Finite Group Databasebeta

← #8141461

Subgroups — #8141461

Order 512.

4596 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#56817C214yesmaximal, complemented
2#56500C214yesmaximal, complemented
3#55911C214yesmaximal, complemented
4#54825C214yesmaximal, complemented
5#51683C214yesmaximal, complemented
6#48788C214yesmaximal, complemented
7#48451C214yesmaximal, complemented
8#48342C214yesmaximal, complemented
9#46199C212yesmaximal, complemented
10#46144C212yesmaximal, complemented
11#43076C214yesmaximal, complemented
12#40760C214yesmaximal, complemented
13#39677C212yesmaximal, complemented
14#37932C212yesmaximal, complemented
15#37873C212yesmaximal, complemented
16#37872C212yesmaximal, complemented
17#37692C212yesmaximal
18#37478C212yesmaximal, complemented
19#36732C212yesmaximal, complemented
20#36156C212yesmaximal, complemented
21#35012C211yesmaximal, characteristic, complemented
22#34994C211yesmaximal, characteristic, complemented
23C2×#2420C211yesmaximal, characteristic
24C2×#552C2212yescomplemented
25C2×#539C2212yes—
26C22×#121C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28#2851C2212yes—
29#2851C2212yes—
30#2851C2212yes—
31#2848C2212yes—
32#2848C2212yes—
33#2848C2212yes—
34#2845C2212yescomplemented
35#2841C2214yescomplemented
36#2841C2214yescomplemented
37#2836C2214yescomplemented
38#2836C2214yescomplemented
39#2830C2214yescomplemented
40#2822C2212yescomplemented
41#2806C2214yescomplemented
42#2802C2214yescomplemented
43#2798C2214yescomplemented
44#2798C2214yescomplemented
45#2788C2214yescomplemented
46#2784C2214yescomplemented
47#2780C2214yescomplemented
48#2779C2214yescomplemented
49#2779C2214yescomplemented
50#2774C2214yescomplemented
51#2772C2214yescomplemented
52#2768C2214yescomplemented
53#2767C2214yescomplemented
54#2767C2214yescomplemented
55#2767C2214yescomplemented
56#2767C2214yescomplemented
57#2761C2214yescomplemented
58#2750C2214yescomplemented
59#2748C2214yescomplemented
60#2744C2214yescomplemented
61#2744C2214yescomplemented
62#2743C2214yescomplemented
63#2743C2214yescomplemented
64#2742C2214yescomplemented
65#2741C2214yescomplemented
66#2739C2214yescomplemented
67#2739C2214yescomplemented
68#2739C2214yescomplemented
69#2727C2212yescomplemented
70#2727C2212yescomplemented
71#2726C2214yescomplemented
72#2725C2214yescomplemented
73#2724C2212yescomplemented
74#2723C2214yescomplemented
75#2723C2214yescomplemented
76#2722C2214yescomplemented
77#2719C2214yescomplemented
78#2719C2214yescomplemented
79#2711C2214yes—
80#2708C2214yes—
81#2707C2214yescomplemented
82#2707C2214yescomplemented
83#2704C2214yescomplemented
84#2702C2214yescomplemented
85#2698C2214yescomplemented
86#2698C2214yescomplemented
87#2698C2214yescomplemented
88#2695C2214yescomplemented
89#2695C2214yescomplemented
90#2694C2214yescomplemented
91#2692C2214yescomplemented
92#2691C2214yes—
93#2690C2214yescomplemented
94#2689C2214yescomplemented
95#2689C2214yescomplemented
96#2687C2214yescomplemented
97#2683C2212yescomplemented
98#2681C2214yes—
99#2667C2214yescomplemented
100#2665C2214yescomplemented
101#2659C2211yescharacteristic
102#2659C2212yes—
103#2659C2211yescharacteristic
104#2659C2212yescomplemented
105#2652C2214yescomplemented
106#2650C2214yescomplemented
107#2646C2212yes—
108#2646C2212yes—
109#2646C2212yes—
110#2639C2212yes—
111#2637C2214yescomplemented
112#2627C2212yescomplemented
113#2627C2214yescomplemented
114#2627C2214yescomplemented
115#2626C2212yes—
116#2625C2214yescomplemented
117#2618C2212yes—
118#2609C2214yescomplemented
119#2601C2214yescomplemented
120#2590C2214yescomplemented
121#2584C2214yescomplemented
122#2583C2214yes—
123#2579C2214yescomplemented
124#2574C2214yescomplemented
125#2569C2214yes—
126#2569C2214yes—
127#2564C2214yescomplemented
128#2562C2212yescomplemented
129#2556C2214yescomplemented
130#2553C2214yescomplemented
131#2549C2214yes—
132#2536C2212yescomplemented
133#2536C2214yescomplemented
134#2522C2214yescomplemented
135#2505C2214yes—
136#2505C2214yes—
137#2505C2214yes—
138#2505C2214yescomplemented
139#2505C2214yescomplemented
140#2486C2212yescomplemented
141#2485C2212yescomplemented
142#2485C2214yescomplemented
143#2480C2214yes—
144#2480C2214yes—
145#2480C2214yes—
146#2480C2214yes—
147#2478C2214yescomplemented
148#2477C2214yescomplemented
149#2477C2214yescomplemented
150#2473C2214yes—
151#2473C2214yes—
152#2473C2214yes—
153#2473C2214yescomplemented
154#2473C2214yescomplemented
155#2470C2214yescomplemented
156#2470C2214yescomplemented
157#2468C2214yescomplemented
158#2468C2214yescomplemented
159#2465C2214yescomplemented
160#2462C2214yescomplemented
161#2460C2214yescomplemented
162#2460C2214yescomplemented
163#2458C2214yescomplemented
164#2453C2214yescomplemented
165#2450C2214yescomplemented
166#2449C2214yescomplemented
167#2443C2214yes—
168#2442C2214yescomplemented
169#2438C2214yescomplemented
170#2438C2214yescomplemented
171#2438C2214yescomplemented
172#2437C2214yes—
173#2437C2214yes—
174#2437C2214yes—
175#2437C2214yes—
176#2425C2214yes—
177#2421C2214yescomplemented
178#2420C2214yes—
179#2420C2214yes—
180#2420C2214yes—
181#2420C2214yes—
182#2419C2214yescomplemented
183#2417C2212yescomplemented
184#2415C2212yescomplemented
185#2405C2214yes—
186#2405C2214yes—
187C2×#397C2212yes—
188C2×#394C2212yes—
189#2382C2212yescomplemented
190#2382C2212yescomplemented
191#2376C2214yescomplemented
192#2360C2214yes—
193#2359C2214yescomplemented
194#2352C2212yescomplemented
195#2342C2214yes—
196#2342C2214yes—
197D4×C22⋊C4C2214yes—
198#2329C2212yes—
199#2329C2212yes—
200#2329C2212yes—
201#2329C2212yescomplemented
202#2325C2212yes—
203#2316C2212yescomplemented
204#2315C2211yescharacteristic
205#2315C2212yes—
206#2315C2211yescharacteristic
207#2312C2212yes—
208C4×C22⋊Q8C2212yes—
209C2×#390C2211yescharacteristic
210C2×#389C2211yescharacteristic
211C2×#386C2212yes—
212C2×#385C2212yes—
213C2×#382C2211yescharacteristic
214#2280C2212yes—
215C2×#381C2212yes—
216C2×#380C2212yes—
217C2×#380C2211yescharacteristic
218C2×C4×C22⋊C4C2211yescharacteristic
219C23×D4C2311yescharacteristic
220C23×D4C2312yes—
221C24×C4C2312yes—
222C24×C4C2311yescharacteristic
223#552—48no—
224#539—48no—
225C2×#126C2314yes—
226C2×#126C2314yes—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#125C2312yes—
230C2×#125C2312yes—
231C2×#125C2312yes—
232C2×#125C2314yes—
233C2×#125C2314yes—
234C2×#125C2314yes—
235C2×#123C2314yes—
236C2×#123C2314yes—
237C2×#123C2314yes—
238C2×#123C2314yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×#121—44no—
253C2×#121C2312yes—
254C2×#121C2312yes—
255C2×#121C2314yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2314yes—
258C2×C4×D4—44no—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2314yes—
265C2×#117C2314yes—
266C2×#117C2312yes—
267C2×#117C2314yes—
268C2×#117C2312yes—
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2312yes—
277C22×C22⋊C4C2311yescharacteristic
278C22×C22⋊C4C2312yes—
279C22×C22⋊C4C2311yescharacteristic
280C22×C22⋊C4C2312yes—
281C22×C22⋊C4C2314yes—
282C22×C22⋊C4C2312yes—
283C22×C22⋊C4C2312yes—
284C22×C22⋊C4C2312yes—
285C22×C22⋊C4C2312yes—
286C22×C22⋊C4C2312yes—
287C22×C42C2311yescharacteristic
288C22×C42C2311yescharacteristic
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#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#399C2314yes—
312#399C2314yes—
313#399C2314yes—
314#399C2314yes—
315#399C2314yes—
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#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#391C2312yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#390C2312yes—
409#390C2314yes—
410#390C2314yes—
411#390C2312yes—
412#390C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2312yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2312yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2312yes—
440#388C2314yes—
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#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#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
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#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
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#382C2312yes—
546#382C2312yes—
547#382C2312yes—
548#382C2312yes—
549#382C2314yes—
550#382C2314yes—
551#382C2312yes—
552#382C2314yes—
553#382C2314yes—
554#381C2314yes—
555#381C2314yes—
556#381C2314yes—
557#381C2314yes—
558#381C2314yes—
559#381C2314yes—
560#381C2314yes—
561#380C2312yes—
562#380C2312yes—
563#380C2312yes—
564#380C2312yes—
565#380C2312yes—
566#380C2314yes—
567#380C2312yes—
568#380C2312yes—
569#380C2312yes—
570#380C2314yes—
571#380C2314yes—
572#380C2312yes—
573#380C2312yes—
574#380C2312yes—
575#380C2314yes—
576#380C2314yes—
577#380C2312yes—
578#380C2312yes—
579#380C2314yes—
580#380C2312yes—
581#380C2312yes—
582#380C2314yes—
583#380C2312yes—
584#380C2312yes—
585#380C2314yes—
586#380C2314yes—
587#380C2312yes—
588#380C2314yes—
589#380C2312yes—
590#380C2314yes—
591#380C2312yes—
592#380C2314yes—
593#379C2314yes—
594#379C2314yes—
595#379C2314yes—
596#379C2314yes—
597C4×C4⋊C4C2312yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C2×#95C2314yes—
610C2×#95C2312yes—
611C2×#95C2312yes—
612C2×#95C2312yes—
613C2×#95C2311yescharacteristic
614C2×#95C2312yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2311yescharacteristic
618C25C2412yes—
619C25C2411yescharacteristic
620C22×Q8C2412yes—
621C22×Q8C2414yes—
622C22×Q8C2412yes—
623C22×D4—28no—
624C22×D4—24no—
625C22×D4—42no—
626C22×D4—42no—
627C22×D4—44no—
628C22×D4—82no—
629C22×D4C2412yes—
630C22×D4C2414yes—
631C22×D4C2411yescharacteristic
632C22×D4C2414yes—
633C22×D4C2411yescharacteristic
634C23×C4—28no—
635C23×C4—42no—
636C23×C4—42no—
637C23×C4—44no—
638C23×C4—42no—
639C23×C4—82no—
640C23×C4C2411yescharacteristic
641C23×C4C2412yes—
642C23×C4C2412yes—
643C23×C4C2412yes—
644C23×C4C2411yescharacteristic
645C23×C4C2411yescharacteristic
646C23×C4C2411yescharacteristic
647C23×C4C2412yes—
648C23×C4C2411yescharacteristic
649C23×C4C2412yes—
650C23×C4C2412yes—
651C23×C4C2414yes—
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2412yes—
655C23×C4C2412yes—
656C23×C4C2412yes—
657C23×C4C2412yes—
658C23×C4C2414yes—
659C23×C4C2412yes—
660C23×C4C2411yescharacteristic
661#126—48no—
662#126—48no—
663#126—84no—
664#126—84no—
665#125—44no—
666#125—44no—
667#125—44no—
668#125—48no—
669#125—48no—
670#125—84no—
671#123—216no—
672#123—48no—
673#123—48no—
674#123—84no—
675C22⋊Q8—28no—
676C22⋊Q8—48no—
677C22⋊Q8—44no—
678C22⋊Q8—48no—
679C22⋊Q8—44no—
680C22⋊Q8—44no—
681C22⋊Q8—44no—
682C22⋊Q8—44no—
683C22⋊Q8—84no—
684C22⋊Q8—84no—
685C22⋊Q8—84no—
686C22⋊Q8—82no—
687C22⋊Q8—82no—
688#121—28no—
689#121—48no—
690#121—44no—
691C4×Q8—44no—
692C4×Q8—84no—
693C4×D4—28no—
694C4×D4—44no—
695C4×D4—44no—
696C4×D4—44no—
697C4×D4—48no—
698C4×D4—84no—
699#117—44no—
700#117—48no—
701#117—82no—
702#117—84no—
703C2×C4⋊C4—44no—
704C2×C4⋊C4—42no—
705C2×C4⋊C4—42no—
706C2×C4⋊C4—44no—
707C2×C4⋊C4—42no—
708C2×C4⋊C4—44no—
709C2×C4⋊C4—82no—
710C2×C4⋊C4—82no—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C22⋊C4—28no—
772C2×C22⋊C4—24no—
773C2×C22⋊C4—24no—
774C2×C22⋊C4—44no—
775C2×C22⋊C4—48no—
776C2×C22⋊C4—44no—
777C2×C22⋊C4—44no—
778C2×C22⋊C4—82no—
779C2×C22⋊C4—82no—
780C2×C22⋊C4—82no—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C42—42no—
820C2×C42—42no—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2414yes—
827C2×C42C2412yes—
828C2×C42C2414yes—
829C2×C42C2414yes—
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2412yes—
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—
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—
887C24—22no—
888C24—22no—
889C24—24no—
890C24—24no—
891C24—24no—
892C24—24no—
893C24—41no—
894C24—42no—
895C24—42no—
896C24—41no—
897C24—41no—
898C24—42no—
899C24—41no—
900C242−1+414yes—
901C24C2512yes—
902C24C2512yes—
903C24C2512yes—
904C24C2511yescharacteristic
905C2×Q8—24no—
906C2×Q8—42no—
907C2×Q8—44no—
908C2×Q8—44no—
909C2×Q8—42no—
910C2×Q8—44no—
911C2×Q8—42no—
912C2×Q8—42no—
913C2×Q8—42no—
914C2×D4—24no—
915C2×D4—28no—
916C2×D4—28no—
917C2×D4—28no—
918C2×D4—22no—
919C2×D4—24no—
920C2×D4—44no—
921C2×D4—41no—
922C2×D4—41no—
923C2×D4—41no—
924C2×D4—42no—
925C2×D4—41no—
926C2×D4—416no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—816no—
930C2×D4H(5,𝔽2)14yes—
931C22×C4—22no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—24no—
935C22×C4—24no—
936C22×C4—24no—
937C22×C4—28no—
938C22×C4—24no—
939C22×C4—22no—
940C22×C4—22no—
941C22×C4—22no—
942C22×C4—24no—
943C22×C4—24no—
944C22×C4—24no—
945C22×C4—22no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—24no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—41no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—41no—
958C22×C4—41no—
959C22×C4—41no—
960C22×C4—41no—
961C22×C4—41no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—44no—
965C22×C4—42no—
966C22×C4—41no—
967C22×C4—41no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—41no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—44no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—41no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—44no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—44no—
990C22×C4—42no—
991C22×C4—44no—
992C22×C4—42no—
993C22×C4—88no—
994C22×C4—816no—
995C22×C42−1+414yes—
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2512yes—
999C22×C4C2514yes—
1000C22×C4C2514yes—
1001C22×C4C2512yes—
1002C22×C4C2512yes—
1003C22×C4C2514yes—
1004C22×C4C2514yes—
1005C22×C4C2512yes—
1006C22×C4C2514yes—
1007C22×C4C2514yes—
1008C22×C4C2514yes—
1009C22×C4C2514yes—
1010C22×C4C2514yes—
1011C22×C4C2514yes—
1012C22×C4C2511yescharacteristic
1013C22×C4C2512yes—
1014C22×C4C2511yescharacteristic
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—24no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—44no—
1026C4⋊C4—42no—
1027C4⋊C4—41no—
1028C4⋊C4—41no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—42no—
1034C4⋊C4—44no—
1035C4⋊C4—42no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—42no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—42no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—42no—
1052C4⋊C4—44no—
1053C4⋊C4—42no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—42no—
1057C4⋊C4—44no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—42no—
1067C4⋊C4—44no—
1068C4⋊C4—42no—
1069C4⋊C4—44no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—44no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C22⋊C4—24no—
1076C22⋊C4—24no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—28no—
1081C22⋊C4—28no—
1082C22⋊C4—28no—
1083C22⋊C4—28no—
1084C22⋊C4—28no—
1085C22⋊C4—28no—
1086C22⋊C4—28no—
1087C22⋊C4—28no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C42—24no—
1114C42—24no—
1115C42—42no—
1116C42—42no—
1117C42—44no—
1118C42—44no—
1119C42—44no—
1120C42—44no—
1121C42—44no—
1122C42—44no—
1123C42—44no—
1124C42—44no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—22no—
1130C23—22no—
1131C23—22no—
1132C23—22no—
1133C23—22no—
1134C23—22no—
1135C23—22no—
1136C23—22no—
1137C23—22no—
1138C23—22no—
1139C23—22no—
1140C23—22no—
1141C23—28no—
1142C23—22no—
1143C23—22no—
1144C23—22no—
1145C23—22no—
1146C23—22no—
1147C23—22no—
1148C23—22no—
1149C23—44no—
1150C23—44no—
1151C23—48no—
1152C23—48no—
1153C23—48no—
1154C23—48no—
1155C23—82no—
1156C23—84no—
1157C23—82no—
1158C23—82no—
1159C23—84no—
1160C23—82no—
1161C23—84no—
1162C23C2×H(5,𝔽2)14yes—
1163C23C2×2−1+414yes—
1164C23C2×2−1+412yes—
1165C23C2×2−1+412yes—
1166C23#58512yes—
1167C23C2611yescharacteristic
1168Q8—84no—
1169Q8—88no—
1170Q8—162no—
1171D4—44no—
1172D4—48no—
1173D4—44no—
1174D4—416no—
1175D4—88no—
1176C2×C4—28no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—44no—
1232C2×C4—48no—
1233C2×C4—48no—
1234C2×C4—48no—
1235C2×C4—84no—
1236C2×C4—84no—
1237C2×C4—84no—
1238C2×C4—84no—
1239C2×C4—88no—
1240C2×C4—84no—
1241C2×C4—82no—
1242C2×C4—84no—
1243C2×C4—82no—
1244C2×C4—82no—
1245C2×C4—82no—
1246C2×C4—84no—
1247C2×C4—84no—
1248C2×C4—162no—
1249C2×C4—162no—
1250C2×C4—164no—
1251C2×C4C2×H(5,𝔽2)12yes—
1252C2×C4C2×2−1+414yes—
1253C2×C4#58512yes—
1254C22—22no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—24no—
1261C22—24no—
1262C22—24no—
1263C22—24no—
1264C22—24no—
1265C22—24no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—88no—
1282C22—816no—
1283C22#356314yes—
1284C22C22×H(5,𝔽2)11yescharacteristic
1285C22C22×2−1+411yescharacteristic
1286C22C22×2−1+411yescharacteristic
1287C22C2×#58511yescharacteristic
1288C22C2×#58511yescharacteristic
1289C22H(7,𝔽2)11yescharacteristic
1290C22H(7,𝔽2)11yescharacteristic
1291C4—22no—
1292C4—22no—
1293C4—24no—
1294C4—42no—
1295C4—44no—
1296C4—44no—
1297C4—44no—
1298C4—44no—
1299C4—44no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—44no—
1304C4—44no—
1305C4—44no—
1306C4—44no—
1307C4—42no—
1308C4—44no—
1309C4—42no—
1310C2—24no—
1311C2—44no—
1312C2—44no—
1313C2—82no—
1314C2C2×#356311yescharacteristic
1315C2#6282011yescharacteristic
1316C2#6287011yescharacteristic
1317C2#6289411yescharacteristic
1318C2#6289411yescharacteristic
1319C2#6290211yescharacteristic
1320C2#6292911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #56817C2semidirect
2. #56500C2semidirect
3. #55911C2semidirect
4. #54825C2semidirect
5. #51683C2semidirect
6. #48788C2semidirect
7. #48451C2semidirect
8. #48342C2semidirect
9. #46199C2semidirect
10. #46144C2semidirect
11. #43076C2semidirect
12. #40760C2semidirect
13. #39677C2semidirect
14. #37932C2semidirect
15. #37873C2semidirect
16. #37872C2semidirect
18. #37478C2semidirect
19. #36732C2semidirect
20. #36156C2semidirect
21. #35012C2semidirect
22. #34994C2semidirect
24. C2×#552C22semidirect
34. #2845C22semidirect
35. #2841C22semidirect
36. #2841C22semidirect
37. #2836C22semidirect
38. #2836C22semidirect
39. #2830C22semidirect
40. #2822C22semidirect
41. #2806C22semidirect
42. #2802C22semidirect
43. #2798C22semidirect
44. #2798C22semidirect
45. #2788C22semidirect
46. #2784C22semidirect
47. #2780C22semidirect
48. #2779C22semidirect
49. #2779C22semidirect
50. #2774C22semidirect
51. #2772C22semidirect
52. #2768C22semidirect
53. #2767C22semidirect
54. #2767C22semidirect
55. #2767C22semidirect
56. #2767C22semidirect
57. #2761C22semidirect
58. #2750C22semidirect
59. #2748C22semidirect
60. #2744C22semidirect
61. #2744C22semidirect
62. #2743C22semidirect
63. #2743C22semidirect
64. #2742C22semidirect
65. #2741C22semidirect
66. #2739C22semidirect
67. #2739C22semidirect
68. #2739C22semidirect
69. #2727C22semidirect
70. #2727C22semidirect
71. #2726C22semidirect
72. #2725C22semidirect
73. #2724C22semidirect
74. #2723C22semidirect
75. #2723C22semidirect
76. #2722C22semidirect
77. #2719C22semidirect
78. #2719C22semidirect
81. #2707C22semidirect
82. #2707C22semidirect
83. #2704C22semidirect
84. #2702C22semidirect
85. #2698C22semidirect
86. #2698C22semidirect
87. #2698C22semidirect
88. #2695C22semidirect
89. #2695C22semidirect
90. #2694C22semidirect
91. #2692C22semidirect
93. #2690C22semidirect
94. #2689C22semidirect
95. #2689C22semidirect
96. #2687C22semidirect
97. #2683C22semidirect
99. #2667C22semidirect
100. #2665C22semidirect
104. #2659C22semidirect
105. #2652C22semidirect
106. #2650C22semidirect
111. #2637C22semidirect
112. #2627C22semidirect
113. #2627C22semidirect
114. #2627C22semidirect
116. #2625C22semidirect
118. #2609C22semidirect
119. #2601C22semidirect
120. #2590C22semidirect
121. #2584C22semidirect
123. #2579C22semidirect
124. #2574C22semidirect
127. #2564C22semidirect
128. #2562C22semidirect
129. #2556C22semidirect
130. #2553C22semidirect
132. #2536C22semidirect
133. #2536C22semidirect
134. #2522C22semidirect
138. #2505C22semidirect
139. #2505C22semidirect
140. #2486C22semidirect
141. #2485C22semidirect
142. #2485C22semidirect
147. #2478C22semidirect
148. #2477C22semidirect
149. #2477C22semidirect
153. #2473C22semidirect
154. #2473C22semidirect
155. #2470C22semidirect
156. #2470C22semidirect
157. #2468C22semidirect
158. #2468C22semidirect
159. #2465C22semidirect
160. #2462C22semidirect
161. #2460C22semidirect
162. #2460C22semidirect
163. #2458C22semidirect
164. #2453C22semidirect
165. #2450C22semidirect
166. #2449C22semidirect
168. #2442C22semidirect
169. #2438C22semidirect
170. #2438C22semidirect
171. #2438C22semidirect
177. #2421C22semidirect
182. #2419C22semidirect
183. #2417C22semidirect
184. #2415C22semidirect
189. #2382C22semidirect
190. #2382C22semidirect
191. #2376C22semidirect
193. #2359C22semidirect
194. #2352C22semidirect
201. #2329C22semidirect
203. #2316C22semidirect

Maximal subgroups

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

subgroupindex
#568172
#565002
#559112
#548252
#516832
#487882
#484512
#483422
#461992
#461442
#430762
#407602
#396772
#379322
#378732
#378722
#376922
#374782
#367322
#361562
#350122
#349942
C2×#24202