Finite Group Databasebeta

← #7895369

Subgroups — #7895369

Order 512.

4695 conjugacy classes of subgroups.

The subgroup lattice has 1469 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59905C212yesmaximal, complemented
2#59875C211yesmaximal, characteristic, complemented
3#52162C211yesmaximal, characteristic, complemented
4#49406C214yesmaximal, complemented
5#48979C214yesmaximal, complemented
6#48610C214yesmaximal, complemented
7#46977C214yesmaximal, complemented
8#46290C212yesmaximal, complemented
9#45369C212yesmaximal, complemented
10#45149C212yesmaximal, complemented
11#45146C212yesmaximal, complemented
12#43263C214yesmaximal, complemented
13#42700C212yesmaximal, complemented
14#42518C212yesmaximal, complemented
15#41858C214yesmaximal, complemented
16#39765C211yesmaximal, characteristic, complemented
17#39718C212yesmaximal, complemented
18#39580C212yesmaximal, complemented
19#39356C211yesmaximal, characteristic, complemented
20#38983C212yesmaximal, complemented
21#38781C212yesmaximal, complemented
22#38095C212yesmaximal, complemented
23#37155C212yesmaximal, complemented
24#36469C211yesmaximal, characteristic, complemented
25#35838C212yesmaximal, complemented
26#35628C212yesmaximal, complemented
27#35206C211yesmaximal, characteristic, complemented
28#34472C212yesmaximal, complemented
29#34321C211yesmaximal, characteristic, complemented
30C2×#559C2212yes—
31C2×#555C2211yescharacteristic
32C2×#548C2212yes—
33C2×#536C2212yes—
34C2×#533C2212yes—
35#2858C2211yescharacteristic
36#2855C2212yes—
37#2854C2212yes—
38#2851C2212yes—
39#2850C2212yes—
40#2838C2214yes—
41#2825C2214yes—
42#2810C2212yes—
43#2810C2212yes—
44#2808C2212yes—
45#2808C2212yes—
46#2804C2212yes—
47#2788C2214yes—
48#2785C2214yes—
49#2784C2214yes—
50#2781C2214yes—
51#2781C2214yes—
52#2778C2214yes—
53#2778C2214yes—
54#2775C2214yes—
55#2764C2214yes—
56#2763C2214yes—
57#2762C2214yes—
58#2759C2214yes—
59#2759C2214yes—
60#2758C2214yes—
61#2756C2214yes—
62#2754C2214yes—
63#2745C2214yes—
64#2745C2214yes—
65#2739C2214yes—
66#2734C2211yescharacteristic
67#2732C2211yescharacteristic
68#2731C2214yes—
69#2730C2214yes—
70#2729C2212yes—
71#2726C2211yescharacteristic
72#2724C2212yes—
73#2720C2212yes—
74#2713C2212yes—
75#2712C2214yes—
76#2712C2214yes—
77#2708C2214yes—
78#2706C2214yes—
79#2704C2212yes—
80#2700C2214yes—
81#2696C2214yes—
82#2696C2214yes—
83#2693C2214yes—
84#2692C2212yes—
85#2688C2214yes—
86#2688C2214yes—
87#2687C2214yes—
88#2686C2214yes—
89#2683C2211yescharacteristic
90#2683C2212yes—
91#2683C2212yes—
92#2682C2212yes—
93#2682C2212yes—
94#2677C2212yes—
95#2674C2214yes—
96#2653C2214yes—
97#2652C2214yes—
98#2652C2214yes—
99#2650C2214yes—
100#2643C2214yes—
101#2640C2212yes—
102#2635C2214yes—
103#2631C2214yes—
104#2620C2212yes—
105#2619C2212yes—
106#2609C2214yes—
107#2602C2214yes—
108#2600C2214yes—
109#2598C2214yes—
110#2597C2214yes—
111#2594C2214yes—
112#2593C2214yes—
113#2592C2212yes—
114#2592C2212yes—
115#2592C2212yes—
116#2592C2212yes—
117#2592C2212yes—
118#2586C2214yes—
119#2581C2212yes—
120#2580C2212yes—
121#2575C2214yes—
122#2574C2214yes—
123#2572C2214yes—
124#2568C2211yescharacteristic
125#2568C2212yes—
126#2568C2212yes—
127#2568C2212yes—
128#2568C2212yes—
129#2568C2212yes—
130#2558C2214yes—
131#2557C2214yes—
132#2557C2214yes—
133#2552C2211yescharacteristic
134#2548C2212yes—
135#2547C2211yescharacteristic
136#2547C2211yescharacteristic
137#2545C2212yes—
138#2545C2212yes—
139#2544C2212yes—
140#2544C2212yes—
141#2541C2211yescharacteristic
142#2538C2211yescharacteristic
143#2525C2214yes—
144#2520C2214yes—
145#2518C2214yes—
146#2516C2214yes—
147#2515C2214yes—
148#2515C2214yes—
149#2515C2214yes—
150#2514C2212yes—
151#2514C2212yes—
152#2514C2212yes—
153#2514C2214yes—
154#2514C2214yes—
155#2513C2212yes—
156#2511C2212yes—
157#2510C2214yes—
158#2510C2214yes—
159#2500C2212yes—
160#2499C2212yes—
161#2495C2212yes—
162#2492C2214yes—
163#2492C2214yes—
164#2491C2212yes—
165#2489C2214yes—
166#2489C2214yes—
167#2489C2212yes—
168#2488C2214yes—
169#2488C2214yes—
170#2488C2214yes—
171#2488C2214yes—
172#2488C2214yes—
173#2477C2214yes—
174#2477C2214yes—
175#2475C2214yes—
176#2474C2214yes—
177#2474C2214yes—
178#2463C2214yes—
179#2461C2214yes—
180#2461C2214yes—
181#2461C2214yes—
182#2460C2214yes—
183#2460C2214yes—
184#2459C2214yes—
185#2459C2214yes—
186#2458C2214yes—
187#2457C2214yes—
188#2456C2214yes—
189#2450C2214yes—
190#2450C2214yes—
191#2447C2212yes—
192#2447C2212yes—
193#2446C2212yes—
194#2446C2212yes—
195#2445C2212yes—
196#2436C2212yes—
197#2434C2212yes—
198#2431C2212yes—
199#2431C2212yes—
200#2422C2212yes—
201#2399C2212yes—
202#2396C2212yes—
203#2396C2212yes—
204#2395C2214yes—
205#2379C2214yes—
206#2378C2214yes—
207#2369C2211yescharacteristic
208#2367C2214yes—
209#2367C2212yes—
210#2367C2212yes—
211#2366C2211yescharacteristic
212#2365C2211yescharacteristic
213#2364C2214yes—
214#2363C2212yes—
215#2361C2212yes—
216#2361C2212yes—
217#2360C2212yes—
218#2359C2214yes—
219#2355C2212yes—
220#2355C2212yes—
221#2355C2212yes—
222#2355C2212yes—
223#2354C2212yes—
224#2354C2211yescharacteristic
225#2349C2214yes—
226D4×C4⋊C4C2211yescharacteristic
227#2347C2212yes—
228#2347C2212yes—
229Q8×C22⋊C4C2212yes—
230#2339C2212yes—
231#2337C2214yes—
232#2337C2214yes—
233#2329C2214yes—
234#2326C2212yes—
235#2326C2212yes—
236#2325C2214yes—
237#2324C2212yes—
238#2323C2212yes—
239#2320C2212yes—
240#2318C2214yes—
241#2318C2214yes—
242#2311C2212yes—
243#2310C2212yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2211yescharacteristic
247C4×C22⋊Q8C2212yes—
248C4×#121C2212yes—
249C4×#121C2212yes—
250C4×#121C2212yes—
251#2297C2212yes—
252#2296C2212yes—
253#2295C2211yescharacteristic
254C2×#391C2212yes—
255#2293C2211yescharacteristic
256#2290C2212yes—
257#2274C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260C23×Q8C2312yes—
261#559—48no—
262#555—28no—
263#548—216no—
264#536—48no—
265#533—48no—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×#127C2311yescharacteristic
274C2×#127C2312yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×#124C2314yes—
281C2×#124C2314yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2314yes—
286C2×#124C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2312yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2314yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2311yescharacteristic
329C2×#117C2312yes—
330C2×#117C2312yes—
331C2×#117C2312yes—
332C2×#117C2312yes—
333C2×#117C2314yes—
334C2×#117C2312yes—
335C22×C4⋊C4C2312yes—
336C22×C42C2312yes—
337C22×C42C2312yes—
338#401C2314yes—
339#401C2314yes—
340#401C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2312yes—
359#400C2312yes—
360#399C2312yes—
361#399C2314yes—
362#399C2312yes—
363#398C2314yes—
364#398C2314yes—
365#398C2312yes—
366#398C2312yes—
367#398C2312yes—
368#398C2312yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
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#396C2312yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2312yes—
398#396C2312yes—
399#396C2312yes—
400#396C2314yes—
401#396C2314yes—
402#395C2312yes—
403#395C2314yes—
404#395C2312yes—
405#395C2312yes—
406#395C2314yes—
407#395C2312yes—
408#395C2312yes—
409#395C2312yes—
410#395C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#393C2312yes—
432#393C2314yes—
433#393C2314yes—
434#393C2312yes—
435#393C2314yes—
436#393C2314yes—
437#392C2314yes—
438#392C2314yes—
439#392C2314yes—
440#392C2314yes—
441#392C2314yes—
442#392C2314yes—
443#392C2314yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2314yes—
452#391C2314yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2312yes—
460#391C2314yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2314yes—
465#391C2314yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2314yes—
470#391C2314yes—
471#391C2314yes—
472#391C2314yes—
473#391C2311yescharacteristic
474#391C2312yes—
475#391C2314yes—
476#391C2311yescharacteristic
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2314yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2312yes—
485#390C2314yes—
486#390C2312yes—
487#390C2312yes—
488#390C2312yes—
489#390C2312yes—
490#390C2312yes—
491#390C2311yescharacteristic
492#390C2312yes—
493#390C2311yescharacteristic
494#389C2312yes—
495#389C2311yescharacteristic
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2311yescharacteristic
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#389C2312yes—
510#389C2311yescharacteristic
511#389C2311yescharacteristic
512#389C2312yes—
513#389C2311yescharacteristic
514#389C2311yescharacteristic
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#388C2312yes—
540#388C2312yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2312yes—
553#388C2314yes—
554#388C2312yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
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#387C2312yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2312yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2312yes—
584#387C2314yes—
585#387C2312yes—
586#387C2312yes—
587#387C2312yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2312yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2312yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#385C2312yes—
615#385C2312yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2312yes—
630#385C2314yes—
631#385C2312yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#384C2311yescharacteristic
636#384C2311yescharacteristic
637#384C2311yescharacteristic
638#384C2312yes—
639#383C2314yes—
640#383C2314yes—
641#383C2314yes—
642#383C2314yes—
643#383C2314yes—
644#382C2314yes—
645#382C2314yes—
646#382C2312yes—
647#382C2312yes—
648#382C2312yes—
649#382C2314yes—
650#382C2314yes—
651#382C2314yes—
652#382C2314yes—
653#381C2314yes—
654#381C2314yes—
655#381C2314yes—
656#381C2314yes—
657#381C2314yes—
658#380C2314yes—
659#380C2314yes—
660#380C2312yes—
661#380C2314yes—
662#380C2312yes—
663#380C2314yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2314yes—
712#376C2312yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C2×#95C2314yes—
716C43C2311yescharacteristic
717C2×#41—28no—
718C2×#41—44no—
719C2×#41—44no—
720C22×Q8—28no—
721C22×Q8—44no—
722C22×Q8—44no—
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×Q8C2414yes—
729C22×Q8C2412yes—
730C22×Q8C2412yes—
731C22×D4C2411yescharacteristic
732C22×D4C2412yes—
733C22×D4C2414yes—
734C22×D4C2412yes—
735C22×D4C2414yes—
736C22×D4C2414yes—
737C22×D4C2414yes—
738C22×D4C2414yes—
739C22×D4C2412yes—
740C22×D4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2414yes—
746C23×C4C2414yes—
747C23×C4C2414yes—
748C23×C4C2414yes—
749C23×C4C2414yes—
750C23×C4C2412yes—
751C23×C4C2412yes—
752C4⋊Q8—24no—
753C4⋊Q8—24no—
754C4⋊Q8—42no—
755C4⋊Q8—42no—
756C4⋊Q8—44no—
757C4⋊Q8—44no—
758C4⋊Q8—44no—
759#127—42no—
760#127—44no—
761#125—44no—
762#125—44no—
763#125—82no—
764#124—216no—
765#124—216no—
766#124—28no—
767#124—28no—
768#124—44no—
769#124—44no—
770#124—44no—
771#124—48no—
772#124—84no—
773#123—48no—
774#123—48no—
775#123—48no—
776#123—48no—
777#123—48no—
778C22⋊Q8—28no—
779C22⋊Q8—216no—
780C22⋊Q8—44no—
781C22⋊Q8—44no—
782C22⋊Q8—44no—
783C22⋊Q8—48no—
784C22⋊Q8—48no—
785C22⋊Q8—44no—
786C22⋊Q8—44no—
787C22⋊Q8—82no—
788#121—216no—
789#121—28no—
790#121—28no—
791#121—28no—
792#121—44no—
793#121—82no—
794C4×Q8—28no—
795C4×Q8—24no—
796C4×Q8—28no—
797C4×Q8—44no—
798C4×Q8—44no—
799C4×Q8—44no—
800C4×Q8—44no—
801C4×Q8—44no—
802C4×D4—216no—
803C4×D4—24no—
804C4×D4—24no—
805C4×D4—44no—
806C4×D4—42no—
807C4×D4—44no—
808C4×D4—48no—
809C4×D4—48no—
810C4×D4—82no—
811C4×D4—82no—
812C4×D4—84no—
813C4×D4—84no—
814C4×D4#4118yes—
815#117—28no—
816#117—28no—
817#117—28no—
818#117—44no—
819#117—82no—
820#117—84no—
821C2×C4⋊C4—44no—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C42—44no—
930C2×C42—82no—
931C2×C42C2414yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2414yes—
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2411yescharacteristic
953C2×C42C2411yescharacteristic
954C2×C42C2411yescharacteristic
955C2×C42C2411yescharacteristic
956C2×C42C2411yescharacteristic
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024C24C2514yes—
1025C24C2512yes—
1026C24C2512yes—
1027#41—816no—
1028C2×Q8—24no—
1029C2×Q8—24no—
1030C2×Q8—28no—
1031C2×Q8—24no—
1032C2×Q8—24no—
1033C2×Q8—24no—
1034C2×Q8—22no—
1035C2×Q8—24no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—42no—
1039C2×Q8—42no—
1040C2×Q8—42no—
1041C2×Q8—44no—
1042C2×Q8—42no—
1043C2×Q8—41no—
1044C2×Q8—42no—
1045C2×Q8—42no—
1046C2×Q8—44no—
1047C2×Q8—42no—
1048C2×Q8—42no—
1049C2×Q8—41no—
1050C2×Q8—42no—
1051C2×Q8—42no—
1052C2×Q8—816no—
1053C2×D4—28no—
1054C2×D4—28no—
1055C2×D4—28no—
1056C2×D4—22no—
1057C2×D4—24no—
1058C2×D4—22no—
1059C2×D4—24no—
1060C2×D4—22no—
1061C2×D4—24no—
1062C2×D4—24no—
1063C2×D4—41no—
1064C2×D4—44no—
1065C2×D4—41no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—42no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—42no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—42no—
1079C2×D4—42no—
1080C2×D4—42no—
1081C2×D4—44no—
1082C2×D4C2×#4114yes—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—28no—
1086C22×C4—24no—
1087C22×C4—28no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—42no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—44no—
1097C22×C4—42no—
1098C22×C4—44no—
1099C22×C4—42no—
1100C22×C4—44no—
1101C22×C4—42no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—42no—
1105C22×C4—42no—
1106C22×C4—42no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4C2×#4118yes—
1116C22×C4C2511yescharacteristic
1117C22×C4C2514yes—
1118C22×C4C2514yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2514yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2514yes—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2514yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2511yescharacteristic
1136C22×C4C2511yescharacteristic
1137C22×C4C2512yes—
1138C22×C4C2511yescharacteristic
1139C22×C4C2511yescharacteristic
1140C22×C4C2511yescharacteristic
1141C22×C4C2511yescharacteristic
1142C4⋊C4—22no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—28no—
1146C4⋊C4—24no—
1147C4⋊C4—28no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—22no—
1151C4⋊C4—24no—
1152C4⋊C4—22no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—22no—
1159C4⋊C4—24no—
1160C4⋊C4—28no—
1161C4⋊C4—22no—
1162C4⋊C4—22no—
1163C4⋊C4—24no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—41no—
1168C4⋊C4—41no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—41no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—41no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—42no—
1191C4⋊C4—44no—
1192C4⋊C4—41no—
1193C4⋊C4—42no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—42no—
1197C4⋊C4—41no—
1198C4⋊C4—42no—
1199C4⋊C4—42no—
1200C4⋊C4—42no—
1201C4⋊C4C2×#4114yes—
1202C22⋊C4—28no—
1203C22⋊C4—28no—
1204C22⋊C4—28no—
1205C22⋊C4—24no—
1206C22⋊C4—28no—
1207C22⋊C4—28no—
1208C22⋊C4—28no—
1209C22⋊C4—24no—
1210C22⋊C4—24no—
1211C22⋊C4—24no—
1212C22⋊C4—28no—
1213C22⋊C4—28no—
1214C22⋊C4—24no—
1215C22⋊C4—42no—
1216C22⋊C4—44no—
1217C22⋊C4—42no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—42no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—42no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4C2×#4118yes—
1249C42—28no—
1250C42—28no—
1251C42—24no—
1252C42—24no—
1253C42—24no—
1254C42—24no—
1255C42—24no—
1256C42—22no—
1257C42—22no—
1258C42—42no—
1259C42—42no—
1260C42—41no—
1261C42—42no—
1262C42—42no—
1263C42—42no—
1264C42—41no—
1265C42—41no—
1266C42—44no—
1267C42—44no—
1268C42—44no—
1269C42—44no—
1270C42—44no—
1271C42—44no—
1272C42—44no—
1273C42C2×#4114yes—
1274C42H(5,𝔽2)14yes—
1275C23—22no—
1276C23—22no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—22no—
1282C23—24no—
1283C23—24no—
1284C23—22no—
1285C23—22no—
1286C23—24no—
1287C23—22no—
1288C23—24no—
1289C23—22no—
1290C23—24no—
1291C23—24no—
1292C23—22no—
1293C23—24no—
1294C23—22no—
1295C23C22×#4114yes—
1296C23C2611yescharacteristic
1297Q8—48no—
1298Q8—48no—
1299Q8—84no—
1300Q8—82no—
1301Q8—84no—
1302Q8—88no—
1303Q8—84no—
1304Q8—84no—
1305D4—44no—
1306D4—416no—
1307D4—44no—
1308D4—48no—
1309D4—84no—
1310D4—88no—
1311D4—88no—
1312D4—88no—
1313D4—162no—
1314D4—164no—
1315C2×C4—22no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—22no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—216no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—21no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—21no—
1370C2×C4—21no—
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—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—48no—
1386C2×C4—84no—
1387C2×C4—84no—
1388C2×C4—88no—
1389C2×C4—88no—
1390C2×C4—84no—
1391C2×C4—84no—
1392C2×C4—88no—
1393C2×C4—164no—
1394C2×C4—164no—
1395C2×C4C22×#4112yes—
1396C2×C4C22×#4114yes—
1397C2×C4C22×#4112yes—
1398C2×C4C22×#4112yes—
1399C2×C4C2×H(5,𝔽2)12yes—
1400C2×C4C2×H(5,𝔽2)12yes—
1401C2×C4C2×H(5,𝔽2)12yes—
1402C2×C4#58512yes—
1403C2×C4#58512yes—
1404C22—24no—
1405C22—24no—
1406C22—24no—
1407C22—42no—
1408C22—42no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—44no—
1413C22—44no—
1414C22—42no—
1415C22—44no—
1416C22—42no—
1417C22—42no—
1418C22—44no—
1419C22—42no—
1420C22—44no—
1421C22—42no—
1422C22—44no—
1423C22—44no—
1424C22—42no—
1425C22C23×#4111yescharacteristic
1426C22C22×H(5,𝔽2)11yescharacteristic
1427C22C2×#58511yescharacteristic
1428C22C2×#58511yescharacteristic
1429C22H(7,𝔽2)11yescharacteristic
1430C222−1+611yescharacteristic
1431C222−1+611yescharacteristic
1432C4—22no—
1433C4—24no—
1434C4—22no—
1435C4—22no—
1436C4—22no—
1437C4—22no—
1438C4—44no—
1439C4—44no—
1440C4—44no—
1441C4—42no—
1442C4—41no—
1443C4—42no—
1444C4—44no—
1445C4—42no—
1446C4—42no—
1447C4—42no—
1448C4—42no—
1449C4—42no—
1450C4—42no—
1451C4—42no—
1452C4—42no—
1453C4—42no—
1454C4—42no—
1455C4—44no—
1456C4—42no—
1457C4#351414yes—
1458C2—44no—
1459C2—82no—
1460C2—84no—
1461C2C2×#351411yescharacteristic
1462C2#6284511yescharacteristic
1463C2#6287811yescharacteristic
1464C2#6296011yescharacteristic
1465C2#6296511yescharacteristic
1466C2#6299511yescharacteristic
1467C2#6306211yescharacteristic
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. #59875C2semidirect
3. #52162C2semidirect
4. #49406C2semidirect
5. #48979C2semidirect
6. #48610C2semidirect
7. #46977C2semidirect
8. #46290C2semidirect
9. #45369C2semidirect
10. #45149C2semidirect
11. #45146C2semidirect
12. #43263C2semidirect
13. #42700C2semidirect
14. #42518C2semidirect
15. #41858C2semidirect
16. #39765C2semidirect
17. #39718C2semidirect
18. #39580C2semidirect
19. #39356C2semidirect
20. #38983C2semidirect
21. #38781C2semidirect
22. #38095C2semidirect
23. #37155C2semidirect
24. #36469C2semidirect
25. #35838C2semidirect
26. #35628C2semidirect
27. #35206C2semidirect
28. #34472C2semidirect
29. #34321C2semidirect

Maximal subgroups

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

subgroupindex
#599052
#598752
#521622
#494062
#489792
#486102
#469772
#462902
#453692
#451492
#451462
#432632
#427002
#425182
#418582
#397652
#397182
#395802
#393562
#389832
#387812
#380952
#371552
#364692
#358382
#356282
#352062
#344722
#343212