Finite Group Databasebeta

← #7688844

Subgroups — #7688844

Order 512.

5847 conjugacy classes of subgroups.

The subgroup lattice has 1570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60038C212yesmaximal, complemented
2#59952C211yesmaximal, characteristic, complemented
3#59767C212yesmaximal, complemented
4#59182C214yesmaximal, complemented
5#59115C214yesmaximal, complemented
6#59058C212yesmaximal, complemented
7#45435C211yesmaximal, characteristic, complemented
8#45378C211yesmaximal, characteristic, complemented
9#45036C212yesmaximal, complemented
10#44377C212yesmaximal, complemented
11#44305C212yesmaximal, complemented
12#44200C214yesmaximal, complemented
13#38826C214yesmaximal, complemented
14#38823C214yesmaximal, complemented
15#38285C212yesmaximal, complemented
16#37775C212yesmaximal, complemented
17#36496C211yesmaximal, characteristic, complemented
18#36327C214yesmaximal, complemented
19#36273C212yesmaximal, complemented
20#36126C212yesmaximal, complemented
21#36125C212yesmaximal, complemented
22#35930C211yesmaximal, characteristic, complemented
23#35912C211yesmaximal, characteristic, complemented
24#35697C212yesmaximal, complemented
25#34925C212yesmaximal, complemented
26#34874C211yesmaximal, characteristic, complemented
27#34305C212yesmaximal, complemented
28#34287C212yesmaximal, complemented
29#34153C212yesmaximal, complemented
30C2×#559C2211yescharacteristic
31C2×#555C2214yes—
32C2×#554C2211yescharacteristic
33C2×#553C2212yes—
34C2×#550C2211yescharacteristic
35C2×#547C2212yes—
36C2×#547C2211yescharacteristic
37C2×#540C2212yes—
38C2×#532C2214yes—
39C2×#532C2214yes—
40C2×#529C2212yes—
41#2861C2212yes—
42#2858C2212yes—
43#2858C2211yescharacteristic
44#2856C2212yes—
45#2854C2214yes—
46#2850C2214yes—
47#2808C2214yes—
48#2803C2214yes—
49#2795C2212yes—
50#2792C2212yes—
51#2792C2212yes—
52#2785C2212yes—
53#2784C2214yes—
54#2784C2212yes—
55#2781C2214yes—
56#2734C2214yes—
57#2733C2212yes—
58#2731C2214yes—
59#2727C2214yes—
60#2714C2214yes—
61#2714C2214yes—
62#2714C2214yes—
63#2705C2214yes—
64#2686C2214yes—
65#2686C2214yes—
66#2682C2214yes—
67#2682C2214yes—
68#2673C2214yes—
69#2673C2214yes—
70#2673C2214yes—
71#2663C2212yes—
72#2663C2214yes—
73#2661C2212yes—
74#2657C2211yescharacteristic
75#2640C2211yescharacteristic
76#2620C2212yes—
77#2612C2211yescharacteristic
78#2610C2214yes—
79#2610C2214yes—
80#2610C2212yes—
81#2610C2214yes—
82#2610C2214yes—
83#2609C2211yescharacteristic
84#2602C2214yes—
85#2593C2211yescharacteristic
86#2592C2211yescharacteristic
87#2586C2214yes—
88#2574C2212yes—
89#2567C2211yescharacteristic
90#2567C2211yescharacteristic
91#2566C2212yes—
92#2564C2212yes—
93#2558C2214yes—
94#2557C2214yes—
95#2556C2214yes—
96#2555C2212yes—
97#2555C2214yes—
98#2555C2212yes—
99#2555C2211yescharacteristic
100#2555C2214yes—
101#2555C2214yes—
102#2554C2214yes—
103#2551C2212yes—
104#2551C2212yes—
105#2551C2212yes—
106#2551C2212yes—
107#2548C2211yescharacteristic
108#2546C2212yes—
109#2544C2212yes—
110#2544C2212yes—
111#2543C2212yes—
112#2541C2212yes—
113#2541C2212yes—
114#2541C2212yes—
115#2541C2214yes—
116#2541C2211yescharacteristic
117#2540C2211yescharacteristic
118#2540C2212yes—
119#2537C2212yes—
120#2531C2212yes—
121#2531C2214yes—
122#2529C2212yes—
123#2529C2214yes—
124#2526C2214yes—
125#2500C2214yes—
126#2492C2212yes—
127#2491C2212yes—
128#2491C2212yes—
129#2491C2212yes—
130#2491C2214yes—
131#2491C2214yes—
132#2491C2214yes—
133#2476C2212yes—
134#2476C2214yes—
135#2474C2212yes—
136#2474C2214yes—
137#2471C2214yes—
138#2471C2214yes—
139#2467C2214yes—
140#2464C2214yes—
141#2464C2214yes—
142#2464C2214yes—
143#2464C2214yes—
144#2464C2214yes—
145#2461C2214yes—
146#2461C2214yes—
147#2461C2214yes—
148#2461C2214yes—
149#2461C2214yes—
150#2459C2214yes—
151#2456C2214yes—
152#2456C2214yes—
153#2456C2214yes—
154#2452C2214yes—
155#2452C2214yes—
156#2445C2214yes—
157#2445C2214yes—
158#2439C2214yes—
159#2432C2214yes—
160#2432C2214yes—
161#2431C2214yes—
162#2430C2214yes—
163#2430C2214yes—
164#2430C2212yes—
165#2430C2212yes—
166#2428C2212yes—
167#2428C2212yes—
168#2428C2212yes—
169#2428C2212yes—
170#2428C2214yes—
171#2428C2214yes—
172#2428C2212yes—
173#2428C2214yes—
174#2427C2212yes—
175#2426C2212yes—
176#2426C2212yes—
177#2422C2214yes—
178#2416C2212yes—
179#2416C2212yes—
180#2415C2212yes—
181#2414C2214yes—
182#2414C2212yes—
183#2414C2214yes—
184#2399C2211yescharacteristic
185#2398C2211yescharacteristic
186#2392C2212yes—
187#2388C2212yes—
188#2388C2212yes—
189#2388C2214yes—
190#2374C2214yes—
191#2373C2214yes—
192#2373C2214yes—
193#2373C2214yes—
194#2372C2214yes—
195#2372C2212yes—
196#2370C2212yes—
197#2370C2212yes—
198#2370C2212yes—
199#2367C2212yes—
200#2367C2212yes—
201#2366C2212yes—
202#2366C2212yes—
203#2364C2214yes—
204#2364C2214yes—
205#2363C2212yes—
206#2363C2212yes—
207#2363C2214yes—
208#2363C2214yes—
209#2363C2214yes—
210#2361C2212yes—
211#2361C2212yes—
212#2361C2212yes—
213#2361C2212yes—
214#2361C2212yes—
215#2361C2212yes—
216#2360C2212yes—
217#2360C2212yes—
218#2359C2214yes—
219#2359C2214yes—
220#2359C2214yes—
221#2359C2214yes—
222#2354C2212yes—
223#2349C2214yes—
224D4×C4⋊C4C2212yes—
225#2346C2212yes—
226#2345C2212yes—
227#2335C2214yes—
228#2335C2214yes—
229#2334C2214yes—
230#2333C2214yes—
231#2330C2212yes—
232#2324C2212yes—
233#2319C2212yes—
234C4×#127C2212yes—
235C4×#124C2212yes—
236C4×#124C2211yescharacteristic
237C4×#123C2214yes—
238C4×#121C2214yes—
239C4×#121C2212yes—
240C4×#121C2212yes—
241C4×#121C2214yes—
242#2298C2212yes—
243#2298C2214yes—
244#2296C2214yes—
245#2295C2212yes—
246#2293C2212yes—
247#2293C2212yes—
248#2290C2214yes—
249#2290C2212yes—
250#2290C2214yes—
251#2275C2211yescharacteristic
252#2275C2211yescharacteristic
253#2274C2212yes—
254C42×Q8C2211yescharacteristic
255C42×D4C2212yes—
256C42×D4C2214yes—
257C4×#117C2212yes—
258C2×C4×C4⋊C4C2212yes—
259C22×#41C2312yes—
260C22×#41C2314yes—
261C22×#41C2312yes—
262#559—44no—
263#555—416no—
264#554—44no—
265#553—216no—
266#550—44no—
267#547—44no—
268#547—48no—
269#540—216no—
270#532—416no—
271#532—416no—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2314yes—
276C2×C4⋊Q8C2314yes—
277C2×C4⋊Q8C2314yes—
278C2×#127C2312yes—
279C2×#127C2312yes—
280C2×#127C2312yes—
281C2×#127C2311yescharacteristic
282C2×#127C2311yescharacteristic
283C2×#127C2314yes—
284C2×#127C2314yes—
285#529—216no—
286C2×#126C2314yes—
287C2×#126C2314yes—
288C2×#125C2312yes—
289C2×#125C2312yes—
290C2×#124C2312yes—
291C2×#124C2314yes—
292C2×#124C2312yes—
293C2×#124C2311yescharacteristic
294C2×#124C2314yes—
295C2×#124C2314yes—
296C2×#124C2314yes—
297C2×#124C2312yes—
298C2×#124C2314yes—
299C2×#124C2311yescharacteristic
300C2×#124C2312yes—
301C2×#124C2311yescharacteristic
302C2×#124C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×#123C2312yes—
311C2×#123C2312yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2314yes—
317C2×#121C2312yes—
318C2×#121C2314yes—
319C2×#121C2312yes—
320C2×#121C2312yes—
321C2×#121C2312yes—
322C2×#121C2312yes—
323C2×#121C2314yes—
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×#121C2312yes—
327C2×#121C2314yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×#121C2312yes—
331C2×#121C2312yes—
332C2×#121C2314yes—
333C2×#121C2312yes—
334C2×#121C2312yes—
335C2×#121C2314yes—
336C2×#121C2314yes—
337C2×#121C2314yes—
338C2×#121C2314yes—
339C2×#121C2314yes—
340C2×#121C2314yes—
341C2×#121C2314yes—
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2311yescharacteristic
346C2×C4×D4C2312yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2314yes—
350C2×C4×D4C2314yes—
351C2×C4×D4C2311yescharacteristic
352C2×C4×D4C2311yescharacteristic
353C2×C4×D4C2312yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2314yes—
360C2×C4×D4C2314yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2314yes—
363C2×C4×D4C2314yes—
364C2×C4×D4C2314yes—
365C2×C4×D4C2314yes—
366C2×C4×D4C2314yes—
367C2×C4×D4C2314yes—
368C2×C4×D4C2311yescharacteristic
369C2×C4×D4C2312yes—
370C2×C4×D4C2311yescharacteristic
371C2×#117C2312yes—
372C2×#117C2312yes—
373C2×#117C2312yes—
374C2×#117C2314yes—
375C2×#117C2312yes—
376C2×#117C2314yes—
377C2×#117C2314yes—
378C2×#117C2314yes—
379C22×C4⋊C4C2312yes—
380C22×C4⋊C4C2312yes—
381C22×C4⋊C4C2312yes—
382C22×C42C2312yes—
383C22×C42C2314yes—
384C22×C42C2314yes—
385#400C2311yescharacteristic
386#400C2311yescharacteristic
387#400C2314yes—
388#399C2312yes—
389#399C2314yes—
390#398C2312yes—
391#398C2314yes—
392#398C2311yescharacteristic
393#398C2311yescharacteristic
394#398C2312yes—
395#398C2314yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2312yes—
400#397C2312yes—
401#397C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2312yes—
405#396C2314yes—
406#396C2314yes—
407#396C2312yes—
408#396C2314yes—
409#396C2314yes—
410#395C2312yes—
411#395C2312yes—
412#395C2312yes—
413#395C2312yes—
414#395C2312yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2311yescharacteristic
420#395C2311yescharacteristic
421#394C2312yes—
422#394C2314yes—
423#394C2311yescharacteristic
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2312yes—
433#394C2312yes—
434#394C2312yes—
435#394C2311yescharacteristic
436#394C2312yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#393C2312yes—
448#393C2312yes—
449#393C2312yes—
450#393C2314yes—
451#393C2314yes—
452#393C2314yes—
453#393C2312yes—
454#393C2314yes—
455#392C2314yes—
456#392C2312yes—
457#392C2314yes—
458#392C2314yes—
459#392C2314yes—
460#392C2314yes—
461#392C2312yes—
462#392C2314yes—
463#392C2314yes—
464#392C2312yes—
465#392C2312yes—
466#392C2314yes—
467#392C2314yes—
468#392C2314yes—
469#392C2314yes—
470#392C2314yes—
471#392C2314yes—
472#392C2314yes—
473#392C2314yes—
474#391C2312yes—
475#391C2312yes—
476#391C2311yescharacteristic
477#391C2314yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2314yes—
482#390C2311yescharacteristic
483#390C2312yes—
484#390C2314yes—
485#390C2314yes—
486#390C2312yes—
487#390C2312yes—
488#390C2312yes—
489#390C2312yes—
490#390C2314yes—
491#390C2312yes—
492#390C2314yes—
493#390C2314yes—
494#390C2314yes—
495#390C2312yes—
496#390C2314yes—
497#390C2314yes—
498#390C2312yes—
499#390C2312yes—
500#390C2314yes—
501#390C2314yes—
502#390C2314yes—
503#390C2312yes—
504#390C2314yes—
505#390C2314yes—
506#390C2312yes—
507#390C2314yes—
508#390C2312yes—
509#390C2312yes—
510#390C2312yes—
511#390C2314yes—
512#390C2314yes—
513#390C2314yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2312yes—
526#389C2312yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2312yes—
532#389C2312yes—
533#389C2314yes—
534#388C2312yes—
535#388C2312yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2312yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2312yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2312yes—
551#388C2312yes—
552#388C2312yes—
553#388C2312yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2312yes—
566#388C2314yes—
567#388C2312yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2312yes—
572#388C2312yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2312yes—
579#388C2314yes—
580#388C2312yes—
581#387C2314yes—
582#387C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2312yes—
591#387C2314yes—
592#387C2312yes—
593#387C2314yes—
594#387C2314yes—
595#387C2312yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2312yes—
616#386C2314yes—
617#386C2312yes—
618#386C2314yes—
619#386C2312yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2312yes—
628#386C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2312yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2312yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#384C2312yes—
645#384C2312yes—
646#384C2312yes—
647#382C2311yescharacteristic
648#382C2312yes—
649#382C2314yes—
650#381C2314yes—
651#380C2314yes—
652#380C2312yes—
653#380C2314yes—
654#380C2312yes—
655#380C2314yes—
656#380C2312yes—
657#380C2314yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2311yescharacteristic
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C22⋊C4C2312yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2312yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711#376C2311yescharacteristic
712#376C2311yescharacteristic
713#376C2314yes—
714#376C2312yes—
715#376C2312yes—
716#376C2314yes—
717C2×#95C2312yes—
718C2×#95C2312yes—
719C2×#95C2314yes—
720C43C2312yes—
721C43C2311yescharacteristic
722C43C2312yes—
723C2×#41—44no—
724C2×#41—48no—
725C2×#41—44no—
726C2×#41—48no—
727C2×#41—48no—
728C2×#41—48no—
729C2×#41—48no—
730C22×Q8C2411yescharacteristic
731C22×Q8C2411yescharacteristic
732C22×Q8C2411yescharacteristic
733C22×Q8C2414yes—
734C22×Q8C2412yes—
735C22×Q8C2412yes—
736C22×D4C2411yescharacteristic
737C22×D4C2412yes—
738C22×D4C2411yescharacteristic
739C22×D4C2414yes—
740C22×D4C2414yes—
741C22×D4C2412yes—
742C22×D4C2411yescharacteristic
743C22×D4C2412yes—
744C22×D4C2411yescharacteristic
745C22×D4C2414yes—
746C22×D4C2414yes—
747C22×D4C2414yes—
748C22×D4C2414yes—
749C22×D4C2414yes—
750C22×D4C2412yes—
751C22×D4C2414yes—
752C22×D4C2414yes—
753C22×D4C2414yes—
754C22×D4C2412yes—
755C22×D4C2412yes—
756C22×D4C2414yes—
757C22×D4C2414yes—
758C22×D4C2412yes—
759C23×C4C2412yes—
760C23×C4C2412yes—
761C23×C4C2414yes—
762C23×C4C2414yes—
763C23×C4C2412yes—
764C23×C4C2414yes—
765C23×C4C2412yes—
766C23×C4C2414yes—
767C23×C4C2414yes—
768C23×C4C2414yes—
769C23×C4C2414yes—
770C23×C4C2412yes—
771C23×C4C2412yes—
772C23×C4C2414yes—
773C4⋊Q8—42no—
774C4⋊Q8—44no—
775C4⋊Q8—42no—
776C4⋊Q8—48no—
777C4⋊Q8—48no—
778C4⋊Q8—48no—
779#127—28no—
780#127—44no—
781#127—44no—
782#127—42no—
783#127—42no—
784#127—48no—
785#127—48no—
786#126—216no—
787#126—216no—
788#125—44no—
789#125#41116yescomplemented
790#124—28no—
791#124—216no—
792#124—28no—
793#124—48no—
794#124—48no—
795#124—48no—
796#124—44no—
797#124—42no—
798#124—48no—
799#124—42no—
800#124—42no—
801#124—48no—
802#124—44no—
803#123—216no—
804#123—216no—
805#123—216no—
806#123—216no—
807#123—48no—
808#123—48no—
809#123—48no—
810#123—44no—
811#123—44no—
812C22⋊Q8—28no—
813C22⋊Q8—44no—
814C22⋊Q8—48no—
815C22⋊Q8—48no—
816C22⋊Q8—44no—
817#121—28no—
818#121—216no—
819#121—216no—
820#121—28no—
821#121—28no—
822#121—216no—
823#121—28no—
824#121—28no—
825#121—28no—
826#121—216no—
827#121—48no—
828#121—48no—
829#121—44no—
830#121—48no—
831#121—48no—
832#121—48no—
833#121—48no—
834#121—48no—
835#121—48no—
836#121—48no—
837#121—48no—
838#121—44no—
839#121—44no—
840#121—44no—
841#121—48no—
842C4×Q8—28no—
843C4×Q8—24no—
844C4×Q8—42no—
845C4×Q8—42no—
846C4×D4—28no—
847C4×D4—216no—
848C4×D4—28no—
849C4×D4—28no—
850C4×D4—216no—
851C4×D4—28no—
852C4×D4—24no—
853C4×D4—24no—
854C4×D4—216no—
855C4×D4—28no—
856C4×D4—28no—
857C4×D4—48no—
858C4×D4—48no—
859C4×D4—48no—
860C4×D4—42no—
861C4×D4—44no—
862C4×D4—44no—
863C4×D4—42no—
864C4×D4—44no—
865C4×D4—48no—
866C4×D4—48no—
867C4×D4—48no—
868C4×D4—48no—
869C4×D4—48no—
870C4×D4—48no—
871#117—216no—
872#117—28no—
873#117—28no—
874#117—28no—
875#117—48no—
876#117—44no—
877#117—48no—
878#117—48no—
879C2×C4⋊C4—28no—
880C2×C4⋊C4—28no—
881C2×C4⋊C4—28no—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2411yescharacteristic
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2411yescharacteristic
911C2×C4⋊C4C2411yescharacteristic
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2411yescharacteristic
916C2×C4⋊C4C2411yescharacteristic
917C2×C4⋊C4C2411yescharacteristic
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2411yescharacteristic
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2414yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2414yes—
979C2×C22⋊C4C2414yes—
980C2×C22⋊C4C2414yes—
981C2×C22⋊C4C2412yes—
982C2×C22⋊C4C2412yes—
983C2×C22⋊C4C2414yes—
984C2×C22⋊C4C2412yes—
985C2×C22⋊C4C2412yes—
986C2×C22⋊C4C2412yes—
987C2×C22⋊C4C2412yes—
988C2×C22⋊C4C2412yes—
989C2×C42—28no—
990C2×C42—48no—
991C2×C42—48no—
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2414yes—
995C2×C42C2411yescharacteristic
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2414yes—
999C2×C42C2414yes—
1000C2×C42C2414yes—
1001C2×C42C2412yes—
1002C2×C42C2411yescharacteristic
1003C2×C42C2412yes—
1004C2×C42C2412yes—
1005C2×C42C2411yescharacteristic
1006C2×C42C2411yescharacteristic
1007C2×C42C2412yes—
1008C2×C42C2412yes—
1009C2×C42C2412yes—
1010C2×C42C2414yes—
1011C2×C42C2412yes—
1012C2×C42C2414yes—
1013C2×C42C2414yes—
1014C2×C42C2414yes—
1015C2×C42C2412yes—
1016C2×C42C2414yes—
1017C2×C42C2414yes—
1018C2×C42C2411yescharacteristic
1019C2×C42C2412yes—
1020C2×C42C2412yes—
1021C2×C42C2412yes—
1022#95C2411yescharacteristic
1023#95C2411yescharacteristic
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2414yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2411yescharacteristic
1036#95C2412yes—
1037#95C2414yes—
1038#95C2412yes—
1039#95C2411yescharacteristic
1040#95C2412yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2412yes—
1060#95C2414yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2412yes—
1065#95C2414yes—
1066#95C2414yes—
1067#95C2412yes—
1068#95C2412yes—
1069#95C2414yes—
1070#95C2412yes—
1071C24C2514yes—
1072C24C2512yes—
1073C24C2512yes—
1074C24C2512yes—
1075C24C2512yes—
1076#41—832no—
1077#41—816no—
1078#41—816no—
1079C2×Q8—24no—
1080C2×Q8—22no—
1081C2×Q8—24no—
1082C2×Q8—28no—
1083C2×Q8—22no—
1084C2×Q8—41no—
1085C2×Q8—41no—
1086C2×Q8—44no—
1087C2×Q8—42no—
1088C2×Q8—44no—
1089C2×Q8—44no—
1090C2×Q8—41no—
1091C2×Q8—42no—
1092C2×Q8—44no—
1093C2×D4—28no—
1094C2×D4—28no—
1095C2×D4—24no—
1096C2×D4—24no—
1097C2×D4—24no—
1098C2×D4—28no—
1099C2×D4—28no—
1100C2×D4—24no—
1101C2×D4—28no—
1102C2×D4—24no—
1103C2×D4—28no—
1104C2×D4—24no—
1105C2×D4—24no—
1106C2×D4—24no—
1107C2×D4—28no—
1108C2×D4—28no—
1109C2×D4—28no—
1110C2×D4—28no—
1111C2×D4—28no—
1112C2×D4—22no—
1113C2×D4—24no—
1114C2×D4—22no—
1115C2×D4—24no—
1116C2×D4—28no—
1117C2×D4—22no—
1118C2×D4—24no—
1119C2×D4—41no—
1120C2×D4—44no—
1121C2×D4—42no—
1122C2×D4—41no—
1123C2×D4—44no—
1124C2×D4—41no—
1125C2×D4—42no—
1126C2×D4—44no—
1127C2×D4—44no—
1128C2×D4—44no—
1129C2×D4—44no—
1130C2×D4—44no—
1131C2×D4—42no—
1132C2×D4—44no—
1133C2×D4—44no—
1134C2×D4—44no—
1135C2×D4—44no—
1136C2×D4—44no—
1137C2×D4—44no—
1138C2×D4—44no—
1139C2×D4—44no—
1140C2×D4—42no—
1141C2×D4—44no—
1142C2×D4—44no—
1143C2×D4—44no—
1144C2×D4—44no—
1145C2×D4—44no—
1146C2×D4—44no—
1147C2×D4—42no—
1148C2×D4—44no—
1149C2×D4—44no—
1150C2×D4—44no—
1151C2×D4—42no—
1152C2×D4—44no—
1153C2×D4—42no—
1154C2×D4—42no—
1155C2×D4—44no—
1156C2×D4—42no—
1157C22×C4—24no—
1158C22×C4—28no—
1159C22×C4—24no—
1160C22×C4—24no—
1161C22×C4—24no—
1162C22×C4—24no—
1163C22×C4—28no—
1164C22×C4—24no—
1165C22×C4—24no—
1166C22×C4—24no—
1167C22×C4—28no—
1168C22×C4—24no—
1169C22×C4—24no—
1170C22×C4—28no—
1171C22×C4—28no—
1172C22×C4—28no—
1173C22×C4—28no—
1174C22×C4—28no—
1175C22×C4—28no—
1176C22×C4—28no—
1177C22×C4—28no—
1178C22×C4—24no—
1179C22×C4—24no—
1180C22×C4—44no—
1181C22×C4—44no—
1182C22×C4—42no—
1183C22×C4—44no—
1184C22×C4—42no—
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—
1195C22×C4—44no—
1196C22×C4—44no—
1197C22×C4C2511yescharacteristic
1198C22×C4C2512yes—
1199C22×C4C2512yes—
1200C22×C4C2512yes—
1201C22×C4C2514yes—
1202C22×C4C2511yescharacteristic
1203C22×C4C2512yes—
1204C22×C4C2512yes—
1205C22×C4C2512yes—
1206C22×C4C2512yes—
1207C22×C4C2514yes—
1208C22×C4C2511yescharacteristic
1209C22×C4C2511yescharacteristic
1210C22×C4C2511yescharacteristic
1211C22×C4C2514yes—
1212C22×C4C2512yes—
1213C22×C4C2514yes—
1214C22×C4C2514yes—
1215C22×C4C2512yes—
1216C22×C4C2512yes—
1217C22×C4C2512yes—
1218C22×C4C2512yes—
1219C22×C4C2511yescharacteristic
1220C22×C4C2511yescharacteristic
1221C4⋊C4—24no—
1222C4⋊C4—28no—
1223C4⋊C4—28no—
1224C4⋊C4—24no—
1225C4⋊C4—24no—
1226C4⋊C4—24no—
1227C4⋊C4—28no—
1228C4⋊C4—24no—
1229C4⋊C4—24no—
1230C4⋊C4—28no—
1231C4⋊C4—28no—
1232C4⋊C4—24no—
1233C4⋊C4—24no—
1234C4⋊C4—28no—
1235C4⋊C4—28no—
1236C4⋊C4—24no—
1237C4⋊C4—24no—
1238C4⋊C4—24no—
1239C4⋊C4—42no—
1240C4⋊C4—42no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—41no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—42no—
1251C4⋊C4—41no—
1252C4⋊C4—41no—
1253C4⋊C4—42no—
1254C4⋊C4—42no—
1255C4⋊C4—41no—
1256C4⋊C4—41no—
1257C4⋊C4—41no—
1258C4⋊C4—44no—
1259C4⋊C4—42no—
1260C4⋊C4—44no—
1261C4⋊C4C2×#4118yes—
1262C4⋊C4C2×#4118yes—
1263C4⋊C4C2×#41116yes—
1264C4⋊C4C2×#41116yes—
1265C4⋊C4H(5,𝔽2)14yes—
1266C22⋊C4—24no—
1267C22⋊C4—24no—
1268C22⋊C4—28no—
1269C22⋊C4—24no—
1270C22⋊C4—24no—
1271C22⋊C4—28no—
1272C22⋊C4—28no—
1273C22⋊C4—28no—
1274C22⋊C4—24no—
1275C22⋊C4—28no—
1276C22⋊C4—28no—
1277C22⋊C4—28no—
1278C22⋊C4—28no—
1279C22⋊C4—28no—
1280C22⋊C4—24no—
1281C22⋊C4—28no—
1282C22⋊C4—28no—
1283C22⋊C4—28no—
1284C22⋊C4—28no—
1285C22⋊C4—28no—
1286C22⋊C4—28no—
1287C22⋊C4—28no—
1288C22⋊C4—28no—
1289C22⋊C4—24no—
1290C22⋊C4—28no—
1291C22⋊C4—24no—
1292C22⋊C4—24no—
1293C22⋊C4—24no—
1294C22⋊C4—24no—
1295C22⋊C4—28no—
1296C22⋊C4—24no—
1297C22⋊C4—28no—
1298C22⋊C4—42no—
1299C22⋊C4—42no—
1300C22⋊C4—42no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—44no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—44no—
1308C22⋊C4—44no—
1309C22⋊C4—44no—
1310C22⋊C4—42no—
1311C22⋊C4—42no—
1312C22⋊C4—42no—
1313C22⋊C4—42no—
1314C22⋊C4—42no—
1315C22⋊C4—42no—
1316C22⋊C4—44no—
1317C22⋊C4—44no—
1318C22⋊C4—44no—
1319C22⋊C4—44no—
1320C22⋊C4—44no—
1321C22⋊C4—44no—
1322C22⋊C4—42no—
1323C22⋊C4—42no—
1324C22⋊C4—42no—
1325C22⋊C4—42no—
1326C22⋊C4—44no—
1327C22⋊C4H(5,𝔽2)18yes—
1328C42—24no—
1329C42—24no—
1330C42—24no—
1331C42—24no—
1332C42—28no—
1333C42—28no—
1334C42—28no—
1335C42—24no—
1336C42—28no—
1337C42—24no—
1338C42—24no—
1339C42—22no—
1340C42—24no—
1341C42—22no—
1342C42—24no—
1343C42—22no—
1344C42—22no—
1345C42—24no—
1346C42—44no—
1347C42—44no—
1348C42—44no—
1349C42—44no—
1350C42—41no—
1351C42—42no—
1352C42—42no—
1353C42—42no—
1354C42—44no—
1355C42—44no—
1356C42—42no—
1357C42C2×#4118yes—
1358C23—22no—
1359C23—22no—
1360C23—22no—
1361C23—22no—
1362C23—22no—
1363C23—22no—
1364C23—24no—
1365C23—24no—
1366C23—22no—
1367C23—24no—
1368C23—24no—
1369C23—22no—
1370C23—24no—
1371C23—22no—
1372C23—22no—
1373C23—24no—
1374C23—24no—
1375C23—24no—
1376C23—22no—
1377C23—22no—
1378C23—22no—
1379C23—24no—
1380C23—24no—
1381C23—22no—
1382C23—22no—
1383C23—22no—
1384C23—22no—
1385C23—22no—
1386C23—24no—
1387C23—22no—
1388C23C2×H(5,𝔽2)14yes—
1389C23C2611yescharacteristic
1390Q8—44no—
1391Q8—44no—
1392Q8—82no—
1393Q8—88no—
1394Q8—84no—
1395Q8—162no—
1396D4—416no—
1397D4—48no—
1398D4—416no—
1399D4—48no—
1400D4—44no—
1401D4—44no—
1402D4—44no—
1403D4—48no—
1404D4—44no—
1405D4—88no—
1406D4—88no—
1407D4—88no—
1408D4—88no—
1409D4—88no—
1410D4—84no—
1411D4—88no—
1412D4—88no—
1413D4—88no—
1414D4—88no—
1415D4—84no—
1416D4—162no—
1417D4—164no—
1418D4—162no—
1419C2×C4—22no—
1420C2×C4—21no—
1421C2×C4—24no—
1422C2×C4—24no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—24no—
1427C2×C4—22no—
1428C2×C4—24no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—24no—
1432C2×C4—21no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—24no—
1438C2×C4—22no—
1439C2×C4—22no—
1440C2×C4—24no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—22no—
1444C2×C4—22no—
1445C2×C4—24no—
1446C2×C4—22no—
1447C2×C4—24no—
1448C2×C4—21no—
1449C2×C4—22no—
1450C2×C4—21no—
1451C2×C4—22no—
1452C2×C4—22no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—24no—
1457C2×C4—24no—
1458C2×C4—22no—
1459C2×C4—24no—
1460C2×C4—22no—
1461C2×C4—22no—
1462C2×C4—22no—
1463C2×C4—24no—
1464C2×C4—24no—
1465C2×C4—22no—
1466C2×C4—21no—
1467C2×C4—24no—
1468C2×C4—22no—
1469C2×C4—22no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—22no—
1473C2×C4—22no—
1474C2×C4—21no—
1475C2×C4—416no—
1476C2×C4—48no—
1477C2×C4—416no—
1478C2×C4—48no—
1479C2×C4—416no—
1480C2×C4—48no—
1481C2×C4—48no—
1482C2×C4—88no—
1483C2×C4—88no—
1484C2×C4—88no—
1485C2×C4—88no—
1486C2×C4—84no—
1487C2×C4—84no—
1488C2×C4—88no—
1489C2×C4C22×#4114yes—
1490C2×C4C22×#4114yes—
1491C2×C4C22×#4118yes—
1492C2×C4C22×#4118yes—
1493C2×C4C22×#4114yes—
1494C2×C4C2×H(5,𝔽2)14yes—
1495C2×C4C2×H(5,𝔽2)14yes—
1496C2×C4C2×H(5,𝔽2)14yes—
1497C2×C4C2×H(5,𝔽2)12yes—
1498C2×C4#58512yes—
1499C22—24no—
1500C22—24no—
1501C22—24no—
1502C22—42no—
1503C22—42no—
1504C22—42no—
1505C22—42no—
1506C22—44no—
1507C22—44no—
1508C22—44no—
1509C22—42no—
1510C22—42no—
1511C22—44no—
1512C22—44no—
1513C22—42no—
1514C22—42no—
1515C22—42no—
1516C22—44no—
1517C22—44no—
1518C22—44no—
1519C22—42no—
1520C22—44no—
1521C22—42no—
1522C22—42no—
1523C22—42no—
1524C22—42no—
1525C22—44no—
1526C22—42no—
1527C22—44no—
1528C22—42no—
1529C22—42no—
1530C22C23×#4112yes—
1531C22C22×H(5,𝔽2)12yes—
1532C22C22×H(5,𝔽2)11yescharacteristic
1533C22C2×#58511yescharacteristic
1534C222−1+611yescharacteristic
1535C4—24no—
1536C4—28no—
1537C4—24no—
1538C4—24no—
1539C4—24no—
1540C4—24no—
1541C4—28no—
1542C4—22no—
1543C4—42no—
1544C4—44no—
1545C4—41no—
1546C4—41no—
1547C4—44no—
1548C4—41no—
1549C4—42no—
1550C4—42no—
1551C4—44no—
1552C4—42no—
1553C4—41no—
1554C4—41no—
1555C4—42no—
1556C4—42no—
1557C4—42no—
1558C4#348314yes—
1559C2—44no—
1560C2—84no—
1561C2—82no—
1562C2—82no—
1563C2—82no—
1564C2C2×#348311yescharacteristic
1565C2#6280012yes—
1566C2#6291911yescharacteristic
1567C2#6298512yes—
1568C2#6301111yescharacteristic
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. #60038C2semidirect
2. #59952C2semidirect
3. #59767C2semidirect
4. #59182C2semidirect
5. #59115C2semidirect
6. #59058C2semidirect
7. #45435C2semidirect
8. #45378C2semidirect
9. #45036C2semidirect
10. #44377C2semidirect
11. #44305C2semidirect
12. #44200C2semidirect
13. #38826C2semidirect
14. #38823C2semidirect
15. #38285C2semidirect
16. #37775C2semidirect
17. #36496C2semidirect
18. #36327C2semidirect
19. #36273C2semidirect
20. #36126C2semidirect
21. #36125C2semidirect
22. #35930C2semidirect
23. #35912C2semidirect
24. #35697C2semidirect
25. #34925C2semidirect
26. #34874C2semidirect
27. #34305C2semidirect
28. #34287C2semidirect
29. #34153C2semidirect
789. #125#41semidirect

Maximal subgroups

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

subgroupindex
#600382
#599522
#597672
#591822
#591152
#590582
#454352
#453782
#450362
#443772
#443052
#442002
#388262
#388232
#382852
#377752
#364962
#363272
#362732
#361262
#361252
#359302
#359122
#356972
#349252
#348742
#343052
#342872
#341532