Finite Group Databasebeta

← #7656002

Subgroups — #7656002

Order 512.

4592 conjugacy classes of subgroups.

The subgroup lattice has 1354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41727C214yesmaximal, complemented
2#41622C214yesmaximal, complemented
3#41439C212yesmaximal, complemented
4#41072C214yesmaximal, complemented
5#40923C214yesmaximal, complemented
6#40655C212yesmaximal, complemented
7#40576C214yesmaximal, complemented
8#39558C214yesmaximal, complemented
9#39473C212yesmaximal, complemented
10#39150C212yesmaximal, complemented
11#38256C214yesmaximal, complemented
12#37478C211yesmaximal, characteristic, complemented
13#37462C212yesmaximal, complemented
14#37460C212yesmaximal, complemented
15#37447C211yesmaximal, characteristic, complemented
16#36569C212yesmaximal, complemented
17#36338C212yesmaximal, complemented
18#35960C212yesmaximal, complemented
19#35913C212yesmaximal, complemented
20#35781C214yesmaximal, complemented
21#35013C212yesmaximal, complemented
22#35010C211yesmaximal, characteristic, complemented
23#34584C212yesmaximal, complemented
24#34562C211yesmaximal, characteristic
25#34245C211yesmaximal, characteristic, complemented
26#34233C211yesmaximal, characteristic, complemented
27C2×#2357C211yesmaximal, characteristic, complemented
28C2×#525C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31#2855C2212yes—
32#2855C2214yes—
33#2851C2214yes—
34#2848C2212yes—
35#2841C2214yescomplemented
36#2838C2214yescomplemented
37#2836C2214yescomplemented
38#2831C2214yescomplemented
39#2829C2214yescomplemented
40#2817C2212yescomplemented
41#2816C2212yescomplemented
42#2797C2214yes—
43#2796C2214yes—
44#2786C2214yes—
45#2781C2214yescomplemented
46#2773C2214yescomplemented
47#2770C2214yescomplemented
48#2767C2214yescomplemented
49#2765C2214yescomplemented
50#2762C2214yescomplemented
51#2761C2214yescomplemented
52#2754C2214yescomplemented
53#2752C2214yes—
54#2751C2214yes—
55#2745C2214yescomplemented
56#2745C2214yescomplemented
57#2741C2214yescomplemented
58#2740C2214yes—
59#2740C2214yescomplemented
60#2730C2214yes—
61#2705C2214yes—
62#2700C2214yescomplemented
63#2694C2214yescomplemented
64#2690C2214yescomplemented
65#2689C2214yescomplemented
66#2667C2212yescomplemented
67#2665C2212yescomplemented
68#2664C2214yescomplemented
69#2663C2214yescomplemented
70#2659C2212yes—
71#2659C2212yes—
72#2655C2214yescomplemented
73#2654C2214yescomplemented
74#2654C2214yescomplemented
75#2653C2214yescomplemented
76#2651C2214yescomplemented
77#2651C2214yescomplemented
78#2650C2214yescomplemented
79#2650C2214yescomplemented
80#2646C2212yes—
81#2643C2214yes—
82#2639C2212yes—
83#2638C2212yes—
84#2638C2214yescomplemented
85#2637C2214yescomplemented
86#2635C2212yes—
87#2632C2214yescomplemented
88#2630C2214yes—
89#2627C2211yescharacteristic
90#2627C2212yes—
91#2627C2214yescomplemented
92#2626C2211yescharacteristic
93#2626C2212yes—
94#2623C2214yes—
95#2623C2212yescomplemented
96#2622C2212yes—
97#2618C2211yescharacteristic
98#2617C2211yescharacteristic
99#2614C2212yescomplemented
100#2613C2212yes—
101#2611C2214yescomplemented
102#2602C2214yes—
103#2601C2214yes—
104#2595C2214yes—
105#2590C2214yescomplemented
106#2589C2214yescomplemented
107#2586C2214yescomplemented
108#2586C2214yescomplemented
109#2586C2214yescomplemented
110#2585C2214yescomplemented
111#2585C2214yescomplemented
112#2579C2212yes—
113#2579C2212yes—
114#2575C2214yescomplemented
115#2573C2214yescomplemented
116#2573C2214yescomplemented
117#2569C2212yes—
118#2564C2212yes—
119#2564C2212yes—
120#2564C2214yes—
121#2560C2214yes—
122#2557C2214yes—
123#2556C2214yescomplemented
124#2556C2214yescomplemented
125#2553C2214yescomplemented
126#2549C2212yes—
127#2530C2214yescomplemented
128#2530C2214yescomplemented
129#2528C2214yescomplemented
130#2527C2214yescomplemented
131#2525C2214yescomplemented
132#2524C2214yescomplemented
133#2522C2214yescomplemented
134#2520C2214yescomplemented
135#2520C2214yescomplemented
136#2520C2214yescomplemented
137#2519C2214yescomplemented
138#2517C2214yescomplemented
139#2517C2214yescomplemented
140#2516C2214yes—
141#2510C2214yes—
142#2505C2214yes—
143#2494C2214yescomplemented
144#2487C2212yes—
145#2484C2212yescomplemented
146#2480C2214yes—
147#2480C2214yes—
148#2477C2214yescomplemented
149#2477C2214yescomplemented
150#2473C2214yes—
151#2472C2214yes—
152#2471C2214yes—
153#2470C2214yescomplemented
154#2469C2214yescomplemented
155#2467C2214yes—
156#2466C2214yescomplemented
157#2462C2214yescomplemented
158#2462C2214yescomplemented
159#2461C2214yescomplemented
160#2460C2214yescomplemented
161#2460C2214yescomplemented
162#2449C2214yes—
163#2447C2214yescomplemented
164#2438C2214yescomplemented
165#2437C2214yes—
166#2418C2214yes—
167#2417C2214yes—
168#2415C2214yescomplemented
169#2412C2214yes—
170#2409C2212yes—
171#2406C2212yescomplemented
172#2402C2214yescomplemented
173#2401C2214yescomplemented
174#2396C2214yescomplemented
175#2395C2212yes—
176#2395C2214yescomplemented
177#2392C2214yes—
178#2388C2212yes—
179#2373C2214yescomplemented
180#2370C2214yescomplemented
181#2368C2212yes—
182#2368C2212yes—
183#2368C2214yescomplemented
184#2362C2212yescomplemented
185#2362C2212yescomplemented
186#2361C2212yescomplemented
187#2360C2212yescomplemented
188#2359C2214yescomplemented
189#2358C2214yes—
190#2357C2212yes—
191#2357C2214yes—
192#2357C2212yes—
193#2357C2214yes—
194#2357C2212yes—
195#2357C2212yes—
196#2353C2212yes—
197#2349C2212yes—
198#2347C2211yescharacteristic, complemented
199#2346C2211yescharacteristic, complemented
200#2344C2212yescomplemented
201#2342C2214yes—
202#2341C2211yescharacteristic, complemented
203Q8×C22⋊C4C2212yescomplemented
204#2339C2211yescharacteristic, complemented
205#2335C2214yescomplemented
206#2332C2214yescomplemented
207#2329C2214yes—
208#2318C2212yescomplemented
209#2315C2212yes—
210#2313C2214yes—
211#2313C2212yescomplemented
212#2308C2212yes—
213C4×C22⋊Q8C2212yes—
214C4×C22⋊Q8C2212yes—
215C4×C22⋊Q8C2212yes—
216C4×#123C2212yes—
217C4×#123C2214yes—
218C4×#121C2212yes—
219C4×#120C2212yes—
220C2×#390C2212yes—
221#2290C2214yes—
222C2×#388C2212yes—
223C2×#388C2212yes—
224C2×#382C2211yescharacteristic
225#2280C2211yescharacteristic
226C2×#381C2211yescharacteristic
227C2×#381C2211yescharacteristic
228C2×#380C2211yescharacteristic
229#2275C2212yescomplemented
230#2274C2212yescomplemented
231C2×C4×C4⋊C4C2212yes—
232C2×C4×C4⋊C4C2211yescharacteristic
233C2×C4×C22⋊C4C2211yescharacteristic
234C2×C4×C22⋊C4C2211yescharacteristic
235C22×#41C2311yescharacteristic
236C23×Q8C2311yescharacteristic
237C23×D4C2311yescharacteristic
238C24×C4C2311yescharacteristic
239C24×C4C2311yescharacteristic
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#125C2314yes—
243C2×#125C2314yes—
244C2×#124C2314yes—
245#525—28no—
246C2×#123C2312yes—
247C2×#123C2312yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×C22⋊Q8—28no—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2311yescharacteristic
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2311yescharacteristic
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×#121C2311yescharacteristic
262C2×#121C2311yescharacteristic
263C2×#120C2312yes—
264C2×#120C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×D4—28no—
269C2×C4×D4C2312yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2314yes—
279C2×#117C2311yescharacteristic
280C2×#117C2314yes—
281C2×#117C2314yes—
282C2×#117C2312yes—
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C22⋊C4C2312yes—
290C22×C22⋊C4C2311yescharacteristic
291C22×C22⋊C4C2311yescharacteristic
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2312yes—
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2312yes—
297C22×C42C2311yescharacteristic
298C22×C42C2312yes—
299C22×C42C2312yes—
300C22×C42C2312yes—
301#401C2314yes—
302#401C2314yes—
303#400C2312yes—
304#400C2312yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2312yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#399C2312yes—
322#399C2312yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2312yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
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#398C2314yes—
346#398C2314yes—
347#398C2312yes—
348#398C2314yes—
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#397C2312yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#395C2312yes—
381#395C2312yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2312yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2312yes—
401#394C2314yes—
402#394C2314yes—
403#393C2314yes—
404#393C2312yes—
405#393C2312yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2312yes—
410#392C2312yes—
411#392C2314yes—
412#392C2314yes—
413#391C2314yes—
414#391C2312yes—
415#391C2314yes—
416#391C2314yes—
417#391C2312yes—
418#391C2312yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#390C2314yes—
425#390C2312yes—
426#390C2314yes—
427#390C2314yes—
428#390C2314yes—
429#390C2314yes—
430#390C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2312yes—
434#389C2312yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2312yes—
440#389C2312yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
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#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#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2312yes—
528#386C2312yes—
529#386C2312yes—
530#386C2312yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2312yes—
538#386C2312yes—
539#386C2314yes—
540#386C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2312yes—
547#385C2312yes—
548#385C2312yes—
549#385C2312yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2312yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2312yes—
563#385C2314yes—
564#385C2314yes—
565#383C2312yes—
566#383C2314yes—
567#382C2312yes—
568#382C2312yes—
569#382C2314yes—
570#382C2314yes—
571#382C2312yes—
572#382C2314yes—
573#381C2312yes—
574#381C2314yes—
575#381C2312yes—
576#381C2314yes—
577#381C2312yes—
578#381C2314yes—
579#381C2312yes—
580#381C2312yes—
581#381C2312yes—
582#381C2312yes—
583#381C2312yes—
584#381C2314yes—
585#381C2312yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2312yes—
593#380C2312yes—
594#380C2311yescharacteristic
595#380C2311yescharacteristic
596#380C2312yes—
597#380C2312yes—
598#380C2314yes—
599#380C2311yescharacteristic
600#380C2311yescharacteristic
601#380C2312yes—
602#380C2314yes—
603#379C2314yes—
604#379C2312yes—
605#379C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2311yescharacteristic
631C4×C22⋊C4C2312yes—
632C4×C22⋊C4C2312yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2311yescharacteristic
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2312yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2312yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2311yescharacteristic
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2312yes—
645C4×C22⋊C4C2311yescharacteristic
646C4×C22⋊C4C2312yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650#376C2312yes—
651#376C2314yes—
652C2×#95C2311yescharacteristic
653C2×#95C2312yes—
654C2×#95C2311yescharacteristic
655C2×#95C2312yes—
656C2×#95C2312yes—
657C2×#95C2311yescharacteristic
658C2×#95C2311yescharacteristic
659C2×#95C2312yes—
660C2×#95C2312yes—
661C25C2411yescharacteristic
662C25C2411yescharacteristic
663C2×#41—24no—
664C2×#41—82no—
665C22×Q8—24no—
666C22×Q8—82no—
667C22×Q8C2412yes—
668C22×Q8C2411yescharacteristic
669C22×Q8C2412yes—
670C22×Q8C2414yes—
671C22×D4—24no—
672C22×D4—24no—
673C22×D4—42no—
674C22×D4C2412yes—
675C22×D4C2412yes—
676C22×D4C2412yes—
677C22×D4C2412yes—
678C22×D4C2411yescharacteristic
679C22×D4C2412yes—
680C22×D4C2414yes—
681C23×C4—24no—
682C23×C4—82no—
683C23×C4—82no—
684C23×C4#4118yes—
685C23×C4C2412yes—
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2412yes—
689C23×C4C2412yes—
690C23×C4C2412yes—
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2411yescharacteristic
694C23×C4C2414yes—
695C23×C4C2412yes—
696C23×C4C2412yes—
697C23×C4C2412yes—
698C23×C4C2414yes—
699C23×C4C2411yescharacteristic
700C23×C4C2411yescharacteristic
701C23×C4C2411yescharacteristic
702C23×C4C2411yescharacteristic
703C23×C4C2411yescharacteristic
704C23×C4C2411yescharacteristic
705#126—48no—
706#126—84no—
707#125—48no—
708#125—84no—
709#124—84no—
710#123—28no—
711#123—28no—
712#123—48no—
713#123—84no—
714C22⋊Q8—28no—
715C22⋊Q8—28no—
716C22⋊Q8—28no—
717C22⋊Q8—28no—
718C22⋊Q8—24no—
719C22⋊Q8—24no—
720C22⋊Q8—48no—
721C22⋊Q8—48no—
722C22⋊Q8—84no—
723C22⋊Q8—84no—
724#121—24no—
725#121—24no—
726#120—28no—
727#120—44no—
728C4×Q8—82no—
729C4×Q8—82no—
730C4×Q8—82no—
731C4×D4—28no—
732C4×D4—28no—
733C4×D4—28no—
734C4×D4—28no—
735C4×D4—28no—
736C4×D4—28no—
737C4×D4—48no—
738C4×D4—48no—
739C4×D4—82no—
740C4×D4—84no—
741#117—24no—
742#117—48no—
743#117—84no—
744#117—82no—
745C2×C4⋊C4—24no—
746C2×C4⋊C4—24no—
747C2×C4⋊C4—28no—
748C2×C4⋊C4—28no—
749C2×C4⋊C4—44no—
750C2×C4⋊C4—82no—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
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×C22⋊C4—24no—
798C2×C22⋊C4—28no—
799C2×C22⋊C4—24no—
800C2×C22⋊C4—44no—
801C2×C22⋊C4—44no—
802C2×C22⋊C4—44no—
803C2×C22⋊C4—82no—
804C2×C22⋊C4—82no—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
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×C42—24no—
851C2×C42—44no—
852C2×C42—82no—
853C2×C42—82no—
854C2×C42C2412yes—
855C2×C42C2414yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2412yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873#95C2411yescharacteristic
874#95C2412yes—
875#95C2411yescharacteristic
876#95C2411yescharacteristic
877#95C2412yes—
878#95C2411yescharacteristic
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2412yes—
883#95C2414yes—
884#95C2414yes—
885#95C2412yes—
886#95C2412yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
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—
937C24—22no—
938C24—22no—
939C24—22no—
940C24—22no—
941C24—22no—
942C24—42no—
943C24—42no—
944C24—42no—
945C24—42no—
946C24C2×#4114yes—
947C24C2512yes—
948C24C2512yes—
949C24C2511yescharacteristic
950C24C2511yescharacteristic
951C24C2511yescharacteristic
952#41—88no—
953C2×Q8—24no—
954C2×Q8—22no—
955C2×Q8—24no—
956C2×Q8—42no—
957C2×Q8—42no—
958C2×Q8—42no—
959C2×Q8—44no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—44no—
963C2×Q8—88no—
964C2×D4—24no—
965C2×D4—24no—
966C2×D4—24no—
967C2×D4—24no—
968C2×D4—24no—
969C2×D4—24no—
970C2×D4—24no—
971C2×D4—22no—
972C2×D4—24no—
973C2×D4—24no—
974C2×D4—44no—
975C2×D4—42no—
976C2×D4—42no—
977C2×D4—42no—
978C2×D4—416no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C22×C4—22no—
984C22×C4—22no—
985C22×C4—22no—
986C22×C4—24no—
987C22×C4—22no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—24no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—28no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—44no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—42no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—88no—
1024C22×C4—88no—
1025C22×C4C2×#4114yes—
1026C22×C4C2×#4114yes—
1027C22×C4C2×#4114yes—
1028C22×C4C2×#4114yes—
1029C22×C4C2×#4114yes—
1030C22×C4C2×#4114yes—
1031C22×C42−1+414yes—
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2514yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2514yes—
1039C22×C4C2512yes—
1040C22×C4C2514yes—
1041C22×C4C2512yes—
1042C22×C4C2514yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2514yes—
1048C22×C4C2511yescharacteristic
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C22×C4C2511yescharacteristic
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—28no—
1059C4⋊C4—28no—
1060C4⋊C4—22no—
1061C4⋊C4—22no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—28no—
1068C4⋊C4—28no—
1069C4⋊C4—28no—
1070C4⋊C4—44no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
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—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C22⋊C4—24no—
1101C22⋊C4—24no—
1102C22⋊C4—28no—
1103C22⋊C4—28no—
1104C22⋊C4—24no—
1105C22⋊C4—24no—
1106C22⋊C4—24no—
1107C22⋊C4—24no—
1108C22⋊C4—28no—
1109C22⋊C4—24no—
1110C22⋊C4—24no—
1111C22⋊C4—24no—
1112C22⋊C4—24no—
1113C22⋊C4—24no—
1114C22⋊C4—28no—
1115C22⋊C4—24no—
1116C22⋊C4—24no—
1117C22⋊C4—28no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—42no—
1121C22⋊C4—44no—
1122C22⋊C4—42no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C42—24no—
1146C42—24no—
1147C42—24no—
1148C42—28no—
1149C42—44no—
1150C42—44no—
1151C42—44no—
1152C42—42no—
1153C42—42no—
1154C42—42no—
1155C42—42no—
1156C42—44no—
1157C42—44no—
1158C42—44no—
1159C42—44no—
1160C42—44no—
1161C42—44no—
1162C42—44no—
1163C42—44no—
1164C23—22no—
1165C23—22no—
1166C23—21no—
1167C23—21no—
1168C23—22no—
1169C23—22no—
1170C23—21no—
1171C23—21no—
1172C23—22no—
1173C23—22no—
1174C23—28no—
1175C23—22no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—24no—
1180C23—24no—
1181C23—22no—
1182C23—22no—
1183C23—24no—
1184C23—24no—
1185C23—44no—
1186C23—44no—
1187C23—44no—
1188C23—44no—
1189C23—44no—
1190C23—84no—
1191C23—84no—
1192C23—84no—
1193C23—84no—
1194C23C22×#4112yes—
1195C23C22×#4112yes—
1196C23C22×#4112yes—
1197C23C2×2−1+412yes—
1198C23#58512yes—
1199C23C2611yescharacteristic
1200Q8—48no—
1201Q8—44no—
1202Q8—84no—
1203Q8—164no—
1204D4—48no—
1205D4—48no—
1206D4—44no—
1207D4—48no—
1208D4—48no—
1209D4—84no—
1210D4—88no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—28no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—44no—
1265C2×C4—44no—
1266C2×C4—44no—
1267C2×C4—44no—
1268C2×C4—44no—
1269C2×C4—44no—
1270C2×C4—48no—
1271C2×C4—44no—
1272C2×C4—48no—
1273C2×C4—44no—
1274C2×C4—88no—
1275C2×C4—84no—
1276C2×C4—84no—
1277C2×C4—84no—
1278C2×C4—84no—
1279C2×C4—84no—
1280C2×C4—84no—
1281C2×C4—84no—
1282C2×C4—164no—
1283C2×C4C22×#4112yes—
1284C2×C4C22×#4112yes—
1285C2×C4C22×#4112yes—
1286C2×C4C22×#4112yes—
1287C2×C4C2×2−1+414yes—
1288C2×C4#58514yes—
1289C22—22no—
1290C22—22no—
1291C22—24no—
1292C22—24no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—44no—
1310C22—44no—
1311C22—44no—
1312C22—44no—
1313C22—88no—
1314C22—88no—
1315C22#349514yes—
1316C22C23×#4111yescharacteristic
1317C22C22×2−1+411yescharacteristic
1318C22C2×#58511yescharacteristic
1319C22C2×#58512yes—
1320C22H(7,𝔽2)12yes—
1321C4—24no—
1322C4—22no—
1323C4—22no—
1324C4—22no—
1325C4—22no—
1326C4—24no—
1327C4—42no—
1328C4—42no—
1329C4—42no—
1330C4—44no—
1331C4—42no—
1332C4—44no—
1333C4—42no—
1334C4—44no—
1335C4—42no—
1336C4—42no—
1337C4—44no—
1338C4—42no—
1339C4—44no—
1340C4—44no—
1341C4—44no—
1342C4—44no—
1343C2—24no—
1344C2—42no—
1345C2—42no—
1346C2—82no—
1347C2—82no—
1348C2#6268611yescharacteristic
1349C2C2×#349511yescharacteristic
1350C2#6284411yescharacteristic
1351C2#6296212yes—
1352C2#6296312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34562C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #41727C2semidirect
2. #41622C2semidirect
3. #41439C2semidirect
4. #41072C2semidirect
5. #40923C2semidirect
6. #40655C2semidirect
7. #40576C2semidirect
8. #39558C2semidirect
9. #39473C2semidirect
10. #39150C2semidirect
11. #38256C2semidirect
12. #37478C2semidirect
13. #37462C2semidirect
14. #37460C2semidirect
15. #37447C2semidirect
16. #36569C2semidirect
17. #36338C2semidirect
18. #35960C2semidirect
19. #35913C2semidirect
20. #35781C2semidirect
21. #35013C2semidirect
22. #35010C2semidirect
23. #34584C2semidirect
25. #34245C2semidirect
26. #34233C2semidirect
27. C2×#2357C2semidirect
35. #2841C22semidirect
36. #2838C22semidirect
37. #2836C22semidirect
38. #2831C22semidirect
39. #2829C22semidirect
40. #2817C22semidirect
41. #2816C22semidirect
45. #2781C22semidirect
46. #2773C22semidirect
47. #2770C22semidirect
48. #2767C22semidirect
49. #2765C22semidirect
50. #2762C22semidirect
51. #2761C22semidirect
52. #2754C22semidirect
55. #2745C22semidirect
56. #2745C22semidirect
57. #2741C22semidirect
59. #2740C22semidirect
62. #2700C22semidirect
63. #2694C22semidirect
64. #2690C22semidirect
65. #2689C22semidirect
66. #2667C22semidirect
67. #2665C22semidirect
68. #2664C22semidirect
69. #2663C22semidirect
72. #2655C22semidirect
73. #2654C22semidirect
74. #2654C22semidirect
75. #2653C22semidirect
76. #2651C22semidirect
77. #2651C22semidirect
78. #2650C22semidirect
79. #2650C22semidirect
84. #2638C22semidirect
85. #2637C22semidirect
87. #2632C22semidirect
91. #2627C22semidirect
95. #2623C22semidirect
99. #2614C22semidirect
101. #2611C22semidirect
105. #2590C22semidirect
106. #2589C22semidirect
107. #2586C22semidirect
108. #2586C22semidirect
109. #2586C22semidirect
110. #2585C22semidirect
111. #2585C22semidirect
114. #2575C22semidirect
115. #2573C22semidirect
116. #2573C22semidirect
123. #2556C22semidirect
124. #2556C22semidirect
125. #2553C22semidirect
127. #2530C22semidirect
128. #2530C22semidirect
129. #2528C22semidirect
130. #2527C22semidirect
131. #2525C22semidirect
132. #2524C22semidirect
133. #2522C22semidirect
134. #2520C22semidirect
135. #2520C22semidirect
136. #2520C22semidirect
137. #2519C22semidirect
138. #2517C22semidirect
139. #2517C22semidirect
143. #2494C22semidirect
145. #2484C22semidirect
148. #2477C22semidirect
149. #2477C22semidirect
153. #2470C22semidirect
154. #2469C22semidirect
156. #2466C22semidirect
157. #2462C22semidirect
158. #2462C22semidirect
159. #2461C22semidirect
160. #2460C22semidirect
161. #2460C22semidirect
163. #2447C22semidirect
164. #2438C22semidirect
168. #2415C22semidirect
171. #2406C22semidirect
172. #2402C22semidirect
173. #2401C22semidirect
174. #2396C22semidirect
176. #2395C22semidirect
179. #2373C22semidirect
180. #2370C22semidirect
183. #2368C22semidirect
184. #2362C22semidirect
185. #2362C22semidirect
186. #2361C22semidirect
187. #2360C22semidirect
188. #2359C22semidirect
198. #2347C22semidirect
199. #2346C22semidirect
200. #2344C22semidirect
202. #2341C22semidirect
203. Q8×C22⋊C4C22semidirect
204. #2339C22semidirect
205. #2335C22semidirect
206. #2332C22semidirect
208. #2318C22semidirect
211. #2313C22semidirect
229. #2275C22semidirect
230. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#417272
#416222
#414392
#410722
#409232
#406552
#405762
#395582
#394732
#391502
#382562
#374782
#374622
#374602
#374472
#365692
#363382
#359602
#359132
#357812
#350132
#350102
#345842
#345622
#342452
#342332
C2×#23572