Finite Group Databasebeta

← #8908382

Subgroups — #8908382

Order 512.

4718 conjugacy classes of subgroups.

The subgroup lattice has 1307 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59628C212yesmaximal, complemented
2#59070C211yesmaximal, characteristic, complemented
3#58035C214yesmaximal, complemented
4#55549C214yesmaximal, complemented
5#53557C214yesmaximal, complemented
6#52054C212yesmaximal, complemented
7#52025C214yesmaximal, complemented
8#51201C212yesmaximal, complemented
9#50237C212yesmaximal, complemented
10#49710C214yesmaximal, complemented
11#48343C214yesmaximal, complemented
12#48184C212yesmaximal, complemented
13#48059C214yesmaximal, complemented
14#47255C214yesmaximal, complemented
15#46359C212yesmaximal, complemented
16#46228C211yesmaximal, characteristic, complemented
17#45692C212yesmaximal, complemented
18#39540C212yesmaximal, complemented
19#39016C214yesmaximal, complemented
20#38801C212yesmaximal, complemented
21#37717C214yesmaximal, complemented
22#35533C211yesmaximal, characteristic
23#35453C212yesmaximal, complemented
24C2×#563C2211yescharacteristic, complemented
25C2×#559C2212yes—
26C2×#559C2211yescharacteristic, complemented
27C2×#539C2212yes—
28C2×#535C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C22×#125C2212yescomplemented
32C2×#520C2211yescharacteristic
33#2852C2214yescomplemented
34#2851C2212yes—
35#2830C2214yescomplemented
36#2830C2214yescomplemented
37#2827C2214yescomplemented
38#2820C2212yescomplemented
39#2816C2212yes—
40#2810C2212yescomplemented
41#2809C2212yescomplemented
42#2804C2212yes—
43#2800C2214yescomplemented
44#2798C2214yescomplemented
45#2796C2214yescomplemented
46#2786C2214yescomplemented
47#2786C2214yescomplemented
48#2784C2214yescomplemented
49#2781C2214yescomplemented
50#2780C2214yescomplemented
51#2779C2214yes—
52#2773C2214yescomplemented
53#2770C2214yes—
54#2762C2214yescomplemented
55#2761C2214yes—
56#2759C2214yescomplemented
57#2757C2214yescomplemented
58#2754C2214yescomplemented
59#2753C2214yescomplemented
60#2751C2214yes—
61#2750C2214yescomplemented
62#2749C2214yescomplemented
63#2746C2214yescomplemented
64#2745C2214yescomplemented
65#2742C2214yescomplemented
66#2740C2214yescomplemented
67#2737C2214yescomplemented
68#2734C2212yescomplemented
69#2734C2212yescomplemented
70#2729C2214yes—
71#2726C2212yescomplemented
72#2721C2214yescomplemented
73#2720C2214yescomplemented
74#2717C2214yes—
75#2717C2212yes—
76#2717C2212yescomplemented
77#2717C2212yescomplemented
78#2716C2214yescomplemented
79#2715C2214yescomplemented
80#2715C2214yescomplemented
81#2712C2214yescomplemented
82#2711C2214yes—
83#2709C2212yes—
84#2709C2214yes—
85#2709C2212yes—
86#2709C2212yescomplemented
87#2708C2214yes—
88#2707C2214yes—
89#2707C2214yescomplemented
90#2700C2214yescomplemented
91#2697C2214yes—
92#2694C2214yes—
93#2694C2214yescomplemented
94#2691C2214yes—
95#2691C2214yescomplemented
96#2690C2214yescomplemented
97#2686C2214yes—
98#2686C2214yes—
99#2685C2214yes—
100#2684C2214yes—
101#2684C2214yes—
102#2674C2214yes—
103#2672C2214yes—
104#2666C2214yescomplemented
105#2664C2214yescomplemented
106#2653C2214yes—
107#2651C2214yescomplemented
108#2638C2214yescomplemented
109#2636C2214yescomplemented
110#2633C2214yescomplemented
111#2632C2214yes—
112#2626C2212yes—
113#2626C2212yes—
114#2601C2214yes—
115#2600C2214yescomplemented
116#2599C2214yes—
117#2598C2214yescomplemented
118#2595C2214yescomplemented
119#2594C2214yescomplemented
120#2591C2212yes—
121#2589C2214yescomplemented
122#2579C2212yes—
123#2579C2212yescomplemented
124#2578C2214yescomplemented
125#2577C2214yes—
126#2576C2214yescomplemented
127#2574C2214yes—
128#2574C2214yescomplemented
129#2567C2212yescomplemented
130#2558C2214yes—
131#2556C2214yescomplemented
132#2548C2212yes—
133#2545C2212yes—
134#2544C2212yes—
135#2541C2212yes—
136#2524C2214yescomplemented
137#2524C2214yescomplemented
138#2522C2214yescomplemented
139#2521C2214yes—
140#2521C2214yescomplemented
141#2491C2214yescomplemented
142#2491C2214yescomplemented
143#2486C2212yes—
144#2486C2212yescomplemented
145#2484C2212yescomplemented
146#2484C2212yescomplemented
147#2481C2214yescomplemented
148#2480C2214yes—
149#2479C2214yes—
150#2476C2214yescomplemented
151#2475C2214yes—
152#2475C2214yescomplemented
153#2473C2214yes—
154#2473C2214yescomplemented
155#2473C2214yescomplemented
156#2472C2214yes—
157#2468C2214yescomplemented
158#2466C2214yescomplemented
159#2462C2214yescomplemented
160#2462C2214yescomplemented
161#2462C2214yescomplemented
162#2460C2214yes—
163#2460C2214yes—
164#2460C2214yescomplemented
165#2459C2214yescomplemented
166#2459C2214yescomplemented
167#2458C2214yes—
168#2458C2214yescomplemented
169#2451C2214yescomplemented
170#2449C2214yescomplemented
171#2449C2214yescomplemented
172#2447C2214yescomplemented
173#2445C2214yes—
174#2443C2214yes—
175#2443C2214yes—
176#2443C2214yescomplemented
177#2443C2214yescomplemented
178#2439C2214yescomplemented
179#2432C2212yes—
180#2427C2214yes—
181#2424C2214yes—
182#2424C2214yes—
183#2422C2214yes—
184#2418C2214yes—
185#2418C2214yes—
186#2418C2214yes—
187#2417C2214yescomplemented
188#2416C2214yes—
189#2414C2214yes—
190#2406C2212yes—
191#2406C2212yes—
192#2406C2212yes—
193#2405C2214yes—
194#2383C2214yescomplemented
195#2380C2212yes—
196#2379C2212yes—
197#2379C2211yescharacteristic, complemented
198#2374C2212yes—
199#2366C2211yescharacteristic, complemented
200#2365C2214yescomplemented
201#2361C2214yescomplemented
202D4×C4⋊C4C2214yescomplemented
203#2342C2214yes—
204#2336C2214yescomplemented
205#2333C2212yes—
206#2322C2212yes—
207#2322C2212yescomplemented
208#2315C2212yes—
209#2314C2214yescomplemented
210#2313C2212yescomplemented
211#2312C2212yes—
212#2311C2211yescharacteristic
213C4×C22⋊Q8C2212yes—
214C4×#123C2212yes—
215C4×#123C2212yescomplemented
216C4×#121C2214yescomplemented
217#2296C2211yescharacteristic
218C2×#390C2211yescharacteristic
219C22×#41C2311yescharacteristic
220C22×#41C2311yescharacteristic
221C23×D4C2311yescharacteristic
222#563—44no—
223#559—48no—
224#559—44no—
225#539—48no—
226#535—44no—
227#535—44no—
228#532—44no—
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2314yes—
231C2×C4⋊Q8C2312yes—
232C2×#127C2311yescharacteristic
233C2×#127C2312yes—
234C2×#127C2312yes—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#126C2314yes—
238C2×#125—48no—
239C2×#125C2314yes—
240C2×#125C2312yes—
241C2×#125C2314yes—
242C2×#125C2314yes—
243C2×#125C2314yes—
244C2×#124C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2312yes—
247C2×#124C2312yes—
248C2×#124C2312yes—
249C2×#124C2314yes—
250C2×#124C2314yes—
251C2×#124C2314yes—
252C2×#123C2312yes—
253C2×#123C2312yes—
254C2×#123C2312yes—
255C2×#123C2312yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×#123C2312yes—
259C2×#123C2312yes—
260C2×#123C2314yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×#121C2312yes—
266C2×#121C2312yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#120C2314yes—
272C2×#120C2314yes—
273#520—44no—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2314yes—
276C2×C4×Q8C2312yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2314yes—
286C2×#117C2311yescharacteristic
287C2×#117C2311yescharacteristic
288C2×#117C2314yes—
289C2×#117C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2312yes—
294C22×C4⋊C4C2312yes—
295C22×C4⋊C4C2312yes—
296C22×C4⋊C4C2312yes—
297C22×C4⋊C4C2312yes—
298C22×C22⋊C4C2312yes—
299C22×C22⋊C4C2314yes—
300C22×C22⋊C4C2312yes—
301C22×C42C2311yescharacteristic
302C22×C42C2312yes—
303#401C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#399C2314yes—
314#399C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
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#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#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
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#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#392C2314yes—
410#392C2314yes—
411#391C2312yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2312yes—
419#391C2312yes—
420#390C2312yes—
421#390C2314yes—
422#390C2314yes—
423#390C2314yes—
424#390C2314yes—
425#390C2314yes—
426#390C2314yes—
427#390C2312yes—
428#390C2314yes—
429#390C2312yes—
430#390C2312yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2312yes—
436#389C2314yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2312yes—
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#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#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#386C2312yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2312yes—
523#386C2312yes—
524#386C2314yes—
525#386C2314yes—
526#386C2312yes—
527#386C2312yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2312yes—
538#386C2312yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2312yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2312yes—
554#385C2314yes—
555#385C2312yes—
556#385C2314yes—
557#385C2314yes—
558#385C2312yes—
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#384C2314yes—
574#383C2314yes—
575#383C2314yes—
576#383C2314yes—
577#382C2312yes—
578#382C2314yes—
579#382C2314yes—
580#381C2312yes—
581#381C2312yes—
582#381C2312yes—
583#381C2314yes—
584#381C2312yes—
585#381C2312yes—
586#381C2312yes—
587#381C2312yes—
588#380C2314yes—
589#380C2312yes—
590#380C2312yes—
591#380C2312yes—
592#380C2312yes—
593#380C2314yes—
594#380C2314yes—
595#380C2312yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#379C2314yes—
603#379C2314yes—
604#379C2314yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2312yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2312yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2312yes—
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2314yes—
621C4×C22⋊C4C2314yes—
622C4×C22⋊C4C2314yes—
623C25C2412yes—
624C2×#41—24no—
625C2×#41—42no—
626C2×#41—42no—
627C2×#41—42no—
628C2×#41—42no—
629C2×#41—42no—
630C22×Q8C2411yescharacteristic
631C22×Q8C2412yes—
632C22×Q8C2411yescharacteristic
633C22×Q8C2414yes—
634C22×Q8C2412yes—
635C22×D4—42no—
636C22×D4—42no—
637C22×D4—42no—
638C22×D4C2414yes—
639C22×D4C2412yes—
640C22×D4C2414yes—
641C22×D4C2414yes—
642C22×D4C2414yes—
643C22×D4C2412yes—
644C22×D4C2412yes—
645C22×D4C2412yes—
646C22×D4C2411yescharacteristic
647C22×D4C2414yes—
648C22×D4C2411yescharacteristic
649C23×C4C2411yescharacteristic
650C23×C4C2412yes—
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2412yes—
655C23×C4C2412yes—
656C23×C4C2412yes—
657C23×C4C2411yescharacteristic
658C23×C4C2411yescharacteristic
659C23×C4C2414yes—
660C23×C4C2414yes—
661C23×C4C2412yes—
662C23×C4C2412yes—
663C23×C4C2412yes—
664C23×C4C2412yes—
665C4⋊Q8—42no—
666C4⋊Q8—48no—
667C4⋊Q8—44no—
668#127—24no—
669#127—28no—
670#127—44no—
671#126—48no—
672#126—48no—
673#126—48no—
674#125—216no—
675#125—48no—
676#125—44no—
677#125—48no—
678#125—48no—
679#124—24no—
680#124—44no—
681#124—42no—
682#124—44no—
683#124—44no—
684#124—48no—
685#124—48no—
686#124—48no—
687#123—28no—
688#123—28no—
689#123—44no—
690#123—44no—
691#123—44no—
692#123—48no—
693#123—48no—
694#123—44no—
695#123—48no—
696C22⋊Q8—48no—
697C22⋊Q8—48no—
698C22⋊Q8—44no—
699C22⋊Q8—44no—
700#121—28no—
701#121—48no—
702#121—48no—
703#121—48no—
704#121—44no—
705#121—48no—
706#120—48no—
707#120—48no—
708C4×Q8—44no—
709C4×Q8—44no—
710C4×Q8—48no—
711C4×D4—48no—
712C4×D4—48no—
713C4×D4—44no—
714C4×D4—44no—
715C4×D4—44no—
716C4×D4—48no—
717C4×D4—48no—
718C4×D4—48no—
719C4×D4—48no—
720#117—24no—
721#117—42no—
722#117—48no—
723#117—44no—
724C2×C4⋊C4—28no—
725C2×C4⋊C4—42no—
726C2×C4⋊C4—44no—
727C2×C4⋊C4—44no—
728C2×C4⋊C4—44no—
729C2×C4⋊C4—44no—
730C2×C4⋊C4—44no—
731C2×C4⋊C4—44no—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C22⋊C4—44no—
780C2×C22⋊C4—44no—
781C2×C22⋊C4—48no—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
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×C42—44no—
833C2×C42—42no—
834C2×C42C2412yes—
835C2×C42C2414yes—
836C2×C42C2412yes—
837C2×C42C2414yes—
838C2×C42C2411yescharacteristic
839C2×C42C2411yescharacteristic
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2414yes—
843C2×C42C2412yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2412yes—
848C2×C42C2414yes—
849C2×C42C2412yes—
850C2×C42C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
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—
899C24—24no—
900C24—42no—
901C24—42no—
902C24—42no—
903C24—42no—
904C24—42no—
905C24—42no—
906C24C2514yes—
907C24C2512yes—
908C24C2512yes—
909C24C2511yescharacteristic
910#41—416no—
911#41—88no—
912C2×Q8—22no—
913C2×Q8—22no—
914C2×Q8—24no—
915C2×Q8—41no—
916C2×Q8—41no—
917C2×Q8—42no—
918C2×Q8—44no—
919C2×Q8—41no—
920C2×Q8—44no—
921C2×Q8—42no—
922C2×Q8—44no—
923C2×Q8—41no—
924C2×Q8—42no—
925C2×Q8—42no—
926C2×Q8—42no—
927C2×D4—28no—
928C2×D4—24no—
929C2×D4—24no—
930C2×D4—28no—
931C2×D4—28no—
932C2×D4—24no—
933C2×D4—28no—
934C2×D4—24no—
935C2×D4—24no—
936C2×D4—22no—
937C2×D4—28no—
938C2×D4—41no—
939C2×D4—42no—
940C2×D4—44no—
941C2×D4—41no—
942C2×D4—42no—
943C2×D4—42no—
944C2×D4—42no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—42no—
950C2×D4—41no—
951C2×D4—42no—
952C2×D4—42no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—41no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—88no—
960C2×D4H(5,𝔽2)14yes—
961C22×C4—22no—
962C22×C4—22no—
963C22×C4—22no—
964C22×C4—24no—
965C22×C4—24no—
966C22×C4—24no—
967C22×C4—24no—
968C22×C4—24no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—24no—
972C22×C4—42no—
973C22×C4—44no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—44no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—44no—
982C22×C4—42no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—44no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—44no—
995C22×C4—42no—
996C22×C4—41no—
997C22×C4—41no—
998C22×C4—42no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—42no—
1002C22×C4C2512yes—
1003C22×C4C2514yes—
1004C22×C4C2514yes—
1005C22×C4C2514yes—
1006C22×C4C2514yes—
1007C22×C4C2514yes—
1008C22×C4C2512yes—
1009C22×C4C2514yes—
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2514yes—
1014C22×C4C2514yes—
1015C22×C4C2512yes—
1016C22×C4C2514yes—
1017C22×C4C2511yescharacteristic
1018C22×C4C2511yescharacteristic
1019C22×C4C2512yes—
1020C22×C4C2512yes—
1021C4⋊C4—24no—
1022C4⋊C4—24no—
1023C4⋊C4—24no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—22no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—28no—
1033C4⋊C4—24no—
1034C4⋊C4—28no—
1035C4⋊C4—42no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—42no—
1056C4⋊C4—44no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—42no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4H(5,𝔽2)14yes—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—24no—
1072C22⋊C4—24no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—24no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—44no—
1113C22⋊C4—42no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C42—28no—
1119C42—22no—
1120C42—22no—
1121C42—24no—
1122C42—24no—
1123C42—28no—
1124C42—42no—
1125C42—44no—
1126C42—44no—
1127C42—42no—
1128C42—42no—
1129C42—44no—
1130C42—44no—
1131C42—44no—
1132C42—42no—
1133C42—42no—
1134C42—44no—
1135C23—21no—
1136C23—22no—
1137C23—21no—
1138C23—22no—
1139C23—22no—
1140C23—24no—
1141C23—22no—
1142C23—24no—
1143C23—24no—
1144C23—22no—
1145C23—24no—
1146C23—22no—
1147C23—24no—
1148C23—24no—
1149C23—22no—
1150C23—24no—
1151C23—24no—
1152C23—24no—
1153C23—24no—
1154C23—24no—
1155C23—48no—
1156C23—84no—
1157C23—84no—
1158C23—162no—
1159C23—162no—
1160C23—162no—
1161C23—162no—
1162C23C2×H(5,𝔽2)14yes—
1163C23#58512yes—
1164C23C2611yescharacteristic
1165Q8—44no—
1166Q8—84no—
1167Q8—82no—
1168Q8—88no—
1169Q8—162no—
1170D4—44no—
1171D4—416no—
1172D4—48no—
1173D4—88no—
1174D4—84no—
1175D4—84no—
1176D4—82no—
1177D4—88no—
1178D4—88no—
1179D4—84no—
1180D4—164no—
1181C2×C4—28no—
1182C2×C4—21no—
1183C2×C4—22no—
1184C2×C4—21no—
1185C2×C4—24no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—24no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
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—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—48no—
1232C2×C4—48no—
1233C2×C4—84no—
1234C2×C4—84no—
1235C2×C4—84no—
1236C2×C4—84no—
1237C2×C4—84no—
1238C2×C4—84no—
1239C2×C4—84no—
1240C2×C4—84no—
1241C2×C4—88no—
1242C2×C4—161no—
1243C2×C4—161no—
1244C2×C4—162no—
1245C2×C4—164no—
1246C2×C4C2×H(5,𝔽2)12yes—
1247C2×C4C2×H(5,𝔽2)14yes—
1248C2×C4C2×H(5,𝔽2)12yes—
1249C2×C4#58514yes—
1250C22—22no—
1251C22—24no—
1252C22—28no—
1253C22—24no—
1254C22—42no—
1255C22—41no—
1256C22—42no—
1257C22—41no—
1258C22—42no—
1259C22—44no—
1260C22—42no—
1261C22—44no—
1262C22—42no—
1263C22—44no—
1264C22—42no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—168no—
1273C22C22×H(5,𝔽2)11yescharacteristic
1274C22C22×H(5,𝔽2)11yescharacteristic
1275C22C2×#58512yes—
1276C22C2×#58511yescharacteristic
1277C222−1+612yes—
1278C4—24no—
1279C4—22no—
1280C4—22no—
1281C4—24no—
1282C4—44no—
1283C4—42no—
1284C4—42no—
1285C4—44no—
1286C4—42no—
1287C4—42no—
1288C4—44no—
1289C4—44no—
1290C4—42no—
1291C4—42no—
1292C4—44no—
1293C4—44no—
1294C4—44no—
1295C4—44no—
1296C4—44no—
1297C2—44no—
1298C2—42no—
1299C2—82no—
1300C2—84no—
1301C2#6281811yescharacteristic
1302C2#6289812yes—
1303C2#6290712yes—
1304C2#6302111yescharacteristic
1305C2#6304811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35533C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59628C2semidirect
2. #59070C2semidirect
3. #58035C2semidirect
4. #55549C2semidirect
5. #53557C2semidirect
6. #52054C2semidirect
7. #52025C2semidirect
8. #51201C2semidirect
9. #50237C2semidirect
10. #49710C2semidirect
11. #48343C2semidirect
12. #48184C2semidirect
13. #48059C2semidirect
14. #47255C2semidirect
15. #46359C2semidirect
16. #46228C2semidirect
17. #45692C2semidirect
18. #39540C2semidirect
19. #39016C2semidirect
20. #38801C2semidirect
21. #37717C2semidirect
23. #35453C2semidirect
24. C2×#563C22semidirect
26. C2×#559C22semidirect
31. C22×#125C22semidirect
33. #2852C22semidirect
35. #2830C22semidirect
36. #2830C22semidirect
37. #2827C22semidirect
38. #2820C22semidirect
40. #2810C22semidirect
41. #2809C22semidirect
43. #2800C22semidirect
44. #2798C22semidirect
45. #2796C22semidirect
46. #2786C22semidirect
47. #2786C22semidirect
48. #2784C22semidirect
49. #2781C22semidirect
50. #2780C22semidirect
52. #2773C22semidirect
54. #2762C22semidirect
56. #2759C22semidirect
57. #2757C22semidirect
58. #2754C22semidirect
59. #2753C22semidirect
61. #2750C22semidirect
62. #2749C22semidirect
63. #2746C22semidirect
64. #2745C22semidirect
65. #2742C22semidirect
66. #2740C22semidirect
67. #2737C22semidirect
68. #2734C22semidirect
69. #2734C22semidirect
71. #2726C22semidirect
72. #2721C22semidirect
73. #2720C22semidirect
76. #2717C22semidirect
77. #2717C22semidirect
78. #2716C22semidirect
79. #2715C22semidirect
80. #2715C22semidirect
81. #2712C22semidirect
86. #2709C22semidirect
89. #2707C22semidirect
90. #2700C22semidirect
93. #2694C22semidirect
95. #2691C22semidirect
96. #2690C22semidirect
104. #2666C22semidirect
105. #2664C22semidirect
107. #2651C22semidirect
108. #2638C22semidirect
109. #2636C22semidirect
110. #2633C22semidirect
115. #2600C22semidirect
117. #2598C22semidirect
118. #2595C22semidirect
119. #2594C22semidirect
121. #2589C22semidirect
123. #2579C22semidirect
124. #2578C22semidirect
126. #2576C22semidirect
128. #2574C22semidirect
129. #2567C22semidirect
131. #2556C22semidirect
136. #2524C22semidirect
137. #2524C22semidirect
138. #2522C22semidirect
140. #2521C22semidirect
141. #2491C22semidirect
142. #2491C22semidirect
144. #2486C22semidirect
145. #2484C22semidirect
146. #2484C22semidirect
147. #2481C22semidirect
150. #2476C22semidirect
152. #2475C22semidirect
154. #2473C22semidirect
155. #2473C22semidirect
157. #2468C22semidirect
158. #2466C22semidirect
159. #2462C22semidirect
160. #2462C22semidirect
161. #2462C22semidirect
164. #2460C22semidirect
165. #2459C22semidirect
166. #2459C22semidirect
168. #2458C22semidirect
169. #2451C22semidirect
170. #2449C22semidirect
171. #2449C22semidirect
172. #2447C22semidirect
176. #2443C22semidirect
177. #2443C22semidirect
178. #2439C22semidirect
187. #2417C22semidirect
194. #2383C22semidirect
197. #2379C22semidirect
199. #2366C22semidirect
200. #2365C22semidirect
201. #2361C22semidirect
202. D4×C4⋊C4C22semidirect
204. #2336C22semidirect
207. #2322C22semidirect
209. #2314C22semidirect
210. #2313C22semidirect
215. C4×#123C22semidirect
216. C4×#121C22semidirect

Maximal subgroups

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

subgroupindex
#596282
#590702
#580352
#555492
#535572
#520542
#520252
#512012
#502372
#497102
#483432
#481842
#480592
#472552
#463592
#462282
#456922
#395402
#390162
#388012
#377172
#355332
#354532