Finite Group Databasebeta

← #7714745

Subgroups — #7714745

Order 512.

4482 conjugacy classes of subgroups.

The subgroup lattice has 1319 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51882C212yesmaximal, complemented
2#51873C212yesmaximal, complemented
3#51739C212yesmaximal, complemented
4#51738C214yesmaximal, complemented
5#51726C212yesmaximal, complemented
6#51725C214yesmaximal, complemented
7#47546C212yesmaximal, complemented
8#47544C212yesmaximal, complemented
9#47537C214yesmaximal, complemented
10#46973C214yesmaximal, complemented
11#46969C212yesmaximal, complemented
12#46966C212yesmaximal, complemented
13#39051C214yesmaximal, complemented
14#39039C214yesmaximal, complemented
15#37896C212yesmaximal, complemented
16#37886C212yesmaximal, complemented
17#37708C212yesmaximal, complemented
18#37698C212yesmaximal
19#37518C212yesmaximal, complemented
20#37258C212yesmaximal, complemented
21#37124C212yesmaximal, complemented
22#35179C211yesmaximal, characteristic, complemented
23#35178C211yesmaximal, characteristic
24#35099C212yesmaximal, complemented
25#35092C212yesmaximal, complemented
26#34409C212yesmaximal, complemented
27C2×#2327C211yesmaximal, characteristic, complemented
28C2×#539C2212yes—
29C2×#536C2212yes—
30C2×#533C2211yescharacteristic
31C2×#532C2211yescharacteristic
32C22×C4⋊Q8C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2855C2212yes—
36#2855C2212yes—
37#2854C2212yes—
38#2854C2212yes—
39#2853C2214yes—
40#2853C2214yes—
41#2833C2212yes—
42#2832C2212yes—
43#2831C2214yes—
44#2795C2214yes—
45#2794C2214yes—
46#2793C2214yes—
47#2793C2214yes—
48#2791C2214yes—
49#2790C2214yes—
50#2789C2212yes—
51#2785C2212yes—
52#2783C2214yes—
53#2783C2214yes—
54#2782C2212yes—
55#2781C2214yes—
56#2779C2214yes—
57#2776C2214yes—
58#2775C2214yes—
59#2772C2214yes—
60#2769C2212yes—
61#2767C2214yes—
62#2767C2214yes—
63#2766C2214yes—
64#2766C2214yes—
65#2765C2214yes—
66#2762C2214yes—
67#2762C2214yes—
68#2762C2214yes—
69#2761C2214yes—
70#2761C2214yes—
71#2747C2214yes—
72#2747C2214yes—
73#2745C2214yes—
74#2744C2214yes—
75#2744C2214yes—
76#2739C2214yes—
77#2737C2214yes—
78#2734C2212yes—
79#2734C2212yes—
80#2734C2214yes—
81#2731C2212yes—
82#2731C2212yes—
83#2731C2214yes—
84#2729C2214yes—
85#2729C2214yes—
86#2729C2214yes—
87#2729C2214yes—
88#2729C2214yes—
89#2719C2214yes—
90#2716C2214yes—
91#2715C2214yes—
92#2713C2214yes—
93#2709C2214yes—
94#2707C2214yes—
95#2700C2214yes—
96#2666C2214yes—
97#2665C2214yes—
98#2653C2214yes—
99#2650C2214yes—
100#2646C2212yes—
101#2643C2214yes—
102#2639C2212yes—
103#2627C2212yes—
104#2627C2212yes—
105#2627C2212yes—
106#2618C2212yes—
107#2618C2212yes—
108#2618C2212yes—
109#2614C2214yes—
110#2608C2214yes—
111#2605C2214yes—
112#2597C2214yes—
113#2597C2214yes—
114#2594C2214yes—
115#2594C2214yes—
116#2590C2214yes—
117#2586C2212yes—
118#2585C2214yes—
119#2582C2212yes—
120#2582C2212yes—
121#2581C2212yes—
122#2581C2212yes—
123#2577C2214yes—
124#2576C2214yes—
125#2574C2214yes—
126#2574C2214yes—
127#2573C2214yes—
128#2572C2212yes—
129#2570C2214yes—
130#2569C2214yes—
131#2568C2211yescharacteristic
132#2568C2211yescharacteristic
133#2567C2211yescharacteristic
134#2567C2211yescharacteristic
135#2565C2212yes—
136#2565C2212yes—
137#2548C2211yescharacteristic
138#2548C2211yescharacteristic
139#2546C2211yescharacteristic
140#2546C2211yescharacteristic
141#2545C2212yes—
142#2545C2212yes—
143#2538C2212yes—
144#2538C2212yes—
145#2536C2212yes—
146#2536C2212yes—
147#2533C2214yes—
148#2533C2214yes—
149#2532C2214yes—
150#2531C2214yes—
151#2531C2214yes—
152#2530C2214yes—
153#2529C2214yes—
154#2528C2214yes—
155#2528C2214yes—
156#2527C2214yes—
157#2526C2214yes—
158#2524C2214yes—
159#2520C2214yes—
160#2520C2214yes—
161#2518C2214yes—
162#2515C2214yes—
163#2510C2214yes—
164#2505C2214yes—
165#2497C2214yes—
166#2493C2214yes—
167#2493C2214yes—
168#2488C2214yes—
169#2484C2214yes—
170#2469C2214yes—
171#2469C2214yes—
172#2469C2214yes—
173#2466C2214yes—
174#2465C2214yes—
175#2465C2214yes—
176#2462C2214yes—
177#2462C2214yes—
178#2460C2214yes—
179#2458C2214yes—
180#2458C2214yes—
181#2458C2214yes—
182#2453C2214yes—
183#2450C2214yes—
184#2450C2214yes—
185#2444C2214yes—
186#2425C2214yes—
187#2421C2214yes—
188#2419C2214yes—
189#2419C2214yes—
190#2413C2214yes—
191#2413C2214yes—
192#2406C2214yes—
193#2381C2212yes—
194#2379C2212yes—
195#2378C2214yes—
196#2372C2212yes—
197#2369C2212yes—
198#2368C2214yes—
199#2359C2214yes—
200#2359C2214yes—
201#2343C2214yes—
202#2339C2214yes—
203#2337C2214yes—
204#2332C2214yes—
205#2331C2214yes—
206#2329C2212yes—
207#2329C2214yes—
208#2327C2212yes—
209#2327C2212yes—
210#2327C2212yes—
211#2327C2212yes—
212#2327C2212yes—
213#2327C2212yes—
214#2327C2212yes—
215#2327C2212yes—
216#2325C2212yes—
217#2322C2214yes—
218#2318C2214yes—
219#2317C2212yes—
220#2313C2212yes—
221#2311C2212yes—
222#2310C2212yes—
223C4×#123C2214yes—
224C4×#123C2214yes—
225C2×#391C2211yescharacteristic
226C2×#391C2211yescharacteristic
227C2×#387C2212yes—
228C2×#387C2212yes—
229C2×#387C2212yes—
230C2×#387C2212yes—
231#2285C2211yescharacteristic
232#2285C2211yescharacteristic
233C2×#382C2211yescharacteristic
234C2×#376C2211yescharacteristic
235C22×#41C2312yes—
236C23×Q8C2311yescharacteristic
237C23×Q8C2311yescharacteristic
238#539—48no—
239#536—216no—
240#533—44no—
241#532—44no—
242C2×C4⋊Q8—28no—
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2311yescharacteristic
250C2×C4⋊Q8C2311yescharacteristic
251C2×C4⋊Q8C2311yescharacteristic
252C2×#127C2311yescharacteristic
253C2×#126C2314yes—
254C2×#125C2312yes—
255C2×#125C2314yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2314yes—
269C2×#121C2312yes—
270C2×#121C2312yes—
271C2×C4×Q8—44no—
272C2×C4×Q8—44no—
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×#117C2312yes—
292C2×#117C2312yes—
293C2×#117C2312yes—
294C22×C4⋊C4C2312yes—
295C22×C4⋊C4C2312yes—
296C22×C4⋊C4C2312yes—
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2311yescharacteristic
300C22×C4⋊C4C2311yescharacteristic
301C22×C42C2311yescharacteristic
302C22×C42C2311yescharacteristic
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305C22×C42C2312yes—
306C22×C42C2311yescharacteristic
307#401C2314yes—
308#401C2314yes—
309#401C2314yes—
310#400C2312yes—
311#400C2312yes—
312#400C2312yes—
313#400C2312yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2312yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2312yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2312yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2312yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#395C2312yes—
384#395C2312yes—
385#395C2312yes—
386#395C2312yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#394C2312yes—
395#394C2312yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2312yes—
400#394C2312yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2314yes—
416#391C2314yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2312yes—
456#389C2314yes—
457#389C2314yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#384C2312yes—
592#384C2312yes—
593#384C2312yes—
594#384C2312yes—
595#383C2314yes—
596#383C2314yes—
597#383C2314yes—
598#383C2314yes—
599#382C2312yes—
600#382C2312yes—
601#382C2314yes—
602#382C2314yes—
603#382C2314yes—
604#382C2312yes—
605#382C2312yes—
606#382C2312yes—
607#382C2312yes—
608#382C2312yes—
609#382C2314yes—
610#382C2312yes—
611#381C2314yes—
612#381C2314yes—
613#381C2314yes—
614#381C2314yes—
615#381C2314yes—
616#381C2314yes—
617#381C2314yes—
618#381C2314yes—
619#380C2314yes—
620#380C2314yes—
621#380C2312yes—
622#380C2312yes—
623#380C2314yes—
624#380C2314yes—
625#380C2314yes—
626#380C2314yes—
627#380C2312yes—
628#380C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2311yescharacteristic
631C4×C4⋊C4C2311yescharacteristic
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2311yescharacteristic
641C4×C4⋊C4C2311yescharacteristic
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2314yes—
651#376C2312yes—
652#376C2312yes—
653#376C2312yes—
654#376C2312yes—
655#376C2314yes—
656C2×#95C2314yes—
657C2×#95C2312yes—
658C2×#95C2312yes—
659C2×#95C2312yes—
660C2×#95C2312yes—
661C2×#95C2312yes—
662C2×#95C2312yes—
663C2×#95C2312yes—
664C2×#95C2312yes—
665C2×#41—28no—
666C2×#41—44no—
667C2×#41—44no—
668C22×Q8—24no—
669C22×Q8—42no—
670C22×Q8—42no—
671C22×Q8—42no—
672C22×Q8—42no—
673C22×Q8#4118yes—
674C22×Q8C2412yes—
675C22×Q8C2412yes—
676C22×Q8C2412yes—
677C22×Q8C2412yes—
678C22×Q8C2412yes—
679C22×Q8C2411yescharacteristic
680C22×Q8C2411yescharacteristic
681C22×Q8C2411yescharacteristic
682C22×Q8C2411yescharacteristic
683C22×D4C2414yes—
684C22×D4C2412yes—
685C22×D4C2412yes—
686C22×D4C2412yes—
687C23×C4C2412yes—
688C23×C4C2411yescharacteristic
689C23×C4C2411yescharacteristic
690C23×C4C2411yescharacteristic
691C23×C4C2412yes—
692C23×C4C2411yescharacteristic
693C23×C4C2411yescharacteristic
694C23×C4C2412yes—
695C23×C4C2411yescharacteristic
696C23×C4C2414yes—
697C23×C4C2412yes—
698C23×C4C2414yes—
699C23×C4C2414yes—
700C23×C4C2411yescharacteristic
701C4⋊Q8—28no—
702C4⋊Q8—28no—
703C4⋊Q8—28no—
704C4⋊Q8—28no—
705C4⋊Q8—28no—
706C4⋊Q8—28no—
707C4⋊Q8—42no—
708C4⋊Q8—42no—
709C4⋊Q8—42no—
710#127—42no—
711#126—48no—
712#125—44no—
713#125—48no—
714#124—28no—
715#124—28no—
716#124—44no—
717#123—216no—
718#123—216no—
719#123—48no—
720#123—48no—
721#123—48no—
722C22⋊Q8—216no—
723C22⋊Q8—216no—
724C22⋊Q8—28no—
725C22⋊Q8—44no—
726C22⋊Q8—48no—
727#121—28no—
728#121—44no—
729C4×Q8—42no—
730C4×Q8—42no—
731C4×Q8—42no—
732C4×Q8—42no—
733C4×Q8—42no—
734C4×Q8—42no—
735C4×Q8—42no—
736C4×Q8—42no—
737C4×Q8—44no—
738C4×Q8—44no—
739C4×Q8—44no—
740C4×Q8—44no—
741C4×Q8—44no—
742C4×Q8—44no—
743C4×D4—44no—
744C4×D4—44no—
745C4×D4—48no—
746C4×D4—48no—
747#117—28no—
748#117—44no—
749#117—44no—
750C2×C4⋊C4—28no—
751C2×C4⋊C4—28no—
752C2×C4⋊C4—28no—
753C2×C4⋊C4—42no—
754C2×C4⋊C4—42no—
755C2×C4⋊C4—42no—
756C2×C4⋊C4—42no—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C42—24no—
843C2×C42—24no—
844C2×C42—24no—
845C2×C42—24no—
846C2×C42—44no—
847C2×C42—42no—
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2411yescharacteristic
851C2×C42C2411yescharacteristic
852C2×C42C2411yescharacteristic
853C2×C42C2411yescharacteristic
854C2×C42C2411yescharacteristic
855C2×C42C2411yescharacteristic
856C2×C42C2411yescharacteristic
857C2×C42C2411yescharacteristic
858C2×C42C2411yescharacteristic
859C2×C42C2411yescharacteristic
860C2×C42C2411yescharacteristic
861C2×C42C2411yescharacteristic
862C2×C42C2412yes—
863C2×C42C2412yes—
864C2×C42C2414yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2412yes—
913#95C2414yes—
914#95C2412yes—
915#95C2414yes—
916#95C2414yes—
917#95C2412yes—
918#95C2414yes—
919#95C2412yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943C24C2514yes—
944C24C2511yescharacteristic
945#41—816no—
946C2×Q8—24no—
947C2×Q8—24no—
948C2×Q8—24no—
949C2×Q8—24no—
950C2×Q8—41no—
951C2×Q8—41no—
952C2×Q8—41no—
953C2×Q8—41no—
954C2×Q8—42no—
955C2×Q8—42no—
956C2×Q8—416no—
957C2×Q8—41no—
958C2×Q8—41no—
959C2×Q8—41no—
960C2×Q8—41no—
961C2×Q8—42no—
962C2×Q8—42no—
963C2×Q8—42no—
964C2×Q8—42no—
965C2×Q8—42no—
966C2×Q8—42no—
967C2×Q8—44no—
968C2×Q8—42no—
969C2×Q8—416no—
970C2×Q8C2×#4114yes—
971C2×Q8C2×#4114yes—
972C2×Q8C2×#4114yes—
973C2×Q8C2×#4114yes—
974C2×D4—28no—
975C2×D4—28no—
976C2×D4—28no—
977C2×D4—24no—
978C2×D4—24no—
979C2×D4—42no—
980C2×D4—42no—
981C2×D4—42no—
982C2×D4—42no—
983C2×D4—44no—
984C2×D4—42no—
985C22×C4—22no—
986C22×C4—22no—
987C22×C4—22no—
988C22×C4—22no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—22no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—24no—
999C22×C4—24no—
1000C22×C4—28no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—44no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—42no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4C2×#4114yes—
1020C22×C4C2×#4114yes—
1021C22×C4C2×#4114yes—
1022C22×C4H(5,𝔽2)14yes—
1023C22×C4C2514yes—
1024C22×C4C2514yes—
1025C22×C4C2514yes—
1026C22×C4C2511yescharacteristic
1027C22×C4C2511yescharacteristic
1028C22×C4C2514yes—
1029C22×C4C2514yes—
1030C22×C4C2514yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2511yescharacteristic
1034C22×C4C2511yescharacteristic
1035C22×C4C2514yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2511yescharacteristic
1038C22×C4C2514yes—
1039C22×C4C2514yes—
1040C22×C4C2511yescharacteristic
1041C22×C4C2511yescharacteristic
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C22×C4C2511yescharacteristic
1047C22×C4C2511yescharacteristic
1048C4⋊C4—28no—
1049C4⋊C4—28no—
1050C4⋊C4—28no—
1051C4⋊C4—28no—
1052C4⋊C4—28no—
1053C4⋊C4—28no—
1054C4⋊C4—28no—
1055C4⋊C4—28no—
1056C4⋊C4—28no—
1057C4⋊C4—28no—
1058C4⋊C4—28no—
1059C4⋊C4—24no—
1060C4⋊C4—28no—
1061C4⋊C4—24no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—41no—
1068C4⋊C4—41no—
1069C4⋊C4—41no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C42—24no—
1134C42—24no—
1135C42—24no—
1136C42—24no—
1137C42—22no—
1138C42—22no—
1139C42—22no—
1140C42—22no—
1141C42—22no—
1142C42—22no—
1143C42—22no—
1144C42—22no—
1145C42—22no—
1146C42—22no—
1147C42—22no—
1148C42—22no—
1149C42—42no—
1150C42—42no—
1151C42—44no—
1152C42—44no—
1153C42—44no—
1154C42—44no—
1155C42—44no—
1156C42—44no—
1157C42—42no—
1158C42—42no—
1159C42—44no—
1160C42—44no—
1161C42—44no—
1162C23—22no—
1163C23—22no—
1164C23—24no—
1165C23—24no—
1166C23—24no—
1167C23—24no—
1168C23—24no—
1169C23—24no—
1170C23—24no—
1171C23C22×#4112yes—
1172C23C2×H(5,𝔽2)12yes—
1173C23#58512yes—
1174C23C2611yescharacteristic
1175Q8—44no—
1176Q8—44no—
1177Q8—44no—
1178Q8—44no—
1179Q8—48no—
1180Q8—48no—
1181Q8—84no—
1182Q8—84no—
1183Q8—84no—
1184D4—416no—
1185D4—84no—
1186D4—84no—
1187D4—84no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—28no—
1203C2×C4—28no—
1204C2×C4—28no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—44no—
1251C2×C4—48no—
1252C2×C4—44no—
1253C2×C4—48no—
1254C2×C4—88no—
1255C2×C4—84no—
1256C2×C4—84no—
1257C2×C4—82no—
1258C2×C4—82no—
1259C2×C4—164no—
1260C2×C4—164no—
1261C2×C4C22×#4112yes—
1262C2×C4C22×#4112yes—
1263C2×C4C22×#4112yes—
1264C2×C4C22×#4112yes—
1265C2×C4C22×#4112yes—
1266C2×C4C22×#4112yes—
1267C2×C4C2×H(5,𝔽2)12yes—
1268C2×C4C2×H(5,𝔽2)12yes—
1269C22—24no—
1270C22—22no—
1271C22—24no—
1272C22—22no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—44no—
1277C22—44no—
1278C22—44no—
1279C22—44no—
1280C22#350514yes—
1281C22C23×#4111yescharacteristic
1282C22C22×H(5,𝔽2)11yescharacteristic
1283C22C2×#58511yescharacteristic
1284C222−1+612yes—
1285C222−1+612yes—
1286C4—22no—
1287C4—22no—
1288C4—22no—
1289C4—22no—
1290C4—22no—
1291C4—22no—
1292C4—22no—
1293C4—22no—
1294C4—44no—
1295C4—44no—
1296C4—44no—
1297C4—44no—
1298C4—44no—
1299C4—44no—
1300C4—44no—
1301C4—44no—
1302C4—44no—
1303C4—44no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—44no—
1311C2—24no—
1312C2—84no—
1313C2C2×#350511yescharacteristic
1314C2#6285012yes—
1315C2#6287111yescharacteristic
1316C2#6287312yes—
1317C2#6288611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51882C2semidirect
2. #51873C2semidirect
3. #51739C2semidirect
4. #51738C2semidirect
5. #51726C2semidirect
6. #51725C2semidirect
7. #47546C2semidirect
8. #47544C2semidirect
9. #47537C2semidirect
10. #46973C2semidirect
11. #46969C2semidirect
12. #46966C2semidirect
13. #39051C2semidirect
14. #39039C2semidirect
15. #37896C2semidirect
16. #37886C2semidirect
17. #37708C2semidirect
19. #37518C2semidirect
20. #37258C2semidirect
21. #37124C2semidirect
22. #35179C2semidirect
24. #35099C2semidirect
25. #35092C2semidirect
26. #34409C2semidirect
27. C2×#2327C2semidirect

Maximal subgroups

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

subgroupindex
#518822
#518732
#517392
#517382
#517262
#517252
#475462
#475442
#475372
#469732
#469692
#469662
#390512
#390392
#378962
#378862
#377082
#376982
#375182
#372582
#371242
#351792
#351782
#350992
#350922
#344092
C2×#23272