Finite Group Databasebeta

← #7726915

Subgroups — #7726915

Order 512.

4222 conjugacy classes of subgroups.

The subgroup lattice has 1389 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51619C214yesmaximal, complemented
2#51618C214yesmaximal, complemented
3#47780C214yesmaximal, complemented
4#47779C214yesmaximal, complemented
5#45431C211yesmaximal, characteristic, complemented
6#45425C211yesmaximal, characteristic, complemented
7#45347C211yesmaximal, characteristic, complemented
8#45318C211yesmaximal, characteristic, complemented
9#45306C211yesmaximal, characteristic, complemented
10#45276C211yesmaximal, characteristic, complemented
11#45231C211yesmaximal, characteristic, complemented
12#45163C211yesmaximal, characteristic, complemented
13#39811C212yesmaximal, complemented
14#39802C212yesmaximal, complemented
15#39758C212yesmaximal, complemented
16#39750C212yesmaximal, complemented
17#39559C214yesmaximal, complemented
18#39512C212yesmaximal, complemented
19#39199C212yesmaximal
20#37967C214yesmaximal, complemented
21#37632C211yesmaximal, characteristic
22#36999C214yesmaximal, complemented
23#36487C212yesmaximal
24#36177C212yesmaximal, complemented
25#35461C214yesmaximal, complemented
26#35326C211yesmaximal, characteristic
27#35320C211yesmaximal, characteristic, complemented
28#34878C211yesmaximal, characteristic, complemented
29#34399C211yesmaximal, characteristic, complemented
30#34229C211yesmaximal, characteristic
31C2×#2331C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C2×#529C2211yescharacteristic
35#2862C2212yes—
36#2862C2212yes—
37#2857C2211yescharacteristic
38#2857C2211yescharacteristic
39#2855C2214yes—
40#2853C2214yes—
41#2850C2211yescharacteristic
42#2850C2211yescharacteristic
43#2821C2212yes—
44#2821C2212yes—
45#2810C2214yes—
46#2807C2214yes—
47#2805C2214yes—
48#2799C2214yes—
49#2799C2214yes—
50#2798C2214yes—
51#2798C2214yes—
52#2798C2214yes—
53#2798C2214yes—
54#2789C2214yes—
55#2776C2214yes—
56#2776C2214yes—
57#2774C2214yes—
58#2773C2214yes—
59#2773C2214yes—
60#2771C2214yes—
61#2767C2214yes—
62#2767C2214yes—
63#2766C2214yes—
64#2764C2214yes—
65#2763C2214yes—
66#2762C2214yes—
67#2762C2214yes—
68#2762C2214yes—
69#2759C2214yes—
70#2759C2214yes—
71#2759C2214yes—
72#2758C2214yes—
73#2758C2214yes—
74#2758C2214yes—
75#2755C2214yes—
76#2755C2214yes—
77#2755C2214yes—
78#2754C2214yes—
79#2754C2214yes—
80#2754C2214yes—
81#2747C2214yes—
82#2745C2214yes—
83#2742C2214yes—
84#2738C2214yes—
85#2660C2212yes—
86#2660C2211yescharacteristic
87#2658C2211yescharacteristic
88#2642C2211yescharacteristic
89#2642C2212yes—
90#2642C2212yes—
91#2640C2212yes—
92#2640C2211yescharacteristic
93#2628C2214yes—
94#2627C2214yes—
95#2623C2214yes—
96#2614C2212yes—
97#2614C2212yes—
98#2612C2212yes—
99#2612C2212yes—
100#2612C2214yes—
101#2611C2214yes—
102#2607C2214yes—
103#2606C2212yes—
104#2605C2212yes—
105#2605C2214yes—
106#2605C2214yes—
107#2604C2214yes—
108#2596C2214yes—
109#2596C2214yes—
110#2592C2212yes—
111#2590C2214yes—
112#2589C2214yes—
113#2589C2214yes—
114#2589C2214yes—
115#2588C2214yes—
116#2588C2214yes—
117#2588C2214yes—
118#2586C2214yes—
119#2582C2212yes—
120#2581C2212yes—
121#2581C2212yes—
122#2580C2212yes—
123#2577C2214yes—
124#2575C2214yes—
125#2575C2214yes—
126#2571C2212yes—
127#2571C2212yes—
128#2570C2212yes—
129#2570C2212yes—
130#2570C2212yes—
131#2570C2212yes—
132#2569C2212yes—
133#2568C2211yescharacteristic
134#2568C2211yescharacteristic
135#2568C2212yes—
136#2568C2211yescharacteristic
137#2568C2214yes—
138#2568C2211yescharacteristic
139#2567C2211yescharacteristic
140#2567C2211yescharacteristic
141#2564C2214yes—
142#2563C2211yescharacteristic
143#2563C2211yescharacteristic
144#2549C2212yes—
145#2533C2214yes—
146#2533C2214yes—
147#2533C2214yes—
148#2533C2214yes—
149#2532C2214yes—
150#2532C2214yes—
151#2530C2214yes—
152#2528C2214yes—
153#2528C2214yes—
154#2527C2214yes—
155#2527C2214yes—
156#2527C2214yes—
157#2524C2214yes—
158#2523C2214yes—
159#2523C2214yes—
160#2520C2214yes—
161#2520C2214yes—
162#2520C2214yes—
163#2517C2214yes—
164#2514C2212yes—
165#2514C2212yes—
166#2514C2212yes—
167#2514C2214yes—
168#2514C2212yes—
169#2513C2212yes—
170#2513C2212yes—
171#2511C2212yes—
172#2511C2212yes—
173#2509C2214yes—
174#2505C2214yes—
175#2503C2212yes—
176#2503C2212yes—
177#2503C2212yes—
178#2503C2212yes—
179#2503C2212yes—
180#2501C2212yes—
181#2498C2214yes—
182#2493C2214yes—
183#2493C2214yes—
184#2493C2214yes—
185#2493C2214yes—
186#2493C2214yes—
187#2488C2214yes—
188#2488C2214yes—
189#2486C2214yes—
190#2448C2212yes—
191#2447C2212yes—
192#2446C2212yes—
193#2446C2212yes—
194#2438C2212yes—
195#2438C2212yes—
196#2419C2214yes—
197#2419C2214yes—
198#2402C2211yescharacteristic
199#2402C2211yescharacteristic
200#2399C2211yescharacteristic
201#2399C2211yescharacteristic
202#2382C2214yes—
203#2367C2212yes—
204#2365C2212yes—
205#2361C2212yes—
206#2360C2212yes—
207#2360C2212yes—
208#2360C2212yes—
209#2359C2214yes—
210#2357C2211yescharacteristic
211#2357C2212yes—
212#2356C2212yes—
213#2356C2211yescharacteristic
214#2356C2212yes—
215#2356C2211yescharacteristic
216#2356C2211yescharacteristic
217#2355C2212yes—
218#2355C2212yes—
219#2355C2212yes—
220#2351C2211yescharacteristic
221#2351C2211yescharacteristic
222#2351C2211yescharacteristic
223#2349C2211yescharacteristic
224#2346C2212yes—
225#2343C2212yes—
226#2343C2212yes—
227#2343C2212yes—
228#2334C2214yes—
229#2331C2211yescharacteristic
230#2331C2211yescharacteristic
231#2331C2212yes—
232#2331C2212yes—
233#2331C2211yescharacteristic
234#2331C2211yescharacteristic
235#2331C2214yes—
236#2331C2214yes—
237#2331C2212yes—
238#2329C2214yes—
239#2327C2211yescharacteristic
240#2327C2212yes—
241#2327C2211yescharacteristic
242#2326C2211yescharacteristic
243#2326C2211yescharacteristic
244#2322C2214yes—
245#2320C2212yes—
246#2320C2212yes—
247#2318C2212yes—
248#2313C2214yes—
249#2310C2214yes—
250C4×#125C2212yes—
251C4×#124C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×#123C2214yes—
255#2295C2212yes—
256#2295C2212yes—
257C2×#391C2214yes—
258C2×#389C2212yes—
259C2×#387C2214yes—
260#2283C2211yescharacteristic
261#2283C2214yes—
262C2×#382C2211yescharacteristic
263#2275C2212yes—
264C4×#117C2211yescharacteristic
265C2×C4×C4⋊C4C2212yes—
266C2×#376C2211yescharacteristic
267C23×Q8C2312yes—
268#533—28no—
269C2×C4⋊Q8—28no—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2311yescharacteristic
279#529—28no—
280C2×#126C2312yes—
281C2×#125C2311yescharacteristic
282C2×#125C2312yes—
283C2×#124C2311yescharacteristic
284C2×#124C2311yescharacteristic
285C2×#124C2311yescharacteristic
286C2×#123C2312yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2311yescharacteristic
291C2×C22⋊Q8C2311yescharacteristic
292C2×C22⋊Q8C2311yescharacteristic
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×#121C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2312yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2312yes—
309C2×#117C2312yes—
310C2×#117C2312yes—
311C2×#117C2312yes—
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2314yes—
315C22×C4⋊C4C2312yes—
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2314yes—
319C22×C42C2311yescharacteristic
320#401C2314yes—
321#401C2314yes—
322#401C2314yes—
323#401C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2312yes—
330#400C2314yes—
331#400C2312yes—
332#400C2314yes—
333#400C2312yes—
334#400C2312yes—
335#400C2312yes—
336#400C2312yes—
337#400C2312yes—
338#400C2314yes—
339#400C2314yes—
340#400C2312yes—
341#400C2312yes—
342#400C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2312yes—
359#400C2312yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#399C2314yes—
367#399C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2314yes—
371#399C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2312yes—
384#398C2314yes—
385#398C2312yes—
386#398C2312yes—
387#398C2312yes—
388#398C2314yes—
389#398C2312yes—
390#398C2312yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#395C2314yes—
403#395C2312yes—
404#395C2312yes—
405#395C2312yes—
406#395C2312yes—
407#395C2314yes—
408#395C2314yes—
409#395C2312yes—
410#395C2314yes—
411#395C2312yes—
412#395C2314yes—
413#395C2312yes—
414#395C2312yes—
415#393C2312yes—
416#393C2312yes—
417#393C2312yes—
418#393C2312yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2314yes—
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2314yes—
444#391C2314yes—
445#391C2311yescharacteristic
446#391C2311yescharacteristic
447#391C2311yescharacteristic
448#391C2311yescharacteristic
449#391C2314yes—
450#391C2312yes—
451#391C2311yescharacteristic
452#391C2311yescharacteristic
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2312yes—
462#391C2314yes—
463#391C2314yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2311yescharacteristic
472#390C2311yescharacteristic
473#390C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2312yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2312yes—
537#387C2312yes—
538#387C2312yes—
539#387C2312yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2312yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
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#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2312yes—
591#387C2312yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2312yes—
596#387C2312yes—
597#387C2312yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2312yes—
604#385C2312yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2312yes—
615#385C2312yes—
616#384C2312yes—
617#384C2312yes—
618#384C2311yescharacteristic
619#384C2311yescharacteristic
620#383C2311yescharacteristic
621#383C2311yescharacteristic
622#383C2312yes—
623#383C2312yes—
624#383C2312yes—
625#383C2314yes—
626#383C2314yes—
627#383C2314yes—
628#383C2314yes—
629#383C2314yes—
630#383C2314yes—
631#382C2312yes—
632#382C2312yes—
633#382C2312yes—
634#382C2312yes—
635#382C2312yes—
636#382C2312yes—
637#382C2312yes—
638#382C2314yes—
639#382C2314yes—
640#382C2314yes—
641#382C2311yescharacteristic
642#382C2311yescharacteristic
643#382C2314yes—
644#382C2314yes—
645#382C2312yes—
646#382C2314yes—
647#382C2312yes—
648#382C2312yes—
649#382C2312yes—
650#382C2312yes—
651#382C2311yescharacteristic
652#382C2311yescharacteristic
653#382C2312yes—
654#381C2314yes—
655#381C2314yes—
656#381C2314yes—
657#381C2314yes—
658#381C2314yes—
659#381C2312yes—
660#381C2314yes—
661#381C2314yes—
662#381C2311yescharacteristic
663#381C2311yescharacteristic
664#381C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2311yescharacteristic
706C4×C22⋊C4C2311yescharacteristic
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715#376C2312yes—
716#376C2312yes—
717#376C2311yescharacteristic
718#376C2311yescharacteristic
719#376C2312yes—
720#376C2312yes—
721#376C2312yes—
722#376C2311yescharacteristic
723#376C2311yescharacteristic
724#376C2311yescharacteristic
725#376C2311yescharacteristic
726#376C2312yes—
727#376C2314yes—
728#376C2314yes—
729C2×#95C2312yes—
730C2×#95C2312yes—
731C2×#95C2312yes—
732C2×#95C2312yes—
733C2×#95C2314yes—
734C2×#95C2314yes—
735C2×#95C2312yes—
736C43C2312yes—
737C22×Q8—28no—
738C22×Q8—48no—
739C22×Q8C2411yescharacteristic
740C22×Q8C2411yescharacteristic
741C22×Q8C2411yescharacteristic
742C22×Q8C2412yes—
743C22×Q8C2412yes—
744C22×Q8C2412yes—
745C22×Q8C2412yes—
746C22×Q8C2414yes—
747C22×Q8C2412yes—
748C22×D4C2412yes—
749C22×D4C2411yescharacteristic
750C23×C4C2414yes—
751C23×C4C2412yes—
752C23×C4C2411yescharacteristic
753C23×C4C2411yescharacteristic
754C23×C4C2414yes—
755C23×C4C2412yes—
756C23×C4C2412yes—
757C23×C4C2414yes—
758C23×C4C2411yescharacteristic
759C4⋊Q8—28no—
760C4⋊Q8—24no—
761C4⋊Q8—24no—
762C4⋊Q8—28no—
763C4⋊Q8—28no—
764C4⋊Q8—24no—
765C4⋊Q8—24no—
766C4⋊Q8—24no—
767C4⋊Q8—42no—
768#126—28no—
769#125—24no—
770#125—28no—
771#124—24no—
772#124—24no—
773#124—42no—
774#123—28no—
775#123—48no—
776#123—48no—
777C22⋊Q8—24no—
778C22⋊Q8—24no—
779C22⋊Q8—24no—
780C22⋊Q8—28no—
781C22⋊Q8—44no—
782C22⋊Q8—44no—
783#121—24no—
784C4×Q8—24no—
785C4×Q8—24no—
786C4×Q8—24no—
787C4×Q8—28no—
788C4×Q8—28no—
789C4×Q8—44no—
790C4×Q8—44no—
791C4×Q8—44no—
792C4×Q8—44no—
793C4×D4—28no—
794C4×D4—24no—
795C4×D4—44no—
796C4×D4—48no—
797#117—28no—
798#117—28no—
799#117—44no—
800C2×C4⋊C4—28no—
801C2×C4⋊C4—28no—
802C2×C4⋊C4—44no—
803C2×C4⋊C4—48no—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C42—24no—
892C2×C42—42no—
893C2×C42—48no—
894C2×C42#4118yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2411yescharacteristic
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2411yescharacteristic
923C2×C42C2411yescharacteristic
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927#95C2411yescharacteristic
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2411yescharacteristic
952#95C2412yes—
953#95C2412yes—
954#95C2411yescharacteristic
955#95C2411yescharacteristic
956#95C2414yes—
957#95C2411yescharacteristic
958#95C2411yescharacteristic
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2411yescharacteristic
985#95C2411yescharacteristic
986#95C2412yes—
987#95C2414yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023C24C2512yes—
1024C24C2511yescharacteristic
1025C2×Q8—22no—
1026C2×Q8—22no—
1027C2×Q8—22no—
1028C2×Q8—24no—
1029C2×Q8—24no—
1030C2×Q8—24no—
1031C2×Q8—28no—
1032C2×Q8—22no—
1033C2×Q8—22no—
1034C2×Q8—22no—
1035C2×Q8—24no—
1036C2×Q8—22no—
1037C2×Q8—22no—
1038C2×Q8—22no—
1039C2×Q8—42no—
1040C2×Q8—42no—
1041C2×Q8—42no—
1042C2×Q8—44no—
1043C2×Q8—44no—
1044C2×Q8—44no—
1045C2×Q8—44no—
1046C2×Q8—44no—
1047C2×Q8—42no—
1048C2×Q8—42no—
1049C2×Q8—816no—
1050C2×D4—24no—
1051C2×D4—28no—
1052C2×D4—22no—
1053C2×D4—22no—
1054C2×D4—22no—
1055C22×C4—24no—
1056C22×C4—22no—
1057C22×C4—22no—
1058C22×C4—28no—
1059C22×C4—24no—
1060C22×C4—28no—
1061C22×C4—28no—
1062C22×C4—28no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—24no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4C2×#4114yes—
1077C22×C4C2×#4114yes—
1078C22×C4C2×#4114yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2514yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2514yes—
1094C22×C4C2514yes—
1095C22×C4C2514yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2511yescharacteristic
1105C22×C4C2511yescharacteristic
1106C22×C4C2512yes—
1107C22×C4C2511yescharacteristic
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—28no—
1111C4⋊C4—28no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—22no—
1119C4⋊C4—24no—
1120C4⋊C4—22no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—22no—
1127C4⋊C4—22no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—28no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C22⋊C4—24no—
1174C22⋊C4—24no—
1175C22⋊C4—24no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—24no—
1184C22⋊C4—28no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C42—24no—
1196C42—24no—
1197C42—24no—
1198C42—24no—
1199C42—22no—
1200C42—24no—
1201C42—24no—
1202C42—22no—
1203C42—22no—
1204C42—24no—
1205C42—24no—
1206C42—44no—
1207C42—44no—
1208C42—42no—
1209C42—44no—
1210C42—44no—
1211C42—42no—
1212C42—42no—
1213C42—44no—
1214C42—44no—
1215C42—44no—
1216C42—42no—
1217C42—42no—
1218C42—44no—
1219C42—44no—
1220C42—44no—
1221C42—44no—
1222C42C2×#4114yes—
1223C42C2×#4114yes—
1224C42C2×#4114yes—
1225C42C2×#4114yes—
1226C422−1+414yes—
1227C23—21no—
1228C23—21no—
1229C23—22no—
1230C23—22no—
1231C23—22no—
1232C23—24no—
1233C23—22no—
1234C23—24no—
1235C23C22×#4112yes—
1236C23#58514yes—
1237C23C2611yescharacteristic
1238Q8—44no—
1239Q8—44no—
1240Q8—44no—
1241Q8—84no—
1242Q8—84no—
1243Q8—88no—
1244Q8—84no—
1245Q8—84no—
1246Q8—84no—
1247D4—48no—
1248D4—44no—
1249C2×C4—21no—
1250C2×C4—22no—
1251C2×C4—21no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—28no—
1258C2×C4—28no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
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—44no—
1322C2×C4—48no—
1323C2×C4—416no—
1324C2×C4—84no—
1325C2×C4—88no—
1326C2×C4—84no—
1327C2×C4—164no—
1328C2×C4C22×#4112yes—
1329C2×C4C22×#4112yes—
1330C2×C4C22×#4112yes—
1331C2×C4C22×#4112yes—
1332C2×C4C22×#4112yes—
1333C2×C4C22×#4112yes—
1334C2×C4C2×2−1+414yes—
1335C2×C4C2×2−1+412yes—
1336C2×C4#58512yes—
1337C22—22no—
1338C22—22no—
1339C22—24no—
1340C22—24no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—44no—
1345C22—44no—
1346C22#351014yes—
1347C22C23×#4111yescharacteristic
1348C22C22×2−1+411yescharacteristic
1349C22C2×#58511yescharacteristic
1350C22C2×#58512yes—
1351C222−1+612yes—
1352C4—22no—
1353C4—22no—
1354C4—22no—
1355C4—22no—
1356C4—22no—
1357C4—24no—
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—44no—
1362C4—44no—
1363C4—42no—
1364C4—42no—
1365C4—42no—
1366C4—42no—
1367C4—42no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—42no—
1374C4—44no—
1375C4—44no—
1376C4—42no—
1377C4—42no—
1378C4—42no—
1379C4—42no—
1380C4#350714yes—
1381C2—24no—
1382C2—82no—
1383C2C2×#350711yescharacteristic
1384C2C2×#351011yescharacteristic
1385C2#6286011yescharacteristic
1386C2#6292812yes—
1387C2#6294012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51619C2semidirect
2. #51618C2semidirect
3. #47780C2semidirect
4. #47779C2semidirect
5. #45431C2semidirect
6. #45425C2semidirect
7. #45347C2semidirect
8. #45318C2semidirect
9. #45306C2semidirect
10. #45276C2semidirect
11. #45231C2semidirect
12. #45163C2semidirect
13. #39811C2semidirect
14. #39802C2semidirect
15. #39758C2semidirect
16. #39750C2semidirect
17. #39559C2semidirect
18. #39512C2semidirect
20. #37967C2semidirect
22. #36999C2semidirect
24. #36177C2semidirect
25. #35461C2semidirect
27. #35320C2semidirect
28. #34878C2semidirect
29. #34399C2semidirect
31. C2×#2331C2semidirect

Maximal subgroups

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

subgroupindex
#516192
#516182
#477802
#477792
#454312
#454252
#453472
#453182
#453062
#452762
#452312
#451632
#398112
#398022
#397582
#397502
#395592
#395122
#391992
#379672
#376322
#369992
#364872
#361772
#354612
#353262
#353202
#348782
#343992
#342292
C2×#23312