
1071C22×C4—22no—
1072C22×C4—24no—
1073C22×C4—42no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4C2512yes—
1085C22×C4C2511yescharacteristic
1086C22×C4C2514yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2511yescharacteristic
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2514yes—
1105C22×C4C2514yes—
1106C22×C4C2512yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2511yescharacteristic
1113C4⋊C4—22no—
1114C4⋊C4—22no—
1115C4⋊C4—22no—
1116C4⋊C4—24no—
1117C4⋊C4—22no—
1118C4⋊C4—24no—
1119C4⋊C4—22no—
1120C4⋊C4—24no—
1121C4⋊C4—22no—
1122C4⋊C4—24no—
1123C4⋊C4—22no—
1124C4⋊C4—22no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—28no—
1132C4⋊C4—24no—
1133C4⋊C4—28no—
1134C4⋊C4—28no—
1135C4⋊C4—28no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—24no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C22⋊C4—28no—
1194C22⋊C4—28no—
1195C22⋊C4—28no—
1196C22⋊C4—22no—
1197C22⋊C4—22no—
1198C22⋊C4—24no—
1199C22⋊C4—28no—
1200C22⋊C4—24no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—44no—
1207C22⋊C4—42no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—42no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C42—22no—
1218C42—24no—
1219C42—24no—
1220C42—24no—
1221C42—24no—
1222C42—24no—
1223C42—24no—
1224C42—28no—
1225C42—24no—
1226C42—22no—
1227C42—22no—
1228C42—22no—
1229C42—22no—
1230C42—24no—
1231C42—24no—
1232C42—24no—
1233C42—42no—
1234C42—42no—
1235C42—42no—
1236C42—44no—
1237C42—44no—
1238C42—42no—
1239C42—44no—
1240C42—44no—
1241C42—44no—
1242C42—44no—
1243C42—44no—
1244C42H(5,𝔽2)14yes—
1245C23—22no—
1246C23—22no—
1247C23—24no—
1248C23—24no—
1249C23—21no—
1250C23—21no—
1251C23—21no—
1252C23—22no—
1253C23—22no—
1254C23C2×2−1+414yes—
1255C23C2611yescharacteristic
1256Q8—28no—
1257Q8—44no—
1258Q8—44no—
1259Q8—44no—
1260Q8—44no—
1261Q8—84no—
1262Q8—84no—
1263Q8—164no—
1264D4—28no—
1265D4—48no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—21no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—21no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—21no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—48no—
1339C2×C4—44no—
1340C2×C4—84no—
1341C2×C4—88no—
1342C2×C4—164no—
1343C2×C4—162no—
1344C2×C4—162no—
1345C2×C4C2×H(5,𝔽2)12yes—
1346C2×C4C2×H(5,𝔽2)12yes—
1347C2×C4C2×H(5,𝔽2)12yes—
1348C2×C4C2×2−1+414yes—
1349C2×C4C2×2−1+412yes—
1350C2×C4C2×2−1+412yes—
1351C2×C4#58514yes—
1352C22—24no—
1353C22—28no—
1354C22—42no—
1355C22—42no—
1356C22—44no—
1357C22—41no—
1358C22—41no—
1359C22—41no—
1360C22—42no—
1361C22—42no—
1362C22C22×H(5,𝔽2)11yescharacteristic
1363C22C22×2−1+411yescharacteristic
1364C22C22×2−1+411yescharacteristic
1365C22C2×#58512yes—
1366C222−1+612yes—
1367C4—24no—
1368C4—22no—
1369C4—22no—
1370C4—24no—
1371C4—41no—
1372C4—42no—
1373C4—42no—
1374C4—41no—
1375C4—42no—
1376C4—44no—
1377C4—42no—
1378C4—44no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—42no—
1383C4—41no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—44no—
1388C4—42no—
1389C4—42no—
1390C4—42no—
1391C4—42no—
1392C4—42no—
1393C4—44no—
1394C4—42no—
1395C4#353814yes—
1396C2—44no—
1397C2—81no—
1398C2C2×#353811yescharacteristic
1399C2#6283611yescharacteristic
1400C2#6288711yescharacteristic
1401C2#6294912yes—
1402C2#6295012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #58910C2semidirect
3. #58289C2semidirect
4. #57312C2semidirect
5. #55884C2semidirect
6. #53042C2semidirect
7. #51121C2semidirect
8. #49537C2semidirect
9. #46116C2semidirect
10. #45389C2semidirect
11. #45347C2semidirect
12. #45231C2semidirect
14. #45139C2semidirect
15. #42879C2semidirect
16. #42826C2semidirect
17. #42793C2semidirect
18. #42721C2semidirect
19. #41494C2semidirect
20. #41155C2semidirect
21. #40215C2semidirect
22. #39976C2semidirect
23. #39617C2semidirect
24. #38970C2semidirect
25. #37320C2semidirect
26. #36560C2semidirect
27. #36394C2semidirect
31. #34604C2semidirect

Maximal subgroups

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

subgroupindex
#594792
#589102
#582892
#573122
#558842
#530422
#511212
#495372
#461162
#453892
#453472
#452312
#452302
#451392
#428792
#428262
#427932
#427212
#414942
#411552
#402152
#399762
#396172
#389702
#373202
#365602
#363942
#360402
#360312
#356222
#346042