Finite Group Databasebeta

← #8108453

Subgroups — #8108453

Order 512.

4696 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59624C212yesmaximal, complemented
2#59370C212yesmaximal, complemented
3#53243C214yesmaximal, complemented
4#53231C214yesmaximal, complemented
5#45895C214yesmaximal, complemented
6#45893C214yesmaximal, complemented
7#45569C212yesmaximal, complemented
8#45568C212yesmaximal, complemented
9#38324C214yesmaximal, complemented
10#38295C214yesmaximal, complemented
11#38178C214yesmaximal, complemented
12#38147C214yesmaximal, complemented
13#37958C212yesmaximal, complemented
14#37951C212yesmaximal, complemented
15#37755C212yesmaximal, complemented
16#37746C212yesmaximal, complemented
17#36802C214yesmaximal, complemented
18#36784C214yesmaximal, complemented
19#36730C212yesmaximal, complemented
20#36721C211yesmaximal, characteristic
21#36711C211yesmaximal, characteristic, complemented
22#36621C212yesmaximal, complemented
23C2×#2853C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic, complemented
25C2×#534C2211yescharacteristic
26C2×#529C2212yes—
27C22×#123C2211yescharacteristic
28C23×C42C2211yescharacteristic, complemented
29#2855C2212yescomplemented
30#2854C2212yes—
31#2853C2214yescomplemented
32#2853C2214yescomplemented
33#2853C2214yescomplemented
34#2853C2214yescomplemented
35#2853C2214yescomplemented
36#2852C2214yescomplemented
37#2852C2214yescomplemented
38#2851C2212yescomplemented
39#2851C2212yescomplemented
40#2850C2212yescomplemented
41#2850C2212yescomplemented
42#2849C2214yescomplemented
43#2848C2212yescomplemented
44#2847C2212yes—
45#2834C2212yescomplemented
46#2826C2212yescomplemented
47#2824C2214yes—
48#2808C2214yescomplemented
49#2807C2214yescomplemented
50#2807C2212yescomplemented
51#2807C2212yescomplemented
52#2804C2212yescomplemented
53#2800C2214yescomplemented
54#2800C2214yescomplemented
55#2798C2214yescomplemented
56#2796C2214yescomplemented
57#2787C2214yescomplemented
58#2783C2214yescomplemented
59#2782C2214yescomplemented
60#2779C2214yescomplemented
61#2778C2214yescomplemented
62#2777C2214yescomplemented
63#2775C2214yescomplemented
64#2775C2214yescomplemented
65#2772C2214yescomplemented
66#2770C2214yescomplemented
67#2769C2214yescomplemented
68#2767C2214yescomplemented
69#2766C2214yescomplemented
70#2759C2214yescomplemented
71#2759C2214yescomplemented
72#2757C2214yescomplemented
73#2757C2214yescomplemented
74#2753C2214yes—
75#2753C2214yes—
76#2749C2214yes—
77#2748C2214yescomplemented
78#2748C2212yescomplemented
79#2746C2214yescomplemented
80#2745C2214yescomplemented
81#2744C2214yescomplemented
82#2741C2214yescomplemented
83#2738C2214yescomplemented
84#2738C2214yescomplemented
85#2737C2214yescomplemented
86#2737C2214yescomplemented
87#2737C2214yescomplemented
88#2736C2214yescomplemented
89#2735C2214yescomplemented
90#2731C2214yescomplemented
91#2725C2214yescomplemented
92#2719C2214yescomplemented
93#2716C2214yescomplemented
94#2712C2214yes—
95#2712C2212yescomplemented
96#2706C2214yes—
97#2706C2214yes—
98#2701C2214yescomplemented
99#2700C2214yescomplemented
100#2695C2214yescomplemented
101#2694C2214yescomplemented
102#2694C2214yescomplemented
103#2694C2214yescomplemented
104#2693C2212yescomplemented
105#2687C2214yescomplemented
106#2686C2214yescomplemented
107#2685C2214yescomplemented
108#2684C2212yescomplemented
109#2684C2214yescomplemented
110#2684C2214yescomplemented
111#2684C2212yescomplemented
112#2678C2214yes—
113#2678C2214yes—
114#2674C2214yescomplemented
115#2674C2214yescomplemented
116#2659C2212yescomplemented
117#2653C2214yescomplemented
118#2652C2214yescomplemented
119#2651C2214yescomplemented
120#2650C2214yescomplemented
121#2639C2212yes—
122#2626C2212yes—
123#2618C2212yes—
124#2612C2214yescomplemented
125#2604C2214yescomplemented
126#2603C2214yes—
127#2602C2214yescomplemented
128#2595C2214yescomplemented
129#2594C2214yescomplemented
130#2593C2214yescomplemented
131#2589C2214yescomplemented
132#2589C2214yescomplemented
133#2583C2212yescomplemented
134#2580C2214yescomplemented
135#2578C2214yescomplemented
136#2574C2214yescomplemented
137#2561C2214yes—
138#2557C2214yes—
139#2539C2212yes—
140#2534C2214yescomplemented
141#2532C2214yescomplemented
142#2531C2214yescomplemented
143#2530C2214yescomplemented
144#2529C2214yescomplemented
145#2520C2214yescomplemented
146#2518C2214yescomplemented
147#2517C2212yescomplemented
148#2510C2214yescomplemented
149#2504C2212yes—
150#2494C2214yescomplemented
151#2493C2214yescomplemented
152#2488C2214yescomplemented
153#2488C2214yescomplemented
154#2488C2214yescomplemented
155#2486C2214yescomplemented
156#2482C2212yes—
157#2482C2212yescomplemented
158#2480C2214yes—
159#2480C2214yescomplemented
160#2475C2214yescomplemented
161#2472C2214yescomplemented
162#2470C2214yescomplemented
163#2469C2214yescomplemented
164#2467C2214yes—
165#2460C2214yescomplemented
166#2458C2214yescomplemented
167#2458C2214yescomplemented
168#2455C2212yescomplemented
169#2450C2214yescomplemented
170#2450C2214yescomplemented
171#2446C2214yescomplemented
172#2443C2214yes—
173#2439C2214yescomplemented
174#2435C2212yes—
175#2425C2214yes—
176#2418C2214yescomplemented
177#2418C2214yescomplemented
178#2413C2214yescomplemented
179#2411C2214yescomplemented
180#2405C2214yes—
181#2405C2212yes—
182#2403C2212yes—
183#2379C2212yescomplemented
184#2376C2214yescomplemented
185#2375C2212yescomplemented
186#2372C2212yescomplemented
187#2367C2214yescomplemented
188#2360C2214yescomplemented
189#2359C2214yescomplemented
190#2358C2212yescomplemented
191#2353C2214yescomplemented
192D4×C22⋊C4C2214yes—
193#2335C2214yescomplemented
194#2334C2214yescomplemented
195#2329C2212yescomplemented
196#2325C2212yes—
197#2320C2214yescomplemented
198#2313C2211yescharacteristic, complemented
199#2312C2211yescharacteristic
200#2312C2214yescomplemented
201C4×C22⋊Q8C2212yescomplemented
202C4×C22⋊Q8C2212yescomplemented
203C4×#123C2214yescomplemented
204C4×#121C2212yescomplemented
205C4×#121C2212yescomplemented
206C4×#120C2214yescomplemented
207#2290C2214yescomplemented
208#2290C2214yescomplemented
209C2×#388C2212yes—
210C2×#388C2212yes—
211C2×#387C2212yescomplemented
212C2×#387C2212yescomplemented
213C2×#386C2211yescharacteristic
214C2×#386C2211yescharacteristic
215C2×#385C2211yescharacteristic, complemented
216C2×#385C2211yescharacteristic, complemented
217#2283C2212yescomplemented
218C2×#381C2211yescharacteristic, complemented
219C23×D4C2312yes—
220C23×D4C2311yescharacteristic
221C24×C4C2311yescharacteristic
222C24×C4C2311yescharacteristic
223C24×C4C2311yescharacteristic
224#544—44no—
225#534—44no—
226C2×C4⋊Q8C2314yes—
227#529—48no—
228C2×#126C2314yes—
229C2×#126C2314yes—
230C2×#125C2312yes—
231C2×#125C2314yes—
232C2×#124C2312yes—
233C2×#124C2314yes—
234C2×#124C2312yes—
235C2×#124C2312yes—
236C2×#123—44no—
237C2×#123C2314yes—
238C2×#123C2314yes—
239C2×#123C2314yes—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2312yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2312yes—
250C2×#121C2312yes—
251C2×#121C2312yes—
252C2×#121C2312yes—
253C2×#121C2312yes—
254C2×#120C2314yes—
255C2×#120C2312yes—
256C2×#120C2312yes—
257C2×#120C2314yes—
258C2×C4×Q8C2314yes—
259C2×C4×Q8C2312yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2312yes—
265C2×#117C2312yes—
266C2×#117C2314yes—
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C22⋊C4C2311yescharacteristic
272C22×C22⋊C4C2312yes—
273C22×C22⋊C4C2314yes—
274C22×C22⋊C4C2312yes—
275C22×C22⋊C4C2311yescharacteristic
276C22×C22⋊C4C2311yescharacteristic
277C22×C22⋊C4C2311yescharacteristic
278C22×C22⋊C4C2311yescharacteristic
279C22×C42—44no—
280C22×C42C2312yes—
281C22×C42C2312yes—
282C22×C42C2312yes—
283C22×C42C2312yes—
284C22×C42C2312yes—
285C22×C42C2312yes—
286#401C2314yes—
287#401C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#399C2312yes—
302#399C2312yes—
303#399C2314yes—
304#399C2314yes—
305#399C2314yes—
306#399C2314yes—
307#399C2312yes—
308#399C2312yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2312yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2312yes—
341#397C2314yes—
342#397C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#394C2314yes—
357#394C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#393C2314yes—
373#393C2314yes—
374#393C2314yes—
375#393C2314yes—
376#393C2314yes—
377#393C2314yes—
378#393C2314yes—
379#393C2314yes—
380#393C2314yes—
381#393C2314yes—
382#392C2314yes—
383#392C2312yes—
384#392C2314yes—
385#392C2312yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2312yes—
392#391C2312yes—
393#391C2314yes—
394#391C2314yes—
395#390C2314yes—
396#390C2314yes—
397#390C2314yes—
398#390C2314yes—
399#390C2314yes—
400#390C2312yes—
401#390C2312yes—
402#390C2312yes—
403#390C2312yes—
404#390C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
418#389C2312yes—
419#389C2314yes—
420#389C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
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#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
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#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#386C2312yes—
506#386C2314yes—
507#386C2312yes—
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#386C2314yes—
524#386C2312yes—
525#386C2314yes—
526#386C2312yes—
527#386C2312yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2312yes—
532#385C2314yes—
533#385C2312yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2312yes—
553#385C2312yes—
554#385C2312yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#383C2314yes—
559#383C2314yes—
560#383C2314yes—
561#383C2314yes—
562#382C2314yes—
563#382C2314yes—
564#382C2314yes—
565#382C2314yes—
566#382C2312yes—
567#382C2312yes—
568#381C2314yes—
569#381C2314yes—
570#381C2312yes—
571#381C2314yes—
572#381C2314yes—
573#381C2314yes—
574#380C2312yes—
575#380C2314yes—
576#380C2314yes—
577#380C2312yes—
578#380C2314yes—
579#380C2314yes—
580#380C2314yes—
581#380C2312yes—
582#380C2312yes—
583#380C2312yes—
584#380C2312yes—
585#380C2314yes—
586#380C2314yes—
587#379C2312yes—
588#379C2314yes—
589#379C2314yes—
590#379C2314yes—
591#379C2314yes—
592#379C2314yes—
593#379C2314yes—
594C4×C4⋊C4C2312yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2312yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611#376C2314yes—
612#376C2314yes—
613C2×#95C2312yes—
614C2×#95C2312yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C2×#95C2312yes—
619C25C2411yescharacteristic
620C25C2411yescharacteristic
621C25C2412yes—
622C22×Q8C2412yes—
623C22×Q8C2414yes—
624C22×Q8C2412yes—
625C22×D4—42no—
626C22×D4—44no—
627C22×D4—48no—
628C22×D4—42no—
629C22×D4—42no—
630C22×D4C2414yes—
631C22×D4C2412yes—
632C22×D4C2414yes—
633C22×D4C2414yes—
634C22×D4C2412yes—
635C22×D4C2412yes—
636C22×D4C2412yes—
637C22×D4C2414yes—
638C23×C4—24no—
639C23×C4—44no—
640C23×C4—44no—
641C23×C4—42no—
642C23×C4—42no—
643C23×C4—42no—
644C23×C4—42no—
645C23×C4C2411yescharacteristic
646C23×C4C2412yes—
647C23×C4C2412yes—
648C23×C4C2411yescharacteristic
649C23×C4C2412yes—
650C23×C4C2412yes—
651C23×C4C2411yescharacteristic
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2411yescharacteristic
655C23×C4C2414yes—
656C23×C4C2411yescharacteristic
657C23×C4C2412yes—
658C23×C4C2414yes—
659C23×C4C2412yes—
660C23×C4C2411yescharacteristic
661C23×C4C2412yes—
662C23×C4C2411yescharacteristic
663C23×C4C2411yescharacteristic
664C23×C4C2411yescharacteristic
665C4⋊Q8—48no—
666#126—48no—
667#126—48no—
668#125—44no—
669#125—48no—
670#124—44no—
671#124—48no—
672#124—44no—
673#124—44no—
674#123—48no—
675#123—48no—
676#123—48no—
677#123—48no—
678#123—48no—
679#123—48no—
680#123—48no—
681#123—48no—
682C22⋊Q8—28no—
683C22⋊Q8—48no—
684C22⋊Q8—44no—
685C22⋊Q8—44no—
686C22⋊Q8—44no—
687#121—28no—
688#121—44no—
689#121—44no—
690#121—44no—
691#120—48no—
692#120—48no—
693#120—44no—
694#120—44no—
695C4×Q8—48no—
696C4×Q8—44no—
697C4×D4—44no—
698C4×D4—48no—
699C4×D4—48no—
700C4×D4—48no—
701C4×D4—48no—
702#117—48no—
703#117—44no—
704C2×C4⋊C4—24no—
705C2×C4⋊C4—44no—
706C2×C4⋊C4—44no—
707C2×C4⋊C4—42no—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
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×C22⋊C4—24no—
748C2×C22⋊C4—44no—
749C2×C22⋊C4—48no—
750C2×C22⋊C4—42no—
751C2×C22⋊C4—42no—
752C2×C22⋊C4—44no—
753C2×C22⋊C4—42no—
754C2×C22⋊C4—42no—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2412yes—
759C2×C22⋊C4C2412yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2412yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
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×C42—28no—
806C2×C42—44no—
807C2×C42—44no—
808C2×C42—44no—
809C2×C42—44no—
810C2×C42—44no—
811C2×C42C2412yes—
812C2×C42C2414yes—
813C2×C42C2412yes—
814C2×C42C2412yes—
815C2×C42C2412yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2412yes—
823C2×C42C2412yes—
824C2×C42C2414yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2412yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2412yes—
863#95C2412yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2412yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2412yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883C24—22no—
884C24—22no—
885C24—22no—
886C24—24no—
887C24—22no—
888C24—24no—
889C24—42no—
890C24—42no—
891C24—41no—
892C24—41no—
893C24—42no—
894C24—44no—
895C24—44no—
896C24—42no—
897C24—42no—
898C24C2512yes—
899C24C2514yes—
900C24C2511yescharacteristic
901C24C2511yescharacteristic
902C24C2511yescharacteristic
903C2×Q8—24no—
904C2×Q8—44no—
905C2×Q8—42no—
906C2×Q8—42no—
907C2×Q8—44no—
908C2×Q8—44no—
909C2×Q8—42no—
910C2×Q8—42no—
911C2×Q8—42no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—28no—
915C2×D4—28no—
916C2×D4—28no—
917C2×D4—24no—
918C2×D4—24no—
919C2×D4—24no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—44no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—44no—
933C2×D4—42no—
934C2×D4—44no—
935C2×D4—816no—
936C2×D4—88no—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—22no—
940C22×C4—22no—
941C22×C4—24no—
942C22×C4—24no—
943C22×C4—24no—
944C22×C4—24no—
945C22×C4—24no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—24no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—28no—
956C22×C4—41no—
957C22×C4—42no—
958C22×C4—41no—
959C22×C4—42no—
960C22×C4—41no—
961C22×C4—41no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—41no—
965C22×C4—41no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—41no—
969C22×C4—41no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—42no—
983C22×C4—44no—
984C22×C4—41no—
985C22×C4—41no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—416no—
990C22×C4—416no—
991C22×C4—416no—
992C22×C4H(5,𝔽2)14yes—
993C22×C4C2514yes—
994C22×C4C2514yes—
995C22×C4C2512yes—
996C22×C4C2514yes—
997C22×C4C2512yes—
998C22×C4C2512yes—
999C22×C4C2512yes—
1000C22×C4C2512yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2514yes—
1004C22×C4C2514yes—
1005C22×C4C2514yes—
1006C22×C4C2512yes—
1007C22×C4C2512yes—
1008C22×C4C2514yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—42no—
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—
1050C22⋊C4—28no—
1051C22⋊C4—24no—
1052C22⋊C4—24no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—44no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—42no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—42no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C42—24no—
1101C42—24no—
1102C42—24no—
1103C42—24no—
1104C42—28no—
1105C42—42no—
1106C42—42no—
1107C42—42no—
1108C42—42no—
1109C42—44no—
1110C42—44no—
1111C42—44no—
1112C42—44no—
1113C42—44no—
1114C42—44no—
1115C42—44no—
1116C42—42no—
1117C42—42no—
1118C23—22no—
1119C23—21no—
1120C23—21no—
1121C23—28no—
1122C23—21no—
1123C23—21no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—21no—
1128C23—21no—
1129C23—22no—
1130C23—22no—
1131C23—24no—
1132C23—24no—
1133C23—24no—
1134C23—24no—
1135C23—24no—
1136C23—24no—
1137C23—22no—
1138C23—22no—
1139C23—24no—
1140C23—24no—
1141C23—24no—
1142C23—48no—
1143C23—48no—
1144C23—44no—
1145C23—44no—
1146C23—44no—
1147C23—82no—
1148C23—84no—
1149C23—82no—
1150C23—84no—
1151C23—84no—
1152C23—88no—
1153C23—162no—
1154C23—162no—
1155C23—164no—
1156C23C2×H(5,𝔽2)12yes—
1157C23#58512yes—
1158C23#58512yes—
1159C23#58514yes—
1160C23C2611yescharacteristic
1161Q8—84no—
1162Q8—88no—
1163Q8—162no—
1164D4—416no—
1165D4—84no—
1166D4—88no—
1167D4—88no—
1168D4—84no—
1169D4—84no—
1170D4—88no—
1171D4—162no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—22no—
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—24no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—44no—
1223C2×C4—44no—
1224C2×C4—48no—
1225C2×C4—48no—
1226C2×C4—48no—
1227C2×C4—48no—
1228C2×C4—44no—
1229C2×C4—44no—
1230C2×C4—48no—
1231C2×C4—44no—
1232C2×C4—44no—
1233C2×C4—44no—
1234C2×C4—48no—
1235C2×C4—88no—
1236C2×C4—84no—
1237C2×C4—82no—
1238C2×C4—84no—
1239C2×C4—82no—
1240C2×C4—84no—
1241C2×C4—164no—
1242C2×C4C2×H(5,𝔽2)14yes—
1243C2×C4#58514yes—
1244C22—24no—
1245C22—22no—
1246C22—22no—
1247C22—24no—
1248C22—24no—
1249C22—22no—
1250C22—22no—
1251C22—24no—
1252C22—416no—
1253C22—41no—
1254C22—41no—
1255C22—42no—
1256C22—41no—
1257C22—41no—
1258C22—42no—
1259C22—42no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—42no—
1265C22—44no—
1266C22—44no—
1267C22—42no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—164no—
1272C22—168no—
1273C22#354014yes—
1274C22C22×H(5,𝔽2)11yescharacteristic
1275C22C2×#58512yes—
1276C22C2×#58511yescharacteristic
1277C22C2×#58512yes—
1278C22C2×#58511yescharacteristic
1279C4—24no—
1280C4—24no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—44no—
1285C4—44no—
1286C4—44no—
1287C4—44no—
1288C4—42no—
1289C4—42no—
1290C4—44no—
1291C4—42no—
1292C4—44no—
1293C4—42no—
1294C4—44no—
1295C4—44no—
1296C4—44no—
1297C2—24no—
1298C2—42no—
1299C2—42no—
1300C2—84no—
1301C2—82no—
1302C2C2×#354011yescharacteristic
1303C2#6275512yes—
1304C2#6282011yescharacteristic
1305C2#6282111yescharacteristic
1306C2#6282812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36721C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59624C2semidirect
2. #59370C2semidirect
3. #53243C2semidirect
4. #53231C2semidirect
5. #45895C2semidirect
6. #45893C2semidirect
7. #45569C2semidirect
8. #45568C2semidirect
9. #38324C2semidirect
10. #38295C2semidirect
11. #38178C2semidirect
12. #38147C2semidirect
13. #37958C2semidirect
14. #37951C2semidirect
15. #37755C2semidirect
16. #37746C2semidirect
17. #36802C2semidirect
18. #36784C2semidirect
19. #36730C2semidirect
21. #36711C2semidirect
22. #36621C2semidirect
23. C2×#2853C2semidirect
24. C2×#544C22semidirect
28. C23×C42C22semidirect
29. #2855C22semidirect
31. #2853C22semidirect
32. #2853C22semidirect
33. #2853C22semidirect
34. #2853C22semidirect
35. #2853C22semidirect
36. #2852C22semidirect
37. #2852C22semidirect
38. #2851C22semidirect
39. #2851C22semidirect
40. #2850C22semidirect
41. #2850C22semidirect
42. #2849C22semidirect
43. #2848C22semidirect
45. #2834C22semidirect
46. #2826C22semidirect
48. #2808C22semidirect
49. #2807C22semidirect
50. #2807C22semidirect
51. #2807C22semidirect
52. #2804C22semidirect
53. #2800C22semidirect
54. #2800C22semidirect
55. #2798C22semidirect
56. #2796C22semidirect
57. #2787C22semidirect
58. #2783C22semidirect
59. #2782C22semidirect
60. #2779C22semidirect
61. #2778C22semidirect
62. #2777C22semidirect
63. #2775C22semidirect
64. #2775C22semidirect
65. #2772C22semidirect
66. #2770C22semidirect
67. #2769C22semidirect
68. #2767C22semidirect
69. #2766C22semidirect
70. #2759C22semidirect
71. #2759C22semidirect
72. #2757C22semidirect
73. #2757C22semidirect
77. #2748C22semidirect
78. #2748C22semidirect
79. #2746C22semidirect
80. #2745C22semidirect
81. #2744C22semidirect
82. #2741C22semidirect
83. #2738C22semidirect
84. #2738C22semidirect
85. #2737C22semidirect
86. #2737C22semidirect
87. #2737C22semidirect
88. #2736C22semidirect
89. #2735C22semidirect
90. #2731C22semidirect
91. #2725C22semidirect
92. #2719C22semidirect
93. #2716C22semidirect
95. #2712C22semidirect
98. #2701C22semidirect
99. #2700C22semidirect
100. #2695C22semidirect
101. #2694C22semidirect
102. #2694C22semidirect
103. #2694C22semidirect
104. #2693C22semidirect
105. #2687C22semidirect
106. #2686C22semidirect
107. #2685C22semidirect
108. #2684C22semidirect
109. #2684C22semidirect
110. #2684C22semidirect
111. #2684C22semidirect
114. #2674C22semidirect
115. #2674C22semidirect
116. #2659C22semidirect
117. #2653C22semidirect
118. #2652C22semidirect
119. #2651C22semidirect
120. #2650C22semidirect
124. #2612C22semidirect
125. #2604C22semidirect
127. #2602C22semidirect
128. #2595C22semidirect
129. #2594C22semidirect
130. #2593C22semidirect
131. #2589C22semidirect
132. #2589C22semidirect
133. #2583C22semidirect
134. #2580C22semidirect
135. #2578C22semidirect
136. #2574C22semidirect
140. #2534C22semidirect
141. #2532C22semidirect
142. #2531C22semidirect
143. #2530C22semidirect
144. #2529C22semidirect
145. #2520C22semidirect
146. #2518C22semidirect
147. #2517C22semidirect
148. #2510C22semidirect
150. #2494C22semidirect
151. #2493C22semidirect
152. #2488C22semidirect
153. #2488C22semidirect
154. #2488C22semidirect
155. #2486C22semidirect
157. #2482C22semidirect
159. #2480C22semidirect
160. #2475C22semidirect
161. #2472C22semidirect
162. #2470C22semidirect
163. #2469C22semidirect
165. #2460C22semidirect
166. #2458C22semidirect
167. #2458C22semidirect
168. #2455C22semidirect
169. #2450C22semidirect
170. #2450C22semidirect
171. #2446C22semidirect
173. #2439C22semidirect
176. #2418C22semidirect
177. #2418C22semidirect
178. #2413C22semidirect
179. #2411C22semidirect
183. #2379C22semidirect
184. #2376C22semidirect
185. #2375C22semidirect
186. #2372C22semidirect
187. #2367C22semidirect
188. #2360C22semidirect
189. #2359C22semidirect
190. #2358C22semidirect
191. #2353C22semidirect
193. #2335C22semidirect
194. #2334C22semidirect
195. #2329C22semidirect
197. #2320C22semidirect
198. #2313C22semidirect
200. #2312C22semidirect
201. C4×C22⋊Q8C22semidirect
202. C4×C22⋊Q8C22semidirect
203. C4×#123C22semidirect
204. C4×#121C22semidirect
205. C4×#121C22semidirect
206. C4×#120C22semidirect
207. #2290C22semidirect
208. #2290C22semidirect
211. C2×#387C22semidirect
212. C2×#387C22semidirect
215. C2×#385C22semidirect
216. C2×#385C22semidirect
217. #2283C22semidirect
218. C2×#381C22semidirect

Maximal subgroups

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

subgroupindex
#596242
#593702
#532432
#532312
#458952
#458932
#455692
#455682
#383242
#382952
#381782
#381472
#379582
#379512
#377552
#377462
#368022
#367842
#367302
#367212
#367112
#366212
C2×#28532