Finite Group Databasebeta

← #7710715

Subgroups — #7710715

Order 512.

4308 conjugacy classes of subgroups.

The subgroup lattice has 1427 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59616C214yesmaximal, complemented
2#59295C212yesmaximal, complemented
3#59294C212yesmaximal, complemented
4#46157C211yesmaximal, characteristic, complemented
5#46157C211yesmaximal, characteristic, complemented
6#46152C211yesmaximal, characteristic, complemented
7#46147C211yesmaximal, characteristic, complemented
8#46143C212yesmaximal, complemented
9#46132C212yesmaximal
10#40472C214yesmaximal, complemented
11#40096C212yesmaximal, complemented
12#40051C212yesmaximal, complemented
13#40010C212yesmaximal
14#39987C212yesmaximal, complemented
15#38808C212yesmaximal, complemented
16#38801C212yesmaximal, complemented
17#38790C212yesmaximal, complemented
18#38781C212yesmaximal
19#38647C214yesmaximal, complemented
20#37603C212yesmaximal, complemented
21#36939C214yesmaximal, complemented
22#36640C211yesmaximal, characteristic, complemented
23#36640C211yesmaximal, characteristic, complemented
24#36556C212yesmaximal, complemented
25#36201C212yesmaximal, complemented
26#36191C212yesmaximal, complemented
27#36171C212yesmaximal, complemented
28#35142C212yesmaximal, complemented
29#35132C212yesmaximal, complemented
30#34528C212yesmaximal, complemented
31C4×#529C211yesmaximal, characteristic
32C2×#563C2212yes—
33C2×#529C2211yescharacteristic
34#2864C2212yes—
35#2864C2212yes—
36#2864C2212yes—
37#2864C2212yes—
38#2864C2212yes—
39#2862C2212yes—
40#2859C2211yescharacteristic
41#2859C2211yescharacteristic
42#2859C2211yescharacteristic
43#2859C2211yescharacteristic
44#2859C2211yescharacteristic
45#2859C2211yescharacteristic
46#2859C2211yescharacteristic
47#2859C2211yescharacteristic
48#2851C2212yes—
49#2851C2212yes—
50#2851C2212yes—
51#2851C2212yes—
52#2851C2212yes—
53#2851C2212yes—
54#2851C2212yes—
55#2851C2212yes—
56#2851C2212yes—
57#2851C2212yes—
58#2844C2212yes—
59#2822C2212yes—
60#2822C2212yes—
61#2822C2212yes—
62#2810C2212yes—
63#2810C2212yes—
64#2809C2212yes—
65#2790C2214yes—
66#2789C2214yes—
67#2788C2214yes—
68#2782C2214yes—
69#2776C2214yes—
70#2770C2214yes—
71#2767C2214yes—
72#2767C2214yes—
73#2763C2214yes—
74#2758C2214yes—
75#2746C2214yes—
76#2745C2214yes—
77#2744C2214yes—
78#2739C2214yes—
79#2734C2212yes—
80#2729C2214yes—
81#2726C2212yes—
82#2726C2212yes—
83#2724C2212yes—
84#2722C2214yes—
85#2720C2214yes—
86#2720C2214yes—
87#2719C2214yes—
88#2719C2214yes—
89#2719C2214yes—
90#2708C2214yes—
91#2698C2214yes—
92#2698C2214yes—
93#2695C2214yes—
94#2690C2214yes—
95#2689C2214yes—
96#2687C2214yes—
97#2683C2212yes—
98#2666C2214yes—
99#2666C2214yes—
100#2666C2214yes—
101#2666C2214yes—
102#2655C2214yes—
103#2655C2214yes—
104#2655C2214yes—
105#2652C2214yes—
106#2612C2214yes—
107#2612C2214yes—
108#2609C2214yes—
109#2605C2214yes—
110#2599C2214yes—
111#2588C2214yes—
112#2588C2214yes—
113#2577C2214yes—
114#2577C2214yes—
115#2575C2214yes—
116#2575C2214yes—
117#2574C2214yes—
118#2574C2214yes—
119#2570C2214yes—
120#2570C2212yes—
121#2570C2212yes—
122#2570C2212yes—
123#2570C2212yes—
124#2567C2212yes—
125#2550C2212yes—
126#2550C2212yes—
127#2546C2212yes—
128#2533C2214yes—
129#2530C2214yes—
130#2528C2214yes—
131#2528C2214yes—
132#2528C2214yes—
133#2524C2214yes—
134#2524C2214yes—
135#2524C2214yes—
136#2524C2214yes—
137#2520C2214yes—
138#2520C2214yes—
139#2520C2214yes—
140#2520C2214yes—
141#2520C2214yes—
142#2520C2214yes—
143#2517C2214yes—
144#2515C2214yes—
145#2515C2214yes—
146#2511C2214yes—
147#2509C2212yes—
148#2509C2212yes—
149#2509C2212yes—
150#2509C2212yes—
151#2508C2212yes—
152#2508C2212yes—
153#2508C2212yes—
154#2508C2212yes—
155#2507C2212yes—
156#2507C2212yes—
157#2506C2212yes—
158#2506C2212yes—
159#2497C2212yes—
160#2497C2212yes—
161#2496C2212yes—
162#2496C2212yes—
163#2495C2212yes—
164#2495C2212yes—
165#2494C2212yes—
166#2494C2212yes—
167#2493C2214yes—
168#2489C2214yes—
169#2489C2214yes—
170#2487C2212yes—
171#2486C2212yes—
172#2485C2212yes—
173#2485C2212yes—
174#2478C2214yes—
175#2477C2214yes—
176#2475C2214yes—
177#2475C2214yes—
178#2475C2214yes—
179#2468C2214yes—
180#2462C2214yes—
181#2460C2214yes—
182#2450C2214yes—
183#2450C2214yes—
184#2446C2214yes—
185#2442C2212yes—
186#2442C2212yes—
187#2440C2212yes—
188#2440C2212yes—
189#2440C2212yes—
190#2440C2212yes—
191#2439C2212yes—
192#2439C2212yes—
193#2438C2214yes—
194#2438C2214yes—
195#2419C2214yes—
196#2382C2212yes—
197#2382C2212yes—
198#2379C2212yes—
199#2373C2214yes—
200#2373C2214yes—
201#2371C2214yes—
202#2369C2212yes—
203#2368C2214yes—
204#2368C2214yes—
205#2365C2212yes—
206#2365C2214yes—
207#2362C2214yes—
208#2359C2214yes—
209#2355C2214yes—
210#2352C2212yes—
211#2352C2212yes—
212#2347C2212yes—
213#2346C2212yes—
214#2345C2212yes—
215#2344C2212yes—
216#2343C2214yes—
217#2336C2214yes—
218#2335C2214yes—
219#2334C2214yes—
220#2334C2214yes—
221#2331C2214yes—
222#2329C2214yes—
223#2329C2214yes—
224#2323C2214yes—
225C4×#125C2212yes—
226C4×#125C2212yes—
227C4×#125C2212yes—
228C4×#125C2212yes—
229C4×#125C2212yes—
230C4×#125C2212yes—
231C4×#125C2212yes—
232C4×#125C2212yes—
233C4×#125C2212yes—
234C4×#125C2212yes—
235C4×#125C2211yescharacteristic
236C4×#125C2211yescharacteristic
237C4×#126C2212yes—
238C4×#126C2212yes—
239C4×#124C2211yescharacteristic
240C4×#124C2211yescharacteristic
241C4×C22⋊Q8C2211yescharacteristic
242C4×C22⋊Q8C2211yescharacteristic
243C4×#123C2212yes—
244C4×#123C2212yes—
245C4×#121C2211yescharacteristic
246C4×#121C2211yescharacteristic
247#2298C2212yes—
248#2296C2212yes—
249#2296C2212yes—
250#2296C2212yes—
251#2296C2212yes—
252#2295C2211yescharacteristic
253#2293C2211yescharacteristic
254#2290C2212yes—
255#2285C2211yescharacteristic
256#2285C2211yescharacteristic
257#2285C2211yescharacteristic
258#2285C2211yescharacteristic
259#2283C2212yes—
260#2283C2211yescharacteristic
261C2×#382C2212yes—
262C42×Q8C2211yescharacteristic
263C42×D4C2211yescharacteristic
264C42×D4C2212yes—
265C4×#117C2212yes—
266C2×C43C2211yescharacteristic
267#563—216no—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271#529—28no—
272C2×#126C2312yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#125C2312yes—
276C2×#125C2311yescharacteristic
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#125C2314yes—
286C2×#124C2311yescharacteristic
287C2×#123C2314yes—
288C2×#123C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2311yescharacteristic
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×#121C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2314yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×D4C2312yes—
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2312yes—
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2312yes—
304C2×C4×D4C2311yescharacteristic
305C2×#117C2312yes—
306C2×#117C2312yes—
307C2×#117C2314yes—
308C2×#117C2312yes—
309C2×#117C2312yes—
310C2×#117C2312yes—
311C2×#117C2312yes—
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2312yes—
314C22×C42C2311yescharacteristic
315C22×C42C2311yescharacteristic
316C22×C42C2312yes—
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321C22×C42C2311yescharacteristic
322#401C2314yes—
323#401C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#399C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
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#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#394C2314yes—
399#394C2314yes—
400#393C2314yes—
401#393C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2311yescharacteristic
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2311yescharacteristic
417#390C2311yescharacteristic
418#390C2311yescharacteristic
419#389C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2312yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2311yescharacteristic
437#389C2311yescharacteristic
438#389C2312yes—
439#389C2311yescharacteristic
440#389C2311yescharacteristic
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2314yes—
446#389C2314yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2314yes—
454#389C2314yes—
455#389C2312yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#388C2312yes—
477#388C2312yes—
478#388C2312yes—
479#388C2312yes—
480#388C2312yes—
481#388C2312yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2312yes—
497#388C2312yes—
498#387C2312yes—
499#387C2312yes—
500#387C2312yes—
501#387C2312yes—
502#387C2312yes—
503#387C2312yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2312yes—
525#387C2312yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
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#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2312yes—
576#386C2312yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2312yes—
596#385C2314yes—
597#385C2312yes—
598#384C2314yes—
599#384C2311yescharacteristic
600#384C2311yescharacteristic
601#384C2311yescharacteristic
602#384C2311yescharacteristic
603#384C2311yescharacteristic
604#384C2311yescharacteristic
605#384C2311yescharacteristic
606#384C2311yescharacteristic
607#383C2312yes—
608#383C2314yes—
609#383C2314yes—
610#383C2314yes—
611#383C2314yes—
612#382C2311yescharacteristic
613#382C2312yes—
614#382C2312yes—
615#382C2312yes—
616#382C2312yes—
617#382C2312yes—
618#382C2312yes—
619#382C2312yes—
620#382C2312yes—
621#382C2312yes—
622#382C2312yes—
623#382C2311yescharacteristic
624#382C2312yes—
625#382C2312yes—
626#382C2312yes—
627#382C2312yes—
628#382C2314yes—
629#382C2314yes—
630#382C2314yes—
631#382C2314yes—
632#382C2314yes—
633#382C2314yes—
634#382C2312yes—
635#382C2312yes—
636#382C2314yes—
637#381C2314yes—
638#381C2314yes—
639#381C2314yes—
640#381C2312yes—
641#380C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2314yes—
645#380C2314yes—
646#380C2312yes—
647#380C2312yes—
648#380C2312yes—
649#380C2312yes—
650#380C2312yes—
651#380C2312yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2311yescharacteristic
659#380C2311yescharacteristic
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2311yescharacteristic
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2311yescharacteristic
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2314yes—
717C4×C22⋊C4C2314yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2312yes—
721#376C2314yes—
722#376C2314yes—
723#376C2312yes—
724#376C2312yes—
725C2×#95C2314yes—
726C2×#95C2314yes—
727C43C2311yescharacteristic
728C43C2311yescharacteristic
729C43C2311yescharacteristic
730C43C2311yescharacteristic
731C43C2312yes—
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C22×Q8C2414yes—
737C22×Q8C2414yes—
738C22×Q8C2411yescharacteristic
739C22×D4C2412yes—
740C22×D4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2411yescharacteristic
743C23×C4C2412yes—
744C23×C4C2411yescharacteristic
745C23×C4C2411yescharacteristic
746C23×C4C2411yescharacteristic
747C23×C4C2411yescharacteristic
748C23×C4C2414yes—
749C23×C4C2412yes—
750C23×C4C2411yescharacteristic
751C23×C4C2414yes—
752C23×C4C2411yescharacteristic
753C4⋊Q8—216no—
754C4⋊Q8—44no—
755C4⋊Q8—44no—
756#126—28no—
757#126—216no—
758#126—216no—
759#125—24no—
760#125—28no—
761#125—28no—
762#125—28no—
763#125—44no—
764#125—44no—
765#125—44no—
766#125—44no—
767#125—44no—
768#125—48no—
769#125—48no—
770#124#4118yes—
771#123—216no—
772#123—28no—
773C22⋊Q8—24no—
774C22⋊Q8—216no—
775C22⋊Q8—216no—
776C22⋊Q8—48no—
777C22⋊Q8—48no—
778#121—24no—
779C4×Q8—24no—
780C4×Q8—42no—
781C4×Q8—42no—
782C4×Q8—48no—
783C4×D4—24no—
784C4×D4—28no—
785C4×D4—28no—
786C4×D4—42no—
787C4×D4—42no—
788C4×D4—44no—
789#117—28no—
790#117—28no—
791#117—44no—
792#117—44no—
793#117—48no—
794#117—44no—
795#117—44no—
796C2×C4⋊C4—44no—
797C2×C4⋊C4—44no—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C42—24no—
894C2×C42—24no—
895C2×C42—24no—
896C2×C42—28no—
897C2×C42—42no—
898C2×C42—42no—
899C2×C42—42no—
900C2×C42—42no—
901C2×C42C2414yes—
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2414yes—
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915C2×C42C2411yescharacteristic
916C2×C42C2414yes—
917C2×C42C2411yescharacteristic
918C2×C42C2411yescharacteristic
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923C2×C42C2411yescharacteristic
924C2×C42C2411yescharacteristic
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
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#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
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—
1023#95C2414yes—
1024C24C2512yes—
1025C24C2511yescharacteristic
1026C2×Q8—28no—
1027C2×Q8—41no—
1028C2×Q8—41no—
1029C2×Q8—44no—
1030C2×Q8—44no—
1031C2×Q8—44no—
1032C2×Q8—44no—
1033C2×Q8—44no—
1034C2×Q8C2×#4114yes—
1035C2×D4—24no—
1036C2×D4—24no—
1037C2×D4—41no—
1038C2×D4—41no—
1039C2×D4—42no—
1040C2×D4C2×#4114yes—
1041C22×C4—22no—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—22no—
1046C22×C4—24no—
1047C22×C4—22no—
1048C22×C4—28no—
1049C22×C4—22no—
1050C22×C4—22no—
1051C22×C4—22no—
1052C22×C4—22no—
1053C22×C4—22no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—22no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—41no—
1061C22×C4—41no—
1062C22×C4—41no—
1063C22×C4—41no—
1064C22×C4—41no—
1065C22×C4—41no—
1066C22×C4—41no—
1067C22×C4—41no—
1068C22×C4—42no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C42−1+414yes—
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2514yes—
1086C22×C4C2514yes—
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2514yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2511yescharacteristic
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2511yescharacteristic
1097C22×C4C2511yescharacteristic
1098C22×C4C2511yescharacteristic
1099C22×C4C2511yescharacteristic
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2511yescharacteristic
1105C22×C4C2511yescharacteristic
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—22no—
1109C4⋊C4—24no—
1110C4⋊C4—22no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—28no—
1115C4⋊C4—28no—
1116C4⋊C4—28no—
1117C4⋊C4—28no—
1118C4⋊C4—28no—
1119C4⋊C4—28no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—28no—
1126C4⋊C4—28no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—28no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—28no—
1141C4⋊C4—28no—
1142C4⋊C4—24no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—41no—
1150C4⋊C4—41no—
1151C4⋊C4—41no—
1152C4⋊C4—41no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—28no—
1181C22⋊C4—28no—
1182C22⋊C4—28no—
1183C22⋊C4—28no—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—24no—
1188C22⋊C4—24no—
1189C22⋊C4—24no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4C2×#4118yes—
1200C22⋊C4C2×#4118yes—
1201C42—22no—
1202C42—22no—
1203C42—22no—
1204C42—24no—
1205C42—28no—
1206C42—22no—
1207C42—22no—
1208C42—22no—
1209C42—22no—
1210C42—22no—
1211C42—22no—
1212C42—22no—
1213C42—24no—
1214C42—24no—
1215C42—24no—
1216C42—28no—
1217C42—24no—
1218C42—22no—
1219C42—22no—
1220C42—22no—
1221C42—22no—
1222C42—22no—
1223C42—22no—
1224C42—22no—
1225C42—22no—
1226C42—28no—
1227C42—24no—
1228C42—41no—
1229C42—41no—
1230C42—41no—
1231C42—41no—
1232C42—41no—
1233C42—41no—
1234C42—41no—
1235C42—41no—
1236C42—42no—
1237C42—44no—
1238C42—44no—
1239C42—44no—
1240C42—42no—
1241C42—42no—
1242C42—44no—
1243C42—44no—
1244C42—44no—
1245C42—44no—
1246C42C2×#4114yes—
1247C422−1+414yes—
1248C23—21no—
1249C23—22no—
1250C23—21no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—21no—
1256C23—21no—
1257C23—21no—
1258C23—21no—
1259C23—22no—
1260C23C22×#4114yes—
1261C23C2×2−1+412yes—
1262C23C2611yescharacteristic
1263Q8—44no—
1264Q8—88no—
1265Q8—164no—
1266D4—44no—
1267D4—48no—
1268C2×C4—28no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—22no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—22no—
1288C2×C4—21no—
1289C2×C4—28no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—21no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—24no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—21no—
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—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—44no—
1345C2×C4—44no—
1346C2×C4—48no—
1347C2×C4—44no—
1348C2×C4—44no—
1349C2×C4—44no—
1350C2×C4—48no—
1351C2×C4—84no—
1352C2×C4—88no—
1353C2×C4—164no—
1354C2×C4C22×#4114yes—
1355C2×C4C22×#4112yes—
1356C2×C4C22×#4112yes—
1357C2×C4C22×#4112yes—
1358C2×C4C2×2−1+412yes—
1359C2×C4C2×2−1+412yes—
1360C2×C4C2×2−1+412yes—
1361C2×C4C2×2−1+412yes—
1362C2×C4C2×2−1+412yes—
1363C2×C4#58512yes—
1364C2×C4#58512yes—
1365C2×C4#58512yes—
1366C2×C4#58512yes—
1367C22—22no—
1368C22—24no—
1369C22—22no—
1370C22—24no—
1371C22—24no—
1372C22—22no—
1373C22—42no—
1374C22—41no—
1375C22—42no—
1376C22—41no—
1377C22—41no—
1378C22—42no—
1379C22—41no—
1380C22—42no—
1381C22C23×#4111yescharacteristic
1382C22C22×2−1+411yescharacteristic
1383C22C22×2−1+411yescharacteristic
1384C22C2×#58511yescharacteristic
1385C22C2×#58511yescharacteristic
1386C22C2×#58511yescharacteristic
1387C22C2×#58511yescharacteristic
1388C4—22no—
1389C4—22no—
1390C4—22no—
1391C4—22no—
1392C4—24no—
1393C4—22no—
1394C4—22no—
1395C4—22no—
1396C4—22no—
1397C4—22no—
1398C4—42no—
1399C4—44no—
1400C4—42no—
1401C4—41no—
1402C4—44no—
1403C4—44no—
1404C4—44no—
1405C4—44no—
1406C4—42no—
1407C4—41no—
1408C4—42no—
1409C4—42no—
1410C4—44no—
1411C4—41no—
1412C4—41no—
1413C4—44no—
1414C4—44no—
1415C4—42no—
1416C4#356314yes—
1417C2—42no—
1418C2—44no—
1419C2C2×#356311yescharacteristic
1420C2#6275211yescharacteristic
1421C2#6278111yescharacteristic
1422C2#6280511yescharacteristic
1423C2#6280511yescharacteristic
1424C2#6282511yescharacteristic
1425C2#6284111yescharacteristic
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. #59616C2semidirect
2. #59295C2semidirect
3. #59294C2semidirect
4. #46157C2semidirect
5. #46157C2semidirect
6. #46152C2semidirect
7. #46147C2semidirect
8. #46143C2semidirect
10. #40472C2semidirect
11. #40096C2semidirect
12. #40051C2semidirect
14. #39987C2semidirect
15. #38808C2semidirect
16. #38801C2semidirect
17. #38790C2semidirect
19. #38647C2semidirect
20. #37603C2semidirect
21. #36939C2semidirect
22. #36640C2semidirect
23. #36640C2semidirect
24. #36556C2semidirect
25. #36201C2semidirect
26. #36191C2semidirect
27. #36171C2semidirect
28. #35142C2semidirect
29. #35132C2semidirect
30. #34528C2semidirect

Maximal subgroups

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

subgroupindex
#596162
#592952
#592942
#461572
#461522
#461472
#461432
#461322
#404722
#400962
#400512
#400102
#399872
#388082
#388012
#387902
#387812
#386472
#376032
#369392
#366402
#365562
#362012
#361912
#361712
#351422
#351322
#345282
C4×#5292