Finite Group Databasebeta

← #7900909

Subgroups — #7900909

Order 512.

4521 conjugacy classes of subgroups.

The subgroup lattice has 1423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59828C211yesmaximal, characteristic, complemented
2#59663C212yesmaximal, complemented
3#52162C211yesmaximal, characteristic, complemented
4#50900C214yesmaximal, complemented
5#48863C214yesmaximal, complemented
6#47978C214yesmaximal, complemented
7#46441C214yesmaximal, complemented
8#45793C212yesmaximal, complemented
9#45415C212yesmaximal, complemented
10#45276C212yesmaximal, complemented
11#45275C212yesmaximal, complemented
12#43138C214yesmaximal, complemented
13#42931C212yesmaximal, complemented
14#42495C212yesmaximal, complemented
15#40624C214yesmaximal, complemented
16#39984C212yesmaximal, complemented
17#39751C212yesmaximal, complemented
18#39710C212yesmaximal, complemented
19#39629C211yesmaximal, characteristic, complemented
20#39591C212yesmaximal, complemented
21#39493C211yesmaximal, characteristic, complemented
22#38100C212yesmaximal, complemented
23#37135C212yesmaximal, complemented
24#36476C211yesmaximal, characteristic, complemented
25#36040C212yesmaximal, complemented
26#35519C212yesmaximal, complemented
27#35177C211yesmaximal, characteristic, complemented
28#34473C212yesmaximal
29#34308C211yesmaximal, characteristic
30C2×#557C2212yes—
31C2×#547C2211yescharacteristic
32C2×#533C2212yes—
33C2×#520C2212yes—
34#2862C2211yescharacteristic
35#2857C2212yes—
36#2855C2212yes—
37#2855C2212yes—
38#2851C2212yes—
39#2841C2214yes—
40#2841C2214yes—
41#2806C2212yes—
42#2806C2212yes—
43#2806C2212yes—
44#2805C2212yes—
45#2805C2212yes—
46#2805C2212yes—
47#2804C2214yes—
48#2804C2212yes—
49#2802C2214yes—
50#2802C2214yes—
51#2792C2214yes—
52#2791C2214yes—
53#2790C2214yes—
54#2790C2214yes—
55#2788C2214yes—
56#2788C2214yes—
57#2784C2214yes—
58#2780C2214yes—
59#2780C2214yes—
60#2774C2214yes—
61#2774C2214yes—
62#2774C2214yes—
63#2768C2214yes—
64#2763C2214yes—
65#2763C2214yes—
66#2755C2214yes—
67#2755C2214yes—
68#2755C2214yes—
69#2755C2214yes—
70#2755C2214yes—
71#2742C2214yes—
72#2734C2211yescharacteristic
73#2734C2214yes—
74#2732C2211yescharacteristic
75#2732C2212yes—
76#2732C2214yes—
77#2729C2212yes—
78#2729C2214yes—
79#2729C2214yes—
80#2726C2212yes—
81#2726C2212yes—
82#2726C2211yescharacteristic
83#2720C2214yes—
84#2720C2212yes—
85#2720C2214yes—
86#2713C2214yes—
87#2713C2212yes—
88#2704C2212yes—
89#2692C2214yes—
90#2692C2214yes—
91#2692C2212yes—
92#2683C2214yes—
93#2683C2211yescharacteristic
94#2677C2212yes—
95#2667C2214yes—
96#2667C2214yes—
97#2665C2214yes—
98#2665C2214yes—
99#2659C2214yes—
100#2647C2212yes—
101#2629C2212yes—
102#2628C2212yes—
103#2628C2214yes—
104#2627C2214yes—
105#2607C2214yes—
106#2607C2214yes—
107#2590C2214yes—
108#2590C2214yes—
109#2589C2214yes—
110#2589C2214yes—
111#2588C2214yes—
112#2587C2214yes—
113#2587C2214yes—
114#2586C2214yes—
115#2586C2214yes—
116#2586C2214yes—
117#2584C2214yes—
118#2584C2212yes—
119#2584C2212yes—
120#2582C2212yes—
121#2582C2212yes—
122#2582C2212yes—
123#2581C2212yes—
124#2581C2212yes—
125#2581C2212yes—
126#2580C2212yes—
127#2580C2214yes—
128#2580C2212yes—
129#2579C2214yes—
130#2570C2212yes—
131#2570C2212yes—
132#2569C2214yes—
133#2568C2212yes—
134#2567C2211yescharacteristic
135#2567C2212yes—
136#2563C2211yescharacteristic
137#2563C2211yescharacteristic
138#2563C2214yes—
139#2556C2214yes—
140#2556C2214yes—
141#2552C2212yes—
142#2551C2211yescharacteristic
143#2550C2214yes—
144#2549C2214yes—
145#2549C2214yes—
146#2546C2212yes—
147#2542C2211yescharacteristic
148#2538C2211yescharacteristic
149#2538C2212yes—
150#2522C2214yes—
151#2520C2214yes—
152#2520C2214yes—
153#2511C2214yes—
154#2509C2212yes—
155#2508C2214yes—
156#2508C2212yes—
157#2506C2212yes—
158#2506C2214yes—
159#2506C2214yes—
160#2505C2214yes—
161#2505C2214yes—
162#2502C2214yes—
163#2497C2212yes—
164#2492C2212yes—
165#2492C2212yes—
166#2473C2214yes—
167#2465C2214yes—
168#2465C2214yes—
169#2465C2214yes—
170#2462C2214yes—
171#2454C2214yes—
172#2454C2212yes—
173#2454C2214yes—
174#2454C2212yes—
175#2453C2212yes—
176#2453C2212yes—
177#2452C2212yes—
178#2451C2212yes—
179#2451C2212yes—
180#2450C2214yes—
181#2450C2214yes—
182#2450C2214yes—
183#2449C2214yes—
184#2449C2214yes—
185#2446C2214yes—
186#2442C2214yes—
187#2442C2212yes—
188#2442C2214yes—
189#2442C2214yes—
190#2442C2214yes—
191#2442C2212yes—
192#2441C2214yes—
193#2440C2214yes—
194#2440C2212yes—
195#2440C2212yes—
196#2439C2212yes—
197#2439C2212yes—
198#2439C2214yes—
199#2423C2212yes—
200#2399C2212yes—
201#2396C2212yes—
202#2396C2214yes—
203#2396C2212yes—
204#2377C2214yes—
205#2376C2214yes—
206#2374C2214yes—
207#2369C2211yescharacteristic
208#2365C2211yescharacteristic
209#2365C2211yescharacteristic
210#2365C2212yes—
211#2362C2212yes—
212#2361C2212yes—
213#2360C2212yes—
214#2360C2214yes—
215#2360C2212yes—
216#2359C2214yes—
217#2357C2212yes—
218#2355C2212yes—
219#2352C2212yes—
220#2351C2212yes—
221#2351C2212yes—
222#2351C2212yes—
223Q8×C4⋊C4C2212yes—
224D4×C4⋊C4C2211yescharacteristic
225D4×C4⋊C4C2211yescharacteristic
226#2345C2214yes—
227#2344C2212yes—
228#2341C2212yes—
229#2341C2212yes—
230#2339C2212yes—
231#2335C2214yes—
232#2335C2214yes—
233#2333C2214yes—
234#2331C2212yes—
235#2329C2214yes—
236#2327C2212yes—
237#2323C2212yes—
238#2323C2212yes—
239#2322C2214yes—
240#2319C2212yes—
241#2317C2212yes—
242#2317C2212yes—
243#2313C2214yes—
244#2311C2212yes—
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2211yescharacteristic
247C4×C4⋊Q8C2211yescharacteristic
248C4×C22⋊Q8C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×C22⋊Q8C2212yes—
251C4×#121C2212yes—
252#2297C2212yes—
253#2295C2211yescharacteristic
254#2293C2211yescharacteristic
255C2×#389C2212yes—
256C2×#389C2212yes—
257#2290C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260#557—48no—
261#547Q8116yescomplemented
262#533—48no—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×#125C2314yes—
280C2×#123C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×#121C2312yes—
295#520—48no—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2314yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2314yes—
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2314yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2311yescharacteristic
317C2×#117C2312yes—
318C2×#117C2312yes—
319C2×#117C2312yes—
320C2×#117C2314yes—
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2312yes—
323C22×C4⋊C4C2314yes—
324C22×C4⋊C4C2314yes—
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2312yes—
327C22×C42C2312yes—
328C22×C42C2312yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2312yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#399C2314yes—
350#399C2312yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2312yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2312yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2312yes—
383#398C2312yes—
384#398C2312yes—
385#398C2312yes—
386#398C2314yes—
387#398C2312yes—
388#398C2312yes—
389#398C2314yes—
390#398C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2312yes—
397#396C2312yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2312yes—
402#396C2312yes—
403#396C2314yes—
404#396C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2312yes—
416#395C2314yes—
417#395C2312yes—
418#395C2312yes—
419#395C2314yes—
420#395C2312yes—
421#395C2314yes—
422#395C2312yes—
423#395C2312yes—
424#395C2314yes—
425#393C2314yes—
426#393C2312yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#393C2314yes—
432#393C2314yes—
433#393C2312yes—
434#393C2314yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2314yes—
444#391C2314yes—
445#391C2312yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2312yes—
454#391C2312yes—
455#391C2314yes—
456#391C2314yes—
457#391C2311yescharacteristic
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2314yes—
463#391C2314yes—
464#391C2311yescharacteristic
465#390C2312yes—
466#390C2312yes—
467#390C2314yes—
468#390C2314yes—
469#390C2312yes—
470#390C2312yes—
471#390C2314yes—
472#390C2314yes—
473#390C2311yescharacteristic
474#390C2311yescharacteristic
475#389C2312yes—
476#389C2312yes—
477#389C2311yescharacteristic
478#389C2312yes—
479#389C2312yes—
480#389C2311yescharacteristic
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2312yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2312yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2311yescharacteristic
524#389C2312yes—
525#389C2311yescharacteristic
526#389C2312yes—
527#389C2312yes—
528#389C2314yes—
529#389C2312yes—
530#389C2314yes—
531#389C2311yescharacteristic
532#389C2311yescharacteristic
533#389C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2312yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2312yes—
547#388C2312yes—
548#388C2312yes—
549#387C2312yes—
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#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2312yes—
590#387C2312yes—
591#387C2314yes—
592#387C2312yes—
593#387C2314yes—
594#387C2312yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2312yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2312yes—
604#385C2314yes—
605#385C2314yes—
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#385C2312yes—
624#385C2314yes—
625#385C2314yes—
626#385C2312yes—
627#385C2312yes—
628#385C2314yes—
629#385C2312yes—
630#384C2311yescharacteristic
631#384C2311yescharacteristic
632#384C2311yescharacteristic
633#384C2312yes—
634#384C2312yes—
635#384C2312yes—
636#384C2314yes—
637#384C2314yes—
638#382C2312yes—
639#382C2312yes—
640#382C2314yes—
641#382C2314yes—
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2314yes—
646#382C2314yes—
647#382C2314yes—
648#381C2314yes—
649#381C2314yes—
650#381C2314yes—
651#380C2312yes—
652#380C2314yes—
653#380C2314yes—
654#380C2312yes—
655#380C2312yes—
656#380C2312yes—
657#380C2314yes—
658#380C2314yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662#380C2314yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2314yes—
667#380C2312yes—
668#380C2312yes—
669#380C2314yes—
670#380C2312yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712#376C2312yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C43C2311yescharacteristic
716C2×#41—44no—
717C2×#41—44no—
718C2×#41C2×Q8116yes—
719C22×Q8C2412yes—
720C22×Q8C2412yes—
721C22×Q8C2411yescharacteristic
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×Q8C2414yes—
727C22×Q8C2412yes—
728C22×D4C2411yescharacteristic
729C22×D4C2411yescharacteristic
730C22×D4C2414yes—
731C23×C4C2412yes—
732C23×C4C2412yes—
733C23×C4C2412yes—
734C23×C4C2414yes—
735C23×C4C2414yes—
736C23×C4C2414yes—
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2414yes—
740C23×C4C2412yes—
741C4⋊Q8—24no—
742C4⋊Q8—42no—
743C4⋊Q8—42no—
744C4⋊Q8—44no—
745C4⋊Q8—42no—
746C4⋊Q8—48no—
747C4⋊Q8—44no—
748C4⋊Q8—44no—
749C4⋊Q8—82no—
750C4⋊Q8C2×Q818yes—
751#125—44no—
752#125—44no—
753#125—44no—
754#125—44no—
755#125—48no—
756#125—48no—
757#125—84no—
758#123C2×Q8132yes—
759C22⋊Q8—44no—
760C22⋊Q8—44no—
761C22⋊Q8—44no—
762C22⋊Q8—48no—
763C22⋊Q8—44no—
764C22⋊Q8—44no—
765C22⋊Q8—48no—
766C22⋊Q8—44no—
767C22⋊Q8—84no—
768C22⋊Q8—82no—
769C22⋊Q8—84no—
770C22⋊Q8—82no—
771C22⋊Q8C2×Q8116yes—
772#121C2×Q8116yes—
773C4×Q8—28no—
774C4×Q8—24no—
775C4×Q8—28no—
776C4×Q8—44no—
777C4×Q8—44no—
778C4×Q8—44no—
779C4×Q8—44no—
780C4×Q8—44no—
781C4×Q8—44no—
782C4×Q8—44no—
783C4×Q8—48no—
784C4×Q8—44no—
785C4×Q8—82no—
786C4×D4—24no—
787C4×D4—48no—
788C4×D4—42no—
789C4×D4—44no—
790C4×D4—48no—
791C4×D4—82no—
792C4×D4C2×Q818yes—
793C4×D4C2×Q818yes—
794#117—28no—
795#117—44no—
796#117—48no—
797#117—44no—
798C2×C4⋊C4—44no—
799C2×C4⋊C4—48no—
800C2×C4⋊C4—44no—
801C2×C4⋊C4—82no—
802C2×C4⋊C4—84no—
803C2×C4⋊C4C2×Q8116yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C42—44no—
916C2×C42—82no—
917C2×C42C2412yes—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2411yescharacteristic
922C2×C42C2412yes—
923C2×C42C2411yescharacteristic
924C2×C42C2412yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2412yes—
928C2×C42C2414yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2411yescharacteristic
941C2×C42C2414yes—
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013C24C2512yes—
1014C24C2512yes—
1015#41—432no—
1016C2×Q8—24no—
1017C2×Q8—24no—
1018C2×Q8—22no—
1019C2×Q8—24no—
1020C2×Q8—24no—
1021C2×Q8—24no—
1022C2×Q8—42no—
1023C2×Q8—42no—
1024C2×Q8—42no—
1025C2×Q8—42no—
1026C2×Q8—42no—
1027C2×Q8—42no—
1028C2×Q8—41no—
1029C2×Q8—42no—
1030C2×Q8—42no—
1031C2×Q8—42no—
1032C2×Q8—41no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×Q8—42no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×Q8—44no—
1039C2×Q8—42no—
1040C2×Q8—42no—
1041C2×Q8—42no—
1042C2×Q8C22×Q818yes—
1043C2×D4—22no—
1044C2×D4—22no—
1045C2×D4—44no—
1046C2×D4—41no—
1047C2×D4—41no—
1048C2×D4—44no—
1049C2×D4C22×Q814yes—
1050C2×D4C22×Q814yes—
1051C2×D4C22×Q8116yes—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—42no—
1057C22×C4—44no—
1058C22×C4—42no—
1059C22×C4—44no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—44no—
1065C22×C4—42no—
1066C22×C4—44no—
1067C22×C4—42no—
1068C22×C4—44no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4C22×Q818yes—
1080C22×C4C22×Q818yes—
1081C22×C4C22×Q8116yes—
1082C22×C4C2511yescharacteristic
1083C22×C4C2514yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2514yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2512yes—
1103C22×C4C2514yes—
1104C22×C4C2512yes—
1105C22×C4C2511yescharacteristic
1106C22×C4C2511yescharacteristic
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C4⋊C4—24no—
1110C4⋊C4—22no—
1111C4⋊C4—28no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—22no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—22no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—22no—
1128C4⋊C4—22no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—41no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—41no—
1143C4⋊C4—41no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—41no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—41no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—42no—
1186C4⋊C4—41no—
1187C4⋊C4C22×Q814yes—
1188C4⋊C4C22×Q818yes—
1189C4⋊C4C22×Q8116yes—
1190C4⋊C4C22×Q814yes—
1191C4⋊C4C22×Q818yes—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—24no—
1195C22⋊C4—24no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—42no—
1200C22⋊C4—44no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—42no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—42no—
1216C22⋊C4—44no—
1217C22⋊C4C22×Q818yes—
1218C22⋊C4C22×Q818yes—
1219C22⋊C4C22×Q8116yes—
1220C42—24no—
1221C42—24no—
1222C42—24no—
1223C42—28no—
1224C42—24no—
1225C42—22no—
1226C42—22no—
1227C42—24no—
1228C42—42no—
1229C42—42no—
1230C42—41no—
1231C42—42no—
1232C42—42no—
1233C42—42no—
1234C42—44no—
1235C42—41no—
1236C42—41no—
1237C42—44no—
1238C42—44no—
1239C42—44no—
1240C42—44no—
1241C42—44no—
1242C42—44no—
1243C42—44no—
1244C42—44no—
1245C42C22×Q814yes—
1246C42H(5,𝔽2)14yes—
1247C23—22no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23—22no—
1258C23—22no—
1259C23C23×Q814yes—
1260C23C23×Q814yes—
1261C23C2611yescharacteristic
1262Q8—216no—
1263Q8—48no—
1264Q8—82no—
1265Q8—84no—
1266Q8—84no—
1267Q8—84no—
1268Q8—84no—
1269Q8—162no—
1270Q8—164no—
1271D4—28no—
1272D4—44no—
1273D4—416no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—22no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—216no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—21no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
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—21no—
1331C2×C4—21no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—48no—
1346C2×C4—416no—
1347C2×C4—84no—
1348C2×C4—84no—
1349C2×C4—84no—
1350C2×C4—84no—
1351C2×C4—88no—
1352C2×C4—164no—
1353C2×C4—164no—
1354C2×C4C23×Q812yes—
1355C2×C4C23×Q812yes—
1356C2×C4C23×Q814yes—
1357C2×C4C23×Q814yes—
1358C2×C4C23×Q818yes—
1359C2×C4C23×Q812yes—
1360C2×C4C2×H(5,𝔽2)12yes—
1361C2×C4C2×H(5,𝔽2)12yes—
1362C2×C4C2×H(5,𝔽2)12yes—
1363C2×C4#58512yes—
1364C2×C4#58512yes—
1365C22—24no—
1366C22—24no—
1367C22—24no—
1368C22—24no—
1369C22—24no—
1370C22—24no—
1371C22—42no—
1372C22—42no—
1373C22—42no—
1374C22—42no—
1375C22—42no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22C24×Q811yescharacteristic
1380C22C22×H(5,𝔽2)11yescharacteristic
1381C22C2×#58511yescharacteristic
1382C22C2×#58511yescharacteristic
1383C22H(7,𝔽2)11yescharacteristic
1384C222−1+611yescharacteristic
1385C222−1+611yescharacteristic
1386C4—22no—
1387C4—24no—
1388C4—28no—
1389C4—22no—
1390C4—24no—
1391C4—22no—
1392C4—22no—
1393C4—22no—
1394C4—42no—
1395C4—44no—
1396C4—41no—
1397C4—42no—
1398C4—42no—
1399C4—42no—
1400C4—44no—
1401C4—42no—
1402C4—42no—
1403C4—42no—
1404C4—42no—
1405C4—44no—
1406C4—42no—
1407C4—42no—
1408C4—44no—
1409C4—44no—
1410C4—42no—
1411C4—42no—
1412C4#350114yes—
1413C2—44no—
1414C2—44no—
1415C2C2×#350111yescharacteristic
1416C2#6285411yescharacteristic
1417C2#6287811yescharacteristic
1418C2#6292511yescharacteristic
1419C2#6296511yescharacteristic
1420C2#6300411yescharacteristic
1421C2#6306211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#547C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59828C2semidirect
2. #59663C2semidirect
3. #52162C2semidirect
4. #50900C2semidirect
5. #48863C2semidirect
6. #47978C2semidirect
7. #46441C2semidirect
8. #45793C2semidirect
9. #45415C2semidirect
10. #45276C2semidirect
11. #45275C2semidirect
12. #43138C2semidirect
13. #42931C2semidirect
14. #42495C2semidirect
15. #40624C2semidirect
16. #39984C2semidirect
17. #39751C2semidirect
18. #39710C2semidirect
19. #39629C2semidirect
20. #39591C2semidirect
21. #39493C2semidirect
22. #38100C2semidirect
23. #37135C2semidirect
24. #36476C2semidirect
25. #36040C2semidirect
26. #35519C2semidirect
27. #35177C2semidirect
261. #547Q8semidirect

Maximal subgroups

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

subgroupindex
#598282
#596632
#521622
#509002
#488632
#479782
#464412
#457932
#454152
#452762
#452752
#431382
#429312
#424952
#406242
#399842
#397512
#397102
#396292
#395912
#394932
#381002
#371352
#364762
#360402
#355192
#351772
#344732
#343082