Finite Group Databasebeta

← #7714780

Subgroups — #7714780

Order 512.

4482 conjugacy classes of subgroups.

The subgroup lattice has 1223 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51872C214yesmaximal, complemented
2#51737C214yesmaximal, complemented
3#51724C214yesmaximal, complemented
4#51723C214yesmaximal, complemented
5#47379C214yesmaximal, complemented
6#47375C214yesmaximal, complemented
7#47374C214yesmaximal, complemented
8#47370C214yesmaximal, complemented
9#38127C214yesmaximal, complemented
10#38115C214yesmaximal, complemented
11#37943C212yesmaximal, complemented
12#37935C212yesmaximal, complemented
13#37755C212yesmaximal, complemented
14#37747C212yesmaximal
15#37518C212yesmaximal, complemented
16#37258C212yesmaximal, complemented
17#37124C212yesmaximal, complemented
18#35154C211yesmaximal, characteristic, complemented
19#35153C211yesmaximal, characteristic
20#35111C212yesmaximal, complemented
21#35099C212yesmaximal, complemented
22#34409C212yesmaximal, complemented
23C2×#2327C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#537C2211yescharacteristic
26C2×#536C2212yes—
27C22×C4⋊Q8C2211yescharacteristic
28C2×#529C2212yes—
29C22×C4×Q8C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31#2855C2212yes—
32#2855C2212yes—
33#2855C2212yes—
34#2854C2212yes—
35#2854C2212yes—
36#2854C2212yes—
37#2853C2214yes—
38#2833C2212yes—
39#2832C2212yes—
40#2831C2214yes—
41#2802C2214yes—
42#2800C2214yes—
43#2799C2214yes—
44#2796C2214yes—
45#2789C2212yes—
46#2789C2214yes—
47#2786C2214yes—
48#2785C2212yes—
49#2783C2214yes—
50#2783C2214yes—
51#2782C2212yes—
52#2781C2214yes—
53#2780C2214yes—
54#2777C2214yes—
55#2776C2214yes—
56#2776C2214yes—
57#2775C2214yes—
58#2772C2214yes—
59#2769C2212yes—
60#2769C2214yes—
61#2767C2214yes—
62#2767C2214yes—
63#2766C2214yes—
64#2765C2214yes—
65#2765C2214yes—
66#2765C2214yes—
67#2758C2214yes—
68#2758C2214yes—
69#2757C2214yes—
70#2755C2214yes—
71#2751C2214yes—
72#2744C2214yes—
73#2740C2214yes—
74#2739C2214yes—
75#2734C2214yes—
76#2734C2212yes—
77#2734C2212yes—
78#2731C2212yes—
79#2731C2212yes—
80#2731C2214yes—
81#2731C2214yes—
82#2729C2214yes—
83#2729C2214yes—
84#2729C2214yes—
85#2729C2214yes—
86#2725C2214yes—
87#2719C2214yes—
88#2716C2214yes—
89#2691C2214yes—
90#2690C2214yes—
91#2689C2214yes—
92#2686C2214yes—
93#2666C2214yes—
94#2665C2214yes—
95#2653C2214yes—
96#2650C2214yes—
97#2646C2212yes—
98#2643C2214yes—
99#2639C2212yes—
100#2627C2212yes—
101#2627C2212yes—
102#2623C2214yes—
103#2618C2212yes—
104#2618C2212yes—
105#2614C2214yes—
106#2612C2214yes—
107#2606C2214yes—
108#2604C2214yes—
109#2604C2214yes—
110#2599C2214yes—
111#2599C2214yes—
112#2596C2214yes—
113#2595C2214yes—
114#2592C2212yes—
115#2592C2212yes—
116#2587C2214yes—
117#2586C2212yes—
118#2585C2214yes—
119#2585C2214yes—
120#2584C2212yes—
121#2584C2212yes—
122#2581C2212yes—
123#2581C2212yes—
124#2580C2212yes—
125#2580C2212yes—
126#2574C2214yes—
127#2573C2214yes—
128#2572C2212yes—
129#2533C2214yes—
130#2533C2214yes—
131#2532C2214yes—
132#2531C2214yes—
133#2530C2214yes—
134#2530C2214yes—
135#2529C2214yes—
136#2528C2214yes—
137#2528C2214yes—
138#2527C2214yes—
139#2527C2214yes—
140#2526C2214yes—
141#2526C2214yes—
142#2525C2214yes—
143#2525C2214yes—
144#2523C2214yes—
145#2522C2214yes—
146#2517C2214yes—
147#2516C2214yes—
148#2515C2214yes—
149#2510C2214yes—
150#2509C2214yes—
151#2505C2214yes—
152#2505C2214yes—
153#2494C2214yes—
154#2493C2214yes—
155#2493C2214yes—
156#2488C2214yes—
157#2484C2214yes—
158#2476C2214yes—
159#2475C2214yes—
160#2465C2214yes—
161#2460C2214yes—
162#2453C2214yes—
163#2453C2214yes—
164#2451C2214yes—
165#2451C2214yes—
166#2450C2214yes—
167#2446C2214yes—
168#2444C2214yes—
169#2444C2214yes—
170#2439C2214yes—
171#2438C2214yes—
172#2429C2214yes—
173#2429C2214yes—
174#2426C2214yes—
175#2426C2214yes—
176#2425C2214yes—
177#2419C2214yes—
178#2413C2214yes—
179#2413C2214yes—
180#2406C2214yes—
181#2381C2212yes—
182#2379C2212yes—
183#2378C2214yes—
184#2372C2212yes—
185#2369C2212yes—
186#2368C2214yes—
187#2359C2214yes—
188#2359C2214yes—
189#2343C2214yes—
190#2339C2214yes—
191#2337C2214yes—
192#2332C2214yes—
193#2331C2214yes—
194#2329C2214yes—
195#2329C2212yes—
196#2327C2214yes—
197#2327C2214yes—
198#2327C2214yes—
199#2327C2214yes—
200#2325C2212yes—
201#2322C2214yes—
202#2322C2214yes—
203#2318C2214yes—
204#2316C2211yescharacteristic
205#2316C2211yescharacteristic
206#2310C2212yes—
207C4×#123C2214yes—
208#2297C2212yes—
209#2296C2212yes—
210C2×#391C2211yescharacteristic
211C2×#391C2211yescharacteristic
212C2×#387C2212yes—
213C2×#387C2212yes—
214C2×#387C2212yes—
215C2×#387C2212yes—
216#2283C2212yes—
217C2×#382C2211yescharacteristic
218C2×#376C2211yescharacteristic
219C22×#41C2312yes—
220C23×Q8C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222#544—44no—
223#537—44no—
224#536—216no—
225C2×C4⋊Q8—28no—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2314yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2314yes—
232#529—48no—
233C2×#126C2314yes—
234C2×#125C2312yes—
235C2×#125C2314yes—
236C2×#124C2312yes—
237C2×#124C2312yes—
238C2×#124C2312yes—
239C2×#123C2314yes—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2314yes—
248C2×#121C2312yes—
249C2×#121C2312yes—
250C2×#121C2314yes—
251C2×C4×Q8—44no—
252C2×C4×Q8—44no—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2314yes—
259C2×C4×Q8C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2312yes—
263C2×#117C2312yes—
264C2×#117C2312yes—
265C2×#117C2312yes—
266C2×#117C2314yes—
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276C22×C42C2312yes—
277C22×C42C2311yescharacteristic
278C22×C42C2311yescharacteristic
279C22×C42C2311yescharacteristic
280#401C2314yes—
281#401C2314yes—
282#401C2314yes—
283#400C2312yes—
284#400C2314yes—
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#400C2312yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#399C2314yes—
309#399C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2312yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2312yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2312yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2312yes—
363#395C2314yes—
364#395C2314yes—
365#394C2312yes—
366#394C2314yes—
367#394C2312yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#393C2314yes—
374#393C2314yes—
375#393C2314yes—
376#393C2314yes—
377#393C2314yes—
378#393C2314yes—
379#393C2314yes—
380#391C2312yes—
381#391C2314yes—
382#391C2312yes—
383#391C2314yes—
384#391C2312yes—
385#391C2312yes—
386#391C2312yes—
387#391C2312yes—
388#391C2312yes—
389#391C2312yes—
390#391C2312yes—
391#391C2312yes—
392#391C2314yes—
393#391C2312yes—
394#391C2312yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#390C2312yes—
404#390C2312yes—
405#390C2312yes—
406#390C2312yes—
407#390C2314yes—
408#390C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2312yes—
419#389C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
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#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
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#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#383C2314yes—
561#383C2314yes—
562#383C2314yes—
563#383C2314yes—
564#383C2314yes—
565#382C2314yes—
566#382C2314yes—
567#382C2312yes—
568#382C2312yes—
569#382C2312yes—
570#382C2314yes—
571#382C2312yes—
572#382C2314yes—
573#382C2314yes—
574#381C2314yes—
575#381C2314yes—
576#381C2314yes—
577#381C2314yes—
578#381C2314yes—
579#381C2314yes—
580#381C2314yes—
581#381C2314yes—
582#380C2312yes—
583#380C2312yes—
584#380C2312yes—
585#380C2312yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2312yes—
593C4×C4⋊C4C2312yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608#376C2314yes—
609#376C2314yes—
610#376C2314yes—
611#376C2314yes—
612C2×#95C2312yes—
613C2×#95C2312yes—
614C2×#95C2314yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C2×#95C2312yes—
619C2×#95C2312yes—
620C2×#95C2312yes—
621C2×#41—28no—
622C2×#41—44no—
623C2×#41—44no—
624C22×Q8—24no—
625C22×Q8—42no—
626C22×Q8—42no—
627C22×Q8—42no—
628C22×Q8—42no—
629C22×Q8#4118yes—
630C22×Q8C2412yes—
631C22×Q8C2411yescharacteristic
632C22×Q8C2411yescharacteristic
633C22×Q8C2412yes—
634C22×Q8C2412yes—
635C22×Q8C2412yes—
636C22×Q8C2412yes—
637C22×Q8C2412yes—
638C22×D4C2414yes—
639C22×D4C2412yes—
640C22×D4C2412yes—
641C22×D4C2412yes—
642C23×C4C2412yes—
643C23×C4C2411yescharacteristic
644C23×C4C2411yescharacteristic
645C23×C4C2411yescharacteristic
646C23×C4C2412yes—
647C23×C4C2411yescharacteristic
648C23×C4C2411yescharacteristic
649C23×C4C2412yes—
650C23×C4C2411yescharacteristic
651C23×C4C2412yes—
652C23×C4C2414yes—
653C23×C4C2414yes—
654C23×C4C2414yes—
655C23×C4C2411yescharacteristic
656C4⋊Q8—28no—
657C4⋊Q8—216no—
658C4⋊Q8—28no—
659C4⋊Q8—28no—
660C4⋊Q8—28no—
661C4⋊Q8—48no—
662#126—48no—
663#125—44no—
664#125—48no—
665#124—28no—
666#124—28no—
667#124—44no—
668#123—216no—
669#123—216no—
670#123—48no—
671#123—48no—
672C22⋊Q8—216no—
673C22⋊Q8—216no—
674C22⋊Q8—28no—
675C22⋊Q8—44no—
676C22⋊Q8—48no—
677#121—28no—
678#121—48no—
679#121—44no—
680C4×Q8—44no—
681C4×Q8—44no—
682C4×Q8—44no—
683C4×Q8—44no—
684C4×Q8—48no—
685C4×Q8—48no—
686C4×Q8—44no—
687C4×D4—44no—
688C4×D4—48no—
689C4×D4—48no—
690#117—28no—
691#117—48no—
692#117—44no—
693#117—44no—
694C2×C4⋊C4—28no—
695C2×C4⋊C4—28no—
696C2×C4⋊C4—24no—
697C2×C4⋊C4—24no—
698C2×C4⋊C4—42no—
699C2×C4⋊C4—42no—
700C2×C4⋊C4—44no—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
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×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C42—24no—
782C2×C42—24no—
783C2×C42—28no—
784C2×C42—42no—
785C2×C42—42no—
786C2×C42—42no—
787C2×C42C2412yes—
788C2×C42C2412yes—
789C2×C42C2412yes—
790C2×C42C2412yes—
791C2×C42C2412yes—
792C2×C42C2412yes—
793C2×C42C2412yes—
794C2×C42C2412yes—
795C2×C42C2412yes—
796C2×C42C2412yes—
797C2×C42C2414yes—
798C2×C42C2414yes—
799C2×C42C2412yes—
800C2×C42C2412yes—
801C2×C42C2414yes—
802C2×C42C2414yes—
803C2×C42C2414yes—
804C2×C42C2412yes—
805C2×C42C2412yes—
806C2×C42C2414yes—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
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#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2412yes—
861#95C2412yes—
862#95C2412yes—
863#95C2412yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876C24C2514yes—
877C24C2511yescharacteristic
878#41—816no—
879C2×Q8—24no—
880C2×Q8—22no—
881C2×Q8—22no—
882C2×Q8—24no—
883C2×Q8—24no—
884C2×Q8—42no—
885C2×Q8—42no—
886C2×Q8—41no—
887C2×Q8—42no—
888C2×Q8—41no—
889C2×Q8—416no—
890C2×Q8—42no—
891C2×Q8—42no—
892C2×Q8—42no—
893C2×Q8—41no—
894C2×Q8—41no—
895C2×Q8—42no—
896C2×Q8—42no—
897C2×Q8—42no—
898C2×Q8—42no—
899C2×Q8—42no—
900C2×Q8—44no—
901C2×Q8—416no—
902C2×Q8C2×#4118yes—
903C2×Q8C2×#4118yes—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—24no—
908C2×D4—24no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—44no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4—24no—
922C22×C4—24no—
923C22×C4—22no—
924C22×C4—24no—
925C22×C4—24no—
926C22×C4—24no—
927C22×C4—22no—
928C22×C4—22no—
929C22×C4—24no—
930C22×C4—28no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4C2×#4114yes—
950C22×C4C2×#4114yes—
951C22×C4C2×#4114yes—
952C22×C4H(5,𝔽2)14yes—
953C22×C4C2514yes—
954C22×C4C2512yes—
955C22×C4C2514yes—
956C22×C4C2514yes—
957C22×C4C2514yes—
958C22×C4C2514yes—
959C22×C4C2514yes—
960C22×C4C2514yes—
961C22×C4C2512yes—
962C22×C4C2512yes—
963C22×C4C2512yes—
964C22×C4C2512yes—
965C22×C4C2514yes—
966C22×C4C2512yes—
967C22×C4C2512yes—
968C22×C4C2514yes—
969C22×C4C2512yes—
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2512yes—
973C22×C4C2512yes—
974C4⋊C4—28no—
975C4⋊C4—28no—
976C4⋊C4—28no—
977C4⋊C4—28no—
978C4⋊C4—28no—
979C4⋊C4—28no—
980C4⋊C4—28no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—28no—
985C4⋊C4—28no—
986C4⋊C4—24no—
987C4⋊C4—24no—
988C4⋊C4—41no—
989C4⋊C4—42no—
990C4⋊C4—41no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
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—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C22⋊C4—28no—
1028C22⋊C4—28no—
1029C22⋊C4—28no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C22⋊C4—44no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
1046C22⋊C4—44no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C42—24no—
1055C42—24no—
1056C42—24no—
1057C42—24no—
1058C42—24no—
1059C42—24no—
1060C42—24no—
1061C42—24no—
1062C42—24no—
1063C42—24no—
1064C42—42no—
1065C42—42no—
1066C42—44no—
1067C42—44no—
1068C42—44no—
1069C42—44no—
1070C42—44no—
1071C42—44no—
1072C42—42no—
1073C42—42no—
1074C42—44no—
1075C42—44no—
1076C42—44no—
1077C23—22no—
1078C23—22no—
1079C23—24no—
1080C23—24no—
1081C23—24no—
1082C23—24no—
1083C23—24no—
1084C23—24no—
1085C23—24no—
1086C23C22×#4112yes—
1087C23C2×H(5,𝔽2)12yes—
1088C23#58512yes—
1089C23C2611yescharacteristic
1090Q8—48no—
1091Q8—48no—
1092Q8—44no—
1093Q8—48no—
1094Q8—44no—
1095Q8—84no—
1096Q8—84no—
1097Q8—162no—
1098D4—416no—
1099D4—84no—
1100D4—84no—
1101D4—162no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—28no—
1113C2×C4—28no—
1114C2×C4—28no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—44no—
1162C2×C4—48no—
1163C2×C4—44no—
1164C2×C4—48no—
1165C2×C4—88no—
1166C2×C4—82no—
1167C2×C4—82no—
1168C2×C4—84no—
1169C2×C4—84no—
1170C2×C4—88no—
1171C2×C4—164no—
1172C2×C4C22×#4112yes—
1173C2×C4C22×#4112yes—
1174C2×C4C22×#4114yes—
1175C2×C4C22×#4114yes—
1176C2×C4C2×H(5,𝔽2)14yes—
1177C22—24no—
1178C22—22no—
1179C22—24no—
1180C22—22no—
1181C22—44no—
1182C22—44no—
1183C22—44no—
1184C22—44no—
1185C22—44no—
1186C22—44no—
1187C22—44no—
1188C22#350514yes—
1189C22C23×#4111yescharacteristic
1190C22C22×H(5,𝔽2)11yescharacteristic
1191C22C2×#58511yescharacteristic
1192C222−1+612yes—
1193C222−1+612yes—
1194C4—24no—
1195C4—24no—
1196C4—22no—
1197C4—22no—
1198C4—24no—
1199C4—42no—
1200C4—42no—
1201C4—44no—
1202C4—44no—
1203C4—44no—
1204C4—44no—
1205C4—42no—
1206C4—42no—
1207C4—44no—
1208C4—44no—
1209C4—44no—
1210C4—44no—
1211C4—42no—
1212C4—42no—
1213C4—44no—
1214C4—42no—
1215C2—24no—
1216C2—84no—
1217C2C2×#350511yescharacteristic
1218C2#6285012yes—
1219C2#6287111yescharacteristic
1220C2#6287312yes—
1221C2#6288611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51872C2semidirect
2. #51737C2semidirect
3. #51724C2semidirect
4. #51723C2semidirect
5. #47379C2semidirect
6. #47375C2semidirect
7. #47374C2semidirect
8. #47370C2semidirect
9. #38127C2semidirect
10. #38115C2semidirect
11. #37943C2semidirect
12. #37935C2semidirect
13. #37755C2semidirect
15. #37518C2semidirect
16. #37258C2semidirect
17. #37124C2semidirect
18. #35154C2semidirect
20. #35111C2semidirect
21. #35099C2semidirect
22. #34409C2semidirect
23. C2×#2327C2semidirect

Maximal subgroups

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

subgroupindex
#518722
#517372
#517242
#517232
#473792
#473752
#473742
#473702
#381272
#381152
#379432
#379352
#377552
#377472
#375182
#372582
#371242
#351542
#351532
#351112
#350992
#344092
C2×#23272