Finite Group Databasebeta

← #7715941

Subgroups — #7715941

Order 512.

4540 conjugacy classes of subgroups.

The subgroup lattice has 1183 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50197C214yesmaximal, complemented
2#50195C214yesmaximal, complemented
3#48809C214yesmaximal, complemented
4#48807C214yesmaximal, complemented
5#44476C214yesmaximal, complemented
6#44460C214yesmaximal, complemented
7#44000C214yesmaximal, complemented
8#43934C214yesmaximal, complemented
9#39254C214yesmaximal, complemented
10#38223C214yesmaximal, complemented
11#38121C214yesmaximal, complemented
12#36979C211yesmaximal, characteristic, complemented
13#36978C211yesmaximal, characteristic, complemented
14#36977C211yesmaximal, characteristic, complemented
15#36976C211yesmaximal, characteristic, complemented
16#36243C214yesmaximal, complemented
17#35263C212yesmaximal, complemented
18#35099C212yesmaximal, complemented
19#35051C211yesmaximal, characteristic
20#35042C212yesmaximal, complemented
21C2×#2646C211yesmaximal, characteristic, complemented
22#34386C212yesmaximal, complemented
23C2×#2343C211yesmaximal, characteristic, complemented
24C2×#525C2212yes—
25C22×#117C2211yescharacteristic
26#2855C2212yes—
27#2855C2212yes—
28#2854C2212yes—
29#2854C2212yes—
30#2853C2214yes—
31#2852C2214yes—
32#2847C2214yes—
33#2796C2214yes—
34#2787C2214yes—
35#2782C2214yes—
36#2777C2214yescomplemented
37#2776C2214yescomplemented
38#2776C2214yescomplemented
39#2773C2214yescomplemented
40#2773C2214yescomplemented
41#2772C2214yescomplemented
42#2770C2214yes—
43#2770C2214yescomplemented
44#2769C2214yescomplemented
45#2768C2214yescomplemented
46#2767C2214yescomplemented
47#2766C2214yescomplemented
48#2766C2214yescomplemented
49#2766C2214yescomplemented
50#2762C2214yescomplemented
51#2762C2214yescomplemented
52#2758C2214yescomplemented
53#2757C2214yes—
54#2756C2214yescomplemented
55#2755C2214yescomplemented
56#2753C2214yescomplemented
57#2749C2214yescomplemented
58#2747C2214yescomplemented
59#2747C2214yescomplemented
60#2746C2214yes—
61#2746C2214yescomplemented
62#2743C2214yescomplemented
63#2741C2214yescomplemented
64#2741C2214yescomplemented
65#2739C2214yescomplemented
66#2738C2214yescomplemented
67#2738C2214yescomplemented
68#2738C2214yescomplemented
69#2719C2214yescomplemented
70#2711C2214yes—
71#2708C2214yes—
72#2706C2214yescomplemented
73#2659C2211yescharacteristic
74#2656C2211yescharacteristic
75#2646C2214yes—
76#2646C2212yes—
77#2646C2214yes—
78#2646C2211yescharacteristic
79#2646C2211yescharacteristic
80#2646C2214yes—
81#2643C2214yes—
82#2639C2212yes—
83#2625C2212yes—
84#2625C2212yes—
85#2624C2212yes—
86#2624C2212yes—
87#2623C2214yes—
88#2611C2214yescomplemented
89#2606C2214yescomplemented
90#2597C2214yes—
91#2597C2214yescomplemented
92#2596C2214yescomplemented
93#2596C2214yescomplemented
94#2595C2214yes—
95#2591C2214yes—
96#2590C2214yescomplemented
97#2589C2214yescomplemented
98#2585C2214yescomplemented
99#2579C2214yes—
100#2578C2214yes—
101#2578C2214yescomplemented
102#2577C2214yes—
103#2576C2214yes—
104#2569C2214yes—
105#2569C2214yes—
106#2569C2214yescomplemented
107#2564C2214yes—
108#2559C2214yes—
109#2553C2214yescomplemented
110#2543C2214yes—
111#2533C2214yescomplemented
112#2533C2214yescomplemented
113#2533C2214yescomplemented
114#2533C2214yescomplemented
115#2532C2214yescomplemented
116#2532C2214yescomplemented
117#2531C2214yescomplemented
118#2530C2214yes—
119#2530C2214yescomplemented
120#2530C2214yescomplemented
121#2530C2214yescomplemented
122#2529C2214yescomplemented
123#2528C2214yescomplemented
124#2527C2214yescomplemented
125#2526C2214yescomplemented
126#2522C2214yescomplemented
127#2519C2214yescomplemented
128#2510C2214yes—
129#2510C2214yes—
130#2510C2214yes—
131#2510C2214yescomplemented
132#2505C2214yes—
133#2498C2214yes—
134#2498C2214yes—
135#2498C2214yes—
136#2498C2214yescomplemented
137#2493C2214yes—
138#2493C2214yes—
139#2493C2214yescomplemented
140#2487C2214yes—
141#2487C2214yes—
142#2486C2214yes—
143#2485C2214yes—
144#2485C2214yes—
145#2481C2214yes—
146#2479C2214yescomplemented
147#2478C2214yescomplemented
148#2476C2214yes—
149#2473C2214yes—
150#2444C2214yes—
151#2444C2214yes—
152#2443C2214yes—
153#2443C2214yes—
154#2442C2214yes—
155#2430C2214yes—
156#2425C2214yes—
157#2425C2214yes—
158#2412C2214yes—
159#2412C2214yes—
160C2×#400C2214yes—
161C2×#398C2214yes—
162#2378C2214yes—
163#2377C2214yes—
164#2364C2214yes—
165#2358C2214yes—
166#2358C2214yes—
167#2353C2214yes—
168#2353C2214yes—
169#2352C2214yes—
170#2349C2214yes—
171#2345C2214yes—
172#2343C2214yes—
173#2343C2214yes—
174#2343C2214yes—
175#2343C2214yes—
176#2343C2214yes—
177#2339C2214yes—
178#2329C2212yes—
179#2329C2212yes—
180#2325C2212yes—
181#2325C2214yes—
182#2325C2212yes—
183#2322C2214yes—
184#2322C2214yes—
185#2322C2214yes—
186#2319C2214yes—
187#2318C2214yes—
188#2318C2214yes—
189#2316C2212yes—
190#2316C2212yes—
191#2311C2212yes—
192#2311C2212yes—
193C4×#123C2214yes—
194#2290C2214yes—
195C2×#387C2212yes—
196C2×#387C2212yes—
197C2×#385C2214yes—
198C2×#385C2212yes—
199C2×#383C2211yescharacteristic
200C2×#382C2211yescharacteristic
201C2×#381C2211yescharacteristic
202C2×#380C2212yes—
203C2×C4×C4⋊C4C2211yescharacteristic
204C2×C4×C22⋊C4C2212yes—
205C2×#376C2211yescharacteristic
206C22×#95C2211yescharacteristic
207C22×#41C2312yes—
208C24×C4C2312yes—
209C24×C4C2311yescharacteristic
210C2×#126C2314yes—
211C2×#125C2314yes—
212#525—216no—
213C2×#123C2314yes—
214C2×#123C2314yes—
215C2×#123C2314yes—
216C2×#123C2314yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2312yes—
219C2×#121C2312yes—
220C2×#121C2312yes—
221C2×#121C2314yes—
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#120C2314yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2314yes—
231C2×#117—28no—
232C2×#117C2312yes—
233C2×#117C2312yes—
234C2×#117C2312yes—
235C2×#117C2312yes—
236C2×#117C2312yes—
237C2×#117C2314yes—
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2314yes—
244C22×C4⋊C4C2314yes—
245C22×C4⋊C4C2312yes—
246C22×C22⋊C4C2311yescharacteristic
247C22×C22⋊C4C2311yescharacteristic
248C22×C22⋊C4C2312yes—
249C22×C22⋊C4C2314yes—
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
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#399C2314yes—
289#399C2314yes—
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#397C2314yes—
311#397C2314yes—
312#397C2314yes—
313#397C2314yes—
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#396C2314yes—
328#396C2314yes—
329#396C2314yes—
330#395C2314yes—
331#394C2314yes—
332#394C2314yes—
333#394C2314yes—
334#394C2314yes—
335#394C2314yes—
336#394C2314yes—
337#394C2314yes—
338#394C2314yes—
339#394C2314yes—
340#393C2314yes—
341#392C2314yes—
342#391C2312yes—
343#391C2312yes—
344#391C2312yes—
345#391C2312yes—
346#391C2314yes—
347#391C2314yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2312yes—
352#390C2314yes—
353#390C2314yes—
354#389C2314yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#388C2314yes—
377#388C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2314yes—
383#388C2314yes—
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#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
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#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
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#386C2314yes—
478#386C2314yes—
479#386C2314yes—
480#386C2314yes—
481#386C2314yes—
482#386C2314yes—
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#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#383C2314yes—
511#383C2314yes—
512#383C2314yes—
513#383C2314yes—
514#383C2314yes—
515#383C2314yes—
516#383C2314yes—
517#382C2314yes—
518#382C2314yes—
519#382C2314yes—
520#382C2314yes—
521#382C2314yes—
522#381C2314yes—
523#381C2314yes—
524#381C2314yes—
525#381C2314yes—
526#381C2314yes—
527#381C2314yes—
528#381C2314yes—
529#380C2314yes—
530#380C2314yes—
531#380C2314yes—
532#380C2314yes—
533#380C2314yes—
534#380C2314yes—
535#380C2314yes—
536#380C2314yes—
537#380C2314yes—
538#380C2314yes—
539#380C2314yes—
540#380C2314yes—
541#380C2312yes—
542#380C2314yes—
543#380C2312yes—
544#380C2314yes—
545#380C2312yes—
546#380C2312yes—
547#380C2314yes—
548#380C2314yes—
549#380C2314yes—
550C4×C4⋊C4C2314yes—
551C4×C4⋊C4C2314yes—
552C4×C4⋊C4C2314yes—
553C4×C4⋊C4C2314yes—
554C4×C4⋊C4C2314yes—
555C4×C4⋊C4C2314yes—
556C4×C22⋊C4C2314yes—
557C4×C22⋊C4C2314yes—
558C4×C22⋊C4C2314yes—
559C4×C22⋊C4C2314yes—
560C4×C22⋊C4C2314yes—
561C4×C22⋊C4C2314yes—
562C4×C22⋊C4C2314yes—
563C4×C22⋊C4C2314yes—
564C4×C22⋊C4C2314yes—
565C4×C22⋊C4C2314yes—
566C4×C22⋊C4C2314yes—
567C4×C22⋊C4C2314yes—
568#376C2314yes—
569#376C2314yes—
570#376C2314yes—
571#376C2314yes—
572C2×#95C2314yes—
573C2×#95C2314yes—
574C2×#95C2314yes—
575C2×#95C2314yes—
576C2×#95C2312yes—
577C2×#95C2311yescharacteristic
578C2×#95C2311yescharacteristic
579C2×#95C2312yes—
580C2×#95C2314yes—
581C2×#95C2314yes—
582C2×#95C2312yes—
583C2×#95C2311yescharacteristic
584C2×#95C2311yescharacteristic
585C2×#95C2312yes—
586C2×#95C2312yes—
587C2×#95C2312yes—
588C25C2411yescharacteristic
589C2×#41—28no—
590C2×#41—44no—
591C2×#41—44no—
592C22×Q8C2412yes—
593C22×D4C2414yes—
594C22×D4C2414yes—
595C22×D4C2414yes—
596C22×D4C2412yes—
597C22×D4C2414yes—
598C23×C4—44no—
599C23×C4—44no—
600C23×C4—44no—
601C23×C4—82no—
602C23×C4#4118yes—
603C23×C4C2411yescharacteristic
604C23×C4C2411yescharacteristic
605C23×C4C2412yes—
606C23×C4C2414yes—
607C23×C4C2411yescharacteristic
608C23×C4C2412yes—
609C23×C4C2414yes—
610C23×C4C2411yescharacteristic
611C23×C4C2412yes—
612C23×C4C2414yes—
613C23×C4C2412yes—
614C23×C4C2412yes—
615C23×C4C2414yes—
616C23×C4C2414yes—
617C23×C4C2414yes—
618C23×C4C2414yes—
619C23×C4C2411yescharacteristic
620C23×C4C2412yes—
621C23×C4C2411yescharacteristic
622#126—84no—
623#125—84no—
624#123—216no—
625#123—48no—
626#123—48no—
627#123—84no—
628C22⋊Q8—28no—
629C22⋊Q8—28no—
630#121—28no—
631#121—28no—
632#121—48no—
633#121—48no—
634#121—84no—
635#120—216no—
636C4×D4—216no—
637C4×D4—216no—
638C4×D4—48no—
639C4×D4—48no—
640C4×D4—48no—
641C4×D4—48no—
642#117—28no—
643#117—28no—
644#117—28no—
645#117—28no—
646#117—28no—
647#117—84no—
648C2×C4⋊C4—24no—
649C2×C4⋊C4—24no—
650C2×C4⋊C4—44no—
651C2×C4⋊C4—44no—
652C2×C4⋊C4—44no—
653C2×C4⋊C4—48no—
654C2×C4⋊C4—84no—
655C2×C4⋊C4—82no—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C22⋊C4—24no—
700C2×C22⋊C4—24no—
701C2×C22⋊C4—44no—
702C2×C22⋊C4—48no—
703C2×C22⋊C4C2412yes—
704C2×C22⋊C4C2412yes—
705C2×C22⋊C4C2411yescharacteristic
706C2×C22⋊C4C2411yescharacteristic
707C2×C22⋊C4C2411yescharacteristic
708C2×C22⋊C4C2411yescharacteristic
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C42—24no—
741C2×C42—24no—
742C2×C42—44no—
743C2×C42—82no—
744C2×C42C2412yes—
745C2×C42C2412yes—
746C2×C42C2412yes—
747C2×C42C2412yes—
748C2×C42C2414yes—
749C2×C42C2414yes—
750C2×C42C2414yes—
751C2×C42C2414yes—
752C2×C42C2414yes—
753C2×C42C2414yes—
754C2×C42C2414yes—
755C2×C42C2414yes—
756C2×C42C2414yes—
757C2×C42C2414yes—
758C2×C42C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
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—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821C24—24no—
822C24—24no—
823C24—41no—
824C24—41no—
825C24C2×#4114yes—
826C24C2514yes—
827C24C2511yescharacteristic
828C24C2511yescharacteristic
829C24C2511yescharacteristic
830#41—816no—
831C2×Q8—24no—
832C2×Q8—42no—
833C2×Q8—42no—
834C2×D4—28no—
835C2×D4—28no—
836C2×D4—28no—
837C2×D4—28no—
838C2×D4—28no—
839C2×D4—28no—
840C2×D4—28no—
841C2×D4—24no—
842C2×D4—44no—
843C2×D4—44no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—44no—
847C2×D4—44no—
848C2×D4—44no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—28no—
860C22×C4—28no—
861C22×C4—24no—
862C22×C4—28no—
863C22×C4—24no—
864C22×C4—28no—
865C22×C4—41no—
866C22×C4—42no—
867C22×C4—41no—
868C22×C4—416no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—42no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—42no—
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—42no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—816no—
900C22×C4C2×#4118yes—
901C22×C4C2×#4114yes—
902C22×C4C2×#4114yes—
903C22×C4C2×#4118yes—
904C22×C4C2514yes—
905C22×C4C2514yes—
906C22×C4C2514yes—
907C22×C4C2514yes—
908C22×C4C2514yes—
909C22×C4C2514yes—
910C22×C4C2512yes—
911C22×C4C2512yes—
912C22×C4C2514yes—
913C22×C4C2514yes—
914C22×C4C2514yes—
915C22×C4C2511yescharacteristic
916C22×C4C2511yescharacteristic
917C22×C4C2511yescharacteristic
918C22×C4C2511yescharacteristic
919C22×C4C2514yes—
920C22×C4C2514yes—
921C22×C4C2512yes—
922C22×C4C2512yes—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—24no—
926C4⋊C4—24no—
927C4⋊C4—24no—
928C4⋊C4—24no—
929C4⋊C4—28no—
930C4⋊C4—28no—
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—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C22⋊C4—24no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—24no—
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—28no—
973C22⋊C4—28no—
974C22⋊C4—28no—
975C22⋊C4—28no—
976C22⋊C4—28no—
977C22⋊C4—28no—
978C22⋊C4—28no—
979C22⋊C4—28no—
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⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C42—24no—
1004C42—24no—
1005C42—24no—
1006C42—24no—
1007C42—28no—
1008C42—44no—
1009C42—44no—
1010C42—44no—
1011C42—44no—
1012C42—44no—
1013C42—44no—
1014C42—44no—
1015C42—44no—
1016C42—44no—
1017C42—44no—
1018C23—22no—
1019C23—22no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—22no—
1025C23—22no—
1026C23—21no—
1027C23—21no—
1028C23—28no—
1029C23—28no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23—24no—
1034C23—24no—
1035C23—24no—
1036C23—24no—
1037C23—44no—
1038C23—48no—
1039C23—48no—
1040C23C22×#4112yes—
1041C23C22×#4112yes—
1042C23C22×#4112yes—
1043C23#58514yes—
1044C23#58514yes—
1045C23C2611yescharacteristic
1046Q8—84no—
1047D4—416no—
1048D4—416no—
1049D4—84no—
1050D4—88no—
1051D4—164no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—216no—
1057C2×C4—22no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
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—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—21no—
1096C2×C4—24no—
1097C2×C4—21no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—21no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—21no—
1106C2×C4—44no—
1107C2×C4—48no—
1108C2×C4—44no—
1109C2×C4—44no—
1110C2×C4—44no—
1111C2×C4—48no—
1112C2×C4—44no—
1113C2×C4—44no—
1114C2×C4—88no—
1115C2×C4—88no—
1116C2×C4—84no—
1117C2×C4—88no—
1118C2×C4—84no—
1119C2×C4—88no—
1120C2×C4—84no—
1121C2×C4—88no—
1122C2×C4—88no—
1123C2×C4—164no—
1124C2×C4C22×#4114yes—
1125C2×C4C22×#4114yes—
1126C22—22no—
1127C22—22no—
1128C22—22no—
1129C22—22no—
1130C22—24no—
1131C22—24no—
1132C22—24no—
1133C22—24no—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—416no—
1138C22—42no—
1139C22—42no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22—44no—
1144C22—44no—
1145C22—44no—
1146C22—44no—
1147C22#349114yes—
1148C22#351214yes—
1149C22C23×#4111yescharacteristic
1150C22C2×#58512yes—
1151C22C2×#58512yes—
1152C22H(7,𝔽2)11yescharacteristic
1153C222−1+611yescharacteristic
1154C4—24no—
1155C4—24no—
1156C4—44no—
1157C4—42no—
1158C4—41no—
1159C4—41no—
1160C4—44no—
1161C4—42no—
1162C4—41no—
1163C4—41no—
1164C4—44no—
1165C4—44no—
1166C4—44no—
1167C4—44no—
1168C4—44no—
1169C4—44no—
1170C4—44no—
1171C4—44no—
1172C4—44no—
1173C2—24no—
1174C2—24no—
1175C2—42no—
1176C2—84no—
1177C2C2×#349111yescharacteristic
1178C2C2×#351211yescharacteristic
1179C2#6285611yescharacteristic
1180C2#6290912yes—
1181C2#6293312yes—
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. #50197C2semidirect
2. #50195C2semidirect
3. #48809C2semidirect
4. #48807C2semidirect
5. #44476C2semidirect
6. #44460C2semidirect
7. #44000C2semidirect
8. #43934C2semidirect
9. #39254C2semidirect
10. #38223C2semidirect
11. #38121C2semidirect
12. #36979C2semidirect
13. #36978C2semidirect
14. #36977C2semidirect
15. #36976C2semidirect
16. #36243C2semidirect
17. #35263C2semidirect
18. #35099C2semidirect
20. #35042C2semidirect
21. C2×#2646C2semidirect
22. #34386C2semidirect
23. C2×#2343C2semidirect
36. #2777C22semidirect
37. #2776C22semidirect
38. #2776C22semidirect
39. #2773C22semidirect
40. #2773C22semidirect
41. #2772C22semidirect
43. #2770C22semidirect
44. #2769C22semidirect
45. #2768C22semidirect
46. #2767C22semidirect
47. #2766C22semidirect
48. #2766C22semidirect
49. #2766C22semidirect
50. #2762C22semidirect
51. #2762C22semidirect
52. #2758C22semidirect
54. #2756C22semidirect
55. #2755C22semidirect
56. #2753C22semidirect
57. #2749C22semidirect
58. #2747C22semidirect
59. #2747C22semidirect
61. #2746C22semidirect
62. #2743C22semidirect
63. #2741C22semidirect
64. #2741C22semidirect
65. #2739C22semidirect
66. #2738C22semidirect
67. #2738C22semidirect
68. #2738C22semidirect
69. #2719C22semidirect
72. #2706C22semidirect
88. #2611C22semidirect
89. #2606C22semidirect
91. #2597C22semidirect
92. #2596C22semidirect
93. #2596C22semidirect
96. #2590C22semidirect
97. #2589C22semidirect
98. #2585C22semidirect
101. #2578C22semidirect
106. #2569C22semidirect
109. #2553C22semidirect
111. #2533C22semidirect
112. #2533C22semidirect
113. #2533C22semidirect
114. #2533C22semidirect
115. #2532C22semidirect
116. #2532C22semidirect
117. #2531C22semidirect
119. #2530C22semidirect
120. #2530C22semidirect
121. #2530C22semidirect
122. #2529C22semidirect
123. #2528C22semidirect
124. #2527C22semidirect
125. #2526C22semidirect
126. #2522C22semidirect
127. #2519C22semidirect
131. #2510C22semidirect
136. #2498C22semidirect
139. #2493C22semidirect
146. #2479C22semidirect
147. #2478C22semidirect

Maximal subgroups

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

subgroupindex
#501972
#501952
#488092
#488072
#444762
#444602
#440002
#439342
#392542
#382232
#381212
#369792
#369782
#369772
#369762
#362432
#352632
#350992
#350512
#350422
C2×#26462
#343862
C2×#23432