Finite Group Databasebeta

← #7717545

Subgroups — #7717545

Order 512.

4518 conjugacy classes of subgroups.

The subgroup lattice has 1235 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51429C214yesmaximal, complemented
2#51428C214yesmaximal, complemented
3#50882C214yesmaximal, complemented
4#50881C214yesmaximal, complemented
5#44718C214yesmaximal, complemented
6#44580C214yesmaximal, complemented
7#44350C214yesmaximal, complemented
8#44164C214yesmaximal, complemented
9#39039C214yesmaximal, complemented
10#39037C214yesmaximal, complemented
11#38979C214yesmaximal, complemented
12#36975C212yesmaximal, complemented
13#36730C212yesmaximal, complemented
14#36521C214yesmaximal, complemented
15#35325C211yesmaximal, characteristic, complemented
16#35301C211yesmaximal, characteristic
17#35180C211yesmaximal, characteristic, complemented
18#35099C212yesmaximal, complemented
19#34997C212yesmaximal, complemented
20#34595C211yesmaximal, characteristic, complemented
21#34389C211yesmaximal, characteristic, complemented
22#34388C211yesmaximal, characteristic, complemented
23C2×#2343C211yesmaximal, characteristic, complemented
24C2×#533C2211yescharacteristic
25C2×#532C2211yescharacteristic
26C22×#117C2211yescharacteristic
27#2855C2212yes—
28#2854C2212yes—
29#2853C2214yes—
30#2850C2214yes—
31#2849C2214yes—
32#2848C2212yes—
33#2847C2212yes—
34#2789C2214yescomplemented
35#2786C2214yescomplemented
36#2774C2214yescomplemented
37#2772C2214yescomplemented
38#2767C2214yescomplemented
39#2767C2214yescomplemented
40#2764C2214yes—
41#2763C2214yes—
42#2763C2214yescomplemented
43#2762C2214yescomplemented
44#2762C2214yescomplemented
45#2762C2214yescomplemented
46#2761C2214yescomplemented
47#2761C2214yescomplemented
48#2758C2214yescomplemented
49#2754C2214yescomplemented
50#2749C2214yes—
51#2748C2214yes—
52#2747C2214yescomplemented
53#2747C2214yescomplemented
54#2746C2214yes—
55#2746C2214yes—
56#2745C2214yes—
57#2745C2214yescomplemented
58#2744C2214yescomplemented
59#2743C2214yes—
60#2740C2214yescomplemented
61#2738C2214yes—
62#2737C2214yes—
63#2737C2214yescomplemented
64#2723C2214yescomplemented
65#2717C2214yes—
66#2715C2214yescomplemented
67#2706C2214yes—
68#2701C2214yes—
69#2700C2214yes—
70#2700C2214yescomplemented
71#2698C2214yescomplemented
72#2687C2214yes—
73#2686C2214yes—
74#2666C2214yescomplemented
75#2666C2214yescomplemented
76#2659C2212yes—
77#2646C2212yes—
78#2643C2214yes—
79#2643C2214yes—
80#2639C2212yes—
81#2639C2212yes—
82#2628C2212yes—
83#2628C2212yes—
84#2627C2214yes—
85#2621C2212yes—
86#2619C2212yes—
87#2611C2214yes—
88#2610C2214yes—
89#2607C2214yes—
90#2605C2214yescomplemented
91#2603C2214yes—
92#2602C2214yes—
93#2599C2214yes—
94#2598C2214yes—
95#2597C2214yes—
96#2597C2214yescomplemented
97#2596C2214yescomplemented
98#2595C2214yes—
99#2594C2214yescomplemented
100#2592C2214yescomplemented
101#2591C2212yes—
102#2589C2214yes—
103#2589C2214yes—
104#2583C2212yes—
105#2578C2214yes—
106#2577C2214yescomplemented
107#2575C2214yes—
108#2574C2214yescomplemented
109#2573C2214yescomplemented
110#2573C2214yescomplemented
111#2569C2214yescomplemented
112#2568C2212yescomplemented
113#2564C2214yes—
114#2563C2212yescomplemented
115#2562C2214yescomplemented
116#2561C2212yes—
117#2557C2214yes—
118#2557C2214yes—
119#2553C2214yes—
120#2548C2212yescomplemented
121#2547C2212yescomplemented
122#2539C2212yes—
123#2533C2214yescomplemented
124#2532C2214yescomplemented
125#2531C2214yescomplemented
126#2531C2214yescomplemented
127#2530C2214yescomplemented
128#2529C2214yescomplemented
129#2528C2214yescomplemented
130#2527C2214yes—
131#2527C2214yescomplemented
132#2526C2214yescomplemented
133#2525C2214yescomplemented
134#2520C2214yescomplemented
135#2517C2214yes—
136#2516C2214yes—
137#2510C2214yes—
138#2510C2214yes—
139#2505C2214yes—
140#2494C2214yescomplemented
141#2493C2214yes—
142#2493C2214yescomplemented
143#2488C2214yes—
144#2488C2214yes—
145#2484C2212yes—
146#2482C2212yes—
147#2481C2214yes—
148#2472C2214yes—
149#2469C2214yescomplemented
150#2461C2214yes—
151#2459C2214yes—
152#2458C2214yes—
153#2450C2214yes—
154#2450C2214yes—
155#2449C2214yes—
156#2444C2214yes—
157#2425C2214yes—
158#2421C2214yescomplemented
159#2419C2214yes—
160#2419C2214yes—
161#2419C2214yes—
162#2418C2214yes—
163#2406C2212yes—
164#2404C2212yes—
165#2402C2212yescomplemented
166#2402C2212yescomplemented
167#2399C2212yescomplemented
168#2399C2212yescomplemented
169#2381C2212yescomplemented
170#2381C2212yescomplemented
171#2381C2212yescomplemented
172#2380C2212yescomplemented
173#2374C2214yes—
174#2374C2214yes—
175#2368C2214yes—
176#2367C2214yes—
177#2364C2214yes—
178#2357C2214yes—
179#2356C2214yescomplemented
180#2353C2214yescomplemented
181#2343C2214yes—
182#2343C2214yes—
183#2343C2214yes—
184#2343C2214yes—
185#2343C2214yes—
186#2339C2214yes—
187#2337C2212yescomplemented
188#2337C2212yescomplemented
189#2336C2212yescomplemented
190#2336C2212yescomplemented
191#2329C2212yes—
192#2329C2212yes—
193#2325C2212yes—
194#2325C2212yes—
195#2324C2212yes—
196#2324C2212yes—
197#2323C2212yes—
198#2323C2212yes—
199#2320C2214yescomplemented
200#2318C2214yes—
201#2318C2214yes—
202#2318C2214yescomplemented
203#2311C2214yes—
204C4×C22⋊Q8C2214yes—
205C4×#123C2214yes—
206C4×#120C2214yes—
207C2×#387C2212yes—
208C2×#387C2212yes—
209C2×#385C2212yes—
210#2283C2211yescharacteristic
211#2283C2211yescharacteristic
212C2×#383C2211yescharacteristic
213C2×#382C2211yescharacteristic
214C2×#381C2211yescharacteristic
215C2×C4×C4⋊C4C2211yescharacteristic
216C2×C4×C22⋊C4C2212yes—
217C2×#376C2211yescharacteristic
218C22×#95C2211yescharacteristic
219C22×#41C2312yes—
220C24×C4C2311yescharacteristic
221C24×C4C2312yes—
222#533—28no—
223#532—28no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×#127C2311yescharacteristic
228C2×#126C2314yes—
229C2×#125C2312yes—
230C2×#124C2312yes—
231C2×#124C2314yes—
232C2×#124C2314yes—
233C2×#123C2314yes—
234C2×#123C2314yes—
235C2×#123C2314yes—
236C2×#123C2314yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×#121C2312yes—
244C2×#121C2312yes—
245C2×#121C2312yes—
246C2×#121C2312yes—
247C2×#120C2314yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×#117—28no—
258C2×#117C2312yes—
259C2×#117C2312yes—
260C2×#117C2312yes—
261C2×#117C2312yes—
262C2×#117C2312yes—
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C22⋊C4C2311yescharacteristic
268C22×C22⋊C4C2311yescharacteristic
269C22×C22⋊C4C2312yes—
270C22×C42C2311yescharacteristic
271C22×C42C2312yes—
272C22×C42C2312yes—
273C22×C42C2311yescharacteristic
274#401C2314yes—
275#401C2314yes—
276#401C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
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#400C2314yes—
298#399C2314yes—
299#399C2314yes—
300#399C2314yes—
301#399C2314yes—
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#398C2314yes—
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#397C2314yes—
332#397C2314yes—
333#396C2314yes—
334#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#395C2314yes—
339#395C2314yes—
340#395C2314yes—
341#395C2314yes—
342#395C2314yes—
343#395C2314yes—
344#395C2314yes—
345#394C2314yes—
346#394C2314yes—
347#394C2314yes—
348#394C2314yes—
349#394C2314yes—
350#394C2314yes—
351#394C2314yes—
352#394C2314yes—
353#393C2314yes—
354#393C2314yes—
355#393C2314yes—
356#393C2314yes—
357#393C2314yes—
358#393C2314yes—
359#393C2314yes—
360#392C2314yes—
361#392C2314yes—
362#391C2314yes—
363#391C2314yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#391C2312yes—
369#391C2312yes—
370#391C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2314yes—
374#391C2314yes—
375#391C2314yes—
376#390C2314yes—
377#390C2314yes—
378#390C2314yes—
379#390C2314yes—
380#390C2314yes—
381#390C2312yes—
382#390C2312yes—
383#390C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2314yes—
393#389C2314yes—
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#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
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#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
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#386C2314yes—
477#386C2314yes—
478#386C2314yes—
479#386C2314yes—
480#386C2314yes—
481#386C2314yes—
482#386C2314yes—
483#386C2314yes—
484#386C2314yes—
485#386C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#386C2314yes—
495#386C2314yes—
496#386C2314yes—
497#386C2314yes—
498#386C2314yes—
499#385C2314yes—
500#385C2314yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#383C2314yes—
523#383C2314yes—
524#383C2312yes—
525#383C2312yes—
526#383C2314yes—
527#383C2312yes—
528#383C2312yes—
529#383C2312yes—
530#383C2312yes—
531#383C2314yes—
532#382C2314yes—
533#382C2314yes—
534#382C2314yes—
535#382C2312yes—
536#382C2312yes—
537#382C2314yes—
538#382C2314yes—
539#382C2314yes—
540#382C2314yes—
541#381C2314yes—
542#381C2314yes—
543#381C2314yes—
544#381C2314yes—
545#381C2314yes—
546#381C2314yes—
547#381C2312yes—
548#381C2312yes—
549#381C2314yes—
550#381C2314yes—
551#381C2314yes—
552#380C2314yes—
553#380C2314yes—
554#380C2314yes—
555#380C2314yes—
556#380C2314yes—
557#380C2314yes—
558#380C2314yes—
559#380C2314yes—
560#380C2312yes—
561#380C2312yes—
562#380C2312yes—
563#380C2312yes—
564#380C2312yes—
565#380C2312yes—
566#380C2314yes—
567#379C2314yes—
568C4×C4⋊C4C2312yes—
569C4×C4⋊C4C2312yes—
570C4×C4⋊C4C2312yes—
571C4×C4⋊C4C2314yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2314yes—
574C4×C4⋊C4C2314yes—
575C4×C4⋊C4C2314yes—
576C4×C4⋊C4C2311yescharacteristic
577C4×C4⋊C4C2311yescharacteristic
578C4×C4⋊C4C2311yescharacteristic
579C4×C4⋊C4C2311yescharacteristic
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2312yes—
583C4×C4⋊C4C2314yes—
584C4×C22⋊C4C2312yes—
585C4×C22⋊C4C2314yes—
586C4×C22⋊C4C2314yes—
587C4×C22⋊C4C2314yes—
588C4×C22⋊C4C2314yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2314yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2312yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2314yes—
599#376C2314yes—
600#376C2314yes—
601#376C2314yes—
602#376C2312yes—
603#376C2312yes—
604C2×#95C2314yes—
605C2×#95C2312yes—
606C2×#95C2312yes—
607C2×#95C2311yescharacteristic
608C2×#95C2311yescharacteristic
609C2×#95C2312yes—
610C2×#95C2314yes—
611C2×#95C2314yes—
612C2×#95C2312yes—
613C2×#95C2311yescharacteristic
614C2×#95C2311yescharacteristic
615C2×#95C2312yes—
616C2×#95C2312yes—
617C25C2411yescharacteristic
618C2×#41—28no—
619C2×#41—48no—
620C22×Q8C2412yes—
621C22×Q8C2412yes—
622C22×Q8C2412yes—
623C22×Q8C2414yes—
624C22×D4C2414yes—
625C22×D4C2414yes—
626C22×D4C2414yes—
627C22×D4C2412yes—
628C22×D4C2412yes—
629C22×D4C2412yes—
630C23×C4—24no—
631C23×C4—44no—
632C23×C4—44no—
633C23×C4—44no—
634C23×C4—82no—
635C23×C4C2411yescharacteristic
636C23×C4C2412yes—
637C23×C4C2412yes—
638C23×C4C2411yescharacteristic
639C23×C4C2411yescharacteristic
640C23×C4C2412yes—
641C23×C4C2412yes—
642C23×C4C2411yescharacteristic
643C23×C4C2412yes—
644C23×C4C2412yes—
645C23×C4C2414yes—
646C23×C4C2414yes—
647C23×C4C2414yes—
648C23×C4C2414yes—
649C23×C4C2414yes—
650C23×C4C2411yescharacteristic
651C23×C4C2411yescharacteristic
652C4⋊Q8—24no—
653C4⋊Q8—24no—
654C4⋊Q8—24no—
655#127—24no—
656#126—84no—
657#125—28no—
658#124—28no—
659#124—48no—
660#124—84no—
661#123—48no—
662#123—48no—
663#123—48no—
664#123—84no—
665C22⋊Q8—28no—
666C22⋊Q8—28no—
667C22⋊Q8—48no—
668C22⋊Q8—44no—
669C22⋊Q8—44no—
670C22⋊Q8—84no—
671#121—28no—
672#121—28no—
673#121—44no—
674#121—44no—
675#120—48no—
676C4×Q8—28no—
677C4×Q8—28no—
678C4×Q8—84no—
679C4×D4—28no—
680C4×D4—28no—
681C4×D4—48no—
682C4×D4—48no—
683C4×D4—48no—
684C4×D4—84no—
685#117—28no—
686#117—28no—
687#117—28no—
688#117—28no—
689#117—28no—
690C2×C4⋊C4—24no—
691C2×C4⋊C4—24no—
692C2×C4⋊C4—44no—
693C2×C4⋊C4—82no—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C22⋊C4—24no—
736C2×C22⋊C4—24no—
737C2×C22⋊C4—44no—
738C2×C22⋊C4C2412yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2412yes—
741C2×C22⋊C4C2412yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊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×C42—24no—
776C2×C42—44no—
777C2×C42—82no—
778C2×C42#4118yes—
779C2×C42C2412yes—
780C2×C42C2412yes—
781C2×C42C2414yes—
782C2×C42C2414yes—
783C2×C42C2414yes—
784C2×C42C2414yes—
785C2×C42C2414yes—
786C2×C42C2412yes—
787C2×C42C2412yes—
788C2×C42C2414yes—
789C2×C42C2414yes—
790C2×C42C2414yes—
791C2×C42C2414yes—
792C2×C42C2414yes—
793C2×C42C2412yes—
794C2×C42C2414yes—
795C2×C42C2412yes—
796C2×C42C2411yescharacteristic
797C2×C42C2411yescharacteristic
798C2×C42C2411yescharacteristic
799C2×C42C2411yescharacteristic
800#95C2412yes—
801#95C2412yes—
802#95C2414yes—
803#95C2414yes—
804#95C2412yes—
805#95C2412yes—
806#95C2414yes—
807#95C2414yes—
808#95C2412yes—
809#95C2412yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2412yes—
818#95C2412yes—
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#95C2412yes—
852#95C2412yes—
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—
868C24—22no—
869C24—24no—
870C24—24no—
871C24—41no—
872C24—41no—
873C24C2514yes—
874C24C2512yes—
875C24C2511yescharacteristic
876#41—816no—
877C2×Q8—24no—
878C2×Q8—24no—
879C2×Q8—24no—
880C2×Q8—44no—
881C2×Q8—42no—
882C2×Q8—42no—
883C2×Q8—44no—
884C2×Q8—44no—
885C2×Q8—42no—
886C2×Q8—42no—
887C2×Q8—44no—
888C2×D4—28no—
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—24no—
894C2×D4—24no—
895C2×D4—24no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—44no—
904C2×D4—44no—
905C22×C4—24no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—24no—
910C22×C4—24no—
911C22×C4—24no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—28no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—28no—
920C22×C4—41no—
921C22×C4—42no—
922C22×C4—41no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—42no—
939C22×C4—44no—
940C22×C4—42no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—416no—
950C22×C4—816no—
951C22×C4C2×#4114yes—
952C22×C4C2×#4114yes—
953C22×C4C2×#4114yes—
954C22×C4C2514yes—
955C22×C4C2514yes—
956C22×C4C2514yes—
957C22×C4C2512yes—
958C22×C4C2514yes—
959C22×C4C2514yes—
960C22×C4C2514yes—
961C22×C4C2512yes—
962C22×C4C2514yes—
963C22×C4C2514yes—
964C22×C4C2514yes—
965C22×C4C2512yes—
966C22×C4C2514yes—
967C22×C4C2514yes—
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2511yescharacteristic
973C22×C4C2511yescharacteristic
974C4⋊C4—24no—
975C4⋊C4—24no—
976C4⋊C4—24no—
977C4⋊C4—24no—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—24no—
981C4⋊C4—24no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—24no—
985C4⋊C4—24no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
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—
1015C22⋊C4—28no—
1016C22⋊C4—28no—
1017C22⋊C4—28no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—24no—
1022C22⋊C4—24no—
1023C22⋊C4—24no—
1024C22⋊C4—24no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
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—
1052C42—24no—
1053C42—24no—
1054C42—28no—
1055C42—44no—
1056C42—44no—
1057C42—44no—
1058C42—44no—
1059C42—42no—
1060C42—42no—
1061C42—44no—
1062C42—44no—
1063C42—44no—
1064C42—44no—
1065C42—44no—
1066C42—42no—
1067C42—42no—
1068C42—44no—
1069C42C2×#4114yes—
1070C42C2×#4114yes—
1071C42C2×#4114yes—
1072C42C2×#4114yes—
1073C23—22no—
1074C23—21no—
1075C23—21no—
1076C23—28no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—24no—
1084C23—24no—
1085C23—24no—
1086C23—24no—
1087C23—24no—
1088C23—24no—
1089C23—24no—
1090C23—48no—
1091C23—48no—
1092C23—44no—
1093C23—44no—
1094C23C22×#4112yes—
1095C23#58514yes—
1096C23#58514yes—
1097C23C2611yescharacteristic
1098Q8—84no—
1099Q8—84no—
1100Q8—84no—
1101Q8—88no—
1102D4—416no—
1103D4—84no—
1104D4—84no—
1105D4—84no—
1106D4—88no—
1107D4—88no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—28no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—24no—
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—44no—
1160C2×C4—44no—
1161C2×C4—48no—
1162C2×C4—48no—
1163C2×C4—44no—
1164C2×C4—44no—
1165C2×C4—48no—
1166C2×C4—44no—
1167C2×C4—88no—
1168C2×C4—84no—
1169C2×C4—84no—
1170C2×C4—88no—
1171C2×C4—84no—
1172C2×C4—88no—
1173C2×C4—164no—
1174C2×C4—164no—
1175C2×C4C22×#4112yes—
1176C2×C4C22×#4112yes—
1177C2×C4C22×#4112yes—
1178C2×C4C22×#4112yes—
1179C2×C4C22×#4112yes—
1180C2×C4C22×#4112yes—
1181C22—22no—
1182C22—22no—
1183C22—24no—
1184C22—24no—
1185C22—24no—
1186C22—24no—
1187C22—24no—
1188C22—416no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—44no—
1194C22—44no—
1195C22—44no—
1196C22—44no—
1197C22—44no—
1198C22—44no—
1199C22—44no—
1200C22#351014yes—
1201C22C23×#4111yescharacteristic
1202C22C2×#58512yes—
1203C22C2×#58512yes—
1204C22H(7,𝔽2)11yescharacteristic
1205C222−1+611yescharacteristic
1206C4—22no—
1207C4—22no—
1208C4—22no—
1209C4—22no—
1210C4—22no—
1211C4—22no—
1212C4—42no—
1213C4—44no—
1214C4—42no—
1215C4—44no—
1216C4—42no—
1217C4—44no—
1218C4—44no—
1219C4—44no—
1220C4—44no—
1221C4—44no—
1222C4—44no—
1223C4—44no—
1224C4—44no—
1225C4—44no—
1226C2—24no—
1227C2—44no—
1228C2—84no—
1229C2C2×#351011yescharacteristic
1230C2#6281411yescharacteristic
1231C2#6285611yescharacteristic
1232C2#6290912yes—
1233C2#6293312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35301C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51429C2semidirect
2. #51428C2semidirect
3. #50882C2semidirect
4. #50881C2semidirect
5. #44718C2semidirect
6. #44580C2semidirect
7. #44350C2semidirect
8. #44164C2semidirect
9. #39039C2semidirect
10. #39037C2semidirect
11. #38979C2semidirect
12. #36975C2semidirect
13. #36730C2semidirect
14. #36521C2semidirect
15. #35325C2semidirect
17. #35180C2semidirect
18. #35099C2semidirect
19. #34997C2semidirect
20. #34595C2semidirect
21. #34389C2semidirect
22. #34388C2semidirect
23. C2×#2343C2semidirect
34. #2789C22semidirect
35. #2786C22semidirect
36. #2774C22semidirect
37. #2772C22semidirect
38. #2767C22semidirect
39. #2767C22semidirect
42. #2763C22semidirect
43. #2762C22semidirect
44. #2762C22semidirect
45. #2762C22semidirect
46. #2761C22semidirect
47. #2761C22semidirect
48. #2758C22semidirect
49. #2754C22semidirect
52. #2747C22semidirect
53. #2747C22semidirect
57. #2745C22semidirect
58. #2744C22semidirect
60. #2740C22semidirect
63. #2737C22semidirect
64. #2723C22semidirect
66. #2715C22semidirect
70. #2700C22semidirect
71. #2698C22semidirect
74. #2666C22semidirect
75. #2666C22semidirect
90. #2605C22semidirect
96. #2597C22semidirect
97. #2596C22semidirect
99. #2594C22semidirect
100. #2592C22semidirect
106. #2577C22semidirect
108. #2574C22semidirect
109. #2573C22semidirect
110. #2573C22semidirect
111. #2569C22semidirect
112. #2568C22semidirect
114. #2563C22semidirect
115. #2562C22semidirect
120. #2548C22semidirect
121. #2547C22semidirect
123. #2533C22semidirect
124. #2532C22semidirect
125. #2531C22semidirect
126. #2531C22semidirect
127. #2530C22semidirect
128. #2529C22semidirect
129. #2528C22semidirect
131. #2527C22semidirect
132. #2526C22semidirect
133. #2525C22semidirect
134. #2520C22semidirect
140. #2494C22semidirect
142. #2493C22semidirect
149. #2469C22semidirect
158. #2421C22semidirect
165. #2402C22semidirect
166. #2402C22semidirect
167. #2399C22semidirect
168. #2399C22semidirect
169. #2381C22semidirect
170. #2381C22semidirect
171. #2381C22semidirect
172. #2380C22semidirect
179. #2356C22semidirect
180. #2353C22semidirect
187. #2337C22semidirect
188. #2337C22semidirect
189. #2336C22semidirect
190. #2336C22semidirect
199. #2320C22semidirect
202. #2318C22semidirect

Maximal subgroups

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

subgroupindex
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