Finite Group Databasebeta

← #8757602

Subgroups — #8757602

Order 512.

5258 conjugacy classes of subgroups.

The subgroup lattice has 1359 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58033C214yesmaximal, complemented
2#56680C214yesmaximal, complemented
3#56631C214yesmaximal, complemented
4#55574C214yesmaximal, complemented
5#55384C214yesmaximal, complemented
6#55144C214yesmaximal, complemented
7#52075C212yesmaximal, complemented
8#52072C211yesmaximal, characteristic, complemented
9#52072C212yesmaximal, complemented
10#51988C212yesmaximal, complemented
11#51984C212yesmaximal, complemented
12#51668C212yesmaximal, complemented
13#51542C211yesmaximal, characteristic, complemented
14#47180C212yesmaximal, complemented
15#47166C214yesmaximal, complemented
16#46363C214yesmaximal, complemented
17#46359C212yesmaximal, complemented
18#45472C212yesmaximal, complemented
19#45466C214yesmaximal, complemented
20#45453C212yesmaximal, complemented
21#45446C214yesmaximal, complemented
22#35305C212yesmaximal, complemented
23#35149C211yesmaximal, characteristic
24C23×#41C2211yescharacteristic
25C2×#563C2212yes—
26C2×#563C2211yescharacteristic, complemented
27C2×Q82C2211yescharacteristic, complemented
28C2×#539C2212yescomplemented
29C2×#536C2212yes—
30C2×#536C2211yescharacteristic
31C2×#536C2212yes—
32C2×#535C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C22×C22⋊Q8C2212yes—
35#2849C2214yes—
36#2848C2214yes—
37#2848C2214yes—
38#2841C2212yes—
39#2837C2214yescomplemented
40#2837C2214yescomplemented
41#2830C2212yescomplemented
42#2829C2214yescomplemented
43#2824C2214yescomplemented
44#2824C2214yescomplemented
45#2817C2212yes—
46#2816C2212yescomplemented
47#2814C2214yes—
48#2814C2214yescomplemented
49#2809C2212yescomplemented
50#2803C2214yescomplemented
51#2803C2214yescomplemented
52#2800C2214yescomplemented
53#2800C2214yescomplemented
54#2795C2214yescomplemented
55#2785C2214yescomplemented
56#2784C2212yescomplemented
57#2784C2214yescomplemented
58#2781C2214yescomplemented
59#2774C2214yescomplemented
60#2770C2214yescomplemented
61#2768C2214yescomplemented
62#2758C2214yescomplemented
63#2757C2214yescomplemented
64#2756C2214yescomplemented
65#2756C2214yescomplemented
66#2753C2214yescomplemented
67#2747C2214yescomplemented
68#2744C2214yescomplemented
69#2742C2214yescomplemented
70#2741C2214yescomplemented
71#2737C2214yescomplemented
72#2736C2212yes—
73#2736C2214yes—
74#2735C2212yes—
75#2735C2214yes—
76#2735C2214yes—
77#2734C2212yescomplemented
78#2734C2212yescomplemented
79#2734C2212yescomplemented
80#2731C2212yescomplemented
81#2731C2214yescomplemented
82#2730C2214yescomplemented
83#2729C2214yescomplemented
84#2728C2214yescomplemented
85#2724C2212yescomplemented
86#2723C2214yescomplemented
87#2720C2214yescomplemented
88#2718C2214yescomplemented
89#2717C2212yescomplemented
90#2715C2214yescomplemented
91#2713C2214yescomplemented
92#2711C2214yescomplemented
93#2709C2214yescomplemented
94#2708C2214yescomplemented
95#2707C2214yescomplemented
96#2706C2214yescomplemented
97#2705C2214yescomplemented
98#2704C2214yescomplemented
99#2704C2214yescomplemented
100#2702C2214yescomplemented
101#2698C2214yes—
102#2698C2214yescomplemented
103#2698C2214yescomplemented
104#2697C2214yes—
105#2697C2212yes—
106#2691C2214yescomplemented
107#2690C2214yescomplemented
108#2690C2214yescomplemented
109#2689C2214yes—
110#2687C2214yescomplemented
111#2685C2214yes—
112#2685C2214yes—
113#2684C2212yes—
114#2683C2214yescomplemented
115#2681C2214yescomplemented
116#2680C2214yes—
117#2677C2214yescomplemented
118#2677C2214yescomplemented
119#2677C2214yescomplemented
120#2674C2214yes—
121#2674C2214yescomplemented
122#2674C2214yescomplemented
123#2666C2214yescomplemented
124#2662C2214yescomplemented
125#2660C2212yescomplemented
126#2651C2214yescomplemented
127#2648C2214yescomplemented
128#2632C2214yescomplemented
129#2632C2212yescomplemented
130#2616C2214yes—
131#2616C2214yes—
132#2613C2214yes—
133#2611C2212yes—
134#2602C2214yescomplemented
135#2601C2214yescomplemented
136#2599C2212yes—
137#2599C2214yescomplemented
138#2597C2214yescomplemented
139#2593C2212yescomplemented
140#2591C2212yescomplemented
141#2578C2214yescomplemented
142#2577C2214yescomplemented
143#2573C2214yes—
144#2560C2214yescomplemented
145#2557C2214yescomplemented
146#2556C2214yescomplemented
147#2553C2214yes—
148#2550C2214yescomplemented
149#2531C2214yescomplemented
150#2530C2214yescomplemented
151#2522C2214yescomplemented
152#2521C2214yescomplemented
153#2520C2214yescomplemented
154#2518C2214yescomplemented
155#2515C2214yes—
156#2481C2214yescomplemented
157#2481C2214yescomplemented
158#2480C2214yes—
159#2480C2214yes—
160#2478C2214yes—
161#2478C2214yescomplemented
162#2475C2214yes—
163#2473C2214yescomplemented
164#2472C2214yes—
165#2470C2214yescomplemented
166#2468C2214yescomplemented
167#2465C2214yescomplemented
168#2465C2214yescomplemented
169#2465C2214yescomplemented
170#2461C2214yescomplemented
171#2460C2214yescomplemented
172#2458C2214yes—
173#2458C2214yescomplemented
174#2458C2214yescomplemented
175#2452C2214yescomplemented
176#2449C2214yescomplemented
177#2449C2214yescomplemented
178#2445C2214yescomplemented
179#2442C2214yescomplemented
180#2440C2214yescomplemented
181#2440C2214yescomplemented
182#2435C2212yes—
183#2435C2212yes—
184#2434C2212yes—
185#2434C2212yes—
186#2434C2214yescomplemented
187#2432C2212yes—
188#2432C2212yes—
189#2432C2212yes—
190#2432C2212yes—
191#2432C2212yes—
192#2432C2212yes—
193#2432C2212yes—
194#2431C2212yes—
195#2431C2212yes—
196#2418C2214yes—
197#2409C2214yescomplemented
198#2407C2214yes—
199#2407C2214yes—
200#2406C2212yes—
201#2406C2214yes—
202#2406C2214yes—
203#2405C2214yes—
204#2405C2214yes—
205#2381C2212yescomplemented
206#2381C2211yescharacteristic, complemented
207#2378C2214yes—
208#2376C2212yes—
209#2372C2211yescharacteristic, complemented
210#2369C2212yescomplemented
211#2335C2214yescomplemented
212#2333C2212yescomplemented
213#2311C2212yes—
214#2311C2212yes—
215#2310C2211yescharacteristic
216#2309C2211yescharacteristic
217#2280C2211yescharacteristic
218#2280C2212yes—
219C22×#41—44no—
220C22×#41—44no—
221C22×#41—44no—
222C22×#41C2312yes—
223C22×#41C2312yes—
224C22×#41C2312yes—
225C22×#41C2312yes—
226C22×#41C2311yescharacteristic
227C23×Q8C2311yescharacteristic
228C23×Q8C2312yes—
229C23×D4C2311yescharacteristic
230C23×D4C2312yes—
231C24×C4C2311yescharacteristic
232C24×C4C2312yes—
233#563—48no—
234#563—44no—
235Q82—44no—
236#539—48no—
237#536—48no—
238#536—44no—
239#536—48no—
240#535—44no—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2311yescharacteristic
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2311yescharacteristic
245C2×C4⋊Q8C2314yes—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2314yes—
249C2×C4⋊Q8C2312yes—
250C2×#127C2312yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#125C2312yes—
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#124C2311yescharacteristic
259C2×#124C2311yescharacteristic
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2312yes—
266#525—44no—
267C2×#123C2314yes—
268C2×#123C2312yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2312yes—
274C2×#123C2312yes—
275C2×#123C2314yes—
276C2×C22⋊Q8—48no—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#120C2314yes—
297C2×#120C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2314yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×#117C2311yescharacteristic
303C2×#117C2311yescharacteristic
304C2×#117C2311yescharacteristic
305C2×#117C2312yes—
306C2×#117C2312yes—
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2314yes—
310C22×C22⋊C4C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2312yes—
321#400C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2312yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2312yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2312yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#397C2314yes—
347#397C2312yes—
348#397C2312yes—
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#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2312yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2312yes—
429#393C2314yes—
430#393C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#391C2314yes—
436#391C2312yes—
437#391C2314yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2314yes—
444#391C2314yes—
445#391C2312yes—
446#391C2314yes—
447#390C2314yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2314yes—
457#390C2314yes—
458#390C2312yes—
459#390C2314yes—
460#390C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2312yes—
553#386C2312yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#384C2314yes—
583#383C2314yes—
584#383C2312yes—
585#383C2314yes—
586#382C2314yes—
587#382C2314yes—
588#382C2314yes—
589#381C2312yes—
590#381C2312yes—
591#381C2314yes—
592#381C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2314yes—
604#379C2314yes—
605#379C2314yes—
606#379C2314yes—
607#379C2314yes—
608#379C2314yes—
609#379C2312yes—
610#379C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C22⋊C4C2312yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2312yes—
618C4×C22⋊C4C2312yes—
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2312yes—
621C4×C22⋊C4C2314yes—
622C4×C22⋊C4C2314yes—
623C4×C22⋊C4C2314yes—
624C4×C22⋊C4C2312yes—
625C4×C22⋊C4C2312yes—
626#376C2312yes—
627C25C2412yes—
628C25C2411yescharacteristic
629C2×#41—28no—
630C2×#41—28no—
631C2×#41—44no—
632C2×#41—44no—
633C2×#41—44no—
634C2×#41—44no—
635C2×#41—42no—
636C2×#41—44no—
637C2×#41—44no—
638C2×#41—42no—
639C2×#41—44no—
640C2×#41—44no—
641C2×#41—44no—
642C2×#41—44no—
643C2×#41—42no—
644C2×#41—464no—
645C22×Q8—24no—
646C22×Q8—42no—
647C22×Q8—44no—
648C22×Q8—42no—
649C22×Q8—44no—
650C22×Q8—44no—
651C22×Q8C2412yes—
652C22×Q8C2414yes—
653C22×Q8C2412yes—
654C22×Q8C2412yes—
655C22×Q8C2411yescharacteristic
656C22×Q8C2411yescharacteristic
657C22×Q8C2412yes—
658C22×Q8C2412yes—
659C22×Q8C2411yescharacteristic
660C22×D4—24no—
661C22×D4—42no—
662C22×D4—44no—
663C22×D4—42no—
664C22×D4—44no—
665C22×D4—44no—
666C22×D4C2412yes—
667C22×D4C2412yes—
668C22×D4C2414yes—
669C22×D4C2412yes—
670C22×D4C2411yescharacteristic
671C22×D4C2411yescharacteristic
672C22×D4C2412yes—
673C22×D4C2412yes—
674C22×D4C2414yes—
675C22×D4C2414yes—
676C22×D4C2412yes—
677C22×D4C2411yescharacteristic
678C23×C4—28no—
679C23×C4—24no—
680C23×C4—42no—
681C23×C4—42no—
682C23×C4—44no—
683C23×C4—44no—
684C23×C4C2412yes—
685C23×C4C2411yescharacteristic
686C23×C4C2412yes—
687C23×C4C2412yes—
688C23×C4C2412yes—
689C23×C4C2412yes—
690C23×C4C2412yes—
691C23×C4C2414yes—
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2414yes—
695C23×C4C2412yes—
696C23×C4C2412yes—
697C23×C4C2411yescharacteristic
698C4⋊Q8—28no—
699C4⋊Q8—24no—
700C4⋊Q8—28no—
701C4⋊Q8—42no—
702C4⋊Q8—44no—
703C4⋊Q8—44no—
704C4⋊Q8—48no—
705C4⋊Q8—44no—
706C4⋊Q8—48no—
707#127—44no—
708#126—48no—
709#126—48no—
710#126—48no—
711#126—48no—
712#125—44no—
713#125—48no—
714#125—48no—
715#124—24no—
716#124—44no—
717#124—42no—
718#124—44no—
719#124—44no—
720#124—44no—
721#124—44no—
722#124—44no—
723#123—216no—
724#123—28no—
725#123—48no—
726#123—44no—
727#123—48no—
728#123—48no—
729#123—48no—
730#123—48no—
731#123—44no—
732C22⋊Q8—216no—
733C22⋊Q8—44no—
734C22⋊Q8—44no—
735C22⋊Q8—48no—
736C22⋊Q8—48no—
737C22⋊Q8—48no—
738C22⋊Q8—48no—
739C22⋊Q8—48no—
740C22⋊Q8—44no—
741C22⋊Q8—44no—
742C22⋊Q8—44no—
743C22⋊Q8—48no—
744C22⋊Q8—48no—
745C22⋊Q8—48no—
746C22⋊Q8—44no—
747C22⋊Q8—48no—
748#121—28no—
749#121—44no—
750#121—44no—
751#120—44no—
752#120—48no—
753C4×Q8—44no—
754C4×Q8—48no—
755C4×D4—48no—
756C4×D4—48no—
757#117—42no—
758#117—44no—
759#117—42no—
760#117—44no—
761#117—42no—
762C2×C4⋊C4—48no—
763C2×C4⋊C4—44no—
764C2×C4⋊C4—44no—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C22⋊C4—48no—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C42C2411yescharacteristic
861C2×C42C2412yes—
862C2×C42C2411yescharacteristic
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2414yes—
869C2×C42C2412yes—
870C2×C42C2414yes—
871C2×C42C2412yes—
872C2×C42C2414yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876#95C2412yes—
877#95C2412yes—
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—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2412yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924C24—24no—
925C24—22no—
926C24—24no—
927C24—42no—
928C24—41no—
929C24—41no—
930C24—44no—
931C24—44no—
932C24—44no—
933C24C2512yes—
934C24C2512yes—
935C24C2512yes—
936C24C2511yescharacteristic
937C24C2512yes—
938#41—432no—
939#41—432no—
940#41—432no—
941#41—432no—
942#41—88no—
943C2×Q8—24no—
944C2×Q8—22no—
945C2×Q8—24no—
946C2×Q8—28no—
947C2×Q8—24no—
948C2×Q8—24no—
949C2×Q8—22no—
950C2×Q8—42no—
951C2×Q8—42no—
952C2×Q8—41no—
953C2×Q8—41no—
954C2×Q8—41no—
955C2×Q8—41no—
956C2×Q8—44no—
957C2×Q8—44no—
958C2×Q8—44no—
959C2×Q8—42no—
960C2×Q8—42no—
961C2×Q8—41no—
962C2×Q8—41no—
963C2×Q8—42no—
964C2×Q8—42no—
965C2×Q8—42no—
966C2×Q8—42no—
967C2×Q8—42no—
968C2×Q8—416no—
969C2×Q8—816no—
970C2×Q8H(5,𝔽2)14yes—
971C2×D4—24no—
972C2×D4—24no—
973C2×D4—24no—
974C2×D4—28no—
975C2×D4—24no—
976C2×D4—22no—
977C2×D4—24no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—22no—
981C2×D4—41no—
982C2×D4—41no—
983C2×D4—42no—
984C2×D4—42no—
985C2×D4—42no—
986C2×D4—42no—
987C2×D4—41no—
988C2×D4—41no—
989C2×D4—42no—
990C2×D4—42no—
991C2×D4—42no—
992C2×D4—42no—
993C2×D4—42no—
994C2×D4—416no—
995C2×D4—44no—
996C2×D4—42no—
997C2×D4—41no—
998C2×D4—42no—
999C2×D4—41no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—432no—
1008C2×D4H(5,𝔽2)14yes—
1009C22×C4—22no—
1010C22×C4—24no—
1011C22×C4—24no—
1012C22×C4—22no—
1013C22×C4—22no—
1014C22×C4—24no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—28no—
1018C22×C4—24no—
1019C22×C4—24no—
1020C22×C4—24no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—41no—
1029C22×C4—41no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—42no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—416no—
1050C22×C4—432no—
1051C22×C4H(5,𝔽2)14yes—
1052C22×C4C2514yes—
1053C22×C4C2514yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2514yes—
1057C22×C4C2514yes—
1058C22×C4C2514yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2514yes—
1062C22×C4C2514yes—
1063C22×C4C2514yes—
1064C22×C4C2512yes—
1065C22×C4C2514yes—
1066C22×C4C2512yes—
1067C22×C4C2511yescharacteristic
1068C22×C4C2511yescharacteristic
1069C22×C4C2512yes—
1070C4⋊C4—28no—
1071C4⋊C4—28no—
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—24no—
1075C4⋊C4—28no—
1076C4⋊C4—28no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—42no—
1101C4⋊C4—44no—
1102C4⋊C4—42no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—24no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—42no—
1148C22⋊C4—42no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—42no—
1163C22⋊C4—42no—
1164C42—24no—
1165C42—22no—
1166C42—22no—
1167C42—24no—
1168C42—44no—
1169C42—44no—
1170C42—44no—
1171C42—42no—
1172C42—42no—
1173C42—42no—
1174C42—42no—
1175C42—44no—
1176C42—44no—
1177C42—42no—
1178C42—42no—
1179C42—44no—
1180C23—21no—
1181C23—22no—
1182C23—21no—
1183C23—22no—
1184C23—24no—
1185C23—24no—
1186C23—24no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—24no—
1197C23—24no—
1198C23—24no—
1199C23—24no—
1200C23—24no—
1201C23—24no—
1202C23—48no—
1203C23—44no—
1204C23—48no—
1205C23—88no—
1206C23—84no—
1207C23—84no—
1208C23—88no—
1209C23—84no—
1210C23—84no—
1211C23C2×H(5,𝔽2)12yes—
1212C23C2×H(5,𝔽2)14yes—
1213C23C2611yescharacteristic
1214Q8—44no—
1215Q8—48no—
1216Q8—44no—
1217Q8—48no—
1218Q8—88no—
1219Q8—84no—
1220Q8—84no—
1221Q8—82no—
1222Q8—162no—
1223D4—44no—
1224D4—48no—
1225D4—48no—
1226D4—44no—
1227D4—48no—
1228D4—48no—
1229D4—48no—
1230D4—82no—
1231D4—88no—
1232D4—84no—
1233D4—88no—
1234D4—164no—
1235C2×C4—28no—
1236C2×C4—216no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—44no—
1286C2×C4—48no—
1287C2×C4—48no—
1288C2×C4—48no—
1289C2×C4—48no—
1290C2×C4—48no—
1291C2×C4—48no—
1292C2×C4—84no—
1293C2×C4—88no—
1294C2×C4—84no—
1295C2×C4—88no—
1296C2×C4—162no—
1297C2×C4C2×H(5,𝔽2)14yes—
1298C2×C4C2×H(5,𝔽2)12yes—
1299C2×C4C2×H(5,𝔽2)14yes—
1300C2×C4C2×H(5,𝔽2)12yes—
1301C22—28no—
1302C22—22no—
1303C22—24no—
1304C22—24no—
1305C22—44no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—44no—
1311C22—44no—
1312C22—44no—
1313C22—42no—
1314C22—42no—
1315C22—44no—
1316C22—44no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—44no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22—816no—
1326C22—88no—
1327C22C22×H(5,𝔽2)11yescharacteristic
1328C22C22×H(5,𝔽2)11yescharacteristic
1329C22C22×H(5,𝔽2)11yescharacteristic
1330C222−1+614yes—
1331C4—24no—
1332C4—22no—
1333C4—22no—
1334C4—24no—
1335C4—42no—
1336C4—44no—
1337C4—44no—
1338C4—42no—
1339C4—44no—
1340C4—44no—
1341C4—44no—
1342C4—42no—
1343C4—44no—
1344C4—42no—
1345C4—44no—
1346C4—44no—
1347C4—44no—
1348C4—44no—
1349C2—44no—
1350C2—42no—
1351C2—82no—
1352C2—82no—
1353C2—82no—
1354C2#6281711yescharacteristic
1355C2#6288612yes—
1356C2#6304412yes—
1357C2#6306312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35149C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58033C2semidirect
2. #56680C2semidirect
3. #56631C2semidirect
4. #55574C2semidirect
5. #55384C2semidirect
6. #55144C2semidirect
7. #52075C2semidirect
8. #52072C2semidirect
9. #52072C2semidirect
10. #51988C2semidirect
11. #51984C2semidirect
12. #51668C2semidirect
13. #51542C2semidirect
14. #47180C2semidirect
15. #47166C2semidirect
16. #46363C2semidirect
17. #46359C2semidirect
18. #45472C2semidirect
19. #45466C2semidirect
20. #45453C2semidirect
21. #45446C2semidirect
22. #35305C2semidirect
26. C2×#563C22semidirect
27. C2×Q82C22semidirect
28. C2×#539C22semidirect
39. #2837C22semidirect
40. #2837C22semidirect
41. #2830C22semidirect
42. #2829C22semidirect
43. #2824C22semidirect
44. #2824C22semidirect
46. #2816C22semidirect
48. #2814C22semidirect
49. #2809C22semidirect
50. #2803C22semidirect
51. #2803C22semidirect
52. #2800C22semidirect
53. #2800C22semidirect
54. #2795C22semidirect
55. #2785C22semidirect
56. #2784C22semidirect
57. #2784C22semidirect
58. #2781C22semidirect
59. #2774C22semidirect
60. #2770C22semidirect
61. #2768C22semidirect
62. #2758C22semidirect
63. #2757C22semidirect
64. #2756C22semidirect
65. #2756C22semidirect
66. #2753C22semidirect
67. #2747C22semidirect
68. #2744C22semidirect
69. #2742C22semidirect
70. #2741C22semidirect
71. #2737C22semidirect
77. #2734C22semidirect
78. #2734C22semidirect
79. #2734C22semidirect
80. #2731C22semidirect
81. #2731C22semidirect
82. #2730C22semidirect
83. #2729C22semidirect
84. #2728C22semidirect
85. #2724C22semidirect
86. #2723C22semidirect
87. #2720C22semidirect
88. #2718C22semidirect
89. #2717C22semidirect
90. #2715C22semidirect
91. #2713C22semidirect
92. #2711C22semidirect
93. #2709C22semidirect
94. #2708C22semidirect
95. #2707C22semidirect
96. #2706C22semidirect
97. #2705C22semidirect
98. #2704C22semidirect
99. #2704C22semidirect
100. #2702C22semidirect
102. #2698C22semidirect
103. #2698C22semidirect
106. #2691C22semidirect
107. #2690C22semidirect
108. #2690C22semidirect
110. #2687C22semidirect
114. #2683C22semidirect
115. #2681C22semidirect
117. #2677C22semidirect
118. #2677C22semidirect
119. #2677C22semidirect
121. #2674C22semidirect
122. #2674C22semidirect
123. #2666C22semidirect
124. #2662C22semidirect
125. #2660C22semidirect
126. #2651C22semidirect
127. #2648C22semidirect
128. #2632C22semidirect
129. #2632C22semidirect
134. #2602C22semidirect
135. #2601C22semidirect
137. #2599C22semidirect
138. #2597C22semidirect
139. #2593C22semidirect
140. #2591C22semidirect
141. #2578C22semidirect
142. #2577C22semidirect
144. #2560C22semidirect
145. #2557C22semidirect
146. #2556C22semidirect
148. #2550C22semidirect
149. #2531C22semidirect
150. #2530C22semidirect
151. #2522C22semidirect
152. #2521C22semidirect
153. #2520C22semidirect
154. #2518C22semidirect
156. #2481C22semidirect
157. #2481C22semidirect
161. #2478C22semidirect
163. #2473C22semidirect
165. #2470C22semidirect
166. #2468C22semidirect
167. #2465C22semidirect
168. #2465C22semidirect
169. #2465C22semidirect
170. #2461C22semidirect
171. #2460C22semidirect
173. #2458C22semidirect
174. #2458C22semidirect
175. #2452C22semidirect
176. #2449C22semidirect
177. #2449C22semidirect
178. #2445C22semidirect
179. #2442C22semidirect
180. #2440C22semidirect
181. #2440C22semidirect
186. #2434C22semidirect
197. #2409C22semidirect
205. #2381C22semidirect
206. #2381C22semidirect
209. #2372C22semidirect
210. #2369C22semidirect
211. #2335C22semidirect
212. #2333C22semidirect

Maximal subgroups

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

subgroupindex
#580332
#566802
#566312
#555742
#553842
#551442
#520752
#520722
#519882
#519842
#516682
#515422
#471802
#471662
#463632
#463592
#454722
#454662
#454532
#454462
#353052
#351492