Finite Group Databasebeta

← #7713162

Subgroups — #7713162

Order 512.

4410 conjugacy classes of subgroups.

The subgroup lattice has 1165 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48891C214yesmaximal, complemented
2#48890C214yesmaximal, complemented
3#48020C214yesmaximal, complemented
4#48019C214yesmaximal, complemented
5#47233C214yesmaximal, complemented
6#47011C214yesmaximal, complemented
7#46467C214yesmaximal, complemented
8#46408C214yesmaximal, complemented
9#39254C214yesmaximal, complemented
10#39050C214yesmaximal, complemented
11#38221C214yesmaximal, complemented
12#38210C214yesmaximal, complemented
13#37442C212yesmaximal, complemented
14#36762C212yesmaximal, complemented
15#36761C212yesmaximal, complemented
16#35098C212yesmaximal, complemented
17#35035C212yesmaximal, complemented
18#35032C211yesmaximal, characteristic
19#35020C211yesmaximal, characteristic, complemented
20#34386C212yesmaximal, complemented
21C2×#2332C211yesmaximal, characteristic, complemented
22C2×#525C2212yes—
23C22×C22⋊Q8C2211yescharacteristic
24#2857C2211yescharacteristic
25#2856C2211yescharacteristic
26#2853C2214yes—
27#2852C2214yes—
28#2851C2211yescharacteristic
29#2851C2212yes—
30#2851C2211yescharacteristic
31#2850C2212yes—
32#2814C2214yes—
33#2814C2214yes—
34#2802C2214yescomplemented
35#2800C2214yescomplemented
36#2796C2214yes—
37#2794C2214yescomplemented
38#2791C2214yescomplemented
39#2789C2214yescomplemented
40#2787C2214yes—
41#2786C2214yes—
42#2786C2214yescomplemented
43#2781C2214yes—
44#2780C2214yescomplemented
45#2779C2214yes—
46#2778C2214yes—
47#2778C2214yes—
48#2776C2214yescomplemented
49#2776C2214yescomplemented
50#2772C2214yescomplemented
51#2770C2214yes—
52#2770C2214yescomplemented
53#2766C2214yescomplemented
54#2766C2214yescomplemented
55#2764C2214yescomplemented
56#2762C2214yescomplemented
57#2761C2214yescomplemented
58#2758C2214yescomplemented
59#2758C2214yescomplemented
60#2756C2214yes—
61#2754C2214yescomplemented
62#2753C2214yes—
63#2750C2214yes—
64#2747C2214yes—
65#2747C2214yes—
66#2747C2214yescomplemented
67#2746C2214yes—
68#2746C2214yescomplemented
69#2741C2214yes—
70#2741C2214yes—
71#2741C2214yescomplemented
72#2740C2214yescomplemented
73#2739C2214yescomplemented
74#2719C2214yescomplemented
75#2713C2214yescomplemented
76#2709C2214yescomplemented
77#2707C2214yescomplemented
78#2702C2214yescomplemented
79#2698C2214yescomplemented
80#2690C2214yescomplemented
81#2687C2214yescomplemented
82#2659C2214yes—
83#2646C2214yes—
84#2643C2214yes—
85#2639C2214yes—
86#2627C2212yes—
87#2627C2212yes—
88#2625C2214yes—
89#2623C2214yes—
90#2618C2212yes—
91#2618C2212yes—
92#2617C2214yes—
93#2616C2214yes—
94#2612C2214yescomplemented
95#2606C2214yescomplemented
96#2602C2214yes—
97#2602C2214yes—
98#2602C2214yes—
99#2598C2214yes—
100#2597C2214yes—
101#2596C2214yescomplemented
102#2595C2214yescomplemented
103#2594C2214yescomplemented
104#2588C2214yescomplemented
105#2587C2214yescomplemented
106#2585C2214yescomplemented
107#2578C2214yes—
108#2578C2214yes—
109#2578C2214yescomplemented
110#2577C2214yes—
111#2569C2214yes—
112#2569C2214yes—
113#2569C2214yescomplemented
114#2562C2214yes—
115#2556C2214yescomplemented
116#2532C2214yescomplemented
117#2531C2214yes—
118#2530C2214yes—
119#2530C2214yescomplemented
120#2529C2214yescomplemented
121#2528C2214yescomplemented
122#2527C2214yescomplemented
123#2525C2214yescomplemented
124#2524C2214yescomplemented
125#2522C2214yescomplemented
126#2522C2214yescomplemented
127#2521C2214yescomplemented
128#2520C2214yescomplemented
129#2520C2214yescomplemented
130#2519C2214yescomplemented
131#2516C2214yescomplemented
132#2515C2214yescomplemented
133#2510C2214yescomplemented
134#2505C2214yes—
135#2500C2212yes—
136#2499C2212yes—
137#2495C2214yes—
138#2494C2214yes—
139#2493C2214yes—
140#2493C2214yes—
141#2488C2214yescomplemented
142#2486C2214yes—
143#2485C2214yes—
144#2477C2214yescomplemented
145#2475C2214yescomplemented
146#2474C2214yescomplemented
147#2473C2214yes—
148#2468C2214yes—
149#2467C2214yes—
150#2460C2214yes—
151#2457C2214yes—
152#2444C2214yes—
153#2443C2214yes—
154#2442C2212yes—
155#2442C2212yes—
156#2442C2212yes—
157#2442C2212yes—
158#2438C2214yescomplemented
159#2432C2212yes—
160#2431C2212yes—
161#2425C2214yes—
162#2425C2214yes—
163#2417C2214yes—
164#2417C2214yes—
165#2412C2214yes—
166#2412C2214yes—
167#2409C2214yes—
168#2378C2214yes—
169#2377C2214yes—
170#2358C2214yes—
171#2358C2214yes—
172#2353C2214yes—
173#2349C2214yes—
174#2343C2214yes—
175#2339C2214yes—
176#2332C2214yes—
177#2332C2214yes—
178#2332C2214yes—
179#2332C2214yes—
180#2329C2212yes—
181#2329C2212yes—
182#2325C2212yes—
183#2325C2214yes—
184#2325C2212yes—
185#2322C2214yes—
186#2322C2214yes—
187#2322C2214yes—
188#2319C2214yes—
189#2318C2214yes—
190#2318C2214yes—
191#2315C2214yes—
192C4×#123C2214yes—
193C2×#391C2212yes—
194#2290C2214yes—
195C2×#388C2212yes—
196C2×#388C2212yes—
197C2×#387C2212yes—
198C2×#387C2212yes—
199C2×#381C2211yescharacteristic
200C2×#380C2212yes—
201C2×C4×C4⋊C4C2212yes—
202C2×C4×C22⋊C4C2211yescharacteristic
203C22×#41C2312yes—
204C23×Q8C2311yescharacteristic
205C24×C4C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#127C2311yescharacteristic
208C2×#126C2314yes—
209C2×#125C2314yes—
210C2×#125C2312yes—
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#124C2312yes—
214#525—216no—
215C2×#123C2314yes—
216C2×#123C2314yes—
217C2×#123C2314yes—
218C2×#123C2314yes—
219C2×C22⋊Q8—28no—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×#121C2312yes—
227C2×#121C2312yes—
228C2×#121C2314yes—
229C2×#120C2314yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×#117C2312yes—
237C2×#117C2314yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2312yes—
244C22×C22⋊C4C2312yes—
245C22×C22⋊C4C2314yes—
246C22×C22⋊C4C2312yes—
247C22×C22⋊C4C2311yescharacteristic
248C22×C22⋊C4C2311yescharacteristic
249C22×C42C2312yes—
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252C22×C42C2312yes—
253#401C2314yes—
254#401C2314yes—
255#401C2314yes—
256#400C2314yes—
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#399C2314yes—
279#399C2314yes—
280#399C2314yes—
281#398C2314yes—
282#398C2314yes—
283#398C2314yes—
284#398C2314yes—
285#398C2314yes—
286#398C2314yes—
287#398C2314yes—
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#397C2314yes—
303#397C2314yes—
304#397C2314yes—
305#397C2314yes—
306#397C2314yes—
307#397C2314yes—
308#397C2314yes—
309#397C2314yes—
310#397C2314yes—
311#397C2314yes—
312#397C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#397C2314yes—
318#397C2314yes—
319#397C2314yes—
320#396C2314yes—
321#396C2314yes—
322#396C2314yes—
323#396C2314yes—
324#396C2314yes—
325#396C2314yes—
326#396C2314yes—
327#395C2314yes—
328#395C2314yes—
329#395C2314yes—
330#395C2314yes—
331#394C2314yes—
332#394C2314yes—
333#394C2314yes—
334#394C2314yes—
335#394C2314yes—
336#394C2314yes—
337#394C2314yes—
338#394C2314yes—
339#394C2314yes—
340#394C2314yes—
341#394C2314yes—
342#394C2314yes—
343#394C2314yes—
344#394C2314yes—
345#393C2314yes—
346#393C2314yes—
347#392C2314yes—
348#392C2314yes—
349#391C2314yes—
350#391C2314yes—
351#391C2314yes—
352#391C2314yes—
353#391C2314yes—
354#391C2314yes—
355#391C2312yes—
356#391C2312yes—
357#391C2314yes—
358#391C2314yes—
359#390C2314yes—
360#390C2314yes—
361#390C2312yes—
362#390C2314yes—
363#390C2312yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
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#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
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#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
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#386C2314yes—
484#386C2314yes—
485#386C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
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#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#384C2311yescharacteristic
514#384C2311yescharacteristic
515#383C2314yes—
516#383C2314yes—
517#383C2314yes—
518#383C2314yes—
519#383C2314yes—
520#382C2314yes—
521#382C2314yes—
522#382C2312yes—
523#382C2312yes—
524#382C2311yescharacteristic
525#382C2311yescharacteristic
526#382C2314yes—
527#381C2314yes—
528#381C2314yes—
529#381C2314yes—
530#381C2314yes—
531#381C2314yes—
532#381C2314yes—
533#381C2314yes—
534#380C2314yes—
535#380C2314yes—
536#380C2314yes—
537#380C2314yes—
538#380C2314yes—
539#380C2314yes—
540#380C2314yes—
541#380C2314yes—
542#380C2314yes—
543#380C2314yes—
544#380C2312yes—
545#380C2312yes—
546#380C2314yes—
547#380C2314yes—
548#380C2312yes—
549#380C2312yes—
550#380C2314yes—
551#380C2314yes—
552#380C2314yes—
553#380C2314yes—
554#380C2314yes—
555C4×C4⋊C4C2314yes—
556C4×C4⋊C4C2314yes—
557C4×C4⋊C4C2314yes—
558C4×C4⋊C4C2314yes—
559C4×C4⋊C4C2314yes—
560C4×C4⋊C4C2314yes—
561C4×C4⋊C4C2314yes—
562C4×C4⋊C4C2314yes—
563C4×C22⋊C4C2312yes—
564C4×C22⋊C4C2312yes—
565C4×C22⋊C4C2314yes—
566C4×C22⋊C4C2314yes—
567C4×C22⋊C4C2314yes—
568C4×C22⋊C4C2314yes—
569C4×C22⋊C4C2314yes—
570C4×C22⋊C4C2314yes—
571C4×C22⋊C4C2314yes—
572C4×C22⋊C4C2314yes—
573C4×C22⋊C4C2312yes—
574C4×C22⋊C4C2312yes—
575#376C2314yes—
576#376C2314yes—
577C2×#95C2314yes—
578C2×#95C2314yes—
579C2×#95C2312yes—
580C2×#95C2312yes—
581C2×#95C2312yes—
582C2×#95C2312yes—
583C2×#95C2312yes—
584C2×#95C2312yes—
585C2×#95C2312yes—
586C25C2411yescharacteristic
587C2×#41—28no—
588C2×#41—82no—
589C2×#41—82no—
590C22×Q8—24no—
591C22×Q8—81no—
592C22×Q8—81no—
593C22×Q8C2414yes—
594C22×Q8C2412yes—
595C22×D4C2414yes—
596C22×D4C2414yes—
597C22×D4C2414yes—
598C22×D4C2412yes—
599C22×D4C2414yes—
600C23×C4—81no—
601C23×C4—81no—
602C23×C4#4118yes—
603C23×C4C2412yes—
604C23×C4C2412yes—
605C23×C4C2412yes—
606C23×C4C2412yes—
607C23×C4C2412yes—
608C23×C4C2412yes—
609C23×C4C2414yes—
610C23×C4C2414yes—
611C23×C4C2414yes—
612C23×C4C2414yes—
613C23×C4C2414yes—
614C23×C4C2412yes—
615C23×C4C2411yescharacteristic
616C23×C4C2411yescharacteristic
617C23×C4C2412yes—
618C4⋊Q8—81no—
619#127—81no—
620#126—84no—
621#125—81no—
622#125—82no—
623#125—81no—
624#125—84no—
625#124—82no—
626#123—216no—
627#123—48no—
628#123—48no—
629#123—84no—
630C22⋊Q8—216no—
631C22⋊Q8—216no—
632C22⋊Q8—28no—
633C22⋊Q8—28no—
634C22⋊Q8—84no—
635C22⋊Q8—84no—
636#121—28no—
637#121—28no—
638#121—48no—
639#120—216no—
640C4×D4—216no—
641C4×D4—216no—
642C4×D4—48no—
643C4×D4—48no—
644C4×D4—84no—
645C4×D4—84no—
646#117—28no—
647#117—84no—
648C2×C4⋊C4—24no—
649C2×C4⋊C4—28no—
650C2×C4⋊C4—44no—
651C2×C4⋊C4—82no—
652C2×C4⋊C4—82no—
653C2×C4⋊C4—82no—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
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×C22⋊C4—28no—
697C2×C22⋊C4—48no—
698C2×C22⋊C4—44no—
699C2×C22⋊C4—81no—
700C2×C22⋊C4—81no—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2412yes—
713C2×C22⋊C4C2412yes—
714C2×C22⋊C4C2412yes—
715C2×C22⋊C4C2412yes—
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×C42—44no—
739C2×C42—82no—
740C2×C42—81no—
741C2×C42—81no—
742C2×C42C2414yes—
743C2×C42C2414yes—
744C2×C42C2414yes—
745C2×C42C2414yes—
746C2×C42C2414yes—
747C2×C42C2414yes—
748C2×C42C2412yes—
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2412yes—
752C2×C42C2414yes—
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2414yes—
756C2×C42C2414yes—
757C2×C42C2414yes—
758C2×C42C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2412yes—
764#95C2412yes—
765#95C2412yes—
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—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821C24—24no—
822C24—41no—
823C24—41no—
824C24—42no—
825C24C2×#4114yes—
826C24C2514yes—
827C24C2512yes—
828C24C2511yescharacteristic
829#41—816no—
830C2×Q8—28no—
831C2×Q8—24no—
832C2×Q8—44no—
833C2×Q8—44no—
834C2×Q8—42no—
835C2×Q8—42no—
836C2×Q8—88no—
837C2×D4—28no—
838C2×D4—28no—
839C2×D4—28no—
840C2×D4—28no—
841C2×D4—28no—
842C2×D4—24no—
843C2×D4—44no—
844C2×D4—44no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—44no—
848C2×D4—44no—
849C2×D4—44no—
850C2×D4—44no—
851C2×D4—44no—
852C22×C4—24no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—28no—
861C22×C4—42no—
862C22×C4—41no—
863C22×C4—41no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—42no—
881C22×C4—42no—
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—44no—
892C22×C4—44no—
893C22×C4—88no—
894C22×C4C2×#4114yes—
895C22×C4C2×#4114yes—
896C22×C4C2×#4118yes—
897C22×C4C2×#4118yes—
898C22×C4C2514yes—
899C22×C4C2512yes—
900C22×C4C2514yes—
901C22×C4C2514yes—
902C22×C4C2514yes—
903C22×C4C2514yes—
904C22×C4C2512yes—
905C22×C4C2512yes—
906C22×C4C2514yes—
907C22×C4C2514yes—
908C22×C4C2514yes—
909C22×C4C2514yes—
910C22×C4C2512yes—
911C22×C4C2514yes—
912C22×C4C2514yes—
913C22×C4C2511yescharacteristic
914C22×C4C2512yes—
915C22×C4C2511yescharacteristic
916C4⋊C4—28no—
917C4⋊C4—28no—
918C4⋊C4—28no—
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—28no—
922C4⋊C4—28no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
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—
958C22⋊C4—28no—
959C22⋊C4—28no—
960C22⋊C4—28no—
961C22⋊C4—28no—
962C22⋊C4—28no—
963C22⋊C4—28no—
964C22⋊C4—28no—
965C22⋊C4—28no—
966C22⋊C4—28no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
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—
995C42—28no—
996C42—44no—
997C42—44no—
998C42—44no—
999C42—42no—
1000C42—41no—
1001C42—41no—
1002C42—42no—
1003C42—44no—
1004C42—41no—
1005C42—41no—
1006C42—44no—
1007C42—44no—
1008C42—44no—
1009C42—44no—
1010C42—44no—
1011C42—44no—
1012C23—21no—
1013C23—21no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—28no—
1022C23—24no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—24no—
1029C23—44no—
1030C23—44no—
1031C23—84no—
1032C23—84no—
1033C23C22×#4114yes—
1034C23C22×#4112yes—
1035C23#58514yes—
1036C23C2611yescharacteristic
1037Q8—88no—
1038Q8—84no—
1039D4—416no—
1040D4—416no—
1041D4—84no—
1042D4—88no—
1043D4—164no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—48no—
1096C2×C4—44no—
1097C2×C4—44no—
1098C2×C4—48no—
1099C2×C4—48no—
1100C2×C4—48no—
1101C2×C4—48no—
1102C2×C4—88no—
1103C2×C4—84no—
1104C2×C4—84no—
1105C2×C4—84no—
1106C2×C4—88no—
1107C2×C4—164no—
1108C2×C4—164no—
1109C2×C4—164no—
1110C2×C4C22×#4114yes—
1111C2×C4C22×#4112yes—
1112C2×C4C22×#4112yes—
1113C22—22no—
1114C22—22no—
1115C22—24no—
1116C22—24no—
1117C22—24no—
1118C22—24no—
1119C22—24no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—44no—
1125C22—44no—
1126C22—44no—
1127C22—44no—
1128C22—44no—
1129C22—44no—
1130C22—44no—
1131C22—88no—
1132C22#351214yes—
1133C22C23×#4111yescharacteristic
1134C22C2×#58512yes—
1135C22H(7,𝔽2)11yescharacteristic
1136C22H(7,𝔽2)11yescharacteristic
1137C222−1+612yes—
1138C4—24no—
1139C4—22no—
1140C4—22no—
1141C4—44no—
1142C4—44no—
1143C4—44no—
1144C4—44no—
1145C4—44no—
1146C4—42no—
1147C4—42no—
1148C4—44no—
1149C4—44no—
1150C4—44no—
1151C4—42no—
1152C4—44no—
1153C4—42no—
1154C4—44no—
1155C4—44no—
1156C2—24no—
1157C2—44no—
1158C2—84no—
1159C2C2×#351211yescharacteristic
1160C2#6284411yescharacteristic
1161C2#6286011yescharacteristic
1162C2#6286812yes—
1163C2#6287212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35032C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #48891C2semidirect
2. #48890C2semidirect
3. #48020C2semidirect
4. #48019C2semidirect
5. #47233C2semidirect
6. #47011C2semidirect
7. #46467C2semidirect
8. #46408C2semidirect
9. #39254C2semidirect
10. #39050C2semidirect
11. #38221C2semidirect
12. #38210C2semidirect
13. #37442C2semidirect
14. #36762C2semidirect
15. #36761C2semidirect
16. #35098C2semidirect
17. #35035C2semidirect
19. #35020C2semidirect
20. #34386C2semidirect
21. C2×#2332C2semidirect
34. #2802C22semidirect
35. #2800C22semidirect
37. #2794C22semidirect
38. #2791C22semidirect
39. #2789C22semidirect
42. #2786C22semidirect
44. #2780C22semidirect
48. #2776C22semidirect
49. #2776C22semidirect
50. #2772C22semidirect
52. #2770C22semidirect
53. #2766C22semidirect
54. #2766C22semidirect
55. #2764C22semidirect
56. #2762C22semidirect
57. #2761C22semidirect
58. #2758C22semidirect
59. #2758C22semidirect
61. #2754C22semidirect
66. #2747C22semidirect
68. #2746C22semidirect
71. #2741C22semidirect
72. #2740C22semidirect
73. #2739C22semidirect
74. #2719C22semidirect
75. #2713C22semidirect
76. #2709C22semidirect
77. #2707C22semidirect
78. #2702C22semidirect
79. #2698C22semidirect
80. #2690C22semidirect
81. #2687C22semidirect
94. #2612C22semidirect
95. #2606C22semidirect
101. #2596C22semidirect
102. #2595C22semidirect
103. #2594C22semidirect
104. #2588C22semidirect
105. #2587C22semidirect
106. #2585C22semidirect
109. #2578C22semidirect
113. #2569C22semidirect
115. #2556C22semidirect
116. #2532C22semidirect
119. #2530C22semidirect
120. #2529C22semidirect
121. #2528C22semidirect
122. #2527C22semidirect
123. #2525C22semidirect
124. #2524C22semidirect
125. #2522C22semidirect
126. #2522C22semidirect
127. #2521C22semidirect
128. #2520C22semidirect
129. #2520C22semidirect
130. #2519C22semidirect
131. #2516C22semidirect
132. #2515C22semidirect
133. #2510C22semidirect
141. #2488C22semidirect
144. #2477C22semidirect
145. #2475C22semidirect
146. #2474C22semidirect
158. #2438C22semidirect

Maximal subgroups

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

subgroupindex
#488912
#488902
#480202
#480192
#472332
#470112
#464672
#464082
#392542
#390502
#382212
#382102
#374422
#367622
#367612
#350982
#350352
#350322
#350202
#343862
C2×#23322