Finite Group Databasebeta

← #7658112

Subgroups — #7658112

Order 512.

4522 conjugacy classes of subgroups.

The subgroup lattice has 1377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42347C214yesmaximal, complemented
2#42346C214yesmaximal, complemented
3#42319C214yesmaximal, complemented
4#41684C214yesmaximal, complemented
5#41678C214yesmaximal, complemented
6#41395C212yesmaximal
7#41393C212yesmaximal, complemented
8#39683C212yesmaximal, complemented
9#39681C212yesmaximal, complemented
10#37962C212yesmaximal, complemented
11#37961C212yesmaximal, complemented
12#37884C212yesmaximal, complemented
13#37883C212yesmaximal, complemented
14#37632C211yesmaximal, characteristic
15#37597C212yesmaximal, complemented
16#37592C212yesmaximal, complemented
17#37549C211yesmaximal, characteristic
18#36181C212yesmaximal, complemented
19#36171C212yesmaximal, complemented
20#36086C214yesmaximal, complemented
21#36024C212yesmaximal
22#36023C212yesmaximal, complemented
23#35304C211yesmaximal, characteristic, complemented
24#35282C212yesmaximal, complemented
25#34625C212yesmaximal, complemented
26C2×#2660C211yesmaximal, characteristic, complemented
27#34239C211yesmaximal, characteristic, complemented
28#34209C211yesmaximal, characteristic, complemented
29#34149C211yesmaximal, characteristic
30C2×#552C2214yes—
31C22×C4⋊Q8C2211yescharacteristic
32C2×#529C2211yescharacteristic
33C22×#125C2211yescharacteristic
34C2×#519C2212yes—
35#2864C2212yes—
36#2859C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2851C2212yes—
40#2851C2212yes—
41#2839C2214yes—
42#2836C2214yes—
43#2833C2214yes—
44#2831C2214yes—
45#2822C2212yes—
46#2821C2214yes—
47#2820C2212yes—
48#2806C2214yes—
49#2805C2214yes—
50#2799C2214yes—
51#2793C2214yes—
52#2793C2214yes—
53#2791C2214yes—
54#2791C2214yes—
55#2791C2214yes—
56#2791C2214yes—
57#2788C2214yes—
58#2786C2214yes—
59#2775C2214yes—
60#2774C2214yes—
61#2774C2214yes—
62#2773C2214yes—
63#2767C2214yes—
64#2767C2214yes—
65#2762C2214yes—
66#2762C2214yes—
67#2759C2214yes—
68#2755C2214yes—
69#2754C2214yes—
70#2745C2214yes—
71#2740C2214yes—
72#2667C2214yes—
73#2666C2214yes—
74#2666C2214yes—
75#2666C2214yes—
76#2665C2214yes—
77#2664C2214yes—
78#2664C2214yes—
79#2660C2212yes—
80#2660C2212yes—
81#2660C2212yes—
82#2660C2211yescharacteristic
83#2660C2214yes—
84#2660C2212yes—
85#2660C2211yescharacteristic
86#2660C2212yes—
87#2660C2211yescharacteristic
88#2660C2211yescharacteristic
89#2660C2212yes—
90#2655C2214yes—
91#2655C2214yes—
92#2654C2214yes—
93#2650C2214yes—
94#2647C2212yes—
95#2647C2212yes—
96#2647C2212yes—
97#2640C2212yes—
98#2637C2214yes—
99#2634C2214yes—
100#2629C2212yes—
101#2629C2212yes—
102#2629C2212yes—
103#2628C2212yes—
104#2628C2212yes—
105#2628C2212yes—
106#2627C2212yes—
107#2618C2212yes—
108#2614C2214yes—
109#2612C2214yes—
110#2606C2212yes—
111#2605C2212yes—
112#2604C2214yes—
113#2601C2214yes—
114#2599C2214yes—
115#2588C2214yes—
116#2586C2214yes—
117#2585C2214yes—
118#2584C2211yescharacteristic
119#2584C2211yescharacteristic
120#2584C2214yes—
121#2581C2214yes—
122#2575C2214yes—
123#2574C2214yes—
124#2569C2212yes—
125#2567C2212yes—
126#2565C2214yes—
127#2565C2214yes—
128#2563C2212yes—
129#2562C2211yescharacteristic
130#2562C2211yescharacteristic
131#2560C2214yes—
132#2556C2214yes—
133#2549C2212yes—
134#2528C2214yes—
135#2528C2214yes—
136#2524C2214yes—
137#2524C2214yes—
138#2524C2214yes—
139#2522C2214yes—
140#2520C2214yes—
141#2520C2214yes—
142#2519C2214yes—
143#2517C2214yes—
144#2509C2212yes—
145#2509C2212yes—
146#2508C2212yes—
147#2508C2212yes—
148#2507C2212yes—
149#2507C2212yes—
150#2506C2212yes—
151#2506C2212yes—
152#2506C2214yes—
153#2506C2214yes—
154#2503C2212yes—
155#2503C2214yes—
156#2501C2212yes—
157#2499C2214yes—
158#2498C2214yes—
159#2497C2212yes—
160#2497C2212yes—
161#2496C2212yes—
162#2496C2212yes—
163#2496C2214yes—
164#2495C2212yes—
165#2495C2212yes—
166#2494C2212yes—
167#2494C2212yes—
168#2493C2214yes—
169#2493C2214yes—
170#2488C2214yes—
171#2487C2212yes—
172#2486C2212yes—
173#2486C2212yes—
174#2486C2214yes—
175#2486C2212yes—
176#2484C2214yes—
177#2484C2214yes—
178#2469C2214yes—
179#2469C2214yes—
180#2465C2214yes—
181#2465C2214yes—
182#2462C2214yes—
183#2462C2214yes—
184#2462C2214yes—
185#2462C2214yes—
186#2438C2214yes—
187#2438C2214yes—
188#2419C2214yes—
189#2413C2214yes—
190#2413C2214yes—
191#2413C2214yes—
192#2402C2214yes—
193#2399C2214yes—
194#2396C2214yes—
195#2396C2214yes—
196C2×#398C2212yes—
197C2×#398C2212yes—
198C2×#395C2214yes—
199#2373C2212yes—
200#2373C2212yes—
201#2372C2212yes—
202#2371C2212yes—
203#2371C2214yes—
204#2370C2212yes—
205#2370C2212yes—
206#2368C2211yescharacteristic
207#2368C2211yescharacteristic
208#2365C2212yes—
209#2365C2212yes—
210#2365C2214yes—
211#2364C2211yescharacteristic
212#2364C2211yescharacteristic
213#2359C2214yes—
214#2359C2212yes—
215#2359C2212yes—
216#2345C2211yescharacteristic
217#2345C2211yescharacteristic
218#2344C2212yes—
219#2344C2212yes—
220#2344C2211yescharacteristic
221#2344C2214yes—
222#2344C2212yes—
223#2344C2212yes—
224#2344C2212yes—
225#2344C2212yes—
226#2344C2211yescharacteristic
227#2343C2214yes—
228#2336C2214yes—
229#2331C2212yes—
230#2331C2212yes—
231#2330C2212yes—
232#2330C2212yes—
233#2327C2214yes—
234#2314C2212yes—
235#2314C2212yes—
236#2313C2212yes—
237#2310C2212yes—
238C4×C4⋊Q8C2212yes—
239C4×C4⋊Q8C2212yes—
240C4×C4⋊Q8C2212yes—
241C4×#125C2212yes—
242C4×#125C2212yes—
243C4×#125C2212yes—
244#2298C2212yes—
245#2295C2212yes—
246#2290C2212yes—
247#2290C2212yes—
248#2285C2212yes—
249#2285C2211yescharacteristic
250C2×#384C2212yes—
251#2283C2211yescharacteristic
252#2283C2212yes—
253C2×#382C2212yes—
254#2274C2212yes—
255C42×D4C2212yes—
256C4×#117C2212yes—
257C4×#117C2211yescharacteristic
258C2×#376C2211yescharacteristic
259C23×Q8C2312yes—
260#552—416no—
261C2×C4⋊Q8—28no—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268#529—28no—
269C2×#126C2312yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#125—28no—
273C2×#125C2311yescharacteristic
274C2×#125C2311yescharacteristic
275C2×#125C2312yes—
276C2×#125C2311yescharacteristic
277C2×#125C2311yescharacteristic
278C2×#125C2312yes—
279C2×#125C2311yescharacteristic
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#124C2311yescharacteristic
285C2×#123C2312yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×C22⋊Q8C2311yescharacteristic
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×#121C2311yescharacteristic
293#519—48no—
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2314yes—
296C2×C4×Q8C2314yes—
297C2×C4×Q8C2314yes—
298C2×C4×Q8C2314yes—
299C2×C4×Q8C2314yes—
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×#117C2312yes—
305C2×#117C2314yes—
306C2×#117C2312yes—
307C2×#117C2311yescharacteristic
308C2×#117C2312yes—
309C2×#117C2311yescharacteristic
310C2×#117C2312yes—
311C2×#117C2314yes—
312C2×#117C2314yes—
313C2×#117C2312yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2311yescharacteristic
318C22×C4⋊C4C2312yes—
319C22×C4⋊C4C2311yescharacteristic
320C22×C4⋊C4C2314yes—
321C22×C4⋊C4C2314yes—
322C22×C42C2312yes—
323C22×C42C2312yes—
324C22×C42C2311yescharacteristic
325#401C2314yes—
326#401C2314yes—
327#400C2312yes—
328#400C2312yes—
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#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#398C2314yes—
358#398C2312yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2312yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2312yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2312yes—
389#398C2312yes—
390#398C2312yes—
391#398C2312yes—
392#398C2312yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#395C2312yes—
414#395C2312yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#394C2312yes—
431#394C2312yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2312yes—
450#391C2312yes—
451#390C2314yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2312yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2312yes—
484#389C2314yes—
485#389C2312yes—
486#389C2314yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2312yes—
503#388C2312yes—
504#388C2314yes—
505#388C2314yes—
506#388C2312yes—
507#388C2312yes—
508#388C2312yes—
509#388C2312yes—
510#388C2312yes—
511#388C2312yes—
512#388C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2312yes—
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#387C2312yes—
543#387C2312yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2312yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2312yes—
569#387C2312yes—
570#387C2312yes—
571#387C2312yes—
572#387C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2312yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#386C2312yes—
582#386C2314yes—
583#386C2312yes—
584#386C2312yes—
585#386C2312yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2312yes—
592#385C2312yes—
593#385C2312yes—
594#385C2312yes—
595#384C2312yes—
596#384C2312yes—
597#384C2314yes—
598#384C2314yes—
599#384C2312yes—
600#384C2312yes—
601#384C2312yes—
602#384C2312yes—
603#384C2314yes—
604#383C2312yes—
605#383C2314yes—
606#383C2314yes—
607#383C2314yes—
608#382C2312yes—
609#382C2312yes—
610#382C2314yes—
611#382C2312yes—
612#382C2314yes—
613#382C2314yes—
614#382C2312yes—
615#382C2312yes—
616#382C2314yes—
617#382C2314yes—
618#382C2314yes—
619#382C2312yes—
620#382C2312yes—
621#382C2314yes—
622#381C2314yes—
623#381C2314yes—
624#381C2312yes—
625#381C2312yes—
626#381C2314yes—
627#381C2314yes—
628#381C2312yes—
629#381C2314yes—
630#381C2314yes—
631#380C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2312yes—
637#380C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2312yes—
641#380C2312yes—
642#380C2314yes—
643#380C2314yes—
644#380C2311yescharacteristic
645#380C2312yes—
646#380C2311yescharacteristic
647#380C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2311yescharacteristic
684C4×C22⋊C4C2312yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2311yescharacteristic
690C4×C22⋊C4C2311yescharacteristic
691C4×C22⋊C4C2311yescharacteristic
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700#376C2312yes—
701#376C2312yes—
702#376C2312yes—
703#376C2314yes—
704#376C2311yescharacteristic
705#376C2311yescharacteristic
706#376C2312yes—
707#376C2312yes—
708#376C2311yescharacteristic
709#376C2311yescharacteristic
710C2×#95C2311yescharacteristic
711C2×#95C2314yes—
712C2×#95C2312yes—
713C2×#95C2314yes—
714C2×#95C2311yescharacteristic
715C43C2312yes—
716C43C2312yes—
717C22×Q8—28no—
718C22×Q8—44no—
719C22×Q8—44no—
720C22×Q8C2412yes—
721C22×Q8C2412yes—
722C22×Q8C2414yes—
723C22×Q8C2414yes—
724C22×Q8C2411yescharacteristic
725C22×D4C2412yes—
726C22×D4C2411yescharacteristic
727C23×C4C2412yes—
728C23×C4C2414yes—
729C23×C4C2412yes—
730C23×C4C2412yes—
731C23×C4C2412yes—
732C23×C4C2412yes—
733C23×C4C2411yescharacteristic
734C23×C4C2411yescharacteristic
735C23×C4C2412yes—
736C23×C4C2412yes—
737C23×C4C2411yescharacteristic
738C4⋊Q8—24no—
739C4⋊Q8—24no—
740C4⋊Q8—28no—
741C4⋊Q8—28no—
742C4⋊Q8—28no—
743C4⋊Q8—28no—
744#126—28no—
745#126—48no—
746#126—48no—
747#125—24no—
748#125—24no—
749#125—24no—
750#125—24no—
751#125—28no—
752#125—28no—
753#125—24no—
754#125—28no—
755#125—48no—
756#125—48no—
757#125—48no—
758#124—24no—
759#123—28no—
760#123—48no—
761#123—48no—
762#123—48no—
763C22⋊Q8—24no—
764C22⋊Q8—48no—
765C22⋊Q8—48no—
766#121—24no—
767C4×Q8—24no—
768C4×Q8—48no—
769C4×Q8—48no—
770C4×Q8—48no—
771C4×Q8—48no—
772C4×Q8—48no—
773C4×D4—28no—
774C4×D4—28no—
775C4×D4—24no—
776C4×D4—44no—
777#117—24no—
778#117—216no—
779#117—28no—
780#117—28no—
781#117—28no—
782#117—48no—
783#117—42no—
784#117—44no—
785#117—48no—
786#117—44no—
787C2×C4⋊C4—24no—
788C2×C4⋊C4—28no—
789C2×C4⋊C4—28no—
790C2×C4⋊C4—24no—
791C2×C4⋊C4—28no—
792C2×C4⋊C4—28no—
793C2×C4⋊C4—48no—
794C2×C4⋊C4—48no—
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C22⋊C4C2411yescharacteristic
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2411yescharacteristic
871C2×C22⋊C4C2411yescharacteristic
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2411yescharacteristic
894C2×C42—28no—
895C2×C42—28no—
896C2×C42#4118yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928C2×C42C2412yes—
929#95C2412yes—
930#95C2411yescharacteristic
931#95C2411yescharacteristic
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2411yescharacteristic
938#95C2411yescharacteristic
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2414yes—
980#95C2412yes—
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#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009C24C2512yes—
1010C24C2511yescharacteristic
1011C2×Q8—24no—
1012C2×Q8—24no—
1013C2×Q8—28no—
1014C2×Q8—22no—
1015C2×Q8—28no—
1016C2×Q8—42no—
1017C2×Q8—42no—
1018C2×Q8—44no—
1019C2×Q8—42no—
1020C2×Q8—42no—
1021C2×Q8—44no—
1022C2×Q8—44no—
1023C2×Q8—42no—
1024C2×Q8—44no—
1025C2×Q8—432no—
1026C2×D4—24no—
1027C2×D4—24no—
1028C2×D4—24no—
1029C2×D4—22no—
1030C2×D4—42no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—28no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—28no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—28no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—42no—
1052C22×C4—42no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—42no—
1057C22×C4—44no—
1058C22×C4C2×#4114yes—
1059C22×C4C2×#4114yes—
1060C22×C4C2×#4114yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2514yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2514yes—
1074C22×C4C2514yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2511yescharacteristic
1080C22×C4C2511yescharacteristic
1081C22×C4C2511yescharacteristic
1082C22×C4C2511yescharacteristic
1083C22×C4C2511yescharacteristic
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2511yescharacteristic
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—22no—
1099C4⋊C4—22no—
1100C4⋊C4—22no—
1101C4⋊C4—22no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—22no—
1111C4⋊C4—24no—
1112C4⋊C4—22no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—28no—
1116C4⋊C4—28no—
1117C4⋊C4—28no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C22⋊C4—24no—
1162C22⋊C4—22no—
1163C22⋊C4—28no—
1164C22⋊C4—24no—
1165C22⋊C4—22no—
1166C22⋊C4—22no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—24no—
1172C22⋊C4—24no—
1173C22⋊C4—24no—
1174C22⋊C4—24no—
1175C22⋊C4—42no—
1176C22⋊C4—42no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—42no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4H(5,𝔽2)14yes—
1187C42—24no—
1188C42—28no—
1189C42—28no—
1190C42—24no—
1191C42—28no—
1192C42—24no—
1193C42—24no—
1194C42—24no—
1195C42—24no—
1196C42—24no—
1197C42—24no—
1198C42—24no—
1199C42—24no—
1200C42—42no—
1201C42—42no—
1202C42—44no—
1203C42—42no—
1204C42—44no—
1205C42—42no—
1206C42—44no—
1207C42—42no—
1208C42—44no—
1209C42—42no—
1210C42—42no—
1211C42—44no—
1212C42—44no—
1213C42—42no—
1214C42C2×#4114yes—
1215C42C2×#4114yes—
1216C42C2×#4114yes—
1217C42C2×#4114yes—
1218C422−1+418yes—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—22no—
1228C23C22×#4112yes—
1229C23C2×H(5,𝔽2)12yes—
1230C23#58512yes—
1231C23C2611yescharacteristic
1232Q8—48no—
1233Q8—48no—
1234Q8—416no—
1235Q8—82no—
1236Q8—88no—
1237D4—48no—
1238D4—82no—
1239C2×C4—21no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—22no—
1246C2×C4—21no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—28no—
1253C2×C4—28no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—44no—
1307C2×C4—48no—
1308C2×C4—48no—
1309C2×C4—48no—
1310C2×C4—48no—
1311C2×C4—416no—
1312C2×C4—48no—
1313C2×C4—84no—
1314C2×C4—84no—
1315C2×C4C22×#4112yes—
1316C2×C4C22×#4112yes—
1317C2×C4C22×#4112yes—
1318C2×C4C22×#4112yes—
1319C2×C4C22×#4112yes—
1320C2×C4C22×#4112yes—
1321C2×C4C2×H(5,𝔽2)14yes—
1322C2×C4C2×2−1+414yes—
1323C2×C4C2×2−1+414yes—
1324C2×C4C2×2−1+414yes—
1325C22—22no—
1326C22—22no—
1327C22—24no—
1328C22—24no—
1329C22—42no—
1330C22—42no—
1331C22—42no—
1332C22—42no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22#346014yes—
1337C22C23×#4111yescharacteristic
1338C22C22×H(5,𝔽2)11yescharacteristic
1339C22C22×2−1+412yes—
1340C22C2×#58511yescharacteristic
1341C222−1+612yes—
1342C4—22no—
1343C4—22no—
1344C4—22no—
1345C4—24no—
1346C4—24no—
1347C4—24no—
1348C4—22no—
1349C4—22no—
1350C4—42no—
1351C4—42no—
1352C4—42no—
1353C4—42no—
1354C4—42no—
1355C4—44no—
1356C4—42no—
1357C4—44no—
1358C4—44no—
1359C4—42no—
1360C4—44no—
1361C4—42no—
1362C4—42no—
1363C4—42no—
1364C4—42no—
1365C4—44no—
1366C4—44no—
1367C4—42no—
1368C4#350914yes—
1369C2—24no—
1370C2—82no—
1371C2C2×#346011yescharacteristic
1372C2C2×#350911yescharacteristic
1373C2#6286011yescharacteristic
1374C2#6291512yes—
1375C2#6292812yes—
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. #42347C2semidirect
2. #42346C2semidirect
3. #42319C2semidirect
4. #41684C2semidirect
5. #41678C2semidirect
7. #41393C2semidirect
8. #39683C2semidirect
9. #39681C2semidirect
10. #37962C2semidirect
11. #37961C2semidirect
12. #37884C2semidirect
13. #37883C2semidirect
15. #37597C2semidirect
16. #37592C2semidirect
18. #36181C2semidirect
19. #36171C2semidirect
20. #36086C2semidirect
22. #36023C2semidirect
23. #35304C2semidirect
24. #35282C2semidirect
25. #34625C2semidirect
26. C2×#2660C2semidirect
27. #34239C2semidirect
28. #34209C2semidirect

Maximal subgroups

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

subgroupindex
#423472
#423462
#423192
#416842
#416782
#413952
#413932
#396832
#396812
#379622
#379612
#378842
#378832
#376322
#375972
#375922
#375492
#361812
#361712
#360862
#360242
#360232
#353042
#352822
#346252
C2×#26602
#342392
#342092
#341492