Finite Group Databasebeta

← #7758012

Subgroups — #7758012

Order 512.

5152 conjugacy classes of subgroups.

The subgroup lattice has 1291 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59012C214yesmaximal, complemented
2#59011C214yesmaximal, complemented
3#48878C214yesmaximal, complemented
4#48876C214yesmaximal, complemented
5#43601C214yesmaximal, complemented
6#43528C214yesmaximal, complemented
7#41974C214yesmaximal, complemented
8#41710C214yesmaximal, complemented
9#41694C214yesmaximal, complemented
10#41395C212yesmaximal, complemented
11#41389C212yesmaximal, complemented
12#39558C214yesmaximal, complemented
13#39476C214yesmaximal, complemented
14#37440C211yesmaximal, characteristic
15#36024C212yesmaximal, complemented
16#36012C212yesmaximal, complemented
17#35988C214yesmaximal, complemented
18#35065C211yesmaximal, characteristic, complemented
19C2×#2501C211yesmaximal, characteristic, complemented
20C2×#2623C211yesmaximal, characteristic, complemented
21#34358C211yesmaximal, characteristic, complemented
22#34238C211yesmaximal, characteristic, complemented
23#34178C211yesmaximal, characteristic, complemented
24C2×#552C2214yescomplemented
25C2×#551C2214yescomplemented
26C22×#123C2211yescharacteristic
27C22×#123C2214yes—
28C22×#121C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30#2855C2214yescomplemented
31#2837C2214yescomplemented
32#2836C2214yescomplemented
33#2813C2214yes—
34#2807C2214yescomplemented
35#2798C2214yescomplemented
36#2797C2214yescomplemented
37#2796C2214yescomplemented
38#2794C2214yescomplemented
39#2794C2214yescomplemented
40#2793C2214yescomplemented
41#2793C2214yescomplemented
42#2791C2214yescomplemented
43#2791C2214yescomplemented
44#2786C2214yescomplemented
45#2773C2214yescomplemented
46#2771C2214yescomplemented
47#2752C2214yescomplemented
48#2751C2214yescomplemented
49#2740C2214yescomplemented
50#2732C2214yescomplemented
51#2730C2214yescomplemented
52#2727C2214yescomplemented
53#2721C2214yescomplemented
54#2721C2214yescomplemented
55#2707C2214yescomplemented
56#2706C2214yescomplemented
57#2705C2214yescomplemented
58#2705C2214yescomplemented
59#2696C2214yescomplemented
60#2695C2214yescomplemented
61#2694C2214yescomplemented
62#2694C2214yescomplemented
63#2694C2214yescomplemented
64#2693C2214yescomplemented
65#2687C2214yescomplemented
66#2667C2214yescomplemented
67#2667C2212yescomplemented
68#2665C2212yescomplemented
69#2664C2214yescomplemented
70#2663C2214yescomplemented
71#2661C2212yes—
72#2661C2212yes—
73#2654C2214yescomplemented
74#2651C2214yescomplemented
75#2649C2214yescomplemented
76#2623C2214yes—
77#2623C2212yes—
78#2623C2212yes—
79#2623C2212yes—
80#2623C2212yescomplemented
81#2623C2214yescomplemented
82#2623C2212yescomplemented
83#2618C2212yes—
84#2617C2212yes—
85#2613C2212yes—
86#2608C2212yescomplemented
87#2607C2212yescomplemented
88#2602C2214yescomplemented
89#2601C2214yescomplemented
90#2596C2214yescomplemented
91#2596C2214yescomplemented
92#2595C2214yescomplemented
93#2591C2212yes—
94#2589C2214yescomplemented
95#2575C2214yescomplemented
96#2570C2214yescomplemented
97#2569C2212yescomplemented
98#2565C2214yescomplemented
99#2560C2214yescomplemented
100#2558C2214yescomplemented
101#2557C2214yescomplemented
102#2557C2214yescomplemented
103#2556C2214yescomplemented
104#2554C2214yescomplemented
105#2553C2214yescomplemented
106#2553C2214yescomplemented
107#2549C2212yescomplemented
108#2539C2212yes—
109#2534C2214yescomplemented
110#2522C2214yescomplemented
111#2521C2214yescomplemented
112#2519C2214yescomplemented
113#2516C2214yescomplemented
114#2516C2214yescomplemented
115#2511C2214yescomplemented
116#2506C2214yescomplemented
117#2501C2214yes—
118#2501C2212yes—
119#2501C2212yes—
120#2501C2214yescomplemented
121#2501C2214yescomplemented
122#2499C2214yescomplemented
123#2498C2214yescomplemented
124#2498C2214yescomplemented
125#2496C2214yescomplemented
126#2488C2214yescomplemented
127#2488C2214yescomplemented
128#2486C2214yescomplemented
129#2481C2214yes—
130#2481C2214yes—
131#2480C2214yescomplemented
132#2480C2214yescomplemented
133#2479C2214yescomplemented
134#2479C2214yescomplemented
135#2473C2214yescomplemented
136#2473C2214yescomplemented
137#2472C2214yes—
138#2471C2214yescomplemented
139#2471C2214yescomplemented
140#2470C2214yescomplemented
141#2467C2214yescomplemented
142#2458C2214yescomplemented
143#2457C2214yescomplemented
144#2454C2214yescomplemented
145#2448C2214yescomplemented
146#2442C2214yescomplemented
147#2441C2214yescomplemented
148#2438C2214yescomplemented
149#2437C2214yes—
150#2437C2214yescomplemented
151#2423C2214yescomplemented
152#2419C2214yescomplemented
153#2419C2214yescomplemented
154#2418C2214yes—
155#2417C2214yes—
156#2413C2214yescomplemented
157#2413C2214yescomplemented
158#2412C2214yes—
159#2412C2214yescomplemented
160#2411C2214yes—
161#2411C2214yescomplemented
162#2405C2212yes—
163#2403C2212yes—
164#2396C2214yescomplemented
165#2395C2214yescomplemented
166C2×#400C2212yescomplemented
167C2×#399C2212yescomplemented
168C2×#399C2212yescomplemented
169C2×#399C2212yescomplemented
170C2×#398C2212yescomplemented
171C2×#397C2212yescomplemented
172#2377C2214yescomplemented
173#2374C2214yescomplemented
174#2364C2212yes—
175#2364C2212yes—
176#2360C2214yescomplemented
177#2359C2214yes—
178#2359C2214yescomplemented
179#2359C2214yescomplemented
180#2358C2214yes—
181#2352C2214yes—
182#2345C2212yescomplemented
183#2345C2214yescomplemented
184#2345C2212yescomplemented
185#2345C2212yescomplemented
186#2344C2214yescomplemented
187#2344C2212yescomplemented
188#2344C2212yescomplemented
189#2342C2212yes—
190#2342C2212yescomplemented
191#2342C2214yescomplemented
192#2342C2214yescomplemented
193D4×C22⋊C4C2214yes—
194D4×C22⋊C4C2212yes—
195#2335C2214yescomplemented
196#2333C2212yescomplemented
197#2333C2212yescomplemented
198#2329C2214yescomplemented
199#2325C2214yes—
200#2316C2212yescomplemented
201#2313C2212yescomplemented
202#2313C2214yescomplemented
203#2313C2211yescharacteristic, complemented
204#2312C2211yescharacteristic, complemented
205#2308C2212yescomplemented
206C4×#123C2214yes—
207C2×#390C2212yescomplemented
208C2×#386C2212yes—
209C2×#385C2212yes—
210C2×#384C2212yescomplemented
211#2280C2211yescharacteristic
212#2280C2211yescharacteristic
213#2280C2214yes—
214C2×#381C2211yescharacteristic
215#2274C2212yescomplemented
216#2274C2211yescharacteristic, complemented
217#2273C2211yescharacteristic, complemented
218C2×C4×C22⋊C4C2211yescharacteristic
219C23×D4C2311yescharacteristic
220C23×D4C2311yescharacteristic
221C23×D4C2312yes—
222C24×C4C2312yes—
223C24×C4C2311yescharacteristic
224#552—416no—
225#551—416no—
226C2×#126C2314yes—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#126C2314yes—
230C2×#125C2314yes—
231C2×#125C2314yes—
232C2×#125C2314yes—
233C2×#124C2314yes—
234C2×#123—28no—
235C2×#123—416no—
236C2×#123C2312yes—
237C2×#123C2312yes—
238C2×#123C2312yes—
239C2×#123C2314yes—
240C2×#123C2314yes—
241C2×#123C2312yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×#121—28no—
256C2×#121C2312yes—
257C2×#121C2312yes—
258C2×#121C2312yes—
259C2×#121C2312yes—
260C2×#120C2314yes—
261C2×#120C2314yes—
262C2×C4×Q8C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×#117C2312yes—
268C2×#117C2312yes—
269C2×#117C2312yes—
270C2×#117C2314yes—
271C2×#117C2314yes—
272C2×#117C2314yes—
273C2×#117C2314yes—
274C22×C4⋊C4—28no—
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2311yescharacteristic
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2312yes—
281C22×C4⋊C4C2312yes—
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2314yes—
286C22×C4⋊C4C2314yes—
287C22×C4⋊C4C2314yes—
288C22×C22⋊C4C2311yescharacteristic
289C22×C22⋊C4C2312yes—
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2311yescharacteristic
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2311yescharacteristic
294C22×C22⋊C4C2314yes—
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2314yes—
297C22×C22⋊C4C2314yes—
298C22×C22⋊C4C2314yes—
299C22×C42C2312yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#399C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#398C2314yes—
331#398C2312yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2312yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2312yes—
343#398C2312yes—
344#398C2312yes—
345#398C2312yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2312yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2312yes—
361#397C2312yes—
362#397C2312yes—
363#397C2312yes—
364#397C2314yes—
365#397C2312yes—
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#396C2314yes—
381#396C2314yes—
382#395C2314yes—
383#394C2312yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2312yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#392C2312yes—
400#392C2312yes—
401#392C2314yes—
402#392C2314yes—
403#392C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#390C2314yes—
410#390C2314yes—
411#390C2314yes—
412#390C2314yes—
413#390C2314yes—
414#390C2314yes—
415#390C2314yes—
416#390C2314yes—
417#390C2314yes—
418#390C2314yes—
419#390C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#384C2314yes—
541#384C2314yes—
542#384C2314yes—
543#384C2314yes—
544#382C2314yes—
545#382C2314yes—
546#381C2312yes—
547#381C2312yes—
548#381C2312yes—
549#381C2312yes—
550#381C2314yes—
551#381C2311yescharacteristic
552#381C2311yescharacteristic
553#381C2312yes—
554#381C2314yes—
555#381C2314yes—
556#381C2312yes—
557#381C2314yes—
558#380C2312yes—
559#380C2314yes—
560#380C2314yes—
561#380C2314yes—
562#380C2312yes—
563#380C2314yes—
564#380C2312yes—
565#380C2312yes—
566#380C2312yes—
567#380C2314yes—
568#380C2314yes—
569#380C2312yes—
570#380C2314yes—
571#380C2314yes—
572#380C2314yes—
573#380C2314yes—
574#380C2314yes—
575#379C2314yes—
576#379C2312yes—
577#379C2312yes—
578#379C2314yes—
579#379C2312yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2314yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2311yescharacteristic
591C4×C22⋊C4C2311yescharacteristic
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2311yescharacteristic
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2312yes—
597C4×C22⋊C4C2312yes—
598C4×C22⋊C4C2312yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2312yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2311yescharacteristic
609C4×C22⋊C4C2311yescharacteristic
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2311yescharacteristic
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C2×#95C2314yes—
619C2×#95C2314yes—
620C25C2411yescharacteristic
621C25C2411yescharacteristic
622C25C2412yes—
623C22×Q8C2414yes—
624C22×D4—28no—
625C22×D4—24no—
626C22×D4—24no—
627C22×D4—44no—
628C22×D4—48no—
629C22×D4—44no—
630C22×D4C2412yes—
631C22×D4C2414yes—
632C22×D4C2414yes—
633C22×D4C2412yes—
634C22×D4C2412yes—
635C22×D4C2412yes—
636C22×D4C2414yes—
637C22×D4C2414yes—
638C23×C4—28no—
639C23×C4—44no—
640C23×C4—48no—
641C23×C4#4118yes—
642C23×C4C2411yescharacteristic
643C23×C4C2414yes—
644C23×C4C2414yes—
645C23×C4C2411yescharacteristic
646C23×C4C2411yescharacteristic
647C23×C4C2412yes—
648C23×C4C2412yes—
649C23×C4C2414yes—
650C23×C4C2411yescharacteristic
651C23×C4C2412yes—
652C23×C4C2414yes—
653C23×C4C2414yes—
654C23×C4C2411yescharacteristic
655C23×C4C2414yes—
656C23×C4C2414yes—
657C23×C4C2411yescharacteristic
658C23×C4C2411yescharacteristic
659C23×C4C2411yescharacteristic
660C23×C4C2411yescharacteristic
661#126—48no—
662#126—48no—
663#126—48no—
664#126—48no—
665#125—48no—
666#125—48no—
667#125—48no—
668#124—48no—
669#123—28no—
670#123—28no—
671#123—28no—
672#123—28no—
673#123—216no—
674#123—216no—
675#123—48no—
676#123—48no—
677#123—48no—
678#123—48no—
679#123—48no—
680#123—48no—
681#123—48no—
682#123—48no—
683#123—48no—
684C22⋊Q8—216no—
685C22⋊Q8—48no—
686C22⋊Q8—48no—
687C22⋊Q8—48no—
688#121—28no—
689#121—28no—
690#121—28no—
691#121—28no—
692#120—48no—
693#120—48no—
694C4×Q8—48no—
695C4×D4—48no—
696C4×D4—48no—
697C4×D4—48no—
698C4×D4—48no—
699#117—28no—
700#117—48no—
701#117—44no—
702#117—44no—
703#117—48no—
704#117—48no—
705#117—48no—
706C2×C4⋊C4—28no—
707C2×C4⋊C4—28no—
708C2×C4⋊C4—24no—
709C2×C4⋊C4—24no—
710C2×C4⋊C4—28no—
711C2×C4⋊C4—28no—
712C2×C4⋊C4—28no—
713C2×C4⋊C4—24no—
714C2×C4⋊C4—24no—
715C2×C4⋊C4—24no—
716C2×C4⋊C4—48no—
717C2×C4⋊C4—48no—
718C2×C4⋊C4—48no—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C22⋊C4—24no—
766C2×C22⋊C4—28no—
767C2×C22⋊C4—24no—
768C2×C22⋊C4—24no—
769C2×C22⋊C4—28no—
770C2×C22⋊C4—28no—
771C2×C22⋊C4—48no—
772C2×C22⋊C4—48no—
773C2×C22⋊C4—44no—
774C2×C22⋊C4—48no—
775C2×C22⋊C4—48no—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
827C2×C42—44no—
828C2×C42C2414yes—
829C2×C42C2414yes—
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2412yes—
835C2×C42C2412yes—
836C2×C42C2412yes—
837C2×C42C2412yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2412yes—
842C2×C42C2414yes—
843C2×C42C2412yes—
844#95C2412yes—
845#95C2412yes—
846#95C2412yes—
847#95C2414yes—
848#95C2412yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2412yes—
853#95C2414yes—
854#95C2412yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2412yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2412yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2412yes—
878#95C2414yes—
879#95C2412yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895C24—24no—
896C24—24no—
897C24—22no—
898C24—24no—
899C24—24no—
900C24—28no—
901C24—42no—
902C24—44no—
903C24—42no—
904C24—42no—
905C24—42no—
906C24—42no—
907C24C2×#4114yes—
908C24C2512yes—
909C24C2514yes—
910C24C2511yescharacteristic
911C24C2511yescharacteristic
912C24C2511yescharacteristic
913C2×Q8—28no—
914C2×Q8—44no—
915C2×Q8—44no—
916C2×D4—28no—
917C2×D4—24no—
918C2×D4—28no—
919C2×D4—28no—
920C2×D4—28no—
921C2×D4—28no—
922C2×D4—24no—
923C2×D4—24no—
924C2×D4—24no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—42no—
930C2×D4—44no—
931C2×D4—42no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4—88no—
938C2×D4—88no—
939C2×D4—816no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—22no—
943C22×C4—28no—
944C22×C4—28no—
945C22×C4—24no—
946C22×C4—28no—
947C22×C4—28no—
948C22×C4—22no—
949C22×C4—24no—
950C22×C4—28no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—22no—
954C22×C4—28no—
955C22×C4—28no—
956C22×C4—28no—
957C22×C4—416no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—42no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—42no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—816no—
981C22×C4C2×#4114yes—
982C22×C4C2×#4114yes—
983C22×C4C2×#4114yes—
984C22×C4C2×#4114yes—
985C22×C4C2×#4114yes—
986C22×C4C2×#4114yes—
987C22×C4C2512yes—
988C22×C4C2512yes—
989C22×C4C2514yes—
990C22×C4C2514yes—
991C22×C4C2514yes—
992C22×C4C2514yes—
993C22×C4C2514yes—
994C22×C4C2514yes—
995C22×C4C2514yes—
996C22×C4C2514yes—
997C22×C4C2514yes—
998C22×C4C2514yes—
999C22×C4C2512yes—
1000C22×C4C2511yescharacteristic
1001C22×C4C2511yescharacteristic
1002C22×C4C2511yescharacteristic
1003C22×C4C2511yescharacteristic
1004C22×C4C2514yes—
1005C4⋊C4—24no—
1006C4⋊C4—24no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—24no—
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C22⋊C4—24no—
1052C22⋊C4—24no—
1053C22⋊C4—24no—
1054C22⋊C4—24no—
1055C22⋊C4—24no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4—24no—
1063C22⋊C4—24no—
1064C22⋊C4—24no—
1065C22⋊C4—24no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—28no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4H(5,𝔽2)18yes—
1102C42—28no—
1103C42—42no—
1104C42—44no—
1105C42—42no—
1106C42—44no—
1107C42—42no—
1108C42—42no—
1109C42—42no—
1110C42—42no—
1111C42—44no—
1112C42—44no—
1113C42—44no—
1114C42—44no—
1115C42—44no—
1116C42—44no—
1117C42—44no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—22no—
1123C23—22no—
1124C23—22no—
1125C23—28no—
1126C23—28no—
1127C23—22no—
1128C23—24no—
1129C23—22no—
1130C23—24no—
1131C23—24no—
1132C23—22no—
1133C23—24no—
1134C23—24no—
1135C23—24no—
1136C23—24no—
1137C23—24no—
1138C23—24no—
1139C23—44no—
1140C23—416no—
1141C23—48no—
1142C23—44no—
1143C23—82no—
1144C23—84no—
1145C23—82no—
1146C23—84no—
1147C23—88no—
1148C23—88no—
1149C23—88no—
1150C23C22×#4112yes—
1151C23C22×#4112yes—
1152C23C22×#4112yes—
1153C23C2×H(5,𝔽2)14yes—
1154C23#58514yes—
1155C23C2611yescharacteristic
1156Q8—88no—
1157D4—48no—
1158D4—416no—
1159D4—84no—
1160D4—84no—
1161D4—84no—
1162D4—88no—
1163D4—88no—
1164D4—164no—
1165C2×C4—24no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—28no—
1172C2×C4—28no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—44no—
1211C2×C4—44no—
1212C2×C4—44no—
1213C2×C4—44no—
1214C2×C4—416no—
1215C2×C4—44no—
1216C2×C4—416no—
1217C2×C4—88no—
1218C2×C4—82no—
1219C2×C4—88no—
1220C2×C4—84no—
1221C2×C4—84no—
1222C2×C4—88no—
1223C2×C4—82no—
1224C2×C4—84no—
1225C2×C4—88no—
1226C2×C4—164no—
1227C2×C4C22×#4112yes—
1228C2×C4C22×#4112yes—
1229C2×C4C22×#4112yes—
1230C2×C4C22×#4112yes—
1231C2×C4C2×H(5,𝔽2)18yes—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—22no—
1236C22—28no—
1237C22—28no—
1238C22—22no—
1239C22—22no—
1240C22—22no—
1241C22—416no—
1242C22—44no—
1243C22—42no—
1244C22—44no—
1245C22—44no—
1246C22—42no—
1247C22—42no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—168no—
1256C22—164no—
1257C22#349114yes—
1258C22#350814yes—
1259C22C23×#4111yescharacteristic
1260C22C22×H(5,𝔽2)12yes—
1261C22C2×#58512yes—
1262C222−1+612yes—
1263C4—22no—
1264C4—22no—
1265C4—22no—
1266C4—22no—
1267C4—28no—
1268C4—42no—
1269C4—42no—
1270C4—44no—
1271C4—44no—
1272C4—44no—
1273C4—42no—
1274C4—44no—
1275C4—44no—
1276C4—44no—
1277C4—44no—
1278C4—44no—
1279C4—44no—
1280C4—44no—
1281C2—24no—
1282C2—24no—
1283C2—42no—
1284C2—82no—
1285C2—84no—
1286C2C2×#349111yescharacteristic
1287C2C2×#350811yescharacteristic
1288C2#6286011yescharacteristic
1289C2#6289814yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37440C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59012C2semidirect
2. #59011C2semidirect
3. #48878C2semidirect
4. #48876C2semidirect
5. #43601C2semidirect
6. #43528C2semidirect
7. #41974C2semidirect
8. #41710C2semidirect
9. #41694C2semidirect
10. #41395C2semidirect
11. #41389C2semidirect
12. #39558C2semidirect
13. #39476C2semidirect
15. #36024C2semidirect
16. #36012C2semidirect
17. #35988C2semidirect
18. #35065C2semidirect
19. C2×#2501C2semidirect
20. C2×#2623C2semidirect
21. #34358C2semidirect
22. #34238C2semidirect
23. #34178C2semidirect
24. C2×#552C22semidirect
25. C2×#551C22semidirect
30. #2855C22semidirect
31. #2837C22semidirect
32. #2836C22semidirect
34. #2807C22semidirect
35. #2798C22semidirect
36. #2797C22semidirect
37. #2796C22semidirect
38. #2794C22semidirect
39. #2794C22semidirect
40. #2793C22semidirect
41. #2793C22semidirect
42. #2791C22semidirect
43. #2791C22semidirect
44. #2786C22semidirect
45. #2773C22semidirect
46. #2771C22semidirect
47. #2752C22semidirect
48. #2751C22semidirect
49. #2740C22semidirect
50. #2732C22semidirect
51. #2730C22semidirect
52. #2727C22semidirect
53. #2721C22semidirect
54. #2721C22semidirect
55. #2707C22semidirect
56. #2706C22semidirect
57. #2705C22semidirect
58. #2705C22semidirect
59. #2696C22semidirect
60. #2695C22semidirect
61. #2694C22semidirect
62. #2694C22semidirect
63. #2694C22semidirect
64. #2693C22semidirect
65. #2687C22semidirect
66. #2667C22semidirect
67. #2667C22semidirect
68. #2665C22semidirect
69. #2664C22semidirect
70. #2663C22semidirect
73. #2654C22semidirect
74. #2651C22semidirect
75. #2649C22semidirect
80. #2623C22semidirect
81. #2623C22semidirect
82. #2623C22semidirect
86. #2608C22semidirect
87. #2607C22semidirect
88. #2602C22semidirect
89. #2601C22semidirect
90. #2596C22semidirect
91. #2596C22semidirect
92. #2595C22semidirect
94. #2589C22semidirect
95. #2575C22semidirect
96. #2570C22semidirect
97. #2569C22semidirect
98. #2565C22semidirect
99. #2560C22semidirect
100. #2558C22semidirect
101. #2557C22semidirect
102. #2557C22semidirect
103. #2556C22semidirect
104. #2554C22semidirect
105. #2553C22semidirect
106. #2553C22semidirect
107. #2549C22semidirect
109. #2534C22semidirect
110. #2522C22semidirect
111. #2521C22semidirect
112. #2519C22semidirect
113. #2516C22semidirect
114. #2516C22semidirect
115. #2511C22semidirect
116. #2506C22semidirect
120. #2501C22semidirect
121. #2501C22semidirect
122. #2499C22semidirect
123. #2498C22semidirect
124. #2498C22semidirect
125. #2496C22semidirect
126. #2488C22semidirect
127. #2488C22semidirect
128. #2486C22semidirect
131. #2480C22semidirect
132. #2480C22semidirect
133. #2479C22semidirect
134. #2479C22semidirect
135. #2473C22semidirect
136. #2473C22semidirect
138. #2471C22semidirect
139. #2471C22semidirect
140. #2470C22semidirect
141. #2467C22semidirect
142. #2458C22semidirect
143. #2457C22semidirect
144. #2454C22semidirect
145. #2448C22semidirect
146. #2442C22semidirect
147. #2441C22semidirect
148. #2438C22semidirect
150. #2437C22semidirect
151. #2423C22semidirect
152. #2419C22semidirect
153. #2419C22semidirect
156. #2413C22semidirect
157. #2413C22semidirect
159. #2412C22semidirect
161. #2411C22semidirect
164. #2396C22semidirect
165. #2395C22semidirect
166. C2×#400C22semidirect
167. C2×#399C22semidirect
168. C2×#399C22semidirect
169. C2×#399C22semidirect
170. C2×#398C22semidirect
171. C2×#397C22semidirect
172. #2377C22semidirect
173. #2374C22semidirect
176. #2360C22semidirect
178. #2359C22semidirect
179. #2359C22semidirect
182. #2345C22semidirect
183. #2345C22semidirect
184. #2345C22semidirect
185. #2345C22semidirect
186. #2344C22semidirect
187. #2344C22semidirect
188. #2344C22semidirect
190. #2342C22semidirect
191. #2342C22semidirect
192. #2342C22semidirect
195. #2335C22semidirect
196. #2333C22semidirect
197. #2333C22semidirect
198. #2329C22semidirect
200. #2316C22semidirect
201. #2313C22semidirect
202. #2313C22semidirect
203. #2313C22semidirect
204. #2312C22semidirect
205. #2308C22semidirect
207. C2×#390C22semidirect
210. C2×#384C22semidirect
215. #2274C22semidirect
216. #2274C22semidirect
217. #2273C22semidirect

Maximal subgroups

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

subgroupindex
#590122
#590112
#488782
#488762
#436012
#435282
#419742
#417102
#416942
#413952
#413892
#395582
#394762
#374402
#360242
#360122
#359882
#350652
C2×#25012
C2×#26232
#343582
#342382
#341782