Finite Group Databasebeta

← #7695675

Subgroups — #7695675

Order 512.

4903 conjugacy classes of subgroups.

The subgroup lattice has 1435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59880C212yesmaximal, complemented
2#59870C211yesmaximal, characteristic, complemented
3#59618C214yesmaximal, complemented
4#59425C212yesmaximal, complemented
5#52304C212yesmaximal, complemented
6#52267C211yesmaximal, characteristic, complemented
7#45323C212yesmaximal, complemented
8#45156C212yesmaximal, complemented
9#44960C212yesmaximal, complemented
10#44867C214yesmaximal, complemented
11#44644C214yesmaximal, complemented
12#44616C214yesmaximal, complemented
13#40407C214yesmaximal, complemented
14#39820C212yesmaximal, complemented
15#39765C211yesmaximal, characteristic, complemented
16#39356C211yesmaximal, characteristic
17#38771C212yesmaximal, complemented
18#38770C212yesmaximal, complemented
19#38518C214yesmaximal, complemented
20#38083C212yesmaximal, complemented
21#36538C211yesmaximal, characteristic, complemented
22#36437C212yesmaximal, complemented
23#36037C212yesmaximal, complemented
24#35974C212yesmaximal, complemented
25#35749C212yesmaximal, complemented
26#34328C211yesmaximal, characteristic, complemented
27#34317C211yesmaximal, characteristic, complemented
28#34293C212yesmaximal, complemented
29#34268C212yesmaximal, complemented
30C2×#559C2211yescharacteristic
31C2×#557C2211yescharacteristic
32C2×#557C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#548C2212yes—
35C2×#536C2212yes—
36C2×#519C2212yes—
37C2×C4×#41C2212yes—
38#2861C2212yes—
39#2858C2211yescharacteristic
40#2853C2214yes—
41#2850C2212yes—
42#2808C2212yes—
43#2808C2212yes—
44#2807C2212yes—
45#2806C2211yescharacteristic
46#2805C2211yescharacteristic
47#2805C2212yes—
48#2805C2212yes—
49#2804C2211yescharacteristic
50#2804C2212yes—
51#2802C2212yes—
52#2793C2214yes—
53#2790C2212yes—
54#2790C2214yes—
55#2789C2214yes—
56#2788C2212yes—
57#2783C2214yes—
58#2782C2214yes—
59#2780C2212yes—
60#2772C2214yes—
61#2765C2214yes—
62#2765C2214yes—
63#2758C2214yes—
64#2757C2214yes—
65#2752C2214yes—
66#2749C2214yes—
67#2741C2214yes—
68#2732C2211yescharacteristic
69#2729C2212yes—
70#2724C2212yes—
71#2717C2214yes—
72#2707C2214yes—
73#2704C2214yes—
74#2700C2214yes—
75#2700C2214yes—
76#2694C2214yes—
77#2690C2214yes—
78#2690C2214yes—
79#2690C2214yes—
80#2683C2212yes—
81#2683C2212yes—
82#2682C2212yes—
83#2682C2212yes—
84#2654C2214yes—
85#2650C2214yes—
86#2640C2212yes—
87#2634C2214yes—
88#2621C2212yes—
89#2620C2212yes—
90#2611C2214yes—
91#2610C2214yes—
92#2605C2214yes—
93#2602C2214yes—
94#2600C2214yes—
95#2599C2214yes—
96#2597C2214yes—
97#2595C2214yes—
98#2594C2214yes—
99#2592C2212yes—
100#2589C2214yes—
101#2588C2214yes—
102#2587C2214yes—
103#2587C2214yes—
104#2581C2212yes—
105#2581C2212yes—
106#2578C2214yes—
107#2576C2214yes—
108#2576C2214yes—
109#2573C2214yes—
110#2573C2214yes—
111#2572C2214yes—
112#2571C2212yes—
113#2568C2211yescharacteristic
114#2568C2212yes—
115#2567C2212yes—
116#2566C2212yes—
117#2558C2214yes—
118#2558C2214yes—
119#2558C2214yes—
120#2556C2214yes—
121#2548C2211yescharacteristic
122#2546C2212yes—
123#2545C2212yes—
124#2545C2212yes—
125#2545C2212yes—
126#2545C2212yes—
127#2545C2212yes—
128#2532C2214yes—
129#2532C2214yes—
130#2531C2214yes—
131#2527C2214yes—
132#2526C2214yes—
133#2525C2214yes—
134#2525C2214yes—
135#2525C2214yes—
136#2525C2214yes—
137#2516C2214yes—
138#2515C2214yes—
139#2514C2212yes—
140#2514C2212yes—
141#2513C2212yes—
142#2513C2212yes—
143#2511C2214yes—
144#2509C2214yes—
145#2504C2212yes—
146#2503C2212yes—
147#2493C2214yes—
148#2493C2214yes—
149#2475C2214yes—
150#2475C2214yes—
151#2474C2214yes—
152#2471C2214yes—
153#2470C2214yes—
154#2465C2214yes—
155#2462C2214yes—
156#2462C2214yes—
157#2461C2214yes—
158#2461C2214yes—
159#2461C2214yes—
160#2458C2214yes—
161#2458C2214yes—
162#2457C2214yes—
163#2450C2214yes—
164#2450C2214yes—
165#2448C2212yes—
166#2447C2212yes—
167#2446C2212yes—
168#2446C2212yes—
169#2446C2212yes—
170#2445C2212yes—
171#2444C2214yes—
172#2444C2214yes—
173#2438C2214yes—
174#2434C2212yes—
175#2434C2212yes—
176#2432C2212yes—
177#2431C2212yes—
178#2402C2212yes—
179#2401C2214yes—
180#2401C2214yes—
181#2399C2214yes—
182#2396C2212yes—
183#2396C2212yes—
184#2371C2214yes—
185#2370C2212yes—
186#2370C2212yes—
187#2369C2211yescharacteristic
188#2367C2214yes—
189#2367C2212yes—
190#2367C2212yes—
191#2367C2212yes—
192#2367C2212yes—
193#2367C2212yes—
194#2365C2212yes—
195#2365C2212yes—
196#2365C2211yescharacteristic
197#2365C2212yes—
198#2365C2212yes—
199#2363C2212yes—
200#2363C2214yes—
201#2362C2214yes—
202#2362C2212yes—
203#2362C2214yes—
204#2362C2212yes—
205#2359C2214yes—
206#2359C2214yes—
207#2359C2214yes—
208#2359C2214yes—
209#2357C2212yes—
210#2357C2212yes—
211#2356C2212yes—
212#2356C2212yes—
213#2356C2212yes—
214#2355C2211yescharacteristic
215#2355C2211yescharacteristic
216#2355C2211yescharacteristic
217#2355C2212yes—
218#2354C2211yescharacteristic
219#2354C2214yes—
220Q8×C4⋊C4C2212yes—
221#2344C2212yes—
222#2343C2214yes—
223#2341C2212yes—
224Q8×C22⋊C4C2212yes—
225#2336C2214yes—
226#2332C2214yes—
227#2327C2212yes—
228#2326C2214yes—
229#2326C2212yes—
230#2324C2214yes—
231#2324C2212yes—
232#2323C2212yes—
233#2323C2214yes—
234#2323C2214yes—
235#2311C2212yes—
236C4×C4⋊Q8C2211yescharacteristic
237C4×C4⋊Q8C2211yescharacteristic
238C4×C4⋊Q8C2211yescharacteristic
239C4×#125C2212yes—
240C4×#125C2212yes—
241C4×#124C2212yes—
242C4×C22⋊Q8C2212yes—
243C4×C22⋊Q8C2212yes—
244C4×C22⋊Q8C2214yes—
245C4×C22⋊Q8C2214yes—
246C4×C22⋊Q8C2214yes—
247C4×#123C2214yes—
248#2296C2212yes—
249#2295C2211yescharacteristic
250#2295C2212yes—
251C2×#391C2212yes—
252#2293C2211yescharacteristic
253#2293C2212yes—
254#2290C2212yes—
255#2290C2214yes—
256#2276C2212yes—
257#2274C2212yes—
258C42×Q8C2211yescharacteristic
259C22×#41C2312yes—
260C23×Q8C2312yes—
261#559—44no—
262#557—28no—
263#557—44no—
264#554—28no—
265#548—216no—
266#536—216no—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×#127C2311yescharacteristic
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#124C2312yes—
281C2×#124C2314yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#124C2312yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2312yes—
298C2×#121C2312yes—
299C2×#121C2314yes—
300#519—48no—
301C4×#41—48no—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2314yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2311yescharacteristic
328C2×#117C2312yes—
329C2×#117C2312yes—
330C2×#117C2312yes—
331C2×#117C2314yes—
332C2×#117C2314yes—
333C2×#117C2314yes—
334C2×#117C2314yes—
335C22×C4⋊C4C2312yes—
336C22×C42C2312yes—
337C22×C42C2314yes—
338#401C2314yes—
339#401C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2312yes—
346#400C2312yes—
347#400C2314yes—
348#400C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2312yes—
359#400C2312yes—
360#399C2314yes—
361#399C2312yes—
362#399C2312yes—
363#398C2312yes—
364#398C2314yes—
365#398C2314yes—
366#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2312yes—
377#398C2312yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2312yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2312yes—
401#396C2312yes—
402#396C2312yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2312yes—
412#395C2312yes—
413#395C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#393C2312yes—
422#393C2314yes—
423#393C2314yes—
424#393C2312yes—
425#393C2314yes—
426#392C2314yes—
427#392C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2311yescharacteristic
431#391C2311yescharacteristic
432#391C2312yes—
433#391C2312yes—
434#391C2314yes—
435#391C2312yes—
436#391C2314yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2314yes—
442#391C2312yes—
443#391C2312yes—
444#391C2314yes—
445#391C2312yes—
446#391C2314yes—
447#391C2314yes—
448#391C2312yes—
449#391C2312yes—
450#391C2311yescharacteristic
451#391C2312yes—
452#391C2312yes—
453#391C2314yes—
454#391C2311yescharacteristic
455#390C2312yes—
456#390C2312yes—
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2314yes—
461#390C2314yes—
462#390C2312yes—
463#390C2314yes—
464#390C2312yes—
465#390C2314yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2311yescharacteristic
471#390C2312yes—
472#390C2311yescharacteristic
473#389C2311yescharacteristic
474#389C2311yescharacteristic
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2314yes—
498#389C2314yes—
499#389C2311yescharacteristic
500#389C2311yescharacteristic
501#389C2312yes—
502#389C2312yes—
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#388C2312yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2312yes—
542#388C2314yes—
543#388C2314yes—
544#388C2312yes—
545#388C2314yes—
546#388C2312yes—
547#388C2314yes—
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#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2312yes—
579#387C2314yes—
580#387C2312yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2312yes—
588#387C2312yes—
589#387C2312yes—
590#387C2314yes—
591#387C2312yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2312yes—
602#386C2314yes—
603#386C2312yes—
604#386C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2312yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2312yes—
614#385C2314yes—
615#385C2312yes—
616#385C2314yes—
617#385C2312yes—
618#385C2314yes—
619#385C2314yes—
620#385C2312yes—
621#385C2314yes—
622#385C2314yes—
623#385C2312yes—
624#385C2312yes—
625#385C2314yes—
626#385C2314yes—
627#385C2312yes—
628#385C2314yes—
629#384C2311yescharacteristic
630#384C2311yescharacteristic
631#384C2311yescharacteristic
632#384C2314yes—
633#383C2314yes—
634#383C2314yes—
635#383C2314yes—
636#383C2314yes—
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#382C2312yes—
642#382C2314yes—
643#382C2312yes—
644#381C2314yes—
645#381C2314yes—
646#381C2314yes—
647#381C2314yes—
648#381C2314yes—
649#380C2314yes—
650#380C2314yes—
651#380C2312yes—
652#380C2314yes—
653#380C2314yes—
654#380C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
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⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712#376C2312yes—
713#376C2314yes—
714#376C2314yes—
715#376C2314yes—
716C2×#95C2314yes—
717C2×#95C2314yes—
718C43C2312yes—
719C43C2311yescharacteristic
720C2×#41—28no—
721C2×#41—28no—
722C2×#41—44no—
723C22×Q8—28no—
724C22×Q8—28no—
725C22×Q8—44no—
726C22×Q8C2411yescharacteristic
727C22×Q8C2412yes—
728C22×Q8C2414yes—
729C22×Q8C2412yes—
730C22×Q8C2411yescharacteristic
731C22×Q8C2411yescharacteristic
732C22×Q8C2411yescharacteristic
733C22×Q8C2412yes—
734C22×D4C2412yes—
735C22×D4C2414yes—
736C22×D4C2414yes—
737C22×D4C2412yes—
738C22×D4C2412yes—
739C22×D4C2411yescharacteristic
740C23×C4C2414yes—
741C23×C4C2414yes—
742C23×C4C2412yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C23×C4C2412yes—
746C23×C4C2414yes—
747C23×C4C2412yes—
748C4⋊Q8—28no—
749C4⋊Q8—28no—
750C4⋊Q8—24no—
751C4⋊Q8—42no—
752C4⋊Q8—44no—
753C4⋊Q8—42no—
754C4⋊Q8#4118yes—
755#127—42no—
756#125—28no—
757#125—216no—
758#125—28no—
759#125—48no—
760#125—44no—
761#124—28no—
762#124—216no—
763#124—28no—
764#124—28no—
765#124—44no—
766#124—44no—
767#124—44no—
768#123—216no—
769#123—216no—
770#123—48no—
771#123—48no—
772C22⋊Q8—28no—
773C22⋊Q8—28no—
774C22⋊Q8—216no—
775C22⋊Q8—216no—
776C22⋊Q8—216no—
777C22⋊Q8—216no—
778C22⋊Q8—44no—
779#121—216no—
780#121—28no—
781C4×Q8—28no—
782C4×Q8—28no—
783C4×Q8—28no—
784C4×Q8—28no—
785C4×Q8—24no—
786C4×Q8—28no—
787C4×Q8—24no—
788C4×Q8—24no—
789C4×Q8—24no—
790C4×Q8—48no—
791C4×Q8—44no—
792C4×Q8—42no—
793C4×Q8—42no—
794C4×Q8—44no—
795C4×Q8—48no—
796C4×Q8—44no—
797C4×Q8—44no—
798C4×Q8—44no—
799C4×D4—28no—
800C4×D4—28no—
801C4×D4—216no—
802C4×D4—48no—
803C4×D4—44no—
804C4×D4—44no—
805C4×D4—48no—
806C4×D4#4118yes—
807#117—28no—
808#117—28no—
809#117—44no—
810#117—48no—
811#117—48no—
812#117—48no—
813#117—48no—
814C2×C4⋊C4—28no—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2412yes—
920C2×C42—48no—
921C2×C42—44no—
922C2×C42C2414yes—
923C2×C42C2412yes—
924C2×C42C2414yes—
925C2×C42C2412yes—
926C2×C42C2414yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2414yes—
932C2×C42C2412yes—
933C2×C42C2411yescharacteristic
934C2×C42C2412yes—
935C2×C42C2414yes—
936C2×C42C2411yescharacteristic
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2411yescharacteristic
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2412yes—
953C2×C42C2411yescharacteristic
954C2×C42C2411yescharacteristic
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024C24C2514yes—
1025C24C2512yes—
1026#41—432no—
1027C2×Q8—24no—
1028C2×Q8—22no—
1029C2×Q8—22no—
1030C2×Q8—22no—
1031C2×Q8—28no—
1032C2×Q8—28no—
1033C2×Q8—24no—
1034C2×Q8—24no—
1035C2×Q8—24no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—22no—
1039C2×Q8—22no—
1040C2×Q8—22no—
1041C2×Q8—41no—
1042C2×Q8—44no—
1043C2×Q8—41no—
1044C2×Q8—41no—
1045C2×Q8—41no—
1046C2×Q8—41no—
1047C2×Q8—42no—
1048C2×Q8—42no—
1049C2×Q8—41no—
1050C2×Q8—432no—
1051C2×Q8C2×#4118yes—
1052C2×D4—28no—
1053C2×D4—28no—
1054C2×D4—24no—
1055C2×D4—28no—
1056C2×D4—24no—
1057C2×D4—24no—
1058C2×D4—24no—
1059C2×D4—44no—
1060C2×D4—41no—
1061C2×D4—41no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—44no—
1065C2×D4—44no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C2×D4—42no—
1069C2×D4C2×#4114yes—
1070C22×C4—24no—
1071C22×C4—24no—
1072C22×C4—28no—
1073C22×C4—28no—
1074C22×C4—28no—
1075C22×C4—28no—
1076C22×C4—28no—
1077C22×C4—28no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—42no—
1082C22×C4—42no—
1083C22×C4—44no—
1084C22×C4—42no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—42no—
1089C22×C4—44no—
1090C22×C4—42no—
1091C22×C4—44no—
1092C22×C4—42no—
1093C22×C4C2×#4118yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2514yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2514yes—
1108C22×C4C2514yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2511yescharacteristic
1114C22×C4C2511yescharacteristic
1115C22×C4C2514yes—
1116C22×C4C2512yes—
1117C22×C4C2511yescharacteristic
1118C22×C4C2512yes—
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C4⋊C4—22no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—24no—
1128C4⋊C4—22no—
1129C4⋊C4—28no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—28no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—22no—
1136C4⋊C4—28no—
1137C4⋊C4—28no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—28no—
1141C4⋊C4—24no—
1142C4⋊C4—28no—
1143C4⋊C4—28no—
1144C4⋊C4—24no—
1145C4⋊C4—28no—
1146C4⋊C4—24no—
1147C4⋊C4—41no—
1148C4⋊C4—41no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—41no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—41no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
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—42no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—41no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—41no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—44no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—44no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4C2×#4114yes—
1185C4⋊C4C2×#4118yes—
1186C4⋊C4C2×#4118yes—
1187C4⋊C4H(5,𝔽2)14yes—
1188C22⋊C4—28no—
1189C22⋊C4—28no—
1190C22⋊C4—24no—
1191C22⋊C4—24no—
1192C22⋊C4—28no—
1193C22⋊C4—28no—
1194C22⋊C4—28no—
1195C22⋊C4—28no—
1196C22⋊C4—28no—
1197C22⋊C4—28no—
1198C22⋊C4—28no—
1199C22⋊C4—28no—
1200C22⋊C4—28no—
1201C22⋊C4—24no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—42no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4C2×#4118yes—
1226C42—24no—
1227C42—28no—
1228C42—24no—
1229C42—28no—
1230C42—24no—
1231C42—24no—
1232C42—28no—
1233C42—28no—
1234C42—24no—
1235C42—24no—
1236C42—28no—
1237C42—24no—
1238C42—24no—
1239C42—22no—
1240C42—24no—
1241C42—22no—
1242C42—42no—
1243C42—42no—
1244C42—44no—
1245C42—42no—
1246C42—41no—
1247C42—42no—
1248C42—41no—
1249C42—44no—
1250C42—44no—
1251C42—41no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42C2×#4114yes—
1258C42C2×#4114yes—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—22no—
1263C23—22no—
1264C23—22no—
1265C23—24no—
1266C23—24no—
1267C23—24no—
1268C23—24no—
1269C23—24no—
1270C23—24no—
1271C23—24no—
1272C23C22×#4114yes—
1273C23C2611yescharacteristic
1274Q8—216no—
1275Q8—416no—
1276Q8—44no—
1277Q8—44no—
1278Q8—44no—
1279Q8—48no—
1280Q8—84no—
1281Q8—82no—
1282D4—44no—
1283D4—416no—
1284D4—48no—
1285D4—84no—
1286D4—88no—
1287D4—162no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—21no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—216no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—21no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—416no—
1360C2×C4—416no—
1361C2×C4—88no—
1362C2×C4—88no—
1363C2×C4—84no—
1364C2×C4—88no—
1365C2×C4—84no—
1366C2×C4C22×#4112yes—
1367C2×C4C22×#4112yes—
1368C2×C4C22×#4112yes—
1369C2×C4C22×#4118yes—
1370C2×C4C22×#4112yes—
1371C2×C4C22×#4114yes—
1372C2×C4C22×#4112yes—
1373C2×C4C22×#4112yes—
1374C2×C4C2×H(5,𝔽2)14yes—
1375C2×C4C2×H(5,𝔽2)12yes—
1376C2×C4#58512yes—
1377C22—24no—
1378C22—24no—
1379C22—24no—
1380C22—42no—
1381C22—42no—
1382C22—42no—
1383C22—42no—
1384C22—44no—
1385C22—44no—
1386C22—44no—
1387C22—44no—
1388C22—44no—
1389C22—44no—
1390C22—44no—
1391C22C23×#4111yescharacteristic
1392C22C23×#4111yescharacteristic
1393C22C22×H(5,𝔽2)11yescharacteristic
1394C22C2×#58511yescharacteristic
1395C222−1+611yescharacteristic
1396C222−1+611yescharacteristic
1397C222−1+611yescharacteristic
1398C4—22no—
1399C4—22no—
1400C4—24no—
1401C4—22no—
1402C4—22no—
1403C4—22no—
1404C4—24no—
1405C4—28no—
1406C4—42no—
1407C4—44no—
1408C4—42no—
1409C4—42no—
1410C4—42no—
1411C4—42no—
1412C4—42no—
1413C4—42no—
1414C4—41no—
1415C4—42no—
1416C4—42no—
1417C4—44no—
1418C4—44no—
1419C4—42no—
1420C4—42no—
1421C4—42no—
1422C4—44no—
1423C4—42no—
1424C4#348114yes—
1425C2—44no—
1426C2—84no—
1427C2C2×#348111yescharacteristic
1428C2#6285011yescharacteristic
1429C2#6286011yescharacteristic
1430C2#6289711yescharacteristic
1431C2#6299511yescharacteristic
1432C2#6300711yescharacteristic
1433C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#39356C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59880C2semidirect
2. #59870C2semidirect
3. #59618C2semidirect
4. #59425C2semidirect
5. #52304C2semidirect
6. #52267C2semidirect
7. #45323C2semidirect
8. #45156C2semidirect
9. #44960C2semidirect
10. #44867C2semidirect
11. #44644C2semidirect
12. #44616C2semidirect
13. #40407C2semidirect
14. #39820C2semidirect
15. #39765C2semidirect
17. #38771C2semidirect
18. #38770C2semidirect
19. #38518C2semidirect
20. #38083C2semidirect
21. #36538C2semidirect
22. #36437C2semidirect
23. #36037C2semidirect
24. #35974C2semidirect
25. #35749C2semidirect
26. #34328C2semidirect
27. #34317C2semidirect
28. #34293C2semidirect
29. #34268C2semidirect

Maximal subgroups

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

subgroupindex
#598802
#598702
#596182
#594252
#523042
#522672
#453232
#451562
#449602
#448672
#446442
#446162
#404072
#398202
#397652
#393562
#387712
#387702
#385182
#380832
#365382
#364372
#360372
#359742
#357492
#343282
#343172
#342932
#342682