Finite Group Databasebeta

← #7658607

Subgroups — #7658607

Order 512.

4521 conjugacy classes of subgroups.

The subgroup lattice has 1283 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42756C213yesmaximal, complemented
2#42754C213yesmaximal, complemented
3#42729C213yesmaximal, complemented
4#42722C213yesmaximal, complemented
5#42698C213yesmaximal, complemented
6#42694C213yesmaximal, complemented
7#42665C213yesmaximal, complemented
8#42660C213yesmaximal, complemented
9#42640C213yesmaximal, complemented
10#42632C213yesmaximal, complemented
11#42628C213yesmaximal, complemented
12#42621C213yesmaximal, complemented
13#37631C213yesmaximal, complemented
14#37598C213yesmaximal, complemented
15#37573C213yesmaximal, complemented
16#36693C213yesmaximal, complemented
17#35948C211yesmaximal, characteristic, complemented
18#35937C211yesmaximal, characteristic, complemented
19#35920C211yesmaximal, characteristic, complemented
20#35910C211yesmaximal, characteristic, complemented
21#35883C211yesmaximal, characteristic, complemented
22#35854C211yesmaximal, characteristic, complemented
23#35816C211yesmaximal, characteristic, complemented
24#35801C211yesmaximal, characteristic, complemented
25#35801C211yesmaximal, characteristic, complemented
26#35786C211yesmaximal, characteristic, complemented
27#35737C211yesmaximal, characteristic
28#35711C211yesmaximal, characteristic, complemented
29#34336C211yesmaximal, characteristic, complemented
30#34311C211yesmaximal, characteristic, complemented
31#34263C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#519C2211yescharacteristic
40C2×#519C2211yescharacteristic
41#2839C2213yes—
42#2839C2213yes—
43#2838C2213yes—
44#2838C2213yes—
45#2838C2213yes—
46#2838C2213yes—
47#2838C2216yes—
48#2837C2213yes—
49#2837C2213yes—
50#2832C2213yes—
51#2832C2213yes—
52#2831C2213yes—
53#2831C2213yes—
54#2830C2211yescharacteristic
55#2830C2213yes—
56#2829C2213yes—
57#2829C2213yes—
58#2800C2216yes—
59#2799C2216yes—
60#2798C2216yes—
61#2772C2216yes—
62#2767C2216yes—
63#2754C2216yes—
64#2747C2216yes—
65#2745C2216yes—
66#2742C2216yes—
67#2741C2216yes—
68#2738C2216yes—
69#2737C2216yes—
70#2731C2216yes—
71#2716C2216yes—
72#2702C2216yes—
73#2700C2216yes—
74#2666C2216yes—
75#2662C2216yes—
76#2660C2213yes—
77#2655C2216yes—
78#2654C2216yes—
79#2654C2216yes—
80#2653C2216yes—
81#2650C2216yes—
82#2650C2216yes—
83#2650C2216yes—
84#2649C2216yes—
85#2645C2213yes—
86#2645C2213yes—
87#2642C2213yes—
88#2640C2213yes—
89#2640C2213yes—
90#2629C2213yes—
91#2629C2213yes—
92#2628C2213yes—
93#2628C2216yes—
94#2625C2216yes—
95#2624C2213yes—
96#2624C2213yes—
97#2621C2213yes—
98#2592C2213yes—
99#2592C2213yes—
100#2584C2213yes—
101#2582C2213yes—
102#2581C2213yes—
103#2568C2213yes—
104#2568C2213yes—
105#2566C2213yes—
106#2565C2213yes—
107#2563C2213yes—
108#2562C2213yes—
109#2551C2213yes—
110#2551C2213yes—
111#2550C2213yes—
112#2550C2213yes—
113#2547C2213yes—
114#2547C2213yes—
115#2546C2213yes—
116#2538C2213yes—
117#2535C2213yes—
118#2525C2216yes—
119#2520C2216yes—
120#2514C2213yes—
121#2514C2213yes—
122#2511C2213yes—
123#2511C2213yes—
124#2511C2213yes—
125#2511C2213yes—
126#2500C2213yes—
127#2500C2213yes—
128#2497C2213yes—
129#2496C2213yes—
130#2496C2213yes—
131#2496C2213yes—
132#2495C2213yes—
133#2494C2213yes—
134#2494C2216yes—
135#2492C2216yes—
136#2492C2213yes—
137#2492C2213yes—
138#2492C2213yes—
139#2492C2213yes—
140#2491C2213yes—
141#2491C2213yes—
142#2490C2213yes—
143#2490C2213yes—
144#2489C2213yes—
145#2489C2213yes—
146#2489C2213yes—
147#2489C2213yes—
148#2485C2213yes—
149#2485C2213yes—
150#2479C2216yes—
151#2474C2216yes—
152#2454C2213yes—
153#2453C2213yes—
154#2452C2213yes—
155#2451C2213yes—
156#2451C2213yes—
157#2451C2213yes—
158#2448C2213yes—
159#2448C2213yes—
160#2448C2213yes—
161#2448C2213yes—
162#2442C2213yes—
163#2441C2213yes—
164#2440C2213yes—
165#2439C2213yes—
166#2439C2213yes—
167#2439C2213yes—
168#2427C2213yes—
169#2427C2213yes—
170#2423C2213yes—
171#2423C2213yes—
172#2421C2213yes—
173#2421C2213yes—
174#2417C2213yes—
175#2417C2213yes—
176#2401C2213yes—
177#2401C2213yes—
178#2399C2213yes—
179#2398C2213yes—
180#2398C2213yes—
181#2398C2213yes—
182#2396C2213yes—
183#2396C2213yes—
184#2396C2213yes—
185#2395C2213yes—
186#2395C2213yes—
187#2392C2213yes—
188#2370C2213yes—
189#2370C2213yes—
190#2369C2213yes—
191#2365C2213yes—
192#2362C2213yes—
193#2362C2213yes—
194#2357C2213yes—
195#2355C2213yes—
196#2354C2213yes—
197#2354C2213yes—
198#2351C2211yescharacteristic
199#2351C2211yescharacteristic
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202#2351C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206Q8×C4⋊C4C2211yescharacteristic
207Q8×C4⋊C4C2211yescharacteristic
208#2345C2213yes—
209#2344C2213yes—
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218Q8×C22⋊C4C2211yescharacteristic
219Q8×C22⋊C4C2211yescharacteristic
220Q8×C22⋊C4C2211yescharacteristic
221Q8×C22⋊C4C2211yescharacteristic
222#2331C2213yes—
223#2330C2213yes—
224#2323C2213yes—
225#2323C2213yes—
226#2319C2213yes—
227#2314C2213yes—
228C4×C4⋊Q8C2213yes—
229C4×#125C2213yes—
230#2298C2213yes—
231#2295C2213yes—
232#2293C2213yes—
233#2293C2213yes—
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241Q82—44no—
242#557—28no—
243#557—44no—
244D4×Q8—28no—
245#548—44no—
246#548—44no—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2316yes—
254C2×#126C2316yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#124C2313yes—
260C2×#124C2313yes—
261C2×#124C2316yes—
262C2×C22⋊Q8C2313yes—
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2313yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2316yes—
267C2×#121C2313yes—
268C2×#121C2313yes—
269#520—28no—
270#519—44no—
271#519—44no—
272C2×C4×Q8C2313yes—
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2311yescharacteristic
291C2×C4×D4C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×#117C2313yes—
297C2×#117C2313yes—
298C2×#117C2313yes—
299C2×#117C2313yes—
300C2×#117C2313yes—
301C2×#117C2316yes—
302C22×C4⋊C4C2313yes—
303#401C2313yes—
304#401C2313yes—
305#401C2316yes—
306#400C2316yes—
307#400C2313yes—
308#400C2313yes—
309#400C2316yes—
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#400C2313yes—
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#400C2313yes—
322#400C2313yes—
323#400C2313yes—
324#400C2313yes—
325#400C2316yes—
326#400C2316yes—
327#400C2316yes—
328#400C2316yes—
329#400C2316yes—
330#400C2316yes—
331#400C2316yes—
332#399C2313yes—
333#399C2313yes—
334#399C2313yes—
335#399C2313yes—
336#399C2313yes—
337#399C2316yes—
338#399C2316yes—
339#398C2313yes—
340#398C2316yes—
341#398C2313yes—
342#398C2313yes—
343#398C2311yescharacteristic
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2316yes—
353#398C2313yes—
354#398C2316yes—
355#398C2316yes—
356#398C2316yes—
357#397C2313yes—
358#397C2313yes—
359#397C2313yes—
360#397C2313yes—
361#397C2311yescharacteristic
362#397C2311yescharacteristic
363#397C2313yes—
364#397C2313yes—
365#397C2311yescharacteristic
366#397C2313yes—
367#397C2311yescharacteristic
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#397C2313yes—
373#397C2313yes—
374#397C2313yes—
375#397C2313yes—
376#397C2316yes—
377#397C2316yes—
378#397C2316yes—
379#397C2316yes—
380#397C2316yes—
381#397C2316yes—
382#397C2316yes—
383#396C2313yes—
384#396C2316yes—
385#396C2313yes—
386#396C2313yes—
387#396C2313yes—
388#396C2311yescharacteristic
389#396C2311yescharacteristic
390#396C2313yes—
391#396C2313yes—
392#396C2313yes—
393#396C2313yes—
394#396C2316yes—
395#396C2316yes—
396#395C2311yescharacteristic
397#395C2313yes—
398#395C2313yes—
399#395C2313yes—
400#395C2313yes—
401#395C2313yes—
402#395C2313yes—
403#395C2316yes—
404#395C2316yes—
405#395C2316yes—
406#394C2313yes—
407#394C2311yescharacteristic
408#394C2313yes—
409#394C2313yes—
410#394C2313yes—
411#394C2313yes—
412#394C2313yes—
413#394C2313yes—
414#394C2313yes—
415#394C2313yes—
416#394C2311yescharacteristic
417#394C2313yes—
418#394C2313yes—
419#394C2316yes—
420#394C2316yes—
421#393C2313yes—
422#393C2316yes—
423#393C2311yescharacteristic
424#393C2313yes—
425#393C2311yescharacteristic
426#393C2313yes—
427#393C2313yes—
428#393C2313yes—
429#393C2313yes—
430#393C2313yes—
431#393C2316yes—
432#393C2316yes—
433#393C2316yes—
434#392C2313yes—
435#391C2313yes—
436#391C2313yes—
437#391C2313yes—
438#391C2313yes—
439#391C2313yes—
440#391C2313yes—
441#391C2313yes—
442#391C2313yes—
443#391C2316yes—
444#391C2316yes—
445#391C2316yes—
446#391C2313yes—
447#391C2313yes—
448#391C2313yes—
449#391C2313yes—
450#391C2313yes—
451#391C2313yes—
452#391C2313yes—
453#391C2313yes—
454#391C2316yes—
455#391C2316yes—
456#391C2313yes—
457#391C2313yes—
458#391C2316yes—
459#391C2316yes—
460#390C2316yes—
461#390C2313yes—
462#390C2313yes—
463#390C2311yescharacteristic
464#390C2313yes—
465#390C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2313yes—
470#390C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2316yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2316yes—
484#389C2313yes—
485#389C2313yes—
486#389C2313yes—
487#389C2313yes—
488#389C2316yes—
489#389C2316yes—
490#389C2316yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#389C2313yes—
495#389C2313yes—
496#389C2313yes—
497#389C2313yes—
498#389C2313yes—
499#389C2313yes—
500#388C2316yes—
501#388C2316yes—
502#388C2316yes—
503#388C2316yes—
504#388C2313yes—
505#388C2313yes—
506#388C2313yes—
507#388C2313yes—
508#388C2313yes—
509#388C2313yes—
510#388C2313yes—
511#388C2313yes—
512#388C2316yes—
513#388C2316yes—
514#388C2316yes—
515#388C2316yes—
516#388C2316yes—
517#388C2316yes—
518#388C2316yes—
519#388C2316yes—
520#388C2316yes—
521#388C2316yes—
522#388C2316yes—
523#388C2316yes—
524#388C2316yes—
525#387C2313yes—
526#387C2316yes—
527#387C2316yes—
528#387C2316yes—
529#387C2313yes—
530#387C2316yes—
531#387C2313yes—
532#387C2311yescharacteristic
533#387C2313yes—
534#387C2311yescharacteristic
535#387C2313yes—
536#387C2313yes—
537#387C2316yes—
538#387C2316yes—
539#387C2316yes—
540#387C2316yes—
541#387C2316yes—
542#387C2316yes—
543#387C2316yes—
544#387C2316yes—
545#387C2316yes—
546#387C2316yes—
547#387C2316yes—
548#387C2316yes—
549#387C2316yes—
550#386C2316yes—
551#386C2316yes—
552#385C2316yes—
553#385C2316yes—
554#384C2313yes—
555#384C2313yes—
556#384C2313yes—
557#384C2313yes—
558#384C2313yes—
559#383C2316yes—
560#382C2313yes—
561#382C2316yes—
562#382C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2316yes—
566#382C2313yes—
567#381C2316yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2316yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2316yes—
582#380C2316yes—
583#380C2316yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2316yes—
587C4×C4⋊C4C2316yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2316yes—
590C4×C4⋊C4C2316yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2316yes—
623#376C2313yes—
624#376C2313yes—
625#376C2313yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C22×Q8—24no—
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2411yescharacteristic
640C22×Q8C2413yes—
641C22×Q8C2416yes—
642C22×Q8C2411yescharacteristic
643C22×D4C2413yes—
644C22×D4C2411yescharacteristic
645C22×D4C2413yes—
646C22×D4C2413yes—
647C23×C4C2413yes—
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2416yes—
651C4⋊Q8—212no—
652C4⋊Q8—212no—
653C4⋊Q8—46no—
654C4⋊Q8—46no—
655C4⋊Q8—46no—
656C4⋊Q8—46no—
657C4⋊Q8—86no—
658#126—86no—
659#125—212no—
660#125—212no—
661#125—46no—
662#125—46no—
663#124—46no—
664#124—46no—
665#124—86no—
666C22⋊Q8—212no—
667C22⋊Q8—212no—
668C22⋊Q8—46no—
669C22⋊Q8—46no—
670C22⋊Q8—86no—
671#121—46no—
672#121—46no—
673C4×Q8—24no—
674C4×Q8—24no—
675C4×Q8—24no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—24no—
683C4×Q8—24no—
684C4×Q8—212no—
685C4×Q8—46no—
686C4×Q8—46no—
687C4×Q8—46no—
688C4×Q8—46no—
689C4×Q8—46no—
690C4×Q8—46no—
691C4×Q8#4118yes—
692C4×D4—212no—
693C4×D4—212no—
694C4×D4—212no—
695C4×D4—46no—
696C4×D4—46no—
697#117—212no—
698#117—46no—
699#117—46no—
700#117—46no—
701#117—46no—
702#117—86no—
703C2×C4⋊C4—212no—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2416yes—
722C2×C4⋊C4C2416yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2416yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C22⋊C4C2413yes—
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2413yes—
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2411yescharacteristic
769C2×C22⋊C4C2411yescharacteristic
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2416yes—
772C2×C22⋊C4C2411yescharacteristic
773C2×C22⋊C4C2411yescharacteristic
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2416yes—
777C2×C22⋊C4C2416yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2416yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2411yescharacteristic
786C2×C22⋊C4C2411yescharacteristic
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2411yescharacteristic
789C2×C22⋊C4C2411yescharacteristic
790C2×C22⋊C4C2411yescharacteristic
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2411yescharacteristic
793C2×C22⋊C4C2411yescharacteristic
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2416yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2416yes—
804C2×C42C2413yes—
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2416yes—
817C2×C42C2416yes—
818C2×C42C2416yes—
819C2×C42C2416yes—
820C2×C42C2411yescharacteristic
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2416yes—
824C2×C42C2413yes—
825#95C2411yescharacteristic
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2411yescharacteristic
838#95C2411yescharacteristic
839#95C2411yescharacteristic
840#95C2411yescharacteristic
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2416yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2416yes—
864#95C2413yes—
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2413yes—
868#95C2411yescharacteristic
869#95C2411yescharacteristic
870#95C2411yescharacteristic
871#95C2413yes—
872#95C2416yes—
873#95C2416yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2416yes—
880#95C2416yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2416yes—
888#95C2416yes—
889#95C2416yes—
890#95C2416yes—
891#95C2416yes—
892#95C2416yes—
893#95C2416yes—
894#95C2416yes—
895C24C2511yescharacteristic
896C24C2511yescharacteristic
897C24C2513yes—
898#41—416no—
899C2×Q8—26no—
900C2×Q8—26no—
901C2×Q8—26no—
902C2×Q8—26no—
903C2×Q8—26no—
904C2×Q8—26no—
905C2×Q8—26no—
906C2×Q8—41no—
907C2×Q8—41no—
908C2×Q8—41no—
909C2×Q8—43no—
910C2×Q8—43no—
911C2×Q8—43no—
912C2×Q8—43no—
913C2×Q8—43no—
914C2×Q8—46no—
915C2×Q8—46no—
916C2×Q8—46no—
917C2×Q8—416no—
918C2×Q8—416no—
919C2×Q8C2×#4114yes—
920C2×Q8H(5,𝔽2)14yes—
921C2×Q82−1+414yes—
922C2×D4—22no—
923C2×D4—26no—
924C2×D4—26no—
925C2×D4—26no—
926C2×D4—41no—
927C2×D4—41no—
928C2×D4—43no—
929C2×D4—43no—
930C2×D4—43no—
931C2×D4—43no—
932C2×D4—43no—
933C2×D4—43no—
934C22×C4—26no—
935C22×C4—26no—
936C22×C4—26no—
937C22×C4—26no—
938C22×C4—26no—
939C22×C4—26no—
940C22×C4—26no—
941C22×C4—26no—
942C22×C4—26no—
943C22×C4—212no—
944C22×C4—46no—
945C22×C4—46no—
946C22×C4C2511yescharacteristic
947C22×C4C2511yescharacteristic
948C22×C4C2511yescharacteristic
949C22×C4C2513yes—
950C22×C4C2513yes—
951C22×C4C2511yescharacteristic
952C22×C4C2513yes—
953C22×C4C2511yescharacteristic
954C22×C4C2511yescharacteristic
955C22×C4C2513yes—
956C22×C4C2513yes—
957C22×C4C2513yes—
958C22×C4C2513yes—
959C22×C4C2511yescharacteristic
960C22×C4C2511yescharacteristic
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2513yes—
964C22×C4C2513yes—
965C22×C4C2513yes—
966C22×C4C2513yes—
967C22×C4C2511yescharacteristic
968C22×C4C2513yes—
969C22×C4C2513yes—
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2513yes—
973C22×C4C2513yes—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—22no—
977C4⋊C4—26no—
978C4⋊C4—22no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—26no—
982C4⋊C4—26no—
983C4⋊C4—212no—
984C4⋊C4—212no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—26no—
989C4⋊C4—26no—
990C4⋊C4—26no—
991C4⋊C4—26no—
992C4⋊C4—26no—
993C4⋊C4—41no—
994C4⋊C4—43no—
995C4⋊C4—43no—
996C4⋊C4—43no—
997C4⋊C4—43no—
998C4⋊C4—43no—
999C4⋊C4—43no—
1000C4⋊C4—41no—
1001C4⋊C4—46no—
1002C4⋊C4—43no—
1003C4⋊C4—41no—
1004C4⋊C4—43no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—43no—
1008C4⋊C4—43no—
1009C4⋊C4—43no—
1010C4⋊C4—43no—
1011C4⋊C4—43no—
1012C4⋊C4—43no—
1013C4⋊C4—43no—
1014C4⋊C4—43no—
1015C4⋊C4—46no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—41no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C4—43no—
1025C4⋊C4—46no—
1026C4⋊C4—46no—
1027C4⋊C4—46no—
1028C4⋊C4—46no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4C2×#41112yes—
1032C22⋊C4—26no—
1033C22⋊C4—26no—
1034C22⋊C4—26no—
1035C22⋊C4—26no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—43no—
1039C22⋊C4—43no—
1040C22⋊C4—43no—
1041C22⋊C4—43no—
1042C22⋊C4—46no—
1043C22⋊C4—43no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—43no—
1047C22⋊C4—41no—
1048C22⋊C4—43no—
1049C22⋊C4—46no—
1050C22⋊C4—43no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—43no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—43no—
1058C22⋊C4—43no—
1059C22⋊C4—43no—
1060C22⋊C4—46no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—43no—
1064C22⋊C4—43no—
1065C22⋊C4—46no—
1066C22⋊C4—46no—
1067C22⋊C4—43no—
1068C22⋊C4—46no—
1069C22⋊C4—43no—
1070C22⋊C4—43no—
1071C22⋊C4—43no—
1072C22⋊C4—43no—
1073C22⋊C4—43no—
1074C42—26no—
1075C42—26no—
1076C42—26no—
1077C42—26no—
1078C42—26no—
1079C42—26no—
1080C42—26no—
1081C42—26no—
1082C42—26no—
1083C42—26no—
1084C42—26no—
1085C42—43no—
1086C42—41no—
1087C42—43no—
1088C42—46no—
1089C42—46no—
1090C42—46no—
1091C42—43no—
1092C42—46no—
1093C42—46no—
1094C42C2×#41112yes—
1095C23—21no—
1096C23—21no—
1097C23—23no—
1098C23—23no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—23no—
1104C23—21no—
1105C23—23no—
1106C23—21no—
1107C23—21no—
1108C23—23no—
1109C23—21no—
1110C23—23no—
1111C23—21no—
1112C23—23no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23C2611yescharacteristic
1117Q8—44no—
1118Q8—412no—
1119Q8—412no—
1120Q8—86no—
1121Q8—86no—
1122Q8—166no—
1123Q8#542116yes—
1124D4—44no—
1125D4—412no—
1126D4—86no—
1127D4—86no—
1128C2×C4—23no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—23no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—23no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—23no—
1148C2×C4—23no—
1149C2×C4—23no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—23no—
1154C2×C4—23no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—21no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—21no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—21no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—21no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—23no—
1188C2×C4—23no—
1189C2×C4—23no—
1190C2×C4—23no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—23no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—23no—
1207C2×C4—412no—
1208C2×C4—412no—
1209C2×C4—412no—
1210C2×C4—812no—
1211C2×C4C22×#4112yes—
1212C2×C4C22×#4116yes—
1213C2×C4C22×#4116yes—
1214C2×C4C2×H(5,𝔽2)16yes—
1215C2×C4C2×2−1+416yes—
1216C22—41no—
1217C22—43no—
1218C22—41no—
1219C22—41no—
1220C22—43no—
1221C22—41no—
1222C22—41no—
1223C22—41no—
1224C22—43no—
1225C22—41no—
1226C22—41no—
1227C22—43no—
1228C22—41no—
1229C22—41no—
1230C22—43no—
1231C22—43no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—43no—
1237C22C23×#4111yescharacteristic
1238C22C22×H(5,𝔽2)11yescharacteristic
1239C22C22×2−1+411yescharacteristic
1240C22H(7,𝔽2)11yescharacteristic
1241C222−1+611yescharacteristic
1242C222−1+611yescharacteristic
1243C222−1+611yescharacteristic
1244C4—22no—
1245C4—26no—
1246C4—41no—
1247C4—43no—
1248C4—43no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—43no—
1254C4—43no—
1255C4—41no—
1256C4—43no—
1257C4—43no—
1258C4—41no—
1259C4—41no—
1260C4—43no—
1261C4—43no—
1262C4—41no—
1263C4—41no—
1264C4—43no—
1265C4—43no—
1266C4—43no—
1267C4—41no—
1268C4—41no—
1269C4—43no—
1270C4—43no—
1271C4C2×#542112yes—
1272C2—81no—
1273C2—83no—
1274C2—81no—
1275C2C22×#54211yescharacteristic
1276C2#6285011yescharacteristic
1277C2#6285711yescharacteristic
1278C2#6304411yescharacteristic
1279C2#6305211yescharacteristic
1280C2#6305711yescharacteristic
1281C2#6306111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35737C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42756C2semidirect
2. #42754C2semidirect
3. #42729C2semidirect
4. #42722C2semidirect
5. #42698C2semidirect
6. #42694C2semidirect
7. #42665C2semidirect
8. #42660C2semidirect
9. #42640C2semidirect
10. #42632C2semidirect
11. #42628C2semidirect
12. #42621C2semidirect
13. #37631C2semidirect
14. #37598C2semidirect
15. #37573C2semidirect
16. #36693C2semidirect
17. #35948C2semidirect
18. #35937C2semidirect
19. #35920C2semidirect
20. #35910C2semidirect
21. #35883C2semidirect
22. #35854C2semidirect
23. #35816C2semidirect
24. #35801C2semidirect
25. #35801C2semidirect
26. #35786C2semidirect
28. #35711C2semidirect
29. #34336C2semidirect
30. #34311C2semidirect
31. #34263C2semidirect

Maximal subgroups

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

subgroupindex
#427562
#427542
#427292
#427222
#426982
#426942
#426652
#426602
#426402
#426322
#426282
#426212
#376312
#375982
#375732
#366932
#359482
#359372
#359202
#359102
#358832
#358542
#358162
#358012
#357862
#357372
#357112
#343362
#343112
#342632