Finite Group Databasebeta

← #7689024

Subgroups — #7689024

Order 512.

5309 conjugacy classes of subgroups.

The subgroup lattice has 1559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59865C211yesmaximal, characteristic, complemented
2#59799C212yesmaximal, complemented
3#59741C214yesmaximal, complemented
4#59738C214yesmaximal, complemented
5#59308C212yesmaximal, complemented
6#59307C212yesmaximal, complemented
7#45330C211yesmaximal, characteristic, complemented
8#45126C212yesmaximal, complemented
9#45115C211yesmaximal, characteristic, complemented
10#44841C212yesmaximal, complemented
11#44260C214yesmaximal, complemented
12#43432C212yesmaximal, complemented
13#40135C214yesmaximal, complemented
14#40132C214yesmaximal, complemented
15#39462C212yesmaximal, complemented
16#39462C212yesmaximal, complemented
17#36514C212yesmaximal, complemented
18#36500C214yesmaximal, complemented
19#36486C212yesmaximal, complemented
20#36415C211yesmaximal, characteristic, complemented
21#36191C212yesmaximal, complemented
22#36087C211yesmaximal, characteristic, complemented
23#35756C211yesmaximal, characteristic, complemented
24#35682C212yesmaximal, complemented
25#34962C212yesmaximal, complemented
26#34925C211yesmaximal, characteristic, complemented
27#34208C212yesmaximal, complemented
28#34206C212yesmaximal, complemented
29C4×#553C212yesmaximal, complemented
30C2×#555C2211yescharacteristic
31C2×#553C2212yes—
32C2×#547C2211yescharacteristic
33C2×#532C2212yes—
34C2×#532C2212yes—
35C2×#520C2212yes—
36C2×#520C2211yescharacteristic
37C2×#520C2211yescharacteristic
38#2866C2214yes—
39#2862C2211yescharacteristic
40#2853C2214yes—
41#2851C2212yes—
42#2851C2212yes—
43#2850C2212yes—
44#2799C2212yes—
45#2797C2214yes—
46#2794C2212yes—
47#2772C2214yes—
48#2764C2212yes—
49#2759C2214yes—
50#2757C2214yes—
51#2753C2214yes—
52#2741C2214yes—
53#2740C2214yes—
54#2737C2214yes—
55#2728C2212yes—
56#2716C2214yes—
57#2716C2214yes—
58#2714C2214yes—
59#2714C2214yes—
60#2709C2212yes—
61#2703C2214yes—
62#2696C2214yes—
63#2693C2212yes—
64#2688C2214yes—
65#2688C2214yes—
66#2673C2214yes—
67#2673C2214yes—
68#2632C2212yes—
69#2631C2212yes—
70#2630C2214yes—
71#2615C2212yes—
72#2615C2211yescharacteristic
73#2615C2211yescharacteristic
74#2602C2214yes—
75#2600C2212yes—
76#2599C2212yes—
77#2598C2212yes—
78#2597C2214yes—
79#2596C2214yes—
80#2595C2214yes—
81#2595C2214yes—
82#2594C2214yes—
83#2593C2212yes—
84#2592C2212yes—
85#2590C2214yes—
86#2586C2212yes—
87#2578C2214yes—
88#2577C2214yes—
89#2577C2214yes—
90#2576C2214yes—
91#2576C2214yes—
92#2574C2214yes—
93#2574C2214yes—
94#2572C2212yes—
95#2570C2212yes—
96#2570C2212yes—
97#2563C2211yescharacteristic
98#2562C2212yes—
99#2562C2212yes—
100#2560C2214yes—
101#2559C2214yes—
102#2557C2214yes—
103#2557C2214yes—
104#2557C2214yes—
105#2557C2214yes—
106#2557C2214yes—
107#2555C2211yescharacteristic
108#2555C2212yes—
109#2555C2211yescharacteristic
110#2554C2214yes—
111#2554C2214yes—
112#2551C2211yescharacteristic
113#2547C2211yescharacteristic
114#2543C2214yes—
115#2541C2212yes—
116#2540C2212yes—
117#2537C2211yescharacteristic
118#2535C2212yes—
119#2535C2212yes—
120#2533C2214yes—
121#2531C2214yes—
122#2523C2212yes—
123#2520C2214yes—
124#2520C2214yes—
125#2520C2214yes—
126#2518C2214yes—
127#2516C2214yes—
128#2516C2214yes—
129#2510C2214yes—
130#2504C2211yescharacteristic
131#2501C2211yescharacteristic
132#2500C2212yes—
133#2499C2212yes—
134#2497C2212yes—
135#2496C2212yes—
136#2495C2212yes—
137#2494C2212yes—
138#2493C2214yes—
139#2491C2212yes—
140#2491C2212yes—
141#2487C2211yescharacteristic
142#2486C2211yescharacteristic
143#2486C2212yes—
144#2486C2212yes—
145#2485C2212yes—
146#2485C2212yes—
147#2485C2212yes—
148#2467C2214yes—
149#2465C2214yes—
150#2464C2214yes—
151#2464C2214yes—
152#2464C2214yes—
153#2463C2214yes—
154#2461C2214yes—
155#2461C2214yes—
156#2459C2214yes—
157#2459C2214yes—
158#2459C2214yes—
159#2458C2214yes—
160#2457C2214yes—
161#2456C2214yes—
162#2456C2214yes—
163#2456C2214yes—
164#2456C2214yes—
165#2450C2214yes—
166#2450C2214yes—
167#2444C2214yes—
168#2440C2212yes—
169#2440C2212yes—
170#2439C2212yes—
171#2439C2212yes—
172#2431C2212yes—
173#2428C2212yes—
174#2428C2212yes—
175#2425C2214yes—
176#2416C2212yes—
177#2416C2212yes—
178#2414C2212yes—
179#2414C2212yes—
180#2407C2214yes—
181#2396C2212yes—
182#2392C2212yes—
183#2388C2211yescharacteristic
184#2388C2211yescharacteristic
185#2388C2212yes—
186#2388C2214yes—
187#2374C2214yes—
188#2374C2214yes—
189#2374C2212yes—
190#2373C2214yes—
191#2370C2212yes—
192#2368C2214yes—
193#2368C2214yes—
194#2367C2214yes—
195#2367C2214yes—
196#2366C2214yes—
197#2365C2214yes—
198#2364C2214yes—
199#2364C2214yes—
200#2364C2214yes—
201#2364C2214yes—
202#2364C2214yes—
203#2364C2214yes—
204#2363C2212yes—
205#2361C2212yes—
206#2357C2212yes—
207#2354C2212yes—
208#2354C2212yes—
209#2353C2214yes—
210#2352C2212yes—
211#2352C2212yes—
212#2352C2212yes—
213#2352C2212yes—
214#2352C2212yes—
215#2352C2212yes—
216#2352C2212yes—
217#2352C2212yes—
218#2352C2212yes—
219#2352C2212yes—
220#2352C2212yes—
221D4×C4⋊C4C2212yes—
222D4×C4⋊C4C2212yes—
223#2347C2212yes—
224#2347C2211yescharacteristic
225#2347C2211yescharacteristic
226#2345C2212yes—
227#2345C2212yes—
228#2328C2214yes—
229#2327C2214yes—
230#2325C2214yes—
231#2325C2214yes—
232#2311C2212yes—
233#2311C2212yes—
234#2311C2212yes—
235#2311C2212yes—
236C4×#127C2211yescharacteristic
237C4×#125C2212yes—
238C4×#126C2214yes—
239C4×#126C2214yes—
240C4×#124C2214yes—
241C4×#124C2214yes—
242C4×#123C2214yes—
243C4×#123C2214yes—
244C4×#121C2212yes—
245C4×#121C2212yes—
246C4×#121C2214yes—
247C4×#121C2214yes—
248C4×#121C2212yes—
249C4×#121C2212yes—
250C4×#121C2214yes—
251#2297C2212yes—
252#2285C2212yes—
253C2×#382C2212yes—
254C42×D4C2211yescharacteristic
255C42×D4C2212yes—
256C42×D4C2214yes—
257C4×#117C2212yes—
258C2×C4×C4⋊C4C2212yes—
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C22×#41C2312yes—
262C22×#41C2312yes—
263#555—44no—
264#553—216no—
265#547—44no—
266#532—216no—
267#532—216no—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×#127C2312yes—
273C2×#127C2312yes—
274C2×#127C2311yescharacteristic
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#125C2312yes—
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2312yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2314yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2311yescharacteristic
307C2×#121C2312yes—
308C2×#121C2311yescharacteristic
309C2×#121C2314yes—
310C2×#121C2312yes—
311C2×#121C2312yes—
312C2×#121C2314yes—
313#520—44no—
314#520—48no—
315#520—44no—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2314yes—
318C2×C4×Q8C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2314yes—
344C2×C4×D4C2312yes—
345C2×#117C2312yes—
346C2×#117C2311yescharacteristic
347C2×#117C2311yescharacteristic
348C2×#117C2312yes—
349C2×#117C2312yes—
350C2×#117C2312yes—
351C2×#117C2312yes—
352C2×#117C2312yes—
353C22×C4⋊C4C2312yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2312yes—
356C22×C4⋊C4C2312yes—
357C22×C4⋊C4C2312yes—
358C22×C4⋊C4C2311yescharacteristic
359C22×C4⋊C4C2311yescharacteristic
360C22×C42C2312yes—
361C22×C42C2312yes—
362C22×C42C2312yes—
363C22×C42C2314yes—
364#401C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2312yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#399C2312yes—
374#399C2312yes—
375#399C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2312yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2312yes—
390#397C2312yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2312yes—
395#397C2312yes—
396#397C2314yes—
397#397C2312yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2311yescharacteristic
406#395C2311yescharacteristic
407#395C2312yes—
408#394C2312yes—
409#394C2314yes—
410#394C2314yes—
411#394C2311yescharacteristic
412#394C2312yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2311yescharacteristic
418#394C2314yes—
419#394C2312yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2312yes—
424#394C2312yes—
425#394C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2311yescharacteristic
430#393C2312yes—
431#393C2312yes—
432#393C2314yes—
433#393C2311yescharacteristic
434#393C2312yes—
435#392C2312yes—
436#392C2311yescharacteristic
437#392C2314yes—
438#392C2314yes—
439#392C2312yes—
440#392C2314yes—
441#392C2314yes—
442#392C2314yes—
443#392C2311yescharacteristic
444#392C2314yes—
445#392C2312yes—
446#392C2312yes—
447#392C2314yes—
448#392C2312yes—
449#392C2312yes—
450#392C2312yes—
451#392C2314yes—
452#392C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2312yes—
459#391C2312yes—
460#391C2314yes—
461#391C2312yes—
462#391C2314yes—
463#390C2314yes—
464#390C2311yescharacteristic
465#390C2311yescharacteristic
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#390C2314yes—
470#390C2314yes—
471#390C2314yes—
472#390C2314yes—
473#390C2314yes—
474#390C2312yes—
475#390C2314yes—
476#390C2314yes—
477#390C2312yes—
478#390C2312yes—
479#390C2314yes—
480#390C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#388C2312yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2312yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2312yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2312yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2312yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2312yes—
596#386C2312yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2312yes—
604#386C2312yes—
605#386C2314yes—
606#386C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2312yes—
617#385C2314yes—
618#385C2314yes—
619#384C2311yescharacteristic
620#384C2312yes—
621#384C2312yes—
622#383C2314yes—
623#383C2314yes—
624#383C2312yes—
625#383C2312yes—
626#382C2312yes—
627#382C2312yes—
628#382C2312yes—
629#382C2312yes—
630#382C2312yes—
631#382C2312yes—
632#382C2314yes—
633#382C2314yes—
634#381C2314yes—
635#381C2314yes—
636#381C2314yes—
637#381C2312yes—
638#380C2312yes—
639#380C2311yescharacteristic
640#380C2311yescharacteristic
641#380C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2312yes—
645#380C2312yes—
646#380C2312yes—
647#380C2312yes—
648#380C2312yes—
649#380C2312yes—
650#380C2312yes—
651#380C2312yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2314yes—
657#380C2312yes—
658#380C2314yes—
659#380C2314yes—
660#380C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2311yescharacteristic
703C4×C22⋊C4C2311yescharacteristic
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714#376C2314yes—
715C2×#95C2314yes—
716C2×#95C2314yes—
717C2×#95C2314yes—
718C43C2314yes—
719C43C2311yescharacteristic
720C2×#41—28no—
721C2×#41—28no—
722C2×#41—28no—
723C2×#41—28no—
724C2×#41—42no—
725C2×#41—44no—
726C2×#41—42no—
727C2×#41—44no—
728C2×#41—44no—
729C2×#41—82no—
730C22×Q8C2411yescharacteristic
731C22×Q8C2412yes—
732C22×Q8C2411yescharacteristic
733C22×Q8C2412yes—
734C22×Q8C2412yes—
735C22×D4C2411yescharacteristic
736C22×D4C2412yes—
737C22×D4C2412yes—
738C22×D4C2411yescharacteristic
739C22×D4C2412yes—
740C22×D4C2411yescharacteristic
741C22×D4C2412yes—
742C22×D4C2412yes—
743C22×D4C2412yes—
744C22×D4C2412yes—
745C22×D4C2414yes—
746C22×D4C2414yes—
747C22×D4C2412yes—
748C22×D4C2411yescharacteristic
749C22×D4C2412yes—
750C22×D4C2412yes—
751C22×D4C2412yes—
752C22×D4C2411yescharacteristic
753C22×D4C2412yes—
754C22×D4C2412yes—
755C22×D4C2414yes—
756C22×D4C2412yes—
757C23×C4C2412yes—
758C23×C4C2411yescharacteristic
759C23×C4C2411yescharacteristic
760C23×C4C2412yes—
761C23×C4C2412yes—
762C23×C4C2412yes—
763C23×C4C2412yes—
764C23×C4C2414yes—
765C23×C4C2414yes—
766C23×C4C2414yes—
767C23×C4C2414yes—
768C23×C4C2412yes—
769C23×C4C2412yes—
770C23×C4C2412yes—
771C23×C4C2412yes—
772C23×C4C2414yes—
773C23×C4C2414yes—
774C23×C4C2412yes—
775C4⋊Q8—28no—
776C4⋊Q8—28no—
777C4⋊Q8—42no—
778C4⋊Q8—42no—
779#127—28no—
780#127—28no—
781#127—42no—
782#126—216no—
783#126—48no—
784#125—28no—
785#124—28no—
786#124—28no—
787#124—28no—
788#124—28no—
789#124—44no—
790#124—44no—
791#124—82no—
792#123—216no—
793#123—48no—
794#123—48no—
795#123—44no—
796#123—48no—
797#123—84no—
798C22⋊Q8—48no—
799C22⋊Q8—48no—
800C22⋊Q8—44no—
801#121—28no—
802#121—28no—
803#121—216no—
804#121—28no—
805#121—28no—
806#121—28no—
807#121—28no—
808#121—28no—
809#121—28no—
810#121—28no—
811#121—28no—
812#121—44no—
813#121—48no—
814#121—44no—
815#121—44no—
816#121—44no—
817#121—42no—
818#121—42no—
819#121—84no—
820C4×Q8—44no—
821C4×Q8—44no—
822C4×Q8—48no—
823C4×D4—28no—
824C4×D4—28no—
825C4×D4—28no—
826C4×D4—28no—
827C4×D4—24no—
828C4×D4—216no—
829C4×D4—28no—
830C4×D4—28no—
831C4×D4—28no—
832C4×D4—44no—
833C4×D4—44no—
834C4×D4—48no—
835C4×D4—44no—
836C4×D4—48no—
837C4×D4—42no—
838C4×D4—42no—
839C4×D4—48no—
840C4×D4—48no—
841C4×D4—44no—
842C4×D4—48no—
843C4×D4—48no—
844C4×D4—48no—
845C4×D4—84no—
846C4×D4—84no—
847C4×D4—84no—
848C4×D4#41116yescomplemented
849#117—28no—
850#117—28no—
851#117—24no—
852#117—24no—
853#117—44no—
854#117—44no—
855#117—44no—
856#117—44no—
857C2×C4⋊C4—28no—
858C2×C4⋊C4—28no—
859C2×C4⋊C4—28no—
860C2×C4⋊C4—42no—
861C2×C4⋊C4—44no—
862C2×C4⋊C4—42no—
863C2×C4⋊C4—44no—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2411yescharacteristic
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2411yescharacteristic
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2411yescharacteristic
944C2×C22⋊C4C2411yescharacteristic
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C42—28no—
968C2×C42—28no—
969C2×C42—82no—
970C2×C42—84no—
971C2×C42C2412yes—
972C2×C42C2412yes—
973C2×C42C2414yes—
974C2×C42C2414yes—
975C2×C42C2411yescharacteristic
976C2×C42C2411yescharacteristic
977C2×C42C2412yes—
978C2×C42C2412yes—
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2414yes—
984C2×C42C2414yes—
985C2×C42C2414yes—
986C2×C42C2414yes—
987C2×C42C2414yes—
988C2×C42C2412yes—
989C2×C42C2414yes—
990C2×C42C2414yes—
991C2×C42C2414yes—
992C2×C42C2412yes—
993C2×C42C2414yes—
994C2×C42C2414yes—
995C2×C42C2411yescharacteristic
996C2×C42C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2411yescharacteristic
1025#95C2411yescharacteristic
1026#95C2411yescharacteristic
1027#95C2412yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2411yescharacteristic
1040#95C2414yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2412yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052C24C2512yes—
1053C24C2511yescharacteristic
1054C24C2511yescharacteristic
1055C24C2512yes—
1056C24C2512yes—
1057C24C2512yes—
1058#41—416no—
1059#41—432no—
1060#41—416no—
1061#41—816no—
1062C2×Q8—24no—
1063C2×Q8—24no—
1064C2×Q8—24no—
1065C2×Q8—24no—
1066C2×Q8—24no—
1067C2×Q8—41no—
1068C2×Q8—42no—
1069C2×Q8—41no—
1070C2×Q8—42no—
1071C2×Q8—42no—
1072C2×Q8—44no—
1073C2×Q8—42no—
1074C2×D4—28no—
1075C2×D4—24no—
1076C2×D4—24no—
1077C2×D4—24no—
1078C2×D4—24no—
1079C2×D4—24no—
1080C2×D4—24no—
1081C2×D4—24no—
1082C2×D4—24no—
1083C2×D4—24no—
1084C2×D4—24no—
1085C2×D4—24no—
1086C2×D4—24no—
1087C2×D4—28no—
1088C2×D4—24no—
1089C2×D4—24no—
1090C2×D4—24no—
1091C2×D4—24no—
1092C2×D4—24no—
1093C2×D4—24no—
1094C2×D4—24no—
1095C2×D4—22no—
1096C2×D4—24no—
1097C2×D4—24no—
1098C2×D4—22no—
1099C2×D4—22no—
1100C2×D4—42no—
1101C2×D4—42no—
1102C2×D4—42no—
1103C2×D4—42no—
1104C2×D4—41no—
1105C2×D4—41no—
1106C2×D4—42no—
1107C2×D4—42no—
1108C2×D4—42no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—41no—
1112C2×D4—42no—
1113C2×D4—42no—
1114C2×D4—41no—
1115C2×D4—41no—
1116C2×D4—44no—
1117C2×D4—44no—
1118C2×D4—42no—
1119C2×D4—42no—
1120C2×D4—44no—
1121C2×D4—42no—
1122C2×D4—42no—
1123C2×D4—42no—
1124C2×D4—44no—
1125C2×D4—42no—
1126C2×D4—41no—
1127C2×D4—42no—
1128C2×D4—42no—
1129C2×D4—44no—
1130C2×D4—42no—
1131C2×D4—42no—
1132C2×D4—44no—
1133C2×D4—44no—
1134C2×D4C2×#4118yes—
1135C22×C4—24no—
1136C22×C4—24no—
1137C22×C4—24no—
1138C22×C4—24no—
1139C22×C4—28no—
1140C22×C4—24no—
1141C22×C4—24no—
1142C22×C4—24no—
1143C22×C4—24no—
1144C22×C4—24no—
1145C22×C4—24no—
1146C22×C4—22no—
1147C22×C4—22no—
1148C22×C4—24no—
1149C22×C4—24no—
1150C22×C4—24no—
1151C22×C4—24no—
1152C22×C4—24no—
1153C22×C4—24no—
1154C22×C4—28no—
1155C22×C4—28no—
1156C22×C4—28no—
1157C22×C4—42no—
1158C22×C4—42no—
1159C22×C4—44no—
1160C22×C4—44no—
1161C22×C4—44no—
1162C22×C4—42no—
1163C22×C4—42no—
1164C22×C4—44no—
1165C22×C4—42no—
1166C22×C4—44no—
1167C22×C4—42no—
1168C22×C4—44no—
1169C22×C4—42no—
1170C22×C4—42no—
1171C22×C4—44no—
1172C22×C4—44no—
1173C22×C4—42no—
1174C22×C4—44no—
1175C22×C4—42no—
1176C22×C4—44no—
1177C22×C4—42no—
1178C22×C4—44no—
1179C22×C4—44no—
1180C22×C4—44no—
1181C22×C4—44no—
1182C22×C4—44no—
1183C22×C4—42no—
1184C22×C4C2×#4118yes—
1185C22×C4C2×#4118yes—
1186C22×C4C2512yes—
1187C22×C4C2512yes—
1188C22×C4C2512yes—
1189C22×C4C2514yes—
1190C22×C4C2514yes—
1191C22×C4C2512yes—
1192C22×C4C2514yes—
1193C22×C4C2511yescharacteristic
1194C22×C4C2511yescharacteristic
1195C22×C4C2512yes—
1196C22×C4C2514yes—
1197C22×C4C2514yes—
1198C22×C4C2514yes—
1199C22×C4C2511yescharacteristic
1200C22×C4C2512yes—
1201C22×C4C2512yes—
1202C22×C4C2512yes—
1203C22×C4C2512yes—
1204C22×C4C2512yes—
1205C22×C4C2512yes—
1206C22×C4C2511yescharacteristic
1207C22×C4C2512yes—
1208C22×C4C2511yescharacteristic
1209C4⋊C4—24no—
1210C4⋊C4—24no—
1211C4⋊C4—28no—
1212C4⋊C4—24no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
1217C4⋊C4—24no—
1218C4⋊C4—24no—
1219C4⋊C4—28no—
1220C4⋊C4—28no—
1221C4⋊C4—24no—
1222C4⋊C4—24no—
1223C4⋊C4—28no—
1224C4⋊C4—28no—
1225C4⋊C4—24no—
1226C4⋊C4—22no—
1227C4⋊C4—22no—
1228C4⋊C4—24no—
1229C4⋊C4—28no—
1230C4⋊C4—28no—
1231C4⋊C4—28no—
1232C4⋊C4—28no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—42no—
1236C4⋊C4—42no—
1237C4⋊C4—41no—
1238C4⋊C4—42no—
1239C4⋊C4—42no—
1240C4⋊C4—41no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—42no—
1249C4⋊C4—44no—
1250C4⋊C4C2×#4118yes—
1251C4⋊C4H(5,𝔽2)14yes—
1252C22⋊C4—28no—
1253C22⋊C4—24no—
1254C22⋊C4—24no—
1255C22⋊C4—24no—
1256C22⋊C4—24no—
1257C22⋊C4—24no—
1258C22⋊C4—24no—
1259C22⋊C4—24no—
1260C22⋊C4—24no—
1261C22⋊C4—24no—
1262C22⋊C4—24no—
1263C22⋊C4—24no—
1264C22⋊C4—24no—
1265C22⋊C4—28no—
1266C22⋊C4—28no—
1267C22⋊C4—28no—
1268C22⋊C4—28no—
1269C22⋊C4—24no—
1270C22⋊C4—24no—
1271C22⋊C4—24no—
1272C22⋊C4—24no—
1273C22⋊C4—28no—
1274C22⋊C4—24no—
1275C22⋊C4—24no—
1276C22⋊C4—24no—
1277C22⋊C4—24no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—42no—
1282C22⋊C4—42no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—42no—
1286C22⋊C4—42no—
1287C22⋊C4—41no—
1288C22⋊C4—41no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—44no—
1294C22⋊C4—42no—
1295C22⋊C4—44no—
1296C22⋊C4—42no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—42no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—44no—
1305C22⋊C4—44no—
1306C22⋊C4—42no—
1307C22⋊C4—44no—
1308C22⋊C4—44no—
1309C22⋊C4—44no—
1310C22⋊C4C2×#4118yes—
1311C22⋊C4C2×#4118yes—
1312C42—24no—
1313C42—24no—
1314C42—24no—
1315C42—24no—
1316C42—24no—
1317C42—24no—
1318C42—28no—
1319C42—24no—
1320C42—24no—
1321C42—28no—
1322C42—22no—
1323C42—22no—
1324C42—41no—
1325C42—44no—
1326C42—44no—
1327C42—44no—
1328C42—44no—
1329C42—42no—
1330C42—44no—
1331C42—44no—
1332C42—44no—
1333C42—42no—
1334C42—44no—
1335C42—44no—
1336C42—44no—
1337C42C2×#4118yes—
1338C23—22no—
1339C23—22no—
1340C23—22no—
1341C23—22no—
1342C23—22no—
1343C23—22no—
1344C23—22no—
1345C23—22no—
1346C23—22no—
1347C23—22no—
1348C23—22no—
1349C23—22no—
1350C23—24no—
1351C23—22no—
1352C23—22no—
1353C23—22no—
1354C23—22no—
1355C23—21no—
1356C23—21no—
1357C23—22no—
1358C23—22no—
1359C23—22no—
1360C23—24no—
1361C23—22no—
1362C23—22no—
1363C23—21no—
1364C23—22no—
1365C23—22no—
1366C23—21no—
1367C23—22no—
1368C23—21no—
1369C23—21no—
1370C23—22no—
1371C23—22no—
1372C23C22×#4114yes—
1373C23C22×#4114yes—
1374C23C2611yescharacteristic
1375Q8—44no—
1376Q8—48no—
1377Q8—44no—
1378Q8—84no—
1379Q8—162no—
1380D4—48no—
1381D4—48no—
1382D4—48no—
1383D4—48no—
1384D4—48no—
1385D4—48no—
1386D4—48no—
1387D4—44no—
1388D4—44no—
1389D4—44no—
1390D4—48no—
1391D4—416no—
1392D4—44no—
1393D4—84no—
1394D4—84no—
1395D4—82no—
1396D4—88no—
1397D4—84no—
1398D4—84no—
1399D4—88no—
1400D4—162no—
1401D4—162no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—21no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—21no—
1416C2×C4—216no—
1417C2×C4—216no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—24no—
1422C2×C4—24no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—22no—
1427C2×C4—24no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—22no—
1431C2×C4—24no—
1432C2×C4—21no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—24no—
1436C2×C4—24no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—24no—
1440C2×C4—22no—
1441C2×C4—24no—
1442C2×C4—24no—
1443C2×C4—24no—
1444C2×C4—24no—
1445C2×C4—22no—
1446C2×C4—22no—
1447C2×C4—24no—
1448C2×C4—22no—
1449C2×C4—24no—
1450C2×C4—24no—
1451C2×C4—24no—
1452C2×C4—24no—
1453C2×C4—24no—
1454C2×C4—24no—
1455C2×C4—24no—
1456C2×C4—24no—
1457C2×C4—22no—
1458C2×C4—48no—
1459C2×C4—48no—
1460C2×C4—48no—
1461C2×C4—44no—
1462C2×C4—44no—
1463C2×C4—88no—
1464C2×C4—84no—
1465C2×C4—84no—
1466C2×C4—84no—
1467C2×C4—88no—
1468C2×C4—88no—
1469C2×C4—88no—
1470C2×C4—162no—
1471C2×C4—164no—
1472C2×C4—162no—
1473C2×C4—164no—
1474C2×C4C22×#4114yes—
1475C2×C4C22×#4114yes—
1476C2×C4C22×#4114yes—
1477C2×C4C22×#4114yes—
1478C2×C4C22×#4114yes—
1479C2×C4C2×H(5,𝔽2)14yes—
1480C2×C4C2×H(5,𝔽2)12yes—
1481C2×C4#58512yes—
1482C2×C4#58514yes—
1483C22—24no—
1484C22—24no—
1485C22—24no—
1486C22—24no—
1487C22—24no—
1488C22—24no—
1489C22—42no—
1490C22—42no—
1491C22—42no—
1492C22—42no—
1493C22—42no—
1494C22—42no—
1495C22—42no—
1496C22—42no—
1497C22—44no—
1498C22—42no—
1499C22—42no—
1500C22—42no—
1501C22—42no—
1502C22—41no—
1503C22—41no—
1504C22—42no—
1505C22—42no—
1506C22—44no—
1507C22—42no—
1508C22—42no—
1509C22—42no—
1510C22—42no—
1511C22—42no—
1512C22—42no—
1513C22—41no—
1514C22—41no—
1515C22—41no—
1516C22—41no—
1517C22—42no—
1518C22—42no—
1519C22C23×#4112yes—
1520C22C22×H(5,𝔽2)11yescharacteristic
1521C22C2×#58512yes—
1522C22C2×#58511yescharacteristic
1523C22H(7,𝔽2)11yescharacteristic
1524C4—24no—
1525C4—24no—
1526C4—24no—
1527C4—22no—
1528C4—24no—
1529C4—24no—
1530C4—24no—
1531C4—44no—
1532C4—44no—
1533C4—42no—
1534C4—44no—
1535C4—42no—
1536C4—42no—
1537C4—41no—
1538C4—42no—
1539C4—42no—
1540C4—44no—
1541C4—44no—
1542C4—44no—
1543C4—41no—
1544C4—41no—
1545C4—42no—
1546C4#348114yes—
1547C2—44no—
1548C2—44no—
1549C2—82no—
1550C2—81no—
1551C2—82no—
1552C2—81no—
1553C2C2×#348111yescharacteristic
1554C2#6281512yes—
1555C2#6291811yescharacteristic
1556C2#6300812yes—
1557C2#6303511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59865C2semidirect
2. #59799C2semidirect
3. #59741C2semidirect
4. #59738C2semidirect
5. #59308C2semidirect
6. #59307C2semidirect
7. #45330C2semidirect
8. #45126C2semidirect
9. #45115C2semidirect
10. #44841C2semidirect
11. #44260C2semidirect
12. #43432C2semidirect
13. #40135C2semidirect
14. #40132C2semidirect
15. #39462C2semidirect
16. #39462C2semidirect
17. #36514C2semidirect
18. #36500C2semidirect
19. #36486C2semidirect
20. #36415C2semidirect
21. #36191C2semidirect
22. #36087C2semidirect
23. #35756C2semidirect
24. #35682C2semidirect
25. #34962C2semidirect
26. #34925C2semidirect
27. #34208C2semidirect
28. #34206C2semidirect
29. C4×#553C2semidirect
848. C4×D4#41semidirect

Maximal subgroups

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

subgroupindex
#598652
#597992
#597412
#597382
#593082
#593072
#453302
#451262
#451152
#448412
#442602
#434322
#401352
#401322
#394622
#365142
#365002
#364862
#364152
#361912
#360872
#357562
#356822
#349622
#349252
#342082
#342062
C4×#5532