Finite Group Databasebeta

← #7681622

Subgroups — #7681622

Order 512.

4497 conjugacy classes of subgroups.

The subgroup lattice has 1283 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59616C214yesmaximal, complemented
2#59608C214yesmaximal, complemented
3#59589C214yesmaximal, complemented
4#59523C214yesmaximal, complemented
5#44646C214yesmaximal, complemented
6#44629C214yesmaximal, complemented
7#44309C214yesmaximal, complemented
8#44154C214yesmaximal
9#39750C211yesmaximal, characteristic, complemented
10#39612C211yesmaximal, characteristic, complemented
11#38931C212yesmaximal, complemented
12#38927C212yesmaximal, complemented
13#38927C212yesmaximal, complemented
14#37963C212yesmaximal, complemented
15#37765C212yesmaximal, complemented
16#36505C212yesmaximal
17#36196C211yesmaximal, characteristic, complemented
18#36151C211yesmaximal, characteristic, complemented
19#35657C212yesmaximal, complemented
20#35604C212yesmaximal, complemented
21#35337C211yesmaximal, characteristic, complemented
22#35304C212yesmaximal, complemented
23#34898C212yesmaximal, complemented
24#34336C212yesmaximal, complemented
25#34221C212yesmaximal, complemented
26#34123C211yesmaximal, characteristic
27C4×#541C211yesmaximal, characteristic, complemented
28C2×#557C2212yes—
29C2×#541C2211yescharacteristic
30C2×#533C2212yes—
31C2×C4×#41C2211yescharacteristic
32#2862C2211yescharacteristic
33#2859C2211yescharacteristic
34#2857C2212yes—
35#2857C2212yes—
36#2851C2212yes—
37#2851C2212yes—
38#2851C2212yes—
39#2799C2214yes—
40#2777C2214yes—
41#2770C2214yes—
42#2770C2214yes—
43#2769C2214yes—
44#2769C2214yes—
45#2768C2214yes—
46#2768C2214yes—
47#2767C2214yes—
48#2767C2214yes—
49#2758C2214yes—
50#2758C2214yes—
51#2758C2214yes—
52#2755C2214yes—
53#2734C2214yes—
54#2726C2214yes—
55#2723C2214yes—
56#2721C2214yes—
57#2720C2214yes—
58#2719C2214yes—
59#2700C2214yes—
60#2698C2214yes—
61#2698C2214yes—
62#2689C2214yes—
63#2660C2212yes—
64#2660C2212yes—
65#2647C2211yescharacteristic
66#2647C2211yescharacteristic
67#2647C2212yes—
68#2647C2212yes—
69#2628C2212yes—
70#2612C2214yes—
71#2612C2214yes—
72#2606C2214yes—
73#2605C2214yes—
74#2605C2214yes—
75#2597C2214yes—
76#2596C2214yes—
77#2589C2214yes—
78#2589C2214yes—
79#2588C2214yes—
80#2588C2214yes—
81#2588C2214yes—
82#2588C2214yes—
83#2587C2214yes—
84#2577C2214yes—
85#2577C2214yes—
86#2575C2214yes—
87#2575C2214yes—
88#2575C2214yes—
89#2573C2214yes—
90#2571C2212yes—
91#2570C2212yes—
92#2570C2212yes—
93#2570C2214yes—
94#2569C2214yes—
95#2567C2212yes—
96#2565C2212yes—
97#2565C2212yes—
98#2562C2212yes—
99#2562C2212yes—
100#2549C2214yes—
101#2547C2212yes—
102#2538C2212yes—
103#2536C2212yes—
104#2536C2212yes—
105#2533C2214yes—
106#2533C2214yes—
107#2533C2214yes—
108#2532C2214yes—
109#2530C2214yes—
110#2529C2214yes—
111#2529C2214yes—
112#2526C2214yes—
113#2525C2214yes—
114#2524C2214yes—
115#2524C2214yes—
116#2524C2214yes—
117#2524C2214yes—
118#2524C2214yes—
119#2521C2214yes—
120#2521C2214yes—
121#2520C2214yes—
122#2520C2214yes—
123#2515C2214yes—
124#2515C2214yes—
125#2515C2214yes—
126#2508C2214yes—
127#2497C2212yes—
128#2497C2212yes—
129#2496C2212yes—
130#2496C2214yes—
131#2496C2212yes—
132#2495C2212yes—
133#2495C2212yes—
134#2495C2214yes—
135#2489C2214yes—
136#2479C2214yes—
137#2478C2214yes—
138#2475C2214yes—
139#2475C2214yes—
140#2475C2214yes—
141#2474C2214yes—
142#2469C2214yes—
143#2468C2214yes—
144#2466C2214yes—
145#2462C2214yes—
146#2462C2214yes—
147#2462C2214yes—
148#2460C2214yes—
149#2460C2214yes—
150#2453C2214yes—
151#2446C2214yes—
152#2438C2214yes—
153#2438C2214yes—
154#2432C2214yes—
155#2423C2212yes—
156#2423C2212yes—
157#2421C2212yes—
158#2421C2212yes—
159#2421C2212yes—
160#2421C2212yes—
161#2415C2214yes—
162#2402C2214yes—
163#2395C2214yes—
164#2373C2214yes—
165#2371C2214yes—
166#2371C2214yes—
167#2370C2212yes—
168#2370C2212yes—
169#2370C2214yes—
170#2370C2214yes—
171#2369C2212yes—
172#2369C2214yes—
173#2368C2214yes—
174#2368C2214yes—
175#2367C2214yes—
176#2362C2214yes—
177#2362C2214yes—
178#2356C2212yes—
179#2356C2214yes—
180#2356C2214yes—
181#2355C2212yes—
182#2355C2214yes—
183#2353C2212yes—
184#2353C2212yes—
185#2351C2212yes—
186#2351C2212yes—
187Q8×C4⋊C4C2212yes—
188#2349C2212yes—
189#2346C2212yes—
190#2343C2214yes—
191#2343C2212yes—
192#2343C2212yes—
193#2343C2214yes—
194#2339C2212yes—
195#2336C2214yes—
196#2334C2214yes—
197#2331C2212yes—
198#2331C2212yes—
199#2331C2214yes—
200#2331C2212yes—
201#2330C2214yes—
202#2330C2212yes—
203#2330C2211yescharacteristic
204#2327C2211yescharacteristic
205#2327C2212yes—
206#2323C2212yes—
207#2320C2212yes—
208#2320C2212yes—
209#2320C2212yes—
210#2314C2211yescharacteristic
211#2314C2211yescharacteristic
212#2314C2211yescharacteristic
213C4×C4⋊Q8C2211yescharacteristic
214C4×#125C2212yes—
215C4×#125C2214yes—
216C4×#125C2211yescharacteristic
217C4×#125C2214yes—
218C4×#126C2214yes—
219C4×#126C2214yes—
220C4×C22⋊Q8C2212yes—
221C4×C22⋊Q8C2212yes—
222C4×C22⋊Q8C2212yes—
223C4×C22⋊Q8C2212yes—
224C4×C22⋊Q8C2212yes—
225#2298C2214yes—
226#2295C2211yescharacteristic
227#2295C2214yes—
228#2295C2211yescharacteristic
229#2290C2212yes—
230#2290C2212yes—
231#2285C2212yes—
232#2283C2211yescharacteristic
233#2283C2212yes—
234#2283C2212yes—
235#2283C2212yes—
236#2276C2212yes—
237#2276C2212yes—
238C42×Q8C2212yes—
239C42×D4C2211yescharacteristic
240C42×D4C2211yescharacteristic
241C4×#117C2211yescharacteristic
242C2×#376C2212yes—
243C22×#41C2311yescharacteristic
244#557—216no—
245#541—28no—
246#533—216no—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2314yes—
250C2×C4⋊Q8C2311yescharacteristic
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#125C2312yes—
255C2×#125C2311yescharacteristic
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#125C2312yes—
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#124C2314yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C4×#41—28no—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2314yes—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×D4C2311yescharacteristic
281C2×C4×D4C2312yes—
282C2×C4×D4C2311yescharacteristic
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×#117C2311yescharacteristic
287C2×#117C2311yescharacteristic
288C2×#117C2312yes—
289C2×#117C2314yes—
290C2×#117C2311yescharacteristic
291C2×#117C2314yes—
292C22×C42C2311yescharacteristic
293C22×C42C2312yes—
294C22×C42C2312yes—
295C22×C42C2312yes—
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#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#393C2314yes—
368#391C2312yes—
369#391C2312yes—
370#391C2312yes—
371#391C2312yes—
372#391C2314yes—
373#391C2312yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2312yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#390C2314yes—
389#389C2312yes—
390#389C2314yes—
391#389C2314yes—
392#389C2312yes—
393#389C2314yes—
394#389C2312yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2312yes—
400#389C2312yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2312yes—
405#389C2312yes—
406#389C2312yes—
407#389C2314yes—
408#389C2312yes—
409#389C2312yes—
410#389C2312yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2312yes—
417#389C2312yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2312yes—
423#389C2314yes—
424#389C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2312yes—
443#388C2314yes—
444#388C2312yes—
445#388C2312yes—
446#388C2312yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2312yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
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#387C2312yes—
505#387C2312yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2312yes—
514#387C2312yes—
515#387C2312yes—
516#387C2312yes—
517#387C2312yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#386C2312yes—
524#386C2312yes—
525#386C2312yes—
526#386C2312yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2312yes—
534#385C2314yes—
535#385C2312yes—
536#385C2314yes—
537#385C2314yes—
538#385C2312yes—
539#385C2312yes—
540#385C2314yes—
541#385C2314yes—
542#384C2311yescharacteristic
543#384C2311yescharacteristic
544#384C2312yes—
545#384C2311yescharacteristic
546#384C2312yes—
547#384C2314yes—
548#384C2312yes—
549#383C2314yes—
550#383C2314yes—
551#383C2314yes—
552#383C2314yes—
553#383C2314yes—
554#383C2314yes—
555#383C2314yes—
556#383C2311yescharacteristic
557#383C2311yescharacteristic
558#383C2312yes—
559#383C2312yes—
560#382C2311yescharacteristic
561#382C2312yes—
562#382C2314yes—
563#382C2314yes—
564#382C2312yes—
565#382C2311yescharacteristic
566#382C2311yescharacteristic
567#382C2312yes—
568#382C2312yes—
569#382C2314yes—
570#382C2312yes—
571#382C2314yes—
572#382C2314yes—
573#382C2314yes—
574#382C2314yes—
575#382C2312yes—
576#382C2312yes—
577#382C2312yes—
578#381C2314yes—
579#381C2311yescharacteristic
580#381C2312yes—
581#381C2314yes—
582#381C2312yes—
583#381C2311yescharacteristic
584#380C2312yes—
585#380C2312yes—
586#380C2312yes—
587#380C2312yes—
588#380C2312yes—
589#380C2312yes—
590#380C2312yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2312yes—
595#380C2312yes—
596#380C2312yes—
597#380C2312yes—
598#380C2312yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2312yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2311yescharacteristic
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2314yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2311yescharacteristic
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2314yes—
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2312yes—
644C4×C22⋊C4C2312yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2312yes—
648C4×C22⋊C4C2312yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2312yes—
652C4×C22⋊C4C2312yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2312yes—
658#376C2312yes—
659#376C2311yescharacteristic
660#376C2311yescharacteristic
661#376C2312yes—
662#376C2312yes—
663#376C2314yes—
664#376C2314yes—
665#376C2312yes—
666#376C2312yes—
667#376C2312yes—
668#376C2314yes—
669#376C2312yes—
670#376C2314yes—
671C2×#95C2312yes—
672C2×#95C2312yes—
673C2×#95C2312yes—
674C2×#95C2312yes—
675C43C2314yes—
676C43C2311yescharacteristic
677C43C2311yescharacteristic
678C2×#41—24no—
679C2×#41—44no—
680C22×Q8C2412yes—
681C22×Q8C2414yes—
682C22×Q8C2414yes—
683C22×Q8C2411yescharacteristic
684C22×D4C2411yescharacteristic
685C22×D4C2412yes—
686C23×C4C2411yescharacteristic
687C23×C4C2412yes—
688C23×C4C2412yes—
689C23×C4C2412yes—
690C23×C4C2412yes—
691C23×C4C2411yescharacteristic
692C23×C4C2412yes—
693C23×C4C2411yescharacteristic
694C23×C4C2412yes—
695C23×C4C2412yes—
696C4⋊Q8—216no—
697C4⋊Q8—28no—
698C4⋊Q8—28no—
699C4⋊Q8#4118yescomplemented
700#126—216no—
701#126—48no—
702#126—48no—
703#125—216no—
704#125—216no—
705#125—216no—
706#125—216no—
707#125—24no—
708#125—28no—
709#125—28no—
710#124—48no—
711C22⋊Q8—28no—
712C22⋊Q8—28no—
713C22⋊Q8—28no—
714C22⋊Q8—216no—
715C22⋊Q8—48no—
716C22⋊Q8—48no—
717C4×Q8—24no—
718C4×Q8—28no—
719C4×Q8—28no—
720C4×Q8—28no—
721C4×Q8—216no—
722C4×Q8—216no—
723C4×Q8—28no—
724C4×Q8—28no—
725C4×Q8—28no—
726C4×Q8—28no—
727C4×Q8#4118yes—
728C4×D4—28no—
729C4×D4—24no—
730C4×D4—24no—
731C4×D4—28no—
732C4×D4—44no—
733C4×D4—44no—
734#117—28no—
735#117—24no—
736#117—216no—
737#117—24no—
738#117—24no—
739#117—48no—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2414yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2414yes—
821C2×C42—24no—
822C2×C42—28no—
823C2×C42—28no—
824C2×C42—28no—
825C2×C42C2412yes—
826C2×C42C2411yescharacteristic
827C2×C42C2411yescharacteristic
828C2×C42C2414yes—
829C2×C42C2414yes—
830C2×C42C2411yescharacteristic
831C2×C42C2412yes—
832C2×C42C2411yescharacteristic
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2414yes—
836C2×C42C2412yes—
837C2×C42C2412yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2411yescharacteristic
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2412yes—
848C2×C42C2412yes—
849C2×C42C2414yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2411yescharacteristic
859C2×C42C2411yescharacteristic
860C2×C42C2412yes—
861C2×C42C2411yescharacteristic
862#95C2412yes—
863#95C2412yes—
864#95C2412yes—
865#95C2412yes—
866#95C2412yes—
867#95C2412yes—
868#95C2412yes—
869#95C2412yes—
870#95C2412yes—
871#95C2412yes—
872#95C2412yes—
873#95C2412yes—
874#95C2412yes—
875#95C2412yes—
876#95C2412yes—
877#95C2412yes—
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#95C2411yescharacteristic
893#95C2411yescharacteristic
894#95C2411yescharacteristic
895#95C2411yescharacteristic
896#95C2412yes—
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2412yes—
905#95C2414yes—
906#95C2414yes—
907#95C2412yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2412yes—
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2412yes—
927#95C2412yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943C24C2511yescharacteristic
944C24C2512yes—
945#41—416no—
946C2×Q8—24no—
947C2×Q8—28no—
948C2×Q8—28no—
949C2×Q8—24no—
950C2×Q8—42no—
951C2×Q8—44no—
952C2×Q8—44no—
953C2×Q8—44no—
954C2×Q8—44no—
955C2×Q8C2×#4118yes—
956C2×Q8C2×#4114yes—
957C2×D4—24no—
958C2×D4—24no—
959C2×D4—22no—
960C2×D4—24no—
961C2×D4—42no—
962C22×C4—24no—
963C22×C4—24no—
964C22×C4—24no—
965C22×C4—24no—
966C22×C4—24no—
967C22×C4—22no—
968C22×C4—24no—
969C22×C4—22no—
970C22×C4—24no—
971C22×C4—22no—
972C22×C4—24no—
973C22×C4—24no—
974C22×C4—22no—
975C22×C4—22no—
976C22×C4—24no—
977C22×C4—24no—
978C22×C4—24no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4C2511yescharacteristic
991C22×C4C2512yes—
992C22×C4C2512yes—
993C22×C4C2514yes—
994C22×C4C2512yes—
995C22×C4C2511yescharacteristic
996C22×C4C2512yes—
997C22×C4C2511yescharacteristic
998C22×C4C2512yes—
999C22×C4C2512yes—
1000C22×C4C2514yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2512yes—
1004C22×C4C2514yes—
1005C22×C4C2514yes—
1006C22×C4C2514yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2511yescharacteristic
1010C22×C4C2514yes—
1011C22×C4C2512yes—
1012C22×C4C2511yescharacteristic
1013C22×C4C2512yes—
1014C22×C4C2511yescharacteristic
1015C4⋊C4—24no—
1016C4⋊C4—22no—
1017C4⋊C4—24no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—24no—
1024C4⋊C4—24no—
1025C4⋊C4—24no—
1026C4⋊C4—28no—
1027C4⋊C4—24no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—28no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—28no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—24no—
1041C4⋊C4—28no—
1042C4⋊C4—24no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—44no—
1047C4⋊C4—42no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4C2×#4118yes—
1071C4⋊C4C2×#4114yes—
1072C4⋊C4C2×#41116yes—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—24no—
1076C22⋊C4—24no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—24no—
1080C22⋊C4—24no—
1081C22⋊C4—24no—
1082C22⋊C4—28no—
1083C22⋊C4—28no—
1084C22⋊C4—24no—
1085C22⋊C4—28no—
1086C22⋊C4—24no—
1087C22⋊C4—44no—
1088C22⋊C4—42no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C42—22no—
1097C42—22no—
1098C42—24no—
1099C42—24no—
1100C42—22no—
1101C42—24no—
1102C42—24no—
1103C42—24no—
1104C42—28no—
1105C42—28no—
1106C42—22no—
1107C42—28no—
1108C42—28no—
1109C42—28no—
1110C42—28no—
1111C42—24no—
1112C42—24no—
1113C42—24no—
1114C42—22no—
1115C42—28no—
1116C42—42no—
1117C42—42no—
1118C42—44no—
1119C42—44no—
1120C42—44no—
1121C42—44no—
1122C42—44no—
1123C42—44no—
1124C42—42no—
1125C42—42no—
1126C42—44no—
1127C42—44no—
1128C42—44no—
1129C42C2×#4114yes—
1130C42C2×#4114yes—
1131C42C2×#4118yes—
1132C422−1+414yes—
1133C23—22no—
1134C23—22no—
1135C23—22no—
1136C23—22no—
1137C23—22no—
1138C23—22no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—22no—
1143C23—22no—
1144C23#58514yes—
1145C23C2611yescharacteristic
1146Q8—216no—
1147Q8—44no—
1148Q8—88no—
1149Q8—88no—
1150D4—28no—
1151D4—48no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—21no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—24no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—22no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—48no—
1214C2×C4—48no—
1215C2×C4—48no—
1216C2×C4—44no—
1217C2×C4—48no—
1218C2×C4—44no—
1219C2×C4—84no—
1220C2×C4—84no—
1221C2×C4—82no—
1222C2×C4—84no—
1223C2×C4C22×#4112yes—
1224C2×C4C22×#4114yes—
1225C2×C4C22×#4114yes—
1226C2×C4C22×#4118yes—
1227C2×C4C22×#4114yes—
1228C2×C4C22×#4112yes—
1229C2×C4C22×#4112yes—
1230C2×C4C22×#4112yes—
1231C2×C4C2×2−1+414yes—
1232C2×C4C2×2−1+412yes—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—41no—
1242C22—41no—
1243C22—42no—
1244C22—41no—
1245C22C23×#4111yescharacteristic
1246C22C23×#4111yescharacteristic
1247C22C22×2−1+411yescharacteristic
1248C22C2×#58512yes—
1249C222−1+612yes—
1250C4—24no—
1251C4—22no—
1252C4—24no—
1253C4—22no—
1254C4—24no—
1255C4—24no—
1256C4—28no—
1257C4—42no—
1258C4—44no—
1259C4—42no—
1260C4—42no—
1261C4—44no—
1262C4—44no—
1263C4—41no—
1264C4—44no—
1265C4—44no—
1266C4—44no—
1267C4—41no—
1268C4—42no—
1269C4—44no—
1270C4—42no—
1271C4—42no—
1272C4—42no—
1273C4—41no—
1274C4#348214yes—
1275C2—44no—
1276C2—81no—
1277C2C2×#348211yescharacteristic
1278C2#6281411yescharacteristic
1279C2#6286111yescharacteristic
1280C2#6292812yes—
1281C2#6300512yes—
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
1. #59616C2semidirect
2. #59608C2semidirect
3. #59589C2semidirect
4. #59523C2semidirect
5. #44646C2semidirect
6. #44629C2semidirect
7. #44309C2semidirect
9. #39750C2semidirect
10. #39612C2semidirect
11. #38931C2semidirect
12. #38927C2semidirect
13. #38927C2semidirect
14. #37963C2semidirect
15. #37765C2semidirect
17. #36196C2semidirect
18. #36151C2semidirect
19. #35657C2semidirect
20. #35604C2semidirect
21. #35337C2semidirect
22. #35304C2semidirect
23. #34898C2semidirect
24. #34336C2semidirect
25. #34221C2semidirect
27. C4×#541C2semidirect
699. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#596162
#596082
#595892
#595232
#446462
#446292
#443092
#441542
#397502
#396122
#389312
#389272
#379632
#377652
#365052
#361962
#361512
#356572
#356042
#353372
#353042
#348982
#343362
#342212
#341232
C4×#5412