Finite Group Databasebeta

← #7710584

Subgroups — #7710584

Order 512.

4516 conjugacy classes of subgroups.

The subgroup lattice has 1265 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59344C214yesmaximal, complemented
2#59343C214yesmaximal, complemented
3#46138C214yesmaximal, complemented
4#45981C214yesmaximal, complemented
5#39601C212yesmaximal, complemented
6#39473C212yesmaximal, complemented
7#37995C214yesmaximal, complemented
8#37992C214yesmaximal, complemented
9#37927C214yesmaximal, complemented
10#37926C214yesmaximal, complemented
11#37854C214yesmaximal, complemented
12#37562C211yesmaximal, characteristic, complemented
13#37557C211yesmaximal, characteristic, complemented
14#36732C212yesmaximal, complemented
15#36730C212yesmaximal
16#36625C211yesmaximal, characteristic, complemented
17#36621C211yesmaximal, characteristic
18#36531C212yesmaximal, complemented
19#36351C214yesmaximal, complemented
20#36338C212yesmaximal, complemented
21#35042C212yesmaximal, complemented
22#35013C212yesmaximal, complemented
23#34401C211yesmaximal, characteristic, complemented
24#34389C211yesmaximal, characteristic, complemented
25C2×#2283C211yesmaximal, characteristic, complemented
26C2×#533C2211yescharacteristic
27C2×#529C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2857C2212yes—
30#2857C2212yes—
31#2855C2211yescharacteristic
32#2855C2212yes—
33#2855C2212yes—
34#2854C2211yescharacteristic
35#2853C2212yes—
36#2852C2214yes—
37#2852C2214yes—
38#2851C2212yes—
39#2851C2214yes—
40#2851C2214yes—
41#2850C2212yes—
42#2849C2212yes—
43#2848C2211yescharacteristic
44#2848C2212yes—
45#2848C2212yes—
46#2847C2211yescharacteristic
47#2843C2214yescomplemented
48#2821C2212yescomplemented
49#2821C2212yescomplemented
50#2774C2214yescomplemented
51#2773C2214yescomplemented
52#2768C2214yescomplemented
53#2767C2214yescomplemented
54#2763C2214yescomplemented
55#2762C2214yescomplemented
56#2755C2214yescomplemented
57#2754C2214yescomplemented
58#2748C2214yes—
59#2747C2214yes—
60#2747C2214yes—
61#2746C2214yes—
62#2745C2214yes—
63#2744C2214yes—
64#2744C2214yes—
65#2742C2214yes—
66#2741C2214yes—
67#2741C2214yes—
68#2739C2214yes—
69#2739C2214yes—
70#2738C2214yes—
71#2737C2214yes—
72#2722C2214yes—
73#2717C2214yes—
74#2701C2214yes—
75#2700C2214yes—
76#2698C2214yes—
77#2698C2214yes—
78#2689C2214yes—
79#2689C2214yes—
80#2687C2214yes—
81#2686C2214yes—
82#2666C2214yescomplemented
83#2666C2214yescomplemented
84#2659C2212yes—
85#2659C2212yes—
86#2646C2212yes—
87#2639C2212yes—
88#2634C2212yescomplemented
89#2634C2212yescomplemented
90#2633C2212yescomplemented
91#2632C2212yescomplemented
92#2627C2214yes—
93#2623C2214yes—
94#2612C2214yescomplemented
95#2611C2214yescomplemented
96#2606C2214yescomplemented
97#2606C2212yescomplemented
98#2605C2212yescomplemented
99#2604C2214yescomplemented
100#2599C2214yescomplemented
101#2597C2214yescomplemented
102#2596C2214yescomplemented
103#2590C2214yescomplemented
104#2589C2214yescomplemented
105#2586C2214yescomplemented
106#2586C2214yescomplemented
107#2585C2214yescomplemented
108#2585C2214yescomplemented
109#2578C2214yes—
110#2577C2214yes—
111#2577C2214yes—
112#2575C2214yescomplemented
113#2574C2214yes—
114#2574C2214yescomplemented
115#2569C2212yes—
116#2564C2212yes—
117#2564C2212yes—
118#2560C2214yes—
119#2556C2214yes—
120#2553C2214yes—
121#2553C2214yes—
122#2549C2212yes—
123#2533C2214yescomplemented
124#2533C2214yescomplemented
125#2533C2214yescomplemented
126#2532C2214yescomplemented
127#2532C2214yescomplemented
128#2531C2214yes—
129#2530C2214yes—
130#2530C2214yes—
131#2530C2214yescomplemented
132#2529C2214yescomplemented
133#2529C2214yescomplemented
134#2528C2214yescomplemented
135#2528C2214yescomplemented
136#2528C2214yescomplemented
137#2524C2214yescomplemented
138#2523C2214yes—
139#2522C2214yes—
140#2521C2214yes—
141#2521C2214yes—
142#2520C2214yescomplemented
143#2520C2214yescomplemented
144#2520C2214yescomplemented
145#2517C2214yes—
146#2517C2214yescomplemented
147#2510C2214yes—
148#2508C2214yescomplemented
149#2505C2214yes—
150#2505C2214yes—
151#2505C2214yescomplemented
152#2498C2214yes—
153#2480C2214yes—
154#2480C2214yes—
155#2479C2214yescomplemented
156#2478C2214yescomplemented
157#2477C2214yes—
158#2472C2214yes—
159#2466C2214yes—
160#2465C2214yes—
161#2462C2214yescomplemented
162#2462C2214yescomplemented
163#2460C2214yes—
164#2450C2214yes—
165#2438C2214yes—
166#2418C2214yes—
167#2383C2214yescomplemented
168#2381C2212yescomplemented
169#2381C2212yescomplemented
170#2373C2214yes—
171#2373C2214yes—
172#2373C2214yescomplemented
173#2371C2214yescomplemented
174#2368C2212yes—
175#2368C2212yes—
176#2367C2214yes—
177#2359C2214yes—
178#2359C2214yes—
179#2356C2214yescomplemented
180#2356C2214yescomplemented
181#2353C2212yes—
182#2349C2212yes—
183#2347C2212yescomplemented
184#2346C2214yescomplemented
185#2343C2214yes—
186#2343C2212yescomplemented
187#2337C2212yescomplemented
188#2336C2212yescomplemented
189#2336C2214yescomplemented
190#2329C2212yes—
191#2329C2212yes—
192#2329C2212yes—
193#2325C2212yes—
194#2322C2214yes—
195#2320C2214yescomplemented
196#2320C2212yescomplemented
197#2318C2212yescomplemented
198#2313C2214yes—
199C4×C22⋊Q8C2212yes—
200C4×C22⋊Q8C2214yes—
201C4×C22⋊Q8C2212yes—
202C4×C22⋊Q8C2212yes—
203C4×C22⋊Q8C2214yes—
204C4×#123C2212yes—
205C4×#121C2212yes—
206C4×#120C2212yes—
207#2296C2212yes—
208#2290C2214yes—
209#2290C2214yes—
210#2285C2211yescharacteristic
211#2283C2211yescharacteristic
212#2283C2214yes—
213#2283C2214yes—
214#2283C2214yes—
215#2283C2214yes—
216C2×#383C2211yescharacteristic
217C2×#383C2211yescharacteristic
218C2×#382C2211yescharacteristic
219C2×#382C2211yescharacteristic
220#2280C2212yes—
221C2×#381C2212yes—
222C2×#380C2212yes—
223C2×C4×C4⋊C4C2212yes—
224C2×C4×C22⋊C4C2211yescharacteristic
225C2×C4×C22⋊C4C2211yescharacteristic
226C2×#376C2212yes—
227C24×C4C2311yescharacteristic
228C24×C4C2311yescharacteristic
229C24×C4C2311yescharacteristic
230#533—28no—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233#529—28no—
234C2×#126C2312yes—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#126C2314yes—
238C2×#125C2312yes—
239C2×#125C2311yescharacteristic
240C2×#125C2314yes—
241C2×#124C2311yescharacteristic
242C2×#124C2314yes—
243C2×#123C2312yes—
244C2×#123C2312yes—
245C2×#123C2314yes—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2312yes—
248C2×C22⋊Q8C2311yescharacteristic
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2314yes—
254C2×#121C2311yescharacteristic
255C2×#121C2312yes—
256C2×#120C2312yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2314yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×#117C2312yes—
266C2×#117C2312yes—
267C2×#117C2314yes—
268C2×#117C2312yes—
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C22⋊C4C2312yes—
272C22×C22⋊C4C2312yes—
273C22×C42—28no—
274C22×C42C2312yes—
275C22×C42C2312yes—
276C22×C42C2312yes—
277C22×C42C2311yescharacteristic
278C22×C42C2311yescharacteristic
279C22×C42C2311yescharacteristic
280C22×C42C2312yes—
281C22×C42C2312yes—
282C22×C42C2312yes—
283C22×C42C2311yescharacteristic
284#401C2314yes—
285#400C2312yes—
286#400C2312yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#399C2312yes—
306#399C2312yes—
307#399C2314yes—
308#399C2314yes—
309#399C2314yes—
310#399C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#395C2312yes—
349#395C2312yes—
350#395C2314yes—
351#395C2314yes—
352#395C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#393C2312yes—
364#393C2312yes—
365#393C2314yes—
366#393C2314yes—
367#393C2314yes—
368#391C2314yes—
369#391C2314yes—
370#391C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2314yes—
374#391C2314yes—
375#391C2312yes—
376#391C2312yes—
377#391C2314yes—
378#391C2312yes—
379#391C2314yes—
380#391C2314yes—
381#390C2314yes—
382#390C2312yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2312yes—
390#389C2314yes—
391#389C2312yes—
392#389C2314yes—
393#389C2314yes—
394#389C2312yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2312yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
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#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
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#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#386C2314yes—
495#386C2314yes—
496#386C2314yes—
497#386C2314yes—
498#386C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2312yes—
503#386C2314yes—
504#386C2312yes—
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#385C2314yes—
523#385C2314yes—
524#385C2312yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2312yes—
529#385C2314yes—
530#384C2312yes—
531#383C2312yes—
532#383C2312yes—
533#383C2312yes—
534#383C2314yes—
535#383C2312yes—
536#383C2314yes—
537#383C2312yes—
538#383C2312yes—
539#383C2312yes—
540#383C2314yes—
541#383C2312yes—
542#383C2312yes—
543#383C2312yes—
544#382C2312yes—
545#382C2314yes—
546#382C2314yes—
547#382C2314yes—
548#382C2312yes—
549#382C2312yes—
550#382C2314yes—
551#382C2314yes—
552#382C2314yes—
553#382C2314yes—
554#382C2314yes—
555#381C2312yes—
556#381C2314yes—
557#381C2312yes—
558#381C2312yes—
559#381C2314yes—
560#381C2314yes—
561#381C2314yes—
562#381C2314yes—
563#380C2314yes—
564#380C2314yes—
565#380C2314yes—
566#380C2312yes—
567#380C2312yes—
568#380C2314yes—
569#380C2314yes—
570#380C2314yes—
571#380C2312yes—
572#380C2311yescharacteristic
573#380C2311yescharacteristic
574#380C2312yes—
575#380C2312yes—
576#380C2312yes—
577#380C2312yes—
578#380C2314yes—
579#380C2314yes—
580#380C2314yes—
581#380C2314yes—
582#380C2314yes—
583#379C2314yes—
584#379C2312yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2312yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2312yes—
596C4×C4⋊C4C2312yes—
597C4×C4⋊C4C2311yescharacteristic
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2311yescharacteristic
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2314yes—
620#376C2314yes—
621#376C2312yes—
622#376C2314yes—
623#376C2314yes—
624#376C2312yes—
625#376C2314yes—
626#376C2314yes—
627#376C2314yes—
628C2×#95C2311yescharacteristic
629C2×#95C2311yescharacteristic
630C2×#95C2312yes—
631C2×#95C2312yes—
632C2×#95C2312yes—
633C2×#95C2311yescharacteristic
634C2×#95C2311yescharacteristic
635C2×#95C2312yes—
636C2×#95C2312yes—
637C2×#95C2312yes—
638C2×#95C2312yes—
639C25C2411yescharacteristic
640C22×Q8C2411yescharacteristic
641C22×Q8C2412yes—
642C22×Q8C2412yes—
643C22×Q8C2414yes—
644C22×D4C2412yes—
645C22×D4C2414yes—
646C22×D4C2411yescharacteristic
647C23×C4—24no—
648C23×C4—24no—
649C23×C4—24no—
650C23×C4—24no—
651C23×C4—44no—
652C23×C4—42no—
653C23×C4—44no—
654C23×C4C2411yescharacteristic
655C23×C4C2412yes—
656C23×C4C2412yes—
657C23×C4C2412yes—
658C23×C4C2412yes—
659C23×C4C2412yes—
660C23×C4C2412yes—
661C23×C4C2411yescharacteristic
662C23×C4C2411yescharacteristic
663C23×C4C2412yes—
664C23×C4C2412yes—
665C23×C4C2412yes—
666C23×C4C2412yes—
667C23×C4C2412yes—
668C23×C4C2411yescharacteristic
669C23×C4C2414yes—
670C23×C4C2411yescharacteristic
671C23×C4C2411yescharacteristic
672C4⋊Q8—24no—
673C4⋊Q8—24no—
674#126—28no—
675#126—48no—
676#126—48no—
677#126—48no—
678#125—24no—
679#125—28no—
680#125—48no—
681#124—24no—
682#124—48no—
683#123—28no—
684#123—28no—
685#123—48no—
686C22⋊Q8—24no—
687C22⋊Q8—28no—
688C22⋊Q8—28no—
689C22⋊Q8—48no—
690C22⋊Q8—44no—
691C22⋊Q8—44no—
692C22⋊Q8—44no—
693C22⋊Q8—48no—
694#121—24no—
695#121—44no—
696#120—44no—
697C4×Q8—24no—
698C4×Q8—28no—
699C4×Q8—28no—
700C4×Q8—48no—
701C4×D4—28no—
702C4×D4—24no—
703C4×D4—48no—
704C4×D4—48no—
705#117—28no—
706#117—28no—
707#117—48no—
708#117—44no—
709C2×C4⋊C4—28no—
710C2×C4⋊C4—44no—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C22⋊C4—44no—
761C2×C22⋊C4—44no—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2412yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C42—24no—
793C2×C42—24no—
794C2×C42—24no—
795C2×C42—28no—
796C2×C42—28no—
797C2×C42—28no—
798C2×C42—28no—
799C2×C42—44no—
800C2×C42—44no—
801C2×C42#4118yes—
802C2×C42C2412yes—
803C2×C42C2414yes—
804C2×C42C2414yes—
805C2×C42C2414yes—
806C2×C42C2412yes—
807C2×C42C2412yes—
808C2×C42C2412yes—
809C2×C42C2412yes—
810C2×C42C2412yes—
811C2×C42C2412yes—
812C2×C42C2414yes—
813C2×C42C2412yes—
814C2×C42C2412yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2411yescharacteristic
825C2×C42C2411yescharacteristic
826C2×C42C2411yescharacteristic
827C2×C42C2411yescharacteristic
828#95C2412yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2412yes—
838#95C2412yes—
839#95C2412yes—
840#95C2412yes—
841#95C2412yes—
842#95C2412yes—
843#95C2412yes—
844#95C2412yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2412yes—
855#95C2412yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2412yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898C24—22no—
899C24—24no—
900C24—22no—
901C24—22no—
902C24—42no—
903C24C2512yes—
904C24C2512yes—
905C24C2511yescharacteristic
906C2×Q8—22no—
907C2×Q8—24no—
908C2×Q8—24no—
909C2×Q8—44no—
910C2×Q8—42no—
911C2×Q8—42no—
912C2×Q8—44no—
913C2×Q8—42no—
914C2×Q8—44no—
915C2×Q8—44no—
916C2×D4—24no—
917C2×D4—24no—
918C2×D4—24no—
919C2×D4—28no—
920C2×D4—22no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—42no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—22no—
929C22×C4—24no—
930C22×C4—22no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—24no—
934C22×C4—24no—
935C22×C4—24no—
936C22×C4—24no—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—24no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—24no—
943C22×C4—24no—
944C22×C4—24no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—416no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—416no—
971C22×C4—416no—
972C22×C4C2×#4114yes—
973C22×C4C2×#4114yes—
974C22×C4C2×#4114yes—
975C22×C42−1+414yes—
976C22×C4C2514yes—
977C22×C4C2512yes—
978C22×C4C2512yes—
979C22×C4C2514yes—
980C22×C4C2514yes—
981C22×C4C2514yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2512yes—
985C22×C4C2514yes—
986C22×C4C2514yes—
987C22×C4C2514yes—
988C22×C4C2512yes—
989C22×C4C2514yes—
990C22×C4C2511yescharacteristic
991C22×C4C2511yescharacteristic
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C22×C4C2511yescharacteristic
995C22×C4C2511yescharacteristic
996C22×C4C2512yes—
997C22×C4C2512yes—
998C4⋊C4—24no—
999C4⋊C4—24no—
1000C4⋊C4—24no—
1001C4⋊C4—24no—
1002C4⋊C4—22no—
1003C4⋊C4—24no—
1004C4⋊C4—22no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—28no—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—28no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—44no—
1026C4⋊C4—42no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C22⋊C4—28no—
1048C22⋊C4—24no—
1049C22⋊C4—24no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—24no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—24no—
1058C22⋊C4—24no—
1059C22⋊C4—24no—
1060C22⋊C4—24no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C42—24no—
1078C42—24no—
1079C42—24no—
1080C42—24no—
1081C42—24no—
1082C42—24no—
1083C42—24no—
1084C42—28no—
1085C42—28no—
1086C42—28no—
1087C42—44no—
1088C42—44no—
1089C42—42no—
1090C42—42no—
1091C42—44no—
1092C42—44no—
1093C42—44no—
1094C42—44no—
1095C42—44no—
1096C42—44no—
1097C42—44no—
1098C42—44no—
1099C42C2×#4114yes—
1100C42C2×#4114yes—
1101C42C2×#4114yes—
1102C42C2×#4114yes—
1103C23—22no—
1104C23—22no—
1105C23—28no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—24no—
1115C23—24no—
1116C23—22no—
1117C23—48no—
1118C23—48no—
1119C23—44no—
1120C23—44no—
1121C23C22×#4112yes—
1122C23C2×2−1+412yes—
1123C23#58514yes—
1124C23#58512yes—
1125C23C2611yescharacteristic
1126Q8—82no—
1127Q8—84no—
1128Q8—84no—
1129Q8—88no—
1130D4—48no—
1131D4—82no—
1132D4—88no—
1133C2×C4—28no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—21no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—28no—
1147C2×C4—28no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—22no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—22no—
1188C2×C4—44no—
1189C2×C4—44no—
1190C2×C4—48no—
1191C2×C4—48no—
1192C2×C4—48no—
1193C2×C4—48no—
1194C2×C4—48no—
1195C2×C4—48no—
1196C2×C4—44no—
1197C2×C4—84no—
1198C2×C4—84no—
1199C2×C4—84no—
1200C2×C4—84no—
1201C2×C4—84no—
1202C2×C4—88no—
1203C2×C4C22×#4112yes—
1204C2×C4C22×#4112yes—
1205C2×C4C22×#4112yes—
1206C2×C4C22×#4112yes—
1207C2×C4C22×#4112yes—
1208C2×C4C22×#4112yes—
1209C2×C4C2×2−1+414yes—
1210C2×C4#58514yes—
1211C22—24no—
1212C22—22no—
1213C22—22no—
1214C22—24no—
1215C22—24no—
1216C22—24no—
1217C22—24no—
1218C22—416no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—44no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—44no—
1228C22#349514yes—
1229C22C23×#4111yescharacteristic
1230C22C22×2−1+411yescharacteristic
1231C22C2×#58511yescharacteristic
1232C22C2×#58512yes—
1233C22C2×#58512yes—
1234C4—22no—
1235C4—22no—
1236C4—24no—
1237C4—24no—
1238C4—22no—
1239C4—22no—
1240C4—22no—
1241C4—22no—
1242C4—44no—
1243C4—44no—
1244C4—44no—
1245C4—44no—
1246C4—44no—
1247C4—42no—
1248C4—42no—
1249C4—42no—
1250C4—44no—
1251C4—42no—
1252C4—44no—
1253C4—44no—
1254C4—44no—
1255C4—44no—
1256C2—24no—
1257C2—44no—
1258C2—82no—
1259C2#6275512yes—
1260C2C2×#349511yescharacteristic
1261C2#6281411yescharacteristic
1262C2#6281411yescharacteristic
1263C2#6283112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2847C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59344C2semidirect
2. #59343C2semidirect
3. #46138C2semidirect
4. #45981C2semidirect
5. #39601C2semidirect
6. #39473C2semidirect
7. #37995C2semidirect
8. #37992C2semidirect
9. #37927C2semidirect
10. #37926C2semidirect
11. #37854C2semidirect
12. #37562C2semidirect
13. #37557C2semidirect
14. #36732C2semidirect
16. #36625C2semidirect
18. #36531C2semidirect
19. #36351C2semidirect
20. #36338C2semidirect
21. #35042C2semidirect
22. #35013C2semidirect
23. #34401C2semidirect
24. #34389C2semidirect
25. C2×#2283C2semidirect
47. #2843C22semidirect
48. #2821C22semidirect
49. #2821C22semidirect
50. #2774C22semidirect
51. #2773C22semidirect
52. #2768C22semidirect
53. #2767C22semidirect
54. #2763C22semidirect
55. #2762C22semidirect
56. #2755C22semidirect
57. #2754C22semidirect
82. #2666C22semidirect
83. #2666C22semidirect
88. #2634C22semidirect
89. #2634C22semidirect
90. #2633C22semidirect
91. #2632C22semidirect
94. #2612C22semidirect
95. #2611C22semidirect
96. #2606C22semidirect
97. #2606C22semidirect
98. #2605C22semidirect
99. #2604C22semidirect
100. #2599C22semidirect
101. #2597C22semidirect
102. #2596C22semidirect
103. #2590C22semidirect
104. #2589C22semidirect
105. #2586C22semidirect
106. #2586C22semidirect
107. #2585C22semidirect
108. #2585C22semidirect
112. #2575C22semidirect
114. #2574C22semidirect
123. #2533C22semidirect
124. #2533C22semidirect
125. #2533C22semidirect
126. #2532C22semidirect
127. #2532C22semidirect
131. #2530C22semidirect
132. #2529C22semidirect
133. #2529C22semidirect
134. #2528C22semidirect
135. #2528C22semidirect
136. #2528C22semidirect
137. #2524C22semidirect
142. #2520C22semidirect
143. #2520C22semidirect
144. #2520C22semidirect
146. #2517C22semidirect
148. #2508C22semidirect
151. #2505C22semidirect
155. #2479C22semidirect
156. #2478C22semidirect
161. #2462C22semidirect
162. #2462C22semidirect
167. #2383C22semidirect
168. #2381C22semidirect
169. #2381C22semidirect
172. #2373C22semidirect
173. #2371C22semidirect
179. #2356C22semidirect
180. #2356C22semidirect
183. #2347C22semidirect
184. #2346C22semidirect
186. #2343C22semidirect
187. #2337C22semidirect
188. #2336C22semidirect
189. #2336C22semidirect
195. #2320C22semidirect
196. #2320C22semidirect
197. #2318C22semidirect

Maximal subgroups

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

subgroupindex
#593442
#593432
#461382
#459812
#396012
#394732
#379952
#379922
#379272
#379262
#378542
#375622
#375572
#367322
#367302
#366252
#366212
#365312
#363512
#363382
#350422
#350132
#344012
#343892
C2×#22832