Finite Group Databasebeta

← #7678999

Subgroups — #7678999

Order 512.

4924 conjugacy classes of subgroups.

The subgroup lattice has 1505 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59903C212yesmaximal, complemented
2#59549C212yesmaximal, complemented
3#59364C214yesmaximal, complemented
4#59341C214yesmaximal, complemented
5#59227C212yesmaximal, complemented
6#59145C212yesmaximal, complemented
7#45434C211yesmaximal, characteristic, complemented
8#45421C211yesmaximal, characteristic, complemented
9#45306C211yesmaximal, characteristic, complemented
10#45299C211yesmaximal, characteristic, complemented
11#45211C211yesmaximal, characteristic, complemented
12#45163C211yesmaximal, characteristic, complemented
13#45041C211yesmaximal, characteristic, complemented
14#44963C211yesmaximal, characteristic, complemented
15#43968C214yesmaximal, complemented
16#43966C214yesmaximal, complemented
17#40313C214yesmaximal, complemented
18#38713C214yesmaximal, complemented
19#38419C214yesmaximal, complemented
20#36359C214yesmaximal, complemented
21#35658C212yesmaximal, complemented
22#35561C212yesmaximal, complemented
23#35197C212yesmaximal, complemented
24#35190C211yesmaximal, characteristic, complemented
25#34977C211yesmaximal, characteristic, complemented
26#34878C211yesmaximal, characteristic, complemented
27#34329C212yesmaximal, complemented
28#34222C211yesmaximal, characteristic, complemented
29#34197C211yesmaximal, characteristic, complemented
30#34123C211yesmaximal, characteristic, complemented
31#34070C211yesmaximal, characteristic, complemented
32C2×#559C2212yes—
33C2×#532C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37#2854C2214yes—
38#2850C2214yes—
39#2850C2214yes—
40#2781C2214yes—
41#2781C2214yes—
42#2778C2214yes—
43#2768C2214yes—
44#2767C2214yes—
45#2761C2214yes—
46#2759C2214yes—
47#2758C2214yes—
48#2757C2214yes—
49#2756C2214yes—
50#2756C2214yes—
51#2749C2214yes—
52#2745C2214yes—
53#2743C2214yes—
54#2730C2214yes—
55#2706C2214yes—
56#2704C2214yes—
57#2703C2214yes—
58#2703C2214yes—
59#2702C2214yes—
60#2688C2214yes—
61#2686C2214yes—
62#2676C2214yes—
63#2672C2214yes—
64#2648C2214yes—
65#2648C2214yes—
66#2635C2212yes—
67#2635C2212yes—
68#2612C2212yes—
69#2612C2214yes—
70#2612C2212yes—
71#2610C2212yes—
72#2610C2214yes—
73#2610C2212yes—
74#2606C2212yes—
75#2605C2212yes—
76#2603C2214yes—
77#2602C2214yes—
78#2598C2212yes—
79#2598C2212yes—
80#2597C2214yes—
81#2596C2214yes—
82#2594C2214yes—
83#2592C2212yes—
84#2592C2212yes—
85#2582C2212yes—
86#2577C2214yes—
87#2576C2214yes—
88#2571C2212yes—
89#2571C2212yes—
90#2569C2212yes—
91#2568C2211yescharacteristic
92#2567C2211yescharacteristic
93#2563C2211yescharacteristic
94#2562C2214yes—
95#2560C2214yes—
96#2558C2214yes—
97#2556C2214yes—
98#2553C2214yes—
99#2553C2214yes—
100#2552C2212yes—
101#2549C2214yes—
102#2549C2212yes—
103#2548C2211yescharacteristic
104#2548C2211yescharacteristic
105#2548C2212yes—
106#2545C2212yes—
107#2544C2212yes—
108#2543C2214yes—
109#2542C2211yescharacteristic
110#2541C2212yes—
111#2541C2211yescharacteristic
112#2541C2211yescharacteristic
113#2538C2212yes—
114#2538C2212yes—
115#2533C2214yes—
116#2532C2214yes—
117#2532C2214yes—
118#2531C2214yes—
119#2531C2214yes—
120#2530C2214yes—
121#2529C2214yes—
122#2529C2214yes—
123#2529C2214yes—
124#2527C2214yes—
125#2526C2214yes—
126#2526C2214yes—
127#2526C2214yes—
128#2522C2214yes—
129#2518C2214yes—
130#2515C2214yes—
131#2514C2212yes—
132#2513C2212yes—
133#2513C2212yes—
134#2513C2212yes—
135#2512C2212yes—
136#2511C2212yes—
137#2500C2212yes—
138#2500C2212yes—
139#2489C2214yes—
140#2488C2214yes—
141#2488C2214yes—
142#2476C2214yes—
143#2466C2214yes—
144#2464C2214yes—
145#2464C2214yes—
146#2463C2214yes—
147#2461C2214yes—
148#2460C2214yes—
149#2459C2214yes—
150#2457C2214yes—
151#2457C2214yes—
152#2457C2214yes—
153#2457C2214yes—
154#2456C2214yes—
155#2450C2214yes—
156#2448C2212yes—
157#2447C2212yes—
158#2446C2212yes—
159#2445C2212yes—
160#2445C2212yes—
161#2445C2212yes—
162#2438C2212yes—
163#2438C2212yes—
164#2431C2212yes—
165#2431C2212yes—
166#2427C2214yes—
167#2425C2214yes—
168#2425C2214yes—
169#2420C2214yes—
170#2419C2214yes—
171#2415C2214yes—
172#2414C2214yes—
173#2407C2214yes—
174#2402C2211yescharacteristic
175#2402C2211yescharacteristic
176#2399C2211yescharacteristic
177#2399C2211yescharacteristic
178#2388C2212yes—
179#2388C2212yes—
180#2374C2214yes—
181#2372C2214yes—
182#2372C2214yes—
183#2372C2214yes—
184#2367C2212yes—
185#2367C2212yes—
186#2366C2212yes—
187#2364C2214yes—
188#2364C2214yes—
189#2359C2214yes—
190#2357C2212yes—
191#2357C2212yes—
192#2357C2211yescharacteristic
193#2357C2212yes—
194#2357C2211yescharacteristic
195#2356C2212yes—
196#2356C2211yescharacteristic
197#2356C2211yescharacteristic
198#2355C2212yes—
199#2354C2212yes—
200#2353C2214yes—
201#2353C2214yes—
202#2353C2212yes—
203#2353C2212yes—
204#2353C2214yes—
205#2351C2211yescharacteristic
206#2351C2211yescharacteristic
207#2349C2211yescharacteristic
208#2349C2211yescharacteristic
209#2346C2214yes—
210#2346C2214yes—
211#2346C2212yes—
212#2346C2212yes—
213#2343C2214yes—
214#2341C2212yes—
215#2339C2212yes—
216#2339C2214yes—
217#2337C2214yes—
218#2335C2214yes—
219#2331C2211yescharacteristic
220#2331C2211yescharacteristic
221#2328C2211yescharacteristic
222#2328C2211yescharacteristic
223#2328C2212yes—
224#2328C2211yescharacteristic
225#2328C2211yescharacteristic
226#2327C2211yescharacteristic
227#2327C2211yescharacteristic
228#2326C2211yescharacteristic
229#2326C2211yescharacteristic
230#2326C2211yescharacteristic
231#2326C2211yescharacteristic
232#2326C2212yes—
233#2325C2214yes—
234#2325C2214yes—
235#2319C2212yes—
236#2319C2212yes—
237#2319C2214yes—
238C4×#127C2212yes—
239C4×#124C2212yes—
240C4×C22⋊Q8C2212yes—
241C4×C22⋊Q8C2212yes—
242C4×#123C2214yes—
243C4×#121C2212yes—
244C4×#121C2212yes—
245C4×#121C2214yes—
246#2297C2211yescharacteristic
247#2297C2211yescharacteristic
248#2295C2212yes—
249#2295C2212yes—
250#2295C2212yes—
251#2290C2214yes—
252#2290C2214yes—
253#2290C2214yes—
254#2290C2214yes—
255#2285C2211yescharacteristic
256#2283C2212yes—
257#2283C2211yescharacteristic
258#2283C2211yescharacteristic
259#2283C2212yes—
260#2283C2212yes—
261#2276C2212yes—
262#2275C2212yes—
263C42×D4C2212yes—
264C4×#117C2211yescharacteristic
265C2×#376C2212yes—
266C2×#376C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C22×#41C2311yescharacteristic
269C22×#41C2312yes—
270#559—216no—
271#532—28no—
272#532—28no—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×#127C2311yescharacteristic
276C2×#127C2311yescharacteristic
277C2×#127C2312yes—
278C2×#127C2312yes—
279C2×#126C2314yes—
280C2×#125C2314yes—
281C2×#124C2311yescharacteristic
282C2×#124C2314yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#124C2314yes—
287C2×#124C2311yescharacteristic
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×#121C2314yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C4×#41—28no—
306C4×#41—28no—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2312yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2314yes—
336C2×#117C2312yes—
337C2×#117C2312yes—
338C2×#117C2311yescharacteristic
339C2×#117C2311yescharacteristic
340C2×#117C2314yes—
341C2×#117C2312yes—
342C22×C42C2312yes—
343C22×C42C2312yes—
344C22×C42C2311yescharacteristic
345C22×C42C2314yes—
346C22×C42C2311yescharacteristic
347C22×C42C2311yescharacteristic
348#401C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2312yes—
353#400C2312yes—
354#400C2312yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2312yes—
359#400C2312yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#399C2314yes—
364#399C2312yes—
365#399C2312yes—
366#398C2314yes—
367#398C2312yes—
368#398C2312yes—
369#398C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2312yes—
377#398C2314yes—
378#398C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#395C2312yes—
399#395C2312yes—
400#395C2312yes—
401#395C2312yes—
402#395C2312yes—
403#395C2312yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2312yes—
409#394C2312yes—
410#394C2314yes—
411#394C2314yes—
412#394C2312yes—
413#394C2312yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#393C2314yes—
423#393C2312yes—
424#393C2312yes—
425#393C2314yes—
426#392C2312yes—
427#392C2312yes—
428#392C2314yes—
429#392C2314yes—
430#392C2312yes—
431#392C2312yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#392C2314yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2314yes—
440#391C2311yescharacteristic
441#391C2311yescharacteristic
442#391C2311yescharacteristic
443#391C2311yescharacteristic
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#390C2314yes—
456#390C2312yes—
457#390C2314yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#390C2314yes—
463#390C2314yes—
464#390C2312yes—
465#390C2311yescharacteristic
466#390C2311yescharacteristic
467#390C2311yescharacteristic
468#390C2311yescharacteristic
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2314yes—
473#390C2312yes—
474#390C2314yes—
475#390C2314yes—
476#390C2314yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
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#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
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#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#387C2314yes—
544#387C2312yes—
545#387C2312yes—
546#387C2312yes—
547#387C2312yes—
548#387C2312yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2312yes—
560#387C2314yes—
561#387C2312yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2312yes—
566#387C2312yes—
567#387C2312yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2312yes—
573#387C2312yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
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#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#385C2312yes—
604#385C2312yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2312yes—
616#385C2314yes—
617#385C2312yes—
618#384C2312yes—
619#384C2312yes—
620#384C2311yescharacteristic
621#384C2311yescharacteristic
622#383C2314yes—
623#383C2314yes—
624#383C2311yescharacteristic
625#383C2311yescharacteristic
626#383C2312yes—
627#383C2312yes—
628#383C2312yes—
629#382C2312yes—
630#382C2312yes—
631#382C2311yescharacteristic
632#382C2311yescharacteristic
633#382C2314yes—
634#382C2314yes—
635#382C2314yes—
636#382C2311yescharacteristic
637#382C2311yescharacteristic
638#382C2312yes—
639#382C2314yes—
640#382C2312yes—
641#382C2312yes—
642#381C2312yes—
643#381C2314yes—
644#381C2314yes—
645#381C2314yes—
646#381C2314yes—
647#381C2314yes—
648#381C2311yescharacteristic
649#381C2311yescharacteristic
650#381C2312yes—
651#381C2312yes—
652#380C2312yes—
653#380C2314yes—
654#380C2314yes—
655#380C2314yes—
656#380C2314yes—
657#380C2312yes—
658#380C2312yes—
659#380C2314yes—
660#380C2314yes—
661#380C2312yes—
662#380C2314yes—
663#380C2314yes—
664#380C2312yes—
665#380C2312yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2311yescharacteristic
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2311yescharacteristic
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715#376C2311yescharacteristic
716#376C2312yes—
717#376C2314yes—
718#376C2311yescharacteristic
719#376C2311yescharacteristic
720#376C2311yescharacteristic
721#376C2314yes—
722#376C2314yes—
723#376C2312yes—
724#376C2314yes—
725#376C2312yes—
726#376C2312yes—
727#376C2312yes—
728#376C2311yescharacteristic
729#376C2311yescharacteristic
730#376C2312yes—
731#376C2314yes—
732C2×#95C2312yes—
733C2×#95C2312yes—
734C2×#95C2314yes—
735C2×#95C2314yes—
736C2×#95C2312yes—
737C2×#95C2312yes—
738C43C2312yes—
739C2×#41—24no—
740C2×#41—24no—
741C2×#41—24no—
742C2×#41—24no—
743C2×#41—28no—
744C2×#41—42no—
745C2×#41—42no—
746C2×#41—84no—
747C22×Q8C2411yescharacteristic
748C22×Q8C2411yescharacteristic
749C22×Q8C2412yes—
750C22×Q8C2412yes—
751C22×Q8C2412yes—
752C22×D4C2412yes—
753C22×D4C2411yescharacteristic
754C22×D4C2412yes—
755C22×D4C2412yes—
756C22×D4C2411yescharacteristic
757C22×D4C2414yes—
758C22×D4C2414yes—
759C22×D4C2414yes—
760C22×D4C2412yes—
761C22×D4C2414yes—
762C22×D4C2414yes—
763C22×D4C2412yes—
764C22×D4C2414yes—
765C23×C4C2412yes—
766C23×C4C2412yes—
767C23×C4C2411yescharacteristic
768C23×C4C2414yes—
769C23×C4C2412yes—
770C23×C4C2414yes—
771C23×C4C2412yes—
772C23×C4C2414yes—
773C23×C4C2412yes—
774C23×C4C2412yes—
775C23×C4C2414yes—
776C23×C4C2412yes—
777C23×C4C2414yes—
778C23×C4C2412yes—
779C23×C4C2411yescharacteristic
780C23×C4C2411yescharacteristic
781C4⋊Q8—24no—
782C4⋊Q8—24no—
783#127—24no—
784#127—28no—
785#127—24no—
786#127—44no—
787#126—84no—
788#125—84no—
789#124—28no—
790#124—216no—
791#124—28no—
792#124—24no—
793#124—48no—
794#124—44no—
795#124#4118yescomplemented
796#123—216no—
797#123—216no—
798#123—84no—
799#123—84no—
800#123—84no—
801C22⋊Q8—44no—
802C22⋊Q8—44no—
803C22⋊Q8—84no—
804C22⋊Q8—84no—
805C22⋊Q8—84no—
806#121—28no—
807#121—28no—
808#121—216no—
809#121—48no—
810#121—48no—
811#121—84no—
812#121—84no—
813C4×Q8—28no—
814C4×Q8—24no—
815C4×Q8—24no—
816C4×Q8—24no—
817C4×Q8—24no—
818C4×Q8—28no—
819C4×Q8—44no—
820C4×Q8—44no—
821C4×D4—28no—
822C4×D4—28no—
823C4×D4—28no—
824C4×D4—28no—
825C4×D4—28no—
826C4×D4—216no—
827C4×D4—216no—
828C4×D4—24no—
829C4×D4—24no—
830C4×D4—24no—
831C4×D4—24no—
832C4×D4—28no—
833C4×D4—28no—
834C4×D4—28no—
835C4×D4—44no—
836C4×D4—44no—
837C4×D4—48no—
838C4×D4—84no—
839C4×D4—84no—
840C4×D4—84no—
841C4×D4—84no—
842#117—24no—
843#117—24no—
844#117—28no—
845#117—28no—
846#117—44no—
847#117—48no—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C42—28no—
945C2×C42—28no—
946C2×C42—24no—
947C2×C42—48no—
948C2×C42—42no—
949C2×C42#4118yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2414yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2411yescharacteristic
956C2×C42C2412yes—
957C2×C42C2414yes—
958C2×C42C2412yes—
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2412yes—
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967C2×C42C2412yes—
968C2×C42C2414yes—
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2414yes—
972C2×C42C2414yes—
973C2×C42C2414yes—
974C2×C42C2414yes—
975C2×C42C2412yes—
976C2×C42C2414yes—
977C2×C42C2414yes—
978C2×C42C2411yescharacteristic
979C2×C42C2411yescharacteristic
980C2×C42C2411yescharacteristic
981C2×C42C2411yescharacteristic
982C2×C42C2411yescharacteristic
983#95C2412yes—
984#95C2412yes—
985#95C2411yescharacteristic
986#95C2411yescharacteristic
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2411yescharacteristic
1010#95C2411yescharacteristic
1011#95C2412yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2411yescharacteristic
1028#95C2411yescharacteristic
1029#95C2414yes—
1030#95C2412yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2411yescharacteristic
1039#95C2411yescharacteristic
1040#95C2414yes—
1041#95C2414yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2414yes—
1054#95C2414yes—
1055C24C2514yes—
1056C24C2512yes—
1057C24C2512yes—
1058C24C2511yescharacteristic
1059#41—416no—
1060#41—416no—
1061#41—816no—
1062C2×Q8—22no—
1063C2×Q8—22no—
1064C2×Q8—22no—
1065C2×Q8—24no—
1066C2×Q8—24no—
1067C2×Q8—22no—
1068C2×Q8—22no—
1069C2×Q8—24no—
1070C2×Q8—42no—
1071C2×Q8—42no—
1072C2×Q8—42no—
1073C2×Q8—42no—
1074C2×Q8—44no—
1075C2×Q8C2×#4114yes—
1076C2×D4—24no—
1077C2×D4—24no—
1078C2×D4—24no—
1079C2×D4—28no—
1080C2×D4—28no—
1081C2×D4—28no—
1082C2×D4—28no—
1083C2×D4—22no—
1084C2×D4—22no—
1085C2×D4—24no—
1086C2×D4—24no—
1087C2×D4—24no—
1088C2×D4—22no—
1089C2×D4—24no—
1090C2×D4—24no—
1091C2×D4—22no—
1092C2×D4—24no—
1093C2×D4—22no—
1094C2×D4—28no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—42no—
1098C2×D4—42no—
1099C2×D4—44no—
1100C2×D4—44no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C2×D4C2×#4114yes—
1113C22×C4—22no—
1114C22×C4—22no—
1115C22×C4—24no—
1116C22×C4—28no—
1117C22×C4—24no—
1118C22×C4—24no—
1119C22×C4—24no—
1120C22×C4—24no—
1121C22×C4—24no—
1122C22×C4—24no—
1123C22×C4—24no—
1124C22×C4—24no—
1125C22×C4—28no—
1126C22×C4—28no—
1127C22×C4—28no—
1128C22×C4—44no—
1129C22×C4—42no—
1130C22×C4—42no—
1131C22×C4—42no—
1132C22×C4—42no—
1133C22×C4—44no—
1134C22×C4—42no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4—42no—
1138C22×C4—44no—
1139C22×C4—42no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—42no—
1147C22×C4—42no—
1148C22×C4—44no—
1149C22×C4—44no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4C2×#4114yes—
1153C22×C4C2×#4114yes—
1154C22×C4C2×#4114yes—
1155C22×C4C2512yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2514yes—
1162C22×C4C2512yes—
1163C22×C4C2514yes—
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2514yes—
1168C22×C4C2512yes—
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2512yes—
1173C22×C4C2511yescharacteristic
1174C22×C4C2511yescharacteristic
1175C22×C4C2511yescharacteristic
1176C22×C4C2511yescharacteristic
1177C22×C4C2511yescharacteristic
1178C22×C4C2512yes—
1179C22×C4C2512yes—
1180C22×C4C2512yes—
1181C22×C4C2511yescharacteristic
1182C4⋊C4—24no—
1183C4⋊C4—24no—
1184C4⋊C4—22no—
1185C4⋊C4—22no—
1186C4⋊C4—22no—
1187C4⋊C4—22no—
1188C4⋊C4—24no—
1189C4⋊C4—24no—
1190C4⋊C4—24no—
1191C4⋊C4—24no—
1192C4⋊C4—28no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—24no—
1196C4⋊C4—28no—
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—44no—
1204C4⋊C4—42no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—42no—
1210C4⋊C4—44no—
1211C4⋊C4—42no—
1212C4⋊C4—42no—
1213C4⋊C4—42no—
1214C4⋊C4—42no—
1215C4⋊C4—42no—
1216C4⋊C4—42no—
1217C4⋊C4—42no—
1218C4⋊C4—42no—
1219C4⋊C4—44no—
1220C4⋊C4—44no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—42no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C4⋊C4—44no—
1229C4⋊C4—42no—
1230C4⋊C4—42no—
1231C22⋊C4—24no—
1232C22⋊C4—24no—
1233C22⋊C4—28no—
1234C22⋊C4—24no—
1235C22⋊C4—24no—
1236C22⋊C4—24no—
1237C22⋊C4—24no—
1238C22⋊C4—28no—
1239C22⋊C4—28no—
1240C22⋊C4—28no—
1241C22⋊C4—28no—
1242C22⋊C4—28no—
1243C22⋊C4—28no—
1244C22⋊C4—28no—
1245C22⋊C4—24no—
1246C22⋊C4—42no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—42no—
1265C22⋊C4—42no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4C2×#41116yes—
1278C42—24no—
1279C42—24no—
1280C42—24no—
1281C42—24no—
1282C42—24no—
1283C42—24no—
1284C42—24no—
1285C42—22no—
1286C42—28no—
1287C42—24no—
1288C42—24no—
1289C42—24no—
1290C42—28no—
1291C42—22no—
1292C42—22no—
1293C42—24no—
1294C42—24no—
1295C42—44no—
1296C42—42no—
1297C42—44no—
1298C42—42no—
1299C42—44no—
1300C42—44no—
1301C42—42no—
1302C42—42no—
1303C42—44no—
1304C42—44no—
1305C42—44no—
1306C42C2×#4114yes—
1307C42C2×#4114yes—
1308C42C2×#4114yes—
1309C42C2×#4114yes—
1310C42C2×#4114yes—
1311C23—22no—
1312C23—21no—
1313C23—22no—
1314C23—22no—
1315C23—24no—
1316C23—21no—
1317C23—24no—
1318C23—22no—
1319C23—24no—
1320C23—22no—
1321C23—22no—
1322C23—24no—
1323C23—24no—
1324C23—24no—
1325C23—24no—
1326C23—24no—
1327C23—22no—
1328C23—24no—
1329C23—24no—
1330C23—24no—
1331C23C22×#4112yes—
1332C23C22×#4114yes—
1333C23C2611yescharacteristic
1334Q8—28no—
1335Q8—44no—
1336Q8—84no—
1337Q8—84no—
1338Q8—84no—
1339D4—28no—
1340D4—48no—
1341D4—48no—
1342D4—416no—
1343D4—48no—
1344D4—44no—
1345D4—84no—
1346D4—88no—
1347D4—84no—
1348D4—88no—
1349D4—88no—
1350D4—88no—
1351D4—88no—
1352C2×C4—22no—
1353C2×C4—21no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—21no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—28no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—24no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—24no—
1403C2×C4—24no—
1404C2×C4—24no—
1405C2×C4—24no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—24no—
1411C2×C4—24no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—44no—
1416C2×C4—44no—
1417C2×C4—48no—
1418C2×C4—48no—
1419C2×C4—48no—
1420C2×C4—88no—
1421C2×C4—84no—
1422C2×C4—84no—
1423C2×C4—84no—
1424C2×C4—84no—
1425C2×C4—88no—
1426C2×C4—88no—
1427C2×C4—88no—
1428C2×C4—84no—
1429C2×C4—164no—
1430C2×C4C22×#4112yes—
1431C2×C4C22×#4112yes—
1432C2×C4C22×#4112yes—
1433C2×C4C22×#4112yes—
1434C2×C4C22×#4112yes—
1435C2×C4C22×#4114yes—
1436C2×C4C22×#4114yes—
1437C2×C4C22×#4112yes—
1438C2×C4C22×#4112yes—
1439C2×C4#58514yes—
1440C2×C4#58512yes—
1441C22—28no—
1442C22—22no—
1443C22—22no—
1444C22—22no—
1445C22—24no—
1446C22—42no—
1447C22—42no—
1448C22—42no—
1449C22—44no—
1450C22—42no—
1451C22—44no—
1452C22—44no—
1453C22—44no—
1454C22—42no—
1455C22—44no—
1456C22—44no—
1457C22—42no—
1458C22—44no—
1459C22—44no—
1460C22—44no—
1461C22—42no—
1462C22—44no—
1463C22C23×#4111yescharacteristic
1464C22C23×#4111yescharacteristic
1465C22C2×#58512yes—
1466C22C2×#58511yescharacteristic
1467C22H(7,𝔽2)12yes—
1468C4—24no—
1469C4—22no—
1470C4—22no—
1471C4—22no—
1472C4—22no—
1473C4—24no—
1474C4—22no—
1475C4—24no—
1476C4—44no—
1477C4—42no—
1478C4—42no—
1479C4—42no—
1480C4—42no—
1481C4—42no—
1482C4—42no—
1483C4—42no—
1484C4—42no—
1485C4—42no—
1486C4—44no—
1487C4—42no—
1488C4—44no—
1489C4—42no—
1490C4—42no—
1491C4—42no—
1492C4—42no—
1493C4—42no—
1494C4#347514yes—
1495C2—44no—
1496C2—42no—
1497C2—84no—
1498C2—82no—
1499C2C2×#347511yescharacteristic
1500C2#6281511yescharacteristic
1501C2#6285511yescharacteristic
1502C2#6294112yes—
1503C2#6299412yes—
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. #59903C2semidirect
2. #59549C2semidirect
3. #59364C2semidirect
4. #59341C2semidirect
5. #59227C2semidirect
6. #59145C2semidirect
7. #45434C2semidirect
8. #45421C2semidirect
9. #45306C2semidirect
10. #45299C2semidirect
11. #45211C2semidirect
12. #45163C2semidirect
13. #45041C2semidirect
14. #44963C2semidirect
15. #43968C2semidirect
16. #43966C2semidirect
17. #40313C2semidirect
18. #38713C2semidirect
19. #38419C2semidirect
20. #36359C2semidirect
21. #35658C2semidirect
22. #35561C2semidirect
23. #35197C2semidirect
24. #35190C2semidirect
25. #34977C2semidirect
26. #34878C2semidirect
27. #34329C2semidirect
28. #34222C2semidirect
29. #34197C2semidirect
30. #34123C2semidirect
31. #34070C2semidirect
795. #124#41semidirect

Maximal subgroups

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

subgroupindex
#599032
#595492
#593642
#593412
#592272
#591452
#454342
#454212
#453062
#452992
#452112
#451632
#450412
#449632
#439682
#439662
#403132
#387132
#384192
#363592
#356582
#355612
#351972
#351902
#349772
#348782
#343292
#342222
#341972
#341232
#340702