Finite Group Databasebeta

← #7710290

Subgroups — #7710290

Order 512.

4470 conjugacy classes of subgroups.

The subgroup lattice has 1489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59898C214yesmaximal, complemented
2#59709C212yesmaximal, complemented
3#59474C212yesmaximal, complemented
4#46246C212yesmaximal, complemented
5#46244C212yesmaximal, complemented
6#46158C211yesmaximal, characteristic, complemented
7#46022C211yesmaximal, characteristic, complemented
8#46016C211yesmaximal, characteristic, complemented
9#46014C211yesmaximal, characteristic, complemented
10#40019C214yesmaximal, complemented
11#39838C212yesmaximal, complemented
12#39837C212yesmaximal, complemented
13#39795C212yesmaximal, complemented
14#39792C212yesmaximal, complemented
15#39530C212yesmaximal, complemented
16#39528C212yesmaximal, complemented
17#39517C214yesmaximal, complemented
18#38475C212yesmaximal, complemented
19#38472C212yesmaximal, complemented
20#37541C212yesmaximal, complemented
21#36773C214yesmaximal, complemented
22#36635C211yesmaximal, characteristic, complemented
23#36631C211yesmaximal, characteristic, complemented
24#36503C212yesmaximal, complemented
25#36395C212yesmaximal, complemented
26#36392C212yesmaximal, complemented
27#36379C212yesmaximal, complemented
28#35110C212yesmaximal, complemented
29#35038C212yesmaximal, complemented
30#34405C212yesmaximal, complemented
31C4×#529C211yesmaximal, characteristic, complemented
32C2×#529C2212yes—
33C2×#529C2211yescharacteristic
34#2864C2212yes—
35#2863C2212yes—
36#2863C2212yes—
37#2862C2211yescharacteristic
38#2861C2212yes—
39#2861C2212yes—
40#2860C2212yes—
41#2860C2212yes—
42#2860C2212yes—
43#2859C2211yescharacteristic
44#2859C2211yescharacteristic
45#2858C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2856C2211yescharacteristic
50#2855C2212yes—
51#2855C2212yes—
52#2855C2212yes—
53#2854C2212yes—
54#2854C2212yes—
55#2851C2212yes—
56#2851C2212yes—
57#2850C2212yes—
58#2822C2212yes—
59#2820C2212yes—
60#2820C2212yes—
61#2819C2212yes—
62#2809C2212yes—
63#2805C2212yes—
64#2805C2212yes—
65#2804C2212yes—
66#2803C2214yes—
67#2801C2214yes—
68#2798C2214yes—
69#2797C2214yes—
70#2789C2214yes—
71#2787C2214yes—
72#2779C2214yes—
73#2778C2214yes—
74#2778C2214yes—
75#2773C2214yes—
76#2773C2214yes—
77#2772C2214yes—
78#2766C2214yes—
79#2765C2214yes—
80#2762C2214yes—
81#2757C2214yes—
82#2753C2214yes—
83#2752C2214yes—
84#2750C2214yes—
85#2746C2214yes—
86#2745C2214yes—
87#2740C2214yes—
88#2733C2212yes—
89#2730C2214yes—
90#2727C2212yes—
91#2727C2212yes—
92#2725C2214yes—
93#2724C2212yes—
94#2723C2214yes—
95#2715C2214yes—
96#2712C2214yes—
97#2707C2214yes—
98#2663C2214yes—
99#2661C2214yes—
100#2655C2214yes—
101#2648C2214yes—
102#2638C2214yes—
103#2635C2214yes—
104#2630C2214yes—
105#2630C2214yes—
106#2604C2214yes—
107#2604C2214yes—
108#2603C2214yes—
109#2601C2214yes—
110#2601C2214yes—
111#2600C2214yes—
112#2599C2214yes—
113#2598C2214yes—
114#2597C2214yes—
115#2596C2214yes—
116#2595C2214yes—
117#2594C2214yes—
118#2594C2214yes—
119#2594C2214yes—
120#2594C2214yes—
121#2593C2214yes—
122#2592C2212yes—
123#2584C2212yes—
124#2578C2214yes—
125#2577C2214yes—
126#2576C2214yes—
127#2576C2214yes—
128#2575C2214yes—
129#2566C2212yes—
130#2565C2212yes—
131#2562C2212yes—
132#2559C2214yes—
133#2554C2214yes—
134#2550C2212yes—
135#2550C2212yes—
136#2536C2212yes—
137#2530C2214yes—
138#2530C2214yes—
139#2528C2214yes—
140#2527C2214yes—
141#2527C2214yes—
142#2527C2214yes—
143#2526C2214yes—
144#2525C2214yes—
145#2525C2214yes—
146#2522C2214yes—
147#2521C2214yes—
148#2520C2214yes—
149#2518C2214yes—
150#2516C2214yes—
151#2516C2214yes—
152#2514C2212yes—
153#2514C2212yes—
154#2513C2212yes—
155#2512C2212yes—
156#2511C2212yes—
157#2509C2214yes—
158#2505C2214yes—
159#2497C2212yes—
160#2496C2212yes—
161#2494C2212yes—
162#2494C2212yes—
163#2494C2214yes—
164#2492C2212yes—
165#2491C2212yes—
166#2490C2212yes—
167#2490C2212yes—
168#2489C2212yes—
169#2489C2212yes—
170#2485C2212yes—
171#2479C2214yes—
172#2474C2214yes—
173#2469C2214yes—
174#2468C2214yes—
175#2467C2214yes—
176#2467C2214yes—
177#2466C2214yes—
178#2456C2214yes—
179#2454C2212yes—
180#2454C2212yes—
181#2453C2212yes—
182#2453C2212yes—
183#2448C2212yes—
184#2446C2212yes—
185#2445C2212yes—
186#2441C2212yes—
187#2441C2212yes—
188#2432C2212yes—
189#2431C2212yes—
190#2427C2212yes—
191#2420C2212yes—
192#2419C2214yes—
193#2414C2212yes—
194#2407C2212yes—
195#2407C2212yes—
196#2382C2212yes—
197#2382C2212yes—
198#2379C2212yes—
199#2379C2212yes—
200#2373C2214yes—
201#2373C2214yes—
202#2373C2214yes—
203#2373C2214yes—
204#2370C2212yes—
205#2370C2212yes—
206#2367C2212yes—
207#2367C2214yes—
208#2362C2212yes—
209#2357C2212yes—
210#2356C2214yes—
211#2353C2214yes—
212#2353C2214yes—
213#2347C2214yes—
214#2346C2212yes—
215#2343C2214yes—
216#2341C2212yes—
217#2339C2212yes—
218#2335C2214yes—
219#2335C2214yes—
220#2335C2214yes—
221#2334C2214yes—
222#2333C2214yes—
223#2332C2214yes—
224#2319C2214yes—
225#2318C2214yes—
226C4×C4⋊Q8C2211yescharacteristic
227C4×C4⋊Q8C2211yescharacteristic
228C4×C4⋊Q8C2211yescharacteristic
229C4×#127C2211yescharacteristic
230C4×#125C2212yes—
231C4×#125C2212yes—
232C4×#125C2211yescharacteristic
233C4×#125C2211yescharacteristic
234C4×#126C2212yes—
235C4×#126C2212yes—
236C4×#124C2212yes—
237C4×#124C2211yescharacteristic
238C4×#124C2211yescharacteristic
239C4×C22⋊Q8C2212yes—
240C4×C22⋊Q8C2212yes—
241C4×C22⋊Q8C2211yescharacteristic
242C4×C22⋊Q8C2211yescharacteristic
243C4×#123C2212yes—
244C4×#123C2212yes—
245C4×#121C2212yes—
246C4×#121C2212yes—
247C4×#121C2212yes—
248C4×#121C2211yescharacteristic
249C4×#121C2211yescharacteristic
250#2298C2212yes—
251#2297C2212yes—
252#2295C2212yes—
253#2295C2212yes—
254#2295C2212yes—
255#2295C2211yescharacteristic
256#2293C2212yes—
257#2293C2212yes—
258#2293C2211yescharacteristic
259#2290C2212yes—
260#2283C2212yes—
261#2283C2211yescharacteristic
262C42×Q8C2211yescharacteristic
263C42×D4C2212yes—
264C42×D4C2211yescharacteristic
265C4×#117C2212yes—
266C2×C43C2211yescharacteristic
267C22×#41C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×#127C2311yescharacteristic
272#529—216no—
273#529—28no—
274C2×#126C2312yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#125C2311yescharacteristic
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#124C2311yescharacteristic
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2314yes—
290C2×#123C2314yes—
291C2×#123C2312yes—
292C2×#123C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2311yescharacteristic
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×#121C2312yes—
299C2×#121C2311yescharacteristic
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×D4C2312yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2314yes—
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2312yes—
322C2×#117C2314yes—
323C2×#117C2312yes—
324C2×#117C2312yes—
325C2×#117C2312yes—
326C22×C42C2311yescharacteristic
327C22×C42C2311yescharacteristic
328C22×C42C2312yes—
329C22×C42C2311yescharacteristic
330C22×C42C2311yescharacteristic
331C22×C42C2311yescharacteristic
332C22×C42C2311yescharacteristic
333C22×C42C2311yescharacteristic
334#401C2314yes—
335#401C2314yes—
336#401C2314yes—
337#401C2314yes—
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#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#392C2314yes—
410#392C2314yes—
411#392C2314yes—
412#392C2314yes—
413#392C2314yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2314yes—
420#391C2314yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2314yes—
430#391C2312yes—
431#391C2311yescharacteristic
432#391C2311yescharacteristic
433#390C2312yes—
434#390C2312yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2314yes—
439#390C2314yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#390C2314yes—
444#390C2312yes—
445#390C2312yes—
446#390C2314yes—
447#390C2314yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2311yescharacteristic
453#390C2311yescharacteristic
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2311yescharacteristic
459#389C2311yescharacteristic
460#389C2311yescharacteristic
461#389C2311yescharacteristic
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#388C2312yes—
493#388C2312yes—
494#388C2312yes—
495#388C2312yes—
496#388C2312yes—
497#388C2312yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
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#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2312yes—
545#388C2312yes—
546#387C2312yes—
547#387C2312yes—
548#387C2312yes—
549#387C2312yes—
550#387C2312yes—
551#387C2312yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2312yes—
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#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2312yes—
607#386C2312yes—
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#385C2312yes—
623#385C2312yes—
624#384C2311yescharacteristic
625#384C2311yescharacteristic
626#384C2311yescharacteristic
627#384C2311yescharacteristic
628#383C2312yes—
629#383C2314yes—
630#383C2314yes—
631#383C2314yes—
632#382C2312yes—
633#382C2312yes—
634#382C2311yescharacteristic
635#382C2311yescharacteristic
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2314yes—
640#382C2314yes—
641#382C2314yes—
642#382C2312yes—
643#381C2312yes—
644#381C2314yes—
645#381C2314yes—
646#381C2314yes—
647#381C2314yes—
648#381C2314yes—
649#380C2312yes—
650#380C2312yes—
651#380C2312yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2314yes—
657#380C2311yescharacteristic
658#380C2311yescharacteristic
659#380C2314yes—
660#380C2312yes—
661#380C2314yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2312yes—
721#376C2314yes—
722#376C2314yes—
723#376C2314yes—
724#376C2312yes—
725#376C2312yes—
726C2×#95C2314yes—
727C43C2311yescharacteristic
728C43C2311yescharacteristic
729C43C2311yescharacteristic
730C43C2311yescharacteristic
731C43C2312yes—
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C2×#41—44no—
737C2×#41—44no—
738C2×#41—44no—
739C22×Q8C2412yes—
740C22×Q8C2411yescharacteristic
741C22×Q8C2412yes—
742C22×Q8C2412yes—
743C22×D4C2412yes—
744C22×D4C2412yes—
745C22×D4C2411yescharacteristic
746C22×D4C2414yes—
747C22×D4C2412yes—
748C22×D4C2412yes—
749C22×D4C2414yes—
750C22×D4C2414yes—
751C23×C4C2412yes—
752C23×C4C2411yescharacteristic
753C23×C4C2411yescharacteristic
754C23×C4C2412yes—
755C23×C4C2414yes—
756C23×C4C2412yes—
757C23×C4C2411yescharacteristic
758C23×C4C2414yes—
759C23×C4C2414yes—
760C23×C4C2411yescharacteristic
761C23×C4C2411yescharacteristic
762C23×C4C2411yescharacteristic
763C23×C4C2411yescharacteristic
764C4⋊Q8—42no—
765C4⋊Q8—42no—
766C4⋊Q8—42no—
767#127—42no—
768#126—216no—
769#126—28no—
770#126—48no—
771#126—48no—
772#126—48no—
773#125—24no—
774#125—28no—
775#125—44no—
776#125—44no—
777#125—44no—
778#125—44no—
779#124—24no—
780#124—28no—
781#124—44no—
782#124—44no—
783#124—48no—
784#123—28no—
785#123—216no—
786#123—48no—
787C22⋊Q8—28no—
788C22⋊Q8—24no—
789C22⋊Q8—44no—
790C22⋊Q8—44no—
791C22⋊Q8—44no—
792#121—28no—
793#121—24no—
794#121—44no—
795#121—44no—
796#121—44no—
797C4×Q8—24no—
798C4×Q8—28no—
799C4×Q8—42no—
800C4×Q8—42no—
801C4×Q8—44no—
802C4×Q8—44no—
803C4×Q8—44no—
804C4×D4—28no—
805C4×D4—216no—
806C4×D4—24no—
807C4×D4—28no—
808C4×D4—44no—
809C4×D4—44no—
810C4×D4—44no—
811C4×D4—42no—
812C4×D4—42no—
813C4×D4—44no—
814C4×D4—48no—
815C4×D4—44no—
816#117—216no—
817#117—28no—
818#117—44no—
819#117—44no—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C42—44no—
921C2×C42—42no—
922C2×C42—42no—
923C2×C42—42no—
924C2×C42—42no—
925C2×C42—42no—
926C2×C42—42no—
927C2×C42#4118yescomplemented
928C2×C42C2411yescharacteristic
929C2×C42C2412yes—
930C2×C42C2414yes—
931C2×C42C2411yescharacteristic
932C2×C42C2411yescharacteristic
933C2×C42C2412yes—
934C2×C42C2411yescharacteristic
935C2×C42C2411yescharacteristic
936C2×C42C2412yes—
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945C2×C42C2411yescharacteristic
946C2×C42C2412yes—
947C2×C42C2414yes—
948C2×C42C2412yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2411yescharacteristic
957C2×C42C2411yescharacteristic
958C2×C42C2411yescharacteristic
959C2×C42C2411yescharacteristic
960C2×C42C2411yescharacteristic
961C2×C42C2411yescharacteristic
962C2×C42C2411yescharacteristic
963C2×C42C2411yescharacteristic
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2411yescharacteristic
971C2×C42C2411yescharacteristic
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
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#95C2412yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038C24C2512yes—
1039C24C2514yes—
1040C24C2511yescharacteristic
1041#41—816no—
1042C2×Q8—22no—
1043C2×Q8—24no—
1044C2×Q8—24no—
1045C2×Q8—24no—
1046C2×Q8—24no—
1047C2×Q8—24no—
1048C2×Q8—41no—
1049C2×Q8—41no—
1050C2×Q8—42no—
1051C2×Q8—42no—
1052C2×Q8—42no—
1053C2×Q8—42no—
1054C2×D4—24no—
1055C2×D4—28no—
1056C2×D4—22no—
1057C2×D4—24no—
1058C2×D4—24no—
1059C2×D4—24no—
1060C2×D4—24no—
1061C2×D4—24no—
1062C2×D4—41no—
1063C2×D4—41no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—44no—
1067C2×D4—42no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—42no—
1072C2×D4—44no—
1073C2×D4—42no—
1074C2×D4—42no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C22×C4—24no—
1079C22×C4—22no—
1080C22×C4—22no—
1081C22×C4—22no—
1082C22×C4—22no—
1083C22×C4—22no—
1084C22×C4—22no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—28no—
1089C22×C4—24no—
1090C22×C4—41no—
1091C22×C4—41no—
1092C22×C4—41no—
1093C22×C4—41no—
1094C22×C4—41no—
1095C22×C4—42no—
1096C22×C4—41no—
1097C22×C4—41no—
1098C22×C4—41no—
1099C22×C4—41no—
1100C22×C4—41no—
1101C22×C4—41no—
1102C22×C4—41no—
1103C22×C4—42no—
1104C22×C4—42no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—42no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4C2×#4114yes—
1115C22×C4C2×#4114yes—
1116C22×C4C2×#4114yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2514yes—
1120C22×C4C2514yes—
1121C22×C4C2511yescharacteristic
1122C22×C4C2511yescharacteristic
1123C22×C4C2511yescharacteristic
1124C22×C4C2511yescharacteristic
1125C22×C4C2512yes—
1126C22×C4C2514yes—
1127C22×C4C2512yes—
1128C22×C4C2514yes—
1129C22×C4C2512yes—
1130C22×C4C2514yes—
1131C22×C4C2514yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2514yes—
1135C22×C4C2511yescharacteristic
1136C22×C4C2511yescharacteristic
1137C22×C4C2511yescharacteristic
1138C22×C4C2511yescharacteristic
1139C22×C4C2511yescharacteristic
1140C22×C4C2511yescharacteristic
1141C22×C4C2511yescharacteristic
1142C22×C4C2511yescharacteristic
1143C22×C4C2511yescharacteristic
1144C22×C4C2511yescharacteristic
1145C4⋊C4—28no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—28no—
1149C4⋊C4—22no—
1150C4⋊C4—24no—
1151C4⋊C4—28no—
1152C4⋊C4—24no—
1153C4⋊C4—22no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—28no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—28no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—28no—
1169C4⋊C4—42no—
1170C4⋊C4—41no—
1171C4⋊C4—41no—
1172C4⋊C4—42no—
1173C4⋊C4—41no—
1174C4⋊C4—41no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—42no—
1198C4⋊C4—42no—
1199C4⋊C4—42no—
1200C4⋊C4—42no—
1201C22⋊C4—24no—
1202C22⋊C4—28no—
1203C22⋊C4—28no—
1204C22⋊C4—24no—
1205C22⋊C4—24no—
1206C22⋊C4—28no—
1207C22⋊C4—24no—
1208C22⋊C4—28no—
1209C22⋊C4—28no—
1210C22⋊C4—24no—
1211C22⋊C4—24no—
1212C22⋊C4—28no—
1213C22⋊C4—24no—
1214C22⋊C4—28no—
1215C22⋊C4—42no—
1216C22⋊C4—44no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—44no—
1224C22⋊C4—42no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C42—28no—
1246C42—24no—
1247C42—22no—
1248C42—22no—
1249C42—22no—
1250C42—22no—
1251C42—22no—
1252C42—22no—
1253C42—24no—
1254C42—22no—
1255C42—22no—
1256C42—22no—
1257C42—22no—
1258C42—22no—
1259C42—22no—
1260C42—24no—
1261C42—24no—
1262C42—24no—
1263C42—41no—
1264C42—41no—
1265C42—41no—
1266C42—41no—
1267C42—41no—
1268C42—42no—
1269C42—42no—
1270C42—41no—
1271C42—41no—
1272C42—41no—
1273C42—41no—
1274C42—41no—
1275C42—41no—
1276C42—41no—
1277C42—42no—
1278C42—44no—
1279C42—42no—
1280C42—44no—
1281C42—44no—
1282C42—44no—
1283C42—44no—
1284C42—44no—
1285C42—44no—
1286C42—44no—
1287C42C2×#4114yes—
1288C42C2×#4114yes—
1289C42C2×#4114yes—
1290C42C2×#4114yes—
1291C23—21no—
1292C23—21no—
1293C23—21no—
1294C23—21no—
1295C23—21no—
1296C23—21no—
1297C23—22no—
1298C23—24no—
1299C23—22no—
1300C23—24no—
1301C23—22no—
1302C23—24no—
1303C23—24no—
1304C23—22no—
1305C23—22no—
1306C23—24no—
1307C23—22no—
1308C23—24no—
1309C23—22no—
1310C23—24no—
1311C23C22×#4112yes—
1312C23C2611yescharacteristic
1313Q8—44no—
1314Q8—48no—
1315Q8—84no—
1316Q8—84no—
1317D4—44no—
1318D4—48no—
1319D4—48no—
1320D4—84no—
1321D4—84no—
1322D4—88no—
1323D4—88no—
1324D4—88no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—22no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—22no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—24no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—24no—
1383C2×C4—24no—
1384C2×C4—24no—
1385C2×C4—24no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—24no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—24no—
1395C2×C4—24no—
1396C2×C4—24no—
1397C2×C4—44no—
1398C2×C4—44no—
1399C2×C4—44no—
1400C2×C4—44no—
1401C2×C4—44no—
1402C2×C4—48no—
1403C2×C4—44no—
1404C2×C4—44no—
1405C2×C4—48no—
1406C2×C4—88no—
1407C2×C4—84no—
1408C2×C4—88no—
1409C2×C4—164no—
1410C2×C4C22×#4112yes—
1411C2×C4C22×#4112yes—
1412C2×C4C22×#4112yes—
1413C2×C4C22×#4112yes—
1414C2×C4C22×#4112yes—
1415C2×C4C22×#4112yes—
1416C2×C4#58512yes—
1417C2×C4#58512yes—
1418C2×C4#58512yes—
1419C2×C4#58512yes—
1420C2×C4#58512yes—
1421C2×C4#58512yes—
1422C22—22no—
1423C22—22no—
1424C22—22no—
1425C22—41no—
1426C22—41no—
1427C22—41no—
1428C22—41no—
1429C22—42no—
1430C22—44no—
1431C22—42no—
1432C22—44no—
1433C22—42no—
1434C22—44no—
1435C22—42no—
1436C22—42no—
1437C22—44no—
1438C22—44no—
1439C22—42no—
1440C22—44no—
1441C22—42no—
1442C22—44no—
1443C22C23×#4111yescharacteristic
1444C22C2×#58511yescharacteristic
1445C22C2×#58511yescharacteristic
1446C22C2×#58511yescharacteristic
1447C22C2×#58511yescharacteristic
1448C22C2×#58511yescharacteristic
1449C22C2×#58511yescharacteristic
1450C4—22no—
1451C4—22no—
1452C4—22no—
1453C4—22no—
1454C4—22no—
1455C4—22no—
1456C4—22no—
1457C4—22no—
1458C4—22no—
1459C4—41no—
1460C4—42no—
1461C4—44no—
1462C4—42no—
1463C4—41no—
1464C4—44no—
1465C4—42no—
1466C4—44no—
1467C4—42no—
1468C4—44no—
1469C4—42no—
1470C4—44no—
1471C4—42no—
1472C4—44no—
1473C4—42no—
1474C4—44no—
1475C4—41no—
1476C4—41no—
1477C4#356814yes—
1478C2—42no—
1479C2—82no—
1480C2—84no—
1481C2C2×#356811yescharacteristic
1482C2#6274311yescharacteristic
1483C2#6281511yescharacteristic
1484C2#6281511yescharacteristic
1485C2#6281511yescharacteristic
1486C2#6282811yescharacteristic
1487C2#6284011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59898C2semidirect
2. #59709C2semidirect
3. #59474C2semidirect
4. #46246C2semidirect
5. #46244C2semidirect
6. #46158C2semidirect
7. #46022C2semidirect
8. #46016C2semidirect
9. #46014C2semidirect
10. #40019C2semidirect
11. #39838C2semidirect
12. #39837C2semidirect
13. #39795C2semidirect
14. #39792C2semidirect
15. #39530C2semidirect
16. #39528C2semidirect
17. #39517C2semidirect
18. #38475C2semidirect
19. #38472C2semidirect
20. #37541C2semidirect
21. #36773C2semidirect
22. #36635C2semidirect
23. #36631C2semidirect
24. #36503C2semidirect
25. #36395C2semidirect
26. #36392C2semidirect
27. #36379C2semidirect
28. #35110C2semidirect
29. #35038C2semidirect
30. #34405C2semidirect
31. C4×#529C2semidirect
927. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#598982
#597092
#594742
#462462
#462442
#461582
#460222
#460162
#460142
#400192
#398382
#398372
#397952
#397922
#395302
#395282
#395172
#384752
#384722
#375412
#367732
#366352
#366312
#365032
#363952
#363922
#363792
#351102
#350382
#344052
C4×#5292