Finite Group Databasebeta

← #7656022

Subgroups — #7656022

Order 512.

4330 conjugacy classes of subgroups.

The subgroup lattice has 1432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42662C212yesmaximal, complemented
2#42657C212yesmaximal, complemented
3#42461C212yesmaximal, complemented
4#42456C212yesmaximal, complemented
5#41687C214yesmaximal, complemented
6#41682C214yesmaximal, complemented
7#41011C214yesmaximal, complemented
8#41008C214yesmaximal, complemented
9#39190C212yesmaximal, complemented
10#39051C214yesmaximal, complemented
11#38973C212yesmaximal, complemented
12#38209C214yesmaximal, complemented
13#37549C211yesmaximal, characteristic, complemented
14#37549C211yesmaximal, characteristic, complemented
15#37466C212yesmaximal, complemented
16#37465C212yesmaximal
17#36486C212yesmaximal, complemented
18#36254C212yesmaximal, complemented
19#36039C212yesmaximal, complemented
20#36017C212yesmaximal, complemented
21#35734C212yesmaximal, complemented
22#35708C212yesmaximal, complemented
23#35181C211yesmaximal, characteristic, complemented
24#35021C212yesmaximal, complemented
25#34594C211yesmaximal, characteristic
26#34584C212yesmaximal, complemented
27#34243C211yesmaximal, characteristic, complemented
28#34243C211yesmaximal, characteristic, complemented
29C2×#2370C211yesmaximal, characteristic, complemented
30C2×#529C2211yescharacteristic
31C2×#529C2211yescharacteristic
32C22×#125C2211yescharacteristic
33#2853C2214yes—
34#2852C2214yes—
35#2851C2212yes—
36#2851C2212yes—
37#2839C2214yes—
38#2836C2214yes—
39#2833C2214yes—
40#2829C2214yes—
41#2822C2212yes—
42#2822C2212yes—
43#2820C2212yes—
44#2820C2212yes—
45#2802C2214yes—
46#2802C2214yes—
47#2801C2214yes—
48#2796C2214yes—
49#2795C2214yes—
50#2793C2214yes—
51#2790C2214yes—
52#2787C2214yes—
53#2783C2214yes—
54#2779C2214yes—
55#2777C2214yes—
56#2777C2214yes—
57#2776C2214yes—
58#2776C2214yes—
59#2773C2214yes—
60#2772C2214yes—
61#2772C2214yes—
62#2771C2214yes—
63#2766C2214yes—
64#2766C2214yes—
65#2739C2214yes—
66#2725C2214yes—
67#2718C2214yes—
68#2694C2214yes—
69#2667C2214yes—
70#2666C2214yes—
71#2664C2212yes—
72#2664C2212yes—
73#2664C2214yes—
74#2664C2214yes—
75#2662C2212yes—
76#2662C2212yes—
77#2659C2211yescharacteristic
78#2656C2211yescharacteristic
79#2655C2214yes—
80#2655C2214yes—
81#2655C2214yes—
82#2654C2214yes—
83#2654C2214yes—
84#2651C2214yes—
85#2650C2214yes—
86#2648C2214yes—
87#2646C2212yes—
88#2646C2212yes—
89#2643C2214yes—
90#2639C2211yescharacteristic
91#2639C2211yescharacteristic
92#2634C2214yes—
93#2630C2214yes—
94#2629C2212yes—
95#2629C2212yes—
96#2629C2212yes—
97#2629C2212yes—
98#2627C2212yes—
99#2627C2212yes—
100#2623C2214yes—
101#2618C2212yes—
102#2618C2212yes—
103#2618C2212yes—
104#2618C2212yes—
105#2608C2214yes—
106#2606C2214yes—
107#2597C2214yes—
108#2596C2214yes—
109#2594C2214yes—
110#2594C2214yes—
111#2593C2214yes—
112#2590C2214yes—
113#2590C2214yes—
114#2587C2214yes—
115#2585C2214yes—
116#2584C2212yes—
117#2584C2212yes—
118#2577C2214yes—
119#2576C2214yes—
120#2575C2214yes—
121#2574C2214yes—
122#2573C2214yes—
123#2571C2212yes—
124#2571C2212yes—
125#2570C2214yes—
126#2570C2214yes—
127#2570C2212yes—
128#2570C2214yes—
129#2570C2212yes—
130#2562C2212yes—
131#2562C2212yes—
132#2562C2212yes—
133#2562C2212yes—
134#2552C2212yes—
135#2552C2212yes—
136#2533C2214yes—
137#2529C2214yes—
138#2525C2214yes—
139#2524C2214yes—
140#2524C2214yes—
141#2522C2214yes—
142#2522C2214yes—
143#2518C2214yes—
144#2518C2214yes—
145#2515C2214yes—
146#2509C2212yes—
147#2508C2212yes—
148#2507C2212yes—
149#2507C2214yes—
150#2506C2212yes—
151#2505C2214yes—
152#2497C2214yes—
153#2497C2212yes—
154#2496C2212yes—
155#2495C2212yes—
156#2495C2212yes—
157#2495C2212yes—
158#2494C2212yes—
159#2494C2212yes—
160#2494C2212yes—
161#2493C2214yes—
162#2493C2214yes—
163#2487C2212yes—
164#2487C2212yes—
165#2487C2212yes—
166#2486C2212yes—
167#2486C2212yes—
168#2486C2212yes—
169#2485C2212yes—
170#2485C2212yes—
171#2479C2214yes—
172#2473C2214yes—
173#2470C2214yes—
174#2469C2214yes—
175#2468C2214yes—
176#2462C2214yes—
177#2457C2214yes—
178#2444C2214yes—
179#2443C2214yes—
180#2442C2212yes—
181#2442C2212yes—
182#2441C2212yes—
183#2441C2214yes—
184#2441C2212yes—
185#2425C2214yes—
186#2425C2214yes—
187#2413C2214yes—
188#2413C2214yes—
189#2402C2214yes—
190#2401C2214yes—
191#2396C2214yes—
192#2396C2212yes—
193#2396C2212yes—
194#2395C2214yes—
195#2392C2212yes—
196#2392C2212yes—
197#2370C2214yes—
198#2370C2214yes—
199#2370C2212yes—
200#2370C2212yes—
201#2370C2212yes—
202#2370C2212yes—
203#2370C2212yes—
204#2370C2212yes—
205#2370C2212yes—
206#2370C2212yes—
207#2367C2212yes—
208#2367C2212yes—
209#2359C2214yes—
210#2359C2214yes—
211#2355C2211yescharacteristic
212#2355C2211yescharacteristic
213#2354C2211yescharacteristic
214#2354C2211yescharacteristic
215#2352C2212yes—
216#2352C2212yes—
217#2352C2212yes—
218#2352C2212yes—
219Q8×C4⋊C4C2211yescharacteristic
220Q8×C4⋊C4C2211yescharacteristic
221D4×C4⋊C4C2212yes—
222D4×C4⋊C4C2212yes—
223D4×C4⋊C4C2211yescharacteristic
224D4×C4⋊C4C2211yescharacteristic
225#2347C2212yes—
226#2346C2212yes—
227#2345C2212yes—
228#2344C2212yes—
229#2334C2214yes—
230#2334C2214yes—
231#2322C2214yes—
232#2318C2214yes—
233#2317C2212yes—
234#2317C2212yes—
235#2314C2212yes—
236#2314C2212yes—
237C4×C22⋊Q8C2212yes—
238C4×C22⋊Q8C2212yes—
239C4×#123C2214yes—
240C4×#121C2212yes—
241C4×#121C2212yes—
242C4×#121C2212yes—
243C4×#121C2212yes—
244C2×#389C2211yescharacteristic
245C2×#389C2211yescharacteristic
246C2×#389C2212yes—
247#2290C2214yes—
248C2×#387C2212yes—
249C2×#387C2212yes—
250#2285C2211yescharacteristic
251#2285C2211yescharacteristic
252#2274C2212yes—
253#2274C2212yes—
254C2×C4×C4⋊C4C2212yes—
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259#529—28no—
260#529—28no—
261C2×#126C2312yes—
262C2×#126C2312yes—
263C2×#126C2314yes—
264C2×#125—28no—
265C2×#125C2312yes—
266C2×#125C2312yes—
267C2×#125C2312yes—
268C2×#125C2312yes—
269C2×#125C2311yescharacteristic
270C2×#125C2311yescharacteristic
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#125C2314yes—
274C2×#124C2311yescharacteristic
275C2×#124C2311yescharacteristic
276C2×#123C2312yes—
277C2×#123C2312yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×C22⋊Q8C2311yescharacteristic
282C2×C22⋊Q8C2311yescharacteristic
283C2×#121C2311yescharacteristic
284C2×#121C2311yescharacteristic
285C2×#121C2312yes—
286C2×#121C2312yes—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×#117C2312yes—
302C2×#117C2312yes—
303C2×#117C2312yes—
304C2×#117C2312yes—
305C2×#117C2312yes—
306C2×#117C2312yes—
307C2×#117C2314yes—
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2311yescharacteristic
314C22×C4⋊C4C2311yescharacteristic
315C22×C4⋊C4C2311yescharacteristic
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2311yescharacteristic
318C22×C4⋊C4C2312yes—
319C22×C4⋊C4C2312yes—
320C22×C42C2311yescharacteristic
321C22×C42C2311yescharacteristic
322C22×C42C2312yes—
323C22×C42C2312yes—
324C22×C42C2312yes—
325C22×C42C2311yescharacteristic
326#401C2314yes—
327#401C2314yes—
328#401C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#400C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2312yes—
359#399C2314yes—
360#399C2314yes—
361#399C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2312yes—
386#398C2312yes—
387#398C2314yes—
388#398C2312yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2312yes—
405#397C2314yes—
406#397C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2312yes—
416#396C2312yes—
417#396C2312yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2312yes—
422#396C2312yes—
423#396C2312yes—
424#396C2312yes—
425#396C2312yes—
426#395C2314yes—
427#395C2314yes—
428#395C2312yes—
429#395C2312yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2312yes—
437#394C2312yes—
438#394C2312yes—
439#394C2312yes—
440#394C2312yes—
441#394C2312yes—
442#393C2312yes—
443#393C2312yes—
444#392C2312yes—
445#392C2312yes—
446#391C2312yes—
447#391C2312yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2312yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
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#388C2312yes—
517#388C2312yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2312yes—
526#388C2314yes—
527#388C2312yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
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#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#386C2312yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2312yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2312yes—
589#386C2312yes—
590#386C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#384C2312yes—
607#384C2312yes—
608#384C2314yes—
609#384C2314yes—
610#384C2311yescharacteristic
611#384C2311yescharacteristic
612#384C2311yescharacteristic
613#384C2311yescharacteristic
614#383C2314yes—
615#383C2314yes—
616#383C2314yes—
617#383C2314yes—
618#382C2312yes—
619#382C2312yes—
620#382C2312yes—
621#382C2312yes—
622#382C2312yes—
623#382C2312yes—
624#382C2314yes—
625#382C2314yes—
626#382C2314yes—
627#382C2314yes—
628#381C2314yes—
629#381C2314yes—
630#381C2314yes—
631#381C2314yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2312yes—
637#380C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2312yes—
641#380C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2314yes—
645#380C2314yes—
646#380C2312yes—
647#380C2312yes—
648#380C2312yes—
649#380C2312yes—
650#380C2312yes—
651#380C2312yes—
652#380C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707#376C2314yes—
708C2×#95C2312yes—
709C2×#95C2312yes—
710C2×#95C2311yescharacteristic
711C2×#95C2311yescharacteristic
712C2×#95C2312yes—
713C2×#95C2312yes—
714C2×#95C2312yes—
715C22×Q8C2411yescharacteristic
716C22×Q8C2411yescharacteristic
717C22×D4C2412yes—
718C22×D4C2412yes—
719C22×D4C2411yescharacteristic
720C22×D4C2411yescharacteristic
721C22×D4C2412yes—
722C22×D4C2412yes—
723C23×C4C2412yes—
724C23×C4C2412yes—
725C23×C4C2412yes—
726C23×C4C2412yes—
727C23×C4C2411yescharacteristic
728C23×C4C2411yescharacteristic
729C23×C4C2412yes—
730C23×C4C2412yes—
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2414yes—
734C23×C4C2411yescharacteristic
735C23×C4C2411yescharacteristic
736C23×C4C2414yes—
737C23×C4C2411yescharacteristic
738#126—28no—
739#126—28no—
740#126—84no—
741#125—28no—
742#125—28no—
743#125—28no—
744#125—28no—
745#125—24no—
746#125—24no—
747#125—44no—
748#125—44no—
749#125—84no—
750#124—24no—
751#124—24no—
752#123—28no—
753#123—28no—
754#123—48no—
755#123—48no—
756#123—84no—
757C22⋊Q8—24no—
758C22⋊Q8—24no—
759#121—24no—
760#121—24no—
761#121—44no—
762#121—44no—
763C4×Q8—24no—
764C4×Q8—24no—
765C4×Q8—82no—
766C4×Q8—82no—
767C4×D4—28no—
768C4×D4—28no—
769C4×D4—24no—
770C4×D4—24no—
771C4×D4—44no—
772C4×D4—44no—
773C4×D4—48no—
774C4×D4—48no—
775C4×D4—82no—
776C4×D4—82no—
777#117—28no—
778#117—28no—
779#117—28no—
780#117—44no—
781#117—44no—
782#117—44no—
783#117—84no—
784C2×C4⋊C4—24no—
785C2×C4⋊C4—24no—
786C2×C4⋊C4—28no—
787C2×C4⋊C4—28no—
788C2×C4⋊C4—24no—
789C2×C4⋊C4—28no—
790C2×C4⋊C4—42no—
791C2×C4⋊C4—44no—
792C2×C4⋊C4—42no—
793C2×C4⋊C4—42no—
794C2×C4⋊C4—44no—
795C2×C4⋊C4—82no—
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C42—42no—
909C2×C42—42no—
910C2×C42—44no—
911C2×C42—82no—
912C2×C42—82no—
913C2×C42#4118yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2412yes—
926C2×C42C2414yes—
927C2×C42C2412yes—
928C2×C42C2414yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008C24C2512yes—
1009C24C2512yes—
1010C24C2511yescharacteristic
1011C2×Q8—22no—
1012C2×Q8—22no—
1013C2×Q8—41no—
1014C2×Q8—41no—
1015C2×Q8—41no—
1016C2×Q8—41no—
1017C2×D4—24no—
1018C2×D4—24no—
1019C2×D4—24no—
1020C2×D4—24no—
1021C2×D4—24no—
1022C2×D4—24no—
1023C2×D4—22no—
1024C2×D4—22no—
1025C2×D4—41no—
1026C2×D4—41no—
1027C2×D4—41no—
1028C2×D4—41no—
1029C2×D4—42no—
1030C2×D4—42no—
1031C2×D4—42no—
1032C2×D4—42no—
1033C2×D4—42no—
1034C2×D4—42no—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—22no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—22no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—22no—
1048C22×C4—22no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—28no—
1057C22×C4—41no—
1058C22×C4—41no—
1059C22×C4—42no—
1060C22×C4—41no—
1061C22×C4—41no—
1062C22×C4—42no—
1063C22×C4—41no—
1064C22×C4—42no—
1065C22×C4—41no—
1066C22×C4—41no—
1067C22×C4—41no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—41no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—41no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4C2×#4114yes—
1078C22×C4C2×#4114yes—
1079C22×C4C2×#4114yes—
1080C22×C4C2514yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2514yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2514yes—
1094C22×C4C2514yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2514yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2512yes—
1105C22×C4C2511yescharacteristic
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—28no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—22no—
1119C4⋊C4—22no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—22no—
1123C4⋊C4—22no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—28no—
1128C4⋊C4—22no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—22no—
1132C4⋊C4—22no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C42−1+414yes—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—28no—
1183C22⋊C4—28no—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—24no—
1188C22⋊C4—24no—
1189C22⋊C4—24no—
1190C22⋊C4—24no—
1191C22⋊C4—24no—
1192C22⋊C4—28no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
1199C22⋊C4—44no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—42no—
1218C42—24no—
1219C42—24no—
1220C42—28no—
1221C42—24no—
1222C42—24no—
1223C42—42no—
1224C42—42no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C42—42no—
1229C42—42no—
1230C42—42no—
1231C42—42no—
1232C42—44no—
1233C42—44no—
1234C42—44no—
1235C42—44no—
1236C42—44no—
1237C42—44no—
1238C42—44no—
1239C42—44no—
1240C42C2×#4114yes—
1241C42C2×#4114yes—
1242C42C2×#4114yes—
1243C42C2×#4114yes—
1244C23—21no—
1245C23—21no—
1246C23—21no—
1247C23—21no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23—22no—
1258C23—22no—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23C22×#4112yes—
1263C23#58512yes—
1264C23#58512yes—
1265C23C2611yescharacteristic
1266Q8—44no—
1267Q8—44no—
1268D4—44no—
1269D4—44no—
1270D4—48no—
1271D4—48no—
1272D4—84no—
1273D4—84no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—22no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—22no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—28no—
1287C2×C4—28no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—44no—
1346C2×C4—48no—
1347C2×C4—48no—
1348C2×C4—44no—
1349C2×C4—44no—
1350C2×C4—48no—
1351C2×C4—48no—
1352C2×C4—48no—
1353C2×C4—88no—
1354C2×C4—82no—
1355C2×C4—84no—
1356C2×C4—82no—
1357C2×C4—164no—
1358C2×C4C22×#4112yes—
1359C2×C4C22×#4112yes—
1360C2×C4C22×#4112yes—
1361C2×C4C22×#4112yes—
1362C2×C4C22×#4112yes—
1363C2×C4C22×#4112yes—
1364C2×C4C2×2−1+414yes—
1365C2×C4C2×2−1+412yes—
1366C2×C4#58512yes—
1367C22—22no—
1368C22—22no—
1369C22—22no—
1370C22—22no—
1371C22—22no—
1372C22—22no—
1373C22—42no—
1374C22—42no—
1375C22—42no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22—42no—
1380C22—42no—
1381C22—42no—
1382C22—42no—
1383C22—42no—
1384C22—42no—
1385C22—42no—
1386C22—42no—
1387C22#351214yes—
1388C22C23×#4111yescharacteristic
1389C22C22×2−1+411yescharacteristic
1390C22C2×#58511yescharacteristic
1391C22C2×#58511yescharacteristic
1392C22C2×#58511yescharacteristic
1393C22H(7,𝔽2)11yescharacteristic
1394C222−1+611yescharacteristic
1395C4—22no—
1396C4—22no—
1397C4—22no—
1398C4—22no—
1399C4—22no—
1400C4—24no—
1401C4—44no—
1402C4—42no—
1403C4—42no—
1404C4—44no—
1405C4—42no—
1406C4—42no—
1407C4—44no—
1408C4—42no—
1409C4—42no—
1410C4—42no—
1411C4—42no—
1412C4—42no—
1413C4—42no—
1414C4—44no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—44no—
1419C4—44no—
1420C4#346114yes—
1421C2—24no—
1422C2—82no—
1423C2—82no—
1424C2C2×#346111yescharacteristic
1425C2C2×#351211yescharacteristic
1426C2#6284511yescharacteristic
1427C2#6290711yescharacteristic
1428C2#6290811yescharacteristic
1429C2#6294811yescharacteristic
1430C2#6294911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2656C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42662C2semidirect
2. #42657C2semidirect
3. #42461C2semidirect
4. #42456C2semidirect
5. #41687C2semidirect
6. #41682C2semidirect
7. #41011C2semidirect
8. #41008C2semidirect
9. #39190C2semidirect
10. #39051C2semidirect
11. #38973C2semidirect
12. #38209C2semidirect
13. #37549C2semidirect
14. #37549C2semidirect
15. #37466C2semidirect
17. #36486C2semidirect
18. #36254C2semidirect
19. #36039C2semidirect
20. #36017C2semidirect
21. #35734C2semidirect
22. #35708C2semidirect
23. #35181C2semidirect
24. #35021C2semidirect
26. #34584C2semidirect
27. #34243C2semidirect
28. #34243C2semidirect
29. C2×#2370C2semidirect

Maximal subgroups

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

subgroupindex
#426622
#426572
#424612
#424562
#416872
#416822
#410112
#410082
#391902
#390512
#389732
#382092
#375492
#374662
#374652
#364862
#362542
#360392
#360172
#357342
#357082
#351812
#350212
#345942
#345842
#342432
C2×#23702