Finite Group Databasebeta

← #7679454

Subgroups — #7679454

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#59905C212yesmaximal, complemented
2#59754C212yesmaximal, complemented
3#59349C214yesmaximal, complemented
4#59345C214yesmaximal, complemented
5#59211C212yesmaximal, complemented
6#59145C212yesmaximal, complemented
7#45425C211yesmaximal, characteristic, complemented
8#45421C211yesmaximal, characteristic, complemented
9#45347C211yesmaximal, characteristic, complemented
10#45299C211yesmaximal, characteristic, complemented
11#45056C211yesmaximal, characteristic, complemented
12#45041C211yesmaximal, characteristic, complemented
13#44979C211yesmaximal, characteristic, complemented
14#44963C211yesmaximal, characteristic, complemented
15#43088C214yesmaximal, complemented
16#43086C214yesmaximal, complemented
17#40308C214yesmaximal, complemented
18#38708C214yesmaximal, complemented
19#38414C214yesmaximal, complemented
20#36356C214yesmaximal, complemented
21#35615C212yesmaximal, complemented
22#35562C212yesmaximal, complemented
23#35190C211yesmaximal, characteristic, complemented
24#35188C212yesmaximal, complemented
25#34977C211yesmaximal, characteristic, complemented
26#34878C211yesmaximal, characteristic, complemented
27#34331C212yesmaximal, complemented
28#34222C211yesmaximal, characteristic, complemented
29#34195C211yesmaximal, characteristic, complemented
30#34125C211yesmaximal, characteristic, complemented
31#34070C211yesmaximal, characteristic, complemented
32C2×#559C2212yes—
33C2×#532C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37#2866C2214yes—
38#2865C2214yes—
39#2850C2214yes—
40#2797C2214yes—
41#2779C2214yes—
42#2779C2214yes—
43#2778C2214yes—
44#2777C2214yes—
45#2766C2214yes—
46#2763C2214yes—
47#2762C2214yes—
48#2761C2214yes—
49#2757C2214yes—
50#2756C2214yes—
51#2753C2214yes—
52#2742C2214yes—
53#2741C2214yes—
54#2706C2214yes—
55#2703C2214yes—
56#2703C2214yes—
57#2696C2214yes—
58#2689C2214yes—
59#2688C2214yes—
60#2687C2214yes—
61#2686C2214yes—
62#2676C2214yes—
63#2672C2214yes—
64#2654C2214yes—
65#2650C2214yes—
66#2635C2212yes—
67#2635C2212yes—
68#2612C2212yes—
69#2612C2212yes—
70#2610C2212yes—
71#2610C2212yes—
72#2610C2214yes—
73#2606C2212yes—
74#2605C2212yes—
75#2604C2214yes—
76#2600C2214yes—
77#2598C2214yes—
78#2598C2212yes—
79#2598C2212yes—
80#2597C2214yes—
81#2592C2212yes—
82#2592C2212yes—
83#2589C2214yes—
84#2581C2212yes—
85#2580C2212yes—
86#2578C2214yes—
87#2578C2214yes—
88#2577C2214yes—
89#2576C2214yes—
90#2575C2214yes—
91#2574C2214yes—
92#2573C2214yes—
93#2572C2214yes—
94#2571C2212yes—
95#2570C2212yes—
96#2570C2212yes—
97#2569C2212yes—
98#2568C2211yescharacteristic
99#2567C2211yescharacteristic
100#2563C2211yescharacteristic
101#2559C2214yes—
102#2557C2214yes—
103#2549C2212yes—
104#2548C2212yes—
105#2548C2211yescharacteristic
106#2548C2211yescharacteristic
107#2545C2212yes—
108#2544C2212yes—
109#2543C2214yes—
110#2542C2211yescharacteristic
111#2541C2212yes—
112#2541C2211yescharacteristic
113#2541C2211yescharacteristic
114#2538C2212yes—
115#2536C2214yes—
116#2533C2214yes—
117#2526C2214yes—
118#2525C2214yes—
119#2525C2214yes—
120#2521C2214yes—
121#2520C2214yes—
122#2518C2214yes—
123#2518C2214yes—
124#2518C2214yes—
125#2516C2214yes—
126#2514C2212yes—
127#2513C2212yes—
128#2513C2212yes—
129#2513C2212yes—
130#2512C2212yes—
131#2511C2212yes—
132#2510C2214yes—
133#2510C2214yes—
134#2505C2214yes—
135#2500C2212yes—
136#2500C2212yes—
137#2498C2214yes—
138#2495C2214yes—
139#2488C2214yes—
140#2485C2214yes—
141#2477C2214yes—
142#2477C2214yes—
143#2476C2214yes—
144#2476C2214yes—
145#2471C2214yes—
146#2470C2214yes—
147#2467C2214yes—
148#2467C2214yes—
149#2465C2214yes—
150#2464C2214yes—
151#2464C2214yes—
152#2461C2214yes—
153#2461C2214yes—
154#2459C2214yes—
155#2459C2214yes—
156#2457C2214yes—
157#2456C2214yes—
158#2448C2212yes—
159#2447C2212yes—
160#2446C2212yes—
161#2445C2212yes—
162#2445C2212yes—
163#2445C2212yes—
164#2444C2214yes—
165#2438C2212yes—
166#2438C2212yes—
167#2431C2212yes—
168#2431C2212yes—
169#2425C2214yes—
170#2425C2214yes—
171#2425C2214yes—
172#2414C2214yes—
173#2407C2214yes—
174#2402C2211yescharacteristic
175#2402C2211yescharacteristic
176#2399C2211yescharacteristic
177#2399C2211yescharacteristic
178#2388C2212yes—
179#2388C2212yes—
180#2374C2214yes—
181#2372C2214yes—
182#2367C2212yes—
183#2367C2214yes—
184#2367C2212yes—
185#2366C2212yes—
186#2364C2214yes—
187#2364C2214yes—
188#2362C2214yes—
189#2359C2214yes—
190#2359C2214yes—
191#2359C2214yes—
192#2357C2211yescharacteristic
193#2357C2212yes—
194#2357C2212yes—
195#2357C2211yescharacteristic
196#2356C2211yescharacteristic
197#2356C2211yescharacteristic
198#2355C2212yes—
199#2354C2212yes—
200#2354C2212yes—
201#2353C2212yes—
202#2353C2212yes—
203#2353C2214yes—
204#2351C2211yescharacteristic
205#2351C2211yescharacteristic
206Q8×C4⋊C4C2212yes—
207#2349C2211yescharacteristic
208#2349C2214yes—
209#2349C2211yescharacteristic
210#2347C2212yes—
211#2347C2212yes—
212#2347C2214yes—
213#2343C2214yes—
214#2341C2212yes—
215#2339C2212yes—
216#2339C2214yes—
217#2335C2214yes—
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#2320C2212yes—
236#2319C2212yes—
237#2318C2214yes—
238C4×#127C2212yes—
239C4×#124C2214yes—
240C4×#124C2212yes—
241C4×C22⋊Q8C2212yes—
242C4×C22⋊Q8C2212yes—
243C4×#121C2212yes—
244C4×#121C2212yes—
245C4×#121C2214yes—
246#2297C2211yescharacteristic
247#2297C2211yescharacteristic
248#2295C2212yes—
249#2295C2212yes—
250#2293C2214yes—
251#2293C2212yes—
252#2293C2214yes—
253#2290C2214yes—
254#2290C2214yes—
255#2285C2211yescharacteristic
256#2283C2212yes—
257#2283C2211yescharacteristic
258#2283C2211yescharacteristic
259#2283C2212yes—
260C2×#383C2212yes—
261#2275C2212yes—
262#2275C2212yes—
263C42×Q8C2212yes—
264C4×#117C2212yes—
265C4×#117C2211yescharacteristic
266C2×#376C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C22×#41C2311yescharacteristic
269C22×#41C2312yes—
270#559—216no—
271#532—28no—
272#532—28no—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×#127C2312yes—
276C2×#127C2311yescharacteristic
277C2×#127C2311yescharacteristic
278C2×#127C2312yes—
279C2×#126C2314yes—
280C2×#124C2311yescharacteristic
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×#124C2314yes—
284C2×#124C2312yes—
285C2×#124C2314yes—
286C2×#124C2311yescharacteristic
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×#121C2314yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2314yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C4×#41—28no—
304C4×#41—28no—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2314yes—
314C2×C4×D4C2311yescharacteristic
315C2×C4×D4C2312yes—
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×#117C2312yes—
336C2×#117C2312yes—
337C2×#117C2311yescharacteristic
338C2×#117C2311yescharacteristic
339C2×#117C2312yes—
340C2×#117C2314yes—
341C2×#117C2314yes—
342C2×#117C2314yes—
343C22×C42C2312yes—
344C22×C42C2312yes—
345C22×C42C2311yescharacteristic
346C22×C42C2311yescharacteristic
347C22×C42C2311yescharacteristic
348#401C2314yes—
349#400C2312yes—
350#400C2312yes—
351#400C2312yes—
352#400C2312yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2312yes—
362#400C2312yes—
363#400C2314yes—
364#399C2314yes—
365#399C2314yes—
366#399C2312yes—
367#399C2312yes—
368#398C2312yes—
369#398C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2312yes—
377#398C2312yes—
378#398C2312yes—
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#395C2312yes—
397#395C2312yes—
398#395C2314yes—
399#395C2312yes—
400#395C2312yes—
401#395C2312yes—
402#395C2312yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2312yes—
408#394C2314yes—
409#394C2312yes—
410#394C2312yes—
411#394C2314yes—
412#394C2314yes—
413#394C2312yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#393C2312yes—
422#393C2312yes—
423#393C2314yes—
424#393C2314yes—
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#391C2314yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2311yescharacteristic
444#391C2311yescharacteristic
445#391C2311yescharacteristic
446#391C2311yescharacteristic
447#391C2314yes—
448#391C2314yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#390C2312yes—
454#390C2314yes—
455#390C2312yes—
456#390C2314yes—
457#390C2312yes—
458#390C2312yes—
459#390C2311yescharacteristic
460#390C2311yescharacteristic
461#390C2311yescharacteristic
462#390C2311yescharacteristic
463#390C2312yes—
464#390C2312yes—
465#390C2312yes—
466#390C2312yes—
467#390C2314yes—
468#390C2314yes—
469#390C2312yes—
470#390C2314yes—
471#390C2314yes—
472#390C2314yes—
473#390C2314yes—
474#390C2312yes—
475#389C2314yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#388C2314yes—
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#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#387C2312yes—
542#387C2312yes—
543#387C2312yes—
544#387C2312yes—
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#387C2312yes—
560#387C2314yes—
561#387C2312yes—
562#387C2312yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2312yes—
572#387C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2312yes—
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#386C2314yes—
604#386C2314yes—
605#385C2312yes—
606#385C2312yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2312yes—
621#385C2312yes—
622#384C2312yes—
623#384C2312yes—
624#384C2311yescharacteristic
625#384C2311yescharacteristic
626#383C2314yes—
627#383C2314yes—
628#383C2314yes—
629#383C2314yes—
630#383C2311yescharacteristic
631#383C2311yescharacteristic
632#383C2312yes—
633#383C2312yes—
634#383C2312yes—
635#382C2312yes—
636#382C2312yes—
637#382C2311yescharacteristic
638#382C2311yescharacteristic
639#382C2314yes—
640#382C2314yes—
641#382C2311yescharacteristic
642#382C2311yescharacteristic
643#382C2312yes—
644#382C2314yes—
645#382C2312yes—
646#382C2312yes—
647#381C2314yes—
648#381C2314yes—
649#381C2314yes—
650#381C2312yes—
651#381C2311yescharacteristic
652#381C2311yescharacteristic
653#381C2312yes—
654#381C2312yes—
655#380C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662#380C2314yes—
663#380C2314yes—
664#380C2314yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
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⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C22⋊C4C2311yescharacteristic
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2311yescharacteristic
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718#376C2311yescharacteristic
719#376C2312yes—
720#376C2311yescharacteristic
721#376C2311yescharacteristic
722#376C2311yescharacteristic
723#376C2312yes—
724#376C2312yes—
725#376C2312yes—
726#376C2312yes—
727#376C2311yescharacteristic
728#376C2311yescharacteristic
729#376C2312yes—
730C2×#95C2312yes—
731C2×#95C2314yes—
732C2×#95C2312yes—
733C2×#95C2314yes—
734C2×#95C2314yes—
735C2×#95C2312yes—
736C2×#95C2312yes—
737C43C2312yes—
738C43C2314yes—
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×Q8C2412yes—
749C22×Q8C2411yescharacteristic
750C22×Q8C2412yes—
751C22×Q8C2412yes—
752C22×D4C2412yes—
753C22×D4C2411yescharacteristic
754C22×D4C2414yes—
755C22×D4C2412yes—
756C22×D4C2412yes—
757C22×D4C2411yescharacteristic
758C22×D4C2414yes—
759C22×D4C2414yes—
760C22×D4C2412yes—
761C22×D4C2414yes—
762C22×D4C2412yes—
763C22×D4C2414yes—
764C22×D4C2414yes—
765C23×C4C2412yes—
766C23×C4C2412yes—
767C23×C4C2411yescharacteristic
768C23×C4C2412yes—
769C23×C4C2414yes—
770C23×C4C2414yes—
771C23×C4C2412yes—
772C23×C4C2414yes—
773C23×C4C2412yes—
774C23×C4C2412yes—
775C23×C4C2412yes—
776C23×C4C2414yes—
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#124—28no—
789#124—216no—
790#124—28no—
791#124—24no—
792#124—44no—
793#124—84no—
794#124#4118yescomplemented
795#123—216no—
796#123—216no—
797#123—48no—
798#123—48no—
799#123—84no—
800C22⋊Q8—44no—
801C22⋊Q8—44no—
802C22⋊Q8—48no—
803C22⋊Q8—84no—
804#121—28no—
805#121—28no—
806#121—216no—
807#121—48no—
808#121—48no—
809#121—84no—
810#121—84no—
811C4×Q8—28no—
812C4×Q8—24no—
813C4×Q8—24no—
814C4×Q8—24no—
815C4×Q8—24no—
816C4×Q8—28no—
817C4×Q8—44no—
818C4×Q8—44no—
819C4×Q8—84no—
820C4×D4—28no—
821C4×D4—28no—
822C4×D4—28no—
823C4×D4—28no—
824C4×D4—28no—
825C4×D4—216no—
826C4×D4—216no—
827C4×D4—24no—
828C4×D4—24no—
829C4×D4—24no—
830C4×D4—24no—
831C4×D4—28no—
832C4×D4—28no—
833C4×D4—28no—
834C4×D4—44no—
835C4×D4—44no—
836C4×D4—84no—
837C4×D4—84no—
838C4×D4—84no—
839C4×D4—84no—
840C4×D4—84no—
841#117—24no—
842#117—24no—
843#117—28no—
844#117—28no—
845#117—48no—
846#117—44no—
847#117—84no—
848#117—84no—
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⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
945C2×C42—28no—
946C2×C42—28no—
947C2×C42—24no—
948C2×C42—42no—
949C2×C42#4118yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2411yescharacteristic
955C2×C42C2414yes—
956C2×C42C2412yes—
957C2×C42C2412yes—
958C2×C42C2412yes—
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966C2×C42C2414yes—
967C2×C42C2414yes—
968C2×C42C2414yes—
969C2×C42C2414yes—
970C2×C42C2412yes—
971C2×C42C2412yes—
972C2×C42C2412yes—
973C2×C42C2414yes—
974C2×C42C2414yes—
975C2×C42C2414yes—
976C2×C42C2414yes—
977C2×C42C2412yes—
978C2×C42C2411yescharacteristic
979C2×C42C2411yescharacteristic
980C2×C42C2411yescharacteristic
981C2×C42C2411yescharacteristic
982C2×C42C2411yescharacteristic
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2412yes—
987#95C2411yescharacteristic
988#95C2411yescharacteristic
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2411yescharacteristic
1008#95C2411yescharacteristic
1009#95C2412yes—
1010#95C2411yescharacteristic
1011#95C2411yescharacteristic
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2411yescharacteristic
1019#95C2411yescharacteristic
1020#95C2414yes—
1021#95C2414yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2414yes—
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—24no—
1065C2×Q8—22no—
1066C2×Q8—24no—
1067C2×Q8—22no—
1068C2×Q8—24no—
1069C2×Q8—22no—
1070C2×Q8—42no—
1071C2×Q8—42no—
1072C2×Q8—42no—
1073C2×Q8—44no—
1074C2×Q8—42no—
1075C2×Q8C2×#4114yes—
1076C2×D4—24no—
1077C2×D4—24no—
1078C2×D4—28no—
1079C2×D4—24no—
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—28no—
1094C2×D4—22no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—44no—
1098C2×D4—42no—
1099C2×D4—42no—
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—42no—
1128C22×C4—44no—
1129C22×C4—42no—
1130C22×C4—42no—
1131C22×C4—42no—
1132C22×C4—42no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4—42no—
1136C22×C4—44no—
1137C22×C4—42no—
1138C22×C4—44no—
1139C22×C4—44no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—42no—
1144C22×C4—42no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—44no—
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×C4C2514yes—
1161C22×C4C2514yes—
1162C22×C4C2512yes—
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2514yes—
1167C22×C4C2512yes—
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—28no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—42no—
1205C4⋊C4—44no—
1206C4⋊C4—42no—
1207C4⋊C4—42no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—42no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—42no—
1217C4⋊C4—42no—
1218C4⋊C4—42no—
1219C4⋊C4—44no—
1220C4⋊C4—42no—
1221C4⋊C4—42no—
1222C4⋊C4—42no—
1223C4⋊C4—44no—
1224C4⋊C4—42no—
1225C4⋊C4—42no—
1226C4⋊C4—44no—
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—28no—
1247C22⋊C4—42no—
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—44no—
1265C22⋊C4—42no—
1266C22⋊C4—42no—
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—22no—
1290C42—22no—
1291C42—24no—
1292C42—24no—
1293C42—24no—
1294C42—42no—
1295C42—44no—
1296C42—42no—
1297C42—44no—
1298C42—44no—
1299C42—44no—
1300C42—42no—
1301C42—42no—
1302C42—44no—
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—48no—
1336Q8—44no—
1337Q8—84no—
1338Q8—84no—
1339D4—28no—
1340D4—416no—
1341D4—48no—
1342D4—48no—
1343D4—416no—
1344D4—48no—
1345D4—44no—
1346D4—84no—
1347D4—84no—
1348D4—88no—
1349D4—88no—
1350D4—164no—
1351D4—164no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—21no—
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—24no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—24no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—24no—
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—24no—
1401C2×C4—24no—
1402C2×C4—24no—
1403C2×C4—24no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—24no—
1411C2×C4—22no—
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—84no—
1428C2×C4—164no—
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—42no—
1450C22—44no—
1451C22—44no—
1452C22—44no—
1453C22—44no—
1454C22—42no—
1455C22—44no—
1456C22—44no—
1457C22—42no—
1458C22—42no—
1459C22—44no—
1460C22—44no—
1461C22—44no—
1462C22—44no—
1463C22C23×#4111yescharacteristic
1464C22C23×#4111yescharacteristic
1465C22C2×#58512yes—
1466C22C2×#58511yescharacteristic
1467C22H(7,𝔽2)12yes—
1468C4—24no—
1469C4—24no—
1470C4—22no—
1471C4—22no—
1472C4—22no—
1473C4—22no—
1474C4—22no—
1475C4—24no—
1476C4—44no—
1477C4—42no—
1478C4—42no—
1479C4—42no—
1480C4—42no—
1481C4—42no—
1482C4—42no—
1483C4—42no—
1484C4—42no—
1485C4—44no—
1486C4—42no—
1487C4—42no—
1488C4—42no—
1489C4—42no—
1490C4—44no—
1491C4—42no—
1492C4—42no—
1493C4—42no—
1494C4#347514yes—
1495C2—44no—
1496C2—42no—
1497C2—84no—
1498C2—82no—
1499C2C2×#347511yescharacteristic
1500C2#6281511yescharacteristic
1501C2#6285511yescharacteristic
1502C2#6296612yes—
1503C2#6300812yes—
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. #59905C2semidirect
2. #59754C2semidirect
3. #59349C2semidirect
4. #59345C2semidirect
5. #59211C2semidirect
6. #59145C2semidirect
7. #45425C2semidirect
8. #45421C2semidirect
9. #45347C2semidirect
10. #45299C2semidirect
11. #45056C2semidirect
12. #45041C2semidirect
13. #44979C2semidirect
14. #44963C2semidirect
15. #43088C2semidirect
16. #43086C2semidirect
17. #40308C2semidirect
18. #38708C2semidirect
19. #38414C2semidirect
20. #36356C2semidirect
21. #35615C2semidirect
22. #35562C2semidirect
23. #35190C2semidirect
24. #35188C2semidirect
25. #34977C2semidirect
26. #34878C2semidirect
27. #34331C2semidirect
28. #34222C2semidirect
29. #34195C2semidirect
30. #34125C2semidirect
31. #34070C2semidirect
794. #124#41semidirect

Maximal subgroups

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

subgroupindex
#599052
#597542
#593492
#593452
#592112
#591452
#454252
#454212
#453472
#452992
#450562
#450412
#449792
#449632
#430882
#430862
#403082
#387082
#384142
#363562
#356152
#355622
#351902
#351882
#349772
#348782
#343312
#342222
#341952
#341252
#340702