Finite Group Databasebeta

← #7658946

Subgroups — #7658946

Order 512.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42353C214yesmaximal, complemented
2#42330C212yesmaximal, complemented
3#42323C214yesmaximal, complemented
4#42238C214yesmaximal
5#42164C212yesmaximal, complemented
6#41707C214yesmaximal, complemented
7#41698C214yesmaximal, complemented
8#41684C214yesmaximal, complemented
9#41677C214yesmaximal, complemented
10#41440C212yesmaximal, complemented
11#41439C212yesmaximal, complemented
12#37612C212yesmaximal, complemented
13#37607C211yesmaximal, characteristic
14#37603C212yesmaximal, complemented
15#37603C212yesmaximal, complemented
16#37563C211yesmaximal, characteristic, complemented
17#37540C211yesmaximal, characteristic, complemented
18#36699C211yesmaximal, characteristic
19#36698C212yesmaximal, complemented
20#36090C212yesmaximal, complemented
21#36064C212yesmaximal, complemented
22#35857C212yesmaximal, complemented
23#35835C214yesmaximal, complemented
24#35760C212yesmaximal, complemented
25#34239C211yesmaximal, characteristic, complemented
26#34231C211yesmaximal, characteristic, complemented
27#34227C211yesmaximal, characteristic
28C2×#533C2211yescharacteristic
29C2×#529C2211yescharacteristic
30C22×#125C2211yescharacteristic
31#2844C2212yes—
32#2844C2212yes—
33#2838C2214yes—
34#2838C2214yes—
35#2836C2214yes—
36#2836C2214yes—
37#2833C2214yes—
38#2830C2214yes—
39#2822C2212yes—
40#2822C2211yescharacteristic
41#2822C2211yescharacteristic
42#2822C2212yes—
43#2822C2212yes—
44#2821C2212yes—
45#2821C2212yes—
46#2820C2211yescharacteristic
47#2820C2212yes—
48#2820C2211yescharacteristic
49#2817C2212yes—
50#2816C2212yes—
51#2814C2214yes—
52#2806C2214yes—
53#2805C2214yes—
54#2799C2214yes—
55#2798C2214yes—
56#2793C2214yes—
57#2791C2214yes—
58#2789C2214yes—
59#2776C2214yes—
60#2775C2214yes—
61#2774C2214yes—
62#2773C2214yes—
63#2765C2214yes—
64#2764C2214yes—
65#2762C2214yes—
66#2761C2214yes—
67#2759C2214yes—
68#2759C2214yes—
69#2754C2214yes—
70#2754C2214yes—
71#2751C2214yes—
72#2745C2214yes—
73#2744C2214yes—
74#2740C2214yes—
75#2737C2214yes—
76#2666C2214yes—
77#2666C2214yes—
78#2666C2214yes—
79#2666C2214yes—
80#2666C2214yes—
81#2666C2214yes—
82#2665C2212yes—
83#2665C2214yes—
84#2665C2212yes—
85#2665C2214yes—
86#2664C2214yes—
87#2660C2212yes—
88#2655C2214yes—
89#2655C2214yes—
90#2655C2214yes—
91#2655C2214yes—
92#2655C2214yes—
93#2655C2214yes—
94#2654C2214yes—
95#2654C2214yes—
96#2650C2214yes—
97#2650C2214yes—
98#2642C2212yes—
99#2638C2214yes—
100#2634C2214yes—
101#2634C2212yes—
102#2634C2214yes—
103#2633C2212yes—
104#2627C2214yes—
105#2623C2212yes—
106#2623C2212yes—
107#2611C2214yes—
108#2609C2214yes—
109#2607C2214yes—
110#2605C2214yes—
111#2605C2212yes—
112#2605C2212yes—
113#2605C2214yes—
114#2605C2214yes—
115#2599C2214yes—
116#2599C2214yes—
117#2593C2214yes—
118#2591C2212yes—
119#2589C2214yes—
120#2586C2214yes—
121#2583C2212yes—
122#2581C2214yes—
123#2579C2212yes—
124#2579C2212yes—
125#2577C2214yes—
126#2576C2214yes—
127#2575C2214yes—
128#2574C2214yes—
129#2573C2214yes—
130#2573C2214yes—
131#2572C2214yes—
132#2565C2212yes—
133#2565C2212yes—
134#2565C2214yes—
135#2556C2214yes—
136#2556C2214yes—
137#2533C2214yes—
138#2528C2214yes—
139#2527C2214yes—
140#2527C2214yes—
141#2524C2214yes—
142#2524C2214yes—
143#2524C2214yes—
144#2524C2214yes—
145#2524C2214yes—
146#2524C2214yes—
147#2524C2214yes—
148#2524C2214yes—
149#2524C2214yes—
150#2523C2214yes—
151#2523C2214yes—
152#2520C2214yes—
153#2520C2214yes—
154#2520C2214yes—
155#2520C2214yes—
156#2520C2214yes—
157#2520C2214yes—
158#2520C2214yes—
159#2520C2214yes—
160#2520C2214yes—
161#2517C2214yes—
162#2517C2214yes—
163#2515C2214yes—
164#2515C2214yes—
165#2514C2214yes—
166#2514C2214yes—
167#2503C2212yes—
168#2502C2212yes—
169#2499C2214yes—
170#2484C2212yes—
171#2484C2212yes—
172#2477C2214yes—
173#2475C2214yes—
174#2465C2214yes—
175#2462C2214yes—
176#2401C2214yes—
177#2401C2214yes—
178#2399C2214yes—
179#2399C2212yes—
180#2398C2212yes—
181#2396C2214yes—
182#2396C2214yes—
183#2396C2214yes—
184#2395C2212yes—
185#2395C2214yes—
186#2395C2212yes—
187#2374C2214yes—
188#2373C2214yes—
189#2371C2214yes—
190#2371C2212yes—
191#2371C2212yes—
192#2370C2212yes—
193#2370C2212yes—
194#2369C2212yes—
195#2368C2214yes—
196#2365C2212yes—
197#2362C2214yes—
198#2357C2212yes—
199#2356C2212yes—
200#2356C2212yes—
201#2356C2214yes—
202#2353C2212yes—
203#2347C2211yescharacteristic
204#2347C2212yes—
205#2347C2211yescharacteristic
206#2346C2211yescharacteristic
207#2346C2211yescharacteristic
208#2345C2212yes—
209#2344C2214yes—
210#2344C2212yes—
211#2343C2214yes—
212#2343C2212yes—
213#2336C2214yes—
214#2332C2214yes—
215#2324C2212yes—
216#2323C2212yes—
217#2320C2212yes—
218#2320C2211yescharacteristic
219#2319C2211yescharacteristic
220#2313C2212yes—
221C4×#125C2212yes—
222C4×#125C2212yes—
223C4×#125C2212yes—
224C4×#125C2212yes—
225C4×#125C2212yes—
226C4×#124C2212yes—
227#2283C2211yescharacteristic
228#2283C2211yescharacteristic
229#2283C2211yescharacteristic
230#2276C2211yescharacteristic
231#2276C2212yes—
232#2275C2211yescharacteristic
233#2274C2212yes—
234C4×#117C2211yescharacteristic
235#533—28no—
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238#529—28no—
239C2×#126C2312yes—
240C2×#125—28no—
241C2×#125C2312yes—
242C2×#125C2311yescharacteristic
243C2×#125C2311yescharacteristic
244C2×#125C2311yescharacteristic
245C2×#125C2312yes—
246C2×#125C2312yes—
247C2×#125C2312yes—
248C2×#125C2314yes—
249C2×#124C2311yescharacteristic
250C2×#123C2312yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2311yescharacteristic
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2314yes—
255C2×#121C2311yescharacteristic
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2314yes—
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2314yes—
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2312yes—
264C2×C4×D4C2312yes—
265C2×#117C2312yes—
266C2×#117C2311yescharacteristic
267C2×#117C2311yescharacteristic
268C2×#117C2312yes—
269C2×#117C2314yes—
270C2×#117C2314yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C42C2311yescharacteristic
276#401C2314yes—
277#401C2314yes—
278#401C2314yes—
279#401C2314yes—
280#400C2314yes—
281#400C2312yes—
282#400C2312yes—
283#400C2312yes—
284#400C2312yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#399C2314yes—
314#399C2312yes—
315#399C2312yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#398C2312yes—
320#398C2312yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2312yes—
330#398C2312yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2312yes—
354#397C2312yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#395C2312yes—
377#395C2312yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#394C2312yes—
393#394C2312yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#391C2314yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2312yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#390C2312yes—
427#390C2314yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2312yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
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#386C2312yes—
537#386C2314yes—
538#386C2312yes—
539#386C2312yes—
540#386C2312yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2312yes—
547#385C2312yes—
548#385C2312yes—
549#385C2312yes—
550#385C2314yes—
551#385C2314yes—
552#384C2312yes—
553#384C2312yes—
554#383C2312yes—
555#383C2314yes—
556#383C2314yes—
557#383C2314yes—
558#383C2312yes—
559#383C2312yes—
560#383C2312yes—
561#383C2314yes—
562#383C2312yes—
563#383C2312yes—
564#383C2314yes—
565#383C2314yes—
566#383C2314yes—
567#382C2311yescharacteristic
568#382C2311yescharacteristic
569#382C2312yes—
570#382C2312yes—
571#382C2312yes—
572#382C2312yes—
573#382C2314yes—
574#382C2312yes—
575#382C2314yes—
576#382C2312yes—
577#382C2312yes—
578#382C2314yes—
579#382C2314yes—
580#382C2314yes—
581#382C2314yes—
582#381C2312yes—
583#381C2314yes—
584#381C2314yes—
585#381C2314yes—
586#381C2312yes—
587#381C2314yes—
588#381C2312yes—
589#381C2312yes—
590#380C2314yes—
591#380C2312yes—
592#380C2312yes—
593#380C2311yescharacteristic
594#380C2311yescharacteristic
595#380C2312yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2312yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2312yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2312yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2311yescharacteristic
617C4×C4⋊C4C2311yescharacteristic
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2311yescharacteristic
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2311yescharacteristic
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2314yes—
634C4×C22⋊C4C2311yescharacteristic
635C4×C22⋊C4C2312yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2312yes—
645C4×C22⋊C4C2312yes—
646C4×C22⋊C4C2311yescharacteristic
647C4×C22⋊C4C2312yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2312yes—
650#376C2311yescharacteristic
651#376C2312yes—
652#376C2312yes—
653#376C2312yes—
654#376C2312yes—
655#376C2312yes—
656#376C2312yes—
657#376C2314yes—
658#376C2311yescharacteristic
659C2×#95C2312yes—
660C43C2312yes—
661C22×Q8C2411yescharacteristic
662C22×Q8C2412yes—
663C22×Q8C2412yes—
664C22×Q8C2414yes—
665C22×Q8C2414yes—
666C22×D4C2411yescharacteristic
667C22×D4C2412yes—
668C23×C4C2412yes—
669C23×C4C2412yes—
670C23×C4C2412yes—
671C23×C4C2414yes—
672C23×C4C2411yescharacteristic
673C23×C4C2411yescharacteristic
674C23×C4C2411yescharacteristic
675C4⋊Q8—24no—
676C4⋊Q8—24no—
677#126—28no—
678#125—28no—
679#125—28no—
680#125—28no—
681#125—28no—
682#125—24no—
683#125—24no—
684#125—24no—
685#125—48no—
686#124—24no—
687#123—28no—
688C22⋊Q8—24no—
689C22⋊Q8—28no—
690C22⋊Q8—28no—
691C22⋊Q8—48no—
692#121—24no—
693C4×Q8—24no—
694C4×Q8—28no—
695C4×Q8—28no—
696C4×Q8—48no—
697C4×Q8—44no—
698C4×Q8—48no—
699C4×D4—28no—
700C4×D4—24no—
701C4×D4—44no—
702#117—24no—
703#117—24no—
704#117—28no—
705#117—48no—
706#117—48no—
707#117—44no—
708C2×C4⋊C4—24no—
709C2×C4⋊C4—28no—
710C2×C4⋊C4—28no—
711C2×C4⋊C4—24no—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C42#4118yes—
798C2×C42C2414yes—
799C2×C42C2412yes—
800C2×C42C2412yes—
801C2×C42C2412yes—
802C2×C42C2412yes—
803C2×C42C2414yes—
804C2×C42C2414yes—
805C2×C42C2412yes—
806C2×C42C2414yes—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2412yes—
810C2×C42C2412yes—
811C2×C42C2412yes—
812C2×C42C2412yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2412yes—
816C2×C42C2414yes—
817C2×C42C2412yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2411yescharacteristic
823C2×C42C2411yescharacteristic
824C2×C42C2411yescharacteristic
825C2×C42C2411yescharacteristic
826#95C2411yescharacteristic
827#95C2412yes—
828#95C2414yes—
829#95C2411yescharacteristic
830#95C2412yes—
831#95C2411yescharacteristic
832#95C2412yes—
833#95C2411yescharacteristic
834#95C2414yes—
835#95C2412yes—
836#95C2412yes—
837#95C2412yes—
838#95C2414yes—
839#95C2412yes—
840#95C2412yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2412yes—
854#95C2412yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906C24C2512yes—
907C24C2511yescharacteristic
908C2×Q8—22no—
909C2×Q8—24no—
910C2×Q8—24no—
911C2×Q8—42no—
912C2×Q8—44no—
913C2×Q8—44no—
914C2×Q8—42no—
915C2×Q8—42no—
916C2×Q8—44no—
917C2×Q8—44no—
918C2×Q8—44no—
919C2×Q8—44no—
920C2×Q8—44no—
921C2×D4—24no—
922C2×D4—22no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—28no—
930C22×C4—42no—
931C22×C4—44no—
932C22×C4—42no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4C2×#4114yes—
940C22×C4C2×#4114yes—
941C22×C4C2×#4114yes—
942C22×C4C2514yes—
943C22×C4C2512yes—
944C22×C4C2512yes—
945C22×C4C2514yes—
946C22×C4C2514yes—
947C22×C4C2514yes—
948C22×C4C2514yes—
949C22×C4C2514yes—
950C22×C4C2512yes—
951C22×C4C2512yes—
952C22×C4C2514yes—
953C22×C4C2512yes—
954C22×C4C2512yes—
955C22×C4C2512yes—
956C22×C4C2512yes—
957C22×C4C2512yes—
958C22×C4C2512yes—
959C22×C4C2514yes—
960C22×C4C2511yescharacteristic
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2511yescharacteristic
964C22×C4C2511yescharacteristic
965C22×C4C2511yescharacteristic
966C22×C4C2512yes—
967C4⋊C4—28no—
968C4⋊C4—28no—
969C4⋊C4—24no—
970C4⋊C4—24no—
971C4⋊C4—24no—
972C4⋊C4—24no—
973C4⋊C4—28no—
974C4⋊C4—28no—
975C4⋊C4—24no—
976C4⋊C4—24no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—24no—
983C4⋊C4—22no—
984C4⋊C4—24no—
985C4⋊C4—24no—
986C4⋊C4—24no—
987C4⋊C4—24no—
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—24no—
992C4⋊C4—28no—
993C4⋊C4—28no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—42no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C22⋊C4—24no—
1029C22⋊C4—24no—
1030C22⋊C4—24no—
1031C22⋊C4—24no—
1032C22⋊C4—24no—
1033C22⋊C4—24no—
1034C22⋊C4—24no—
1035C22⋊C4—24no—
1036C22⋊C4—44no—
1037C22⋊C4—42no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C22⋊C4—44no—
1044C22⋊C4—42no—
1045C22⋊C4—44no—
1046C22⋊C4—42no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C42—24no—
1053C42—24no—
1054C42—24no—
1055C42—28no—
1056C42—24no—
1057C42—28no—
1058C42—28no—
1059C42—42no—
1060C42—42no—
1061C42—44no—
1062C42—44no—
1063C42—42no—
1064C42—42no—
1065C42—44no—
1066C42—42no—
1067C42—42no—
1068C42—44no—
1069C42—44no—
1070C42—44no—
1071C42—44no—
1072C42—42no—
1073C42—44no—
1074C42—44no—
1075C42—44no—
1076C42C2×#4114yes—
1077C42C2×#4114yes—
1078C42C2×#4114yes—
1079C42C2×#4114yes—
1080C23—22no—
1081C23—22no—
1082C23—21no—
1083C23—21no—
1084C23—22no—
1085C23—24no—
1086C23—22no—
1087C23—24no—
1088C23—22no—
1089C23C22×#4112yes—
1090C23C2611yescharacteristic
1091Q8—44no—
1092Q8—48no—
1093Q8—84no—
1094Q8—88no—
1095Q8—164no—
1096D4—44no—
1097D4—84no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—22no—
1104C2×C4—21no—
1105C2×C4—22no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—44no—
1159C2×C4—44no—
1160C2×C4—44no—
1161C2×C4—48no—
1162C2×C4—88no—
1163C2×C4—84no—
1164C2×C4—84no—
1165C2×C4C22×#4112yes—
1166C2×C4C22×#4112yes—
1167C2×C4C22×#4112yes—
1168C2×C4C22×#4112yes—
1169C2×C4C22×#4112yes—
1170C2×C4C22×#4112yes—
1171C2×C4#58514yes—
1172C22—22no—
1173C22—22no—
1174C22—22no—
1175C22—42no—
1176C22—42no—
1177C22—44no—
1178C22—44no—
1179C22—42no—
1180C22—42no—
1181C22—42no—
1182C22C23×#4111yescharacteristic
1183C22C2×#58512yes—
1184C222−1+611yescharacteristic
1185C222−1+612yes—
1186C222−1+611yescharacteristic
1187C4—24no—
1188C4—22no—
1189C4—22no—
1190C4—22no—
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—42no—
1195C4—42no—
1196C4—44no—
1197C4—44no—
1198C4—44no—
1199C4—42no—
1200C4—44no—
1201C4—44no—
1202C4—44no—
1203C4—42no—
1204C4—44no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—44no—
1209C4—42no—
1210C4—42no—
1211C4—42no—
1212C2—42no—
1213C2—82no—
1214C2#6268611yescharacteristic
1215C2#6286011yescharacteristic
1216C2#6286011yescharacteristic
1217C2#6305312yes—
1218C2#6306412yes—
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. #42353C2semidirect
2. #42330C2semidirect
3. #42323C2semidirect
5. #42164C2semidirect
6. #41707C2semidirect
7. #41698C2semidirect
8. #41684C2semidirect
9. #41677C2semidirect
10. #41440C2semidirect
11. #41439C2semidirect
12. #37612C2semidirect
14. #37603C2semidirect
15. #37603C2semidirect
16. #37563C2semidirect
17. #37540C2semidirect
19. #36698C2semidirect
20. #36090C2semidirect
21. #36064C2semidirect
22. #35857C2semidirect
23. #35835C2semidirect
24. #35760C2semidirect
25. #34239C2semidirect
26. #34231C2semidirect

Maximal subgroups

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

subgroupindex
#423532
#423302
#423232
#422382
#421642
#417072
#416982
#416842
#416772
#414402
#414392
#376122
#376072
#376032
#375632
#375402
#366992
#366982
#360902
#360642
#358572
#358352
#357602
#342392
#342312
#342272