Finite Group Databasebeta

← #8108455

Subgroups — #8108455

Order 512.

5086 conjugacy classes of subgroups.

The subgroup lattice has 1387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59191C212yesmaximal, complemented
2#59189C212yesmaximal, complemented
3#53263C214yesmaximal, complemented
4#53261C214yesmaximal, complemented
5#45847C214yesmaximal, complemented
6#45821C214yesmaximal, complemented
7#45568C212yesmaximal, complemented
8#45537C212yesmaximal, complemented
9#40013C214yesmaximal, complemented
10#39941C214yesmaximal, complemented
11#38575C214yesmaximal, complemented
12#38572C214yesmaximal, complemented
13#37958C212yesmaximal, complemented
14#37950C212yesmaximal, complemented
15#37754C212yesmaximal, complemented
16#37746C212yesmaximal, complemented
17#36879C214yesmaximal, complemented
18#36877C214yesmaximal, complemented
19#36729C212yesmaximal, complemented
20#36718C211yesmaximal, characteristic, complemented
21#36717C211yesmaximal, characteristic
22#36621C212yesmaximal, complemented
23C2×#2854C211yesmaximal, characteristic, complemented
24C2×#559C2212yescomplemented
25C2×#551C2212yescomplemented
26C2×#543C2211yescharacteristic, complemented
27C2×#534C2211yescharacteristic
28C2×#529C2212yes—
29C22×#123C2211yescharacteristic
30C22×#123C2211yescharacteristic, complemented
31C22×#121C2211yescharacteristic
32C23×C42C2211yescharacteristic, complemented
33#2855C2212yescomplemented
34#2854C2212yes—
35#2854C2214yescomplemented
36#2854C2214yescomplemented
37#2854C2214yescomplemented
38#2854C2214yescomplemented
39#2853C2214yescomplemented
40#2852C2214yescomplemented
41#2852C2214yescomplemented
42#2851C2212yescomplemented
43#2851C2212yescomplemented
44#2850C2212yescomplemented
45#2850C2212yescomplemented
46#2849C2214yescomplemented
47#2848C2212yescomplemented
48#2847C2212yes—
49#2826C2214yescomplemented
50#2824C2214yescomplemented
51#2804C2212yescomplemented
52#2803C2214yescomplemented
53#2801C2214yescomplemented
54#2797C2214yescomplemented
55#2797C2214yescomplemented
56#2786C2214yescomplemented
57#2785C2214yescomplemented
58#2784C2214yescomplemented
59#2783C2214yescomplemented
60#2782C2214yescomplemented
61#2781C2214yescomplemented
62#2778C2214yescomplemented
63#2778C2214yescomplemented
64#2777C2214yescomplemented
65#2777C2214yescomplemented
66#2775C2214yescomplemented
67#2775C2214yescomplemented
68#2774C2214yescomplemented
69#2773C2214yescomplemented
70#2772C2214yescomplemented
71#2759C2214yescomplemented
72#2757C2214yescomplemented
73#2756C2214yescomplemented
74#2755C2214yescomplemented
75#2753C2214yescomplemented
76#2753C2214yescomplemented
77#2748C2212yescomplemented
78#2747C2214yescomplemented
79#2742C2214yescomplemented
80#2742C2214yescomplemented
81#2741C2214yescomplemented
82#2730C2214yescomplemented
83#2724C2212yescomplemented
84#2723C2214yescomplemented
85#2717C2214yescomplemented
86#2717C2212yescomplemented
87#2712C2214yescomplemented
88#2710C2214yescomplemented
89#2709C2214yescomplemented
90#2709C2212yescomplemented
91#2709C2212yescomplemented
92#2706C2214yescomplemented
93#2703C2214yes—
94#2703C2214yes—
95#2702C2214yescomplemented
96#2702C2214yescomplemented
97#2702C2214yescomplemented
98#2697C2212yescomplemented
99#2697C2214yescomplemented
100#2696C2214yescomplemented
101#2695C2214yescomplemented
102#2694C2214yescomplemented
103#2693C2214yescomplemented
104#2692C2214yescomplemented
105#2691C2214yescomplemented
106#2690C2214yescomplemented
107#2685C2214yescomplemented
108#2685C2214yescomplemented
109#2684C2214yescomplemented
110#2684C2212yescomplemented
111#2684C2214yescomplemented
112#2681C2214yescomplemented
113#2681C2214yescomplemented
114#2672C2214yescomplemented
115#2672C2214yescomplemented
116#2672C2214yescomplemented
117#2669C2214yes—
118#2669C2214yes—
119#2663C2214yescomplemented
120#2662C2214yescomplemented
121#2659C2212yescomplemented
122#2655C2214yescomplemented
123#2648C2214yescomplemented
124#2639C2212yes—
125#2626C2212yes—
126#2617C2212yes—
127#2610C2214yescomplemented
128#2604C2214yescomplemented
129#2602C2214yescomplemented
130#2602C2214yescomplemented
131#2595C2214yescomplemented
132#2594C2214yescomplemented
133#2593C2214yescomplemented
134#2591C2212yes—
135#2583C2212yescomplemented
136#2561C2214yes—
137#2557C2214yescomplemented
138#2554C2214yescomplemented
139#2553C2214yescomplemented
140#2534C2214yescomplemented
141#2532C2214yescomplemented
142#2529C2214yescomplemented
143#2525C2214yescomplemented
144#2509C2214yescomplemented
145#2493C2214yescomplemented
146#2488C2214yescomplemented
147#2488C2214yescomplemented
148#2481C2214yescomplemented
149#2480C2214yes—
150#2477C2214yescomplemented
151#2474C2214yescomplemented
152#2472C2214yescomplemented
153#2472C2214yescomplemented
154#2472C2214yescomplemented
155#2471C2214yescomplemented
156#2470C2214yescomplemented
157#2470C2214yescomplemented
158#2469C2214yescomplemented
159#2467C2214yescomplemented
160#2465C2214yescomplemented
161#2463C2214yescomplemented
162#2461C2214yescomplemented
163#2458C2214yescomplemented
164#2458C2214yescomplemented
165#2455C2214yescomplemented
166#2449C2214yescomplemented
167#2449C2214yescomplemented
168#2445C2214yescomplemented
169#2443C2214yes—
170#2435C2212yes—
171#2433C2212yes—
172#2425C2214yes—
173#2421C2214yescomplemented
174#2418C2214yescomplemented
175#2418C2214yescomplemented
176#2418C2214yescomplemented
177#2415C2214yescomplemented
178#2412C2214yescomplemented
179#2411C2214yescomplemented
180#2405C2214yes—
181#2405C2212yes—
182#2405C2212yescomplemented
183#2403C2212yes—
184#2403C2212yes—
185#2380C2212yescomplemented
186#2379C2212yescomplemented
187#2376C2212yescomplemented
188#2375C2212yescomplemented
189#2374C2212yescomplemented
190#2374C2212yescomplemented
191#2360C2214yescomplemented
192#2358C2214yescomplemented
193#2352C2214yescomplemented
194D4×C22⋊C4C2214yes—
195#2335C2214yescomplemented
196#2334C2214yescomplemented
197#2329C2212yescomplemented
198#2325C2212yes—
199#2323C2214yescomplemented
200#2321C2214yescomplemented
201#2312C2211yescharacteristic
202#2312C2211yescharacteristic, complemented
203C4×C22⋊Q8C2212yescomplemented
204C4×C22⋊Q8C2212yescomplemented
205C4×#123C2214yescomplemented
206C4×#121C2212yescomplemented
207C4×#121C2212yescomplemented
208C4×#120C2214yescomplemented
209C2×#390C2212yes—
210C2×#389C2212yescomplemented
211#2290C2214yescomplemented
212#2290C2214yescomplemented
213C2×#388C2212yes—
214C2×#388C2212yescomplemented
215C2×#386C2211yescharacteristic
216C2×#386C2211yescharacteristic, complemented
217#2283C2212yescomplemented
218C2×#380C2211yescharacteristic, complemented
219C23×D4C2312yes—
220C23×D4C2311yescharacteristic
221C23×D4C2311yescharacteristic
222C23×D4C2311yescharacteristic
223C24×C4C2311yescharacteristic
224C24×C4C2311yescharacteristic
225C24×C4C2311yescharacteristic
226#559—48no—
227#551—48no—
228#543—44no—
229#534—44no—
230C2×#127C2312yes—
231C2×#127C2312yes—
232#529—48no—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#125C2312yes—
237C2×#124C2312yes—
238C2×#124C2314yes—
239C2×#124C2312yes—
240C2×#124C2312yes—
241C2×#124C2314yes—
242C2×#123—44no—
243C2×#123—44no—
244C2×#123C2312yes—
245C2×#123C2312yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2312yes—
251C2×#123C2314yes—
252C2×#123C2312yes—
253C2×#123C2312yes—
254C2×#123C2312yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×#121—44no—
268C2×#121C2312yes—
269C2×#121C2312yes—
270C2×#121C2312yes—
271C2×#121C2312yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#120C2314yes—
275C2×#120C2314yes—
276C2×#120C2314yes—
277C2×#120C2312yes—
278C2×#120C2312yes—
279C2×#120C2314yes—
280C2×C4×Q8C2314yes—
281C2×C4×Q8C2312yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2314yes—
288C2×#117C2314yes—
289C2×#117C2314yes—
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2312yes—
294C22×C22⋊C4C2311yescharacteristic
295C22×C22⋊C4C2311yescharacteristic
296C22×C22⋊C4C2312yes—
297C22×C22⋊C4C2314yes—
298C22×C22⋊C4C2312yes—
299C22×C22⋊C4C2312yes—
300C22×C22⋊C4C2312yes—
301C22×C22⋊C4C2311yescharacteristic
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2312yes—
304C22×C42—44no—
305C22×C42C2312yes—
306C22×C42C2312yes—
307C22×C42C2312yes—
308C22×C42C2312yes—
309C22×C42C2312yes—
310C22×C42C2312yes—
311#401C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
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#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#394C2314yes—
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#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#392C2314yes—
401#392C2314yes—
402#392C2314yes—
403#392C2314yes—
404#392C2314yes—
405#392C2314yes—
406#392C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2312yes—
410#391C2312yes—
411#391C2314yes—
412#391C2314yes—
413#390C2314yes—
414#390C2314yes—
415#390C2314yes—
416#390C2314yes—
417#390C2312yes—
418#390C2312yes—
419#390C2314yes—
420#390C2314yes—
421#390C2314yes—
422#390C2314yes—
423#390C2312yes—
424#390C2312yes—
425#390C2312yes—
426#390C2314yes—
427#390C2312yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
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#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
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#386C2312yes—
518#386C2314yes—
519#386C2312yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
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#386C2312yes—
541#386C2314yes—
542#386C2312yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2312yes—
548#386C2312yes—
549#386C2312yes—
550#386C2312yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
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#385C2314yes—
573#383C2314yes—
574#383C2314yes—
575#382C2314yes—
576#382C2312yes—
577#382C2312yes—
578#382C2314yes—
579#382C2314yes—
580#381C2314yes—
581#381C2314yes—
582#380C2312yes—
583#380C2312yes—
584#380C2314yes—
585#380C2314yes—
586#380C2312yes—
587#380C2312yes—
588#380C2312yes—
589#380C2312yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#379C2312yes—
597#379C2314yes—
598#379C2312yes—
599#379C2314yes—
600#379C2314yes—
601#379C2314yes—
602#379C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619#376C2314yes—
620C2×#95C2312yes—
621C2×#95C2312yes—
622C2×#95C2312yes—
623C25C2411yescharacteristic
624C25C2411yescharacteristic
625C25C2411yescharacteristic
626C25C2412yes—
627C22×Q8C2412yes—
628C22×Q8C2414yes—
629C22×Q8C2412yes—
630C22×D4—44no—
631C22×D4—42no—
632C22×D4—42no—
633C22×D4—42no—
634C22×D4—42no—
635C22×D4—42no—
636C22×D4—44no—
637C22×D4—48no—
638C22×D4—42no—
639C22×D4—42no—
640C22×D4C2414yes—
641C22×D4C2412yes—
642C22×D4C2414yes—
643C22×D4C2414yes—
644C22×D4C2412yes—
645C22×D4C2412yes—
646C22×D4C2414yes—
647C22×D4C2412yes—
648C22×D4C2412yes—
649C22×D4C2414yes—
650C22×D4C2412yes—
651C22×D4C2414yes—
652C22×D4C2414yes—
653C23×C4—24no—
654C23×C4—24no—
655C23×C4—44no—
656C23×C4—44no—
657C23×C4—42no—
658C23×C4—42no—
659C23×C4—42no—
660C23×C4C2412yes—
661C23×C4C2411yescharacteristic
662C23×C4C2412yes—
663C23×C4C2412yes—
664C23×C4C2412yes—
665C23×C4C2412yes—
666C23×C4C2412yes—
667C23×C4C2412yes—
668C23×C4C2411yescharacteristic
669C23×C4C2411yescharacteristic
670C23×C4C2414yes—
671C23×C4C2411yescharacteristic
672C23×C4C2414yes—
673C23×C4C2412yes—
674C23×C4C2412yes—
675C23×C4C2412yes—
676C23×C4C2412yes—
677C23×C4C2411yescharacteristic
678C23×C4C2411yescharacteristic
679C23×C4C2411yescharacteristic
680C23×C4C2411yescharacteristic
681#127—44no—
682#127—44no—
683#126—48no—
684#126—48no—
685#126—48no—
686#125—44no—
687#124—48no—
688#124—44no—
689#124—44no—
690#124—44no—
691#124—48no—
692#123—28no—
693#123—28no—
694#123—48no—
695#123—44no—
696#123—48no—
697#123—44no—
698#123—48no—
699#123—48no—
700#123—48no—
701#123—44no—
702#123—44no—
703#123—48no—
704#123—48no—
705#123—48no—
706C22⋊Q8—28no—
707C22⋊Q8—48no—
708C22⋊Q8—44no—
709C22⋊Q8—48no—
710C22⋊Q8—48no—
711C22⋊Q8—48no—
712C22⋊Q8—44no—
713C22⋊Q8—44no—
714C22⋊Q8—48no—
715#121—28no—
716#121—48no—
717#121—48no—
718#121—44no—
719#121—44no—
720#121—44no—
721#120—48no—
722#120—48no—
723#120—48no—
724#120—48no—
725#120—44no—
726#120—44no—
727C4×Q8—48no—
728C4×Q8—44no—
729C4×D4—216no—
730C4×D4—44no—
731C4×D4—48no—
732C4×D4—48no—
733C4×D4—48no—
734C4×D4—48no—
735#117—48no—
736#117—48no—
737C2×C4⋊C4—44no—
738C2×C4⋊C4—44no—
739C2×C4⋊C4—44no—
740C2×C4⋊C4—42no—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
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×C22⋊C4—24no—
778C2×C22⋊C4—24no—
779C2×C22⋊C4—44no—
780C2×C22⋊C4—44no—
781C2×C22⋊C4—48no—
782C2×C22⋊C4—42no—
783C2×C22⋊C4—42no—
784C2×C22⋊C4—44no—
785C2×C22⋊C4—44no—
786C2×C22⋊C4—44no—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C42—28no—
844C2×C42—44no—
845C2×C42—44no—
846C2×C42—44no—
847C2×C42—44no—
848C2×C42—44no—
849C2×C42C2412yes—
850C2×C42C2414yes—
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2412yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2414yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2414yes—
862C2×C42C2412yes—
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
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#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911C24—22no—
912C24—22no—
913C24—22no—
914C24—24no—
915C24—22no—
916C24—22no—
917C24—24no—
918C24—24no—
919C24—42no—
920C24—41no—
921C24—41no—
922C24—42no—
923C24—42no—
924C24—41no—
925C24—41no—
926C24—42no—
927C24—44no—
928C24—42no—
929C24—44no—
930C24—42no—
931C24C2512yes—
932C24C2512yes—
933C24C2514yes—
934C24C2511yescharacteristic
935C24C2511yescharacteristic
936C24C2511yescharacteristic
937C2×Q8—24no—
938C2×Q8—44no—
939C2×Q8—42no—
940C2×Q8—42no—
941C2×Q8—44no—
942C2×Q8—44no—
943C2×Q8—42no—
944C2×Q8—42no—
945C2×Q8—42no—
946C2×D4—28no—
947C2×D4—28no—
948C2×D4—28no—
949C2×D4—28no—
950C2×D4—24no—
951C2×D4—24no—
952C2×D4—28no—
953C2×D4—24no—
954C2×D4—24no—
955C2×D4—24no—
956C2×D4—28no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—44no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—42no—
965C2×D4—42no—
966C2×D4—42no—
967C2×D4—42no—
968C2×D4—42no—
969C2×D4—42no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—42no—
973C2×D4—42no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—42no—
977C2×D4—42no—
978C2×D4—44no—
979C2×D4—42no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—42no—
983C2×D4—44no—
984C2×D4—42no—
985C2×D4—88no—
986C2×D4—816no—
987C2×D4—88no—
988C2×D4—88no—
989C22×C4—22no—
990C22×C4—24no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—22no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—24no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—24no—
1004C22×C4—24no—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—28no—
1008C22×C4—41no—
1009C22×C4—42no—
1010C22×C4—41no—
1011C22×C4—41no—
1012C22×C4—42no—
1013C22×C4—41no—
1014C22×C4—41no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—41no—
1024C22×C4—42no—
1025C22×C4—42no—
1026C22×C4—44no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—42no—
1036C22×C4—44no—
1037C22×C4—41no—
1038C22×C4—41no—
1039C22×C4—42no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—44no—
1043C22×C4—42no—
1044C22×C4—416no—
1045C22×C4—416no—
1046C22×C4—416no—
1047C22×C4H(5,𝔽2)14yes—
1048C22×C4H(5,𝔽2)14yes—
1049C22×C4C2514yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2514yes—
1054C22×C4C2514yes—
1055C22×C4C2514yes—
1056C22×C4C2514yes—
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C4⋊C4—28no—
1067C4⋊C4—28no—
1068C4⋊C4—28no—
1069C4⋊C4—28no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—28no—
1075C4⋊C4—44no—
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—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C22⋊C4—28no—
1103C22⋊C4—24no—
1104C22⋊C4—24no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—42no—
1124C22⋊C4—44no—
1125C22⋊C4—42no—
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—42no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—42no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—42no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—42no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C42—24no—
1159C42—24no—
1160C42—24no—
1161C42—24no—
1162C42—28no—
1163C42—42no—
1164C42—42no—
1165C42—42no—
1166C42—42no—
1167C42—42no—
1168C42—44no—
1169C42—44no—
1170C42—44no—
1171C42—44no—
1172C42—42no—
1173C42—42no—
1174C42—44no—
1175C42—42no—
1176C23—21no—
1177C23—22no—
1178C23—21no—
1179C23—28no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—22no—
1184C23—22no—
1185C23—22no—
1186C23—22no—
1187C23—21no—
1188C23—22no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23—24no—
1193C23—24no—
1194C23—24no—
1195C23—24no—
1196C23—24no—
1197C23—24no—
1198C23—22no—
1199C23—24no—
1200C23—24no—
1201C23—24no—
1202C23—24no—
1203C23—24no—
1204C23—22no—
1205C23—48no—
1206C23—48no—
1207C23—44no—
1208C23—44no—
1209C23—44no—
1210C23—44no—
1211C23—82no—
1212C23—82no—
1213C23—82no—
1214C23—82no—
1215C23—84no—
1216C23—84no—
1217C23—84no—
1218C23—84no—
1219C23—84no—
1220C23—88no—
1221C23—162no—
1222C23—162no—
1223C23—164no—
1224C23C2×H(5,𝔽2)12yes—
1225C23C2×H(5,𝔽2)12yes—
1226C23#58512yes—
1227C23#58514yes—
1228C23C2611yescharacteristic
1229Q8—84no—
1230Q8—88no—
1231Q8—162no—
1232D4—416no—
1233D4—84no—
1234D4—88no—
1235D4—88no—
1236D4—88no—
1237D4—84no—
1238D4—84no—
1239D4—84no—
1240D4—84no—
1241D4—88no—
1242D4—88no—
1243D4—162no—
1244D4—164no—
1245C2×C4—28no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—44no—
1295C2×C4—44no—
1296C2×C4—48no—
1297C2×C4—48no—
1298C2×C4—48no—
1299C2×C4—48no—
1300C2×C4—44no—
1301C2×C4—44no—
1302C2×C4—48no—
1303C2×C4—44no—
1304C2×C4—48no—
1305C2×C4—88no—
1306C2×C4—84no—
1307C2×C4—84no—
1308C2×C4—82no—
1309C2×C4—82no—
1310C2×C4—88no—
1311C2×C4—84no—
1312C2×C4—162no—
1313C2×C4—162no—
1314C2×C4C2×H(5,𝔽2)14yes—
1315C2×C4C2×H(5,𝔽2)14yes—
1316C2×C4#58514yes—
1317C22—24no—
1318C22—22no—
1319C22—22no—
1320C22—24no—
1321C22—24no—
1322C22—22no—
1323C22—22no—
1324C22—24no—
1325C22—416no—
1326C22—41no—
1327C22—41no—
1328C22—42no—
1329C22—41no—
1330C22—41no—
1331C22—42no—
1332C22—42no—
1333C22—44no—
1334C22—42no—
1335C22—44no—
1336C22—44no—
1337C22—44no—
1338C22—44no—
1339C22—44no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—44no—
1345C22—44no—
1346C22—44no—
1347C22—44no—
1348C22—44no—
1349C22—164no—
1350C22—164no—
1351C22—168no—
1352C22#354014yes—
1353C22C22×H(5,𝔽2)11yescharacteristic
1354C22C22×H(5,𝔽2)11yescharacteristic
1355C22C2×#58512yes—
1356C22C2×#58512yes—
1357C22C2×#58511yescharacteristic
1358C4—24no—
1359C4—24no—
1360C4—24no—
1361C4—42no—
1362C4—42no—
1363C4—44no—
1364C4—44no—
1365C4—44no—
1366C4—44no—
1367C4—44no—
1368C4—42no—
1369C4—44no—
1370C4—42no—
1371C4—42no—
1372C4—44no—
1373C4—44no—
1374C4—44no—
1375C2—24no—
1376C2—42no—
1377C2—42no—
1378C2—84no—
1379C2—82no—
1380C2—82no—
1381C2C2×#354011yescharacteristic
1382C2#6274812yes—
1383C2#6281811yescharacteristic
1384C2#6282011yescharacteristic
1385C2#6282912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36717C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59191C2semidirect
2. #59189C2semidirect
3. #53263C2semidirect
4. #53261C2semidirect
5. #45847C2semidirect
6. #45821C2semidirect
7. #45568C2semidirect
8. #45537C2semidirect
9. #40013C2semidirect
10. #39941C2semidirect
11. #38575C2semidirect
12. #38572C2semidirect
13. #37958C2semidirect
14. #37950C2semidirect
15. #37754C2semidirect
16. #37746C2semidirect
17. #36879C2semidirect
18. #36877C2semidirect
19. #36729C2semidirect
20. #36718C2semidirect
22. #36621C2semidirect
23. C2×#2854C2semidirect
24. C2×#559C22semidirect
25. C2×#551C22semidirect
26. C2×#543C22semidirect
30. C22×#123C22semidirect
32. C23×C42C22semidirect
33. #2855C22semidirect
35. #2854C22semidirect
36. #2854C22semidirect
37. #2854C22semidirect
38. #2854C22semidirect
39. #2853C22semidirect
40. #2852C22semidirect
41. #2852C22semidirect
42. #2851C22semidirect
43. #2851C22semidirect
44. #2850C22semidirect
45. #2850C22semidirect
46. #2849C22semidirect
47. #2848C22semidirect
49. #2826C22semidirect
50. #2824C22semidirect
51. #2804C22semidirect
52. #2803C22semidirect
53. #2801C22semidirect
54. #2797C22semidirect
55. #2797C22semidirect
56. #2786C22semidirect
57. #2785C22semidirect
58. #2784C22semidirect
59. #2783C22semidirect
60. #2782C22semidirect
61. #2781C22semidirect
62. #2778C22semidirect
63. #2778C22semidirect
64. #2777C22semidirect
65. #2777C22semidirect
66. #2775C22semidirect
67. #2775C22semidirect
68. #2774C22semidirect
69. #2773C22semidirect
70. #2772C22semidirect
71. #2759C22semidirect
72. #2757C22semidirect
73. #2756C22semidirect
74. #2755C22semidirect
75. #2753C22semidirect
76. #2753C22semidirect
77. #2748C22semidirect
78. #2747C22semidirect
79. #2742C22semidirect
80. #2742C22semidirect
81. #2741C22semidirect
82. #2730C22semidirect
83. #2724C22semidirect
84. #2723C22semidirect
85. #2717C22semidirect
86. #2717C22semidirect
87. #2712C22semidirect
88. #2710C22semidirect
89. #2709C22semidirect
90. #2709C22semidirect
91. #2709C22semidirect
92. #2706C22semidirect
95. #2702C22semidirect
96. #2702C22semidirect
97. #2702C22semidirect
98. #2697C22semidirect
99. #2697C22semidirect
100. #2696C22semidirect
101. #2695C22semidirect
102. #2694C22semidirect
103. #2693C22semidirect
104. #2692C22semidirect
105. #2691C22semidirect
106. #2690C22semidirect
107. #2685C22semidirect
108. #2685C22semidirect
109. #2684C22semidirect
110. #2684C22semidirect
111. #2684C22semidirect
112. #2681C22semidirect
113. #2681C22semidirect
114. #2672C22semidirect
115. #2672C22semidirect
116. #2672C22semidirect
119. #2663C22semidirect
120. #2662C22semidirect
121. #2659C22semidirect
122. #2655C22semidirect
123. #2648C22semidirect
127. #2610C22semidirect
128. #2604C22semidirect
129. #2602C22semidirect
130. #2602C22semidirect
131. #2595C22semidirect
132. #2594C22semidirect
133. #2593C22semidirect
135. #2583C22semidirect
137. #2557C22semidirect
138. #2554C22semidirect
139. #2553C22semidirect
140. #2534C22semidirect
141. #2532C22semidirect
142. #2529C22semidirect
143. #2525C22semidirect
144. #2509C22semidirect
145. #2493C22semidirect
146. #2488C22semidirect
147. #2488C22semidirect
148. #2481C22semidirect
150. #2477C22semidirect
151. #2474C22semidirect
152. #2472C22semidirect
153. #2472C22semidirect
154. #2472C22semidirect
155. #2471C22semidirect
156. #2470C22semidirect
157. #2470C22semidirect
158. #2469C22semidirect
159. #2467C22semidirect
160. #2465C22semidirect
161. #2463C22semidirect
162. #2461C22semidirect
163. #2458C22semidirect
164. #2458C22semidirect
165. #2455C22semidirect
166. #2449C22semidirect
167. #2449C22semidirect
168. #2445C22semidirect
173. #2421C22semidirect
174. #2418C22semidirect
175. #2418C22semidirect
176. #2418C22semidirect
177. #2415C22semidirect
178. #2412C22semidirect
179. #2411C22semidirect
182. #2405C22semidirect
185. #2380C22semidirect
186. #2379C22semidirect
187. #2376C22semidirect
188. #2375C22semidirect
189. #2374C22semidirect
190. #2374C22semidirect
191. #2360C22semidirect
192. #2358C22semidirect
193. #2352C22semidirect
195. #2335C22semidirect
196. #2334C22semidirect
197. #2329C22semidirect
199. #2323C22semidirect
200. #2321C22semidirect
202. #2312C22semidirect
203. C4×C22⋊Q8C22semidirect
204. C4×C22⋊Q8C22semidirect
205. C4×#123C22semidirect
206. C4×#121C22semidirect
207. C4×#121C22semidirect
208. C4×#120C22semidirect
210. C2×#389C22semidirect
211. #2290C22semidirect
212. #2290C22semidirect
214. C2×#388C22semidirect
216. C2×#386C22semidirect
217. #2283C22semidirect
218. C2×#380C22semidirect

Maximal subgroups

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

subgroupindex
#591912
#591892
#532632
#532612
#458472
#458212
#455682
#455372
#400132
#399412
#385752
#385722
#379582
#379502
#377542
#377462
#368792
#368772
#367292
#367182
#367172
#366212
C2×#28542