Finite Group Databasebeta

← #7643905

Subgroups — #7643905

Order 512.

4552 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42161C214yesmaximal, complemented
2#42160C214yesmaximal, complemented
3#41976C214yesmaximal, complemented
4#41975C214yesmaximal, complemented
5#41969C214yesmaximal, complemented
6#41968C214yesmaximal, complemented
7#41967C214yesmaximal, complemented
8#41966C214yesmaximal, complemented
9#37462C212yesmaximal, complemented
10#37461C212yesmaximal, complemented
11#37460C212yesmaximal, complemented
12#37459C212yesmaximal, complemented
13#37198C212yesmaximal, complemented
14#37198C212yesmaximal, complemented
15#37141C212yesmaximal, complemented
16#37139C212yesmaximal, complemented
17#35374C214yesmaximal, complemented
18#35373C214yesmaximal, complemented
19#35120C211yesmaximal, characteristic, complemented
20#35119C211yesmaximal, characteristic, complemented
21#34593C212yesmaximal, complemented
22#34224C212yesmaximal, complemented
23C2×#2319C211yesmaximal, characteristic, complemented
24C2×#529C2212yes—
25C22×C4×D4C2211yescharacteristic
26#2855C2212yes—
27#2855C2212yes—
28#2854C2212yes—
29#2854C2212yes—
30#2838C2214yescomplemented
31#2837C2214yescomplemented
32#2837C2214yescomplemented
33#2836C2214yescomplemented
34#2832C2214yescomplemented
35#2831C2214yescomplemented
36#2829C2214yescomplemented
37#2828C2214yescomplemented
38#2810C2212yescomplemented
39#2809C2212yescomplemented
40#2808C2212yes—
41#2808C2212yes—
42#2808C2212yescomplemented
43#2807C2214yescomplemented
44#2805C2212yescomplemented
45#2803C2214yes—
46#2803C2214yes—
47#2803C2214yes—
48#2803C2214yes—
49#2802C2214yescomplemented
50#2800C2214yes—
51#2800C2214yes—
52#2798C2214yescomplemented
53#2797C2214yes—
54#2797C2214yes—
55#2796C2214yescomplemented
56#2787C2214yescomplemented
57#2783C2214yescomplemented
58#2777C2214yescomplemented
59#2776C2214yescomplemented
60#2773C2214yescomplemented
61#2771C2214yescomplemented
62#2733C2212yes—
63#2733C2212yes—
64#2732C2212yescomplemented
65#2727C2212yes—
66#2727C2212yes—
67#2727C2212yescomplemented
68#2726C2212yescomplemented
69#2724C2212yescomplemented
70#2714C2214yes—
71#2714C2214yes—
72#2710C2214yes—
73#2710C2214yes—
74#2694C2214yescomplemented
75#2689C2214yescomplemented
76#2682C2212yes—
77#2682C2212yes—
78#2664C2214yescomplemented
79#2663C2214yescomplemented
80#2662C2214yescomplemented
81#2661C2214yescomplemented
82#2659C2211yescharacteristic
83#2659C2211yescharacteristic
84#2659C2211yescharacteristic
85#2656C2211yescharacteristic
86#2654C2214yescomplemented
87#2654C2214yescomplemented
88#2653C2214yescomplemented
89#2651C2214yescomplemented
90#2651C2214yescomplemented
91#2650C2214yescomplemented
92#2650C2214yescomplemented
93#2649C2214yescomplemented
94#2646C2212yes—
95#2639C2212yes—
96#2637C2214yescomplemented
97#2636C2214yes—
98#2636C2214yes—
99#2635C2214yescomplemented
100#2633C2214yes—
101#2632C2214yescomplemented
102#2631C2214yes—
103#2630C2214yescomplemented
104#2626C2212yes—
105#2626C2212yes—
106#2623C2214yes—
107#2617C2212yes—
108#2617C2212yes—
109#2613C2214yes—
110#2612C2214yescomplemented
111#2612C2214yescomplemented
112#2611C2214yescomplemented
113#2610C2214yescomplemented
114#2606C2214yescomplemented
115#2605C2214yescomplemented
116#2604C2214yescomplemented
117#2603C2214yescomplemented
118#2578C2214yescomplemented
119#2577C2214yescomplemented
120#2576C2214yescomplemented
121#2575C2214yescomplemented
122#2574C2214yescomplemented
123#2573C2214yescomplemented
124#2572C2214yescomplemented
125#2553C2214yescomplemented
126#2531C2214yescomplemented
127#2530C2214yescomplemented
128#2527C2214yescomplemented
129#2526C2214yescomplemented
130#2525C2214yescomplemented
131#2522C2214yescomplemented
132#2521C2214yescomplemented
133#2521C2214yescomplemented
134#2519C2214yescomplemented
135#2516C2214yescomplemented
136#2516C2214yescomplemented
137#2515C2214yescomplemented
138#2510C2214yes—
139#2505C2214yes—
140#2481C2214yes—
141#2480C2214yes—
142#2480C2214yes—
143#2473C2214yes—
144#2472C2214yes—
145#2472C2214yes—
146#2469C2214yescomplemented
147#2468C2214yescomplemented
148#2468C2214yescomplemented
149#2467C2214yescomplemented
150#2466C2214yescomplemented
151#2464C2214yescomplemented
152#2461C2214yescomplemented
153#2460C2214yescomplemented
154#2459C2214yescomplemented
155#2458C2214yescomplemented
156#2457C2214yescomplemented
157#2457C2214yescomplemented
158#2454C2214yescomplemented
159#2450C2214yes—
160#2450C2214yescomplemented
161#2449C2214yes—
162#2447C2214yescomplemented
163#2444C2214yes—
164#2444C2214yescomplemented
165#2443C2214yes—
166#2427C2214yescomplemented
167#2425C2214yescomplemented
168#2424C2214yes—
169#2424C2214yes—
170#2420C2214yescomplemented
171#2419C2214yescomplemented
172#2418C2214yes—
173#2418C2214yes—
174#2398C2214yes—
175#2397C2214yes—
176#2392C2214yes—
177#2392C2214yes—
178#2373C2214yescomplemented
179#2373C2214yescomplemented
180#2370C2212yescomplemented
181#2370C2212yescomplemented
182#2367C2212yescomplemented
183#2367C2212yescomplemented
184#2357C2212yescomplemented
185#2356C2212yescomplemented
186#2351C2212yescomplemented
187#2349C2212yescomplemented
188#2347C2214yescomplemented
189#2343C2214yescomplemented
190#2329C2212yes—
191#2329C2212yes—
192#2325C2212yes—
193#2325C2212yes—
194#2322C2214yes—
195#2322C2214yes—
196#2319C2214yes—
197#2319C2214yes—
198#2319C2214yes—
199#2319C2214yes—
200#2318C2214yes—
201C4×C22⋊Q8C2212yes—
202C4×C22⋊Q8C2212yes—
203C4×#121C2212yes—
204C4×#121C2212yes—
205C4×#120C2214yes—
206C4×#120C2214yes—
207C2×#390C2211yescharacteristic
208C2×#390C2211yescharacteristic
209C2×#389C2211yescharacteristic
210C2×#389C2211yescharacteristic
211C2×#388C2212yes—
212C2×#388C2212yes—
213#2283C2212yes—
214C2×#381C2212yes—
215C2×#380C2212yes—
216#2275C2214yes—
217C2×C4×C4⋊C4C2211yescharacteristic
218C2×#376C2211yescharacteristic
219C23×D4C2311yescharacteristic
220C24×C4C2312yes—
221#529—216no—
222C2×#126C2314yes—
223C2×#126C2314yes—
224C2×#126C2314yes—
225C2×#126C2314yes—
226C2×#125C2312yes—
227C2×#125C2314yes—
228C2×#124C2312yes—
229C2×#124C2314yes—
230C2×#124C2314yes—
231C2×#123C2314yes—
232C2×#123C2314yes—
233C2×#123C2314yes—
234C2×#123C2314yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2314yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#120C2314yes—
245C2×#120C2314yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×D4—28no—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×#117C2314yes—
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C22⋊C4C2312yes—
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2312yes—
271C22×C22⋊C4C2312yes—
272C22×C22⋊C4C2312yes—
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2312yes—
276C22×C42C2311yescharacteristic
277#401C2314yes—
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#399C2314yes—
293#399C2314yes—
294#399C2314yes—
295#399C2314yes—
296#399C2314yes—
297#399C2314yes—
298#399C2314yes—
299#399C2314yes—
300#399C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#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#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#396C2314yes—
342#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#395C2314yes—
348#395C2314yes—
349#395C2314yes—
350#395C2314yes—
351#394C2314yes—
352#394C2314yes—
353#394C2314yes—
354#394C2314yes—
355#394C2314yes—
356#394C2314yes—
357#394C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#393C2314yes—
375#393C2314yes—
376#393C2314yes—
377#393C2314yes—
378#393C2314yes—
379#393C2314yes—
380#392C2314yes—
381#392C2314yes—
382#392C2314yes—
383#392C2314yes—
384#392C2314yes—
385#392C2314yes—
386#392C2314yes—
387#392C2314yes—
388#392C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2312yes—
392#391C2312yes—
393#391C2312yes—
394#391C2312yes—
395#391C2312yes—
396#391C2312yes—
397#391C2314yes—
398#390C2312yes—
399#390C2312yes—
400#390C2312yes—
401#390C2312yes—
402#390C2314yes—
403#390C2314yes—
404#390C2312yes—
405#390C2312yes—
406#390C2312yes—
407#390C2312yes—
408#390C2312yes—
409#390C2312yes—
410#390C2314yes—
411#390C2314yes—
412#390C2314yes—
413#390C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2312yes—
418#389C2312yes—
419#389C2312yes—
420#389C2312yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2312yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#389C2314yes—
430#389C2312yes—
431#389C2312yes—
432#389C2312yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#383C2314yes—
550#383C2314yes—
551#383C2314yes—
552#382C2314yes—
553#382C2312yes—
554#382C2312yes—
555#382C2314yes—
556#381C2314yes—
557#381C2314yes—
558#381C2314yes—
559#381C2314yes—
560#381C2314yes—
561#381C2314yes—
562#381C2314yes—
563#380C2314yes—
564#380C2314yes—
565#380C2314yes—
566#380C2314yes—
567#380C2314yes—
568#380C2312yes—
569#380C2312yes—
570#380C2312yes—
571#380C2312yes—
572#380C2312yes—
573#380C2312yes—
574#380C2314yes—
575#379C2314yes—
576#379C2314yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2312yes—
580C4×C4⋊C4C2312yes—
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2312yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2312yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2312yes—
589C4×C4⋊C4C2312yes—
590C4×C4⋊C4C2312yes—
591C4×C4⋊C4C2312yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604#376C2314yes—
605#376C2314yes—
606#376C2314yes—
607#376C2314yes—
608C2×#95C2312yes—
609C2×#95C2311yescharacteristic
610C2×#95C2311yescharacteristic
611C2×#95C2314yes—
612C2×#95C2311yescharacteristic
613C2×#95C2311yescharacteristic
614C2×#95C2312yes—
615C2×#95C2312yes—
616C25C2412yes—
617C22×Q8C2412yes—
618C22×Q8C2412yes—
619C22×Q8C2412yes—
620C22×D4—24no—
621C22×D4—42no—
622C22×D4—42no—
623C22×D4C2414yes—
624C22×D4C2412yes—
625C22×D4C2412yes—
626C22×D4C2412yes—
627C22×D4C2414yes—
628C22×D4C2414yes—
629C22×D4C2414yes—
630C22×D4C2414yes—
631C22×D4C2412yes—
632C22×D4C2412yes—
633C23×C4—28no—
634C23×C4—82no—
635C23×C4—82no—
636C23×C4C2411yescharacteristic
637C23×C4C2412yes—
638C23×C4C2412yes—
639C23×C4C2411yescharacteristic
640C23×C4C2411yescharacteristic
641C23×C4C2411yescharacteristic
642C23×C4C2411yescharacteristic
643C23×C4C2412yes—
644C23×C4C2414yes—
645C23×C4C2414yes—
646C23×C4C2414yes—
647C23×C4C2414yes—
648C23×C4C2414yes—
649C23×C4C2411yescharacteristic
650C23×C4C2411yescharacteristic
651#126—216no—
652#126—84no—
653#126—84no—
654#126—84no—
655#125—28no—
656#125—84no—
657#124—28no—
658#124—84no—
659#124—84no—
660#123—216no—
661#123—84no—
662#123—84no—
663#123—84no—
664C22⋊Q8—28no—
665C22⋊Q8—44no—
666C22⋊Q8—44no—
667C22⋊Q8—84no—
668#121—28no—
669#121—44no—
670#121—44no—
671#121—84no—
672#121—84no—
673#120—48no—
674#120—48no—
675C4×Q8—28no—
676C4×Q8—82no—
677C4×Q8—82no—
678C4×D4—216no—
679C4×D4—216no—
680C4×D4—216no—
681C4×D4—28no—
682C4×D4—48no—
683C4×D4—48no—
684C4×D4—82no—
685C4×D4—82no—
686C4×D4—84no—
687C4×D4—84no—
688C4×D4—84no—
689C4×D4—84no—
690#117—216no—
691C2×C4⋊C4—24no—
692C2×C4⋊C4—42no—
693C2×C4⋊C4—42no—
694C2×C4⋊C4—82no—
695C2×C4⋊C4—82no—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C22⋊C4—28no—
747C2×C22⋊C4—82no—
748C2×C22⋊C4—82no—
749C2×C22⋊C4—82no—
750C2×C22⋊C4—82no—
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×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
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×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C42—42no—
797C2×C42—42no—
798C2×C42—82no—
799C2×C42#4118yes—
800C2×C42C2414yes—
801C2×C42C2414yes—
802C2×C42C2414yes—
803C2×C42C2414yes—
804C2×C42C2414yes—
805C2×C42C2412yes—
806C2×C42C2412yes—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2412yes—
810C2×C42C2412yes—
811C2×C42C2414yes—
812C2×C42C2414yes—
813C2×C42C2412yes—
814C2×C42C2412yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2412yes—
819#95C2412yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2412yes—
825#95C2412yes—
826#95C2412yes—
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#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
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—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871C24—24no—
872C24—24no—
873C24—24no—
874C24—42no—
875C24—42no—
876C24—42no—
877C24—42no—
878C24C2514yes—
879C24C2514yes—
880C24C2511yescharacteristic
881C2×Q8—24no—
882C2×Q8—42no—
883C2×Q8—42no—
884C2×Q8—42no—
885C2×Q8—42no—
886C2×Q8—42no—
887C2×Q8—42no—
888C2×Q8—42no—
889C2×Q8—42no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—24no—
894C2×D4—24no—
895C2×D4—24no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—416no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—42no—
921C22×C4—22no—
922C22×C4—22no—
923C22×C4—24no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—28no—
931C22×C4—28no—
932C22×C4—28no—
933C22×C4—41no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—41no—
937C22×C4—41no—
938C22×C4—41no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—41no—
942C22×C4—41no—
943C22×C4—41no—
944C22×C4—41no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—41no—
948C22×C4—41no—
949C22×C4—44no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—44no—
953C22×C4—44no—
954C22×C4—44no—
955C22×C4—41no—
956C22×C4—41no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—816no—
964C22×C4C2×#4114yes—
965C22×C4C2×#4114yes—
966C22×C4C2×#4114yes—
967C22×C4C2514yes—
968C22×C4C2512yes—
969C22×C4C2512yes—
970C22×C4C2512yes—
971C22×C4C2512yes—
972C22×C4C2514yes—
973C22×C4C2514yes—
974C22×C4C2514yes—
975C22×C4C2514yes—
976C22×C4C2514yes—
977C22×C4C2512yes—
978C22×C4C2512yes—
979C22×C4C2514yes—
980C22×C4C2512yes—
981C22×C4C2512yes—
982C22×C4C2514yes—
983C22×C4C2512yes—
984C22×C4C2512yes—
985C22×C4C2511yescharacteristic
986C22×C4C2511yescharacteristic
987C4⋊C4—24no—
988C4⋊C4—24no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—24no—
992C4⋊C4—28no—
993C4⋊C4—24no—
994C4⋊C4—28no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—42no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—42no—
1028C4⋊C4—44no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—44no—
1032C4⋊C4—42no—
1033C4⋊C4—44no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—44no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
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—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C42—28no—
1083C42—42no—
1084C42—42no—
1085C42—42no—
1086C42—42no—
1087C42—42no—
1088C42—42no—
1089C42—42no—
1090C42—42no—
1091C42—44no—
1092C42—44no—
1093C42—44no—
1094C42—44no—
1095C42—44no—
1096C42—44no—
1097C42—44no—
1098C42—44no—
1099C42C2×#4118yes—
1100C42C2×#4118yes—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—24no—
1106C23—24no—
1107C23—24no—
1108C23—24no—
1109C23—24no—
1110C23—24no—
1111C23—24no—
1112C23—24no—
1113C23—24no—
1114C23—24no—
1115C23—24no—
1116C23—24no—
1117C23—24no—
1118C23—24no—
1119C23—48no—
1120C23—48no—
1121C23—48no—
1122C23—84no—
1123C23—84no—
1124C23—84no—
1125C23—84no—
1126C23C22×#4112yes—
1127C23#58512yes—
1128C23#58512yes—
1129C23C2611yescharacteristic
1130Q8—48no—
1131Q8—162no—
1132Q8—162no—
1133D4—48no—
1134D4—48no—
1135D4—48no—
1136D4—416no—
1137D4—88no—
1138D4—88no—
1139D4—88no—
1140D4—88no—
1141D4—162no—
1142D4—162no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—28no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—44no—
1201C2×C4—44no—
1202C2×C4—48no—
1203C2×C4—88no—
1204C2×C4—88no—
1205C2×C4—88no—
1206C2×C4—82no—
1207C2×C4—82no—
1208C2×C4—84no—
1209C2×C4—84no—
1210C2×C4—82no—
1211C2×C4—82no—
1212C2×C4—164no—
1213C2×C4—164no—
1214C2×C4C22×#4114yes—
1215C2×C4C22×#4114yes—
1216C2×C4C22×#4112yes—
1217C2×C4C22×#4112yes—
1218C22—22no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—816no—
1239C22#345514yes—
1240C22C23×#4111yescharacteristic
1241C22C2×#58511yescharacteristic
1242C22C2×#58511yescharacteristic
1243C22H(7,𝔽2)11yescharacteristic
1244C22H(7,𝔽2)11yescharacteristic
1245C22H(7,𝔽2)11yescharacteristic
1246C222−1+611yescharacteristic
1247C4—24no—
1248C4—24no—
1249C4—22no—
1250C4—22no—
1251C4—44no—
1252C4—44no—
1253C4—44no—
1254C4—42no—
1255C4—42no—
1256C4—44no—
1257C4—44no—
1258C4—42no—
1259C4—42no—
1260C4—42no—
1261C4—42no—
1262C4—42no—
1263C4—42no—
1264C4—44no—
1265C4—44no—
1266C4—44no—
1267C2—24no—
1268C2—84no—
1269C2—84no—
1270C2C2×#345511yescharacteristic
1271C2#6284511yescharacteristic
1272C2#6285511yescharacteristic
1273C2#6286911yescharacteristic
1274C2#6286911yescharacteristic
1275C2#6287011yescharacteristic
1276C2#6287011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42161C2semidirect
2. #42160C2semidirect
3. #41976C2semidirect
4. #41975C2semidirect
5. #41969C2semidirect
6. #41968C2semidirect
7. #41967C2semidirect
8. #41966C2semidirect
9. #37462C2semidirect
10. #37461C2semidirect
11. #37460C2semidirect
12. #37459C2semidirect
13. #37198C2semidirect
14. #37198C2semidirect
15. #37141C2semidirect
16. #37139C2semidirect
17. #35374C2semidirect
18. #35373C2semidirect
19. #35120C2semidirect
20. #35119C2semidirect
21. #34593C2semidirect
22. #34224C2semidirect
23. C2×#2319C2semidirect
30. #2838C22semidirect
31. #2837C22semidirect
32. #2837C22semidirect
33. #2836C22semidirect
34. #2832C22semidirect
35. #2831C22semidirect
36. #2829C22semidirect
37. #2828C22semidirect
38. #2810C22semidirect
39. #2809C22semidirect
42. #2808C22semidirect
43. #2807C22semidirect
44. #2805C22semidirect
49. #2802C22semidirect
52. #2798C22semidirect
55. #2796C22semidirect
56. #2787C22semidirect
57. #2783C22semidirect
58. #2777C22semidirect
59. #2776C22semidirect
60. #2773C22semidirect
61. #2771C22semidirect
64. #2732C22semidirect
67. #2727C22semidirect
68. #2726C22semidirect
69. #2724C22semidirect
74. #2694C22semidirect
75. #2689C22semidirect
78. #2664C22semidirect
79. #2663C22semidirect
80. #2662C22semidirect
81. #2661C22semidirect
86. #2654C22semidirect
87. #2654C22semidirect
88. #2653C22semidirect
89. #2651C22semidirect
90. #2651C22semidirect
91. #2650C22semidirect
92. #2650C22semidirect
93. #2649C22semidirect
96. #2637C22semidirect
99. #2635C22semidirect
101. #2632C22semidirect
103. #2630C22semidirect
110. #2612C22semidirect
111. #2612C22semidirect
112. #2611C22semidirect
113. #2610C22semidirect
114. #2606C22semidirect
115. #2605C22semidirect
116. #2604C22semidirect
117. #2603C22semidirect
118. #2578C22semidirect
119. #2577C22semidirect
120. #2576C22semidirect
121. #2575C22semidirect
122. #2574C22semidirect
123. #2573C22semidirect
124. #2572C22semidirect
125. #2553C22semidirect
126. #2531C22semidirect
127. #2530C22semidirect
128. #2527C22semidirect
129. #2526C22semidirect
130. #2525C22semidirect
131. #2522C22semidirect
132. #2521C22semidirect
133. #2521C22semidirect
134. #2519C22semidirect
135. #2516C22semidirect
136. #2516C22semidirect
137. #2515C22semidirect
146. #2469C22semidirect
147. #2468C22semidirect
148. #2468C22semidirect
149. #2467C22semidirect
150. #2466C22semidirect
151. #2464C22semidirect
152. #2461C22semidirect
153. #2460C22semidirect
154. #2459C22semidirect
155. #2458C22semidirect
156. #2457C22semidirect
157. #2457C22semidirect
158. #2454C22semidirect
160. #2450C22semidirect
162. #2447C22semidirect
164. #2444C22semidirect
166. #2427C22semidirect
167. #2425C22semidirect
170. #2420C22semidirect
171. #2419C22semidirect
178. #2373C22semidirect
179. #2373C22semidirect
180. #2370C22semidirect
181. #2370C22semidirect
182. #2367C22semidirect
183. #2367C22semidirect
184. #2357C22semidirect
185. #2356C22semidirect
186. #2351C22semidirect
187. #2349C22semidirect
188. #2347C22semidirect
189. #2343C22semidirect

Maximal subgroups

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

subgroupindex
#421612
#421602
#419762
#419752
#419692
#419682
#419672
#419662
#374622
#374612
#374602
#374592
#371982
#371412
#371392
#353742
#353732
#351202
#351192
#345932
#342242
C2×#23192