Finite Group Databasebeta

← #8943798

Subgroups — #8943798

Order 512.

4310 conjugacy classes of subgroups.

The subgroup lattice has 1227 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58517C214yesmaximal, complemented
2#58311C214yesmaximal, complemented
3#56700C214yesmaximal, complemented
4#51662C214yesmaximal, complemented
5#50879C212yesmaximal, complemented
6#50169C212yesmaximal, complemented
7#49204C214yesmaximal, complemented
8#49193C214yesmaximal, complemented
9#48797C212yesmaximal, complemented
10#46882C212yesmaximal, complemented
11#46837C212yesmaximal
12#43665C214yesmaximal, complemented
13#43507C214yesmaximal, complemented
14#42978C212yesmaximal, complemented
15#41354C214yesmaximal, complemented
16#40627C214yesmaximal, complemented
17#37956C212yesmaximal, complemented
18#37932C212yesmaximal
19#36708C211yesmaximal, characteristic, complemented
20#36064C212yesmaximal, complemented
21#36010C212yesmaximal
22#35644C211yesmaximal, characteristic, complemented
23#35349C211yesmaximal, characteristic
24C2×#552C2212yes—
25C2×#544C2211yescharacteristic, complemented
26C2×#544C2211yescharacteristic, complemented
27C22×C22⋊Q8C2211yescharacteristic
28C2×#518C2211yescharacteristic
29#2848C2212yes—
30#2841C2214yescomplemented
31#2840C2212yes—
32#2839C2214yescomplemented
33#2839C2214yescomplemented
34#2835C2212yescomplemented
35#2822C2214yescomplemented
36#2806C2214yescomplemented
37#2805C2214yescomplemented
38#2799C2214yescomplemented
39#2788C2214yes—
40#2788C2214yes—
41#2787C2214yes—
42#2787C2214yes—
43#2770C2214yescomplemented
44#2769C2214yescomplemented
45#2765C2214yescomplemented
46#2764C2212yes—
47#2764C2214yes—
48#2764C2212yes—
49#2764C2214yescomplemented
50#2763C2214yes—
51#2763C2212yescomplemented
52#2763C2214yescomplemented
53#2762C2214yescomplemented
54#2762C2214yescomplemented
55#2762C2214yescomplemented
56#2762C2214yescomplemented
57#2758C2214yescomplemented
58#2758C2214yescomplemented
59#2758C2214yescomplemented
60#2755C2214yescomplemented
61#2755C2214yescomplemented
62#2750C2214yes—
63#2747C2214yes—
64#2745C2214yescomplemented
65#2745C2214yescomplemented
66#2745C2214yescomplemented
67#2744C2214yescomplemented
68#2744C2214yescomplemented
69#2743C2214yes—
70#2742C2214yescomplemented
71#2729C2214yescomplemented
72#2729C2214yescomplemented
73#2726C2214yescomplemented
74#2722C2212yescomplemented
75#2719C2214yescomplemented
76#2713C2214yescomplemented
77#2698C2214yescomplemented
78#2698C2214yescomplemented
79#2695C2214yes—
80#2690C2214yes—
81#2690C2214yescomplemented
82#2689C2214yescomplemented
83#2689C2214yescomplemented
84#2689C2214yescomplemented
85#2687C2214yes—
86#2687C2214yes—
87#2687C2214yes—
88#2687C2214yes—
89#2687C2214yes—
90#2677C2214yes—
91#2677C2214yescomplemented
92#2666C2214yescomplemented
93#2666C2214yescomplemented
94#2666C2214yescomplemented
95#2665C2214yescomplemented
96#2665C2212yescomplemented
97#2665C2214yescomplemented
98#2659C2212yescomplemented
99#2646C2212yes—
100#2642C2214yescomplemented
101#2638C2212yes—
102#2633C2212yes—
103#2628C2214yescomplemented
104#2627C2212yescomplemented
105#2627C2212yescomplemented
106#2626C2212yes—
107#2626C2212yes—
108#2625C2212yescomplemented
109#2611C2212yes—
110#2611C2214yescomplemented
111#2609C2214yes—
112#2607C2214yescomplemented
113#2599C2212yes—
114#2599C2214yescomplemented
115#2589C2214yes—
116#2589C2214yescomplemented
117#2579C2212yes—
118#2579C2212yes—
119#2577C2214yes—
120#2575C2214yescomplemented
121#2575C2214yescomplemented
122#2574C2214yes—
123#2574C2214yescomplemented
124#2573C2214yescomplemented
125#2573C2214yescomplemented
126#2572C2214yes—
127#2572C2214yes—
128#2572C2214yes—
129#2572C2214yes—
130#2564C2212yes—
131#2561C2212yes—
132#2561C2212yes—
133#2561C2212yes—
134#2561C2214yes—
135#2553C2214yes—
136#2550C2214yescomplemented
137#2533C2214yescomplemented
138#2530C2214yes—
139#2527C2214yescomplemented
140#2524C2214yescomplemented
141#2524C2214yescomplemented
142#2523C2212yescomplemented
143#2515C2214yescomplemented
144#2505C2214yes—
145#2505C2214yescomplemented
146#2503C2212yescomplemented
147#2503C2212yescomplemented
148#2495C2214yes—
149#2493C2214yescomplemented
150#2493C2214yescomplemented
151#2493C2214yescomplemented
152#2492C2214yes—
153#2492C2214yescomplemented
154#2492C2214yescomplemented
155#2489C2214yes—
156#2489C2214yescomplemented
157#2487C2212yes—
158#2486C2212yes—
159#2484C2212yescomplemented
160#2483C2212yes—
161#2482C2212yes—
162#2480C2214yes—
163#2480C2214yes—
164#2478C2214yescomplemented
165#2477C2214yes—
166#2475C2214yes—
167#2475C2214yescomplemented
168#2473C2214yescomplemented
169#2470C2214yes—
170#2466C2214yes—
171#2465C2214yes—
172#2465C2214yescomplemented
173#2460C2214yes—
174#2453C2214yescomplemented
175#2451C2214yescomplemented
176#2450C2214yes—
177#2449C2214yes—
178#2446C2214yescomplemented
179#2442C2214yescomplemented
180#2439C2214yescomplemented
181#2439C2214yescomplemented
182#2438C2214yes—
183#2438C2214yescomplemented
184#2437C2214yes—
185#2434C2212yescomplemented
186#2419C2214yes—
187#2409C2212yes—
188#2405C2214yes—
189#2398C2212yes—
190#2396C2214yescomplemented
191#2395C2212yes—
192C2×#397C2212yes—
193#2381C2214yescomplemented
194#2378C2212yescomplemented
195#2368C2214yescomplemented
196#2360C2214yescomplemented
197#2359C2214yes—
198#2356C2214yescomplemented
199#2353C2212yes—
200#2346C2212yescomplemented
201#2343C2214yescomplemented
202#2342C2214yes—
203#2342C2214yes—
204#2334C2214yescomplemented
205#2329C2212yes—
206#2329C2212yescomplemented
207#2315C2211yescharacteristic
208#2315C2211yescharacteristic
209#2315C2212yes—
210#2313C2212yescomplemented
211#2313C2211yescharacteristic, complemented
212#2312C2214yes—
213#2310C2212yescomplemented
214#2308C2211yescharacteristic
215C2×#386C2211yescharacteristic
216C2×#385C2211yescharacteristic
217#2280C2212yes—
218#2274C2211yescharacteristic, complemented
219C23×Q8C2311yescharacteristic
220C23×D4C2311yescharacteristic
221C24×C4C2311yescharacteristic
222#552—48no—
223#544—44no—
224#544—44no—
225C2×C4⋊Q8C2314yes—
226C2×C4⋊Q8C2314yes—
227C2×C4⋊Q8C2314yes—
228C2×#126C2314yes—
229C2×#126C2314yes—
230C2×#125C2314yes—
231C2×#125C2314yes—
232C2×#125C2312yes—
233C2×#125C2314yes—
234C2×#123C2314yes—
235C2×#123C2314yes—
236C2×C22⋊Q8—44no—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248#518—44no—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2312yes—
255C2×#117C2312yes—
256C2×#117C2312yes—
257C2×#117C2312yes—
258C2×#117C2314yes—
259C2×#117C2314yes—
260C2×#117C2312yes—
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2312yes—
266C22×C22⋊C4C2311yescharacteristic
267C22×C22⋊C4C2314yes—
268C22×C22⋊C4C2311yescharacteristic
269C22×C22⋊C4C2311yescharacteristic
270C22×C22⋊C4C2311yescharacteristic
271C22×C22⋊C4C2312yes—
272C22×C22⋊C4C2311yescharacteristic
273C22×C22⋊C4C2312yes—
274#401C2314yes—
275#401C2314yes—
276#400C2312yes—
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#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#399C2312yes—
311#399C2314yes—
312#399C2314yes—
313#399C2312yes—
314#399C2312yes—
315#398C2312yes—
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#398C2312yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#397C2314yes—
342#397C2312yes—
343#397C2312yes—
344#397C2314yes—
345#397C2312yes—
346#397C2312yes—
347#397C2312yes—
348#397C2312yes—
349#397C2312yes—
350#397C2314yes—
351#397C2312yes—
352#397C2314yes—
353#397C2314yes—
354#397C2312yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2312yes—
359#397C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#395C2312yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#393C2312yes—
384#393C2312yes—
385#393C2314yes—
386#393C2312yes—
387#393C2312yes—
388#393C2314yes—
389#393C2312yes—
390#393C2312yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2312yes—
396#393C2314yes—
397#393C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
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#389C2314yes—
433#389C2314yes—
434#389C2314yes—
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#387C2314yes—
462#387C2314yes—
463#387C2314yes—
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#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#386C2312yes—
506#386C2312yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2312yes—
511#386C2312yes—
512#386C2314yes—
513#385C2314yes—
514#385C2312yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2312yes—
519#385C2312yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2312yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
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#385C2314yes—
542#385C2314yes—
543#383C2314yes—
544#383C2314yes—
545#383C2314yes—
546#383C2314yes—
547#383C2314yes—
548#383C2314yes—
549#383C2314yes—
550#383C2312yes—
551#382C2314yes—
552#382C2314yes—
553#382C2314yes—
554#382C2314yes—
555#382C2314yes—
556#382C2314yes—
557#382C2314yes—
558#381C2314yes—
559#381C2314yes—
560#381C2314yes—
561#381C2314yes—
562#381C2314yes—
563#381C2312yes—
564#381C2312yes—
565#381C2314yes—
566#381C2314yes—
567#381C2314yes—
568#381C2314yes—
569#381C2314yes—
570#380C2314yes—
571#380C2314yes—
572#380C2314yes—
573#380C2312yes—
574#380C2312yes—
575#380C2312yes—
576#380C2314yes—
577#380C2312yes—
578#380C2312yes—
579#380C2312yes—
580#380C2312yes—
581#380C2314yes—
582#380C2312yes—
583#380C2314yes—
584#380C2312yes—
585#380C2312yes—
586#380C2314yes—
587#380C2314yes—
588#379C2314yes—
589#379C2314yes—
590#379C2312yes—
591#379C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C22⋊C4C2312yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2312yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613#376C2314yes—
614#376C2312yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C2×#95C2314yes—
619C25C2411yescharacteristic
620C25C2411yescharacteristic
621C22×Q8—42no—
622C22×Q8—44no—
623C22×Q8C2412yes—
624C22×Q8C2414yes—
625C22×Q8C2414yes—
626C22×Q8C2412yes—
627C22×Q8C2412yes—
628C22×Q8C2412yes—
629C22×D4—24no—
630C22×D4—42no—
631C22×D4—42no—
632C22×D4C2412yes—
633C22×D4C2412yes—
634C23×C4—44no—
635C23×C4—42no—
636C23×C4C2411yescharacteristic
637C23×C4C2411yescharacteristic
638C23×C4C2414yes—
639C23×C4C2412yes—
640C23×C4C2411yescharacteristic
641C23×C4C2411yescharacteristic
642C23×C4C2412yes—
643C23×C4C2414yes—
644C23×C4C2412yes—
645C23×C4C2411yescharacteristic
646C23×C4C2412yes—
647C23×C4C2411yescharacteristic
648C23×C4C2412yes—
649C23×C4C2411yescharacteristic
650C23×C4C2412yes—
651C23×C4C2411yescharacteristic
652C23×C4C2411yescharacteristic
653C4⋊Q8—48no—
654C4⋊Q8—48no—
655C4⋊Q8—48no—
656#126—48no—
657#126—48no—
658#125—48no—
659#125—48no—
660#125—44no—
661#125—48no—
662#123—48no—
663#123—48no—
664C22⋊Q8—28no—
665C22⋊Q8—48no—
666C22⋊Q8—44no—
667C22⋊Q8—44no—
668C22⋊Q8—44no—
669C22⋊Q8—48no—
670C22⋊Q8—48no—
671C22⋊Q8—48no—
672C22⋊Q8—44no—
673C22⋊Q8—44no—
674C22⋊Q8—44no—
675C4×Q8—48no—
676C4×Q8—44no—
677C4×D4—28no—
678C4×D4—44no—
679C4×D4—44no—
680C4×D4—44no—
681#117—28no—
682#117—44no—
683#117—48no—
684#117—44no—
685#117—48no—
686#117—44no—
687C2×C4⋊C4—24no—
688C2×C4⋊C4—24no—
689C2×C4⋊C4—44no—
690C2×C4⋊C4—44no—
691C2×C4⋊C4—42no—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C22⋊C4—216no—
743C2×C22⋊C4—24no—
744C2×C22⋊C4—44no—
745C2×C22⋊C4—44no—
746C2×C22⋊C4—42no—
747C2×C22⋊C4—42no—
748C2×C22⋊C4—42no—
749C2×C22⋊C4—42no—
750C2×C22⋊C4C2412yes—
751C2×C22⋊C4C2412yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2412yes—
754C2×C22⋊C4C2412yes—
755C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
765C2×C22⋊C4C2412yes—
766C2×C22⋊C4C2412yes—
767C2×C22⋊C4C2412yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2412yes—
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×C42C2414yes—
785C2×C42C2414yes—
786C2×C42C2412yes—
787C2×C42C2412yes—
788C2×C42C2414yes—
789C2×C42C2414yes—
790C2×C42C2414yes—
791C2×C42C2414yes—
792C2×C42C2414yes—
793C2×C42C2414yes—
794C2×C42C2414yes—
795C2×C42C2414yes—
796C2×C42C2414yes—
797C2×C42C2414yes—
798#95C2412yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2412yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2412yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2412yes—
815#95C2412yes—
816#95C2412yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2412yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2412yes—
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—
868C24—22no—
869C24—22no—
870C24—22no—
871C24—41no—
872C24—42no—
873C24—41no—
874C24—42no—
875C24—42no—
876C24—42no—
877C242−1+414yes—
878C24C2511yescharacteristic
879C24C2511yescharacteristic
880C24C2512yes—
881C24C2511yescharacteristic
882C2×Q8—24no—
883C2×Q8—28no—
884C2×Q8—44no—
885C2×Q8—44no—
886C2×Q8—44no—
887C2×Q8—44no—
888C2×Q8—44no—
889C2×Q8—44no—
890C2×Q8—42no—
891C2×Q8—42no—
892C2×Q8—42no—
893C2×Q8—42no—
894C2×Q8—42no—
895C2×Q8—44no—
896C2×Q8—44no—
897C2×Q8—88no—
898C2×D4—24no—
899C2×D4—24no—
900C2×D4—24no—
901C2×D4—24no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—416no—
905C22×C4—22no—
906C22×C4—24no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—28no—
913C22×C4—28no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—41no—
919C22×C4—42no—
920C22×C4—41no—
921C22×C4—44no—
922C22×C4—42no—
923C22×C4—44no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—44no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—44no—
931C22×C4—44no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—41no—
937C22×C4—42no—
938C22×C4—41no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—44no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—88no—
946C22×C4H(5,𝔽2)14yes—
947C22×C4C2514yes—
948C22×C4C2514yes—
949C22×C4C2514yes—
950C22×C4C2512yes—
951C22×C4C2514yes—
952C22×C4C2514yes—
953C22×C4C2514yes—
954C22×C4C2514yes—
955C22×C4C2512yes—
956C22×C4C2512yes—
957C22×C4C2512yes—
958C22×C4C2512yes—
959C22×C4C2512yes—
960C22×C4C2514yes—
961C22×C4C2514yes—
962C22×C4C2512yes—
963C22×C4C2514yes—
964C22×C4C2512yes—
965C22×C4C2512yes—
966C4⋊C4—28no—
967C4⋊C4—28no—
968C4⋊C4—24no—
969C4⋊C4—24no—
970C4⋊C4—24no—
971C4⋊C4—24no—
972C4⋊C4—28no—
973C4⋊C4—28no—
974C4⋊C4—28no—
975C4⋊C4—28no—
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—42no—
986C4⋊C4—42no—
987C4⋊C4—44no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—44no—
991C4⋊C4—42no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—42no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—42no—
1000C4⋊C4—44no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C22⋊C4—24no—
1017C22⋊C4—28no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—28no—
1022C22⋊C4—28no—
1023C22⋊C4—24no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—24no—
1027C22⋊C4—24no—
1028C22⋊C4—24no—
1029C22⋊C4—28no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—44no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
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—
1050C42—28no—
1051C42—24no—
1052C42—28no—
1053C42—44no—
1054C42—44no—
1055C42—44no—
1056C42—44no—
1057C42—42no—
1058C42—44no—
1059C42—44no—
1060C42—44no—
1061C42—44no—
1062C42—44no—
1063C42—44no—
1064C23—28no—
1065C23—21no—
1066C23—21no—
1067C23—22no—
1068C23—21no—
1069C23—21no—
1070C23—24no—
1071C23—21no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—21no—
1076C23—22no—
1077C23—22no—
1078C23—24no—
1079C23—22no—
1080C23—22no—
1081C23—44no—
1082C23—48no—
1083C23—82no—
1084C23—82no—
1085C23—84no—
1086C23—84no—
1087C23—161no—
1088C23—161no—
1089C23—162no—
1090C23C2×H(5,𝔽2)12yes—
1091C23C2×2−1+412yes—
1092C23C2×2−1+414yes—
1093C23#58512yes—
1094C23C2611yescharacteristic
1095Q8—84no—
1096Q8—88no—
1097Q8—88no—
1098Q8—162no—
1099Q8—162no—
1100Q8—162no—
1101D4—48no—
1102D4—48no—
1103C2×C4—28no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—24no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—22no—
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—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—24no—
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—44no—
1154C2×C4—44no—
1155C2×C4—84no—
1156C2×C4—84no—
1157C2×C4—84no—
1158C2×C4—88no—
1159C2×C4—82no—
1160C2×C4—88no—
1161C2×C4—84no—
1162C2×C4—82no—
1163C2×C4—82no—
1164C2×C4—82no—
1165C2×C4—162no—
1166C2×C4—161no—
1167C2×C4—161no—
1168C2×C4—162no—
1169C2×C4C2×H(5,𝔽2)14yes—
1170C2×C4#58514yes—
1171C22—22no—
1172C22—24no—
1173C22—22no—
1174C22—22no—
1175C22—22no—
1176C22—22no—
1177C22—28no—
1178C22—24no—
1179C22—24no—
1180C22—41no—
1181C22—41no—
1182C22—42no—
1183C22—42no—
1184C22—41no—
1185C22—41no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—44no—
1191C22—88no—
1192C22—164no—
1193C22C22×H(5,𝔽2)11yescharacteristic
1194C22C22×2−1+411yescharacteristic
1195C22C2×#58511yescharacteristic
1196C22C2×#58512yes—
1197C222−1+612yes—
1198C4—24no—
1199C4—24no—
1200C4—42no—
1201C4—44no—
1202C4—44no—
1203C4—42no—
1204C4—42no—
1205C4—42no—
1206C4—42no—
1207C4—44no—
1208C4—42no—
1209C4—42no—
1210C4—44no—
1211C4—44no—
1212C4—44no—
1213C4—44no—
1214C4—44no—
1215C4—44no—
1216C4—44no—
1217C2—42no—
1218C2—42no—
1219C2—42no—
1220C2—44no—
1221C2#6281911yescharacteristic
1222C2#6282411yescharacteristic
1223C2#6287111yescharacteristic
1224C2#6290412yes—
1225C2#6291112yes—
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. #58517C2semidirect
2. #58311C2semidirect
3. #56700C2semidirect
4. #51662C2semidirect
5. #50879C2semidirect
6. #50169C2semidirect
7. #49204C2semidirect
8. #49193C2semidirect
9. #48797C2semidirect
10. #46882C2semidirect
12. #43665C2semidirect
13. #43507C2semidirect
14. #42978C2semidirect
15. #41354C2semidirect
16. #40627C2semidirect
17. #37956C2semidirect
19. #36708C2semidirect
20. #36064C2semidirect
22. #35644C2semidirect
25. C2×#544C22semidirect
26. C2×#544C22semidirect
30. #2841C22semidirect
32. #2839C22semidirect
33. #2839C22semidirect
34. #2835C22semidirect
35. #2822C22semidirect
36. #2806C22semidirect
37. #2805C22semidirect
38. #2799C22semidirect
43. #2770C22semidirect
44. #2769C22semidirect
45. #2765C22semidirect
49. #2764C22semidirect
51. #2763C22semidirect
52. #2763C22semidirect
53. #2762C22semidirect
54. #2762C22semidirect
55. #2762C22semidirect
56. #2762C22semidirect
57. #2758C22semidirect
58. #2758C22semidirect
59. #2758C22semidirect
60. #2755C22semidirect
61. #2755C22semidirect
64. #2745C22semidirect
65. #2745C22semidirect
66. #2745C22semidirect
67. #2744C22semidirect
68. #2744C22semidirect
70. #2742C22semidirect
71. #2729C22semidirect
72. #2729C22semidirect
73. #2726C22semidirect
74. #2722C22semidirect
75. #2719C22semidirect
76. #2713C22semidirect
77. #2698C22semidirect
78. #2698C22semidirect
81. #2690C22semidirect
82. #2689C22semidirect
83. #2689C22semidirect
84. #2689C22semidirect
91. #2677C22semidirect
92. #2666C22semidirect
93. #2666C22semidirect
94. #2666C22semidirect
95. #2665C22semidirect
96. #2665C22semidirect
97. #2665C22semidirect
98. #2659C22semidirect
100. #2642C22semidirect
103. #2628C22semidirect
104. #2627C22semidirect
105. #2627C22semidirect
108. #2625C22semidirect
110. #2611C22semidirect
112. #2607C22semidirect
114. #2599C22semidirect
116. #2589C22semidirect
120. #2575C22semidirect
121. #2575C22semidirect
123. #2574C22semidirect
124. #2573C22semidirect
125. #2573C22semidirect
136. #2550C22semidirect
137. #2533C22semidirect
139. #2527C22semidirect
140. #2524C22semidirect
141. #2524C22semidirect
142. #2523C22semidirect
143. #2515C22semidirect
145. #2505C22semidirect
146. #2503C22semidirect
147. #2503C22semidirect
149. #2493C22semidirect
150. #2493C22semidirect
151. #2493C22semidirect
153. #2492C22semidirect
154. #2492C22semidirect
156. #2489C22semidirect
159. #2484C22semidirect
164. #2478C22semidirect
167. #2475C22semidirect
168. #2473C22semidirect
172. #2465C22semidirect
174. #2453C22semidirect
175. #2451C22semidirect
178. #2446C22semidirect
179. #2442C22semidirect
180. #2439C22semidirect
181. #2439C22semidirect
183. #2438C22semidirect
185. #2434C22semidirect
190. #2396C22semidirect
193. #2381C22semidirect
194. #2378C22semidirect
195. #2368C22semidirect
196. #2360C22semidirect
198. #2356C22semidirect
200. #2346C22semidirect
201. #2343C22semidirect
204. #2334C22semidirect
206. #2329C22semidirect
210. #2313C22semidirect
211. #2313C22semidirect
213. #2310C22semidirect
218. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#585172
#583112
#567002
#516622
#508792
#501692
#492042
#491932
#487972
#468822
#468372
#436652
#435072
#429782
#413542
#406272
#379562
#379322
#367082
#360642
#360102
#356442
#353492