Finite Group Databasebeta

← #7732383

Subgroups — #7732383

Order 512.

4214 conjugacy classes of subgroups.

The subgroup lattice has 1390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51234C214yesmaximal, complemented
2#50924C214yesmaximal, complemented
3#47782C214yesmaximal, complemented
4#47781C214yesmaximal, complemented
5#44495C214yesmaximal, complemented
6#44495C214yesmaximal, complemented
7#39693C212yesmaximal, complemented
8#39299C212yesmaximal, complemented
9#38279C212yesmaximal, complemented
10#38113C212yesmaximal, complemented
11#37986C212yesmaximal, complemented
12#37943C212yesmaximal
13#37935C212yesmaximal, complemented
14#37896C212yesmaximal
15#37886C212yesmaximal, complemented
16#37883C212yesmaximal, complemented
17#37549C211yesmaximal, characteristic
18#37416C212yesmaximal, complemented
19#37413C212yesmaximal, complemented
20#36304C212yesmaximal, complemented
21#36171C212yesmaximal, complemented
22#35657C212yesmaximal, complemented
23#35642C212yesmaximal, complemented
24#35247C211yesmaximal, characteristic
25#35181C211yesmaximal, characteristic, complemented
26C2×#2565C211yesmaximal, characteristic, complemented
27#34378C211yesmaximal, characteristic, complemented
28#34196C211yesmaximal, characteristic, complemented
29#34083C211yesmaximal, characteristic
30C2×#529C2211yescharacteristic
31C22×#125C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33#2864C2212yes—
34#2863C2212yes—
35#2855C2212yes—
36#2855C2212yes—
37#2854C2212yes—
38#2851C2212yes—
39#2851C2212yes—
40#2851C2212yes—
41#2822C2212yes—
42#2820C2212yes—
43#2802C2214yes—
44#2802C2214yes—
45#2798C2214yes—
46#2794C2214yes—
47#2793C2214yes—
48#2793C2214yes—
49#2793C2214yes—
50#2793C2214yes—
51#2793C2214yes—
52#2791C2214yes—
53#2791C2214yes—
54#2791C2214yes—
55#2790C2214yes—
56#2790C2214yes—
57#2790C2214yes—
58#2789C2214yes—
59#2783C2214yes—
60#2776C2214yes—
61#2776C2214yes—
62#2776C2214yes—
63#2772C2214yes—
64#2772C2214yes—
65#2769C2214yes—
66#2767C2214yes—
67#2767C2214yes—
68#2766C2214yes—
69#2766C2214yes—
70#2766C2214yes—
71#2766C2214yes—
72#2766C2214yes—
73#2766C2214yes—
74#2765C2214yes—
75#2765C2214yes—
76#2765C2214yes—
77#2762C2214yes—
78#2761C2214yes—
79#2758C2214yes—
80#2758C2214yes—
81#2757C2214yes—
82#2754C2214yes—
83#2664C2214yes—
84#2647C2212yes—
85#2646C2212yes—
86#2646C2212yes—
87#2645C2212yes—
88#2637C2214yes—
89#2629C2212yes—
90#2629C2212yes—
91#2629C2212yes—
92#2627C2212yes—
93#2625C2212yes—
94#2618C2212yes—
95#2612C2214yes—
96#2606C2214yes—
97#2606C2214yes—
98#2606C2214yes—
99#2597C2214yes—
100#2594C2214yes—
101#2592C2212yes—
102#2590C2214yes—
103#2590C2214yes—
104#2588C2214yes—
105#2587C2214yes—
106#2587C2214yes—
107#2587C2214yes—
108#2585C2214yes—
109#2585C2214yes—
110#2584C2212yes—
111#2584C2212yes—
112#2582C2211yescharacteristic
113#2582C2211yescharacteristic
114#2575C2214yes—
115#2573C2214yes—
116#2571C2212yes—
117#2571C2212yes—
118#2570C2214yes—
119#2570C2214yes—
120#2570C2214yes—
121#2570C2214yes—
122#2565C2212yes—
123#2565C2214yes—
124#2565C2212yes—
125#2565C2212yes—
126#2565C2212yes—
127#2565C2214yes—
128#2562C2212yes—
129#2552C2212yes—
130#2552C2212yes—
131#2538C2211yescharacteristic
132#2538C2211yescharacteristic
133#2533C2214yes—
134#2533C2214yes—
135#2529C2214yes—
136#2529C2214yes—
137#2528C2214yes—
138#2528C2214yes—
139#2528C2214yes—
140#2527C2214yes—
141#2526C2214yes—
142#2525C2214yes—
143#2525C2214yes—
144#2525C2214yes—
145#2524C2214yes—
146#2524C2214yes—
147#2523C2214yes—
148#2520C2214yes—
149#2520C2214yes—
150#2517C2214yes—
151#2515C2214yes—
152#2515C2214yes—
153#2514C2212yes—
154#2514C2212yes—
155#2510C2214yes—
156#2510C2214yes—
157#2509C2212yes—
158#2508C2212yes—
159#2507C2212yes—
160#2507C2214yes—
161#2507C2212yes—
162#2507C2214yes—
163#2505C2214yes—
164#2505C2214yes—
165#2497C2212yes—
166#2497C2212yes—
167#2495C2212yes—
168#2494C2212yes—
169#2493C2214yes—
170#2493C2214yes—
171#2489C2212yes—
172#2489C2212yes—
173#2487C2212yes—
174#2486C2212yes—
175#2486C2212yes—
176#2484C2214yes—
177#2484C2214yes—
178#2453C2212yes—
179#2453C2212yes—
180#2421C2212yes—
181#2421C2212yes—
182#2419C2214yes—
183#2419C2214yes—
184#2413C2214yes—
185#2413C2214yes—
186#2413C2214yes—
187#2413C2214yes—
188#2409C2212yes—
189C2×#398C2212yes—
190C2×#398C2212yes—
191#2382C2212yes—
192#2382C2212yes—
193#2370C2212yes—
194#2370C2212yes—
195#2359C2214yes—
196#2359C2214yes—
197#2355C2212yes—
198#2355C2211yescharacteristic
199#2355C2211yescharacteristic
200#2355C2212yes—
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203#2345C2212yes—
204#2344C2214yes—
205#2344C2212yes—
206#2344C2212yes—
207#2344C2214yes—
208#2343C2214yes—
209#2343C2214yes—
210Q8×C22⋊C4C2212yes—
211#2337C2212yes—
212#2336C2212yes—
213#2336C2214yes—
214#2334C2212yes—
215#2334C2212yes—
216#2330C2212yes—
217#2330C2212yes—
218#2330C2212yes—
219#2329C2211yescharacteristic
220#2329C2211yescharacteristic
221#2325C2211yescharacteristic
222#2325C2211yescharacteristic
223#2323C2212yes—
224#2323C2212yes—
225#2323C2212yes—
226#2322C2212yes—
227#2322C2212yes—
228#2320C2212yes—
229#2320C2212yes—
230#2320C2214yes—
231#2317C2212yes—
232#2317C2212yes—
233#2316C2212yes—
234#2314C2212yes—
235#2313C2212yes—
236C4×#125C2212yes—
237C4×C22⋊Q8C2212yes—
238#2298C2212yes—
239#2296C2212yes—
240#2295C2212yes—
241#2295C2212yes—
242C2×#391C2211yescharacteristic
243C2×#391C2211yescharacteristic
244#2290C2212yes—
245#2290C2212yes—
246C2×#387C2212yes—
247C2×#387C2212yes—
248#2285C2212yes—
249#2285C2211yescharacteristic
250#2285C2211yescharacteristic
251C2×#384C2211yescharacteristic
252#2283C2211yescharacteristic
253#2283C2212yes—
254#2283C2212yes—
255C2×#382C2211yescharacteristic
256#2276C2212yes—
257C42×D4C2212yes—
258C2×C4×C4⋊C4C2211yescharacteristic
259C23×Q8C2311yescharacteristic
260#529—28no—
261C2×#126C2312yes—
262C2×#125—28no—
263C2×#125C2312yes—
264C2×#125C2312yes—
265C2×#125C2312yes—
266C2×#125C2312yes—
267C2×#125C2311yescharacteristic
268C2×#125C2312yes—
269C2×#125C2312yes—
270C2×#124C2311yescharacteristic
271C2×#123C2312yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2311yescharacteristic
276C2×C22⋊Q8C2312yes—
277C2×#121C2311yescharacteristic
278C2×C4×Q8—28no—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2312yes—
288C2×C4×D4C2311yescharacteristic
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×#117C2312yes—
293C2×#117C2312yes—
294C2×#117C2314yes—
295C2×#117C2312yes—
296C2×#117C2312yes—
297C2×#117C2314yes—
298C22×C4⋊C4C2312yes—
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2311yescharacteristic
302C22×C4⋊C4C2311yescharacteristic
303C22×C4⋊C4C2311yescharacteristic
304C22×C4⋊C4C2311yescharacteristic
305C22×C4⋊C4C2311yescharacteristic
306C22×C4⋊C4C2312yes—
307C22×C4⋊C4C2312yes—
308C22×C42C2312yes—
309C22×C42C2311yescharacteristic
310C22×C42C2311yescharacteristic
311C22×C42C2312yes—
312C22×C42C2311yescharacteristic
313#401C2314yes—
314#401C2314yes—
315#401C2314yes—
316#401C2314yes—
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#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#399C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
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#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#395C2314yes—
398#395C2314yes—
399#394C2314yes—
400#393C2314yes—
401#391C2312yes—
402#391C2314yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2314yes—
407#391C2312yes—
408#391C2314yes—
409#391C2312yes—
410#391C2312yes—
411#391C2314yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#390C2312yes—
418#390C2312yes—
419#389C2312yes—
420#389C2312yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2312yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2312yes—
438#389C2314yes—
439#389C2314yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2314yes—
448#389C2314yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2312yes—
477#388C2312yes—
478#388C2312yes—
479#388C2312yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2312yes—
486#388C2312yes—
487#388C2314yes—
488#388C2312yes—
489#388C2312yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
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#387C2312yes—
513#387C2312yes—
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#387C2312yes—
533#387C2312yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2312yes—
538#387C2312yes—
539#387C2312yes—
540#387C2312yes—
541#387C2312yes—
542#387C2312yes—
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#387C2312yes—
556#387C2312yes—
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#386C2312yes—
576#386C2312yes—
577#386C2312yes—
578#386C2312yes—
579#386C2314yes—
580#386C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2312yes—
586#385C2314yes—
587#385C2312yes—
588#385C2312yes—
589#385C2312yes—
590#385C2312yes—
591#385C2312yes—
592#385C2312yes—
593#385C2312yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#384C2312yes—
600#384C2312yes—
601#384C2314yes—
602#384C2314yes—
603#384C2314yes—
604#384C2311yescharacteristic
605#384C2311yescharacteristic
606#384C2311yescharacteristic
607#384C2311yescharacteristic
608#384C2312yes—
609#384C2312yes—
610#383C2314yes—
611#383C2312yes—
612#383C2314yes—
613#383C2314yes—
614#383C2314yes—
615#383C2314yes—
616#383C2314yes—
617#383C2314yes—
618#382C2312yes—
619#382C2312yes—
620#382C2314yes—
621#382C2312yes—
622#382C2312yes—
623#382C2312yes—
624#382C2314yes—
625#382C2314yes—
626#382C2314yes—
627#382C2314yes—
628#382C2314yes—
629#382C2314yes—
630#382C2312yes—
631#382C2314yes—
632#382C2311yescharacteristic
633#382C2311yescharacteristic
634#382C2312yes—
635#382C2312yes—
636#381C2314yes—
637#381C2314yes—
638#381C2314yes—
639#381C2312yes—
640#381C2314yes—
641#381C2314yes—
642#381C2314yes—
643#380C2312yes—
644#380C2312yes—
645#380C2312yes—
646#380C2312yes—
647#380C2311yescharacteristic
648#380C2312yes—
649#380C2312yes—
650#380C2311yescharacteristic
651#380C2314yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2312yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701#376C2312yes—
702#376C2312yes—
703#376C2314yes—
704#376C2314yes—
705#376C2314yes—
706C2×#95C2311yescharacteristic
707C2×#95C2311yescharacteristic
708C2×#95C2312yes—
709C2×#95C2312yes—
710C2×#95C2312yes—
711C2×#95C2312yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C43C2312yes—
715C22×Q8—24no—
716C22×Q8—24no—
717C22×Q8—42no—
718C22×Q8C2411yescharacteristic
719C22×Q8C2412yes—
720C22×Q8C2411yescharacteristic
721C22×Q8C2411yescharacteristic
722C22×D4C2412yes—
723C22×D4C2411yescharacteristic
724C23×C4C2412yes—
725C23×C4C2412yes—
726C23×C4C2412yes—
727C23×C4C2412yes—
728C23×C4C2411yescharacteristic
729C23×C4C2411yescharacteristic
730C23×C4C2412yes—
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2411yescharacteristic
734C23×C4C2411yescharacteristic
735C23×C4C2412yes—
736C23×C4C2412yes—
737C23×C4C2411yescharacteristic
738#126—28no—
739#125—28no—
740#125—28no—
741#125—28no—
742#125—28no—
743#125—24no—
744#125—44no—
745#125—44no—
746#124—24no—
747#123—28no—
748#123—48no—
749#123—48no—
750C22⋊Q8—28no—
751C22⋊Q8—24no—
752C22⋊Q8—44no—
753#121—24no—
754C4×Q8—28no—
755C4×Q8—24no—
756C4×Q8—24no—
757C4×Q8—24no—
758C4×Q8—24no—
759C4×Q8—28no—
760C4×Q8—28no—
761C4×Q8—24no—
762C4×Q8—44no—
763C4×D4—28no—
764C4×D4—24no—
765C4×D4—44no—
766C4×D4—44no—
767#117—28no—
768#117—44no—
769#117—48no—
770#117—48no—
771#117—44no—
772#117—44no—
773C2×C4⋊C4—24no—
774C2×C4⋊C4—28no—
775C2×C4⋊C4—24no—
776C2×C4⋊C4—28no—
777C2×C4⋊C4—28no—
778C2×C4⋊C4—24no—
779C2×C4⋊C4—42no—
780C2×C4⋊C4—42no—
781C2×C4⋊C4—44no—
782C2×C4⋊C4—44no—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C42—28no—
882C2×C42—42no—
883C2×C42—44no—
884C2×C42—42no—
885C2×C42#4118yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2414yes—
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2414yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2414yes—
909C2×C42C2412yes—
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997C24C2512yes—
998C24C2511yescharacteristic
999C2×Q8—22no—
1000C2×Q8—24no—
1001C2×Q8—22no—
1002C2×Q8—22no—
1003C2×Q8—24no—
1004C2×Q8—22no—
1005C2×Q8—22no—
1006C2×Q8—22no—
1007C2×Q8—42no—
1008C2×Q8—41no—
1009C2×Q8—41no—
1010C2×Q8—416no—
1011C2×Q82−1+414yes—
1012C2×D4—24no—
1013C2×D4—24no—
1014C2×D4—24no—
1015C2×D4—22no—
1016C2×D4—41no—
1017C2×D4—41no—
1018C22×C4—22no—
1019C22×C4—22no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—22no—
1026C22×C4—22no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—41no—
1039C22×C4—41no—
1040C22×C4—41no—
1041C22×C4—41no—
1042C22×C4—41no—
1043C22×C4—41no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—41no—
1047C22×C4—41no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4—42no—
1052C22×C4—42no—
1053C22×C4—42no—
1054C22×C4—41no—
1055C22×C4—41no—
1056C22×C4—42no—
1057C22×C4C2×#4114yes—
1058C22×C4C2×#4114yes—
1059C22×C4C2×#4114yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2514yes—
1066C22×C4C2514yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2514yes—
1076C22×C4C2514yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2511yescharacteristic
1081C22×C4C2511yescharacteristic
1082C22×C4C2511yescharacteristic
1083C22×C4C2511yescharacteristic
1084C22×C4C2511yescharacteristic
1085C22×C4C2512yes—
1086C22×C4C2511yescharacteristic
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—22no—
1091C4⋊C4—22no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—28no—
1095C4⋊C4—28no—
1096C4⋊C4—28no—
1097C4⋊C4—28no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—22no—
1105C4⋊C4—24no—
1106C4⋊C4—22no—
1107C4⋊C4—24no—
1108C4⋊C4—28no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—28no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—41no—
1123C4⋊C4—41no—
1124C4⋊C4—41no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—41no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—28no—
1166C22⋊C4—28no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—28no—
1172C22⋊C4—42no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—42no—
1177C22⋊C4—42no—
1178C22⋊C4—42no—
1179C22⋊C4—42no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C42—24no—
1186C42—24no—
1187C42—24no—
1188C42—24no—
1189C42—24no—
1190C42—28no—
1191C42—24no—
1192C42—24no—
1193C42—24no—
1194C42—24no—
1195C42—42no—
1196C42—42no—
1197C42—42no—
1198C42—42no—
1199C42—44no—
1200C42—42no—
1201C42—44no—
1202C42—42no—
1203C42—44no—
1204C42—44no—
1205C42—44no—
1206C42—44no—
1207C42—44no—
1208C42—44no—
1209C42—42no—
1210C42—42no—
1211C42—44no—
1212C42C2×#4114yes—
1213C42C2×#4114yes—
1214C42C2×#4114yes—
1215C42C2×#4114yes—
1216C23—21no—
1217C23—21no—
1218C23—21no—
1219C23—21no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23C22×#4112yes—
1228C23#58512yes—
1229C23#58512yes—
1230C23C2611yescharacteristic
1231Q8—28no—
1232Q8—48no—
1233Q8—44no—
1234Q8—82no—
1235D4—48no—
1236D4—82no—
1237C2×C4—22no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—22no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—28no—
1250C2×C4—28no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—44no—
1312C2×C4—48no—
1313C2×C4—44no—
1314C2×C4—44no—
1315C2×C4—48no—
1316C2×C4—48no—
1317C2×C4—48no—
1318C2×C4—84no—
1319C2×C4—82no—
1320C2×C4—82no—
1321C2×C4—84no—
1322C2×C4—84no—
1323C2×C4C22×#4112yes—
1324C2×C4C22×#4112yes—
1325C2×C4C22×#4112yes—
1326C2×C4C22×#4112yes—
1327C2×C4C22×#4112yes—
1328C2×C4C22×#4112yes—
1329C2×C4C2×2−1+414yes—
1330C2×C4C2×2−1+412yes—
1331C2×C4#58512yes—
1332C22—22no—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—22no—
1337C22—22no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22#351214yes—
1346C22C23×#4111yescharacteristic
1347C22C22×2−1+411yescharacteristic
1348C22C2×#58511yescharacteristic
1349C22C2×#58511yescharacteristic
1350C22C2×#58511yescharacteristic
1351C222−1+611yescharacteristic
1352C222−1+611yescharacteristic
1353C4—22no—
1354C4—24no—
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—22no—
1359C4—42no—
1360C4—42no—
1361C4—42no—
1362C4—42no—
1363C4—44no—
1364C4—42no—
1365C4—44no—
1366C4—42no—
1367C4—44no—
1368C4—44no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4—42no—
1377C4—44no—
1378C4—44no—
1379C4#349514yes—
1380C2—24no—
1381C2—82no—
1382C2C2×#349511yescharacteristic
1383C2C2×#351211yescharacteristic
1384C2#6286011yescharacteristic
1385C2#6290711yescharacteristic
1386C2#6290711yescharacteristic
1387C2#6294911yescharacteristic
1388C2#6294911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51234C2semidirect
2. #50924C2semidirect
3. #47782C2semidirect
4. #47781C2semidirect
5. #44495C2semidirect
6. #44495C2semidirect
7. #39693C2semidirect
8. #39299C2semidirect
9. #38279C2semidirect
10. #38113C2semidirect
11. #37986C2semidirect
13. #37935C2semidirect
15. #37886C2semidirect
16. #37883C2semidirect
18. #37416C2semidirect
19. #37413C2semidirect
20. #36304C2semidirect
21. #36171C2semidirect
22. #35657C2semidirect
23. #35642C2semidirect
25. #35181C2semidirect
26. C2×#2565C2semidirect
27. #34378C2semidirect
28. #34196C2semidirect

Maximal subgroups

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

subgroupindex
#512342
#509242
#477822
#477812
#444952
#396932
#392992
#382792
#381132
#379862
#379432
#379352
#378962
#378862
#378832
#375492
#374162
#374132
#363042
#361712
#356572
#356422
#352472
#351812
C2×#25652
#343782
#341962
#340832