Finite Group Databasebeta

← #8757410

Subgroups — #8757410

Order 512.

4037 conjugacy classes of subgroups.

The subgroup lattice has 1273 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58972C212yesmaximal, complemented
2#58543C212yesmaximal, complemented
3#58343C212yesmaximal, complemented
4#58290C212yesmaximal, complemented
5#55954C214yesmaximal, complemented
6#54715C214yesmaximal, complemented
7#54641C214yesmaximal, complemented
8#53932C214yesmaximal, complemented
9#51796C212yesmaximal, complemented
10#51708C212yesmaximal, complemented
11#50902C212yesmaximal, complemented
12#50237C212yesmaximal
13#50200C212yesmaximal
14#49032C212yesmaximal, complemented
15#47820C212yesmaximal, complemented
16#47789C212yesmaximal, complemented
17#47595C214yesmaximal, complemented
18#47327C214yesmaximal, complemented
19#46235C212yesmaximal, complemented
20#46229C212yesmaximal, complemented
21#46143C212yesmaximal, complemented
22#46143C212yesmaximal, complemented
23C22⋊#564C212yesmaximal, complemented
24C22⋊#564C212yesmaximal, complemented
25#35333C211yesmaximal, characteristic
26#35200C211yesmaximal, characteristic
27#35138C211yesmaximal, characteristic
28C2×#564C2212yes—
29C2×#533C2211yescharacteristic
30C22×#125C2211yescharacteristic
31C22×#125C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33#2851C2212yes—
34#2851C2212yes—
35#2851C2212yes—
36#2851C2212yes—
37#2851C2212yes—
38#2851C2212yes—
39#2844C2212yes—
40#2843C2212yes—
41#2839C2214yes—
42#2839C2214yes—
43#2836C2214yes—
44#2833C2214yes—
45#2831C2214yes—
46#2831C2214yes—
47#2822C2212yes—
48#2822C2212yes—
49#2822C2212yes—
50#2822C2212yes—
51#2807C2214yes—
52#2804C2212yes—
53#2799C2214yes—
54#2794C2214yes—
55#2794C2212yes—
56#2792C2212yes—
57#2792C2214yes—
58#2791C2214yes—
59#2791C2214yes—
60#2789C2212yes—
61#2788C2214yes—
62#2788C2214yes—
63#2788C2214yes—
64#2788C2214yes—
65#2787C2214yes—
66#2783C2214yes—
67#2783C2214yes—
68#2781C2214yes—
69#2779C2214yes—
70#2777C2214yes—
71#2776C2214yes—
72#2776C2214yes—
73#2774C2214yes—
74#2772C2214yes—
75#2770C2214yes—
76#2770C2214yes—
77#2770C2214yes—
78#2769C2212yes—
79#2767C2214yes—
80#2766C2214yes—
81#2765C2214yes—
82#2763C2214yes—
83#2762C2214yes—
84#2758C2214yes—
85#2758C2214yes—
86#2757C2214yes—
87#2755C2214yes—
88#2755C2214yes—
89#2755C2214yes—
90#2755C2214yes—
91#2748C2212yes—
92#2747C2214yes—
93#2747C2214yes—
94#2745C2214yes—
95#2745C2214yes—
96#2744C2214yes—
97#2742C2214yes—
98#2742C2214yes—
99#2739C2214yes—
100#2739C2214yes—
101#2726C2214yes—
102#2726C2214yes—
103#2726C2214yes—
104#2726C2214yes—
105#2719C2214yes—
106#2719C2214yes—
107#2719C2214yes—
108#2719C2214yes—
109#2719C2214yes—
110#2719C2214yes—
111#2719C2214yes—
112#2719C2214yes—
113#2717C2212yes—
114#2717C2212yes—
115#2713C2214yes—
116#2713C2214yes—
117#2713C2214yes—
118#2707C2214yes—
119#2704C2214yes—
120#2704C2214yes—
121#2690C2214yes—
122#2690C2214yes—
123#2666C2214yes—
124#2665C2214yes—
125#2653C2214yes—
126#2652C2214yes—
127#2649C2214yes—
128#2647C2214yes—
129#2638C2212yes—
130#2638C2212yes—
131#2634C2212yes—
132#2633C2212yes—
133#2629C2212yes—
134#2629C2212yes—
135#2612C2214yes—
136#2612C2214yes—
137#2612C2214yes—
138#2612C2212yes—
139#2612C2214yes—
140#2611C2214yes—
141#2611C2212yes—
142#2611C2212yes—
143#2599C2214yes—
144#2599C2212yes—
145#2599C2212yes—
146#2590C2214yes—
147#2589C2214yes—
148#2589C2214yes—
149#2588C2214yes—
150#2588C2214yes—
151#2587C2214yes—
152#2584C2212yes—
153#2582C2212yes—
154#2579C2212yes—
155#2579C2212yes—
156#2579C2212yes—
157#2579C2212yes—
158#2577C2214yes—
159#2574C2214yes—
160#2574C2214yes—
161#2573C2214yes—
162#2567C2211yescharacteristic
163#2566C2212yes—
164#2566C2212yes—
165#2565C2212yes—
166#2565C2212yes—
167#2563C2211yescharacteristic
168#2562C2212yes—
169#2547C2211yescharacteristic
170#2546C2211yescharacteristic
171#2533C2214yes—
172#2533C2214yes—
173#2533C2214yes—
174#2533C2214yes—
175#2531C2214yes—
176#2530C2214yes—
177#2530C2214yes—
178#2530C2214yes—
179#2529C2214yes—
180#2528C2214yes—
181#2528C2214yes—
182#2508C2214yes—
183#2499C2212yes—
184#2487C2211yescharacteristic
185#2487C2211yescharacteristic
186#2486C2211yescharacteristic
187#2486C2211yescharacteristic
188#2485C2212yes—
189#2485C2212yes—
190#2484C2212yes—
191#2475C2214yes—
192#2475C2214yes—
193#2473C2214yes—
194#2473C2214yes—
195#2473C2214yes—
196#2473C2214yes—
197#2473C2214yes—
198#2473C2214yes—
199#2473C2214yes—
200#2473C2214yes—
201#2462C2214yes—
202#2462C2214yes—
203#2462C2214yes—
204#2462C2214yes—
205#2458C2214yes—
206#2453C2214yes—
207#2453C2214yes—
208#2451C2214yes—
209#2442C2214yes—
210#2442C2214yes—
211#2442C2214yes—
212#2442C2214yes—
213#2432C2212yes—
214#2406C2212yes—
215#2382C2212yes—
216#2382C2212yes—
217#2382C2212yes—
218#2379C2212yes—
219#2376C2212yes—
220#2374C2212yes—
221#2372C2212yes—
222#2330C2214yes—
223#2327C2212yes—
224#2326C2212yes—
225#2322C2212yes—
226#2322C2212yes—
227#2320C2214yes—
228#2317C2211yescharacteristic
229#2317C2211yescharacteristic
230#2311C2211yescharacteristic
231#2311C2211yescharacteristic
232#2285C2211yescharacteristic
233#2283C2211yescharacteristic
234#2283C2211yescharacteristic
235C22×#41C2311yescharacteristic
236#564—48no—
237#533—44no—
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2311yescharacteristic
241C2×#125—44no—
242C2×#125—44no—
243C2×#125C2312yes—
244C2×#125C2312yes—
245C2×#125C2312yes—
246C2×#125C2312yes—
247C2×#125C2312yes—
248C2×#125C2312yes—
249C2×#125C2314yes—
250C2×#125C2312yes—
251C2×#125C2312yes—
252C2×#125C2312yes—
253C2×#125C2314yes—
254C2×#125C2314yes—
255C2×#125C2314yes—
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×#124C2312yes—
260C2×#123C2312yes—
261C2×#123C2312yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2312yes—
264C4×#41—44no—
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2314yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2311yescharacteristic
274C2×C4×D4C2311yescharacteristic
275C2×C4×D4C2311yescharacteristic
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C2×#117C2312yes—
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C42C2311yescharacteristic
291C22×C42C2311yescharacteristic
292C22×C42C2311yescharacteristic
293#401C2314yes—
294#401C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2312yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#399C2312yes—
334#399C2312yes—
335#399C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2312yes—
344#398C2312yes—
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#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#397C2314yes—
380#397C2312yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2312yes—
387#397C2314yes—
388#397C2314yes—
389#397C2312yes—
390#397C2312yes—
391#397C2314yes—
392#397C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#395C2312yes—
402#395C2312yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#393C2312yes—
417#393C2312yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2312yes—
430#391C2314yes—
431#391C2312yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
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#388C2314yes—
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#387C2314yes—
564#387C2314yes—
565#386C2312yes—
566#386C2312yes—
567#386C2312yes—
568#386C2312yes—
569#386C2312yes—
570#386C2312yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2312yes—
576#385C2312yes—
577#385C2312yes—
578#385C2312yes—
579#385C2314yes—
580#385C2314yes—
581#385C2312yes—
582#385C2314yes—
583#385C2314yes—
584#385C2312yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#384C2312yes—
598#384C2312yes—
599#384C2312yes—
600#384C2312yes—
601#383C2314yes—
602#383C2314yes—
603#383C2314yes—
604#383C2312yes—
605#383C2312yes—
606#382C2312yes—
607#382C2312yes—
608#382C2312yes—
609#382C2312yes—
610#382C2312yes—
611#382C2312yes—
612#382C2314yes—
613#382C2314yes—
614#382C2314yes—
615#382C2314yes—
616#382C2314yes—
617#382C2314yes—
618#381C2312yes—
619#381C2312yes—
620#381C2312yes—
621#381C2312yes—
622#380C2312yes—
623#380C2312yes—
624#380C2312yes—
625#380C2312yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2312yes—
632#380C2314yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2312yes—
637#380C2314yes—
638#380C2314yes—
639#380C2314yes—
640#380C2312yes—
641#380C2311yescharacteristic
642#380C2311yescharacteristic
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2311yescharacteristic
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2311yescharacteristic
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2312yes—
654C4×C22⋊C4C2312yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2314yes—
658#376C2314yes—
659#376C2312yes—
660#376C2314yes—
661#376C2312yes—
662#376C2314yes—
663C2×#41—24no—
664C2×#41—42no—
665C2×#41—42no—
666C22×Q8C2411yescharacteristic
667C22×Q8C2412yes—
668C22×Q8C2412yes—
669C22×Q8C2414yes—
670C22×D4C2411yescharacteristic
671C22×D4C2411yescharacteristic
672C22×D4C2411yescharacteristic
673C23×C4C2411yescharacteristic
674C23×C4C2411yescharacteristic
675C23×C4C2411yescharacteristic
676C23×C4C2412yes—
677C23×C4C2411yescharacteristic
678C23×C4C2411yescharacteristic
679C23×C4C2411yescharacteristic
680C23×C4C2411yescharacteristic
681C23×C4C2411yescharacteristic
682C23×C4C2411yescharacteristic
683C23×C4C2412yes—
684C23×C4C2412yes—
685C23×C4C2412yes—
686C4⋊Q8—42no—
687C4⋊Q8—42no—
688C4⋊Q8—44no—
689#125—28no—
690#125—28no—
691#125—28no—
692#125—44no—
693#125—44no—
694#125—44no—
695#125—44no—
696#125—44no—
697#125—44no—
698#125—48no—
699#125—48no—
700#125—48no—
701#125—48no—
702#125—48no—
703#125—48no—
704#125—48no—
705#124—28no—
706#123—28no—
707#123—44no—
708C22⋊Q8—44no—
709C22⋊Q8—44no—
710C4×Q8—42no—
711C4×Q8—42no—
712C4×Q8—48no—
713C4×Q8—44no—
714C4×Q8—44no—
715C4×D4—42no—
716C4×D4—42no—
717C4×D4—42no—
718C4×D4—42no—
719C4×D4—42no—
720C4×D4—42no—
721#117—42no—
722#117—42no—
723#117—42no—
724#117—42no—
725#117—42no—
726#117—44no—
727C2×C4⋊C4—42no—
728C2×C4⋊C4—42no—
729C2×C4⋊C4—44no—
730C2×C4⋊C4—42no—
731C2×C4⋊C4—42no—
732C2×C4⋊C4—44no—
733C2×C4⋊C4—44no—
734C2×C4⋊C4—44no—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2411yescharacteristic
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2411yescharacteristic
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2411yescharacteristic
811C2×C22⋊C4C2411yescharacteristic
812C2×C22⋊C4C2411yescharacteristic
813C2×C22⋊C4C2411yescharacteristic
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
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×C42—24no—
829C2×C42—24no—
830C2×C42—24no—
831C2×C42C2411yescharacteristic
832C2×C42C2411yescharacteristic
833C2×C42C2411yescharacteristic
834C2×C42C2412yes—
835C2×C42C2412yes—
836C2×C42C2411yescharacteristic
837C2×C42C2411yescharacteristic
838C2×C42C2411yescharacteristic
839C2×C42C2411yescharacteristic
840C2×C42C2411yescharacteristic
841C2×C42C2411yescharacteristic
842C2×C42C2412yes—
843C2×C42C2414yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2414yes—
848C2×C42C2412yes—
849C2×C42C2414yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2411yescharacteristic
855#95C2414yes—
856#95C2414yes—
857#95C2412yes—
858#95C2414yes—
859#95C2412yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2412yes—
886#95C2414yes—
887#95C2412yes—
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#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925C24C2511yescharacteristic
926C24C2511yescharacteristic
927C24C2511yescharacteristic
928#41—416no—
929C2×Q8—22no—
930C2×Q8—24no—
931C2×Q8—22no—
932C2×Q8—41no—
933C2×Q8—42no—
934C2×Q8—42no—
935C2×Q8—44no—
936C2×Q8—42no—
937C2×Q8—44no—
938C2×Q8—44no—
939C2×Q8—44no—
940C2×D4—22no—
941C2×D4—22no—
942C2×D4—22no—
943C2×D4—41no—
944C2×D4—41no—
945C2×D4—41no—
946C2×D4—41no—
947C2×D4—41no—
948C2×D42−1+414yes—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4—24no—
954C22×C4—22no—
955C22×C4—22no—
956C22×C4—22no—
957C22×C4—22no—
958C22×C4—22no—
959C22×C4—22no—
960C22×C4—22no—
961C22×C4—22no—
962C22×C4—22no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—41no—
966C22×C4—41no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4C2514yes—
980C22×C4C2514yes—
981C22×C4C2514yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2511yescharacteristic
985C22×C4C2511yescharacteristic
986C22×C4C2514yes—
987C22×C4C2511yescharacteristic
988C22×C4C2511yescharacteristic
989C22×C4C2514yes—
990C22×C4C2514yes—
991C22×C4C2511yescharacteristic
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C22×C4C2514yes—
995C22×C4C2514yes—
996C22×C4C2514yes—
997C22×C4C2514yes—
998C22×C4C2511yescharacteristic
999C22×C4C2511yescharacteristic
1000C22×C4C2511yescharacteristic
1001C22×C4C2511yescharacteristic
1002C22×C4C2511yescharacteristic
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—24no—
1006C4⋊C4—24no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—24no—
1012C4⋊C4—24no—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—44no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—41no—
1058C4⋊C4—44no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C22⋊C4—24no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—41no—
1088C22⋊C4—41no—
1089C22⋊C4—41no—
1090C22⋊C4—41no—
1091C22⋊C4—41no—
1092C22⋊C4—41no—
1093C22⋊C4—44no—
1094C22⋊C4—42no—
1095C22⋊C4—44no—
1096C42—22no—
1097C42—22no—
1098C42—22no—
1099C42—22no—
1100C42—22no—
1101C42—22no—
1102C42—22no—
1103C42—22no—
1104C42—22no—
1105C42—24no—
1106C42—24no—
1107C42—24no—
1108C42—44no—
1109C42—44no—
1110C42—44no—
1111C42—44no—
1112C42—44no—
1113C42—44no—
1114C42—44no—
1115C42—44no—
1116C42—44no—
1117C42—44no—
1118C42—42no—
1119C42H(5,𝔽2)14yes—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—22no—
1132C23—22no—
1133C23C2×2−1+412yes—
1134C23C2×2−1+412yes—
1135C23C2611yescharacteristic
1136Q8—44no—
1137Q8—84no—
1138Q8—88no—
1139Q8—84no—
1140D4—44no—
1141D4—44no—
1142D4—44no—
1143C2×C4—28no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—21no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—21no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—44no—
1204C2×C4—44no—
1205C2×C4—44no—
1206C2×C4—44no—
1207C2×C4—82no—
1208C2×C4—82no—
1209C2×C4—82no—
1210C2×C4—82no—
1211C2×C4—84no—
1212C2×C4—84no—
1213C2×C4—84no—
1214C2×C4—84no—
1215C2×C4C2×H(5,𝔽2)12yes—
1216C2×C4C2×H(5,𝔽2)12yes—
1217C2×C4C2×H(5,𝔽2)12yes—
1218C2×C4C2×2−1+412yes—
1219C2×C4#58512yes—
1220C22—24no—
1221C22—24no—
1222C22—22no—
1223C22—22no—
1224C22—42no—
1225C22—42no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—42no—
1231C22—42no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22C22×H(5,𝔽2)11yescharacteristic
1236C22C22×2−1+411yescharacteristic
1237C22C2×#58511yescharacteristic
1238C222−1+612yes—
1239C222−1+612yes—
1240C4—22no—
1241C4—22no—
1242C4—22no—
1243C4—22no—
1244C4—22no—
1245C4—44no—
1246C4—44no—
1247C4—44no—
1248C4—44no—
1249C4—44no—
1250C4—44no—
1251C4—41no—
1252C4—44no—
1253C4—44no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—44no—
1260C4—44no—
1261C4—44no—
1262C4—41no—
1263C4—44no—
1264C2—42no—
1265C2—42no—
1266C2—81no—
1267C2#6281911yescharacteristic
1268C2#6288611yescharacteristic
1269C2#6288611yescharacteristic
1270C2#6305312yes—
1271C2#6306712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58972C2semidirect
2. #58543C2semidirect
3. #58343C2semidirect
4. #58290C2semidirect
5. #55954C2semidirect
6. #54715C2semidirect
7. #54641C2semidirect
8. #53932C2semidirect
9. #51796C2semidirect
10. #51708C2semidirect
11. #50902C2semidirect
14. #49032C2semidirect
15. #47820C2semidirect
16. #47789C2semidirect
17. #47595C2semidirect
18. #47327C2semidirect
19. #46235C2semidirect
20. #46229C2semidirect
21. #46143C2semidirect
22. #46143C2semidirect
23. C22⋊#564C2semidirect
24. C22⋊#564C2semidirect

Maximal subgroups

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

subgroupindex
#589722
#585432
#583432
#582902
#559542
#547152
#546412
#539322
#517962
#517082
#509022
#502372
#502002
#490322
#478202
#477892
#475952
#473272
#462352
#462292
#461432
C22⋊#5642
#353332
#352002
#351382