Finite Group Databasebeta

← #7709362

Subgroups — #7709362

Order 512.

5030 conjugacy classes of subgroups.

The subgroup lattice has 1353 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59286C214yesmaximal, complemented
2#59269C214yesmaximal, complemented
3#45782C214yesmaximal, complemented
4#45781C214yesmaximal, complemented
5#39729C212yesmaximal, complemented
6#39345C212yesmaximal, complemented
7#37979C214yesmaximal, complemented
8#37966C214yesmaximal, complemented
9#37922C214yesmaximal, complemented
10#37921C214yesmaximal, complemented
11#37661C214yesmaximal, complemented
12#37478C211yesmaximal, characteristic, complemented
13#37446C211yesmaximal, characteristic
14#36980C212yesmaximal, complemented
15#36978C212yesmaximal, complemented
16#36626C211yesmaximal, characteristic, complemented
17C2×#2854C211yesmaximal, characteristic, complemented
18#36522C212yesmaximal, complemented
19#36359C212yesmaximal, complemented
20#36244C214yesmaximal, complemented
21#35042C212yesmaximal, complemented
22#35004C212yesmaximal, complemented
23#34386C211yesmaximal, characteristic, complemented
24#34358C211yesmaximal, characteristic, complemented
25C2×#2283C211yesmaximal, characteristic, complemented
26C2×#539C2214yescomplemented
27C2×#525C2211yescharacteristic
28C22×#123C2212yes—
29C22×#121C2211yescharacteristic
30C23×C42C2211yescharacteristic
31#2855C2211yescharacteristic, complemented
32#2855C2212yescomplemented
33#2855C2211yescharacteristic, complemented
34#2854C2212yes—
35#2854C2212yes—
36#2854C2212yes—
37#2854C2212yes—
38#2854C2212yes—
39#2854C2212yes—
40#2854C2214yes—
41#2854C2211yescharacteristic, complemented
42#2854C2211yescharacteristic, complemented
43#2854C2212yescomplemented
44#2853C2214yes—
45#2852C2214yescomplemented
46#2850C2214yescomplemented
47#2849C2212yes—
48#2849C2212yes—
49#2841C2214yescomplemented
50#2816C2212yes—
51#2815C2212yes—
52#2777C2214yescomplemented
53#2777C2214yescomplemented
54#2775C2214yescomplemented
55#2772C2214yescomplemented
56#2770C2214yescomplemented
57#2766C2214yescomplemented
58#2766C2214yescomplemented
59#2764C2214yescomplemented
60#2761C2214yescomplemented
61#2759C2214yescomplemented
62#2758C2214yescomplemented
63#2757C2214yescomplemented
64#2756C2214yescomplemented
65#2756C2214yescomplemented
66#2753C2214yescomplemented
67#2749C2214yescomplemented
68#2749C2214yescomplemented
69#2738C2214yescomplemented
70#2738C2214yescomplemented
71#2737C2214yescomplemented
72#2723C2214yescomplemented
73#2719C2214yescomplemented
74#2707C2214yescomplemented
75#2706C2214yescomplemented
76#2706C2214yescomplemented
77#2705C2214yescomplemented
78#2698C2214yescomplemented
79#2696C2214yescomplemented
80#2695C2214yescomplemented
81#2694C2214yescomplemented
82#2693C2214yescomplemented
83#2687C2214yescomplemented
84#2667C2212yescomplemented
85#2665C2212yescomplemented
86#2659C2212yescomplemented
87#2656C2212yes—
88#2646C2212yescomplemented
89#2639C2212yes—
90#2635C2214yes—
91#2627C2214yes—
92#2623C2212yes—
93#2623C2214yescomplemented
94#2618C2214yescomplemented
95#2613C2212yes—
96#2612C2214yescomplemented
97#2610C2214yescomplemented
98#2606C2214yescomplemented
99#2603C2214yescomplemented
100#2597C2214yescomplemented
101#2596C2214yescomplemented
102#2590C2214yescomplemented
103#2589C2214yescomplemented
104#2576C2214yescomplemented
105#2576C2214yescomplemented
106#2572C2214yescomplemented
107#2569C2212yescomplemented
108#2557C2214yescomplemented
109#2556C2214yescomplemented
110#2556C2214yescomplemented
111#2554C2214yescomplemented
112#2554C2214yescomplemented
113#2554C2214yescomplemented
114#2553C2214yescomplemented
115#2549C2212yescomplemented
116#2543C2212yes—
117#2543C2212yes—
118#2533C2214yescomplemented
119#2532C2214yescomplemented
120#2532C2214yescomplemented
121#2531C2214yescomplemented
122#2531C2214yescomplemented
123#2530C2214yescomplemented
124#2529C2214yescomplemented
125#2529C2214yescomplemented
126#2529C2214yescomplemented
127#2526C2214yescomplemented
128#2526C2214yescomplemented
129#2526C2214yescomplemented
130#2519C2214yescomplemented
131#2519C2214yescomplemented
132#2519C2214yescomplemented
133#2518C2214yescomplemented
134#2516C2214yescomplemented
135#2515C2214yescomplemented
136#2510C2214yes—
137#2510C2214yescomplemented
138#2505C2214yes—
139#2489C2214yescomplemented
140#2488C2214yescomplemented
141#2488C2214yescomplemented
142#2482C2212yes—
143#2481C2214yes—
144#2480C2214yes—
145#2480C2214yes—
146#2479C2214yescomplemented
147#2478C2214yescomplemented
148#2473C2214yes—
149#2472C2214yes—
150#2471C2214yescomplemented
151#2461C2214yescomplemented
152#2461C2214yescomplemented
153#2457C2214yescomplemented
154#2450C2214yescomplemented
155#2444C2214yescomplemented
156#2444C2214yescomplemented
157#2442C2214yes—
158#2438C2214yes—
159#2437C2214yes—
160#2437C2214yes—
161#2425C2214yescomplemented
162#2425C2214yescomplemented
163#2419C2214yescomplemented
164#2418C2214yes—
165#2417C2214yes—
166#2412C2214yes—
167#2410C2214yes—
168#2404C2212yes—
169#2378C2212yescomplemented
170#2377C2214yes—
171#2377C2212yescomplemented
172#2373C2214yescomplemented
173#2372C2214yescomplemented
174#2368C2214yes—
175#2364C2212yes—
176#2364C2212yes—
177#2358C2214yes—
178#2358C2214yes—
179#2353C2214yes—
180#2353C2212yescomplemented
181#2353C2214yescomplemented
182#2349C2212yescomplemented
183#2346C2214yescomplemented
184#2343C2212yes—
185#2342C2214yes—
186#2342C2214yes—
187#2339C2212yes—
188D4×C22⋊C4C2214yes—
189#2333C2214yes—
190#2329C2212yescomplemented
191#2325C2212yes—
192#2325C2212yes—
193#2325C2212yescomplemented
194#2322C2214yes—
195#2322C2214yescomplemented
196#2319C2212yescomplemented
197#2318C2212yescomplemented
198#2313C2212yes—
199#2308C2212yes—
200C4×#123C2212yescomplemented
201C4×#123C2214yescomplemented
202C4×#123C2212yescomplemented
203C4×#121C2214yescomplemented
204#2297C2212yes—
205#2296C2212yes—
206C2×#390C2212yes—
207C2×#389C2212yes—
208#2290C2214yescomplemented
209C2×#388C2214yes—
210C2×#386C2212yes—
211#2283C2214yes—
212#2283C2214yes—
213#2283C2214yescomplemented
214#2283C2214yescomplemented
215C2×#383C2212yescomplemented
216C2×#382C2211yescharacteristic, complemented
217C2×#382C2211yescharacteristic, complemented
218#2280C2211yescharacteristic
219C2×#381C2211yescharacteristic
220C2×#381C2211yescharacteristic
221C2×#380C2211yescharacteristic
222C2×#380C2212yes—
223C2×C4×C4⋊C4C2212yescomplemented
224C2×C4×C22⋊C4C2212yes—
225C2×#376C2211yescharacteristic, complemented
226C2×#376C2211yescharacteristic, complemented
227C22×#41C2311yescharacteristic
228C23×D4C2311yescharacteristic
229C23×D4C2312yes—
230C24×C4C2311yescharacteristic
231C24×C4C2311yescharacteristic
232C24×C4C2311yescharacteristic
233#539—416no—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#125C2314yes—
238C2×#125C2314yes—
239C2×#124C2314yes—
240#525—28no—
241C2×#123—48no—
242C2×#123C2312yes—
243C2×#123C2314yes—
244C2×#123C2312yes—
245C2×#123C2312yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×C22⋊Q8C2311yescharacteristic
253C2×C22⋊Q8C2311yescharacteristic
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×#121—28no—
259C2×#121C2312yes—
260C2×#121C2312yes—
261C2×#121C2311yescharacteristic
262C2×#121C2312yes—
263C2×#121C2312yes—
264C2×#121C2311yescharacteristic
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#120C2312yes—
268C2×#120C2314yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×#117C2311yescharacteristic
277C2×#117C2312yes—
278C2×#117C2314yes—
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2312yes—
281C22×C4⋊C4C2312yes—
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2314yes—
284C22×C22⋊C4C2312yes—
285C22×C22⋊C4C2314yes—
286C22×C22⋊C4C2312yes—
287C22×C22⋊C4C2314yes—
288C22×C22⋊C4C2312yes—
289C22×C22⋊C4C2312yes—
290C22×C22⋊C4C2314yes—
291C22×C42—28no—
292C22×C42C2312yes—
293C22×C42C2311yescharacteristic
294C22×C42C2311yescharacteristic
295C22×C42C2312yes—
296C22×C42C2311yescharacteristic
297C22×C42C2311yescharacteristic
298C22×C42C2312yes—
299C22×C42C2312yes—
300C22×C42C2312yes—
301C22×C42C2312yes—
302#401C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#398C2312yes—
322#398C2312yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2312yes—
344#397C2312yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#394C2314yes—
366#394C2312yes—
367#394C2312yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#393C2314yes—
377#393C2314yes—
378#393C2314yes—
379#393C2314yes—
380#392C2312yes—
381#392C2312yes—
382#392C2314yes—
383#392C2314yes—
384#392C2314yes—
385#392C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2312yes—
389#391C2312yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#390C2314yes—
394#390C2314yes—
395#390C2314yes—
396#390C2314yes—
397#390C2312yes—
398#390C2314yes—
399#390C2314yes—
400#390C2312yes—
401#390C2312yes—
402#390C2312yes—
403#390C2312yes—
404#390C2312yes—
405#390C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2312yes—
411#389C2312yes—
412#389C2314yes—
413#389C2314yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
418#389C2312yes—
419#389C2312yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
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#387C2314yes—
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#386C2314yes—
495#386C2314yes—
496#386C2314yes—
497#386C2314yes—
498#386C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2312yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2312yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2312yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2312yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#383C2314yes—
545#383C2314yes—
546#383C2312yes—
547#383C2314yes—
548#383C2314yes—
549#383C2314yes—
550#383C2314yes—
551#382C2312yes—
552#382C2314yes—
553#382C2314yes—
554#382C2314yes—
555#382C2314yes—
556#382C2314yes—
557#382C2314yes—
558#381C2312yes—
559#381C2312yes—
560#381C2312yes—
561#381C2314yes—
562#381C2314yes—
563#381C2312yes—
564#381C2312yes—
565#381C2312yes—
566#381C2312yes—
567#381C2312yes—
568#381C2314yes—
569#381C2314yes—
570#381C2312yes—
571#381C2312yes—
572#381C2312yes—
573#381C2312yes—
574#380C2314yes—
575#380C2312yes—
576#380C2314yes—
577#380C2311yescharacteristic
578#380C2311yescharacteristic
579#380C2312yes—
580#380C2311yescharacteristic
581#380C2311yescharacteristic
582#380C2312yes—
583#380C2312yes—
584#380C2312yes—
585#380C2314yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#379C2314yes—
594#379C2312yes—
595#379C2314yes—
596C4×C4⋊C4C2312yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2314yes—
621C4×C22⋊C4C2314yes—
622#376C2312yes—
623#376C2314yes—
624#376C2314yes—
625#376C2314yes—
626#376C2314yes—
627#376C2314yes—
628C2×#95C2311yescharacteristic
629C2×#95C2312yes—
630C2×#95C2312yes—
631C2×#95C2312yes—
632C2×#95C2311yescharacteristic
633C2×#95C2314yes—
634C2×#95C2311yescharacteristic
635C2×#95C2312yes—
636C2×#95C2312yes—
637C2×#95C2312yes—
638C2×#95C2312yes—
639C2×#95C2312yes—
640C2×#95C2311yescharacteristic
641C25C2411yescharacteristic
642C25C2412yes—
643C2×#41—24no—
644C2×#41—44no—
645C22×Q8C2411yescharacteristic
646C22×Q8C2414yes—
647C22×D4—28no—
648C22×D4—24no—
649C22×D4—44no—
650C22×D4—44no—
651C22×D4—44no—
652C22×D4C2412yes—
653C22×D4C2412yes—
654C22×D4C2414yes—
655C22×D4C2412yes—
656C22×D4C2414yes—
657C22×D4C2412yes—
658C22×D4C2412yes—
659C22×D4C2411yescharacteristic
660C22×D4C2414yes—
661C22×D4C2414yes—
662C23×C4—24no—
663C23×C4—24no—
664C23×C4—24no—
665C23×C4—44no—
666C23×C4—42no—
667C23×C4—44no—
668C23×C4#4118yes—
669C23×C4C2411yescharacteristic
670C23×C4C2411yescharacteristic
671C23×C4C2412yes—
672C23×C4C2412yes—
673C23×C4C2412yes—
674C23×C4C2412yes—
675C23×C4C2411yescharacteristic
676C23×C4C2411yescharacteristic
677C23×C4C2411yescharacteristic
678C23×C4C2414yes—
679C23×C4C2412yes—
680C23×C4C2412yes—
681C23×C4C2412yes—
682C23×C4C2412yes—
683C23×C4C2412yes—
684C23×C4C2412yes—
685C23×C4C2411yescharacteristic
686C23×C4C2414yes—
687C23×C4C2414yes—
688C23×C4C2414yes—
689C23×C4C2411yescharacteristic
690C23×C4C2411yescharacteristic
691C23×C4C2411yescharacteristic
692C23×C4C2411yescharacteristic
693#126—48no—
694#126—48no—
695#126—48no—
696#125—48no—
697#125—48no—
698#124—48no—
699#123—28no—
700#123—216no—
701#123—28no—
702#123—48no—
703#123—48no—
704#123—48no—
705#123—48no—
706#123—48no—
707#123—48no—
708#123—44no—
709C22⋊Q8—24no—
710C22⋊Q8—24no—
711C22⋊Q8—48no—
712C22⋊Q8—48no—
713C22⋊Q8—48no—
714C22⋊Q8—48no—
715#121—28no—
716#121—28no—
717#121—28no—
718#121—28no—
719#121—24no—
720#121—24no—
721#121—48no—
722#121—48no—
723#120—28no—
724#120—48no—
725C4×D4—28no—
726C4×D4—28no—
727C4×D4—48no—
728C4×D4—48no—
729C4×D4—48no—
730C4×D4—48no—
731C4×D4—48no—
732#117—24no—
733#117—48no—
734#117—44no—
735C2×C4⋊C4—24no—
736C2×C4⋊C4—28no—
737C2×C4⋊C4—48no—
738C2×C4⋊C4—44no—
739C2×C4⋊C4—44no—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C22⋊C4—28no—
780C2×C22⋊C4—48no—
781C2×C22⋊C4—48no—
782C2×C22⋊C4—44no—
783C2×C22⋊C4—48no—
784C2×C22⋊C4—44no—
785C2×C22⋊C4—44no—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C42—24no—
834C2×C42—24no—
835C2×C42—24no—
836C2×C42—28no—
837C2×C42—28no—
838C2×C42—28no—
839C2×C42—24no—
840C2×C42—28no—
841C2×C42—44no—
842C2×C42—44no—
843C2×C42C2412yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2412yes—
847C2×C42C2412yes—
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2412yes—
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862#95C2412yes—
863#95C2412yes—
864#95C2412yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2412yes—
870#95C2412yes—
871#95C2412yes—
872#95C2412yes—
873#95C2412yes—
874#95C2412yes—
875#95C2414yes—
876#95C2412yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
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—
895#95C2414yes—
896#95C2414yes—
897#95C2412yes—
898#95C2414yes—
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—
920C24—22no—
921C24—24no—
922C24—22no—
923C24—24no—
924C24—28no—
925C24—42no—
926C24—42no—
927C24—44no—
928C24—42no—
929C24C2×#4114yes—
930C24C2514yes—
931C24C2512yes—
932C24C2511yescharacteristic
933C24C2511yescharacteristic
934C24C2511yescharacteristic
935#41—88no—
936C2×Q8—22no—
937C2×Q8—42no—
938C2×Q8—44no—
939C2×Q8—44no—
940C2×Q8—44no—
941C2×D4—24no—
942C2×D4—24no—
943C2×D4—28no—
944C2×D4—24no—
945C2×D4—28no—
946C2×D4—28no—
947C2×D4—28no—
948C2×D4—24no—
949C2×D4—24no—
950C2×D4—28no—
951C2×D4—24no—
952C2×D4—24no—
953C2×D4—22no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—42no—
960C2×D4—44no—
961C2×D4—42no—
962C2×D4—44no—
963C2×D4—42no—
964C2×D4—44no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—88no—
968C2×D4—816no—
969C22×C4—22no—
970C22×C4—22no—
971C22×C4—22no—
972C22×C4—24no—
973C22×C4—24no—
974C22×C4—24no—
975C22×C4—24no—
976C22×C4—24no—
977C22×C4—24no—
978C22×C4—24no—
979C22×C4—22no—
980C22×C4—22no—
981C22×C4—22no—
982C22×C4—22no—
983C22×C4—24no—
984C22×C4—24no—
985C22×C4—24no—
986C22×C4—24no—
987C22×C4—28no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—24no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—416no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—44no—
1009C22×C4—42no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—42no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—416no—
1027C22×C4—416no—
1028C22×C4C2×#4114yes—
1029C22×C4C2×#4114yes—
1030C22×C4C2×#4114yes—
1031C22×C4C2×#4114yes—
1032C22×C4C2×#4114yes—
1033C22×C4C2×#4114yes—
1034C22×C4H(5,𝔽2)14yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2514yes—
1038C22×C4C2514yes—
1039C22×C4C2512yes—
1040C22×C4C2514yes—
1041C22×C4C2512yes—
1042C22×C4C2514yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2514yes—
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2514yes—
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C22×C4C2511yescharacteristic
1052C22×C4C2511yescharacteristic
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—22no—
1058C4⋊C4—22no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—28no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—42no—
1070C4⋊C4—44no—
1071C4⋊C4—42no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—44no—
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—
1094C22⋊C4—24no—
1095C22⋊C4—24no—
1096C22⋊C4—24no—
1097C22⋊C4—28no—
1098C22⋊C4—24no—
1099C22⋊C4—28no—
1100C22⋊C4—28no—
1101C22⋊C4—28no—
1102C22⋊C4—24no—
1103C22⋊C4—28no—
1104C22⋊C4—28no—
1105C22⋊C4—24no—
1106C22⋊C4—24no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—42no—
1120C22⋊C4—44no—
1121C22⋊C4—42no—
1122C22⋊C4—44no—
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—
1141C42—24no—
1142C42—24no—
1143C42—24no—
1144C42—24no—
1145C42—24no—
1146C42—24no—
1147C42—24no—
1148C42—24no—
1149C42—24no—
1150C42—28no—
1151C42—28no—
1152C42—44no—
1153C42—44no—
1154C42—44no—
1155C42—44no—
1156C42—44no—
1157C42—44no—
1158C42—44no—
1159C42—44no—
1160C23—21no—
1161C23—22no—
1162C23—22no—
1163C23—22no—
1164C23—21no—
1165C23—21no—
1166C23—22no—
1167C23—22no—
1168C23—21no—
1169C23—28no—
1170C23—28no—
1171C23—22no—
1172C23—24no—
1173C23—22no—
1174C23—24no—
1175C23—24no—
1176C23—24no—
1177C23—24no—
1178C23—22no—
1179C23—24no—
1180C23—24no—
1181C23—24no—
1182C23—24no—
1183C23—44no—
1184C23—48no—
1185C23—48no—
1186C23—48no—
1187C23—84no—
1188C23—88no—
1189C23—84no—
1190C23—88no—
1191C23C22×#4112yes—
1192C23C22×#4112yes—
1193C23C22×#4112yes—
1194C23C2×H(5,𝔽2)12yes—
1195C23#58514yes—
1196C23#58512yes—
1197C23C2611yescharacteristic
1198Q8—82no—
1199Q8—164no—
1200D4—48no—
1201D4—48no—
1202D4—416no—
1203D4—84no—
1204D4—84no—
1205D4—82no—
1206D4—84no—
1207D4—88no—
1208D4—88no—
1209D4—164no—
1210C2×C4—28no—
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—28no—
1221C2×C4—28no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
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—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—44no—
1263C2×C4—44no—
1264C2×C4—44no—
1265C2×C4—44no—
1266C2×C4—48no—
1267C2×C4—48no—
1268C2×C4—48no—
1269C2×C4—48no—
1270C2×C4—44no—
1271C2×C4—44no—
1272C2×C4—84no—
1273C2×C4—84no—
1274C2×C4—84no—
1275C2×C4—88no—
1276C2×C4—84no—
1277C2×C4—84no—
1278C2×C4—84no—
1279C2×C4—88no—
1280C2×C4—164no—
1281C2×C4—164no—
1282C2×C4C22×#4112yes—
1283C2×C4C22×#4112yes—
1284C2×C4C22×#4112yes—
1285C2×C4C22×#4112yes—
1286C2×C4C2×H(5,𝔽2)14yes—
1287C2×C4#58514yes—
1288C22—24no—
1289C22—24no—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—24no—
1295C22—24no—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—416no—
1300C22—42no—
1301C22—42no—
1302C22—44no—
1303C22—44no—
1304C22—44no—
1305C22—42no—
1306C22—44no—
1307C22—44no—
1308C22—42no—
1309C22—42no—
1310C22—44no—
1311C22—44no—
1312C22—44no—
1313C22—44no—
1314C22—168no—
1315C22#349114yes—
1316C22#349414yes—
1317C22C23×#4111yescharacteristic
1318C22C22×H(5,𝔽2)11yescharacteristic
1319C22C2×#58511yescharacteristic
1320C22C2×#58512yes—
1321C22C2×#58512yes—
1322C4—22no—
1323C4—22no—
1324C4—22no—
1325C4—22no—
1326C4—24no—
1327C4—24no—
1328C4—44no—
1329C4—44no—
1330C4—44no—
1331C4—42no—
1332C4—42no—
1333C4—44no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—44no—
1338C4—44no—
1339C4—44no—
1340C4—44no—
1341C4—44no—
1342C2—24no—
1343C2—24no—
1344C2—42no—
1345C2—82no—
1346C2—84no—
1347C2#6275512yes—
1348C2C2×#349111yescharacteristic
1349C2C2×#349411yescharacteristic
1350C2#6281411yescharacteristic
1351C2#6283012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37446C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59286C2semidirect
2. #59269C2semidirect
3. #45782C2semidirect
4. #45781C2semidirect
5. #39729C2semidirect
6. #39345C2semidirect
7. #37979C2semidirect
8. #37966C2semidirect
9. #37922C2semidirect
10. #37921C2semidirect
11. #37661C2semidirect
12. #37478C2semidirect
14. #36980C2semidirect
15. #36978C2semidirect
16. #36626C2semidirect
17. C2×#2854C2semidirect
18. #36522C2semidirect
19. #36359C2semidirect
20. #36244C2semidirect
21. #35042C2semidirect
22. #35004C2semidirect
23. #34386C2semidirect
24. #34358C2semidirect
25. C2×#2283C2semidirect
26. C2×#539C22semidirect
31. #2855C22semidirect
32. #2855C22semidirect
33. #2855C22semidirect
41. #2854C22semidirect
42. #2854C22semidirect
43. #2854C22semidirect
45. #2852C22semidirect
46. #2850C22semidirect
49. #2841C22semidirect
52. #2777C22semidirect
53. #2777C22semidirect
54. #2775C22semidirect
55. #2772C22semidirect
56. #2770C22semidirect
57. #2766C22semidirect
58. #2766C22semidirect
59. #2764C22semidirect
60. #2761C22semidirect
61. #2759C22semidirect
62. #2758C22semidirect
63. #2757C22semidirect
64. #2756C22semidirect
65. #2756C22semidirect
66. #2753C22semidirect
67. #2749C22semidirect
68. #2749C22semidirect
69. #2738C22semidirect
70. #2738C22semidirect
71. #2737C22semidirect
72. #2723C22semidirect
73. #2719C22semidirect
74. #2707C22semidirect
75. #2706C22semidirect
76. #2706C22semidirect
77. #2705C22semidirect
78. #2698C22semidirect
79. #2696C22semidirect
80. #2695C22semidirect
81. #2694C22semidirect
82. #2693C22semidirect
83. #2687C22semidirect
84. #2667C22semidirect
85. #2665C22semidirect
86. #2659C22semidirect
88. #2646C22semidirect
93. #2623C22semidirect
94. #2618C22semidirect
96. #2612C22semidirect
97. #2610C22semidirect
98. #2606C22semidirect
99. #2603C22semidirect
100. #2597C22semidirect
101. #2596C22semidirect
102. #2590C22semidirect
103. #2589C22semidirect
104. #2576C22semidirect
105. #2576C22semidirect
106. #2572C22semidirect
107. #2569C22semidirect
108. #2557C22semidirect
109. #2556C22semidirect
110. #2556C22semidirect
111. #2554C22semidirect
112. #2554C22semidirect
113. #2554C22semidirect
114. #2553C22semidirect
115. #2549C22semidirect
118. #2533C22semidirect
119. #2532C22semidirect
120. #2532C22semidirect
121. #2531C22semidirect
122. #2531C22semidirect
123. #2530C22semidirect
124. #2529C22semidirect
125. #2529C22semidirect
126. #2529C22semidirect
127. #2526C22semidirect
128. #2526C22semidirect
129. #2526C22semidirect
130. #2519C22semidirect
131. #2519C22semidirect
132. #2519C22semidirect
133. #2518C22semidirect
134. #2516C22semidirect
135. #2515C22semidirect
137. #2510C22semidirect
139. #2489C22semidirect
140. #2488C22semidirect
141. #2488C22semidirect
146. #2479C22semidirect
147. #2478C22semidirect
150. #2471C22semidirect
151. #2461C22semidirect
152. #2461C22semidirect
153. #2457C22semidirect
154. #2450C22semidirect
155. #2444C22semidirect
156. #2444C22semidirect
161. #2425C22semidirect
162. #2425C22semidirect
163. #2419C22semidirect
169. #2378C22semidirect
171. #2377C22semidirect
172. #2373C22semidirect
173. #2372C22semidirect
180. #2353C22semidirect
181. #2353C22semidirect
182. #2349C22semidirect
183. #2346C22semidirect
190. #2329C22semidirect
193. #2325C22semidirect
195. #2322C22semidirect
196. #2319C22semidirect
197. #2318C22semidirect
200. C4×#123C22semidirect
201. C4×#123C22semidirect
202. C4×#123C22semidirect
203. C4×#121C22semidirect
208. #2290C22semidirect
213. #2283C22semidirect
214. #2283C22semidirect
215. C2×#383C22semidirect
216. C2×#382C22semidirect
217. C2×#382C22semidirect
223. C2×C4×C4⋊C4C22semidirect
225. C2×#376C22semidirect
226. C2×#376C22semidirect

Maximal subgroups

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

subgroupindex
#592862
#592692
#457822
#457812
#397292
#393452
#379792
#379662
#379222
#379212
#376612
#374782
#374462
#369802
#369782
#366262
C2×#28542
#365222
#363592
#362442
#350422
#350042
#343862
#343582
C2×#22832