Finite Group Databasebeta

← #7656032

Subgroups — #7656032

Order 512.

4610 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41709C214yesmaximal, complemented
2#41704C214yesmaximal, complemented
3#41040C214yesmaximal, complemented
4#41037C214yesmaximal, complemented
5#40668C214yesmaximal, complemented
6#40665C214yesmaximal, complemented
7#39254C214yesmaximal, complemented
8#38221C214yesmaximal, complemented
9#38121C214yesmaximal, complemented
10#37466C212yesmaximal, complemented
11#37465C212yesmaximal, complemented
12#37442C212yesmaximal, complemented
13#36243C214yesmaximal, complemented
14#35964C214yesmaximal, complemented
15#35951C214yesmaximal, complemented
16#35051C211yesmaximal, characteristic
17#35021C212yesmaximal, complemented
18#34584C212yesmaximal, complemented
19C2×#2646C211yesmaximal, characteristic, complemented
20#34233C212yesmaximal, complemented
21C2×#2368C211yesmaximal, characteristic, complemented
22C2×#525C2212yes—
23C22×C22⋊Q8C2211yescharacteristic
24#2853C2214yes—
25#2852C2214yes—
26#2847C2214yes—
27#2839C2214yescomplemented
28#2836C2214yescomplemented
29#2833C2214yescomplemented
30#2829C2214yescomplemented
31#2814C2214yes—
32#2814C2214yes—
33#2796C2214yes—
34#2787C2214yes—
35#2782C2214yes—
36#2776C2214yescomplemented
37#2772C2214yescomplemented
38#2770C2214yes—
39#2770C2214yescomplemented
40#2766C2214yescomplemented
41#2764C2214yescomplemented
42#2762C2214yescomplemented
43#2758C2214yescomplemented
44#2757C2214yes—
45#2754C2214yescomplemented
46#2747C2214yescomplemented
47#2746C2214yes—
48#2746C2214yescomplemented
49#2741C2214yescomplemented
50#2739C2214yescomplemented
51#2711C2214yes—
52#2708C2214yes—
53#2702C2214yescomplemented
54#2698C2214yescomplemented
55#2690C2214yescomplemented
56#2687C2214yescomplemented
57#2667C2214yescomplemented
58#2666C2214yescomplemented
59#2659C2214yes—
60#2659C2211yescharacteristic
61#2656C2211yescharacteristic
62#2655C2214yescomplemented
63#2655C2214yescomplemented
64#2655C2214yescomplemented
65#2654C2214yescomplemented
66#2654C2214yescomplemented
67#2651C2214yescomplemented
68#2650C2214yescomplemented
69#2648C2214yescomplemented
70#2646C2211yescharacteristic
71#2646C2214yes—
72#2646C2214yes—
73#2646C2214yes—
74#2646C2212yes—
75#2646C2211yescharacteristic
76#2643C2214yes—
77#2639C2212yes—
78#2639C2214yes—
79#2634C2214yescomplemented
80#2630C2214yescomplemented
81#2627C2212yes—
82#2627C2212yes—
83#2625C2214yes—
84#2623C2214yes—
85#2618C2212yes—
86#2618C2212yes—
87#2616C2214yes—
88#2612C2214yescomplemented
89#2606C2214yescomplemented
90#2597C2214yes—
91#2596C2214yescomplemented
92#2595C2214yes—
93#2593C2214yescomplemented
94#2591C2214yes—
95#2585C2214yescomplemented
96#2585C2214yescomplemented
97#2579C2214yes—
98#2578C2214yes—
99#2578C2214yescomplemented
100#2577C2214yes—
101#2576C2214yes—
102#2574C2214yescomplemented
103#2573C2214yescomplemented
104#2569C2214yes—
105#2569C2214yes—
106#2569C2214yescomplemented
107#2564C2214yes—
108#2559C2214yes—
109#2556C2214yescomplemented
110#2543C2214yes—
111#2532C2214yescomplemented
112#2530C2214yes—
113#2530C2214yescomplemented
114#2527C2214yescomplemented
115#2525C2214yescomplemented
116#2524C2214yescomplemented
117#2524C2214yescomplemented
118#2522C2214yescomplemented
119#2522C2214yescomplemented
120#2520C2214yescomplemented
121#2510C2214yes—
122#2510C2214yes—
123#2510C2214yes—
124#2510C2214yescomplemented
125#2505C2214yes—
126#2498C2214yes—
127#2493C2214yes—
128#2493C2214yes—
129#2488C2214yescomplemented
130#2487C2214yes—
131#2486C2214yes—
132#2481C2214yes—
133#2477C2214yescomplemented
134#2476C2214yes—
135#2473C2214yes—
136#2469C2214yescomplemented
137#2468C2214yescomplemented
138#2462C2214yescomplemented
139#2457C2214yescomplemented
140#2444C2214yes—
141#2444C2214yes—
142#2443C2214yes—
143#2443C2214yes—
144#2442C2214yes—
145#2438C2214yescomplemented
146#2430C2214yes—
147#2425C2214yes—
148#2425C2214yes—
149#2417C2214yes—
150#2417C2214yes—
151#2412C2214yes—
152#2412C2214yes—
153#2409C2214yes—
154#2402C2214yescomplemented
155#2401C2214yescomplemented
156#2396C2214yescomplemented
157#2395C2214yescomplemented
158C2×#400C2214yes—
159C2×#398C2214yes—
160#2368C2214yes—
161#2368C2214yes—
162#2368C2214yes—
163#2368C2214yes—
164#2364C2214yes—
165#2361C2212yes—
166#2361C2212yes—
167#2360C2212yes—
168#2360C2212yes—
169#2358C2214yes—
170#2358C2214yes—
171#2353C2214yes—
172#2353C2214yes—
173#2352C2214yes—
174#2349C2214yes—
175#2347C2212yes—
176#2346C2212yes—
177#2345C2214yes—
178#2341C2212yes—
179#2339C2212yes—
180#2335C2214yes—
181#2335C2214yes—
182#2325C2214yes—
183#2322C2214yes—
184#2318C2214yes—
185#2318C2214yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×#123C2214yes—
189C4×#121C2212yes—
190C4×#121C2212yes—
191C2×#391C2212yes—
192#2290C2214yes—
193C2×#387C2212yes—
194C2×#387C2212yes—
195C2×#385C2214yes—
196C2×#385C2212yes—
197C2×#380C2212yes—
198#2275C2214yes—
199C2×C4×C4⋊C4C2212yes—
200C2×C4×C22⋊C4C2212yes—
201C2×C4×C22⋊C4C2211yescharacteristic
202C22×#95C2211yescharacteristic
203C22×#41C2312yes—
204C23×Q8C2311yescharacteristic
205C24×C4C2312yes—
206C24×C4C2311yescharacteristic
207C2×#126C2314yes—
208C2×#125C2314yes—
209#525—216no—
210C2×#123C2314yes—
211C2×#123C2314yes—
212C2×#123C2314yes—
213C2×#123C2314yes—
214C2×C22⋊Q8—28no—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×#121C2312yes—
222C2×#121C2312yes—
223C2×#121C2314yes—
224C2×#121C2314yes—
225C2×#121C2314yes—
226C2×#120C2314yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×#117C2312yes—
238C2×#117C2314yes—
239C22×C4⋊C4C2312yes—
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2314yes—
243C22×C4⋊C4C2314yes—
244C22×C4⋊C4C2312yes—
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2312yes—
247C22×C22⋊C4C2311yescharacteristic
248C22×C22⋊C4C2312yes—
249C22×C22⋊C4C2311yescharacteristic
250C22×C22⋊C4C2314yes—
251C22×C42C2312yes—
252C22×C42C2312yes—
253C22×C42C2312yes—
254#401C2314yes—
255#401C2314yes—
256#401C2314yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#399C2314yes—
285#399C2314yes—
286#399C2314yes—
287#399C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#397C2314yes—
318#397C2314yes—
319#397C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#396C2314yes—
332#396C2314yes—
333#396C2314yes—
334#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#395C2314yes—
339#395C2314yes—
340#395C2314yes—
341#395C2314yes—
342#395C2314yes—
343#394C2314yes—
344#394C2314yes—
345#394C2314yes—
346#394C2314yes—
347#394C2314yes—
348#394C2314yes—
349#394C2314yes—
350#394C2314yes—
351#394C2314yes—
352#394C2314yes—
353#394C2314yes—
354#393C2314yes—
355#393C2314yes—
356#393C2314yes—
357#392C2314yes—
358#391C2312yes—
359#391C2312yes—
360#391C2314yes—
361#391C2314yes—
362#391C2314yes—
363#391C2314yes—
364#391C2314yes—
365#391C2314yes—
366#390C2312yes—
367#390C2314yes—
368#390C2314yes—
369#390C2312yes—
370#389C2312yes—
371#389C2314yes—
372#389C2314yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#388C2314yes—
385#388C2314yes—
386#388C2314yes—
387#388C2314yes—
388#388C2314yes—
389#388C2314yes—
390#388C2314yes—
391#388C2314yes—
392#388C2314yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#388C2314yes—
397#388C2314yes—
398#388C2314yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2314yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#386C2314yes—
455#386C2314yes—
456#386C2314yes—
457#386C2314yes—
458#386C2314yes—
459#386C2314yes—
460#386C2314yes—
461#386C2314yes—
462#386C2314yes—
463#386C2314yes—
464#386C2314yes—
465#386C2314yes—
466#386C2314yes—
467#386C2314yes—
468#386C2314yes—
469#386C2314yes—
470#386C2314yes—
471#386C2314yes—
472#386C2314yes—
473#386C2314yes—
474#386C2314yes—
475#386C2314yes—
476#386C2314yes—
477#385C2314yes—
478#385C2314yes—
479#385C2314yes—
480#385C2314yes—
481#385C2314yes—
482#385C2314yes—
483#385C2314yes—
484#385C2314yes—
485#385C2314yes—
486#385C2314yes—
487#385C2314yes—
488#385C2314yes—
489#385C2314yes—
490#385C2314yes—
491#385C2314yes—
492#385C2314yes—
493#385C2314yes—
494#385C2314yes—
495#385C2314yes—
496#385C2314yes—
497#385C2314yes—
498#385C2314yes—
499#385C2314yes—
500#385C2314yes—
501#385C2314yes—
502#383C2314yes—
503#383C2314yes—
504#383C2314yes—
505#383C2314yes—
506#383C2314yes—
507#382C2314yes—
508#382C2314yes—
509#382C2314yes—
510#381C2314yes—
511#381C2314yes—
512#381C2314yes—
513#381C2314yes—
514#381C2314yes—
515#380C2314yes—
516#380C2314yes—
517#380C2314yes—
518#380C2314yes—
519#380C2314yes—
520#380C2314yes—
521#380C2314yes—
522#380C2314yes—
523#380C2314yes—
524#380C2314yes—
525#380C2314yes—
526#380C2314yes—
527#380C2314yes—
528#380C2314yes—
529#380C2312yes—
530#380C2312yes—
531#380C2314yes—
532#380C2312yes—
533#380C2312yes—
534C4×C4⋊C4C2314yes—
535C4×C4⋊C4C2314yes—
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2312yes—
543C4×C4⋊C4C2312yes—
544C4×C4⋊C4C2312yes—
545C4×C4⋊C4C2312yes—
546C4×C4⋊C4C2314yes—
547C4×C4⋊C4C2314yes—
548C4×C22⋊C4C2314yes—
549C4×C22⋊C4C2314yes—
550C4×C22⋊C4C2314yes—
551C4×C22⋊C4C2314yes—
552C4×C22⋊C4C2312yes—
553C4×C22⋊C4C2314yes—
554C4×C22⋊C4C2314yes—
555C4×C22⋊C4C2314yes—
556C4×C22⋊C4C2314yes—
557C4×C22⋊C4C2314yes—
558C4×C22⋊C4C2314yes—
559C4×C22⋊C4C2312yes—
560C4×C22⋊C4C2312yes—
561C4×C22⋊C4C2314yes—
562C4×C22⋊C4C2314yes—
563C4×C22⋊C4C2314yes—
564C4×C22⋊C4C2314yes—
565C4×C22⋊C4C2312yes—
566#376C2314yes—
567#376C2314yes—
568C2×#95C2314yes—
569C2×#95C2314yes—
570C2×#95C2314yes—
571C2×#95C2314yes—
572C2×#95C2312yes—
573C2×#95C2314yes—
574C2×#95C2312yes—
575C2×#95C2312yes—
576C2×#95C2314yes—
577C2×#95C2311yescharacteristic
578C2×#95C2311yescharacteristic
579C2×#95C2312yes—
580C2×#95C2312yes—
581C2×#95C2312yes—
582C25C2411yescharacteristic
583C2×#41—28no—
584C2×#41—82no—
585C2×#41—82no—
586C22×Q8—24no—
587C22×Q8—82no—
588C22×Q8C2412yes—
589C22×Q8C2414yes—
590C22×D4C2414yes—
591C22×D4C2414yes—
592C22×D4C2412yes—
593C22×D4C2414yes—
594C22×D4C2414yes—
595C23×C4—44no—
596C23×C4—44no—
597C23×C4—82no—
598C23×C4—82no—
599C23×C4#4118yes—
600C23×C4C2412yes—
601C23×C4C2412yes—
602C23×C4C2414yes—
603C23×C4C2412yes—
604C23×C4C2414yes—
605C23×C4C2412yes—
606C23×C4C2414yes—
607C23×C4C2412yes—
608C23×C4C2412yes—
609C23×C4C2414yes—
610C23×C4C2414yes—
611C23×C4C2414yes—
612C23×C4C2414yes—
613C23×C4C2412yes—
614C23×C4C2411yescharacteristic
615C23×C4C2411yescharacteristic
616C23×C4C2412yes—
617#126—84no—
618#125—84no—
619#123—216no—
620#123—48no—
621#123—48no—
622#123—84no—
623C22⋊Q8—216no—
624C22⋊Q8—216no—
625C22⋊Q8—28no—
626C22⋊Q8—28no—
627C22⋊Q8—84no—
628C22⋊Q8—84no—
629#121—28no—
630#121—28no—
631#121—48no—
632#121—48no—
633#121—84no—
634#120—216no—
635C4×Q8—82no—
636C4×Q8—82no—
637C4×D4—216no—
638C4×D4—216no—
639C4×D4—216no—
640C4×D4—48no—
641C4×D4—48no—
642C4×D4—48no—
643C4×D4—82no—
644C4×D4—82no—
645#117—28no—
646#117—84no—
647C2×C4⋊C4—24no—
648C2×C4⋊C4—28no—
649C2×C4⋊C4—44no—
650C2×C4⋊C4—48no—
651C2×C4⋊C4—84no—
652C2×C4⋊C4—82no—
653C2×C4⋊C4—82no—
654C2×C4⋊C4—82no—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C22⋊C4—28no—
698C2×C22⋊C4—24no—
699C2×C22⋊C4—42no—
700C2×C22⋊C4—48no—
701C2×C22⋊C4C2412yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2411yescharacteristic
707C2×C22⋊C4C2412yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2411yescharacteristic
715C2×C22⋊C4C2411yescharacteristic
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2411yescharacteristic
738C2×C42—44no—
739C2×C42—82no—
740C2×C42—82no—
741C2×C42C2414yes—
742C2×C42C2414yes—
743C2×C42C2414yes—
744C2×C42C2414yes—
745C2×C42C2414yes—
746C2×C42C2414yes—
747C2×C42C2412yes—
748C2×C42C2412yes—
749C2×C42C2414yes—
750C2×C42C2414yes—
751C2×C42C2412yes—
752C2×C42C2412yes—
753C2×C42C2414yes—
754C2×C42C2414yes—
755C2×C42C2414yes—
756#95C2412yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2412yes—
763#95C2414yes—
764#95C2412yes—
765#95C2414yes—
766#95C2412yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818C24—22no—
819C24—24no—
820C24—22no—
821C24—42no—
822C24C2×#4114yes—
823C24C2514yes—
824C24C2511yescharacteristic
825C24C2511yescharacteristic
826C24C2511yescharacteristic
827#41—816no—
828C2×Q8—24no—
829C2×Q8—28no—
830C2×Q8—42no—
831C2×Q8—42no—
832C2×Q8—44no—
833C2×Q8—44no—
834C2×Q8—88no—
835C2×D4—28no—
836C2×D4—28no—
837C2×D4—28no—
838C2×D4—28no—
839C2×D4—28no—
840C2×D4—28no—
841C2×D4—28no—
842C2×D4—24no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—44no—
846C2×D4—44no—
847C2×D4—44no—
848C2×D4—44no—
849C2×D4—44no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—24no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—28no—
857C22×C4—28no—
858C22×C4—24no—
859C22×C4—28no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—28no—
863C22×C4—28no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—42no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—42no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—88no—
896C22×C4—816no—
897C22×C4C2×#4114yes—
898C22×C4C2×#4114yes—
899C22×C4C2×#4118yes—
900C22×C4C2×#4118yes—
901C22×C4C2514yes—
902C22×C4C2514yes—
903C22×C4C2514yes—
904C22×C4C2512yes—
905C22×C4C2512yes—
906C22×C4C2514yes—
907C22×C4C2514yes—
908C22×C4C2514yes—
909C22×C4C2514yes—
910C22×C4C2514yes—
911C22×C4C2514yes—
912C22×C4C2514yes—
913C22×C4C2512yes—
914C22×C4C2514yes—
915C22×C4C2512yes—
916C22×C4C2512yes—
917C22×C4C2512yes—
918C4⋊C4—28no—
919C4⋊C4—28no—
920C4⋊C4—28no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—28no—
924C4⋊C4—28no—
925C4⋊C4—28no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—44no—
948C4⋊C4—44no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C22⋊C4—28no—
961C22⋊C4—28no—
962C22⋊C4—28no—
963C22⋊C4—28no—
964C22⋊C4—28no—
965C22⋊C4—22no—
966C22⋊C4—24no—
967C22⋊C4—28no—
968C22⋊C4—28no—
969C22⋊C4—28no—
970C22⋊C4—28no—
971C22⋊C4—24no—
972C22⋊C4—28no—
973C22⋊C4—41no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—41no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C42−1+414yes—
997C42—28no—
998C42—28no—
999C42—44no—
1000C42—44no—
1001C42—44no—
1002C42—42no—
1003C42—42no—
1004C42—42no—
1005C42—42no—
1006C42—44no—
1007C42—44no—
1008C42—44no—
1009C42—44no—
1010C42—44no—
1011C42—44no—
1012C23—21no—
1013C23—22no—
1014C23—21no—
1015C23—22no—
1016C23—22no—
1017C23—21no—
1018C23—22no—
1019C23—21no—
1020C23—22no—
1021C23—28no—
1022C23—28no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—24no—
1029C23—24no—
1030C23—44no—
1031C23—48no—
1032C23—48no—
1033C23C22×#4112yes—
1034C23C22×#4112yes—
1035C23C22×#4112yes—
1036C23C2×2−1+412yes—
1037C23#58512yes—
1038C23#58514yes—
1039C23C2611yescharacteristic
1040Q8—48no—
1041Q8—88no—
1042D4—48no—
1043D4—416no—
1044D4—416no—
1045D4—88no—
1046D4—164no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—48no—
1096C2×C4—44no—
1097C2×C4—44no—
1098C2×C4—48no—
1099C2×C4—48no—
1100C2×C4—48no—
1101C2×C4—48no—
1102C2×C4—48no—
1103C2×C4—88no—
1104C2×C4—88no—
1105C2×C4—88no—
1106C2×C4—84no—
1107C2×C4—88no—
1108C2×C4—88no—
1109C2×C4—84no—
1110C2×C4—88no—
1111C2×C4—164no—
1112C2×C4C22×#4114yes—
1113C2×C4C22×#4114yes—
1114C2×C4C2×2−1+414yes—
1115C22—22no—
1116C22—22no—
1117C22—22no—
1118C22—24no—
1119C22—24no—
1120C22—22no—
1121C22—24no—
1122C22—24no—
1123C22—22no—
1124C22—22no—
1125C22—22no—
1126C22—416no—
1127C22—42no—
1128C22—42no—
1129C22—44no—
1130C22—44no—
1131C22—44no—
1132C22—44no—
1133C22—44no—
1134C22—44no—
1135C22—44no—
1136C22#346114yes—
1137C22#351214yes—
1138C22C23×#4111yescharacteristic
1139C22C22×2−1+411yescharacteristic
1140C22C2×#58512yes—
1141C22C2×#58511yescharacteristic
1142C22H(7,𝔽2)12yes—
1143C4—24no—
1144C4—24no—
1145C4—24no—
1146C4—44no—
1147C4—44no—
1148C4—44no—
1149C4—44no—
1150C4—44no—
1151C4—42no—
1152C4—44no—
1153C4—44no—
1154C4—44no—
1155C4—42no—
1156C4—44no—
1157C4—42no—
1158C4—44no—
1159C4—44no—
1160C2—24no—
1161C2—24no—
1162C2—42no—
1163C2—84no—
1164C2C2×#346111yescharacteristic
1165C2C2×#351211yescharacteristic
1166C2#6284411yescharacteristic
1167C2#6290612yes—
1168C2#6294812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35051C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #41709C2semidirect
2. #41704C2semidirect
3. #41040C2semidirect
4. #41037C2semidirect
5. #40668C2semidirect
6. #40665C2semidirect
7. #39254C2semidirect
8. #38221C2semidirect
9. #38121C2semidirect
10. #37466C2semidirect
11. #37465C2semidirect
12. #37442C2semidirect
13. #36243C2semidirect
14. #35964C2semidirect
15. #35951C2semidirect
17. #35021C2semidirect
18. #34584C2semidirect
19. C2×#2646C2semidirect
20. #34233C2semidirect
21. C2×#2368C2semidirect
27. #2839C22semidirect
28. #2836C22semidirect
29. #2833C22semidirect
30. #2829C22semidirect
36. #2776C22semidirect
37. #2772C22semidirect
39. #2770C22semidirect
40. #2766C22semidirect
41. #2764C22semidirect
42. #2762C22semidirect
43. #2758C22semidirect
45. #2754C22semidirect
46. #2747C22semidirect
48. #2746C22semidirect
49. #2741C22semidirect
50. #2739C22semidirect
53. #2702C22semidirect
54. #2698C22semidirect
55. #2690C22semidirect
56. #2687C22semidirect
57. #2667C22semidirect
58. #2666C22semidirect
62. #2655C22semidirect
63. #2655C22semidirect
64. #2655C22semidirect
65. #2654C22semidirect
66. #2654C22semidirect
67. #2651C22semidirect
68. #2650C22semidirect
69. #2648C22semidirect
79. #2634C22semidirect
80. #2630C22semidirect
88. #2612C22semidirect
89. #2606C22semidirect
91. #2596C22semidirect
93. #2593C22semidirect
95. #2585C22semidirect
96. #2585C22semidirect
99. #2578C22semidirect
102. #2574C22semidirect
103. #2573C22semidirect
106. #2569C22semidirect
109. #2556C22semidirect
111. #2532C22semidirect
113. #2530C22semidirect
114. #2527C22semidirect
115. #2525C22semidirect
116. #2524C22semidirect
117. #2524C22semidirect
118. #2522C22semidirect
119. #2522C22semidirect
120. #2520C22semidirect
124. #2510C22semidirect
129. #2488C22semidirect
133. #2477C22semidirect
136. #2469C22semidirect
137. #2468C22semidirect
138. #2462C22semidirect
139. #2457C22semidirect
145. #2438C22semidirect
154. #2402C22semidirect
155. #2401C22semidirect
156. #2396C22semidirect
157. #2395C22semidirect

Maximal subgroups

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

subgroupindex
#417092
#417042
#410402
#410372
#406682
#406652
#392542
#382212
#381212
#374662
#374652
#374422
#362432
#359642
#359512
#350512
#350212
#345842
C2×#26462
#342332
C2×#23682