Finite Group Databasebeta

← #8757205

Subgroups — #8757205

Order 512.

4180 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57372C214yesmaximal, complemented
2#56894C214yesmaximal, complemented
3#55256C214yesmaximal, complemented
4#54992C214yesmaximal, complemented
5#53434C214yesmaximal, complemented
6#53408C214yesmaximal, complemented
7#50595C214yesmaximal, complemented
8#49639C214yesmaximal, complemented
9#48580C214yesmaximal, complemented
10#47520C214yesmaximal, complemented
11#46683C214yesmaximal, complemented
12#46676C214yesmaximal, complemented
13#46240C212yesmaximal, complemented
14#46240C212yesmaximal, complemented
15#46231C212yesmaximal, complemented
16#46017C212yesmaximal, complemented
17#46017C212yesmaximal, complemented
18#45988C211yesmaximal, characteristic, complemented
19#45988C211yesmaximal, characteristic, complemented
20#35339C211yesmaximal, characteristic, complemented
21#35136C212yesmaximal, complemented
22#2864C2212yes—
23#2864C2212yes—
24#2864C2212yes—
25#2858C2212yes—
26#2850C2212yes—
27#2850C2212yes—
28#2845C2212yes—
29#2845C2211yescharacteristic
30#2845C2211yescharacteristic
31#2839C2214yes—
32#2837C2214yes—
33#2836C2214yes—
34#2827C2214yes—
35#2826C2214yes—
36#2823C2214yes—
37#2819C2212yes—
38#2819C2211yescharacteristic
39#2819C2211yescharacteristic
40#2813C2214yes—
41#2809C2214yes—
42#2809C2214yes—
43#2803C2214yes—
44#2803C2214yes—
45#2796C2214yes—
46#2793C2214yes—
47#2791C2214yes—
48#2790C2214yes—
49#2790C2214yes—
50#2790C2214yes—
51#2790C2214yes—
52#2790C2214yes—
53#2781C2214yes—
54#2781C2214yes—
55#2781C2214yes—
56#2779C2214yes—
57#2768C2214yes—
58#2768C2214yes—
59#2768C2214yes—
60#2768C2214yes—
61#2767C2214yes—
62#2754C2214yes—
63#2754C2214yes—
64#2751C2214yes—
65#2751C2214yes—
66#2750C2214yes—
67#2748C2214yes—
68#2748C2214yes—
69#2743C2214yes—
70#2741C2214yes—
71#2739C2214yes—
72#2739C2214yes—
73#2725C2214yes—
74#2721C2214yes—
75#2721C2214yes—
76#2718C2214yes—
77#2718C2214yes—
78#2718C2214yes—
79#2716C2214yes—
80#2716C2214yes—
81#2714C2214yes—
82#2714C2214yes—
83#2711C2214yes—
84#2708C2214yes—
85#2708C2214yes—
86#2706C2214yes—
87#2706C2214yes—
88#2706C2214yes—
89#2706C2214yes—
90#2706C2214yes—
91#2702C2214yes—
92#2702C2214yes—
93#2701C2214yes—
94#2701C2214yes—
95#2695C2214yes—
96#2694C2214yes—
97#2694C2214yes—
98#2693C2214yes—
99#2691C2214yes—
100#2682C2214yes—
101#2675C2214yes—
102#2673C2214yes—
103#2673C2214yes—
104#2671C2214yes—
105#2671C2214yes—
106#2671C2214yes—
107#2671C2214yes—
108#2671C2214yes—
109#2654C2214yes—
110#2652C2214yes—
111#2651C2214yes—
112#2648C2214yes—
113#2647C2212yes—
114#2647C2212yes—
115#2636C2214yes—
116#2636C2214yes—
117#2630C2214yes—
118#2618C2214yes—
119#2602C2214yes—
120#2602C2214yes—
121#2589C2214yes—
122#2589C2214yes—
123#2579C2214yes—
124#2579C2214yes—
125#2575C2214yes—
126#2570C2214yes—
127#2570C2214yes—
128#2569C2214yes—
129#2569C2214yes—
130#2565C2214yes—
131#2565C2214yes—
132#2559C2214yes—
133#2559C2214yes—
134#2558C2214yes—
135#2557C2214yes—
136#2557C2214yes—
137#2554C2214yes—
138#2554C2214yes—
139#2553C2214yes—
140#2543C2214yes—
141#2543C2214yes—
142#2537C2214yes—
143#2531C2214yes—
144#2526C2214yes—
145#2522C2214yes—
146#2522C2214yes—
147#2522C2214yes—
148#2522C2214yes—
149#2517C2214yes—
150#2501C2214yes—
151#2496C2214yes—
152#2486C2214yes—
153#2481C2214yes—
154#2476C2214yes—
155#2476C2214yes—
156#2476C2214yes—
157#2473C2214yes—
158#2473C2214yes—
159#2473C2214yes—
160#2473C2214yes—
161#2471C2214yes—
162#2468C2214yes—
163#2468C2214yes—
164#2460C2214yes—
165#2459C2214yes—
166#2459C2214yes—
167#2458C2214yes—
168#2458C2214yes—
169#2456C2214yes—
170#2456C2214yes—
171#2450C2214yes—
172#2450C2214yes—
173#2448C2212yes—
174#2447C2212yes—
175#2446C2212yes—
176#2445C2212yes—
177#2443C2214yes—
178#2443C2214yes—
179#2443C2214yes—
180#2429C2212yes—
181#2428C2212yes—
182#2427C2212yes—
183#2426C2212yes—
184#2422C2214yes—
185#2416C2214yes—
186#2379C2212yes—
187#2379C2212yes—
188#2379C2212yes—
189#2379C2212yes—
190#2377C2214yes—
191#2361C2214yes—
192#2335C2214yes—
193#2335C2214yes—
194#2333C2214yes—
195#2322C2214yes—
196#2317C2212yes—
197#2316C2212yes—
198C4×#124C2212yes—
199C4×#124C2212yes—
200#2285C2211yescharacteristic
201C2×#382C2211yescharacteristic
202C4×#117C2211yescharacteristic
203C2×C4⋊Q8C2312yes—
204C2×#127C2312yes—
205C2×#126C2314yes—
206C2×#126C2314yes—
207C2×#126C2314yes—
208C2×#126C2314yes—
209C2×#125C2314yes—
210C2×#125C2314yes—
211C2×#124C2312yes—
212C2×#124C2312yes—
213C2×#124C2312yes—
214C2×#124C2312yes—
215C2×#123C2314yes—
216C2×#123C2314yes—
217C2×#123C2314yes—
218C2×#123C2314yes—
219C2×#123C2314yes—
220C2×#123C2314yes—
221C2×#123C2314yes—
222C2×#123C2314yes—
223C2×#123C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×#121C2314yes—
227C2×#121C2314yes—
228C2×#121C2314yes—
229C2×#121C2312yes—
230C2×#121C2312yes—
231C2×#121C2314yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2314yes—
236C2×#121C2314yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×#117C2311yescharacteristic
246C2×#117C2312yes—
247C2×#117C2311yescharacteristic
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2314yes—
250C22×C4⋊C4C2314yes—
251C22×C42C2311yescharacteristic
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2314yes—
256#400C2314yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#399C2314yes—
268#399C2314yes—
269#399C2314yes—
270#399C2314yes—
271#399C2314yes—
272#399C2314yes—
273#399C2314yes—
274#399C2314yes—
275#399C2314yes—
276#398C2314yes—
277#398C2314yes—
278#398C2314yes—
279#398C2314yes—
280#398C2314yes—
281#398C2314yes—
282#398C2314yes—
283#398C2314yes—
284#398C2314yes—
285#398C2314yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#397C2314yes—
305#397C2314yes—
306#397C2314yes—
307#397C2314yes—
308#397C2314yes—
309#397C2314yes—
310#397C2314yes—
311#397C2314yes—
312#397C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#397C2314yes—
318#396C2314yes—
319#396C2314yes—
320#396C2314yes—
321#396C2314yes—
322#396C2314yes—
323#396C2314yes—
324#396C2314yes—
325#396C2314yes—
326#396C2314yes—
327#396C2314yes—
328#396C2314yes—
329#396C2314yes—
330#396C2314yes—
331#396C2314yes—
332#396C2314yes—
333#396C2314yes—
334#394C2314yes—
335#394C2314yes—
336#394C2314yes—
337#394C2314yes—
338#394C2314yes—
339#394C2314yes—
340#394C2314yes—
341#394C2314yes—
342#394C2314yes—
343#394C2314yes—
344#394C2314yes—
345#394C2314yes—
346#394C2314yes—
347#394C2314yes—
348#394C2314yes—
349#394C2314yes—
350#394C2314yes—
351#394C2314yes—
352#394C2314yes—
353#394C2314yes—
354#394C2314yes—
355#394C2314yes—
356#394C2314yes—
357#394C2314yes—
358#394C2314yes—
359#393C2314yes—
360#393C2314yes—
361#393C2314yes—
362#393C2314yes—
363#392C2314yes—
364#392C2314yes—
365#392C2314yes—
366#392C2314yes—
367#392C2314yes—
368#392C2314yes—
369#392C2314yes—
370#392C2314yes—
371#392C2314yes—
372#391C2314yes—
373#391C2314yes—
374#391C2314yes—
375#391C2314yes—
376#391C2312yes—
377#391C2312yes—
378#391C2312yes—
379#391C2312yes—
380#390C2314yes—
381#390C2314yes—
382#390C2314yes—
383#390C2314yes—
384#390C2312yes—
385#390C2312yes—
386#390C2314yes—
387#390C2314yes—
388#390C2314yes—
389#390C2314yes—
390#390C2312yes—
391#390C2314yes—
392#390C2312yes—
393#389C2314yes—
394#389C2314yes—
395#389C2312yes—
396#389C2312yes—
397#389C2312yes—
398#389C2312yes—
399#389C2312yes—
400#389C2312yes—
401#389C2312yes—
402#389C2312yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2312yes—
408#389C2312yes—
409#389C2312yes—
410#389C2312yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#386C2314yes—
483#386C2314yes—
484#386C2314yes—
485#386C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#386C2314yes—
495#386C2314yes—
496#386C2314yes—
497#386C2314yes—
498#386C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#384C2314yes—
533#384C2314yes—
534#384C2314yes—
535#384C2311yescharacteristic
536#384C2311yescharacteristic
537#382C2311yescharacteristic
538#382C2311yescharacteristic
539#382C2312yes—
540#382C2314yes—
541#382C2314yes—
542#382C2314yes—
543#382C2314yes—
544#382C2312yes—
545#382C2312yes—
546#382C2312yes—
547#381C2314yes—
548#381C2314yes—
549#381C2314yes—
550#380C2314yes—
551#380C2314yes—
552#380C2314yes—
553#380C2314yes—
554#380C2314yes—
555#380C2314yes—
556#380C2314yes—
557#380C2314yes—
558#380C2314yes—
559#380C2314yes—
560#380C2314yes—
561#380C2314yes—
562C4×C4⋊C4C2314yes—
563C4×C4⋊C4C2314yes—
564C4×C4⋊C4C2314yes—
565C4×C4⋊C4C2312yes—
566C4×C4⋊C4C2312yes—
567C4×C22⋊C4C2312yes—
568C4×C22⋊C4C2312yes—
569C4×C22⋊C4C2314yes—
570C4×C22⋊C4C2314yes—
571C4×C22⋊C4C2314yes—
572C4×C22⋊C4C2314yes—
573C4×C22⋊C4C2314yes—
574C4×C22⋊C4C2314yes—
575C4×C22⋊C4C2314yes—
576C4×C22⋊C4C2314yes—
577#376C2312yes—
578C2×#95C2314yes—
579C43C2312yes—
580C22×Q8C2412yes—
581C22×Q8C2412yes—
582C22×D4C2414yes—
583C22×D4C2414yes—
584C22×D4C2412yes—
585C22×D4C2412yes—
586C22×D4C2414yes—
587C22×D4C2414yes—
588C22×D4C2414yes—
589C22×D4C2414yes—
590C22×D4C2414yes—
591C22×D4C2414yes—
592C23×C4C2411yescharacteristic
593C23×C4C2412yes—
594C23×C4C2414yes—
595C23×C4C2414yes—
596C23×C4C2414yes—
597C23×C4C2414yes—
598C23×C4C2414yes—
599C23×C4C2414yes—
600C23×C4C2414yes—
601C4⋊Q8—82no—
602#127—82no—
603#126—84no—
604#126—84no—
605#126—84no—
606#126—84no—
607#125—84no—
608#125—84no—
609#124—28no—
610#124—28no—
611#124—82no—
612#124—82no—
613#123—48no—
614#123—48no—
615#123—48no—
616#123—84no—
617#123—84no—
618#123—84no—
619#123—84no—
620#123—84no—
621#123—84no—
622C22⋊Q8—82no—
623C22⋊Q8—82no—
624#121—48no—
625#121—48no—
626#121—48no—
627#121—84no—
628#121—84no—
629#121—84no—
630#121—84no—
631#121—84no—
632#121—82no—
633#121—82no—
634#121—84no—
635C4×Q8—82no—
636C4×Q8—82no—
637C4×D4—84no—
638C4×D4—84no—
639C4×D4—82no—
640C4×D4—82no—
641C4×D4—84no—
642C4×D4—84no—
643#117—42no—
644#117—44no—
645#117—42no—
646C2×C4⋊C4—44no—
647C2×C4⋊C4—84no—
648C2×C4⋊C4—84no—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C22⋊C4C2412yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2411yescharacteristic
706C2×C22⋊C4C2411yescharacteristic
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C42—24no—
744C2×C42C2411yescharacteristic
745C2×C42C2412yes—
746C2×C42C2412yes—
747C2×C42C2412yes—
748C2×C42C2414yes—
749C2×C42C2414yes—
750C2×C42C2412yes—
751C2×C42C2412yes—
752C2×C42C2414yes—
753C2×C42C2414yes—
754C2×C42C2414yes—
755C2×C42C2414yes—
756C2×C42C2412yes—
757C2×C42C2414yes—
758C2×C42C2412yes—
759C2×C42C2411yescharacteristic
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2412yes—
765#95C2412yes—
766#95C2412yes—
767#95C2412yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810C24C2514yes—
811C24C2514yes—
812C24C2511yescharacteristic
813C2×Q8—24no—
814C2×Q8—24no—
815C2×Q8—42no—
816C2×Q8—42no—
817C2×Q8—42no—
818C2×Q8—42no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—24no—
822C2×D4—24no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—44no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4—44no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—44no—
836C2×D4—44no—
837C2×D4—44no—
838C2×D4—44no—
839C2×D4—44no—
840C2×D4—44no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—44no—
844C2×D4—44no—
845C2×D4—44no—
846C2×D4—44no—
847C2×D4—44no—
848C2×D4—44no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—24no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4C2514yes—
877C22×C4C2514yes—
878C22×C4C2512yes—
879C22×C4C2514yes—
880C22×C4C2514yes—
881C22×C4C2514yes—
882C22×C4C2512yes—
883C22×C4C2512yes—
884C22×C4C2512yes—
885C22×C4C2512yes—
886C22×C4C2514yes—
887C22×C4C2514yes—
888C22×C4C2514yes—
889C22×C4C2514yes—
890C22×C4C2514yes—
891C22×C4C2512yes—
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C4⋊C4—28no—
895C4⋊C4—24no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—41no—
907C4⋊C4—41no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C22⋊C4—24no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—41no—
951C22⋊C4—41no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C42—24no—
989C42—22no—
990C42—44no—
991C42—42no—
992C42—42no—
993C42—44no—
994C42—42no—
995C42—42no—
996C42—44no—
997C42—44no—
998C42—44no—
999C42—44no—
1000C42—42no—
1001C42—44no—
1002C42—42no—
1003C422−1+414yes—
1004C23—21no—
1005C23—21no—
1006C23—22no—
1007C23—22no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23—24no—
1022C23#58512yes—
1023C23C2611yescharacteristic
1024Q8—84no—
1025Q8—84no—
1026D4—84no—
1027D4—84no—
1028D4—88no—
1029D4—88no—
1030D4—88no—
1031D4—88no—
1032D4—164no—
1033D4—164no—
1034D4—164no—
1035D4—164no—
1036C2×C4—28no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—84no—
1089C2×C4—88no—
1090C2×C4—88no—
1091C2×C4—164no—
1092C2×C4—164no—
1093C2×C4—164no—
1094C2×C4—164no—
1095C2×C4—164no—
1096C2×C4C2×2−1+412yes—
1097C2×C4C2×2−1+414yes—
1098C2×C4#58512yes—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—42no—
1103C22—42no—
1104C22—44no—
1105C22—44no—
1106C22—44no—
1107C22—44no—
1108C22—44no—
1109C22—44no—
1110C22—44no—
1111C22—44no—
1112C22—44no—
1113C22—44no—
1114C22—44no—
1115C22—44no—
1116C22—44no—
1117C22—44no—
1118C22C22×2−1+411yescharacteristic
1119C22C2×#58511yescharacteristic
1120C22C2×#58511yescharacteristic
1121C22H(7,𝔽2)12yes—
1122C22H(7,𝔽2)12yes—
1123C4—22no—
1124C4—22no—
1125C4—24no—
1126C4—44no—
1127C4—44no—
1128C4—42no—
1129C4—44no—
1130C4—44no—
1131C4—42no—
1132C4—44no—
1133C4—44no—
1134C4—44no—
1135C4—42no—
1136C4—44no—
1137C4—42no—
1138C4—42no—
1139C4—44no—
1140C4—44no—
1141C2—42no—
1142C2—84no—
1143C2—84no—
1144C2#6282511yescharacteristic
1145C2#6288112yes—
1146C2#6305511yescharacteristic
1147C2#6305511yescharacteristic
1148C2#6306012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #57372C2semidirect
2. #56894C2semidirect
3. #55256C2semidirect
4. #54992C2semidirect
5. #53434C2semidirect
6. #53408C2semidirect
7. #50595C2semidirect
8. #49639C2semidirect
9. #48580C2semidirect
10. #47520C2semidirect
11. #46683C2semidirect
12. #46676C2semidirect
13. #46240C2semidirect
14. #46240C2semidirect
15. #46231C2semidirect
16. #46017C2semidirect
17. #46017C2semidirect
18. #45988C2semidirect
19. #45988C2semidirect
20. #35339C2semidirect
21. #35136C2semidirect

Maximal subgroups

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

subgroupindex
#573722
#568942
#552562
#549922
#534342
#534082
#505952
#496392
#485802
#475202
#466832
#466762
#462402
#462312
#460172
#459882
#353392
#351362