Finite Group Databasebeta

← #7895735

Subgroups — #7895735

Order 512.

4949 conjugacy classes of subgroups.

The subgroup lattice has 1465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59831C212yesmaximal, complemented
2#59817C211yesmaximal, characteristic, complemented
3#52162C211yesmaximal, characteristic, complemented
4#52035C214yesmaximal, complemented
5#51786C214yesmaximal, complemented
6#48852C214yesmaximal, complemented
7#46436C214yesmaximal, complemented
8#46282C212yesmaximal, complemented
9#45362C212yesmaximal, complemented
10#44946C212yesmaximal, complemented
11#44942C212yesmaximal, complemented
12#43100C214yesmaximal, complemented
13#42930C212yesmaximal, complemented
14#42820C212yesmaximal, complemented
15#40616C214yesmaximal, complemented
16#39981C212yesmaximal, complemented
17#39628C211yesmaximal, characteristic, complemented
18#39611C212yesmaximal, complemented
19#39596C212yesmaximal, complemented
20#39493C211yesmaximal, characteristic, complemented
21#38453C212yesmaximal, complemented
22#38098C212yesmaximal, complemented
23#37137C212yesmaximal, complemented
24#36286C211yesmaximal, characteristic, complemented
25#35739C212yesmaximal, complemented
26#35519C212yesmaximal, complemented
27#35208C211yesmaximal, characteristic, complemented
28#34477C212yesmaximal
29#34313C211yesmaximal, characteristic
30C2×#554C2214yes—
31C2×#550C2211yescharacteristic
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2212yes—
34C2×#533C2212yes—
35C2×#520C2212yes—
36#2863C2212yes—
37#2863C2212yes—
38#2862C2211yescharacteristic
39#2859C2212yes—
40#2857C2212yes—
41#2843C2214yes—
42#2841C2214yes—
43#2807C2214yes—
44#2806C2212yes—
45#2805C2212yes—
46#2804C2212yes—
47#2804C2212yes—
48#2804C2214yes—
49#2804C2214yes—
50#2804C2212yes—
51#2792C2214yes—
52#2791C2214yes—
53#2790C2214yes—
54#2784C2214yes—
55#2784C2214yes—
56#2784C2214yes—
57#2780C2214yes—
58#2780C2214yes—
59#2780C2214yes—
60#2780C2214yes—
61#2780C2214yes—
62#2774C2214yes—
63#2763C2214yes—
64#2755C2214yes—
65#2748C2214yes—
66#2734C2211yescharacteristic
67#2734C2214yes—
68#2732C2212yes—
69#2732C2212yes—
70#2732C2212yes—
71#2732C2214yes—
72#2732C2211yescharacteristic
73#2729C2212yes—
74#2729C2214yes—
75#2729C2214yes—
76#2726C2211yescharacteristic
77#2720C2214yes—
78#2720C2214yes—
79#2720C2214yes—
80#2720C2212yes—
81#2713C2214yes—
82#2713C2212yes—
83#2704C2214yes—
84#2704C2214yes—
85#2704C2212yes—
86#2692C2214yes—
87#2692C2212yes—
88#2692C2214yes—
89#2692C2214yes—
90#2692C2214yes—
91#2692C2214yes—
92#2683C2212yes—
93#2683C2214yes—
94#2683C2212yes—
95#2683C2211yescharacteristic
96#2677C2212yes—
97#2666C2214yes—
98#2666C2214yes—
99#2665C2214yes—
100#2665C2214yes—
101#2660C2214yes—
102#2647C2212yes—
103#2646C2214yes—
104#2628C2212yes—
105#2628C2212yes—
106#2627C2214yes—
107#2608C2214yes—
108#2605C2214yes—
109#2605C2214yes—
110#2589C2214yes—
111#2588C2214yes—
112#2587C2214yes—
113#2582C2212yes—
114#2582C2211yescharacteristic
115#2581C2212yes—
116#2581C2212yes—
117#2580C2212yes—
118#2580C2212yes—
119#2580C2212yes—
120#2579C2214yes—
121#2579C2214yes—
122#2579C2214yes—
123#2574C2214yes—
124#2570C2212yes—
125#2570C2212yes—
126#2568C2211yescharacteristic
127#2567C2211yescharacteristic
128#2567C2212yes—
129#2567C2211yescharacteristic
130#2567C2211yescharacteristic
131#2566C2212yes—
132#2566C2212yes—
133#2566C2214yes—
134#2566C2214yes—
135#2564C2214yes—
136#2564C2214yes—
137#2552C2211yescharacteristic
138#2551C2212yes—
139#2549C2214yes—
140#2549C2214yes—
141#2546C2212yes—
142#2542C2214yes—
143#2538C2212yes—
144#2538C2212yes—
145#2538C2212yes—
146#2538C2212yes—
147#2511C2212yes—
148#2511C2212yes—
149#2508C2212yes—
150#2507C2212yes—
151#2506C2212yes—
152#2506C2212yes—
153#2505C2214yes—
154#2505C2214yes—
155#2502C2214yes—
156#2492C2214yes—
157#2473C2214yes—
158#2465C2214yes—
159#2465C2214yes—
160#2462C2214yes—
161#2453C2212yes—
162#2452C2212yes—
163#2452C2212yes—
164#2452C2214yes—
165#2452C2212yes—
166#2452C2212yes—
167#2451C2212yes—
168#2451C2212yes—
169#2451C2212yes—
170#2450C2214yes—
171#2450C2214yes—
172#2450C2214yes—
173#2450C2214yes—
174#2450C2214yes—
175#2450C2214yes—
176#2450C2214yes—
177#2449C2214yes—
178#2449C2214yes—
179#2449C2214yes—
180#2449C2214yes—
181#2449C2214yes—
182#2449C2214yes—
183#2449C2214yes—
184#2449C2214yes—
185#2442C2212yes—
186#2442C2214yes—
187#2441C2214yes—
188#2441C2212yes—
189#2440C2212yes—
190#2440C2214yes—
191#2440C2214yes—
192#2440C2212yes—
193#2440C2212yes—
194#2439C2212yes—
195#2439C2214yes—
196#2438C2214yes—
197#2438C2214yes—
198#2434C2214yes—
199#2409C2214yes—
200#2409C2214yes—
201#2409C2214yes—
202#2399C2212yes—
203#2396C2212yes—
204#2396C2212yes—
205C2×#395C2214yes—
206#2380C2214yes—
207#2377C2214yes—
208#2369C2211yescharacteristic
209#2366C2211yescharacteristic
210#2366C2212yes—
211#2366C2212yes—
212#2365C2211yescharacteristic
213#2364C2214yes—
214#2363C2212yes—
215#2361C2214yes—
216#2361C2212yes—
217#2361C2212yes—
218#2356C2212yes—
219#2355C2212yes—
220#2353C2214yes—
221#2352C2212yes—
222Q8×C4⋊C4C2211yescharacteristic
223#2349C2212yes—
224D4×C4⋊C4C2212yes—
225D4×C4⋊C4C2211yescharacteristic
226D4×C4⋊C4C2212yes—
227D4×C4⋊C4C2212yes—
228#2341C2212yes—
229#2339C2212yes—
230#2339C2212yes—
231#2333C2214yes—
232#2330C2212yes—
233#2329C2214yes—
234#2328C2212yes—
235#2328C2214yes—
236#2325C2214yes—
237#2324C2214yes—
238#2324C2212yes—
239#2324C2212yes—
240#2320C2212yes—
241#2318C2214yes—
242#2317C2212yes—
243#2317C2212yes—
244#2311C2212yes—
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2211yescharacteristic
247C4×#127C2211yescharacteristic
248C4×#127C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×#121C2212yes—
251#2297C2212yes—
252#2295C2212yes—
253#2295C2211yescharacteristic
254#2293C2212yes—
255#2293C2211yescharacteristic
256C2×#389C2212yes—
257#2290C2212yes—
258C42×Q8C2211yescharacteristic
259C22×#41C2312yes—
260C23×Q8C2314yes—
261#554—416no—
262#550Q8116yescomplemented
263D4×Q8—48no—
264D4×Q8—48no—
265#533—48no—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2314yes—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2314yes—
276C2×#127C2311yescharacteristic
277C2×#127C2312yes—
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304#520—48no—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×D4C2312yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2311yescharacteristic
333C2×#117C2312yes—
334C2×#117C2312yes—
335C2×#117C2312yes—
336C2×#117C2314yes—
337C22×C4⋊C4C2312yes—
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2314yes—
340C22×C4⋊C4C2314yes—
341C22×C4⋊C4C2314yes—
342C22×C4⋊C4C2314yes—
343C22×C42C2312yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#400C2314yes—
355#400C2312yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#399C2312yes—
361#399C2314yes—
362#399C2314yes—
363#399C2314yes—
364#399C2314yes—
365#399C2314yes—
366#399C2314yes—
367#399C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2312yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2314yes—
380#398C2314yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2312yes—
391#398C2312yes—
392#398C2312yes—
393#398C2312yes—
394#398C2314yes—
395#398C2314yes—
396#396C2314yes—
397#396C2312yes—
398#396C2312yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2312yes—
414#396C2312yes—
415#396C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2312yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2314yes—
427#395C2312yes—
428#395C2314yes—
429#395C2314yes—
430#395C2312yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2312yes—
435#395C2312yes—
436#395C2312yes—
437#395C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2314yes—
444#393C2314yes—
445#393C2312yes—
446#393C2312yes—
447#393C2314yes—
448#393C2314yes—
449#393C2314yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2314yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2314yes—
461#391C2312yes—
462#391C2314yes—
463#391C2314yes—
464#391C2312yes—
465#391C2314yes—
466#391C2314yes—
467#391C2312yes—
468#391C2314yes—
469#391C2314yes—
470#391C2312yes—
471#391C2312yes—
472#391C2311yescharacteristic
473#391C2312yes—
474#391C2314yes—
475#391C2312yes—
476#391C2311yescharacteristic
477#390C2312yes—
478#390C2311yescharacteristic
479#390C2314yes—
480#390C2312yes—
481#390C2314yes—
482#390C2312yes—
483#390C2312yes—
484#390C2314yes—
485#390C2312yes—
486#390C2314yes—
487#390C2312yes—
488#390C2312yes—
489#390C2312yes—
490#390C2314yes—
491#390C2314yes—
492#390C2311yescharacteristic
493#390C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2311yescharacteristic
497#389C2311yescharacteristic
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2312yes—
525#389C2314yes—
526#389C2311yescharacteristic
527#389C2314yes—
528#389C2311yescharacteristic
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2314yes—
535#389C2314yes—
536#389C2311yescharacteristic
537#389C2314yes—
538#389C2311yescharacteristic
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2312yes—
545#388C2314yes—
546#388C2314yes—
547#388C2312yes—
548#388C2312yes—
549#388C2312yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2312yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2312yes—
579#387C2312yes—
580#387C2312yes—
581#387C2312yes—
582#386C2312yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2312yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2312yes—
637#385C2314yes—
638#385C2312yes—
639#385C2314yes—
640#385C2314yes—
641#385C2312yes—
642#385C2312yes—
643#384C2312yes—
644#384C2311yescharacteristic
645#384C2311yescharacteristic
646#384C2311yescharacteristic
647#384C2312yes—
648#384C2312yes—
649#384C2314yes—
650#384C2312yes—
651#384C2312yes—
652#384C2312yes—
653#384C2314yes—
654#383C2314yes—
655#383C2314yes—
656#382C2314yes—
657#382C2312yes—
658#382C2312yes—
659#382C2312yes—
660#382C2314yes—
661#382C2312yes—
662#382C2314yes—
663#381C2314yes—
664#381C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2312yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2312yes—
676#380C2312yes—
677#380C2312yes—
678#380C2314yes—
679#380C2314yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710#376C2312yes—
711#376C2314yes—
712C2×#95C2314yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C2×#95C2314yes—
716C43C2311yescharacteristic
717C43C2312yes—
718C2×#41—44no—
719C2×#41—44no—
720C2×#41C2×Q8116yescomplemented
721C22×Q8—48no—
722C22×Q8—48no—
723C22×Q8—84no—
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×Q8C2411yescharacteristic
729C22×Q8C2412yes—
730C22×Q8C2414yes—
731C22×Q8C2412yes—
732C22×Q8C2414yes—
733C22×Q8C2412yes—
734C22×D4C2412yes—
735C22×D4C2412yes—
736C22×D4C2414yes—
737C22×D4C2412yes—
738C22×D4C2411yescharacteristic
739C22×D4C2414yes—
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2414yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C23×C4C2414yes—
746C23×C4C2414yes—
747C23×C4C2414yes—
748C23×C4C2414yes—
749C23×C4C2414yes—
750C23×C4C2412yes—
751C23×C4C2414yes—
752C4⋊Q8—24no—
753C4⋊Q8—24no—
754C4⋊Q8—42no—
755C4⋊Q8—42no—
756C4⋊Q8—44no—
757C4⋊Q8—44no—
758C4⋊Q8—48no—
759C4⋊Q8—44no—
760C4⋊Q8—44no—
761C4⋊Q8—48no—
762#127C2×Q818yes—
763#127C2×Q8116yescomplemented
764#125—44no—
765#125—48no—
766#125—48no—
767#125—44no—
768#125—44no—
769C22⋊Q8—216no—
770C22⋊Q8—28no—
771C22⋊Q8—44no—
772C22⋊Q8—44no—
773C22⋊Q8—48no—
774C22⋊Q8—48no—
775C22⋊Q8—48no—
776C22⋊Q8—44no—
777C22⋊Q8—44no—
778C22⋊Q8—48no—
779C22⋊Q8—48no—
780C22⋊Q8—48no—
781C22⋊Q8—48no—
782C22⋊Q8—48no—
783C22⋊Q8—48no—
784C22⋊Q8—84no—
785C22⋊Q8—84no—
786C22⋊Q8—84no—
787C22⋊Q8—84no—
788#121C2×Q8116yescomplemented
789#121C2×Q8132yescomplemented
790C4×Q8—28no—
791C4×Q8—24no—
792C4×Q8—24no—
793C4×Q8—28no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×Q8—44no—
797C4×Q8—42no—
798C4×Q8—44no—
799C4×Q8C2×Q818yescomplemented
800C4×D4—28no—
801C4×D4—48no—
802C4×D4—44no—
803C4×D4—48no—
804C4×D4—48no—
805C4×D4—44no—
806C4×D4—44no—
807C4×D4—44no—
808C4×D4—44no—
809C4×D4—44no—
810C4×D4—48no—
811C4×D4—48no—
812C4×D4—48no—
813C4×D4—82no—
814C4×D4—82no—
815C4×D4—82no—
816C4×D4C2×Q818yescomplemented
817C4×D4C2×Q8116yescomplemented
818#117—28no—
819#117—44no—
820#117—48no—
821#117—44no—
822C2×C4⋊C4—44no—
823C2×C4⋊C4—48no—
824C2×C4⋊C4—44no—
825C2×C4⋊C4—48no—
826C2×C4⋊C4—48no—
827C2×C4⋊C4—84no—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2411yescharacteristic
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2411yescharacteristic
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2411yescharacteristic
904C2×C4⋊C4C2411yescharacteristic
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2411yescharacteristic
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2412yes—
941C2×C42—44no—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2411yescharacteristic
947C2×C42C2412yes—
948C2×C42C2414yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2411yescharacteristic
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2412yes—
955C2×C42C2411yescharacteristic
956C2×C42C2414yes—
957C2×C42C2412yes—
958C2×C42C2412yes—
959C2×C42C2412yes—
960C2×C42C2411yescharacteristic
961C2×C42C2412yes—
962C2×C42C2411yescharacteristic
963C2×C42C2414yes—
964C2×C42C2411yescharacteristic
965C2×C42C2412yes—
966C2×C42C2411yescharacteristic
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030C24C2512yes—
1031C24C2514yes—
1032#41—432no—
1033C2×Q8—22no—
1034C2×Q8—24no—
1035C2×Q8—24no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—22no—
1039C2×Q8—24no—
1040C2×Q8—28no—
1041C2×Q8—22no—
1042C2×Q8—42no—
1043C2×Q8—42no—
1044C2×Q8—42no—
1045C2×Q8—42no—
1046C2×Q8—42no—
1047C2×Q8—44no—
1048C2×Q8—44no—
1049C2×Q8—44no—
1050C2×Q8—42no—
1051C2×Q8—44no—
1052C2×Q8—44no—
1053C2×Q8—42no—
1054C2×Q8—41no—
1055C2×Q8—41no—
1056C2×Q8—42no—
1057C2×Q8—42no—
1058C2×Q8—42no—
1059C2×Q8—42no—
1060C2×Q8—42no—
1061C2×Q8—42no—
1062C2×Q8—832no—
1063C2×Q8C22×Q814yes—
1064C2×D4—24no—
1065C2×D4—24no—
1066C2×D4—44no—
1067C2×D4—42no—
1068C2×D4—44no—
1069C2×D4—41no—
1070C2×D4—42no—
1071C2×D4—44no—
1072C2×D4—42no—
1073C2×D4—42no—
1074C2×D4—41no—
1075C2×D4—44no—
1076C2×D4C22×Q818yes—
1077C2×D4C22×Q818yes—
1078C2×D4C22×Q814yes—
1079C2×D4C22×Q818yes—
1080C2×D4C22×Q8116yes—
1081C2×D4C22×Q8116yes—
1082C22×C4—24no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—28no—
1086C22×C4—28no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—42no—
1090C22×C4—42no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—42no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—42no—
1107C22×C4—44no—
1108C22×C4—42no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4C22×Q818yes—
1117C22×C4C22×Q8116yes—
1118C22×C4C2512yes—
1119C22×C4C2511yescharacteristic
1120C22×C4C2514yes—
1121C22×C4C2512yes—
1122C22×C4C2514yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2514yes—
1129C22×C4C2512yes—
1130C22×C4C2514yes—
1131C22×C4C2512yes—
1132C22×C4C2514yes—
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2511yescharacteristic
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2511yescharacteristic
1139C22×C4C2512yes—
1140C22×C4C2511yescharacteristic
1141C22×C4C2512yes—
1142C22×C4C2511yescharacteristic
1143C22×C4C2511yescharacteristic
1144C22×C4C2511yescharacteristic
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—22no—
1148C4⋊C4—28no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—28no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—22no—
1159C4⋊C4—24no—
1160C4⋊C4—28no—
1161C4⋊C4—24no—
1162C4⋊C4—22no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—22no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—41no—
1180C4⋊C4—42no—
1181C4⋊C4—41no—
1182C4⋊C4—42no—
1183C4⋊C4—41no—
1184C4⋊C4—41no—
1185C4⋊C4—41no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4—44no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—42no—
1196C4⋊C4—41no—
1197C4⋊C4—42no—
1198C4⋊C4—42no—
1199C4⋊C4—42no—
1200C4⋊C4—42no—
1201C4⋊C4—42no—
1202C4⋊C4—42no—
1203C4⋊C4—42no—
1204C4⋊C4—42no—
1205C4⋊C4—42no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—42no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—42no—
1219C4⋊C4—42no—
1220C4⋊C4C22×Q814yes—
1221C4⋊C4C22×Q818yes—
1222C4⋊C4C22×Q814yes—
1223C4⋊C4H(5,𝔽2)14yes—
1224C22⋊C4—24no—
1225C22⋊C4—24no—
1226C22⋊C4—28no—
1227C22⋊C4—28no—
1228C22⋊C4—24no—
1229C22⋊C4—24no—
1230C22⋊C4—28no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—42no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—42no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—42no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—42no—
1256C22⋊C4C22×Q818yes—
1257C22⋊C4C22×Q8116yes—
1258C42—24no—
1259C42—24no—
1260C42—24no—
1261C42—24no—
1262C42—24no—
1263C42—24no—
1264C42—28no—
1265C42—22no—
1266C42—24no—
1267C42—22no—
1268C42—42no—
1269C42—42no—
1270C42—42no—
1271C42—41no—
1272C42—44no—
1273C42—41no—
1274C42—44no—
1275C42—44no—
1276C42—44no—
1277C42—41no—
1278C42—42no—
1279C42—42no—
1280C42C22×Q814yes—
1281C42C22×Q818yes—
1282C42H(5,𝔽2)14yes—
1283C23—24no—
1284C23—22no—
1285C23—22no—
1286C23—24no—
1287C23—22no—
1288C23—24no—
1289C23—22no—
1290C23—24no—
1291C23—24no—
1292C23—24no—
1293C23—22no—
1294C23—22no—
1295C23C23×Q814yes—
1296C23C23×Q818yes—
1297C23C2611yescharacteristic
1298Q8—28no—
1299Q8—48no—
1300Q8—48no—
1301Q8—82no—
1302Q8—84no—
1303Q8—84no—
1304Q8—88no—
1305Q8—84no—
1306Q8—88no—
1307Q8—162no—
1308D4—216no—
1309D4—48no—
1310D4—416no—
1311D4—48no—
1312D4—44no—
1313D4—416no—
1314C2×C4—22no—
1315C2×C4—21no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—21no—
1319C2×C4—22no—
1320C2×C4—21no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—22no—
1326C2×C4—21no—
1327C2×C4—22no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—216no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—21no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—21no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—21no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—416no—
1385C2×C4—84no—
1386C2×C4—88no—
1387C2×C4—88no—
1388C2×C4—88no—
1389C2×C4—84no—
1390C2×C4—88no—
1391C2×C4—88no—
1392C2×C4—88no—
1393C2×C4—164no—
1394C2×C4—164no—
1395C2×C4C23×Q812yes—
1396C2×C4C23×Q812yes—
1397C2×C4C23×Q814yes—
1398C2×C4C23×Q814yes—
1399C2×C4C23×Q814yes—
1400C2×C4C23×Q812yes—
1401C2×C4C2×H(5,𝔽2)12yes—
1402C2×C4C2×H(5,𝔽2)12yes—
1403C2×C4C2×H(5,𝔽2)14yes—
1404C2×C4C2×H(5,𝔽2)12yes—
1405C2×C4C2×H(5,𝔽2)12yes—
1406C2×C4#58512yes—
1407C22—24no—
1408C22—28no—
1409C22—24no—
1410C22—28no—
1411C22—24no—
1412C22—28no—
1413C22—44no—
1414C22—42no—
1415C22—42no—
1416C22—44no—
1417C22—44no—
1418C22—42no—
1419C22—42no—
1420C22—44no—
1421C22C24×Q811yescharacteristic
1422C22C22×H(5,𝔽2)11yescharacteristic
1423C22C22×H(5,𝔽2)11yescharacteristic
1424C22C2×#58511yescharacteristic
1425C22H(7,𝔽2)11yescharacteristic
1426C222−1+611yescharacteristic
1427C222−1+611yescharacteristic
1428C4—24no—
1429C4—22no—
1430C4—24no—
1431C4—24no—
1432C4—22no—
1433C4—22no—
1434C4—22no—
1435C4—24no—
1436C4—22no—
1437C4—42no—
1438C4—42no—
1439C4—44no—
1440C4—41no—
1441C4—42no—
1442C4—42no—
1443C4—42no—
1444C4—42no—
1445C4—42no—
1446C4—44no—
1447C4—44no—
1448C4—42no—
1449C4—42no—
1450C4—42no—
1451C4—44no—
1452C4—42no—
1453C4—44no—
1454C4#350114yes—
1455C2—44no—
1456C2—48no—
1457C2C2×#350111yescharacteristic
1458C2#6285411yescharacteristic
1459C2#6288811yescharacteristic
1460C2#6291211yescharacteristic
1461C2#6296011yescharacteristic
1462C2Q8×H(5,𝔽2)11yescharacteristic
1463C2#6305611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59831C2semidirect
2. #59817C2semidirect
3. #52162C2semidirect
4. #52035C2semidirect
5. #51786C2semidirect
6. #48852C2semidirect
7. #46436C2semidirect
8. #46282C2semidirect
9. #45362C2semidirect
10. #44946C2semidirect
11. #44942C2semidirect
12. #43100C2semidirect
13. #42930C2semidirect
14. #42820C2semidirect
15. #40616C2semidirect
16. #39981C2semidirect
17. #39628C2semidirect
18. #39611C2semidirect
19. #39596C2semidirect
20. #39493C2semidirect
21. #38453C2semidirect
22. #38098C2semidirect
23. #37137C2semidirect
24. #36286C2semidirect
25. #35739C2semidirect
26. #35519C2semidirect
27. #35208C2semidirect
262. #550Q8semidirect
720. C2×#41C2×Q8semidirect
763. #127C2×Q8semidirect
788. #121C2×Q8semidirect
789. #121C2×Q8semidirect
799. C4×Q8C2×Q8semidirect
816. C4×D4C2×Q8semidirect
817. C4×D4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598312
#598172
#521622
#520352
#517862
#488522
#464362
#462822
#453622
#449462
#449422
#431002
#429302
#428202
#406162
#399812
#396282
#396112
#395962
#394932
#384532
#380982
#371372
#362862
#357392
#355192
#352082
#344772
#343132