Finite Group Databasebeta

← #8930830

Subgroups — #8930830

Order 512.

4922 conjugacy classes of subgroups.

The subgroup lattice has 1249 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57590C214yesmaximal, complemented
2#55559C214yesmaximal, complemented
3#55176C214yesmaximal, complemented
4#55165C214yesmaximal, complemented
5#54351C214yesmaximal, complemented
6#54349C214yesmaximal, complemented
7#51438C214yesmaximal, complemented
8#49837C214yesmaximal, complemented
9#47906C214yesmaximal, complemented
10#47215C212yesmaximal, complemented
11#47213C212yesmaximal, complemented
12#47033C212yesmaximal, complemented
13#46265C214yesmaximal, complemented
14#45896C214yesmaximal, complemented
15#45457C214yesmaximal, complemented
16#37016C212yesmaximal, complemented
17#37014C212yesmaximal, complemented
18#36703C212yesmaximal, complemented
19#35624C211yesmaximal, characteristic, complemented
20#35537C211yesmaximal, characteristic, complemented
21#35350C211yesmaximal, characteristic, complemented
22C2×#541C2211yescharacteristic, complemented
23C2×#540C2211yescharacteristic, complemented
24C2×#538C2212yes—
25C22×#120C2211yescharacteristic
26C2×#518C2211yescharacteristic
27#2865C2214yescomplemented
28#2860C2214yescomplemented
29#2846C2214yes—
30#2842C2214yescomplemented
31#2837C2214yescomplemented
32#2829C2214yescomplemented
33#2829C2214yescomplemented
34#2828C2214yescomplemented
35#2827C2214yescomplemented
36#2816C2212yescomplemented
37#2813C2214yescomplemented
38#2812C2214yescomplemented
39#2798C2214yescomplemented
40#2797C2214yescomplemented
41#2797C2214yescomplemented
42#2797C2214yescomplemented
43#2795C2214yescomplemented
44#2793C2214yescomplemented
45#2790C2214yescomplemented
46#2786C2214yescomplemented
47#2781C2214yescomplemented
48#2780C2214yescomplemented
49#2773C2214yescomplemented
50#2773C2214yescomplemented
51#2754C2214yescomplemented
52#2753C2214yescomplemented
53#2744C2214yescomplemented
54#2740C2214yescomplemented
55#2740C2214yescomplemented
56#2739C2214yescomplemented
57#2739C2214yescomplemented
58#2735C2214yes—
59#2735C2214yes—
60#2735C2214yescomplemented
61#2731C2214yescomplemented
62#2727C2214yescomplemented
63#2721C2214yescomplemented
64#2721C2214yescomplemented
65#2721C2214yescomplemented
66#2718C2214yescomplemented
67#2714C2214yescomplemented
68#2711C2214yescomplemented
69#2711C2214yescomplemented
70#2710C2214yescomplemented
71#2710C2214yescomplemented
72#2709C2214yescomplemented
73#2708C2214yescomplemented
74#2707C2214yescomplemented
75#2706C2214yescomplemented
76#2706C2214yescomplemented
77#2705C2214yescomplemented
78#2705C2214yescomplemented
79#2705C2214yescomplemented
80#2703C2214yescomplemented
81#2703C2214yescomplemented
82#2697C2214yes—
83#2697C2214yescomplemented
84#2697C2214yescomplemented
85#2695C2214yescomplemented
86#2695C2214yescomplemented
87#2694C2214yescomplemented
88#2694C2214yescomplemented
89#2693C2214yescomplemented
90#2685C2214yes—
91#2685C2214yes—
92#2685C2214yes—
93#2685C2214yes—
94#2685C2214yes—
95#2685C2214yescomplemented
96#2685C2214yescomplemented
97#2682C2214yescomplemented
98#2678C2214yes—
99#2678C2214yes—
100#2678C2214yes—
101#2678C2214yescomplemented
102#2673C2214yescomplemented
103#2671C2214yescomplemented
104#2670C2214yes—
105#2670C2214yes—
106#2669C2214yes—
107#2669C2214yes—
108#2668C2214yes—
109#2661C2214yescomplemented
110#2654C2214yescomplemented
111#2651C2214yescomplemented
112#2651C2214yescomplemented
113#2648C2214yescomplemented
114#2630C2214yescomplemented
115#2629C2214yescomplemented
116#2618C2214yescomplemented
117#2613C2214yes—
118#2608C2212yescomplemented
119#2602C2214yescomplemented
120#2602C2214yescomplemented
121#2601C2214yescomplemented
122#2596C2214yescomplemented
123#2587C2214yescomplemented
124#2579C2214yescomplemented
125#2566C2212yescomplemented
126#2566C2212yescomplemented
127#2561C2212yes—
128#2559C2214yescomplemented
129#2559C2214yescomplemented
130#2558C2214yescomplemented
131#2557C2214yescomplemented
132#2554C2214yescomplemented
133#2547C2212yescomplemented
134#2541C2212yescomplemented
135#2539C2212yes—
136#2539C2214yescomplemented
137#2534C2214yes—
138#2534C2214yes—
139#2534C2214yescomplemented
140#2531C2214yescomplemented
141#2529C2214yescomplemented
142#2519C2214yescomplemented
143#2501C2214yescomplemented
144#2500C2212yescomplemented
145#2499C2212yescomplemented
146#2490C2214yescomplemented
147#2482C2212yes—
148#2482C2212yes—
149#2482C2214yescomplemented
150#2480C2214yes—
151#2480C2214yescomplemented
152#2480C2214yescomplemented
153#2471C2214yescomplemented
154#2468C2214yescomplemented
155#2467C2214yescomplemented
156#2467C2214yescomplemented
157#2466C2214yescomplemented
158#2460C2214yescomplemented
159#2460C2214yescomplemented
160#2460C2214yescomplemented
161#2459C2214yescomplemented
162#2458C2214yescomplemented
163#2456C2214yescomplemented
164#2456C2214yescomplemented
165#2448C2214yescomplemented
166#2445C2214yescomplemented
167#2443C2214yescomplemented
168#2443C2214yescomplemented
169#2443C2214yescomplemented
170#2435C2212yes—
171#2433C2212yes—
172#2424C2214yes—
173#2424C2214yescomplemented
174#2424C2214yescomplemented
175#2422C2214yescomplemented
176#2418C2214yes—
177#2418C2214yes—
178#2418C2214yes—
179#2418C2214yes—
180#2418C2214yescomplemented
181#2418C2214yescomplemented
182#2411C2214yes—
183#2411C2214yescomplemented
184#2408C2214yes—
185#2405C2212yes—
186#2405C2212yes—
187#2376C2214yescomplemented
188#2375C2214yescomplemented
189#2375C2214yescomplemented
190#2352C2214yescomplemented
191#2333C2212yescomplemented
192#2332C2212yescomplemented
193#2328C2212yescomplemented
194#2326C2212yescomplemented
195#2315C2212yes—
196#2312C2212yes—
197#2308C2211yescharacteristic
198C4×#127C2212yescomplemented
199C4×#124C2212yescomplemented
200#2298C2211yescharacteristic, complemented
201#2298C2211yescharacteristic, complemented
202C2×#379C2212yes—
203C26C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C23×D4C2312yes—
206#541—44no—
207#540—44no—
208#538—48no—
209C2×C4⋊Q8C2311yescharacteristic, complemented
210C2×#127C2312yes—
211C2×#127C2312yes—
212C2×#127C2311yescharacteristic, complemented
213C2×#126C2314yes—
214C2×#126C2314yes—
215C2×#126C2314yes—
216C2×#126C2314yescomplemented
217C2×#126C2314yescomplemented
218C2×#125C2311yescharacteristic, complemented
219C2×#125C2311yescharacteristic, complemented
220C2×#125C2314yescomplemented
221C2×#125C2314yescomplemented
222C2×#124C2312yes—
223C2×#124C2314yes—
224C2×#124C2312yes—
225C2×#123C2314yes—
226C2×#123C2314yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×#123C2314yes—
230C2×#123C2314yes—
231C2×#123C2314yes—
232C2×#123C2314yes—
233C2×#123C2314yescomplemented
234C2×#123C2314yescomplemented
235C2×#123C2314yescomplemented
236C2×C22⋊Q8C2312yes—
237C2×#121C2312yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×#121C2314yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#121C2314yescomplemented
245C2×#120—44no—
246C2×#120C2314yes—
247C2×#120C2314yes—
248C2×#120C2314yes—
249C2×#120C2314yes—
250C2×#120C2314yes—
251C2×#120C2314yes—
252C2×#120C2314yes—
253C2×#120C2314yes—
254C2×#120C2314yes—
255C2×#120C2314yes—
256#518—44no—
257C2×C4×Q8C2312yescomplemented
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2312yescomplemented
266C2×C4×D4C2314yescomplemented
267C2×#117C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C2×#117C2314yes—
270C22×C4⋊C4C2314yescomplemented
271C22×C22⋊C4C2312yes—
272C22×C22⋊C4C2312yes—
273C22×C22⋊C4C2311yescharacteristic
274C22×C22⋊C4C2312yes—
275C22×C22⋊C4C2312yes—
276C22×C22⋊C4C2314yes—
277C22×C22⋊C4C2314yes—
278#400C2314yescomplemented
279#400C2314yescomplemented
280#400C2314yescomplemented
281#400C2314yescomplemented
282#400C2314yescomplemented
283#400C2314yescomplemented
284#399C2314yes—
285#399C2314yes—
286#399C2314yes—
287#399C2314yes—
288#399C2314yes—
289#399C2314yes—
290#399C2314yes—
291#399C2314yes—
292#399C2314yes—
293#399C2314yescomplemented
294#399C2314yescomplemented
295#399C2314yescomplemented
296#398C2314yescomplemented
297#398C2314yescomplemented
298#398C2314yescomplemented
299#398C2314yescomplemented
300#398C2314yescomplemented
301#398C2314yescomplemented
302#398C2314yescomplemented
303#398C2314yescomplemented
304#398C2314yescomplemented
305#398C2314yescomplemented
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#397C2314yescomplemented
320#397C2314yescomplemented
321#397C2314yescomplemented
322#397C2314yescomplemented
323#397C2314yescomplemented
324#397C2314yescomplemented
325#397C2314yescomplemented
326#396C2314yes—
327#396C2314yes—
328#396C2314yes—
329#396C2314yes—
330#396C2314yes—
331#396C2314yes—
332#396C2314yes—
333#396C2314yes—
334#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yescomplemented
341#396C2314yescomplemented
342#396C2314yescomplemented
343#396C2314yescomplemented
344#396C2314yescomplemented
345#396C2314yescomplemented
346#394C2314yes—
347#394C2314yes—
348#394C2314yes—
349#394C2314yes—
350#394C2314yes—
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#394C2314yes—
375#394C2314yes—
376#394C2314yescomplemented
377#394C2314yescomplemented
378#394C2314yescomplemented
379#394C2314yescomplemented
380#394C2314yescomplemented
381#394C2314yescomplemented
382#393C2314yes—
383#393C2314yescomplemented
384#392C2314yes—
385#392C2314yes—
386#392C2314yes—
387#392C2314yes—
388#392C2314yes—
389#392C2314yes—
390#392C2314yes—
391#392C2314yes—
392#392C2314yes—
393#392C2314yes—
394#392C2314yes—
395#392C2314yes—
396#392C2314yes—
397#392C2314yescomplemented
398#391C2312yescomplemented
399#391C2314yescomplemented
400#391C2312yescomplemented
401#390C2312yes—
402#390C2314yes—
403#390C2312yes—
404#390C2312yes—
405#390C2312yes—
406#390C2314yes—
407#390C2314yes—
408#390C2314yes—
409#390C2314yes—
410#390C2314yes—
411#390C2314yes—
412#390C2314yes—
413#390C2314yes—
414#390C2314yes—
415#390C2314yes—
416#390C2314yes—
417#390C2314yes—
418#390C2314yes—
419#390C2314yescomplemented
420#390C2312yescomplemented
421#390C2312yescomplemented
422#390C2314yescomplemented
423#390C2314yescomplemented
424#389C2314yescomplemented
425#389C2314yescomplemented
426#389C2314yescomplemented
427#389C2314yescomplemented
428#389C2314yescomplemented
429#389C2314yescomplemented
430#389C2314yescomplemented
431#389C2314yescomplemented
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
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#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yescomplemented
469#388C2314yescomplemented
470#388C2314yescomplemented
471#388C2314yescomplemented
472#388C2314yescomplemented
473#388C2314yescomplemented
474#388C2314yescomplemented
475#388C2314yescomplemented
476#388C2314yescomplemented
477#388C2314yescomplemented
478#388C2314yescomplemented
479#388C2314yescomplemented
480#387C2314yescomplemented
481#387C2314yescomplemented
482#387C2314yescomplemented
483#387C2314yescomplemented
484#387C2314yescomplemented
485#387C2314yescomplemented
486#387C2314yescomplemented
487#387C2314yescomplemented
488#387C2314yescomplemented
489#387C2314yescomplemented
490#387C2314yescomplemented
491#387C2314yescomplemented
492#387C2314yescomplemented
493#387C2314yescomplemented
494#387C2314yescomplemented
495#387C2314yescomplemented
496#387C2314yescomplemented
497#387C2314yescomplemented
498#387C2314yescomplemented
499#387C2314yescomplemented
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yescomplemented
517#386C2314yescomplemented
518#386C2314yescomplemented
519#386C2314yescomplemented
520#386C2314yescomplemented
521#386C2314yescomplemented
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2312yes—
527#385C2312yes—
528#385C2312yes—
529#385C2312yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yescomplemented
533#385C2314yescomplemented
534#385C2314yescomplemented
535#385C2314yescomplemented
536#385C2314yescomplemented
537#385C2314yescomplemented
538#385C2314yescomplemented
539#385C2314yescomplemented
540#384C2312yescomplemented
541#384C2312yescomplemented
542#384C2314yescomplemented
543#382C2312yescomplemented
544#382C2312yescomplemented
545#382C2314yescomplemented
546#381C2312yes—
547#381C2314yes—
548#381C2314yes—
549#380C2314yes—
550#380C2314yes—
551#380C2314yes—
552#380C2314yes—
553#380C2314yes—
554#380C2314yescomplemented
555#380C2314yescomplemented
556#380C2314yescomplemented
557#380C2314yescomplemented
558#379C2314yes—
559#379C2311yescharacteristic
560#379C2311yescharacteristic
561#379C2314yes—
562#379C2314yes—
563#379C2314yes—
564#379C2314yes—
565#379C2314yes—
566#379C2314yes—
567#379C2314yes—
568#379C2314yes—
569#379C2314yes—
570#379C2312yes—
571#379C2312yes—
572#379C2312yes—
573#379C2312yes—
574C4×C4⋊C4C2312yescomplemented
575C4×C4⋊C4C2312yescomplemented
576C4×C4⋊C4C2314yescomplemented
577C4×C4⋊C4C2314yescomplemented
578C4×C22⋊C4C2312yes—
579C4×C22⋊C4C2312yes—
580C4×C22⋊C4C2314yes—
581C4×C22⋊C4C2314yescomplemented
582C4×C22⋊C4C2314yescomplemented
583C4×C22⋊C4C2314yescomplemented
584C4×C22⋊C4C2314yescomplemented
585#376C2311yescharacteristic, complemented
586#376C2311yescharacteristic, complemented
587C43C2311yescharacteristic, complemented
588C43C2311yescharacteristic, complemented
589C25—42no—
590C25—44no—
591C25—84no—
592C25C2411yescharacteristic
593C25C2414yes—
594C25C2411yescharacteristic
595C25C2412yes—
596C22×Q8C2412yes—
597C22×D4—24no—
598C22×D4—44no—
599C22×D4—44no—
600C22×D4—84no—
601C22×D4C2412yes—
602C22×D4C2412yes—
603C22×D4C2414yes—
604C22×D4C2414yes—
605C22×D4C2414yes—
606C22×D4C2412yes—
607C22×D4C2414yes—
608C22×D4C2414yes—
609C22×D4C2414yes—
610C22×D4C2414yes—
611C22×D4C2414yes—
612C22×D4C2414yes—
613C22×D4C2414yes—
614C22×D4C2414yes—
615C22×D4C2414yes—
616C23×C4C2414yes—
617C23×C4C2412yes—
618C23×C4C2412yes—
619C23×C4C2412yes—
620C23×C4C2412yes—
621C23×C4C2412yes—
622C23×C4C2414yes—
623C23×C4C2414yes—
624C23×C4C2414yes—
625C23×C4C2411yescharacteristic
626C4⋊Q8—42no—
627#127—42no—
628#127—44no—
629#127—44no—
630#126—48no—
631#126—48no—
632#126—84no—
633#126—84no—
634#126—84no—
635#125—42no—
636#125—42no—
637#125—48no—
638#125—84no—
639#124—44no—
640#124—44no—
641#124—48no—
642#123—48no—
643#123—48no—
644#123—48no—
645#123—84no—
646#123—84no—
647#123—84no—
648#123—84no—
649#123—84no—
650#123—84no—
651#123—84no—
652#123—84no—
653C22⋊Q8—28no—
654#121—28no—
655#121—48no—
656#121—48no—
657#121—84no—
658#121—84no—
659#121—84no—
660#121—84no—
661#121—84no—
662#120—48no—
663#120—48no—
664#120—48no—
665#120—48no—
666#120—48no—
667#120—84no—
668#120—84no—
669#120—84no—
670#120—84no—
671#120—84no—
672C4×Q8—44no—
673C4×D4—44no—
674C4×D4—44no—
675C4×D4—44no—
676C4×D4—44no—
677C4×D4—44no—
678C4×D4—48no—
679C4×D4—48no—
680C4×D4—84no—
681C4×D4—84no—
682#117—24no—
683#117—24no—
684#117—84no—
685C2×C4⋊C4—84no—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C22⋊C4—28no—
722C2×C22⋊C4—44no—
723C2×C22⋊C4—44no—
724C2×C22⋊C4—44no—
725C2×C22⋊C4—42no—
726C2×C22⋊C4—84no—
727C2×C22⋊C4—84no—
728C2×C22⋊C4C2412yes—
729C2×C22⋊C4C2412yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2412yes—
737C2×C22⋊C4C2412yes—
738C2×C22⋊C4C2412yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2412yes—
750C2×C22⋊C4C2412yes—
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×C42C2411yescharacteristic
794C2×C42C2411yescharacteristic
795C2×C42C2411yescharacteristic
796C2×C42C2411yescharacteristic
797C2×C42C2414yes—
798C2×C42C2414yes—
799C2×C42C2414yes—
800C2×C42C2414yes—
801C2×C42C2414yes—
802C2×C42C2414yes—
803C2×C42C2412yes—
804C2×C42C2412yes—
805C2×C42C2414yes—
806C2×C42C2412yes—
807C2×C42C2412yes—
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—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
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—
844C24—22no—
845C24—24no—
846C24—24no—
847C24—22no—
848C24—28no—
849C24—44no—
850C24—44no—
851C24—44no—
852C24—44no—
853C24—42no—
854C24—44no—
855C24—44no—
856C24—44no—
857C24—44no—
858C24—44no—
859C24—42no—
860C24—42no—
861C24—44no—
862C24—88no—
863C24—816no—
864C24—832no—
865C24C2514yes—
866C24C2512yes—
867C24C2514yes—
868C24C2511yescharacteristic
869C24C2512yes—
870C2×Q8—24no—
871C2×Q8—42no—
872C2×Q8—42no—
873C2×D4—24no—
874C2×D4—24no—
875C2×D4—28no—
876C2×D4—28no—
877C2×D4—28no—
878C2×D4—24no—
879C2×D4—24no—
880C2×D4—24no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
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—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—416no—
919C2×D4—816no—
920C22×C4—24no—
921C22×C4—28no—
922C22×C4—42no—
923C22×C4—44no—
924C22×C4—44no—
925C22×C4—44no—
926C22×C4—44no—
927C22×C4—44no—
928C22×C4—44no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4H(5,𝔽2)14yes—
944C22×C4C2514yes—
945C22×C4C2514yes—
946C22×C4C2514yes—
947C22×C4C2512yes—
948C22×C4C2514yes—
949C22×C4C2514yes—
950C22×C4C2512yes—
951C22×C4C2514yes—
952C22×C4C2514yes—
953C22×C4C2514yes—
954C22×C4C2512yes—
955C22×C4C2514yes—
956C22×C4C2514yes—
957C22×C4C2512yes—
958C22×C4C2511yescharacteristic
959C22×C4C2511yescharacteristic
960C4⋊C4—24no—
961C4⋊C4—24no—
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—28no—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C22⋊C4—24no—
996C22⋊C4—24no—
997C22⋊C4—28no—
998C22⋊C4—28no—
999C22⋊C4—28no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—28no—
1003C22⋊C4—42no—
1004C22⋊C4—44no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C22⋊C4—44no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
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—
1060C42—22no—
1061C42—22no—
1062C42—22no—
1063C42—22no—
1064C42—44no—
1065C42—44no—
1066C42—44no—
1067C42—44no—
1068C42—44no—
1069C42—44no—
1070C42—42no—
1071C42—42no—
1072C42—44no—
1073C42—42no—
1074C42—42no—
1075C23—28no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—24no—
1080C23—24no—
1081C23—24no—
1082C23—24no—
1083C23—24no—
1084C23—22no—
1085C23—22no—
1086C23—24no—
1087C23—24no—
1088C23—24no—
1089C23—24no—
1090C23—22no—
1091C23—24no—
1092C23—24no—
1093C23—24no—
1094C23—24no—
1095C23—24no—
1096C23—24no—
1097C23—24no—
1098C23—24no—
1099C23—24no—
1100C23—24no—
1101C23—48no—
1102C23—44no—
1103C23—416no—
1104C23—88no—
1105C23—88no—
1106C23—88no—
1107C23—84no—
1108C23—88no—
1109C23—84no—
1110C23—84no—
1111C23—84no—
1112C23—88no—
1113C23—88no—
1114C23—88no—
1115C23—88no—
1116C23—88no—
1117C23—864no—
1118C23—164no—
1119C23C2×H(5,𝔽2)12yes—
1120C23#58514yes—
1121C23C2611yescharacteristic
1122Q8—84no—
1123D4—48no—
1124D4—48no—
1125D4—84no—
1126D4—88no—
1127D4—88no—
1128D4—88no—
1129D4—88no—
1130D4—88no—
1131D4—88no—
1132D4—164no—
1133D4—164no—
1134D4—164no—
1135D4—164no—
1136D4—164no—
1137D4—164no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
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—24no—
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—44no—
1179C2×C4—88no—
1180C2×C4—84no—
1181C2×C4—88no—
1182C2×C4—164no—
1183C2×C4—162no—
1184C2×C4—162no—
1185C2×C4—162no—
1186C2×C4—162no—
1187C2×C4—164no—
1188C2×C4C2×H(5,𝔽2)12yes—
1189C2×C4C2×H(5,𝔽2)12yes—
1190C22—28no—
1191C22—22no—
1192C22—24no—
1193C22—24no—
1194C22—44no—
1195C22—44no—
1196C22—42no—
1197C22—42no—
1198C22—44no—
1199C22—44no—
1200C22—44no—
1201C22—44no—
1202C22—44no—
1203C22—44no—
1204C22—44no—
1205C22—44no—
1206C22—44no—
1207C22—44no—
1208C22—42no—
1209C22—44no—
1210C22—44no—
1211C22—44no—
1212C22—42no—
1213C22—42no—
1214C22—44no—
1215C22—44no—
1216C22—44no—
1217C22—88no—
1218C22—832no—
1219C22—816no—
1220C22—164no—
1221C22C22×H(5,𝔽2)11yescharacteristic
1222C22C2×#58512yes—
1223C22H(7,𝔽2)14yes—
1224C4—22no—
1225C4—22no—
1226C4—44no—
1227C4—44no—
1228C4—44no—
1229C4—44no—
1230C4—44no—
1231C4—44no—
1232C4—44no—
1233C4—44no—
1234C4—42no—
1235C4—42no—
1236C4—42no—
1237C4—42no—
1238C4—44no—
1239C4—44no—
1240C2—44no—
1241C2—42no—
1242C2—84no—
1243C2—84no—
1244C2—82no—
1245C2#6282011yescharacteristic
1246C2#6287612yes—
1247C2#6304214yes—
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. #57590C2semidirect
2. #55559C2semidirect
3. #55176C2semidirect
4. #55165C2semidirect
5. #54351C2semidirect
6. #54349C2semidirect
7. #51438C2semidirect
8. #49837C2semidirect
9. #47906C2semidirect
10. #47215C2semidirect
11. #47213C2semidirect
12. #47033C2semidirect
13. #46265C2semidirect
14. #45896C2semidirect
15. #45457C2semidirect
16. #37016C2semidirect
17. #37014C2semidirect
18. #36703C2semidirect
19. #35624C2semidirect
20. #35537C2semidirect
21. #35350C2semidirect
22. C2×#541C22semidirect
23. C2×#540C22semidirect
27. #2865C22semidirect
28. #2860C22semidirect
30. #2842C22semidirect
31. #2837C22semidirect
32. #2829C22semidirect
33. #2829C22semidirect
34. #2828C22semidirect
35. #2827C22semidirect
36. #2816C22semidirect
37. #2813C22semidirect
38. #2812C22semidirect
39. #2798C22semidirect
40. #2797C22semidirect
41. #2797C22semidirect
42. #2797C22semidirect
43. #2795C22semidirect
44. #2793C22semidirect
45. #2790C22semidirect
46. #2786C22semidirect
47. #2781C22semidirect
48. #2780C22semidirect
49. #2773C22semidirect
50. #2773C22semidirect
51. #2754C22semidirect
52. #2753C22semidirect
53. #2744C22semidirect
54. #2740C22semidirect
55. #2740C22semidirect
56. #2739C22semidirect
57. #2739C22semidirect
60. #2735C22semidirect
61. #2731C22semidirect
62. #2727C22semidirect
63. #2721C22semidirect
64. #2721C22semidirect
65. #2721C22semidirect
66. #2718C22semidirect
67. #2714C22semidirect
68. #2711C22semidirect
69. #2711C22semidirect
70. #2710C22semidirect
71. #2710C22semidirect
72. #2709C22semidirect
73. #2708C22semidirect
74. #2707C22semidirect
75. #2706C22semidirect
76. #2706C22semidirect
77. #2705C22semidirect
78. #2705C22semidirect
79. #2705C22semidirect
80. #2703C22semidirect
81. #2703C22semidirect
83. #2697C22semidirect
84. #2697C22semidirect
85. #2695C22semidirect
86. #2695C22semidirect
87. #2694C22semidirect
88. #2694C22semidirect
89. #2693C22semidirect
95. #2685C22semidirect
96. #2685C22semidirect
97. #2682C22semidirect
101. #2678C22semidirect
102. #2673C22semidirect
103. #2671C22semidirect
109. #2661C22semidirect
110. #2654C22semidirect
111. #2651C22semidirect
112. #2651C22semidirect
113. #2648C22semidirect
114. #2630C22semidirect
115. #2629C22semidirect
116. #2618C22semidirect
118. #2608C22semidirect
119. #2602C22semidirect
120. #2602C22semidirect
121. #2601C22semidirect
122. #2596C22semidirect
123. #2587C22semidirect
124. #2579C22semidirect
125. #2566C22semidirect
126. #2566C22semidirect
128. #2559C22semidirect
129. #2559C22semidirect
130. #2558C22semidirect
131. #2557C22semidirect
132. #2554C22semidirect
133. #2547C22semidirect
134. #2541C22semidirect
136. #2539C22semidirect
139. #2534C22semidirect
140. #2531C22semidirect
141. #2529C22semidirect
142. #2519C22semidirect
143. #2501C22semidirect
144. #2500C22semidirect
145. #2499C22semidirect
146. #2490C22semidirect
149. #2482C22semidirect
151. #2480C22semidirect
152. #2480C22semidirect
153. #2471C22semidirect
154. #2468C22semidirect
155. #2467C22semidirect
156. #2467C22semidirect
157. #2466C22semidirect
158. #2460C22semidirect
159. #2460C22semidirect
160. #2460C22semidirect
161. #2459C22semidirect
162. #2458C22semidirect
163. #2456C22semidirect
164. #2456C22semidirect
165. #2448C22semidirect
166. #2445C22semidirect
167. #2443C22semidirect
168. #2443C22semidirect
169. #2443C22semidirect
173. #2424C22semidirect
174. #2424C22semidirect
175. #2422C22semidirect
180. #2418C22semidirect
181. #2418C22semidirect
183. #2411C22semidirect
187. #2376C22semidirect
188. #2375C22semidirect
189. #2375C22semidirect
190. #2352C22semidirect
191. #2333C22semidirect
192. #2332C22semidirect
193. #2328C22semidirect
194. #2326C22semidirect
198. C4×#127C22semidirect
199. C4×#124C22semidirect
200. #2298C22semidirect
201. #2298C22semidirect
209. C2×C4⋊Q8C23semidirect
212. C2×#127C23semidirect
216. C2×#126C23semidirect
217. C2×#126C23semidirect
218. C2×#125C23semidirect
219. C2×#125C23semidirect
220. C2×#125C23semidirect
221. C2×#125C23semidirect
233. C2×#123C23semidirect
234. C2×#123C23semidirect
235. C2×#123C23semidirect
244. C2×#121C23semidirect
257. C2×C4×Q8C23semidirect
265. C2×C4×D4C23semidirect
266. C2×C4×D4C23semidirect
270. C22×C4⋊C4C23semidirect
278. #400C23semidirect
279. #400C23semidirect
280. #400C23semidirect
281. #400C23semidirect
282. #400C23semidirect
283. #400C23semidirect
293. #399C23semidirect
294. #399C23semidirect
295. #399C23semidirect
296. #398C23semidirect
297. #398C23semidirect
298. #398C23semidirect
299. #398C23semidirect
300. #398C23semidirect
301. #398C23semidirect
302. #398C23semidirect
303. #398C23semidirect
304. #398C23semidirect
305. #398C23semidirect
319. #397C23semidirect
320. #397C23semidirect
321. #397C23semidirect
322. #397C23semidirect
323. #397C23semidirect
324. #397C23semidirect
325. #397C23semidirect
340. #396C23semidirect
341. #396C23semidirect
342. #396C23semidirect
343. #396C23semidirect
344. #396C23semidirect
345. #396C23semidirect
376. #394C23semidirect
377. #394C23semidirect
378. #394C23semidirect
379. #394C23semidirect
380. #394C23semidirect
381. #394C23semidirect
383. #393C23semidirect
397. #392C23semidirect
398. #391C23semidirect
399. #391C23semidirect
400. #391C23semidirect
419. #390C23semidirect
420. #390C23semidirect
421. #390C23semidirect
422. #390C23semidirect
423. #390C23semidirect
424. #389C23semidirect
425. #389C23semidirect
426. #389C23semidirect
427. #389C23semidirect
428. #389C23semidirect
429. #389C23semidirect
430. #389C23semidirect
431. #389C23semidirect
468. #388C23semidirect
469. #388C23semidirect
470. #388C23semidirect
471. #388C23semidirect
472. #388C23semidirect
473. #388C23semidirect
474. #388C23semidirect
475. #388C23semidirect
476. #388C23semidirect
477. #388C23semidirect
478. #388C23semidirect
479. #388C23semidirect
480. #387C23semidirect
481. #387C23semidirect
482. #387C23semidirect
483. #387C23semidirect
484. #387C23semidirect
485. #387C23semidirect
486. #387C23semidirect
487. #387C23semidirect
488. #387C23semidirect
489. #387C23semidirect
490. #387C23semidirect
491. #387C23semidirect
492. #387C23semidirect
493. #387C23semidirect
494. #387C23semidirect
495. #387C23semidirect
496. #387C23semidirect
497. #387C23semidirect
498. #387C23semidirect
499. #387C23semidirect
516. #386C23semidirect
517. #386C23semidirect
518. #386C23semidirect
519. #386C23semidirect
520. #386C23semidirect
521. #386C23semidirect
532. #385C23semidirect
533. #385C23semidirect
534. #385C23semidirect
535. #385C23semidirect
536. #385C23semidirect
537. #385C23semidirect
538. #385C23semidirect
539. #385C23semidirect
540. #384C23semidirect
541. #384C23semidirect
542. #384C23semidirect
543. #382C23semidirect
544. #382C23semidirect
545. #382C23semidirect
554. #380C23semidirect
555. #380C23semidirect
556. #380C23semidirect
557. #380C23semidirect
574. C4×C4⋊C4C23semidirect
575. C4×C4⋊C4C23semidirect
576. C4×C4⋊C4C23semidirect
577. C4×C4⋊C4C23semidirect
581. C4×C22⋊C4C23semidirect
582. C4×C22⋊C4C23semidirect
583. C4×C22⋊C4C23semidirect
584. C4×C22⋊C4C23semidirect
585. #376C23semidirect
586. #376C23semidirect
587. C43C23semidirect
588. C43C23semidirect

Maximal subgroups

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

subgroupindex
#575902
#555592
#551762
#551652
#543512
#543492
#514382
#498372
#479062
#472152
#472132
#470332
#462652
#458962
#454572
#370162
#370142
#367032
#356242
#355372
#353502