Finite Group Databasebeta

← #8757207

Subgroups — #8757207

Order 512.

3908 conjugacy classes of subgroups.

The subgroup lattice has 1079 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58522C214yesmaximal, complemented
2#57242C214yesmaximal, complemented
3#55792C214yesmaximal, complemented
4#55288C214yesmaximal, complemented
5#54128C214yesmaximal, complemented
6#53844C214yesmaximal, complemented
7#50741C214yesmaximal, complemented
8#49640C214yesmaximal, complemented
9#48587C214yesmaximal, complemented
10#47559C214yesmaximal, complemented
11#46660C214yesmaximal, complemented
12#46569C214yesmaximal, complemented
13#46246C212yesmaximal, complemented
14#46245C212yesmaximal, complemented
15#46230C212yesmaximal, complemented
16#46144C211yesmaximal, characteristic, complemented
17#46009C212yesmaximal, complemented
18#46008C212yesmaximal, complemented
19#45988C211yesmaximal, characteristic
20#35339C211yesmaximal, characteristic, complemented
21#35135C212yesmaximal, complemented
22#2864C2212yes—
23#2864C2212yes—
24#2861C2212yes—
25#2859C2212yes—
26#2851C2212yes—
27#2850C2212yes—
28#2845C2211yescharacteristic
29#2845C2211yescharacteristic
30#2844C2212yes—
31#2839C2214yes—
32#2839C2214yes—
33#2836C2214yes—
34#2836C2214yes—
35#2827C2214yes—
36#2827C2214yes—
37#2822C2211yescharacteristic
38#2820C2212yes—
39#2819C2211yescharacteristic
40#2817C2214yes—
41#2807C2214yes—
42#2807C2214yes—
43#2807C2214yes—
44#2806C2214yes—
45#2805C2214yes—
46#2803C2214yes—
47#2802C2214yes—
48#2802C2214yes—
49#2801C2214yes—
50#2798C2214yes—
51#2793C2214yes—
52#2792C2214yes—
53#2792C2214yes—
54#2792C2214yes—
55#2791C2214yes—
56#2790C2214yes—
57#2787C2214yes—
58#2786C2214yes—
59#2786C2214yes—
60#2781C2214yes—
61#2780C2214yes—
62#2779C2214yes—
63#2779C2214yes—
64#2777C2214yes—
65#2777C2214yes—
66#2777C2214yes—
67#2774C2214yes—
68#2773C2214yes—
69#2772C2214yes—
70#2771C2214yes—
71#2771C2214yes—
72#2770C2214yes—
73#2770C2214yes—
74#2767C2214yes—
75#2767C2214yes—
76#2762C2214yes—
77#2758C2214yes—
78#2754C2214yes—
79#2752C2214yes—
80#2750C2214yes—
81#2747C2214yes—
82#2745C2214yes—
83#2744C2214yes—
84#2744C2214yes—
85#2741C2214yes—
86#2739C2214yes—
87#2739C2214yes—
88#2725C2214yes—
89#2721C2214yes—
90#2721C2214yes—
91#2720C2214yes—
92#2720C2214yes—
93#2720C2214yes—
94#2719C2214yes—
95#2719C2214yes—
96#2718C2214yes—
97#2717C2214yes—
98#2717C2214yes—
99#2711C2214yes—
100#2707C2214yes—
101#2706C2214yes—
102#2704C2214yes—
103#2690C2214yes—
104#2690C2214yes—
105#2689C2214yes—
106#2672C2214yes—
107#2672C2214yes—
108#2672C2214yes—
109#2655C2214yes—
110#2654C2214yes—
111#2651C2214yes—
112#2649C2214yes—
113#2649C2214yes—
114#2649C2214yes—
115#2647C2212yes—
116#2647C2212yes—
117#2634C2214yes—
118#2633C2214yes—
119#2604C2214yes—
120#2600C2214yes—
121#2597C2214yes—
122#2596C2214yes—
123#2596C2214yes—
124#2596C2214yes—
125#2590C2214yes—
126#2588C2214yes—
127#2587C2214yes—
128#2587C2214yes—
129#2586C2214yes—
130#2585C2214yes—
131#2584C2214yes—
132#2583C2214yes—
133#2577C2214yes—
134#2573C2214yes—
135#2570C2214yes—
136#2570C2214yes—
137#2569C2214yes—
138#2569C2214yes—
139#2569C2214yes—
140#2556C2214yes—
141#2556C2214yes—
142#2553C2214yes—
143#2543C2214yes—
144#2536C2214yes—
145#2533C2214yes—
146#2530C2214yes—
147#2530C2214yes—
148#2529C2214yes—
149#2528C2214yes—
150#2527C2214yes—
151#2526C2214yes—
152#2525C2214yes—
153#2519C2214yes—
154#2516C2214yes—
155#2512C2212yes—
156#2511C2212yes—
157#2506C2214yes—
158#2506C2214yes—
159#2505C2214yes—
160#2490C2212yes—
161#2489C2212yes—
162#2486C2214yes—
163#2479C2214yes—
164#2474C2214yes—
165#2473C2214yes—
166#2473C2214yes—
167#2470C2214yes—
168#2470C2214yes—
169#2468C2214yes—
170#2467C2214yes—
171#2466C2214yes—
172#2462C2214yes—
173#2462C2214yes—
174#2454C2212yes—
175#2453C2212yes—
176#2453C2214yes—
177#2450C2214yes—
178#2449C2214yes—
179#2449C2214yes—
180#2443C2214yes—
181#2442C2214yes—
182#2423C2212yes—
183#2423C2214yes—
184#2422C2214yes—
185#2422C2212yes—
186#2382C2212yes—
187#2382C2212yes—
188#2379C2212yes—
189#2379C2212yes—
190#2376C2214yes—
191#2367C2214yes—
192#2335C2214yes—
193#2334C2214yes—
194#2330C2214yes—
195#2322C2214yes—
196#2317C2212yes—
197#2316C2212yes—
198C4×#125C2212yes—
199C4×#124C2212yes—
200#2285C2211yescharacteristic
201C2×#382C2211yescharacteristic
202C4×#117C2211yescharacteristic
203C2×#126C2314yes—
204C2×#126C2314yes—
205C2×#125C2312yes—
206C2×#125C2314yes—
207C2×#125C2314yes—
208C2×#125C2312yes—
209C2×#125C2312yes—
210C2×#125C2314yes—
211C2×#125C2314yes—
212C2×#124C2312yes—
213C2×#124C2314yes—
214C2×#123C2314yes—
215C2×#123C2314yes—
216C2×#123C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2312yes—
221C2×#121C2312yes—
222C2×#121C2314yes—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2312yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2312yes—
227C2×C4×D4C2314yes—
228C2×#117C2311yescharacteristic
229C2×#117C2312yes—
230C2×#117C2311yescharacteristic
231C22×C4⋊C4C2312yes—
232C22×C4⋊C4C2314yes—
233C22×C42C2311yescharacteristic
234#401C2314yes—
235#400C2314yes—
236#400C2314yes—
237#400C2314yes—
238#400C2314yes—
239#400C2314yes—
240#400C2314yes—
241#400C2314yes—
242#400C2314yes—
243#400C2314yes—
244#400C2314yes—
245#400C2314yes—
246#400C2314yes—
247#400C2314yes—
248#400C2314yes—
249#400C2314yes—
250#400C2314yes—
251#400C2314yes—
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#399C2314yes—
266#399C2314yes—
267#399C2314yes—
268#399C2314yes—
269#399C2314yes—
270#399C2314yes—
271#399C2314yes—
272#399C2314yes—
273#399C2314yes—
274#398C2314yes—
275#398C2314yes—
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#397C2314yes—
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#397C2314yes—
319#397C2314yes—
320#397C2314yes—
321#396C2314yes—
322#396C2314yes—
323#396C2314yes—
324#396C2314yes—
325#396C2314yes—
326#396C2314yes—
327#396C2314yes—
328#396C2314yes—
329#396C2314yes—
330#396C2314yes—
331#396C2314yes—
332#395C2314yes—
333#395C2314yes—
334#395C2314yes—
335#395C2314yes—
336#395C2314yes—
337#395C2314yes—
338#395C2314yes—
339#395C2314yes—
340#395C2314yes—
341#394C2314yes—
342#394C2314yes—
343#394C2314yes—
344#394C2314yes—
345#394C2314yes—
346#394C2314yes—
347#394C2314yes—
348#394C2314yes—
349#394C2314yes—
350#394C2314yes—
351#394C2314yes—
352#393C2314yes—
353#392C2314yes—
354#391C2312yes—
355#391C2314yes—
356#391C2314yes—
357#391C2312yes—
358#391C2314yes—
359#391C2312yes—
360#391C2314yes—
361#391C2312yes—
362#390C2314yes—
363#390C2312yes—
364#390C2312yes—
365#390C2312yes—
366#390C2314yes—
367#390C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2314yes—
371#389C2314yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2312yes—
404#389C2312yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
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#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
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#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#386C2314yes—
497#386C2314yes—
498#386C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#385C2314yes—
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#384C2314yes—
527#384C2314yes—
528#384C2312yes—
529#384C2312yes—
530#384C2311yescharacteristic
531#384C2311yescharacteristic
532#383C2314yes—
533#383C2314yes—
534#382C2312yes—
535#382C2311yescharacteristic
536#382C2312yes—
537#382C2311yescharacteristic
538#382C2314yes—
539#382C2314yes—
540#382C2312yes—
541#382C2314yes—
542#382C2312yes—
543#382C2314yes—
544#381C2314yes—
545#381C2314yes—
546#381C2314yes—
547#380C2314yes—
548#380C2314yes—
549#380C2312yes—
550#380C2314yes—
551#380C2314yes—
552#380C2314yes—
553#380C2314yes—
554#380C2312yes—
555#380C2314yes—
556#380C2314yes—
557#380C2314yes—
558C4×C4⋊C4C2312yes—
559C4×C4⋊C4C2314yes—
560C4×C4⋊C4C2314yes—
561C4×C4⋊C4C2312yes—
562C4×C4⋊C4C2314yes—
563C4×C4⋊C4C2312yes—
564C4×C4⋊C4C2312yes—
565C4×C4⋊C4C2314yes—
566C4×C4⋊C4C2314yes—
567C4×C4⋊C4C2314yes—
568C4×C4⋊C4C2314yes—
569C4×C22⋊C4C2312yes—
570C4×C22⋊C4C2312yes—
571C4×C22⋊C4C2314yes—
572C4×C22⋊C4C2314yes—
573C4×C22⋊C4C2314yes—
574C4×C22⋊C4C2314yes—
575C4×C22⋊C4C2314yes—
576#376C2314yes—
577#376C2312yes—
578C2×#95C2314yes—
579C43C2312yes—
580C22×Q8C2412yes—
581C22×Q8C2414yes—
582C22×D4C2414yes—
583C22×D4C2412yes—
584C22×D4C2414yes—
585C23×C4C2411yescharacteristic
586C23×C4C2412yes—
587C23×C4C2414yes—
588C23×C4C2414yes—
589C23×C4C2414yes—
590C23×C4C2414yes—
591#126—48no—
592#126—84no—
593#125—28no—
594#125—48no—
595#125—84no—
596#125—84no—
597#125—84no—
598#125—82no—
599#125—82no—
600#124—28no—
601#124—48no—
602#123—48no—
603#123—48no—
604#123—48no—
605C22⋊Q8—82no—
606C22⋊Q8—84no—
607C22⋊Q8—84no—
608C22⋊Q8—84no—
609#121—82no—
610#121—84no—
611C4×Q8—84no—
612C4×Q8—82no—
613C4×D4—82no—
614C4×D4—84no—
615C4×D4—84no—
616#117—42no—
617#117—44no—
618#117—42no—
619C2×C4⋊C4—44no—
620C2×C4⋊C4—84no—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2411yescharacteristic
686C2×C22⋊C4C2411yescharacteristic
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C42—24no—
711C2×C42C2411yescharacteristic
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2414yes—
716C2×C42C2412yes—
717C2×C42C2414yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2414yes—
721C2×C42C2414yes—
722C2×C42C2414yes—
723C2×C42C2412yes—
724C2×C42C2414yes—
725C2×C42C2414yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2414yes—
729C2×C42C2411yescharacteristic
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2412yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
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—
792C24C2514yes—
793C24C2511yescharacteristic
794C2×Q8—24no—
795C2×Q8—42no—
796C2×Q8—44no—
797C2×Q8—44no—
798C2×Q8—44no—
799C2×Q8—42no—
800C2×D4—28no—
801C2×D4—24no—
802C2×D4—42no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—44no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—24no—
813C22×C4—44no—
814C22×C4—42no—
815C22×C4—44no—
816C22×C4—42no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4C2514yes—
828C22×C4C2512yes—
829C22×C4C2514yes—
830C22×C4C2514yes—
831C22×C4C2514yes—
832C22×C4C2512yes—
833C22×C4C2514yes—
834C22×C4C2514yes—
835C22×C4C2514yes—
836C22×C4C2514yes—
837C22×C4C2512yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2514yes—
841C22×C4C2514yes—
842C22×C4C2514yes—
843C22×C4C2512yes—
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C4⋊C4—28no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—24no—
852C4⋊C4—28no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—44no—
873C4⋊C4—42no—
874C4⋊C4—44no—
875C4⋊C4—42no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—42no—
880C4⋊C4—44no—
881C4⋊C4—42no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C22⋊C4—24no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—41no—
918C22⋊C4—41no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C42—24no—
936C42—22no—
937C42—42no—
938C42—42no—
939C42—44no—
940C42—44no—
941C42—42no—
942C42—42no—
943C42—42no—
944C42—44no—
945C42—44no—
946C42—44no—
947C42—44no—
948C42—44no—
949C42—44no—
950C42—44no—
951C42—42no—
952C42—44no—
953C422−1+414yes—
954C23—21no—
955C23—21no—
956C23—22no—
957C23—22no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23#58512yes—
966C23C2611yescharacteristic
967Q8—84no—
968Q8—88no—
969D4—84no—
970D4—88no—
971D4—88no—
972C2×C4—28no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—84no—
1028C2×C4—88no—
1029C2×C4—164no—
1030C2×C4—164no—
1031C2×C4—164no—
1032C2×C4C2×2−1+412yes—
1033C2×C4C2×2−1+414yes—
1034C2×C4#58512yes—
1035C22—22no—
1036C22—22no—
1037C22—22no—
1038C22—42no—
1039C22—42no—
1040C22—44no—
1041C22—44no—
1042C22—44no—
1043C22—44no—
1044C22—44no—
1045C22—44no—
1046C22—44no—
1047C22C22×2−1+411yescharacteristic
1048C22C2×#58511yescharacteristic
1049C22C2×#58511yescharacteristic
1050C22H(7,𝔽2)12yes—
1051C222−1+612yes—
1052C4—22no—
1053C4—22no—
1054C4—24no—
1055C4—42no—
1056C4—44no—
1057C4—44no—
1058C4—44no—
1059C4—42no—
1060C4—42no—
1061C4—44no—
1062C4—44no—
1063C4—44no—
1064C4—44no—
1065C4—44no—
1066C4—42no—
1067C4—44no—
1068C4—44no—
1069C4—42no—
1070C4—44no—
1071C2—42no—
1072C2—84no—
1073C2#6282511yescharacteristic
1074C2#6287912yes—
1075C2#6305511yescharacteristic
1076C2#6305612yes—
1077C2#6306811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#45988C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58522C2semidirect
2. #57242C2semidirect
3. #55792C2semidirect
4. #55288C2semidirect
5. #54128C2semidirect
6. #53844C2semidirect
7. #50741C2semidirect
8. #49640C2semidirect
9. #48587C2semidirect
10. #47559C2semidirect
11. #46660C2semidirect
12. #46569C2semidirect
13. #46246C2semidirect
14. #46245C2semidirect
15. #46230C2semidirect
16. #46144C2semidirect
17. #46009C2semidirect
18. #46008C2semidirect
20. #35339C2semidirect
21. #35135C2semidirect

Maximal subgroups

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

subgroupindex
#585222
#572422
#557922
#552882
#541282
#538442
#507412
#496402
#485872
#475592
#466602
#465692
#462462
#462452
#462302
#461442
#460092
#460082
#459882
#353392
#351352