Finite Group Databasebeta

← #8824379

Subgroups — #8824379

Order 512.

4184 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59923C211yesmaximal, characteristic, complemented
2#56461C214yesmaximal, complemented
3#53951C214yesmaximal, complemented
4#53302C212yesmaximal, complemented
5#51603C214yesmaximal, complemented
6#51542C212yesmaximal
7#50183C212yesmaximal, complemented
8#49877C214yesmaximal, complemented
9#49008C214yesmaximal, complemented
10#48829C214yesmaximal, complemented
11#48433C214yesmaximal, complemented
12#47173C212yesmaximal
13#46453C212yesmaximal, complemented
14#46295C212yesmaximal, complemented
15#46205C211yesmaximal, characteristic, complemented
16#44713C214yesmaximal, complemented
17#43641C214yesmaximal, complemented
18#42623C214yesmaximal, complemented
19#38783C212yesmaximal, complemented
20#38447C212yesmaximal, complemented
21#37135C212yesmaximal, complemented
22#36375C212yesmaximal
23#35307C211yesmaximal, characteristic
24C2×#563C2212yes—
25C2×#552C2212yes—
26C2×#536C2211yescharacteristic
27C2×C4×#41C2211yescharacteristic
28#2855C2212yes—
29#2855C2212yes—
30#2855C2212yes—
31#2855C2212yes—
32#2851C2212yes—
33#2839C2214yes—
34#2833C2212yes—
35#2833C2212yes—
36#2833C2214yes—
37#2817C2212yes—
38#2811C2211yescharacteristic
39#2809C2211yescharacteristic
40#2806C2212yes—
41#2806C2214yes—
42#2805C2212yes—
43#2805C2212yes—
44#2805C2212yes—
45#2802C2214yes—
46#2802C2214yes—
47#2802C2214yes—
48#2792C2214yes—
49#2792C2214yes—
50#2791C2214yes—
51#2791C2214yes—
52#2791C2214yes—
53#2789C2214yes—
54#2789C2214yes—
55#2789C2214yes—
56#2789C2214yes—
57#2789C2214yes—
58#2787C2214yes—
59#2784C2212yes—
60#2776C2214yes—
61#2774C2214yes—
62#2774C2214yes—
63#2766C2214yes—
64#2766C2214yes—
65#2765C2214yes—
66#2765C2214yes—
67#2762C2214yes—
68#2755C2214yes—
69#2755C2214yes—
70#2755C2214yes—
71#2755C2214yes—
72#2750C2214yes—
73#2745C2214yes—
74#2745C2214yes—
75#2745C2214yes—
76#2744C2214yes—
77#2744C2214yes—
78#2739C2214yes—
79#2739C2214yes—
80#2738C2214yes—
81#2734C2211yescharacteristic
82#2734C2211yescharacteristic
83#2734C2212yes—
84#2734C2212yes—
85#2726C2214yes—
86#2726C2212yes—
87#2726C2212yes—
88#2724C2212yes—
89#2722C2214yes—
90#2720C2214yes—
91#2719C2214yes—
92#2717C2214yes—
93#2713C2214yes—
94#2713C2214yes—
95#2713C2214yes—
96#2698C2214yes—
97#2698C2214yes—
98#2698C2214yes—
99#2698C2214yes—
100#2698C2214yes—
101#2689C2214yes—
102#2689C2214yes—
103#2687C2214yes—
104#2680C2214yes—
105#2680C2214yes—
106#2667C2212yes—
107#2666C2214yes—
108#2660C2214yes—
109#2655C2214yes—
110#2655C2214yes—
111#2647C2214yes—
112#2627C2214yes—
113#2625C2212yes—
114#2625C2214yes—
115#2625C2212yes—
116#2625C2212yes—
117#2612C2214yes—
118#2612C2214yes—
119#2611C2214yes—
120#2608C2212yes—
121#2606C2214yes—
122#2588C2214yes—
123#2588C2214yes—
124#2586C2214yes—
125#2586C2212yes—
126#2586C2212yes—
127#2585C2214yes—
128#2584C2212yes—
129#2583C2212yes—
130#2583C2214yes—
131#2581C2212yes—
132#2577C2214yes—
133#2576C2214yes—
134#2570C2214yes—
135#2569C2214yes—
136#2553C2214yes—
137#2553C2214yes—
138#2550C2214yes—
139#2550C2214yes—
140#2549C2214yes—
141#2549C2214yes—
142#2533C2214yes—
143#2530C2214yes—
144#2530C2214yes—
145#2528C2214yes—
146#2527C2214yes—
147#2523C2214yes—
148#2522C2214yes—
149#2520C2214yes—
150#2511C2214yes—
151#2509C2214yes—
152#2508C2214yes—
153#2507C2214yes—
154#2506C2214yes—
155#2499C2214yes—
156#2496C2214yes—
157#2494C2214yes—
158#2494C2214yes—
159#2493C2214yes—
160#2486C2212yes—
161#2485C2212yes—
162#2484C2212yes—
163#2478C2214yes—
164#2478C2214yes—
165#2478C2214yes—
166#2478C2214yes—
167#2475C2214yes—
168#2475C2214yes—
169#2475C2214yes—
170#2473C2214yes—
171#2473C2214yes—
172#2470C2214yes—
173#2466C2214yes—
174#2462C2214yes—
175#2462C2214yes—
176#2451C2214yes—
177#2447C2214yes—
178#2446C2214yes—
179#2442C2214yes—
180#2440C2214yes—
181#2440C2214yes—
182#2438C2214yes—
183#2438C2214yes—
184#2434C2212yes—
185#2434C2212yes—
186#2419C2214yes—
187#2419C2214yes—
188#2419C2214yes—
189#2417C2212yes—
190#2415C2212yes—
191#2406C2214yes—
192#2401C2214yes—
193#2382C2214yes—
194#2381C2212yes—
195#2378C2212yes—
196#2372C2212yes—
197#2371C2214yes—
198#2369C2212yes—
199#2368C2214yes—
200#2359C2214yes—
201#2352C2212yes—
202#2346C2212yes—
203#2344C2214yes—
204#2343C2214yes—
205#2335C2214yes—
206#2332C2212yes—
207#2332C2212yes—
208#2330C2214yes—
209#2330C2214yes—
210#2316C2211yescharacteristic
211#2313C2214yes—
212#2311C2211yescharacteristic
213#2310C2211yescharacteristic
214C4×C22⋊Q8C2212yes—
215#2296C2212yes—
216#2296C2211yescharacteristic
217C2×#391C2211yescharacteristic
218C2×#389C2212yes—
219C22×#41C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221#563—48no—
222#552—48no—
223#536—44no—
224C2×C4⋊Q8C2312yes—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×#126C2314yes—
230C2×#126C2314yes—
231C2×#126C2314yes—
232C2×#125C2314yes—
233C2×#125C2312yes—
234C2×#125C2314yes—
235C2×#125C2314yes—
236C2×#125C2314yes—
237C2×#124C2312yes—
238C2×#123C2314yes—
239C2×#123C2314yes—
240C2×#123C2314yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2312yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2314yes—
251C4×#41—44no—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2312yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2312yes—
257C2×#117C2312yes—
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2312yes—
262C2×#117C2314yes—
263C2×#117C2312yes—
264C2×#117C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2314yes—
269C22×C42C2311yescharacteristic
270C22×C42C2312yes—
271#401C2314yes—
272#401C2314yes—
273#401C2314yes—
274#401C2314yes—
275#401C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2312yes—
289#400C2312yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#399C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2312yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2312yes—
318#398C2314yes—
319#398C2312yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2312yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2312yes—
369#395C2312yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#394C2314yes—
381#394C2314yes—
382#393C2314yes—
383#391C2312yes—
384#391C2314yes—
385#391C2312yes—
386#391C2312yes—
387#391C2311yescharacteristic
388#391C2314yes—
389#391C2312yes—
390#391C2312yes—
391#391C2312yes—
392#391C2311yescharacteristic
393#391C2314yes—
394#391C2314yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2312yes—
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2312yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2312yes—
408#391C2312yes—
409#390C2312yes—
410#389C2314yes—
411#389C2314yes—
412#389C2312yes—
413#389C2312yes—
414#389C2314yes—
415#389C2312yes—
416#389C2312yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2314yes—
427#389C2314yes—
428#389C2312yes—
429#389C2314yes—
430#389C2314yes—
431#389C2312yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2312yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#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#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
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#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#384C2314yes—
557#384C2314yes—
558#384C2314yes—
559#383C2314yes—
560#383C2314yes—
561#382C2314yes—
562#382C2314yes—
563#382C2312yes—
564#382C2314yes—
565#382C2314yes—
566#382C2314yes—
567#382C2314yes—
568#382C2314yes—
569#381C2312yes—
570#381C2312yes—
571#381C2314yes—
572#381C2314yes—
573#381C2314yes—
574#381C2314yes—
575#381C2314yes—
576#381C2314yes—
577#381C2312yes—
578#380C2312yes—
579#380C2312yes—
580#380C2314yes—
581#380C2314yes—
582#380C2312yes—
583#380C2314yes—
584#380C2312yes—
585#380C2312yes—
586#380C2314yes—
587#380C2312yes—
588#380C2312yes—
589#380C2312yes—
590#380C2314yes—
591#380C2312yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2312yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613#376C2314yes—
614#376C2314yes—
615#376C2314yes—
616C2×#95C2314yes—
617C2×#95C2314yes—
618C2×#41—24no—
619C2×#41—42no—
620C2×#41—42no—
621C22×Q8—42no—
622C22×Q8—42no—
623C22×Q8—42no—
624C22×Q8C2411yescharacteristic
625C22×Q8C2412yes—
626C22×Q8C2411yescharacteristic
627C22×Q8C2411yescharacteristic
628C22×Q8C2412yes—
629C22×Q8C2412yes—
630C22×Q8C2412yes—
631C22×Q8C2412yes—
632C22×D4C2412yes—
633C22×D4C2411yescharacteristic
634C23×C4C2411yescharacteristic
635C23×C4C2412yes—
636C23×C4C2412yes—
637C23×C4C2412yes—
638C23×C4C2414yes—
639C23×C4C2414yes—
640C23×C4C2412yes—
641C23×C4C2412yes—
642C23×C4C2412yes—
643C4⋊Q8—44no—
644C4⋊Q8—44no—
645C4⋊Q8—44no—
646C4⋊Q8—44no—
647C4⋊Q8—44no—
648#126—48no—
649#126—48no—
650#126—48no—
651#125—216no—
652#125—44no—
653#125—48no—
654#125—48no—
655#125—48no—
656#124—28no—
657#123—216no—
658#123—48no—
659#123—48no—
660C22⋊Q8—28no—
661C22⋊Q8—44no—
662C22⋊Q8—44no—
663C22⋊Q8—44no—
664C22⋊Q8—44no—
665C22⋊Q8—44no—
666C22⋊Q8—44no—
667C22⋊Q8—44no—
668C22⋊Q8—48no—
669C22⋊Q8—48no—
670C4×Q8—44no—
671C4×Q8—44no—
672C4×D4—28no—
673C4×D4—44no—
674C4×D4—44no—
675#117—28no—
676#117—42no—
677#117—44no—
678#117—44no—
679#117—44no—
680#117—48no—
681#117—42no—
682#117—42no—
683C2×C4⋊C4—28no—
684C2×C4⋊C4—48no—
685C2×C4⋊C4—42no—
686C2×C4⋊C4—44no—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2412yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C22⋊C4C2412yes—
752C2×C22⋊C4C2412yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2411yescharacteristic
763C2×C22⋊C4C2411yescharacteristic
764C2×C22⋊C4C2412yes—
765C2×C22⋊C4C2412yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C42—42no—
772C2×C42—44no—
773C2×C42C2412yes—
774C2×C42C2414yes—
775C2×C42C2412yes—
776C2×C42C2414yes—
777C2×C42C2414yes—
778C2×C42C2411yescharacteristic
779C2×C42C2412yes—
780C2×C42C2414yes—
781C2×C42C2414yes—
782C2×C42C2412yes—
783C2×C42C2412yes—
784C2×C42C2412yes—
785C2×C42C2414yes—
786C2×C42C2412yes—
787C2×C42C2412yes—
788C2×C42C2412yes—
789C2×C42C2412yes—
790C2×C42C2414yes—
791C2×C42C2414yes—
792C2×C42C2414yes—
793C2×C42C2414yes—
794C2×C42C2411yescharacteristic
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2412yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2412yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
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#95C2412yes—
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#95C2412yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865C24C2512yes—
866C24C2511yescharacteristic
867#41—416no—
868C2×Q8—22no—
869C2×Q8—24no—
870C2×Q8—24no—
871C2×Q8—22no—
872C2×Q8—22no—
873C2×Q8—41no—
874C2×Q8—41no—
875C2×Q8—42no—
876C2×Q8—41no—
877C2×Q8—41no—
878C2×Q8—42no—
879C2×Q8—41no—
880C2×Q8—41no—
881C2×Q8—42no—
882C2×Q8—42no—
883C2×Q8—42no—
884C2×Q8—42no—
885C2×Q8—42no—
886C2×Q8—42no—
887C2×Q8—42no—
888C2×Q8—42no—
889C2×Q8—42no—
890C2×Q8—44no—
891C2×Q8—88no—
892C2×D4—24no—
893C2×D4—24no—
894C2×D4—41no—
895C2×D4—41no—
896C2×D4—42no—
897C2×D4H(5,𝔽2)14yes—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—28no—
905C22×C4—24no—
906C22×C4—24no—
907C22×C4—24no—
908C22×C4—24no—
909C22×C4—24no—
910C22×C4—28no—
911C22×C4—24no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—44no—
917C22×C4—44no—
918C22×C4—42no—
919C22×C4—44no—
920C22×C4—44no—
921C22×C4—42no—
922C22×C4—44no—
923C22×C4—42no—
924C22×C4C2514yes—
925C22×C4C2514yes—
926C22×C4C2512yes—
927C22×C4C2514yes—
928C22×C4C2514yes—
929C22×C4C2512yes—
930C22×C4C2512yes—
931C22×C4C2512yes—
932C22×C4C2514yes—
933C22×C4C2512yes—
934C22×C4C2512yes—
935C22×C4C2512yes—
936C22×C4C2514yes—
937C22×C4C2514yes—
938C22×C4C2512yes—
939C22×C4C2514yes—
940C22×C4C2514yes—
941C22×C4C2511yescharacteristic
942C22×C4C2512yes—
943C22×C4C2514yes—
944C22×C4C2511yescharacteristic
945C4⋊C4—24no—
946C4⋊C4—28no—
947C4⋊C4—28no—
948C4⋊C4—28no—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—28no—
952C4⋊C4—28no—
953C4⋊C4—28no—
954C4⋊C4—28no—
955C4⋊C4—28no—
956C4⋊C4—28no—
957C4⋊C4—28no—
958C4⋊C4—28no—
959C4⋊C4—24no—
960C4⋊C4—44no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—42no—
964C4⋊C4—44no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—42no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—44no—
989C4⋊C4—42no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C42−1+418yes—
1009C22⋊C4—24no—
1010C22⋊C4—24no—
1011C22⋊C4—28no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—28no—
1017C22⋊C4—28no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—42no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—42no—
1028C22⋊C4—44no—
1029C42—24no—
1030C42—24no—
1031C42—28no—
1032C42—28no—
1033C42—41no—
1034C42—41no—
1035C42—42no—
1036C42—42no—
1037C42—42no—
1038C42—44no—
1039C42—44no—
1040C42—44no—
1041C42—44no—
1042C42—42no—
1043C42—44no—
1044C42—44no—
1045C42—44no—
1046C42—44no—
1047C42—42no—
1048C42—42no—
1049C42—42no—
1050C42—42no—
1051C23—21no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—21no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23C2×H(5,𝔽2)14yes—
1062C23#58512yes—
1063C23C2611yescharacteristic
1064Q8—44no—
1065Q8—84no—
1066Q8—82no—
1067Q8—82no—
1068Q8—84no—
1069Q8—162no—
1070Q8—162no—
1071Q8—162no—
1072D4—44no—
1073D4—48no—
1074C2×C4—28no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—24no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—48no—
1133C2×C4—48no—
1134C2×C4—48no—
1135C2×C4—84no—
1136C2×C4—88no—
1137C2×C4—84no—
1138C2×C4—88no—
1139C2×C4—84no—
1140C2×C4C2×H(5,𝔽2)12yes—
1141C2×C4C2×2−1+418yes—
1142C2×C4C2×2−1+414yes—
1143C2×C4#58512yes—
1144C22—22no—
1145C22—22no—
1146C22—22no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—42no—
1156C22C22×H(5,𝔽2)11yescharacteristic
1157C22C22×2−1+412yes—
1158C22C2×#58511yescharacteristic
1159C22C2×#58511yescharacteristic
1160C222−1+612yes—
1161C4—22no—
1162C4—22no—
1163C4—24no—
1164C4—28no—
1165C4—44no—
1166C4—42no—
1167C4—42no—
1168C4—44no—
1169C4—42no—
1170C4—42no—
1171C4—42no—
1172C4—44no—
1173C4—44no—
1174C4—44no—
1175C4—44no—
1176C4—42no—
1177C4—42no—
1178C4—42no—
1179C4—44no—
1180C4—44no—
1181C4—44no—
1182C2—42no—
1183C2—44no—
1184C2#6282011yescharacteristic
1185C2#6291512yes—
1186C2#6295012yes—
1187C2#6303811yescharacteristic
1188C2#6306411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59923C2semidirect
2. #56461C2semidirect
3. #53951C2semidirect
4. #53302C2semidirect
5. #51603C2semidirect
7. #50183C2semidirect
8. #49877C2semidirect
9. #49008C2semidirect
10. #48829C2semidirect
11. #48433C2semidirect
13. #46453C2semidirect
14. #46295C2semidirect
15. #46205C2semidirect
16. #44713C2semidirect
17. #43641C2semidirect
18. #42623C2semidirect
19. #38783C2semidirect
20. #38447C2semidirect
21. #37135C2semidirect

Maximal subgroups

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

subgroupindex
#599232
#564612
#539512
#533022
#516032
#515422
#501832
#498772
#490082
#488292
#484332
#471732
#464532
#462952
#462052
#447132
#436412
#426232
#387832
#384472
#371352
#363752
#353072