Finite Group Databasebeta

← #7732482

Subgroups — #7732482

Order 512.

4694 conjugacy classes of subgroups.

The subgroup lattice has 1414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48881C214yesmaximal, complemented
2#48010C214yesmaximal, complemented
3#47225C212yesmaximal, complemented
4#47035C212yesmaximal, complemented
5#46857C212yesmaximal, complemented
6#46452C212yesmaximal, complemented
7#43574C214yesmaximal, complemented
8#43147C214yesmaximal, complemented
9#40352C214yesmaximal, complemented
10#39799C212yesmaximal, complemented
11#39796C212yesmaximal, complemented
12#39768C212yesmaximal, complemented
13#39764C212yesmaximal, complemented
14#38752C214yesmaximal, complemented
15#38480C214yesmaximal, complemented
16#37447C211yesmaximal, characteristic, complemented
17#37013C212yesmaximal, complemented
18#36821C212yesmaximal, complemented
19#36249C214yesmaximal, complemented
20#35501C212yesmaximal, complemented
21#35441C212yesmaximal, complemented
22#35078C211yesmaximal, characteristic
23#35019C211yesmaximal, characteristic, complemented
24C2×#2607C211yesmaximal, characteristic, complemented
25#34358C211yesmaximal, characteristic, complemented
26#34245C211yesmaximal, characteristic, complemented
27#34082C211yesmaximal, characteristic, complemented
28C2×#525C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×#121C2211yescharacteristic
31#2865C2214yescomplemented
32#2856C2211yescharacteristic
33#2856C2211yescharacteristic
34#2853C2214yescomplemented
35#2850C2211yescharacteristic
36#2850C2211yescharacteristic
37#2850C2212yes—
38#2850C2212yes—
39#2817C2212yes—
40#2816C2212yes—
41#2808C2214yescomplemented
42#2804C2214yescomplemented
43#2799C2214yescomplemented
44#2796C2214yescomplemented
45#2794C2214yescomplemented
46#2789C2214yescomplemented
47#2787C2214yescomplemented
48#2786C2214yescomplemented
49#2775C2214yescomplemented
50#2762C2214yescomplemented
51#2762C2214yescomplemented
52#2760C2214yescomplemented
53#2759C2214yescomplemented
54#2759C2214yescomplemented
55#2754C2214yescomplemented
56#2752C2214yescomplemented
57#2751C2214yescomplemented
58#2751C2214yescomplemented
59#2751C2214yescomplemented
60#2751C2214yescomplemented
61#2751C2214yescomplemented
62#2746C2214yes—
63#2746C2214yescomplemented
64#2745C2214yes—
65#2743C2214yescomplemented
66#2738C2214yes—
67#2737C2214yes—
68#2737C2214yescomplemented
69#2736C2214yes—
70#2735C2214yes—
71#2730C2214yescomplemented
72#2712C2214yescomplemented
73#2709C2214yescomplemented
74#2706C2214yescomplemented
75#2700C2214yescomplemented
76#2700C2214yescomplemented
77#2696C2214yescomplemented
78#2689C2214yescomplemented
79#2685C2214yes—
80#2684C2214yes—
81#2661C2214yes—
82#2659C2212yescomplemented
83#2653C2214yescomplemented
84#2650C2214yescomplemented
85#2639C2212yes—
86#2639C2212yes—
87#2639C2212yescomplemented
88#2638C2214yes—
89#2623C2212yescomplemented
90#2614C2212yescomplemented
91#2610C2214yescomplemented
92#2607C2212yes—
93#2607C2214yes—
94#2607C2212yes—
95#2607C2212yescomplemented
96#2607C2214yescomplemented
97#2607C2212yescomplemented
98#2605C2214yescomplemented
99#2599C2214yescomplemented
100#2598C2214yescomplemented
101#2597C2214yescomplemented
102#2596C2214yescomplemented
103#2595C2214yescomplemented
104#2595C2214yescomplemented
105#2594C2214yescomplemented
106#2592C2214yescomplemented
107#2591C2212yes—
108#2591C2212yes—
109#2591C2214yescomplemented
110#2579C2214yescomplemented
111#2577C2214yescomplemented
112#2576C2214yescomplemented
113#2575C2214yes—
114#2575C2214yescomplemented
115#2572C2214yes—
116#2572C2214yescomplemented
117#2564C2214yescomplemented
118#2561C2214yes—
119#2561C2214yes—
120#2560C2214yescomplemented
121#2557C2214yescomplemented
122#2557C2214yescomplemented
123#2544C2214yescomplemented
124#2543C2214yes—
125#2532C2214yescomplemented
126#2532C2214yescomplemented
127#2528C2214yescomplemented
128#2527C2214yes—
129#2527C2214yescomplemented
130#2524C2214yescomplemented
131#2523C2214yescomplemented
132#2520C2214yescomplemented
133#2516C2214yes—
134#2516C2214yescomplemented
135#2516C2214yescomplemented
136#2516C2214yescomplemented
137#2511C2214yescomplemented
138#2510C2214yescomplemented
139#2510C2214yescomplemented
140#2510C2214yescomplemented
141#2504C2211yescharacteristic
142#2504C2212yes—
143#2503C2212yes—
144#2502C2211yescharacteristic
145#2500C2211yescharacteristic
146#2500C2211yescharacteristic
147#2484C2212yescomplemented
148#2482C2214yes—
149#2481C2214yescomplemented
150#2479C2214yescomplemented
151#2477C2214yescomplemented
152#2477C2214yescomplemented
153#2474C2214yescomplemented
154#2474C2214yescomplemented
155#2474C2214yescomplemented
156#2472C2214yes—
157#2471C2214yescomplemented
158#2467C2214yescomplemented
159#2465C2214yescomplemented
160#2458C2214yescomplemented
161#2447C2214yescomplemented
162#2444C2214yescomplemented
163#2444C2214yescomplemented
164#2444C2214yescomplemented
165#2443C2214yescomplemented
166#2436C2212yes—
167#2436C2214yescomplemented
168#2435C2211yescharacteristic
169#2435C2212yes—
170#2433C2211yescharacteristic
171#2431C2211yescharacteristic
172#2431C2211yescharacteristic
173#2418C2214yes—
174#2412C2212yes—
175#2412C2212yes—
176#2410C2214yes—
177#2409C2214yescomplemented
178#2406C2212yescomplemented
179C2×#399C2212yes—
180C2×#393C2212yes—
181#2377C2214yes—
182#2368C2214yescomplemented
183#2364C2214yes—
184#2364C2214yescomplemented
185#2362C2212yes—
186#2362C2212yes—
187#2361C2214yescomplemented
188#2353C2214yescomplemented
189#2352C2214yescomplemented
190#2344C2212yescomplemented
191#2342C2212yes—
192#2342C2212yes—
193#2342C2214yes—
194Q8×C22⋊C4C2212yescomplemented
195D4×C22⋊C4C2212yes—
196D4×C22⋊C4C2212yes—
197#2337C2214yescomplemented
198#2335C2214yescomplemented
199#2333C2212yes—
200#2333C2212yes—
201#2333C2212yes—
202#2332C2212yes—
203#2332C2212yes—
204#2332C2212yes—
205#2332C2214yescomplemented
206#2329C2212yescomplemented
207#2325C2212yes—
208#2325C2212yes—
209#2325C2212yescomplemented
210#2321C2214yes—
211#2321C2214yes—
212#2313C2212yes—
213#2313C2212yescomplemented
214#2308C2212yes—
215#2308C2214yes—
216C4×#126C2214yescomplemented
217C4×C22⋊Q8C2212yescomplemented
218C4×C22⋊Q8C2212yescomplemented
219#2298C2212yescomplemented
220#2297C2212yescomplemented
221C2×#391C2212yescomplemented
222C2×#391C2212yescomplemented
223#2293C2212yes—
224#2290C2212yes—
225#2290C2212yescomplemented
226#2290C2214yescomplemented
227C2×#387C2212yescomplemented
228C2×#387C2212yescomplemented
229#2280C2211yescharacteristic
230C2×#381C2211yescharacteristic
231#2274C2212yescomplemented
232C42×D4C2212yescomplemented
233C2×C4×C22⋊C4C2211yescharacteristic
234C2×C4×C22⋊C4C2211yescharacteristic
235C22×#41C2311yescharacteristic
236C23×Q8C2311yescharacteristic
237C23×Q8C2312yes—
238C23×D4C2312yes—
239C23×D4C2311yescharacteristic
240C24×C4C2311yescharacteristic
241C2×#127C2311yescharacteristic
242C2×#127C2311yescharacteristic
243C2×#126C2314yes—
244C2×#124C2314yes—
245C2×#124C2314yes—
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2312yes—
249C2×#124C2312yes—
250#525—28no—
251C2×#123C2312yes—
252C2×#123C2314yes—
253C2×#123C2312yes—
254C2×#123C2312yes—
255C2×C22⋊Q8—28no—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×#121—28no—
265C2×#121C2311yescharacteristic
266C2×#121C2311yescharacteristic
267C2×#121C2311yescharacteristic
268C2×#121C2311yescharacteristic
269C2×#121C2311yescharacteristic
270C2×#121C2311yescharacteristic
271C2×#121C2312yes—
272C2×#121C2312yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#120C2312yes—
276C2×#120C2314yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×#117C2311yescharacteristic
286C2×#117C2314yes—
287C2×#117C2311yescharacteristic
288C2×#117C2311yescharacteristic
289C2×#117C2314yes—
290C2×#117C2312yes—
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2312yes—
295C22×C4⋊C4C2312yes—
296C22×C4⋊C4C2312yes—
297C22×C22⋊C4C2312yes—
298C22×C22⋊C4C2312yes—
299C22×C22⋊C4C2312yes—
300C22×C22⋊C4C2312yes—
301C22×C22⋊C4C2312yes—
302C22×C22⋊C4C2312yes—
303C22×C22⋊C4C2311yescharacteristic
304C22×C22⋊C4C2311yescharacteristic
305C22×C42C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2312yes—
310#401C2314yes—
311#401C2314yes—
312#401C2314yes—
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#400C2314yes—
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#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#393C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2314yes—
386#393C2314yes—
387#393C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#392C2314yes—
396#392C2314yes—
397#392C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2311yescharacteristic
408#391C2311yescharacteristic
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#390C2311yescharacteristic
420#390C2314yes—
421#390C2314yes—
422#390C2314yes—
423#390C2314yes—
424#390C2314yes—
425#390C2314yes—
426#390C2314yes—
427#390C2311yescharacteristic
428#390C2312yes—
429#390C2312yes—
430#390C2311yescharacteristic
431#390C2311yescharacteristic
432#390C2311yescharacteristic
433#390C2311yescharacteristic
434#389C2314yes—
435#389C2314yes—
436#389C2312yes—
437#389C2312yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#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#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#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
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#386C2314yes—
554#386C2314yes—
555#386C2312yes—
556#386C2312yes—
557#386C2314yes—
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#385C2314yes—
572#385C2312yes—
573#385C2312yes—
574#384C2311yescharacteristic
575#384C2311yescharacteristic
576#383C2314yes—
577#383C2314yes—
578#383C2314yes—
579#383C2314yes—
580#382C2314yes—
581#382C2312yes—
582#382C2312yes—
583#382C2311yescharacteristic
584#382C2311yescharacteristic
585#381C2312yes—
586#381C2314yes—
587#381C2314yes—
588#381C2314yes—
589#381C2314yes—
590#381C2312yes—
591#381C2314yes—
592#381C2314yes—
593#381C2312yes—
594#381C2312yes—
595#381C2312yes—
596#381C2312yes—
597#381C2312yes—
598#381C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2312yes—
602#380C2312yes—
603#380C2314yes—
604#380C2314yes—
605#380C2312yes—
606#380C2312yes—
607#379C2314yes—
608#379C2314yes—
609#379C2314yes—
610#379C2312yes—
611#379C2312yes—
612#379C2312yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2312yes—
624C4×C22⋊C4C2314yes—
625C4×C22⋊C4C2314yes—
626C4×C22⋊C4C2314yes—
627C4×C22⋊C4C2312yes—
628C4×C22⋊C4C2312yes—
629C4×C22⋊C4C2312yes—
630C4×C22⋊C4C2311yescharacteristic
631C4×C22⋊C4C2312yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2312yes—
636C4×C22⋊C4C2312yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2311yescharacteristic
640C4×C22⋊C4C2311yescharacteristic
641C4×C22⋊C4C2312yes—
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2312yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2312yes—
646C4×C22⋊C4C2312yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2311yescharacteristic
649C4×C22⋊C4C2312yes—
650#376C2314yes—
651#376C2312yes—
652C2×#95C2312yes—
653C2×#95C2312yes—
654C2×#95C2312yes—
655C2×#95C2312yes—
656C2×#95C2312yes—
657C2×#95C2312yes—
658C2×#95C2312yes—
659C2×#95C2312yes—
660C43C2312yes—
661C25C2411yescharacteristic
662C25C2412yes—
663C2×#41—24no—
664C2×#41—81no—
665C2×#41—81no—
666C22×Q8—24no—
667C22×Q8—44no—
668C22×Q8—44no—
669C22×Q8—82no—
670C22×Q8—81no—
671C22×Q8—81no—
672C22×Q8C2412yes—
673C22×Q8C2412yes—
674C22×Q8C2411yescharacteristic
675C22×Q8C2414yes—
676C22×Q8C2414yes—
677C22×D4—28no—
678C22×D4—24no—
679C22×D4—48no—
680C22×D4—81no—
681C22×D4—81no—
682C22×D4C2412yes—
683C22×D4C2412yes—
684C22×D4C2412yes—
685C22×D4C2412yes—
686C22×D4C2414yes—
687C22×D4C2412yes—
688C22×D4C2412yes—
689C22×D4C2411yescharacteristic
690C22×D4C2411yescharacteristic
691C22×D4C2411yescharacteristic
692C22×D4C2412yes—
693C22×D4C2412yes—
694C22×D4C2414yes—
695C23×C4—81no—
696C23×C4—81no—
697C23×C4#4118yes—
698C23×C4C2412yes—
699C23×C4C2412yes—
700C23×C4C2412yes—
701C23×C4C2412yes—
702C23×C4C2412yes—
703C23×C4C2412yes—
704C23×C4C2412yes—
705C23×C4C2412yes—
706C23×C4C2412yes—
707C23×C4C2412yes—
708C23×C4C2414yes—
709C23×C4C2414yes—
710C23×C4C2414yes—
711C23×C4C2411yescharacteristic
712C23×C4C2411yescharacteristic
713C23×C4C2411yescharacteristic
714C23×C4C2411yescharacteristic
715C23×C4C2411yescharacteristic
716C23×C4C2411yescharacteristic
717#127—81no—
718#127—81no—
719#126—48no—
720#124—48no—
721#124—81no—
722#124—82no—
723#124—81no—
724#124—82no—
725#124—84no—
726#123—28no—
727#123—82no—
728#123—84no—
729#123—82no—
730C22⋊Q8—28no—
731C22⋊Q8—28no—
732C22⋊Q8—28no—
733C22⋊Q8—28no—
734C22⋊Q8—24no—
735C22⋊Q8—24no—
736C22⋊Q8—48no—
737C22⋊Q8—84no—
738#121—24no—
739#121—24no—
740#121—28no—
741#121—28no—
742#121—24no—
743#121—24no—
744#121—24no—
745#121—24no—
746#121—48no—
747#121—48no—
748#120—28no—
749#120—48no—
750C4×Q8—82no—
751C4×Q8—82no—
752C4×D4—28no—
753C4×D4—28no—
754C4×D4—48no—
755C4×D4—48no—
756C4×D4—48no—
757C4×D4—48no—
758#117—24no—
759#117—48no—
760#117—81no—
761#117—82no—
762#117—84no—
763#117—81no—
764C2×C4⋊C4—24no—
765C2×C4⋊C4—24no—
766C2×C4⋊C4—28no—
767C2×C4⋊C4—44no—
768C2×C4⋊C4—44no—
769C2×C4⋊C4—82no—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C22⋊C4—28no—
805C2×C22⋊C4—28no—
806C2×C22⋊C4—44no—
807C2×C22⋊C4—44no—
808C2×C22⋊C4—81no—
809C2×C22⋊C4—81no—
810C2×C22⋊C4—82no—
811C2×C22⋊C4—82no—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C42—81no—
867C2×C42—82no—
868C2×C42—81no—
869C2×C42—81no—
870C2×C42—81no—
871C2×C42C2412yes—
872C2×C42C2414yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2411yescharacteristic
887C2×C42C2411yescharacteristic
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2411yescharacteristic
891C2×C42C2411yescharacteristic
892C2×C42C2412yes—
893#95C2414yes—
894#95C2412yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2412yes—
899#95C2414yes—
900#95C2412yes—
901#95C2412yes—
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—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951C24—24no—
952C24—24no—
953C24—42no—
954C24—41no—
955C24—41no—
956C24—42no—
957C24—42no—
958C24—44no—
959C24—44no—
960C24C2×#4114yes—
961C24C2512yes—
962C24C2512yes—
963C24C2512yes—
964C24C2511yescharacteristic
965C24C2511yescharacteristic
966C24C2511yescharacteristic
967#41—88no—
968C2×Q8—24no—
969C2×Q8—24no—
970C2×Q8—22no—
971C2×Q8—28no—
972C2×Q8—42no—
973C2×Q8—42no—
974C2×Q8—44no—
975C2×Q8—44no—
976C2×Q8—42no—
977C2×Q8—42no—
978C2×Q8—41no—
979C2×Q8—41no—
980C2×Q8—44no—
981C2×Q8—44no—
982C2×Q8—44no—
983C2×Q8—816no—
984C2×Q8—88no—
985C2×D4—24no—
986C2×D4—24no—
987C2×D4—24no—
988C2×D4—28no—
989C2×D4—28no—
990C2×D4—28no—
991C2×D4—24no—
992C2×D4—24no—
993C2×D4—24no—
994C2×D4—24no—
995C2×D4—24no—
996C2×D4—22no—
997C2×D4—22no—
998C2×D4—22no—
999C2×D4—28no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—42no—
1003C2×D4—42no—
1004C2×D4—44no—
1005C2×D4—41no—
1006C2×D4—41no—
1007C2×D4—42no—
1008C2×D4—42no—
1009C2×D4—41no—
1010C2×D4—41no—
1011C2×D4—41no—
1012C2×D4—41no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—88no—
1019C2×D4—816no—
1020C22×C4—24no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—41no—
1032C22×C4—41no—
1033C22×C4—41no—
1034C22×C4—41no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—44no—
1039C22×C4—41no—
1040C22×C4—41no—
1041C22×C4—42no—
1042C22×C4—41no—
1043C22×C4—41no—
1044C22×C4—41no—
1045C22×C4—41no—
1046C22×C4—41no—
1047C22×C4—41no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4—44no—
1052C22×C4—42no—
1053C22×C4—42no—
1054C22×C4—44no—
1055C22×C4—42no—
1056C22×C4—42no—
1057C22×C4—42no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—44no—
1065C22×C4—42no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—88no—
1070C22×C4C2×#4114yes—
1071C22×C4C2×#4114yes—
1072C22×C4C2×#4114yes—
1073C22×C4C2×#4114yes—
1074C22×C4C2×#4114yes—
1075C22×C4C2×#4114yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2514yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2512yes—
1082C22×C4C2514yes—
1083C22×C4C2514yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2514yes—
1087C22×C4C2514yes—
1088C22×C4C2512yes—
1089C22×C4C2514yes—
1090C22×C4C2514yes—
1091C22×C4C2512yes—
1092C22×C4C2511yescharacteristic
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2511yescharacteristic
1096C22×C4C2512yes—
1097C4⋊C4—24no—
1098C4⋊C4—22no—
1099C4⋊C4—22no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—28no—
1103C4⋊C4—28no—
1104C4⋊C4—22no—
1105C4⋊C4—22no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—24no—
1134C22⋊C4—24no—
1135C22⋊C4—24no—
1136C22⋊C4—28no—
1137C22⋊C4—24no—
1138C22⋊C4—24no—
1139C22⋊C4—24no—
1140C22⋊C4—24no—
1141C22⋊C4—24no—
1142C22⋊C4—24no—
1143C22⋊C4—24no—
1144C22⋊C4—24no—
1145C22⋊C4—28no—
1146C22⋊C4—42no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—42no—
1150C22⋊C4—42no—
1151C22⋊C4—42no—
1152C22⋊C4—42no—
1153C22⋊C4—42no—
1154C22⋊C4—44no—
1155C22⋊C4—42no—
1156C22⋊C4—42no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C42—24no—
1186C42—28no—
1187C42—42no—
1188C42—42no—
1189C42—42no—
1190C42—44no—
1191C42—42no—
1192C42—42no—
1193C42—41no—
1194C42—41no—
1195C42—42no—
1196C42—42no—
1197C42—41no—
1198C42—41no—
1199C42—44no—
1200C42—42no—
1201C42—44no—
1202C42—44no—
1203C42—44no—
1204C42—44no—
1205C42—44no—
1206C42—44no—
1207C23—22no—
1208C23—21no—
1209C23—21no—
1210C23—22no—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23—21no—
1215C23—21no—
1216C23—21no—
1217C23—21no—
1218C23—28no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—24no—
1223C23—24no—
1224C23—24no—
1225C23—24no—
1226C23—24no—
1227C23—24no—
1228C23—22no—
1229C23—22no—
1230C23—22no—
1231C23—22no—
1232C23—22no—
1233C23—22no—
1234C23—44no—
1235C23—44no—
1236C23—48no—
1237C23—84no—
1238C23—84no—
1239C23—84no—
1240C23—84no—
1241C23—164no—
1242C23—164no—
1243C23C22×#4112yes—
1244C23C22×#4112yes—
1245C23C22×#4112yes—
1246C23#58514yes—
1247C23C2611yescharacteristic
1248Q8—48no—
1249Q8—84no—
1250Q8—88no—
1251Q8—82no—
1252Q8—88no—
1253D4—48no—
1254D4—48no—
1255D4—48no—
1256D4—88no—
1257D4—82no—
1258D4—82no—
1259D4—84no—
1260D4—82no—
1261D4—84no—
1262D4—84no—
1263D4—84no—
1264D4—84no—
1265D4—164no—
1266C2×C4—22no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—44no—
1321C2×C4—44no—
1322C2×C4—44no—
1323C2×C4—44no—
1324C2×C4—44no—
1325C2×C4—44no—
1326C2×C4—48no—
1327C2×C4—48no—
1328C2×C4—48no—
1329C2×C4—48no—
1330C2×C4—84no—
1331C2×C4—84no—
1332C2×C4—84no—
1333C2×C4—84no—
1334C2×C4—84no—
1335C2×C4—84no—
1336C2×C4—88no—
1337C2×C4—88no—
1338C2×C4—164no—
1339C2×C4C22×#4112yes—
1340C2×C4C22×#4112yes—
1341C2×C4C22×#4112yes—
1342C2×C4C22×#4112yes—
1343C2×C4#58514yes—
1344C22—22no—
1345C22—22no—
1346C22—24no—
1347C22—24no—
1348C22—22no—
1349C22—22no—
1350C22—22no—
1351C22—22no—
1352C22—22no—
1353C22—22no—
1354C22—42no—
1355C22—42no—
1356C22—42no—
1357C22—42no—
1358C22—42no—
1359C22—42no—
1360C22—42no—
1361C22—42no—
1362C22—42no—
1363C22—42no—
1364C22—42no—
1365C22—42no—
1366C22—42no—
1367C22—44no—
1368C22—44no—
1369C22—44no—
1370C22—44no—
1371C22—44no—
1372C22—44no—
1373C22—88no—
1374C22—168no—
1375C22#351014yes—
1376C22C23×#4111yescharacteristic
1377C22C2×#58512yes—
1378C22C2×#58512yes—
1379C22H(7,𝔽2)11yescharacteristic
1380C22H(7,𝔽2)11yescharacteristic
1381C4—22no—
1382C4—22no—
1383C4—22no—
1384C4—22no—
1385C4—24no—
1386C4—42no—
1387C4—42no—
1388C4—42no—
1389C4—44no—
1390C4—42no—
1391C4—42no—
1392C4—44no—
1393C4—42no—
1394C4—44no—
1395C4—44no—
1396C4—44no—
1397C4—42no—
1398C4—44no—
1399C4—44no—
1400C4—44no—
1401C4—42no—
1402C2—24no—
1403C2—42no—
1404C2—42no—
1405C2—82no—
1406C2—82no—
1407C2—82no—
1408C2C2×#351011yescharacteristic
1409C2#6281511yescharacteristic
1410C2#6284411yescharacteristic
1411C2#6290612yes—
1412C2#6296512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35078C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #48881C2semidirect
2. #48010C2semidirect
3. #47225C2semidirect
4. #47035C2semidirect
5. #46857C2semidirect
6. #46452C2semidirect
7. #43574C2semidirect
8. #43147C2semidirect
9. #40352C2semidirect
10. #39799C2semidirect
11. #39796C2semidirect
12. #39768C2semidirect
13. #39764C2semidirect
14. #38752C2semidirect
15. #38480C2semidirect
16. #37447C2semidirect
17. #37013C2semidirect
18. #36821C2semidirect
19. #36249C2semidirect
20. #35501C2semidirect
21. #35441C2semidirect
23. #35019C2semidirect
24. C2×#2607C2semidirect
25. #34358C2semidirect
26. #34245C2semidirect
27. #34082C2semidirect
31. #2865C22semidirect
34. #2853C22semidirect
41. #2808C22semidirect
42. #2804C22semidirect
43. #2799C22semidirect
44. #2796C22semidirect
45. #2794C22semidirect
46. #2789C22semidirect
47. #2787C22semidirect
48. #2786C22semidirect
49. #2775C22semidirect
50. #2762C22semidirect
51. #2762C22semidirect
52. #2760C22semidirect
53. #2759C22semidirect
54. #2759C22semidirect
55. #2754C22semidirect
56. #2752C22semidirect
57. #2751C22semidirect
58. #2751C22semidirect
59. #2751C22semidirect
60. #2751C22semidirect
61. #2751C22semidirect
63. #2746C22semidirect
65. #2743C22semidirect
68. #2737C22semidirect
71. #2730C22semidirect
72. #2712C22semidirect
73. #2709C22semidirect
74. #2706C22semidirect
75. #2700C22semidirect
76. #2700C22semidirect
77. #2696C22semidirect
78. #2689C22semidirect
82. #2659C22semidirect
83. #2653C22semidirect
84. #2650C22semidirect
87. #2639C22semidirect
89. #2623C22semidirect
90. #2614C22semidirect
91. #2610C22semidirect
95. #2607C22semidirect
96. #2607C22semidirect
97. #2607C22semidirect
98. #2605C22semidirect
99. #2599C22semidirect
100. #2598C22semidirect
101. #2597C22semidirect
102. #2596C22semidirect
103. #2595C22semidirect
104. #2595C22semidirect
105. #2594C22semidirect
106. #2592C22semidirect
109. #2591C22semidirect
110. #2579C22semidirect
111. #2577C22semidirect
112. #2576C22semidirect
114. #2575C22semidirect
116. #2572C22semidirect
117. #2564C22semidirect
120. #2560C22semidirect
121. #2557C22semidirect
122. #2557C22semidirect
123. #2544C22semidirect
125. #2532C22semidirect
126. #2532C22semidirect
127. #2528C22semidirect
129. #2527C22semidirect
130. #2524C22semidirect
131. #2523C22semidirect
132. #2520C22semidirect
134. #2516C22semidirect
135. #2516C22semidirect
136. #2516C22semidirect
137. #2511C22semidirect
138. #2510C22semidirect
139. #2510C22semidirect
140. #2510C22semidirect
147. #2484C22semidirect
149. #2481C22semidirect
150. #2479C22semidirect
151. #2477C22semidirect
152. #2477C22semidirect
153. #2474C22semidirect
154. #2474C22semidirect
155. #2474C22semidirect
157. #2471C22semidirect
158. #2467C22semidirect
159. #2465C22semidirect
160. #2458C22semidirect
161. #2447C22semidirect
162. #2444C22semidirect
163. #2444C22semidirect
164. #2444C22semidirect
165. #2443C22semidirect
167. #2436C22semidirect
177. #2409C22semidirect
178. #2406C22semidirect
182. #2368C22semidirect
184. #2364C22semidirect
187. #2361C22semidirect
188. #2353C22semidirect
189. #2352C22semidirect
190. #2344C22semidirect
194. Q8×C22⋊C4C22semidirect
197. #2337C22semidirect
198. #2335C22semidirect
205. #2332C22semidirect
206. #2329C22semidirect
209. #2325C22semidirect
213. #2313C22semidirect
216. C4×#126C22semidirect
217. C4×C22⋊Q8C22semidirect
218. C4×C22⋊Q8C22semidirect
219. #2298C22semidirect
220. #2297C22semidirect
221. C2×#391C22semidirect
222. C2×#391C22semidirect
225. #2290C22semidirect
226. #2290C22semidirect
227. C2×#387C22semidirect
228. C2×#387C22semidirect
231. #2274C22semidirect
232. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#488812
#480102
#472252
#470352
#468572
#464522
#435742
#431472
#403522
#397992
#397962
#397682
#397642
#387522
#384802
#374472
#370132
#368212
#362492
#355012
#354412
#350782
#350192
C2×#26072
#343582
#342452
#340822