Finite Group Databasebeta

← #8726571

Subgroups — #8726571

Order 512.

4603 conjugacy classes of subgroups.

The subgroup lattice has 1420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59841C211yesmaximal, characteristic
2#59749C212yesmaximal, complemented
3#59455C212yesmaximal, complemented
4#59076C212yesmaximal, complemented
5#59072C212yesmaximal, complemented
6#58946C214yesmaximal, complemented
7#56968C214yesmaximal, complemented
8#56713C212yesmaximal, complemented
9#55315C214yesmaximal, complemented
10#53099C211yesmaximal, characteristic, complemented
11#53003C212yesmaximal, complemented
12#52304C211yesmaximal, characteristic, complemented
13#47788C212yesmaximal, complemented
14#46674C214yesmaximal, complemented
15#45364C211yesmaximal, characteristic, complemented
16#45055C212yesmaximal, complemented
17#44890C214yesmaximal, complemented
18#44862C212yesmaximal, complemented
19#42886C211yesmaximal, characteristic, complemented
20#42611C212yesmaximal, complemented
21#42361C212yesmaximal, complemented
22#41093C214yesmaximal, complemented
23#39977C212yesmaximal, complemented
24#39496C212yesmaximal, complemented
25#39403C212yesmaximal, complemented
26#39173C211yesmaximal, characteristic, complemented
27#39125C212yesmaximal, complemented
28#35937C211yesmaximal, characteristic, complemented
29#35880C212yesmaximal, complemented
30C2×#559C2211yescharacteristic
31C2×Q82C2211yescharacteristic
32C2×#557C2211yescharacteristic
33C2×#555C2212yes—
34C2×#554C2211yescharacteristic
35C2×#542C2214yes—
36C2×#529C2212yes—
37#2862C2211yescharacteristic
38#2857C2212yes—
39#2836C2214yes—
40#2835C2214yes—
41#2832C2214yes—
42#2831C2214yes—
43#2830C2212yes—
44#2827C2214yes—
45#2823C2212yes—
46#2820C2212yes—
47#2814C2214yes—
48#2811C2212yes—
49#2806C2214yes—
50#2806C2214yes—
51#2805C2212yes—
52#2805C2214yes—
53#2802C2214yes—
54#2802C2214yes—
55#2794C2214yes—
56#2792C2212yes—
57#2789C2211yescharacteristic
58#2789C2211yescharacteristic
59#2788C2214yes—
60#2788C2214yes—
61#2787C2214yes—
62#2779C2214yes—
63#2774C2214yes—
64#2772C2214yes—
65#2768C2214yes—
66#2766C2214yes—
67#2765C2212yes—
68#2765C2212yes—
69#2763C2214yes—
70#2754C2214yes—
71#2731C2212yes—
72#2729C2214yes—
73#2725C2214yes—
74#2724C2211yescharacteristic
75#2723C2214yes—
76#2718C2214yes—
77#2717C2214yes—
78#2717C2212yes—
79#2716C2214yes—
80#2716C2214yes—
81#2716C2214yes—
82#2715C2214yes—
83#2715C2214yes—
84#2715C2214yes—
85#2715C2214yes—
86#2712C2214yes—
87#2704C2214yes—
88#2700C2214yes—
89#2699C2212yes—
90#2698C2214yes—
91#2695C2214yes—
92#2694C2214yes—
93#2690C2214yes—
94#2690C2214yes—
95#2690C2212yes—
96#2690C2212yes—
97#2687C2214yes—
98#2686C2214yes—
99#2686C2214yes—
100#2683C2211yescharacteristic
101#2683C2212yes—
102#2680C2212yes—
103#2674C2214yes—
104#2674C2214yes—
105#2674C2214yes—
106#2665C2214yes—
107#2660C2211yescharacteristic
108#2660C2212yes—
109#2653C2214yes—
110#2650C2214yes—
111#2644C2212yes—
112#2642C2212yes—
113#2641C2211yescharacteristic
114#2638C2214yes—
115#2633C2212yes—
116#2632C2212yes—
117#2630C2214yes—
118#2628C2214yes—
119#2627C2214yes—
120#2609C2212yes—
121#2604C2214yes—
122#2596C2214yes—
123#2587C2214yes—
124#2587C2214yes—
125#2586C2212yes—
126#2584C2212yes—
127#2584C2211yescharacteristic
128#2584C2211yescharacteristic
129#2584C2212yes—
130#2582C2212yes—
131#2570C2212yes—
132#2567C2211yescharacteristic
133#2566C2212yes—
134#2565C2212yes—
135#2563C2212yes—
136#2556C2214yes—
137#2551C2212yes—
138#2551C2214yes—
139#2550C2212yes—
140#2550C2214yes—
141#2550C2212yes—
142#2550C2212yes—
143#2550C2212yes—
144#2549C2214yes—
145#2548C2211yescharacteristic
146#2547C2212yes—
147#2547C2211yescharacteristic
148#2547C2214yes—
149#2546C2211yescharacteristic
150#2546C2212yes—
151#2538C2212yes—
152#2536C2212yes—
153#2536C2214yes—
154#2529C2214yes—
155#2527C2214yes—
156#2526C2214yes—
157#2520C2214yes—
158#2517C2214yes—
159#2515C2214yes—
160#2513C2212yes—
161#2512C2212yes—
162#2509C2212yes—
163#2509C2212yes—
164#2508C2212yes—
165#2507C2212yes—
166#2507C2212yes—
167#2504C2212yes—
168#2499C2214yes—
169#2496C2212yes—
170#2491C2212yes—
171#2491C2212yes—
172#2491C2212yes—
173#2488C2214yes—
174#2478C2214yes—
175#2478C2214yes—
176#2476C2214yes—
177#2475C2214yes—
178#2474C2214yes—
179#2470C2214yes—
180#2470C2214yes—
181#2465C2214yes—
182#2461C2214yes—
183#2459C2214yes—
184#2455C2214yes—
185#2454C2212yes—
186#2452C2212yes—
187#2452C2212yes—
188#2452C2212yes—
189#2451C2212yes—
190#2451C2214yes—
191#2450C2214yes—
192#2449C2214yes—
193#2449C2214yes—
194#2448C2212yes—
195#2448C2212yes—
196#2448C2212yes—
197#2447C2214yes—
198#2445C2212yes—
199#2442C2212yes—
200#2442C2212yes—
201#2442C2212yes—
202#2440C2212yes—
203#2439C2214yes—
204#2438C2214yes—
205#2438C2214yes—
206#2438C2214yes—
207#2428C2212yes—
208#2427C2214yes—
209#2426C2212yes—
210#2425C2214yes—
211#2425C2214yes—
212#2422C2212yes—
213#2422C2214yes—
214#2421C2212yes—
215#2421C2212yes—
216#2421C2212yes—
217#2417C2214yes—
218#2416C2212yes—
219#2415C2214yes—
220#2401C2212yes—
221#2401C2212yes—
222#2399C2211yescharacteristic
223#2399C2212yes—
224#2399C2211yescharacteristic
225#2395C2214yes—
226#2369C2212yes—
227#2367C2212yes—
228#2365C2212yes—
229#2362C2214yes—
230#2361C2212yes—
231#2361C2212yes—
232#2361C2214yes—
233#2360C2212yes—
234#2359C2214yes—
235#2357C2212yes—
236#2355C2212yes—
237#2351C2212yes—
238Q8×C4⋊C4C2212yes—
239#2349C2212yes—
240#2349C2214yes—
241#2344C2212yes—
242#2344C2212yes—
243#2331C2212yes—
244#2329C2214yes—
245#2326C2212yes—
246#2323C2214yes—
247#2320C2211yescharacteristic
248#2316C2214yes—
249C4×#125C2212yes—
250C4×#124C2211yescharacteristic
251C4×C22⋊Q8C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×#123C2212yes—
254C4×#121C2212yes—
255#2295C2211yescharacteristic
256#2293C2212yes—
257C2×#389C2212yes—
258#2276C2211yescharacteristic
259#559—44no—
260Q82—44no—
261#557—44no—
262#555—48no—
263#554—44no—
264#542—416no—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2312yes—
275C2×#127C2311yescharacteristic
276#529—48no—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2311yescharacteristic
285C2×#125C2312yes—
286C2×#125C2311yescharacteristic
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2311yescharacteristic
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2314yes—
293C2×#124C2314yes—
294C2×#124C2314yes—
295C2×#123C2312yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2312yes—
310C2×#121C2312yes—
311C2×#121C2314yes—
312C2×#121C2312yes—
313C2×#121C2314yes—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2314yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2311yescharacteristic
335C2×#117C2314yes—
336C2×#117C2314yes—
337C2×#117C2314yes—
338C2×#117C2314yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2314yes—
341C22×C4⋊C4C2312yes—
342C22×C42C2312yes—
343#401C2312yes—
344#401C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2312yes—
348#400C2314yes—
349#400C2312yes—
350#400C2314yes—
351#400C2312yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2312yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2312yes—
362#400C2312yes—
363#400C2314yes—
364#399C2314yes—
365#399C2314yes—
366#399C2314yes—
367#399C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2311yescharacteristic
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2314yes—
375#398C2311yescharacteristic
376#398C2314yes—
377#398C2312yes—
378#398C2311yescharacteristic
379#398C2312yes—
380#398C2314yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#398C2314yes—
385#398C2311yescharacteristic
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2312yes—
393#398C2312yes—
394#398C2314yes—
395#398C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2312yes—
410#397C2314yes—
411#397C2312yes—
412#397C2312yes—
413#397C2312yes—
414#397C2312yes—
415#397C2312yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2312yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2312yes—
432#396C2314yes—
433#395C2311yescharacteristic
434#395C2312yes—
435#395C2312yes—
436#395C2312yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#395C2311yescharacteristic
441#395C2312yes—
442#395C2314yes—
443#395C2314yes—
444#395C2314yes—
445#395C2311yescharacteristic
446#395C2314yes—
447#395C2311yescharacteristic
448#395C2312yes—
449#395C2314yes—
450#395C2312yes—
451#395C2314yes—
452#395C2314yes—
453#394C2312yes—
454#394C2312yes—
455#394C2312yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2312yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#393C2314yes—
468#393C2314yes—
469#393C2314yes—
470#393C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2314yes—
474#393C2314yes—
475#392C2314yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2314yes—
480#391C2312yes—
481#391C2314yes—
482#391C2312yes—
483#391C2312yes—
484#391C2314yes—
485#391C2314yes—
486#391C2314yes—
487#391C2314yes—
488#391C2312yes—
489#391C2314yes—
490#391C2312yes—
491#391C2314yes—
492#391C2314yes—
493#391C2314yes—
494#391C2311yescharacteristic
495#391C2314yes—
496#391C2314yes—
497#391C2312yes—
498#390C2312yes—
499#390C2312yes—
500#390C2312yes—
501#390C2312yes—
502#390C2311yescharacteristic
503#390C2312yes—
504#390C2312yes—
505#390C2314yes—
506#390C2312yes—
507#390C2312yes—
508#390C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2314yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2314yes—
534#389C2312yes—
535#389C2314yes—
536#389C2312yes—
537#389C2312yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2312yes—
542#389C2312yes—
543#389C2314yes—
544#389C2314yes—
545#389C2312yes—
546#389C2314yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2312yes—
574#388C2312yes—
575#388C2312yes—
576#388C2312yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#387C2312yes—
581#387C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2312yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2312yes—
611#387C2312yes—
612#387C2312yes—
613#387C2312yes—
614#387C2312yes—
615#386C2314yes—
616#386C2314yes—
617#386C2312yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2312yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2312yes—
643#385C2312yes—
644#385C2312yes—
645#385C2312yes—
646#384C2312yes—
647#384C2312yes—
648#384C2312yes—
649#384C2314yes—
650#383C2312yes—
651#382C2312yes—
652#382C2312yes—
653#382C2312yes—
654#382C2312yes—
655#382C2311yescharacteristic
656#382C2312yes—
657#382C2314yes—
658#382C2312yes—
659#382C2314yes—
660#382C2314yes—
661#381C2314yes—
662#381C2314yes—
663#381C2314yes—
664#381C2312yes—
665#380C2314yes—
666#380C2314yes—
667#380C2312yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2312yes—
672#380C2312yes—
673#380C2314yes—
674#380C2314yes—
675#380C2314yes—
676#380C2312yes—
677#380C2312yes—
678#380C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712#376C2311yescharacteristic
713#376C2312yes—
714#376C2311yescharacteristic
715#376C2312yes—
716C2×#95C2314yes—
717C2×#95C2314yes—
718C43C2311yescharacteristic
719C22×Q8C2411yescharacteristic
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×Q8C2414yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2411yescharacteristic
725C22×Q8C2412yes—
726C22×Q8C2414yes—
727C22×Q8C2412yes—
728C22×D4C2412yes—
729C22×D4C2414yes—
730C22×D4C2414yes—
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2411yescharacteristic
734C23×C4C2412yes—
735C23×C4C2414yes—
736C23×C4C2412yes—
737C23×C4C2414yes—
738C23×C4C2414yes—
739C23×C4C2412yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C4⋊Q8—28no—
743C4⋊Q8—42no—
744C4⋊Q8—44no—
745C4⋊Q8—42no—
746C4⋊Q8—44no—
747C4⋊Q8—48no—
748C4⋊Q8—42no—
749C4⋊Q8—44no—
750C4⋊Q8—48no—
751C4⋊Q8—44no—
752#127—42no—
753#126—48no—
754#126—48no—
755#126—48no—
756#125—44no—
757#125—44no—
758#125—44no—
759#125—42no—
760#125—42no—
761#125—44no—
762#125—44no—
763#124—28no—
764#124—28no—
765#124—24no—
766#124—44no—
767#124—48no—
768#124—48no—
769#124—48no—
770#124—44no—
771#123—28no—
772#123—48no—
773#123—48no—
774#123—48no—
775#123—48no—
776C22⋊Q8—28no—
777C22⋊Q8—48no—
778C22⋊Q8—48no—
779C22⋊Q8—48no—
780C22⋊Q8—48no—
781C22⋊Q8—44no—
782C22⋊Q8—48no—
783C22⋊Q8—48no—
784C22⋊Q8—48no—
785C22⋊Q8—44no—
786#121—216no—
787#121—28no—
788#121—48no—
789#121—44no—
790C4×Q8—28no—
791C4×Q8—24no—
792C4×Q8—24no—
793C4×Q8—24no—
794C4×Q8—28no—
795C4×Q8—44no—
796C4×Q8—42no—
797C4×Q8—42no—
798C4×Q8—44no—
799C4×Q8—42no—
800C4×Q8—48no—
801C4×D4—28no—
802C4×D4—48no—
803C4×D4—44no—
804C4×D4—44no—
805C4×D4—44no—
806C4×D4—44no—
807C4×D4—42no—
808C4×D4—48no—
809C4×D4—48no—
810C4×D4—48no—
811#117—48no—
812#117—48no—
813#117—48no—
814#117—48no—
815C2×C4⋊C4—28no—
816C2×C4⋊C4—48no—
817C2×C4⋊C4—44no—
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C42—44no—
928C2×C42C2411yescharacteristic
929C2×C42C2414yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2411yescharacteristic
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2414yes—
942C2×C42C2412yes—
943C2×C42C2414yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2412yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2411yescharacteristic
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2411yescharacteristic
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2411yescharacteristic
966#95C2411yescharacteristic
967#95C2414yes—
968#95C2411yescharacteristic
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2414yes—
978#95C2412yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025C24C2514yes—
1026C24C2512yes—
1027C2×Q8—24no—
1028C2×Q8—22no—
1029C2×Q8—24no—
1030C2×Q8—28no—
1031C2×Q8—24no—
1032C2×Q8—41no—
1033C2×Q8—44no—
1034C2×Q8—41no—
1035C2×Q8—42no—
1036C2×Q8—41no—
1037C2×Q8—44no—
1038C2×Q8—42no—
1039C2×Q8—42no—
1040C2×Q8—41no—
1041C2×Q8—42no—
1042C2×Q8—44no—
1043C2×Q8—44no—
1044C2×Q8—42no—
1045C2×Q8—44no—
1046C2×Q8—42no—
1047C2×Q8—44no—
1048C2×Q8—42no—
1049C2×Q8H(5,𝔽2)14yes—
1050C2×D4—28no—
1051C2×D4—28no—
1052C2×D4—24no—
1053C2×D4—24no—
1054C2×D4—28no—
1055C2×D4—24no—
1056C2×D4—41no—
1057C2×D4—44no—
1058C2×D4—41no—
1059C2×D4—44no—
1060C2×D4—42no—
1061C2×D4—44no—
1062C2×D4—44no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4H(5,𝔽2)14yes—
1067C22×C4—28no—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—28no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—28no—
1074C22×C4—24no—
1075C22×C4—28no—
1076C22×C4—44no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—42no—
1083C22×C4—44no—
1084C22×C4—42no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2514yes—
1100C22×C4C2514yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2511yescharacteristic
1104C22×C4C2511yescharacteristic
1105C22×C4C2512yes—
1106C22×C4C2514yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2512yes—
1114C22×C4C2511yescharacteristic
1115C22×C4C2514yes—
1116C22×C4C2512yes—
1117C22×C4C2511yescharacteristic
1118C4⋊C4—22no—
1119C4⋊C4—24no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—22no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—24no—
1128C4⋊C4—22no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—28no—
1132C4⋊C4—24no—
1133C4⋊C4—28no—
1134C4⋊C4—28no—
1135C4⋊C4—24no—
1136C4⋊C4—28no—
1137C4⋊C4—28no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—41no—
1156C4⋊C4—44no—
1157C4⋊C4—41no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—41no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—41no—
1164C4⋊C4—42no—
1165C4⋊C4—41no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—41no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C42−1+418yes—
1189C22⋊C4—24no—
1190C22⋊C4—24no—
1191C22⋊C4—28no—
1192C22⋊C4—28no—
1193C22⋊C4—24no—
1194C22⋊C4—28no—
1195C22⋊C4—24no—
1196C22⋊C4—24no—
1197C22⋊C4—28no—
1198C22⋊C4—28no—
1199C22⋊C4—28no—
1200C22⋊C4—28no—
1201C22⋊C4—28no—
1202C22⋊C4—28no—
1203C22⋊C4—24no—
1204C22⋊C4—28no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—42no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—44no—
1219C22⋊C4—42no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C42—24no—
1228C42—24no—
1229C42—22no—
1230C42—28no—
1231C42—24no—
1232C42—24no—
1233C42—22no—
1234C42—22no—
1235C42—24no—
1236C42—22no—
1237C42—24no—
1238C42—24no—
1239C42—28no—
1240C42—24no—
1241C42—24no—
1242C42—42no—
1243C42—42no—
1244C42—41no—
1245C42—44no—
1246C42—42no—
1247C42—44no—
1248C42—44no—
1249C42—44no—
1250C42—42no—
1251C42—44no—
1252C42—42no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23—22no—
1258C23—22no—
1259C23—24no—
1260C23—24no—
1261C23—24no—
1262C23—24no—
1263C23—24no—
1264C23—24no—
1265C23—24no—
1266C23C2×H(5,𝔽2)14yes—
1267C23C2611yescharacteristic
1268Q8—28no—
1269Q8—44no—
1270Q8—88no—
1271Q8—84no—
1272Q8—82no—
1273Q8—82no—
1274Q8—162no—
1275Q8—164no—
1276Q8—162no—
1277D4—44no—
1278D4—416no—
1279D4—48no—
1280D4—88no—
1281D4—84no—
1282D4—162no—
1283C2×C4—22no—
1284C2×C4—21no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—21no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—22no—
1304C2×C4—21no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—21no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—416no—
1353C2×C4—48no—
1354C2×C4—88no—
1355C2×C4—88no—
1356C2×C4—84no—
1357C2×C4—84no—
1358C2×C4—164no—
1359C2×C4—164no—
1360C2×C4C2×H(5,𝔽2)14yes—
1361C2×C4C2×H(5,𝔽2)12yes—
1362C2×C4C2×H(5,𝔽2)12yes—
1363C2×C4C2×2−1+418yes—
1364C2×C4C2×2−1+414yes—
1365C2×C4#58514yes—
1366C22—24no—
1367C22—24no—
1368C22—24no—
1369C22—42no—
1370C22—42no—
1371C22—42no—
1372C22—42no—
1373C22—44no—
1374C22—44no—
1375C22—44no—
1376C22—44no—
1377C22—44no—
1378C22—44no—
1379C22—44no—
1380C22C22×H(5,𝔽2)11yescharacteristic
1381C22C22×H(5,𝔽2)11yescharacteristic
1382C22C22×2−1+412yes—
1383C22C2×#58512yes—
1384C222−1+611yescharacteristic
1385C4—24no—
1386C4—28no—
1387C4—24no—
1388C4—22no—
1389C4—42no—
1390C4—42no—
1391C4—44no—
1392C4—42no—
1393C4—44no—
1394C4—42no—
1395C4—44no—
1396C4—42no—
1397C4—42no—
1398C4—41no—
1399C4—41no—
1400C4—41no—
1401C4—42no—
1402C4—42no—
1403C4—42no—
1404C4—44no—
1405C4—41no—
1406C4—41no—
1407C4—42no—
1408C4—42no—
1409C4—42no—
1410C4—42no—
1411C4#354414yes—
1412C2—44no—
1413C2—84no—
1414C2C2×#354411yescharacteristic
1415C2#6289511yescharacteristic
1416C2#6295312yes—
1417C2#6301312yes—
1418C2#6302011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#59841C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59749C2semidirect
3. #59455C2semidirect
4. #59076C2semidirect
5. #59072C2semidirect
6. #58946C2semidirect
7. #56968C2semidirect
8. #56713C2semidirect
9. #55315C2semidirect
10. #53099C2semidirect
11. #53003C2semidirect
12. #52304C2semidirect
13. #47788C2semidirect
14. #46674C2semidirect
15. #45364C2semidirect
16. #45055C2semidirect
17. #44890C2semidirect
18. #44862C2semidirect
19. #42886C2semidirect
20. #42611C2semidirect
21. #42361C2semidirect
22. #41093C2semidirect
23. #39977C2semidirect
24. #39496C2semidirect
25. #39403C2semidirect
26. #39173C2semidirect
27. #39125C2semidirect
28. #35937C2semidirect
29. #35880C2semidirect

Maximal subgroups

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

subgroupindex
#598412
#597492
#594552
#590762
#590722
#589462
#569682
#567132
#553152
#530992
#530032
#523042
#477882
#466742
#453642
#450552
#448902
#448622
#428862
#426112
#423612
#410932
#399772
#394962
#394032
#391732
#391252
#359372
#358802