Finite Group Databasebeta

← #8926524

Subgroups — #8926524

Order 512.

4114 conjugacy classes of subgroups.

The subgroup lattice has 1209 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58428C214yesmaximal, complemented
2#58389C212yesmaximal, complemented
3#56074C212yesmaximal, complemented
4#55923C214yesmaximal, complemented
5#54744C214yesmaximal, complemented
6#54431C214yesmaximal, complemented
7#54348C214yesmaximal, complemented
8#46986C214yesmaximal, complemented
9#46911C214yesmaximal, complemented
10#46855C212yesmaximal, complemented
11#46815C212yesmaximal, complemented
12#46815C212yesmaximal, complemented
13#46616C214yesmaximal
14#37392C212yesmaximal, complemented
15#37064C214yesmaximal, complemented
16#37042C214yesmaximal, complemented
17#37014C212yesmaximal, complemented
18#36732C212yesmaximal, complemented
19#36732C212yesmaximal, complemented
20#36720C211yesmaximal, characteristic
21#36711C211yesmaximal, characteristic
22#35488C212yesmaximal, complemented
23#35455C211yesmaximal, characteristic
24C2×#544C2211yescharacteristic
25C2×#543C2211yescharacteristic
26C2×#543C2211yescharacteristic
27C2×#541C2212yes—
28C22×#123C2211yescharacteristic
29#2865C2214yescomplemented
30#2862C2212yescomplemented
31#2859C2212yescomplemented
32#2848C2211yescharacteristic
33#2848C2211yescharacteristic
34#2848C2212yes—
35#2844C2214yescomplemented
36#2841C2212yescomplemented
37#2839C2214yescomplemented
38#2839C2214yescomplemented
39#2836C2214yescomplemented
40#2835C2212yescomplemented
41#2831C2214yescomplemented
42#2827C2214yes—
43#2817C2212yes—
44#2806C2214yescomplemented
45#2802C2214yescomplemented
46#2798C2214yescomplemented
47#2794C2214yescomplemented
48#2793C2214yescomplemented
49#2783C2214yescomplemented
50#2782C2214yes—
51#2781C2214yes—
52#2780C2214yes—
53#2779C2214yes—
54#2775C2214yescomplemented
55#2775C2214yescomplemented
56#2774C2214yescomplemented
57#2773C2214yescomplemented
58#2773C2214yescomplemented
59#2771C2212yescomplemented
60#2769C2214yescomplemented
61#2768C2214yescomplemented
62#2767C2214yescomplemented
63#2767C2214yescomplemented
64#2764C2212yescomplemented
65#2763C2212yescomplemented
66#2758C2214yescomplemented
67#2758C2214yescomplemented
68#2758C2214yescomplemented
69#2757C2214yes—
70#2755C2214yescomplemented
71#2755C2214yescomplemented
72#2754C2214yescomplemented
73#2744C2214yes—
74#2744C2214yes—
75#2744C2214yescomplemented
76#2744C2214yescomplemented
77#2742C2212yescomplemented
78#2739C2214yes—
79#2739C2214yes—
80#2739C2214yescomplemented
81#2739C2214yescomplemented
82#2739C2214yescomplemented
83#2735C2214yes—
84#2735C2214yes—
85#2729C2214yescomplemented
86#2729C2214yescomplemented
87#2720C2214yescomplemented
88#2720C2214yescomplemented
89#2719C2214yescomplemented
90#2719C2214yescomplemented
91#2717C2214yes—
92#2715C2214yes—
93#2713C2214yescomplemented
94#2713C2214yescomplemented
95#2698C2214yes—
96#2698C2214yes—
97#2698C2214yes—
98#2698C2214yes—
99#2698C2214yescomplemented
100#2698C2214yescomplemented
101#2695C2214yes—
102#2694C2214yes—
103#2694C2214yes—
104#2690C2214yescomplemented
105#2690C2214yescomplemented
106#2690C2214yescomplemented
107#2690C2214yescomplemented
108#2689C2214yes—
109#2689C2214yes—
110#2689C2214yes—
111#2689C2214yes—
112#2689C2214yescomplemented
113#2689C2214yescomplemented
114#2687C2214yes—
115#2687C2214yes—
116#2680C2214yes—
117#2680C2214yes—
118#2674C2214yes—
119#2674C2214yes—
120#2666C2214yescomplemented
121#2666C2214yescomplemented
122#2660C2212yescomplemented
123#2659C2212yescomplemented
124#2659C2212yescomplemented
125#2654C2214yescomplemented
126#2654C2214yescomplemented
127#2650C2214yescomplemented
128#2646C2212yescomplemented
129#2646C2212yescomplemented
130#2642C2212yescomplemented
131#2627C2212yes—
132#2626C2211yescharacteristic
133#2626C2211yescharacteristic
134#2608C2212yes—
135#2607C2212yescomplemented
136#2597C2214yes—
137#2596C2214yescomplemented
138#2589C2214yescomplemented
139#2588C2214yescomplemented
140#2588C2214yescomplemented
141#2587C2214yescomplemented
142#2586C2214yescomplemented
143#2583C2212yes—
144#2578C2214yes—
145#2577C2214yescomplemented
146#2573C2214yes—
147#2573C2214yes—
148#2570C2214yescomplemented
149#2568C2212yescomplemented
150#2567C2212yescomplemented
151#2565C2212yescomplemented
152#2565C2212yescomplemented
153#2561C2212yes—
154#2561C2212yes—
155#2561C2212yes—
156#2556C2214yescomplemented
157#2556C2214yescomplemented
158#2553C2214yes—
159#2530C2214yescomplemented
160#2529C2214yescomplemented
161#2524C2214yescomplemented
162#2523C2214yescomplemented
163#2521C2214yes—
164#2518C2214yes—
165#2517C2212yescomplemented
166#2517C2214yescomplemented
167#2515C2214yes—
168#2515C2214yes—
169#2515C2214yescomplemented
170#2508C2214yescomplemented
171#2508C2214yescomplemented
172#2505C2214yescomplemented
173#2505C2214yescomplemented
174#2505C2214yescomplemented
175#2505C2214yescomplemented
176#2503C2212yes—
177#2503C2212yes—
178#2502C2212yes—
179#2499C2212yes—
180#2499C2212yes—
181#2496C2214yescomplemented
182#2489C2214yescomplemented
183#2489C2214yescomplemented
184#2488C2214yes—
185#2488C2214yes—
186#2488C2214yes—
187#2488C2214yes—
188#2483C2212yes—
189#2482C2212yes—
190#2482C2212yes—
191#2480C2214yes—
192#2480C2214yes—
193#2480C2214yes—
194#2480C2214yes—
195#2480C2214yes—
196#2480C2214yes—
197#2465C2214yescomplemented
198#2465C2214yescomplemented
199#2435C2212yes—
200#2421C2214yescomplemented
201#2421C2214yescomplemented
202#2405C2212yes—
203#2337C2214yes—
204#2335C2214yes—
205#2334C2214yescomplemented
206#2332C2212yes—
207#2332C2212yes—
208#2329C2212yescomplemented
209#2329C2212yescomplemented
210#2329C2212yescomplemented
211#2329C2212yescomplemented
212#2313C2211yescharacteristic
213#2312C2211yescharacteristic
214#2308C2212yes—
215C4×#126C2214yescomplemented
216#2298C2212yes—
217C2×#381C2212yes—
218#2273C2211yescharacteristic
219C23×D4C2311yescharacteristic
220C24×C4C2311yescharacteristic
221#544—44no—
222#543—44no—
223#543—44no—
224#541—48no—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2312yes—
228C2×#126C2314yes—
229C2×#126C2314yes—
230C2×#126C2314yes—
231C2×#126C2314yes—
232C2×#125C2312yes—
233C2×#125C2312yes—
234C2×#125C2312yes—
235C2×#125C2314yes—
236C2×#125C2314yes—
237C2×#124C2314yes—
238C2×#123—44no—
239C2×#123C2314yes—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2312yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2311yescharacteristic
251C2×C22⋊Q8C2311yescharacteristic
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2312yes—
259C2×#117C2312yes—
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C22⋊C4C2311yescharacteristic
263C22×C22⋊C4C2311yescharacteristic
264C22×C22⋊C4C2311yescharacteristic
265C22×C22⋊C4C2312yes—
266C22×C22⋊C4C2312yes—
267C22×C22⋊C4C2312yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#399C2314yes—
304#399C2314yes—
305#399C2312yes—
306#399C2314yes—
307#399C2312yes—
308#399C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#397C2312yes—
335#397C2314yes—
336#397C2314yes—
337#397C2312yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
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#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#393C2312yes—
387#393C2314yes—
388#393C2312yes—
389#393C2314yes—
390#393C2312yes—
391#393C2312yes—
392#391C2312yes—
393#391C2312yes—
394#391C2312yes—
395#391C2312yes—
396#391C2312yes—
397#391C2312yes—
398#391C2314yes—
399#391C2312yes—
400#391C2314yes—
401#391C2312yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#390C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
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#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#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2312yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2312yes—
526#385C2314yes—
527#385C2312yes—
528#385C2312yes—
529#385C2312yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2312yes—
542#385C2314yes—
543#384C2312yes—
544#384C2312yes—
545#384C2312yes—
546#384C2312yes—
547#383C2314yes—
548#383C2314yes—
549#383C2314yes—
550#383C2314yes—
551#382C2312yes—
552#382C2312yes—
553#382C2312yes—
554#382C2312yes—
555#382C2314yes—
556#382C2314yes—
557#382C2314yes—
558#382C2314yes—
559#382C2314yes—
560#382C2314yes—
561#382C2314yes—
562#382C2314yes—
563#382C2314yes—
564#381C2314yes—
565#381C2314yes—
566#381C2314yes—
567#381C2312yes—
568#381C2314yes—
569#381C2312yes—
570#381C2312yes—
571#381C2314yes—
572#381C2314yes—
573#380C2312yes—
574#380C2311yescharacteristic
575#380C2311yescharacteristic
576#380C2314yes—
577#380C2314yes—
578#380C2312yes—
579#380C2312yes—
580#380C2312yes—
581#380C2312yes—
582#380C2314yes—
583#380C2314yes—
584#380C2314yes—
585#380C2314yes—
586#379C2314yes—
587#379C2314yes—
588#379C2312yes—
589#379C2312yes—
590#379C2312yes—
591#379C2312yes—
592#379C2312yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2312yes—
597C4×C4⋊C4C2312yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2312yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613#376C2312yes—
614C2×#95C2312yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C43C2312yes—
619C25C2411yescharacteristic
620C25C2411yescharacteristic
621C22×Q8C2412yes—
622C22×Q8C2412yes—
623C22×Q8C2412yes—
624C22×Q8C2411yescharacteristic
625C22×Q8C2411yescharacteristic
626C22×Q8C2412yes—
627C22×Q8C2412yes—
628C22×D4—42no—
629C22×D4—44no—
630C22×D4C2414yes—
631C23×C4—42no—
632C23×C4—44no—
633C23×C4C2411yescharacteristic
634C23×C4C2411yescharacteristic
635C23×C4C2411yescharacteristic
636C23×C4C2411yescharacteristic
637C23×C4C2412yes—
638C23×C4C2412yes—
639C23×C4C2412yes—
640C23×C4C2412yes—
641C23×C4C2412yes—
642C23×C4C2412yes—
643C23×C4C2412yes—
644C23×C4C2412yes—
645C23×C4C2411yescharacteristic
646C4⋊Q8—44no—
647C4⋊Q8—44no—
648C4⋊Q8—44no—
649#126—48no—
650#126—48no—
651#126—48no—
652#126—48no—
653#125—44no—
654#125—44no—
655#125—44no—
656#125—48no—
657#125—48no—
658#124—48no—
659#123—48no—
660#123—48no—
661#123—48no—
662C22⋊Q8—28no—
663C22⋊Q8—28no—
664C22⋊Q8—44no—
665C22⋊Q8—44no—
666C22⋊Q8—44no—
667C22⋊Q8—44no—
668C22⋊Q8—44no—
669C22⋊Q8—44no—
670C22⋊Q8—42no—
671C22⋊Q8—42no—
672C22⋊Q8—44no—
673C22⋊Q8—48no—
674C22⋊Q8—48no—
675C22⋊Q8—48no—
676C22⋊Q8—48no—
677C4×Q8—44no—
678C4×Q8—44no—
679#117—28no—
680C2×C4⋊C4—24no—
681C2×C4⋊C4—42no—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C22⋊C4—24no—
739C2×C22⋊C4—24no—
740C2×C22⋊C4—44no—
741C2×C22⋊C4—44no—
742C2×C22⋊C4—44no—
743C2×C22⋊C4—42no—
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⋊C4C2412yes—
758C2×C22⋊C4C2412yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2412yes—
765C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2414yes—
778C2×C42C2412yes—
779C2×C42C2412yes—
780C2×C42C2414yes—
781C2×C42C2414yes—
782C2×C42C2414yes—
783C2×C42C2414yes—
784C2×C42C2414yes—
785C2×C42C2412yes—
786C2×C42C2414yes—
787C2×C42C2412yes—
788C2×C42C2412yes—
789C2×C42C2412yes—
790C2×C42C2414yes—
791C2×C42C2414yes—
792C2×C42C2414yes—
793C2×C42C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2412yes—
805#95C2414yes—
806#95C2412yes—
807#95C2414yes—
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#95C2412yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2412yes—
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—
860C24—22no—
861C24—24no—
862C24—22no—
863C24—42no—
864C24—41no—
865C24—41no—
866C24—42no—
867C24—42no—
868C24—41no—
869C24—41no—
870C24C2512yes—
871C24C2511yescharacteristic
872C24C2512yes—
873C2×Q8—24no—
874C2×Q8—24no—
875C2×Q8—42no—
876C2×Q8—42no—
877C2×Q8—42no—
878C2×Q8—42no—
879C2×Q8—42no—
880C2×Q8—42no—
881C2×Q8—41no—
882C2×Q8—42no—
883C2×Q8—41no—
884C2×Q8—42no—
885C2×Q8—42no—
886C2×Q8—42no—
887C2×Q8—42no—
888C2×Q8—44no—
889C2×Q8—44no—
890C2×D4—28no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—88no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—44no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—88no—
928C22×C4H(5,𝔽2)14yes—
929C22×C4C2514yes—
930C22×C4C2514yes—
931C22×C4C2514yes—
932C22×C4C2514yes—
933C22×C4C2514yes—
934C22×C4C2514yes—
935C22×C4C2514yes—
936C22×C4C2514yes—
937C22×C4C2514yes—
938C22×C4C2512yes—
939C22×C4C2512yes—
940C22×C4C2512yes—
941C22×C4C2511yescharacteristic
942C22×C4C2511yescharacteristic
943C22×C4C2512yes—
944C22×C4C2512yes—
945C22×C4C2512yes—
946C22×C4C2512yes—
947C22×C4C2514yes—
948C22×C4C2512yes—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—24no—
952C4⋊C4—24no—
953C4⋊C4—24no—
954C4⋊C4—24no—
955C4⋊C4—28no—
956C4⋊C4—28no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
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—42no—
975C4⋊C4—44no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—42no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—41no—
987C4⋊C4—42no—
988C4⋊C4—41no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C22⋊C4—28no—
1006C22⋊C4—28no—
1007C22⋊C4—24no—
1008C22⋊C4—24no—
1009C22⋊C4—28no—
1010C22⋊C4—28no—
1011C22⋊C4—28no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—44no—
1023C22⋊C4—42no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—42no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—42no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C42—24no—
1040C42—24no—
1041C42—42no—
1042C42—42no—
1043C42—42no—
1044C42—42no—
1045C42—44no—
1046C42—44no—
1047C42—44no—
1048C42—44no—
1049C42—44no—
1050C42—44no—
1051C42—44no—
1052C42—44no—
1053C42—44no—
1054C42—44no—
1055C23—28no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—21no—
1064C23—21no—
1065C23—22no—
1066C23—22no—
1067C23—24no—
1068C23—24no—
1069C23—22no—
1070C23—22no—
1071C23—44no—
1072C23—82no—
1073C23—84no—
1074C23—84no—
1075C23—82no—
1076C23—82no—
1077C23—82no—
1078C23—162no—
1079C23—162no—
1080C23C2×H(5,𝔽2)12yes—
1081C23#58514yes—
1082C23C2611yescharacteristic
1083Q8—84no—
1084Q8—84no—
1085Q8—162no—
1086Q8—161no—
1087Q8—161no—
1088Q8—162no—
1089Q8—162no—
1090D4—88no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—44no—
1143C2×C4—82no—
1144C2×C4—82no—
1145C2×C4—82no—
1146C2×C4—84no—
1147C2×C4—84no—
1148C2×C4—82no—
1149C2×C4—162no—
1150C2×C4—162no—
1151C2×C4—162no—
1152C2×C4—162no—
1153C2×C4—162no—
1154C2×C4—162no—
1155C2×C4C2×H(5,𝔽2)14yes—
1156C22—22no—
1157C22—24no—
1158C22—22no—
1159C22—24no—
1160C22—24no—
1161C22—22no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—42no—
1170C22—44no—
1171C22—44no—
1172C22—42no—
1173C22—88no—
1174C22—164no—
1175C22C22×H(5,𝔽2)11yescharacteristic
1176C22C2×#58512yes—
1177C222−1+611yescharacteristic
1178C222−1+611yescharacteristic
1179C222−1+612yes—
1180C4—24no—
1181C4—42no—
1182C4—41no—
1183C4—41no—
1184C4—42no—
1185C4—44no—
1186C4—42no—
1187C4—42no—
1188C4—44no—
1189C4—44no—
1190C4—44no—
1191C4—44no—
1192C4—44no—
1193C4—44no—
1194C4—44no—
1195C4—44no—
1196C4—42no—
1197C4—42no—
1198C4—42no—
1199C4—44no—
1200C2—44no—
1201C2—42no—
1202C2—82no—
1203C2#6282411yescharacteristic
1204C2#6287111yescharacteristic
1205C2#6287312yes—
1206C2#6287312yes—
1207C2#6288711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58428C2semidirect
2. #58389C2semidirect
3. #56074C2semidirect
4. #55923C2semidirect
5. #54744C2semidirect
6. #54431C2semidirect
7. #54348C2semidirect
8. #46986C2semidirect
9. #46911C2semidirect
10. #46855C2semidirect
11. #46815C2semidirect
12. #46815C2semidirect
14. #37392C2semidirect
15. #37064C2semidirect
16. #37042C2semidirect
17. #37014C2semidirect
18. #36732C2semidirect
19. #36732C2semidirect
22. #35488C2semidirect
29. #2865C22semidirect
30. #2862C22semidirect
31. #2859C22semidirect
35. #2844C22semidirect
36. #2841C22semidirect
37. #2839C22semidirect
38. #2839C22semidirect
39. #2836C22semidirect
40. #2835C22semidirect
41. #2831C22semidirect
44. #2806C22semidirect
45. #2802C22semidirect
46. #2798C22semidirect
47. #2794C22semidirect
48. #2793C22semidirect
49. #2783C22semidirect
54. #2775C22semidirect
55. #2775C22semidirect
56. #2774C22semidirect
57. #2773C22semidirect
58. #2773C22semidirect
59. #2771C22semidirect
60. #2769C22semidirect
61. #2768C22semidirect
62. #2767C22semidirect
63. #2767C22semidirect
64. #2764C22semidirect
65. #2763C22semidirect
66. #2758C22semidirect
67. #2758C22semidirect
68. #2758C22semidirect
70. #2755C22semidirect
71. #2755C22semidirect
72. #2754C22semidirect
75. #2744C22semidirect
76. #2744C22semidirect
77. #2742C22semidirect
80. #2739C22semidirect
81. #2739C22semidirect
82. #2739C22semidirect
85. #2729C22semidirect
86. #2729C22semidirect
87. #2720C22semidirect
88. #2720C22semidirect
89. #2719C22semidirect
90. #2719C22semidirect
93. #2713C22semidirect
94. #2713C22semidirect
99. #2698C22semidirect
100. #2698C22semidirect
104. #2690C22semidirect
105. #2690C22semidirect
106. #2690C22semidirect
107. #2690C22semidirect
112. #2689C22semidirect
113. #2689C22semidirect
120. #2666C22semidirect
121. #2666C22semidirect
122. #2660C22semidirect
123. #2659C22semidirect
124. #2659C22semidirect
125. #2654C22semidirect
126. #2654C22semidirect
127. #2650C22semidirect
128. #2646C22semidirect
129. #2646C22semidirect
130. #2642C22semidirect
135. #2607C22semidirect
137. #2596C22semidirect
138. #2589C22semidirect
139. #2588C22semidirect
140. #2588C22semidirect
141. #2587C22semidirect
142. #2586C22semidirect
145. #2577C22semidirect
148. #2570C22semidirect
149. #2568C22semidirect
150. #2567C22semidirect
151. #2565C22semidirect
152. #2565C22semidirect
156. #2556C22semidirect
157. #2556C22semidirect
159. #2530C22semidirect
160. #2529C22semidirect
161. #2524C22semidirect
162. #2523C22semidirect
165. #2517C22semidirect
166. #2517C22semidirect
169. #2515C22semidirect
170. #2508C22semidirect
171. #2508C22semidirect
172. #2505C22semidirect
173. #2505C22semidirect
174. #2505C22semidirect
175. #2505C22semidirect
181. #2496C22semidirect
182. #2489C22semidirect
183. #2489C22semidirect
197. #2465C22semidirect
198. #2465C22semidirect
200. #2421C22semidirect
201. #2421C22semidirect
205. #2334C22semidirect
208. #2329C22semidirect
209. #2329C22semidirect
210. #2329C22semidirect
211. #2329C22semidirect
215. C4×#126C22semidirect

Maximal subgroups

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

subgroupindex
#584282
#583892
#560742
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