Finite Group Databasebeta

← #7901056

Subgroups — #7901056

Order 512.

4423 conjugacy classes of subgroups.

The subgroup lattice has 1402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59863C211yesmaximal, characteristic, complemented
2#59545C212yesmaximal, complemented
3#52274C211yesmaximal, characteristic, complemented
4#50750C214yesmaximal, complemented
5#49777C214yesmaximal, complemented
6#47885C214yesmaximal, complemented
7#47388C214yesmaximal, complemented
8#45807C212yesmaximal, complemented
9#45376C212yesmaximal, complemented
10#45211C212yesmaximal, complemented
11#45164C212yesmaximal, complemented
12#43351C214yesmaximal, complemented
13#42614C212yesmaximal, complemented
14#42479C212yesmaximal
15#42352C214yesmaximal, complemented
16#40130C212yesmaximal, complemented
17#39756C211yesmaximal, characteristic, complemented
18#39637C211yesmaximal, characteristic, complemented
19#39504C212yesmaximal, complemented
20#38467C212yesmaximal, complemented
21#38242C212yesmaximal, complemented
22#38228C212yesmaximal, complemented
23#37324C212yesmaximal, complemented
24#36261C211yesmaximal, characteristic, complemented
25#35963C212yesmaximal, complemented
26#35602C212yesmaximal, complemented
27#35176C211yesmaximal, characteristic, complemented
28#34489C212yesmaximal, complemented
29#34330C211yesmaximal, characteristic
30C2×#554C2212yes—
31C2×#550C2211yescharacteristic
32#2860C2212yes—
33#2859C2211yescharacteristic
34#2857C2212yes—
35#2857C2212yes—
36#2855C2212yes—
37#2831C2214yes—
38#2816C2214yes—
39#2809C2211yescharacteristic
40#2809C2212yes—
41#2808C2212yes—
42#2808C2212yes—
43#2808C2212yes—
44#2808C2212yes—
45#2806C2211yescharacteristic
46#2806C2212yes—
47#2805C2212yes—
48#2805C2214yes—
49#2805C2214yes—
50#2805C2211yescharacteristic
51#2802C2212yes—
52#2800C2214yes—
53#2799C2212yes—
54#2791C2212yes—
55#2783C2214yes—
56#2783C2214yes—
57#2774C2212yes—
58#2774C2214yes—
59#2774C2214yes—
60#2761C2214yes—
61#2755C2212yes—
62#2750C2214yes—
63#2750C2214yes—
64#2744C2214yes—
65#2744C2214yes—
66#2743C2214yes—
67#2743C2214yes—
68#2743C2214yes—
69#2741C2214yes—
70#2741C2214yes—
71#2741C2214yes—
72#2740C2214yes—
73#2727C2212yes—
74#2727C2212yes—
75#2727C2214yes—
76#2726C2211yescharacteristic
77#2726C2212yes—
78#2721C2214yes—
79#2716C2214yes—
80#2715C2214yes—
81#2713C2212yes—
82#2702C2214yes—
83#2702C2214yes—
84#2702C2214yes—
85#2695C2214yes—
86#2694C2214yes—
87#2689C2214yes—
88#2689C2214yes—
89#2681C2214yes—
90#2681C2214yes—
91#2672C2214yes—
92#2672C2214yes—
93#2667C2214yes—
94#2667C2214yes—
95#2664C2214yes—
96#2652C2214yes—
97#2647C2212yes—
98#2644C2212yes—
99#2641C2212yes—
100#2637C2214yes—
101#2618C2214yes—
102#2616C2214yes—
103#2609C2214yes—
104#2607C2214yes—
105#2601C2214yes—
106#2592C2214yes—
107#2590C2214yes—
108#2590C2214yes—
109#2589C2214yes—
110#2589C2214yes—
111#2587C2214yes—
112#2585C2214yes—
113#2584C2212yes—
114#2584C2212yes—
115#2583C2214yes—
116#2580C2212yes—
117#2574C2214yes—
118#2571C2212yes—
119#2571C2212yes—
120#2569C2214yes—
121#2569C2214yes—
122#2563C2212yes—
123#2558C2214yes—
124#2553C2214yes—
125#2553C2214yes—
126#2553C2214yes—
127#2552C2211yescharacteristic
128#2552C2211yescharacteristic
129#2551C2211yescharacteristic
130#2550C2212yes—
131#2549C2214yes—
132#2548C2212yes—
133#2547C2212yes—
134#2546C2211yescharacteristic
135#2542C2211yescharacteristic
136#2538C2211yescharacteristic
137#2522C2214yes—
138#2522C2214yes—
139#2521C2214yes—
140#2519C2214yes—
141#2513C2212yes—
142#2513C2212yes—
143#2512C2212yes—
144#2512C2212yes—
145#2512C2212yes—
146#2512C2212yes—
147#2509C2212yes—
148#2509C2212yes—
149#2508C2212yes—
150#2508C2214yes—
151#2508C2214yes—
152#2508C2212yes—
153#2507C2212yes—
154#2507C2212yes—
155#2506C2212yes—
156#2498C2214yes—
157#2497C2214yes—
158#2496C2214yes—
159#2492C2214yes—
160#2488C2214yes—
161#2488C2214yes—
162#2488C2214yes—
163#2486C2214yes—
164#2485C2214yes—
165#2485C2214yes—
166#2481C2214yes—
167#2479C2214yes—
168#2470C2214yes—
169#2470C2214yes—
170#2468C2214yes—
171#2466C2214yes—
172#2466C2214yes—
173#2466C2214yes—
174#2460C2214yes—
175#2454C2212yes—
176#2454C2212yes—
177#2454C2212yes—
178#2454C2212yes—
179#2454C2212yes—
180#2453C2214yes—
181#2452C2212yes—
182#2452C2212yes—
183#2445C2212yes—
184#2445C2212yes—
185#2445C2212yes—
186#2445C2212yes—
187#2440C2212yes—
188#2440C2212yes—
189#2439C2214yes—
190#2438C2214yes—
191#2438C2214yes—
192#2429C2212yes—
193#2429C2214yes—
194#2423C2212yes—
195#2423C2214yes—
196#2413C2214yes—
197#2406C2214yes—
198#2402C2212yes—
199#2402C2212yes—
200#2399C2212yes—
201#2396C2214yes—
202#2378C2214yes—
203#2378C2214yes—
204#2370C2212yes—
205#2370C2212yes—
206#2370C2212yes—
207#2370C2212yes—
208#2366C2212yes—
209#2366C2211yescharacteristic
210#2365C2212yes—
211#2364C2214yes—
212#2363C2212yes—
213#2362C2214yes—
214#2357C2212yes—
215#2357C2212yes—
216#2357C2212yes—
217#2357C2212yes—
218#2355C2211yescharacteristic
219#2355C2212yes—
220#2354C2211yescharacteristic
221#2354C2212yes—
222#2354C2212yes—
223#2352C2214yes—
224#2349C2212yes—
225D4×C4⋊C4C2211yescharacteristic
226D4×C4⋊C4C2211yescharacteristic
227#2344C2214yes—
228#2339C2212yes—
229#2334C2214yes—
230#2333C2214yes—
231#2332C2214yes—
232#2332C2214yes—
233#2331C2212yes—
234#2331C2212yes—
235#2330C2212yes—
236#2330C2212yes—
237#2328C2212yes—
238#2323C2214yes—
239#2319C2212yes—
240#2319C2212yes—
241#2319C2212yes—
242#2313C2214yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×C4⋊Q8C2211yescharacteristic
245C4×#127C2211yescharacteristic
246C4×#125C2212yes—
247C4×#125C2212yes—
248C4×#121C2212yes—
249#2297C2212yes—
250#2295C2212yes—
251#2295C2211yescharacteristic
252#2295C2211yescharacteristic
253#2295C2212yes—
254#2293C2212yes—
255#2293C2212yes—
256C2×#389C2212yes—
257#2275C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260#554—216no—
261#550—28no—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×#127C2311yescharacteristic
268C2×#127C2312yes—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#124C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×#121C2312yes—
293C2×#121C2314yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2314yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2311yescharacteristic
311C2×#117C2312yes—
312C2×#117C2314yes—
313C2×#117C2314yes—
314C2×#117C2314yes—
315C22×C4⋊C4C2314yes—
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2312yes—
318C22×C42C2312yes—
319#400C2312yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2312yes—
328#400C2314yes—
329#400C2312yes—
330#400C2314yes—
331#400C2312yes—
332#400C2312yes—
333#400C2314yes—
334#400C2312yes—
335#400C2312yes—
336#400C2312yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#398C2312yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2312yes—
361#398C2314yes—
362#398C2312yes—
363#398C2314yes—
364#398C2312yes—
365#398C2312yes—
366#398C2314yes—
367#398C2312yes—
368#398C2312yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2312yes—
403#395C2312yes—
404#395C2312yes—
405#395C2312yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2312yes—
432#391C2314yes—
433#391C2314yes—
434#391C2312yes—
435#391C2314yes—
436#391C2311yescharacteristic
437#391C2312yes—
438#391C2311yescharacteristic
439#391C2312yes—
440#391C2311yescharacteristic
441#391C2312yes—
442#391C2312yes—
443#391C2311yescharacteristic
444#390C2312yes—
445#390C2312yes—
446#390C2312yes—
447#390C2312yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2314yes—
456#390C2314yes—
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2311yescharacteristic
468#389C2312yes—
469#389C2312yes—
470#389C2311yescharacteristic
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2311yescharacteristic
504#389C2312yes—
505#389C2314yes—
506#389C2312yes—
507#389C2311yescharacteristic
508#389C2312yes—
509#389C2314yes—
510#389C2312yes—
511#389C2312yes—
512#389C2311yescharacteristic
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2311yescharacteristic
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#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2312yes—
554#387C2312yes—
555#387C2312yes—
556#387C2312yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2312yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2312yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
583#387C2312yes—
584#387C2314yes—
585#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
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#385C2314yes—
621#384C2311yescharacteristic
622#384C2311yescharacteristic
623#384C2311yescharacteristic
624#384C2312yes—
625#384C2312yes—
626#384C2312yes—
627#384C2311yescharacteristic
628#384C2311yescharacteristic
629#382C2312yes—
630#382C2312yes—
631#382C2312yes—
632#382C2312yes—
633#382C2314yes—
634#382C2314yes—
635#382C2314yes—
636#382C2312yes—
637#382C2314yes—
638#381C2314yes—
639#381C2314yes—
640#381C2314yes—
641#381C2314yes—
642#381C2314yes—
643#381C2314yes—
644#381C2314yes—
645#380C2314yes—
646#380C2314yes—
647#380C2312yes—
648#380C2314yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2314yes—
655#380C2312yes—
656#380C2312yes—
657#380C2312yes—
658#380C2314yes—
659#380C2314yes—
660#380C2314yes—
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707#376C2312yes—
708#376C2312yes—
709#376C2312yes—
710C2×#95C2314yes—
711C2×#95C2314yes—
712C43C2312yes—
713C43C2311yescharacteristic
714C2×#41—28no—
715C2×#41—82no—
716C2×#41—82no—
717C22×Q8C2414yes—
718C22×Q8C2412yes—
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×Q8C2411yescharacteristic
722C22×D4C2412yes—
723C22×D4C2411yescharacteristic
724C22×D4C2412yes—
725C22×D4C2414yes—
726C22×D4C2412yes—
727C22×D4C2414yes—
728C23×C4C2412yes—
729C23×C4C2414yes—
730C23×C4C2414yes—
731C23×C4C2414yes—
732C23×C4C2414yes—
733C23×C4C2414yes—
734C23×C4C2412yes—
735C23×C4C2412yes—
736C4⋊Q8—28no—
737C4⋊Q8—24no—
738C4⋊Q8—42no—
739C4⋊Q8—82no—
740C4⋊Q8—82no—
741#127—28no—
742#127—24no—
743#126—48no—
744#126—84no—
745#126—84no—
746#126—84no—
747#126—84no—
748#125—28no—
749#125—28no—
750#125—28no—
751#125—44no—
752#125—84no—
753#124—84no—
754#123—84no—
755#123—84no—
756#123—84no—
757#123—84no—
758C22⋊Q8—216no—
759C22⋊Q8—216no—
760C22⋊Q8—216no—
761C22⋊Q8—84no—
762C22⋊Q8—84no—
763C22⋊Q8—82no—
764C22⋊Q8—82no—
765C22⋊Q8—82no—
766#121—28no—
767#121—216no—
768C4×Q8—24no—
769C4×Q8—28no—
770C4×Q8—24no—
771C4×Q8—84no—
772C4×Q8—82no—
773C4×D4—28no—
774C4×D4—28no—
775C4×D4—28no—
776C4×D4—24no—
777C4×D4—28no—
778C4×D4—24no—
779C4×D4—28no—
780C4×D4—44no—
781C4×D4—48no—
782C4×D4—82no—
783C4×D4—82no—
784C4×D4#4118yes—
785#117—84no—
786#117—84no—
787#117—84no—
788#117—82no—
789C2×C4⋊C4—216no—
790C2×C4⋊C4—44no—
791C2×C4⋊C4—82no—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2411yescharacteristic
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C42—82no—
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2411yescharacteristic
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2411yescharacteristic
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2411yescharacteristic
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2414yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003C24C2514yes—
1004C24C2512yes—
1005#41—816no—
1006C2×Q8—22no—
1007C2×Q8—24no—
1008C2×Q8—28no—
1009C2×Q8—22no—
1010C2×Q8—24no—
1011C2×Q8—41no—
1012C2×Q8—41no—
1013C2×Q8—44no—
1014C2×Q8—42no—
1015C2×Q8—41no—
1016C2×Q8—42no—
1017C2×Q8—44no—
1018C2×Q8—42no—
1019C2×Q8—42no—
1020C2×Q8—41no—
1021C2×D4—28no—
1022C2×D4—28no—
1023C2×D4—24no—
1024C2×D4—24no—
1025C2×D4—24no—
1026C2×D4—22no—
1027C2×D4—22no—
1028C2×D4—24no—
1029C2×D4—24no—
1030C2×D4—42no—
1031C2×D4—42no—
1032C2×D4—42no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—42no—
1038C2×D4C2×#4114yes—
1039C22×C4—28no—
1040C22×C4—28no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—28no—
1044C22×C4—28no—
1045C22×C4—24no—
1046C22×C4—28no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—42no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4C2×#4118yes—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2514yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2511yescharacteristic
1076C22×C4C2512yes—
1077C22×C4C2514yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2514yes—
1082C22×C4C2511yescharacteristic
1083C22×C4C2511yescharacteristic
1084C22×C4C2512yes—
1085C22×C4C2511yescharacteristic
1086C22×C4C2511yescharacteristic
1087C22×C4C2512yes—
1088C22×C4C2511yescharacteristic
1089C22×C4C2511yescharacteristic
1090C4⋊C4—24no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—22no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—28no—
1101C4⋊C4—28no—
1102C4⋊C4—24no—
1103C4⋊C4—22no—
1104C4⋊C4—22no—
1105C4⋊C4—24no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—22no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—22no—
1115C4⋊C4—24no—
1116C4⋊C4—44no—
1117C4⋊C4—41no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—41no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—42no—
1128C4⋊C4—41no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—41no—
1134C4⋊C4—41no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—41no—
1164C4⋊C4C2×#4114yes—
1165C4⋊C42−1+414yes—
1166C22⋊C4—28no—
1167C22⋊C4—28no—
1168C22⋊C4—28no—
1169C22⋊C4—24no—
1170C22⋊C4—28no—
1171C22⋊C4—28no—
1172C22⋊C4—24no—
1173C22⋊C4—28no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4C2×#4118yes—
1200C42—24no—
1201C42—24no—
1202C42—24no—
1203C42—22no—
1204C42—24no—
1205C42—24no—
1206C42—24no—
1207C42—22no—
1208C42—41no—
1209C42—42no—
1210C42—42no—
1211C42—42no—
1212C42—44no—
1213C42—42no—
1214C42—42no—
1215C42—44no—
1216C42—44no—
1217C42—44no—
1218C42—44no—
1219C42—41no—
1220C42—41no—
1221C42—44no—
1222C42—44no—
1223C42—42no—
1224C42—44no—
1225C42—44no—
1226C42—42no—
1227C42C2×#4114yes—
1228C422−1+414yes—
1229C23—22no—
1230C23—22no—
1231C23—22no—
1232C23—22no—
1233C23—22no—
1234C23—22no—
1235C23—24no—
1236C23—24no—
1237C23—24no—
1238C23—24no—
1239C23—24no—
1240C23—24no—
1241C23—24no—
1242C23C22×#4114yes—
1243C23C2611yescharacteristic
1244Q8—44no—
1245Q8—84no—
1246Q8—88no—
1247Q8—82no—
1248Q8—84no—
1249D4—28no—
1250D4—48no—
1251D4—48no—
1252D4—84no—
1253D4—88no—
1254D4—88no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—22no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—21no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—21no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—48no—
1327C2×C4—48no—
1328C2×C4—84no—
1329C2×C4—88no—
1330C2×C4—88no—
1331C2×C4—88no—
1332C2×C4—88no—
1333C2×C4—88no—
1334C2×C4C22×#4112yes—
1335C2×C4C22×#4112yes—
1336C2×C4C22×#4114yes—
1337C2×C4C22×#4112yes—
1338C2×C4C2×2−1+412yes—
1339C2×C4C2×2−1+412yes—
1340C2×C4C2×2−1+414yes—
1341C2×C4C2×2−1+412yes—
1342C2×C4C2×2−1+412yes—
1343C2×C4#58512yes—
1344C22—24no—
1345C22—24no—
1346C22—24no—
1347C22—42no—
1348C22—42no—
1349C22—42no—
1350C22—42no—
1351C22—44no—
1352C22—44no—
1353C22—44no—
1354C22—44no—
1355C22—44no—
1356C22—44no—
1357C22—44no—
1358C22C23×#4111yescharacteristic
1359C22C22×2−1+411yescharacteristic
1360C22C22×2−1+411yescharacteristic
1361C22C2×#58511yescharacteristic
1362C22H(7,𝔽2)11yescharacteristic
1363C22H(7,𝔽2)11yescharacteristic
1364C22H(7,𝔽2)11yescharacteristic
1365C4—22no—
1366C4—22no—
1367C4—24no—
1368C4—22no—
1369C4—22no—
1370C4—24no—
1371C4—22no—
1372C4—44no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4—42no—
1377C4—41no—
1378C4—42no—
1379C4—44no—
1380C4—42no—
1381C4—42no—
1382C4—44no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4—44no—
1387C4—42no—
1388C4—42no—
1389C4—42no—
1390C4—44no—
1391C4#350914yes—
1392C2—44no—
1393C2—84no—
1394C2C2×#350911yescharacteristic
1395C2#6284611yescharacteristic
1396C2#6288111yescharacteristic
1397C2#6294811yescharacteristic
1398C2#6296211yescharacteristic
1399C2#6299411yescharacteristic
1400C2#6307011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59863C2semidirect
2. #59545C2semidirect
3. #52274C2semidirect
4. #50750C2semidirect
5. #49777C2semidirect
6. #47885C2semidirect
7. #47388C2semidirect
8. #45807C2semidirect
9. #45376C2semidirect
10. #45211C2semidirect
11. #45164C2semidirect
12. #43351C2semidirect
13. #42614C2semidirect
15. #42352C2semidirect
16. #40130C2semidirect
17. #39756C2semidirect
18. #39637C2semidirect
19. #39504C2semidirect
20. #38467C2semidirect
21. #38242C2semidirect
22. #38228C2semidirect
23. #37324C2semidirect
24. #36261C2semidirect
25. #35963C2semidirect
26. #35602C2semidirect
27. #35176C2semidirect
28. #34489C2semidirect

Maximal subgroups

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

subgroupindex
#598632
#595452
#522742
#507502
#497772
#478852
#473882
#458072
#453762
#452112
#451642
#433512
#426142
#424792
#423522
#401302
#397562
#396372
#395042
#384672
#382422
#382282
#373242
#362612
#359632
#356022
#351762
#344892
#343302