Finite Group Databasebeta

← #7713161

Subgroups — #7713161

Order 512.

4450 conjugacy classes of subgroups.

The subgroup lattice has 1374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48915C214yesmaximal, complemented
2#48914C214yesmaximal, complemented
3#48048C214yesmaximal, complemented
4#48047C214yesmaximal, complemented
5#47226C212yesmaximal, complemented
6#47225C212yesmaximal, complemented
7#47035C212yesmaximal, complemented
8#47032C212yesmaximal, complemented
9#46857C212yesmaximal, complemented
10#46855C212yesmaximal, complemented
11#46457C212yesmaximal, complemented
12#46455C212yesmaximal, complemented
13#39266C214yesmaximal, complemented
14#39038C214yesmaximal, complemented
15#38233C214yesmaximal, complemented
16#38198C214yesmaximal, complemented
17#37453C211yesmaximal, characteristic, complemented
18#37451C211yesmaximal, characteristic
19#36764C212yesmaximal, complemented
20#36763C212yesmaximal, complemented
21#35098C212yesmaximal, complemented
22#35035C212yesmaximal, complemented
23#35033C211yesmaximal, characteristic, complemented
24#35019C211yesmaximal, characteristic
25#34359C211yesmaximal, characteristic, complemented
26#34358C211yesmaximal, characteristic
27C2×#2332C211yesmaximal, characteristic, complemented
28C22×C22⋊Q8C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×#121C2211yescharacteristic
31#2857C2212yescomplemented
32#2853C2214yescomplemented
33#2852C2214yescomplemented
34#2851C2212yescomplemented
35#2850C2211yescharacteristic
36#2850C2211yescharacteristic
37#2850C2211yescharacteristic
38#2850C2211yescharacteristic
39#2817C2212yes—
40#2817C2212yes—
41#2816C2212yes—
42#2816C2212yes—
43#2799C2214yescomplemented
44#2798C2214yescomplemented
45#2798C2214yescomplemented
46#2796C2214yescomplemented
47#2796C2214yescomplemented
48#2794C2214yescomplemented
49#2794C2214yescomplemented
50#2793C2214yescomplemented
51#2790C2214yescomplemented
52#2789C2214yescomplemented
53#2777C2214yescomplemented
54#2773C2214yescomplemented
55#2772C2214yescomplemented
56#2767C2214yescomplemented
57#2765C2214yescomplemented
58#2762C2214yescomplemented
59#2761C2214yescomplemented
60#2759C2214yescomplemented
61#2758C2214yescomplemented
62#2755C2214yescomplemented
63#2754C2214yescomplemented
64#2754C2214yescomplemented
65#2751C2214yescomplemented
66#2751C2214yescomplemented
67#2751C2214yescomplemented
68#2750C2214yescomplemented
69#2746C2214yescomplemented
70#2745C2214yes—
71#2744C2214yes—
72#2743C2214yescomplemented
73#2743C2214yescomplemented
74#2740C2214yescomplemented
75#2739C2214yes—
76#2739C2214yescomplemented
77#2738C2214yes—
78#2737C2214yescomplemented
79#2736C2214yes—
80#2735C2214yes—
81#2735C2214yes—
82#2735C2214yes—
83#2729C2214yescomplemented
84#2716C2214yescomplemented
85#2716C2214yescomplemented
86#2716C2214yescomplemented
87#2715C2214yescomplemented
88#2715C2214yescomplemented
89#2700C2214yescomplemented
90#2700C2214yescomplemented
91#2643C2214yescomplemented
92#2639C2214yes—
93#2627C2214yescomplemented
94#2627C2212yescomplemented
95#2627C2212yescomplemented
96#2626C2214yes—
97#2626C2214yes—
98#2623C2214yescomplemented
99#2621C2212yes—
100#2621C2212yes—
101#2620C2212yes—
102#2620C2212yes—
103#2618C2212yes—
104#2618C2212yes—
105#2609C2214yescomplemented
106#2608C2212yes—
107#2608C2212yescomplemented
108#2607C2212yes—
109#2607C2212yescomplemented
110#2607C2214yescomplemented
111#2605C2214yescomplemented
112#2601C2214yescomplemented
113#2595C2214yescomplemented
114#2595C2214yescomplemented
115#2594C2214yescomplemented
116#2591C2214yes—
117#2589C2214yescomplemented
118#2588C2214yescomplemented
119#2588C2214yescomplemented
120#2587C2214yescomplemented
121#2576C2214yescomplemented
122#2575C2214yes—
123#2575C2214yescomplemented
124#2573C2214yes—
125#2572C2214yescomplemented
126#2570C2214yescomplemented
127#2561C2214yes—
128#2561C2214yes—
129#2529C2214yescomplemented
130#2528C2214yescomplemented
131#2527C2214yes—
132#2527C2214yescomplemented
133#2526C2214yescomplemented
134#2525C2214yescomplemented
135#2524C2214yescomplemented
136#2523C2214yescomplemented
137#2522C2214yescomplemented
138#2521C2214yescomplemented
139#2521C2214yescomplemented
140#2520C2214yescomplemented
141#2519C2214yescomplemented
142#2517C2214yescomplemented
143#2516C2214yescomplemented
144#2516C2214yescomplemented
145#2516C2214yescomplemented
146#2515C2214yes—
147#2515C2214yescomplemented
148#2511C2214yescomplemented
149#2510C2214yescomplemented
150#2504C2211yescharacteristic
151#2504C2211yescharacteristic
152#2503C2211yescharacteristic
153#2503C2211yescharacteristic
154#2503C2212yescomplemented
155#2503C2212yescomplemented
156#2502C2212yes—
157#2501C2212yes—
158#2492C2214yescomplemented
159#2488C2214yescomplemented
160#2488C2214yescomplemented
161#2483C2214yes—
162#2482C2214yes—
163#2481C2214yescomplemented
164#2480C2214yes—
165#2480C2214yes—
166#2479C2214yescomplemented
167#2477C2214yescomplemented
168#2475C2214yescomplemented
169#2474C2214yescomplemented
170#2474C2214yescomplemented
171#2450C2214yescomplemented
172#2449C2214yescomplemented
173#2441C2212yes—
174#2441C2212yescomplemented
175#2439C2212yes—
176#2439C2212yescomplemented
177#2439C2214yescomplemented
178#2436C2212yes—
179#2436C2211yescharacteristic
180#2436C2211yescharacteristic
181#2435C2212yes—
182#2435C2211yescharacteristic
183#2435C2211yescharacteristic
184#2434C2212yescomplemented
185#2434C2212yescomplemented
186#2419C2214yescomplemented
187#2419C2214yescomplemented
188#2405C2214yes—
189#2378C2214yes—
190#2377C2214yes—
191#2368C2214yescomplemented
192#2364C2214yes—
193#2344C2212yescomplemented
194#2344C2212yescomplemented
195#2342C2212yes—
196#2342C2212yes—
197#2342C2212yes—
198#2342C2212yes—
199D4×C22⋊C4C2212yes—
200D4×C22⋊C4C2212yes—
201#2333C2212yes—
202#2333C2212yes—
203#2332C2212yes—
204#2332C2212yes—
205#2332C2214yes—
206#2332C2212yes—
207#2332C2212yes—
208#2332C2212yescomplemented
209#2332C2214yescomplemented
210#2332C2212yescomplemented
211#2329C2212yescomplemented
212#2329C2212yescomplemented
213#2329C2214yescomplemented
214#2325C2212yes—
215#2325C2212yes—
216#2322C2214yescomplemented
217#2318C2214yescomplemented
218#2313C2212yes—
219#2313C2212yescomplemented
220#2310C2212yescomplemented
221#2308C2212yes—
222#2308C2214yes—
223C4×#123C2214yescomplemented
224C2×#391C2212yescomplemented
225#2290C2214yescomplemented
226C2×#388C2212yes—
227C2×#388C2212yes—
228C2×#387C2212yescomplemented
229C2×#387C2212yescomplemented
230#2280C2211yescharacteristic
231#2280C2211yescharacteristic
232C2×#381C2211yescharacteristic
233C2×C4×C4⋊C4C2212yescomplemented
234C2×C4×C22⋊C4C2211yescharacteristic
235C23×Q8C2311yescharacteristic
236C23×Q8C2311yescharacteristic
237C23×D4C2312yes—
238C23×D4C2311yescharacteristic
239C24×C4C2311yescharacteristic
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2312yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#125C2312yes—
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×#124C2312yes—
251C2×#124C2312yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×C22⋊Q8—28no—
255C2×C22⋊Q8—28no—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2311yescharacteristic
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2311yescharacteristic
262C2×C22⋊Q8C2311yescharacteristic
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×#121—28no—
269C2×#121C2311yescharacteristic
270C2×#121C2311yescharacteristic
271C2×#121C2311yescharacteristic
272C2×#121C2311yescharacteristic
273C2×#121C2312yes—
274C2×#121C2312yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×#117C2312yes—
278C2×#117C2312yes—
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2314yes—
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C22⋊C4C2312yes—
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2312yes—
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2312yes—
297C22×C22⋊C4C2311yescharacteristic
298C22×C22⋊C4C2311yescharacteristic
299C22×C42C2312yes—
300C22×C42C2311yescharacteristic
301C22×C42C2311yescharacteristic
302C22×C42C2312yes—
303#401C2314yes—
304#401C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#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#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2311yescharacteristic
411#391C2312yes—
412#391C2312yes—
413#391C2311yescharacteristic
414#391C2311yescharacteristic
415#391C2311yescharacteristic
416#391C2314yes—
417#391C2312yes—
418#391C2314yes—
419#391C2312yes—
420#391C2314yes—
421#391C2312yes—
422#391C2312yes—
423#390C2314yes—
424#390C2314yes—
425#390C2311yescharacteristic
426#390C2311yescharacteristic
427#390C2311yescharacteristic
428#390C2311yescharacteristic
429#390C2312yes—
430#390C2312yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2312yes—
439#389C2312yes—
440#389C2314yes—
441#389C2312yes—
442#389C2312yes—
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#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
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#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#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
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#386C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
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#384C2312yes—
572#384C2312yes—
573#384C2312yes—
574#383C2314yes—
575#383C2314yes—
576#383C2314yes—
577#382C2314yes—
578#382C2314yes—
579#382C2314yes—
580#382C2312yes—
581#382C2311yescharacteristic
582#382C2311yescharacteristic
583#382C2311yescharacteristic
584#382C2311yescharacteristic
585#382C2312yes—
586#382C2312yes—
587#381C2312yes—
588#381C2314yes—
589#381C2314yes—
590#381C2314yes—
591#381C2314yes—
592#381C2312yes—
593#381C2312yes—
594#381C2312yes—
595#381C2312yes—
596#381C2312yes—
597#381C2314yes—
598#381C2314yes—
599#381C2314yes—
600#381C2314yes—
601#381C2312yes—
602#381C2312yes—
603#381C2314yes—
604#380C2312yes—
605#380C2312yes—
606#380C2312yes—
607#380C2312yes—
608#380C2314yes—
609#380C2312yes—
610#380C2312yes—
611#380C2314yes—
612#380C2312yes—
613#380C2312yes—
614#380C2314yes—
615#379C2314yes—
616#379C2314yes—
617#379C2314yes—
618#379C2312yes—
619#379C2312yes—
620#379C2312yes—
621#379C2312yes—
622#379C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2314yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C22⋊C4C2312yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2312yes—
635C4×C22⋊C4C2312yes—
636C4×C22⋊C4C2312yes—
637C4×C22⋊C4C2312yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2312yes—
644C4×C22⋊C4C2311yescharacteristic
645C4×C22⋊C4C2312yes—
646C4×C22⋊C4C2311yescharacteristic
647C4×C22⋊C4C2312yes—
648C4×C22⋊C4C2311yescharacteristic
649C4×C22⋊C4C2311yescharacteristic
650C4×C22⋊C4C2312yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2314yes—
653#376C2314yes—
654C2×#95C2312yes—
655C2×#95C2312yes—
656C2×#95C2312yes—
657C2×#95C2312yes—
658C2×#95C2312yes—
659C2×#95C2312yes—
660C2×#95C2312yes—
661C25C2411yescharacteristic
662C25C2412yes—
663C22×Q8—24no—
664C22×Q8—24no—
665C22×Q8—81no—
666C22×Q8—81no—
667C22×Q8—81no—
668C22×Q8—81no—
669C22×Q8C2412yes—
670C22×Q8C2411yescharacteristic
671C22×Q8C2411yescharacteristic
672C22×Q8C2412yes—
673C22×Q8C2412yes—
674C22×Q8C2414yes—
675C22×D4—28no—
676C22×D4—24no—
677C22×D4—48no—
678C22×D4—81no—
679C22×D4—81no—
680C22×D4C2412yes—
681C22×D4C2412yes—
682C22×D4C2411yescharacteristic
683C22×D4C2411yescharacteristic
684C22×D4C2412yes—
685C22×D4C2412yes—
686C22×D4C2412yes—
687C23×C4—81no—
688C23×C4—81no—
689C23×C4#4118yes—
690C23×C4C2412yes—
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2412yes—
696C23×C4C2412yes—
697C23×C4C2412yes—
698C23×C4C2412yes—
699C23×C4C2414yes—
700C23×C4C2414yes—
701C23×C4C2411yescharacteristic
702C23×C4C2411yescharacteristic
703C23×C4C2411yescharacteristic
704C23×C4C2411yescharacteristic
705C23×C4C2411yescharacteristic
706C23×C4C2411yescharacteristic
707C4⋊Q8—82no—
708C4⋊Q8—82no—
709C4⋊Q8—82no—
710#126—84no—
711#126—84no—
712#125—82no—
713#124—81no—
714#124—81no—
715#124—81no—
716#124—81no—
717#124—82no—
718#124—82no—
719#123—48no—
720#123—48no—
721C22⋊Q8—28no—
722C22⋊Q8—28no—
723C22⋊Q8—24no—
724C22⋊Q8—24no—
725C22⋊Q8—28no—
726C22⋊Q8—28no—
727C22⋊Q8—28no—
728C22⋊Q8—28no—
729C22⋊Q8—24no—
730C22⋊Q8—24no—
731C22⋊Q8—48no—
732C22⋊Q8—84no—
733#121—24no—
734#121—24no—
735#121—28no—
736#121—28no—
737#121—24no—
738#121—24no—
739C4×D4—48no—
740C4×D4—48no—
741#117—84no—
742#117—82no—
743#117—81no—
744#117—81no—
745#117—82no—
746#117—81no—
747#117—81no—
748C2×C4⋊C4—24no—
749C2×C4⋊C4—24no—
750C2×C4⋊C4—28no—
751C2×C4⋊C4—28no—
752C2×C4⋊C4—24no—
753C2×C4⋊C4—44no—
754C2×C4⋊C4—82no—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C22⋊C4—28no—
801C2×C22⋊C4—28no—
802C2×C22⋊C4—28no—
803C2×C22⋊C4—44no—
804C2×C22⋊C4—81no—
805C2×C22⋊C4—81no—
806C2×C22⋊C4—82no—
807C2×C22⋊C4—82no—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
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×C42—44no—
857C2×C42—82no—
858C2×C42—81no—
859C2×C42—81no—
860C2×C42C2414yes—
861C2×C42C2412yes—
862C2×C42C2412yes—
863C2×C42C2414yes—
864C2×C42C2412yes—
865C2×C42C2412yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2411yescharacteristic
870C2×C42C2411yescharacteristic
871C2×C42C2411yescharacteristic
872C2×C42C2411yescharacteristic
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2412yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880#95C2414yes—
881#95C2412yes—
882#95C2412yes—
883#95C2412yes—
884#95C2412yes—
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#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942C24—24no—
943C24—24no—
944C24—41no—
945C24—41no—
946C24—42no—
947C24—42no—
948C24—42no—
949C24—44no—
950C24—44no—
951C24C2×#4114yes—
952C24C2512yes—
953C24C2512yes—
954C24C2511yescharacteristic
955C24C2511yescharacteristic
956C24C2511yescharacteristic
957C2×Q8—24no—
958C2×Q8—24no—
959C2×Q8—22no—
960C2×Q8—22no—
961C2×Q8—24no—
962C2×Q8—41no—
963C2×Q8—42no—
964C2×Q8—41no—
965C2×Q8—41no—
966C2×Q8—41no—
967C2×Q8—42no—
968C2×Q8—42no—
969C2×Q8—42no—
970C2×Q8—42no—
971C2×Q8—42no—
972C2×Q8—44no—
973C2×Q8—44no—
974C2×Q8—44no—
975C2×Q8—88no—
976C2×Q8—88no—
977C2×D4—24no—
978C2×D4—24no—
979C2×D4—28no—
980C2×D4—28no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—22no—
984C2×D4—22no—
985C2×D4—24no—
986C2×D4—41no—
987C2×D4—41no—
988C2×D4—42no—
989C2×D4—42no—
990C2×D4—41no—
991C2×D4—41no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—88no—
995C2×D4—816no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—24no—
999C22×C4—24no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—24no—
1004C22×C4—24no—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—42no—
1008C22×C4—41no—
1009C22×C4—41no—
1010C22×C4—42no—
1011C22×C4—42no—
1012C22×C4—41no—
1013C22×C4—41no—
1014C22×C4—41no—
1015C22×C4—41no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—41no—
1019C22×C4—41no—
1020C22×C4—41no—
1021C22×C4—41no—
1022C22×C4—41no—
1023C22×C4—41no—
1024C22×C4—42no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—44no—
1029C22×C4—44no—
1030C22×C4—44no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—44no—
1034C22×C4—42no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—88no—
1040C22×C4C2×#4114yes—
1041C22×C4C2×#4114yes—
1042C22×C4C2×#4114yes—
1043C22×C4C2×#4114yes—
1044C22×C4C2×#4114yes—
1045C22×C4C2×#4114yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2514yes—
1052C22×C4C2514yes—
1053C22×C4C2514yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2514yes—
1057C22×C4C2514yes—
1058C22×C4C2514yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2511yescharacteristic
1065C22×C4C2511yescharacteristic
1066C22×C4C2511yescharacteristic
1067C22×C4C2511yescharacteristic
1068C4⋊C4—22no—
1069C4⋊C4—22no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—22no—
1074C4⋊C4—22no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—28no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
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—42no—
1093C4⋊C4—42no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C22⋊C4—24no—
1114C22⋊C4—24no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—24no—
1118C22⋊C4—24no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—24no—
1122C22⋊C4—24no—
1123C22⋊C4—24no—
1124C22⋊C4—24no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—42no—
1128C22⋊C4—42no—
1129C22⋊C4—42no—
1130C22⋊C4—42no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—42no—
1134C22⋊C4—42no—
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—42no—
1146C22⋊C4—42no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
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—
1161C42—44no—
1162C42—44no—
1163C42—44no—
1164C42—41no—
1165C42—41no—
1166C42—41no—
1167C42—41no—
1168C42—42no—
1169C42—44no—
1170C42—42no—
1171C42—44no—
1172C42—44no—
1173C42—44no—
1174C42—42no—
1175C42—42no—
1176C42—44no—
1177C42—42no—
1178C42—42no—
1179C42—44no—
1180C42—44no—
1181C23—21no—
1182C23—21no—
1183C23—22no—
1184C23—22no—
1185C23—22no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—22no—
1191C23—22no—
1192C23—28no—
1193C23—22no—
1194C23—22no—
1195C23—24no—
1196C23—24no—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—24no—
1202C23—24no—
1203C23—44no—
1204C23—44no—
1205C23—48no—
1206C23—84no—
1207C23—84no—
1208C23—84no—
1209C23—84no—
1210C23—164no—
1211C23—164no—
1212C23C22×#4112yes—
1213C23C22×#4112yes—
1214C23C22×#4112yes—
1215C23#58514yes—
1216C23C2611yescharacteristic
1217Q8—82no—
1218Q8—82no—
1219Q8—84no—
1220Q8—84no—
1221Q8—84no—
1222Q8—164no—
1223D4—48no—
1224D4—48no—
1225D4—82no—
1226D4—82no—
1227D4—84no—
1228D4—84no—
1229D4—84no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—44no—
1289C2×C4—44no—
1290C2×C4—44no—
1291C2×C4—44no—
1292C2×C4—44no—
1293C2×C4—44no—
1294C2×C4—48no—
1295C2×C4—48no—
1296C2×C4—48no—
1297C2×C4—48no—
1298C2×C4—84no—
1299C2×C4—84no—
1300C2×C4—84no—
1301C2×C4—84no—
1302C2×C4—84no—
1303C2×C4—88no—
1304C2×C4—164no—
1305C2×C4C22×#4112yes—
1306C2×C4C22×#4112yes—
1307C2×C4C22×#4112yes—
1308C2×C4C22×#4112yes—
1309C22—22no—
1310C22—22no—
1311C22—24no—
1312C22—24no—
1313C22—22no—
1314C22—22no—
1315C22—22no—
1316C22—22no—
1317C22—22no—
1318C22—22no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—42no—
1327C22—42no—
1328C22—42no—
1329C22—44no—
1330C22—44no—
1331C22—44no—
1332C22—44no—
1333C22—88no—
1334C22—168no—
1335C22#351014yes—
1336C22C23×#4111yescharacteristic
1337C22C2×#58512yes—
1338C22H(7,𝔽2)11yescharacteristic
1339C22H(7,𝔽2)11yescharacteristic
1340C222−1+612yes—
1341C4—22no—
1342C4—22no—
1343C4—22no—
1344C4—22no—
1345C4—44no—
1346C4—42no—
1347C4—42no—
1348C4—44no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—42no—
1353C4—44no—
1354C4—42no—
1355C4—42no—
1356C4—44no—
1357C4—44no—
1358C4—42no—
1359C4—44no—
1360C4—42no—
1361C4—44no—
1362C4—44no—
1363C2—24no—
1364C2—42no—
1365C2—42no—
1366C2—82no—
1367C2—82no—
1368C2C2×#351011yescharacteristic
1369C2#6284411yescharacteristic
1370C2#6286011yescharacteristic
1371C2#6286812yes—
1372C2#6287212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #48915C2semidirect
2. #48914C2semidirect
3. #48048C2semidirect
4. #48047C2semidirect
5. #47226C2semidirect
6. #47225C2semidirect
7. #47035C2semidirect
8. #47032C2semidirect
9. #46857C2semidirect
10. #46855C2semidirect
11. #46457C2semidirect
12. #46455C2semidirect
13. #39266C2semidirect
14. #39038C2semidirect
15. #38233C2semidirect
16. #38198C2semidirect
17. #37453C2semidirect
19. #36764C2semidirect
20. #36763C2semidirect
21. #35098C2semidirect
22. #35035C2semidirect
23. #35033C2semidirect
25. #34359C2semidirect
27. C2×#2332C2semidirect
31. #2857C22semidirect
32. #2853C22semidirect
33. #2852C22semidirect
34. #2851C22semidirect
43. #2799C22semidirect
44. #2798C22semidirect
45. #2798C22semidirect
46. #2796C22semidirect
47. #2796C22semidirect
48. #2794C22semidirect
49. #2794C22semidirect
50. #2793C22semidirect
51. #2790C22semidirect
52. #2789C22semidirect
53. #2777C22semidirect
54. #2773C22semidirect
55. #2772C22semidirect
56. #2767C22semidirect
57. #2765C22semidirect
58. #2762C22semidirect
59. #2761C22semidirect
60. #2759C22semidirect
61. #2758C22semidirect
62. #2755C22semidirect
63. #2754C22semidirect
64. #2754C22semidirect
65. #2751C22semidirect
66. #2751C22semidirect
67. #2751C22semidirect
68. #2750C22semidirect
69. #2746C22semidirect
72. #2743C22semidirect
73. #2743C22semidirect
74. #2740C22semidirect
76. #2739C22semidirect
78. #2737C22semidirect
83. #2729C22semidirect
84. #2716C22semidirect
85. #2716C22semidirect
86. #2716C22semidirect
87. #2715C22semidirect
88. #2715C22semidirect
89. #2700C22semidirect
90. #2700C22semidirect
91. #2643C22semidirect
93. #2627C22semidirect
94. #2627C22semidirect
95. #2627C22semidirect
98. #2623C22semidirect
105. #2609C22semidirect
107. #2608C22semidirect
109. #2607C22semidirect
110. #2607C22semidirect
111. #2605C22semidirect
112. #2601C22semidirect
113. #2595C22semidirect
114. #2595C22semidirect
115. #2594C22semidirect
117. #2589C22semidirect
118. #2588C22semidirect
119. #2588C22semidirect
120. #2587C22semidirect
121. #2576C22semidirect
123. #2575C22semidirect
125. #2572C22semidirect
126. #2570C22semidirect
129. #2529C22semidirect
130. #2528C22semidirect
132. #2527C22semidirect
133. #2526C22semidirect
134. #2525C22semidirect
135. #2524C22semidirect
136. #2523C22semidirect
137. #2522C22semidirect
138. #2521C22semidirect
139. #2521C22semidirect
140. #2520C22semidirect
141. #2519C22semidirect
142. #2517C22semidirect
143. #2516C22semidirect
144. #2516C22semidirect
145. #2516C22semidirect
147. #2515C22semidirect
148. #2511C22semidirect
149. #2510C22semidirect
154. #2503C22semidirect
155. #2503C22semidirect
158. #2492C22semidirect
159. #2488C22semidirect
160. #2488C22semidirect
163. #2481C22semidirect
166. #2479C22semidirect
167. #2477C22semidirect
168. #2475C22semidirect
169. #2474C22semidirect
170. #2474C22semidirect
171. #2450C22semidirect
172. #2449C22semidirect
174. #2441C22semidirect
176. #2439C22semidirect
177. #2439C22semidirect
184. #2434C22semidirect
185. #2434C22semidirect
186. #2419C22semidirect
187. #2419C22semidirect
191. #2368C22semidirect
193. #2344C22semidirect
194. #2344C22semidirect
208. #2332C22semidirect
209. #2332C22semidirect
210. #2332C22semidirect
211. #2329C22semidirect
212. #2329C22semidirect
213. #2329C22semidirect
216. #2322C22semidirect
217. #2318C22semidirect
219. #2313C22semidirect
220. #2310C22semidirect
223. C4×#123C22semidirect
224. C2×#391C22semidirect
225. #2290C22semidirect
228. C2×#387C22semidirect
229. C2×#387C22semidirect
233. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#489152
#489142
#480482
#480472
#472262
#472252
#470352
#470322
#468572
#468552
#464572
#464552
#392662
#390382
#382332
#381982
#374532
#374512
#367642
#367632
#350982
#350352
#350332
#350192
#343592
#343582
C2×#23322