Finite Group Databasebeta

← #7710080

Subgroups — #7710080

Order 512.

4754 conjugacy classes of subgroups.

The subgroup lattice has 1515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59714C212yesmaximal, complemented
2#59478C212yesmaximal, complemented
3#59188C214yesmaximal, complemented
4#46158C211yesmaximal, characteristic, complemented
5#46016C211yesmaximal, characteristic, complemented
6#46006C211yesmaximal, characteristic, complemented
7#45998C211yesmaximal, characteristic, complemented
8#45984C212yesmaximal, complemented
9#45975C212yesmaximal, complemented
10#40127C212yesmaximal, complemented
11#40118C212yesmaximal, complemented
12#40076C212yesmaximal, complemented
13#40047C212yesmaximal, complemented
14#39708C212yesmaximal, complemented
15#39582C212yesmaximal, complemented
16#38673C214yesmaximal, complemented
17#38493C212yesmaximal, complemented
18#38435C212yesmaximal, complemented
19#38003C214yesmaximal, complemented
20#37599C212yesmaximal, complemented
21#37056C214yesmaximal, complemented
22#36635C211yesmaximal, characteristic, complemented
23#36631C211yesmaximal, characteristic, complemented
24#36473C212yesmaximal, complemented
25#36379C212yesmaximal, complemented
26#36371C212yesmaximal, complemented
27#36368C212yesmaximal, complemented
28#35177C212yesmaximal, complemented
29#35038C212yesmaximal, complemented
30#34528C212yesmaximal, complemented
31C4×#529C211yesmaximal, characteristic, complemented
32C2×#563C2212yes—
33C2×#556C2214yes—
34C2×#529C2211yescharacteristic
35C2×#529C2212yes—
36#2864C2212yes—
37#2863C2212yes—
38#2863C2212yes—
39#2862C2211yescharacteristic
40#2861C2212yes—
41#2861C2212yes—
42#2860C2212yes—
43#2860C2212yes—
44#2860C2212yes—
45#2859C2211yescharacteristic
46#2859C2211yescharacteristic
47#2858C2211yescharacteristic
48#2857C2212yes—
49#2857C2211yescharacteristic
50#2857C2211yescharacteristic
51#2857C2211yescharacteristic
52#2856C2211yescharacteristic
53#2855C2212yes—
54#2855C2212yes—
55#2855C2212yes—
56#2854C2212yes—
57#2854C2212yes—
58#2851C2212yes—
59#2850C2212yes—
60#2844C2212yes—
61#2820C2212yes—
62#2820C2212yes—
63#2819C2212yes—
64#2808C2214yes—
65#2805C2212yes—
66#2805C2212yes—
67#2804C2212yes—
68#2798C2214yes—
69#2784C2214yes—
70#2781C2214yes—
71#2779C2214yes—
72#2775C2214yes—
73#2774C2214yes—
74#2773C2214yes—
75#2771C2214yes—
76#2758C2214yes—
77#2753C2214yes—
78#2747C2214yes—
79#2743C2214yes—
80#2737C2214yes—
81#2737C2214yes—
82#2734C2212yes—
83#2733C2212yes—
84#2731C2214yes—
85#2727C2212yes—
86#2727C2212yes—
87#2725C2214yes—
88#2723C2214yes—
89#2716C2214yes—
90#2714C2214yes—
91#2713C2214yes—
92#2712C2214yes—
93#2705C2214yes—
94#2705C2214yes—
95#2702C2214yes—
96#2696C2214yes—
97#2692C2214yes—
98#2683C2212yes—
99#2674C2214yes—
100#2665C2214yes—
101#2665C2214yes—
102#2663C2214yes—
103#2662C2214yes—
104#2650C2214yes—
105#2649C2214yes—
106#2648C2214yes—
107#2635C2214yes—
108#2610C2214yes—
109#2604C2214yes—
110#2604C2214yes—
111#2604C2214yes—
112#2602C2214yes—
113#2601C2214yes—
114#2596C2214yes—
115#2595C2214yes—
116#2592C2212yes—
117#2588C2214yes—
118#2584C2212yes—
119#2578C2214yes—
120#2573C2214yes—
121#2572C2214yes—
122#2567C2212yes—
123#2564C2214yes—
124#2563C2212yes—
125#2559C2214yes—
126#2557C2214yes—
127#2554C2214yes—
128#2551C2212yes—
129#2551C2212yes—
130#2542C2212yes—
131#2538C2212yes—
132#2533C2214yes—
133#2532C2214yes—
134#2530C2214yes—
135#2526C2214yes—
136#2526C2214yes—
137#2525C2214yes—
138#2522C2214yes—
139#2521C2214yes—
140#2521C2214yes—
141#2516C2214yes—
142#2512C2212yes—
143#2512C2212yes—
144#2511C2212yes—
145#2511C2212yes—
146#2511C2212yes—
147#2509C2214yes—
148#2497C2212yes—
149#2497C2212yes—
150#2496C2212yes—
151#2496C2212yes—
152#2492C2212yes—
153#2492C2214yes—
154#2492C2212yes—
155#2492C2212yes—
156#2491C2212yes—
157#2491C2212yes—
158#2490C2212yes—
159#2485C2212yes—
160#2479C2214yes—
161#2478C2214yes—
162#2477C2214yes—
163#2470C2214yes—
164#2469C2214yes—
165#2469C2214yes—
166#2469C2214yes—
167#2467C2214yes—
168#2467C2214yes—
169#2465C2214yes—
170#2465C2214yes—
171#2465C2214yes—
172#2463C2214yes—
173#2461C2214yes—
174#2461C2214yes—
175#2458C2214yes—
176#2457C2214yes—
177#2456C2214yes—
178#2453C2212yes—
179#2452C2212yes—
180#2452C2212yes—
181#2452C2214yes—
182#2452C2214yes—
183#2451C2212yes—
184#2450C2214yes—
185#2448C2212yes—
186#2446C2212yes—
187#2445C2212yes—
188#2441C2212yes—
189#2441C2212yes—
190#2432C2212yes—
191#2431C2212yes—
192#2427C2212yes—
193#2422C2212yes—
194#2415C2214yes—
195#2414C2212yes—
196#2407C2212yes—
197#2407C2212yes—
198#2382C2212yes—
199#2382C2212yes—
200#2379C2212yes—
201#2373C2214yes—
202#2373C2214yes—
203#2373C2214yes—
204#2370C2212yes—
205#2368C2214yes—
206#2367C2212yes—
207#2365C2214yes—
208#2365C2212yes—
209#2362C2214yes—
210#2362C2212yes—
211#2362C2214yes—
212#2359C2214yes—
213#2359C2214yes—
214#2354C2212yes—
215#2347C2212yes—
216#2341C2212yes—
217#2339C2212yes—
218#2335C2214yes—
219#2334C2214yes—
220#2334C2214yes—
221#2333C2214yes—
222#2331C2214yes—
223#2329C2214yes—
224#2323C2214yes—
225#2319C2214yes—
226C4×C4⋊Q8C2212yes—
227C4×C4⋊Q8C2211yescharacteristic
228C4×C4⋊Q8C2211yescharacteristic
229C4×C4⋊Q8C2211yescharacteristic
230C4×#127C2211yescharacteristic
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×D4C2211yescharacteristic
264C42×D4C2212yes—
265C4×#117C2212yes—
266C2×C43C2211yescharacteristic
267C22×#41C2312yes—
268#563—216no—
269#556—416no—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2314yes—
277C2×#127C2311yescharacteristic
278#529—28no—
279#529—48no—
280C2×#126C2312yes—
281C2×#126C2314yes—
282C2×#126C2314yes—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#126C2314yes—
286C2×#126C2314yes—
287C2×#125C2312yes—
288C2×#125C2312yes—
289C2×#125C2312yes—
290C2×#125C2311yescharacteristic
291C2×#124C2311yescharacteristic
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#124C2312yes—
295C2×#124C2314yes—
296C2×#124C2314yes—
297C2×#123C2314yes—
298C2×#123C2312yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2311yescharacteristic
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×#121C2312yes—
312C2×#121C2311yescharacteristic
313C2×#121C2312yes—
314C2×#121C2312yes—
315C2×#121C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2314yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2314yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2314yes—
336C2×C4×D4C2311yescharacteristic
337C2×#117C2312yes—
338C2×#117C2312yes—
339C2×#117C2314yes—
340C2×#117C2312yes—
341C2×#117C2314yes—
342C22×C42C2311yescharacteristic
343C22×C42C2311yescharacteristic
344C22×C42C2311yescharacteristic
345C22×C42C2311yescharacteristic
346C22×C42C2311yescharacteristic
347C22×C42C2311yescharacteristic
348C22×C42C2312yes—
349C22×C42C2311yescharacteristic
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#399C2314yes—
366#399C2314yes—
367#399C2314yes—
368#399C2314yes—
369#399C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#391C2314yes—
434#391C2312yes—
435#391C2312yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2311yescharacteristic
451#391C2312yes—
452#391C2311yescharacteristic
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2314yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2314yes—
465#390C2314yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2311yescharacteristic
473#390C2312yes—
474#390C2311yescharacteristic
475#389C2311yescharacteristic
476#389C2312yes—
477#389C2311yescharacteristic
478#389C2312yes—
479#389C2311yescharacteristic
480#389C2311yescharacteristic
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2312yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2314yes—
516#388C2312yes—
517#388C2312yes—
518#388C2312yes—
519#388C2312yes—
520#388C2312yes—
521#388C2312yes—
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#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2312yes—
563#388C2312yes—
564#387C2312yes—
565#387C2312yes—
566#387C2312yes—
567#387C2312yes—
568#387C2312yes—
569#387C2312yes—
570#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2312yes—
620#386C2312yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2312yes—
633#385C2312yes—
634#384C2311yescharacteristic
635#384C2311yescharacteristic
636#384C2311yescharacteristic
637#384C2311yescharacteristic
638#384C2312yes—
639#384C2312yes—
640#383C2312yes—
641#383C2314yes—
642#383C2314yes—
643#382C2312yes—
644#382C2311yescharacteristic
645#382C2311yescharacteristic
646#382C2314yes—
647#382C2312yes—
648#382C2312yes—
649#382C2312yes—
650#381C2314yes—
651#381C2314yes—
652#381C2314yes—
653#381C2312yes—
654#380C2312yes—
655#380C2312yes—
656#380C2312yes—
657#380C2312yes—
658#380C2314yes—
659#380C2314yes—
660#380C2312yes—
661#380C2314yes—
662#380C2314yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2311yescharacteristic
669#380C2311yescharacteristic
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2311yescharacteristic
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2314yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2312yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2312yes—
724#376C2314yes—
725#376C2312yes—
726#376C2312yes—
727#376C2314yes—
728C2×#95C2314yes—
729C43C2311yescharacteristic
730C43C2311yescharacteristic
731C43C2311yescharacteristic
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C43C2312yes—
735C43C2311yescharacteristic
736C43C2311yescharacteristic
737C43C2311yescharacteristic
738C2×#41—44no—
739C2×#41—44no—
740C2×#41—44no—
741C22×Q8C2412yes—
742C22×Q8C2411yescharacteristic
743C22×Q8C2414yes—
744C22×Q8C2412yes—
745C22×Q8C2412yes—
746C22×Q8C2414yes—
747C22×D4C2412yes—
748C22×D4C2412yes—
749C22×D4C2411yescharacteristic
750C22×D4C2414yes—
751C22×D4C2412yes—
752C22×D4C2412yes—
753C22×D4C2414yes—
754C22×D4C2414yes—
755C23×C4C2412yes—
756C23×C4C2411yescharacteristic
757C23×C4C2412yes—
758C23×C4C2411yescharacteristic
759C23×C4C2411yescharacteristic
760C23×C4C2411yescharacteristic
761C23×C4C2411yescharacteristic
762C23×C4C2414yes—
763C23×C4C2414yes—
764C23×C4C2412yes—
765C23×C4C2411yescharacteristic
766C23×C4C2414yes—
767C23×C4C2411yescharacteristic
768C4⋊Q8—216no—
769C4⋊Q8—44no—
770C4⋊Q8—42no—
771C4⋊Q8—42no—
772C4⋊Q8—44no—
773C4⋊Q8—42no—
774C4⋊Q8—48no—
775#127—42no—
776#126—28no—
777#126—216no—
778#126—216no—
779#126—216no—
780#126—48no—
781#126—48no—
782#126—48no—
783#125—28no—
784#125—44no—
785#125—44no—
786#125#4118yescomplemented
787#124—24no—
788#124—28no—
789#124—44no—
790#124—48no—
791#124—44no—
792#124—48no—
793#123—28no—
794#123—216no—
795#123—48no—
796#123—48no—
797C22⋊Q8—24no—
798C22⋊Q8—216no—
799C22⋊Q8—216no—
800C22⋊Q8—48no—
801C22⋊Q8—48no—
802C22⋊Q8—44no—
803C22⋊Q8—44no—
804C22⋊Q8—48no—
805C22⋊Q8—44no—
806C22⋊Q8—44no—
807#121—28no—
808#121—24no—
809#121—44no—
810#121—44no—
811#121—44no—
812C4×Q8—24no—
813C4×Q8—28no—
814C4×Q8—42no—
815C4×Q8—42no—
816C4×Q8—44no—
817C4×Q8—48no—
818C4×Q8—48no—
819C4×Q8—44no—
820C4×Q8—44no—
821C4×D4—28no—
822C4×D4—24no—
823C4×D4—28no—
824C4×D4—42no—
825C4×D4—44no—
826C4×D4—44no—
827C4×D4—44no—
828C4×D4—44no—
829C4×D4—42no—
830C4×D4—44no—
831C4×D4—48no—
832C4×D4—48no—
833#117—28no—
834#117—28no—
835#117—48no—
836#117—48no—
837#117—44no—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2411yescharacteristic
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2411yescharacteristic
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
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×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C42—24no—
941C2×C42—24no—
942C2×C42—24no—
943C2×C42—44no—
944C2×C42—42no—
945C2×C42—42no—
946C2×C42—42no—
947C2×C42—42no—
948C2×C42C2411yescharacteristic
949C2×C42C2411yescharacteristic
950C2×C42C2412yes—
951C2×C42C2414yes—
952C2×C42C2412yes—
953C2×C42C2411yescharacteristic
954C2×C42C2411yescharacteristic
955C2×C42C2411yescharacteristic
956C2×C42C2412yes—
957C2×C42C2411yescharacteristic
958C2×C42C2411yescharacteristic
959C2×C42C2411yescharacteristic
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2411yescharacteristic
963C2×C42C2412yes—
964C2×C42C2411yescharacteristic
965C2×C42C2414yes—
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968C2×C42C2411yescharacteristic
969C2×C42C2411yescharacteristic
970C2×C42C2411yescharacteristic
971C2×C42C2411yescharacteristic
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974C2×C42C2414yes—
975C2×C42C2414yes—
976C2×C42C2414yes—
977C2×C42C2414yes—
978C2×C42C2414yes—
979C2×C42C2412yes—
980C2×C42C2414yes—
981C2×C42C2414yes—
982C2×C42C2411yescharacteristic
983C2×C42C2411yescharacteristic
984C2×C42C2411yescharacteristic
985C2×C42C2411yescharacteristic
986C2×C42C2411yescharacteristic
987C2×C42C2411yescharacteristic
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2412yes—
991C2×C42C2412yes—
992C2×C42C2411yescharacteristic
993C2×C42C2411yescharacteristic
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054C24C2514yes—
1055C24C2512yes—
1056C24C2511yescharacteristic
1057#41—816no—
1058C2×Q8—22no—
1059C2×Q8—28no—
1060C2×Q8—24no—
1061C2×Q8—24no—
1062C2×Q8—24no—
1063C2×Q8—24no—
1064C2×Q8—24no—
1065C2×Q8—41no—
1066C2×Q8—41no—
1067C2×Q8—44no—
1068C2×Q8—42no—
1069C2×Q8—44no—
1070C2×Q8—42no—
1071C2×Q8—44no—
1072C2×Q8—42no—
1073C2×Q8—44no—
1074C2×Q8—42no—
1075C2×Q8—44no—
1076C2×D4—24no—
1077C2×D4—28no—
1078C2×D4—24no—
1079C2×D4—22no—
1080C2×D4—24no—
1081C2×D4—24no—
1082C2×D4—24no—
1083C2×D4—24no—
1084C2×D4—24no—
1085C2×D4—42no—
1086C2×D4—41no—
1087C2×D4—41no—
1088C2×D4—44no—
1089C2×D4—42no—
1090C2×D4—44no—
1091C2×D4—42no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C2×D4—42no—
1096C2×D4—42no—
1097C2×D4—44no—
1098C2×D4—44no—
1099C2×D4—44no—
1100C22×C4—22no—
1101C22×C4—22no—
1102C22×C4—22no—
1103C22×C4—22no—
1104C22×C4—22no—
1105C22×C4—24no—
1106C22×C4—22no—
1107C22×C4—22no—
1108C22×C4—22no—
1109C22×C4—24no—
1110C22×C4—22no—
1111C22×C4—22no—
1112C22×C4—22no—
1113C22×C4—22no—
1114C22×C4—24no—
1115C22×C4—24no—
1116C22×C4—24no—
1117C22×C4—28no—
1118C22×C4—24no—
1119C22×C4—28no—
1120C22×C4—41no—
1121C22×C4—41no—
1122C22×C4—41no—
1123C22×C4—42no—
1124C22×C4—41no—
1125C22×C4—41no—
1126C22×C4—41no—
1127C22×C4—41no—
1128C22×C4—41no—
1129C22×C4—42no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—42no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4—44no—
1138C22×C42−1+414yes—
1139C22×C4C2511yescharacteristic
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2514yes—
1143C22×C4C2511yescharacteristic
1144C22×C4C2511yescharacteristic
1145C22×C4C2511yescharacteristic
1146C22×C4C2512yes—
1147C22×C4C2514yes—
1148C22×C4C2514yes—
1149C22×C4C2512yes—
1150C22×C4C2514yes—
1151C22×C4C2514yes—
1152C22×C4C2512yes—
1153C22×C4C2514yes—
1154C22×C4C2514yes—
1155C22×C4C2512yes—
1156C22×C4C2511yescharacteristic
1157C22×C4C2511yescharacteristic
1158C22×C4C2511yescharacteristic
1159C22×C4C2512yes—
1160C22×C4C2511yescharacteristic
1161C22×C4C2511yescharacteristic
1162C22×C4C2511yescharacteristic
1163C22×C4C2511yescharacteristic
1164C22×C4C2511yescharacteristic
1165C22×C4C2511yescharacteristic
1166C22×C4C2511yescharacteristic
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—28no—
1171C4⋊C4—28no—
1172C4⋊C4—28no—
1173C4⋊C4—28no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—28no—
1178C4⋊C4—28no—
1179C4⋊C4—28no—
1180C4⋊C4—24no—
1181C4⋊C4—28no—
1182C4⋊C4—24no—
1183C4⋊C4—24no—
1184C4⋊C4—24no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—24no—
1189C4⋊C4—24no—
1190C4⋊C4—28no—
1191C4⋊C4—24no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—41no—
1197C4⋊C4—41no—
1198C4⋊C4—42no—
1199C4⋊C4—41no—
1200C4⋊C4—41no—
1201C4⋊C4—42no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—42no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—42no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—42no—
1217C4⋊C4—42no—
1218C4⋊C4—42no—
1219C4⋊C4—42no—
1220C4⋊C4—44no—
1221C4⋊C4C2×#4118yes—
1222C4⋊C4C2×#4114yes—
1223C4⋊C4C2×#4118yes—
1224C4⋊C4C2×#4114yes—
1225C22⋊C4—24no—
1226C22⋊C4—24no—
1227C22⋊C4—24no—
1228C22⋊C4—24no—
1229C22⋊C4—24no—
1230C22⋊C4—24no—
1231C22⋊C4—28no—
1232C22⋊C4—28no—
1233C22⋊C4—28no—
1234C22⋊C4—28no—
1235C22⋊C4—28no—
1236C22⋊C4—24no—
1237C22⋊C4—24no—
1238C22⋊C4—28no—
1239C22⋊C4—28no—
1240C22⋊C4—28no—
1241C22⋊C4—24no—
1242C22⋊C4—28no—
1243C22⋊C4—24no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—42no—
1250C22⋊C4—44no—
1251C22⋊C4—42no—
1252C22⋊C4—42no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C42—22no—
1270C42—22no—
1271C42—22no—
1272C42—24no—
1273C42—28no—
1274C42—22no—
1275C42—22no—
1276C42—22no—
1277C42—24no—
1278C42—28no—
1279C42—22no—
1280C42—22no—
1281C42—22no—
1282C42—22no—
1283C42—24no—
1284C42—22no—
1285C42—22no—
1286C42—22no—
1287C42—22no—
1288C42—22no—
1289C42—24no—
1290C42—22no—
1291C42—22no—
1292C42—22no—
1293C42—24no—
1294C42—24no—
1295C42—41no—
1296C42—41no—
1297C42—42no—
1298C42—41no—
1299C42—41no—
1300C42—42no—
1301C42—41no—
1302C42—41no—
1303C42—41no—
1304C42—41no—
1305C42—44no—
1306C42—44no—
1307C42—44no—
1308C42—44no—
1309C42—44no—
1310C42—42no—
1311C42—44no—
1312C42—44no—
1313C42C2×#4114yes—
1314C42H(5,𝔽2)14yes—
1315C23—21no—
1316C23—21no—
1317C23—21no—
1318C23—21no—
1319C23—21no—
1320C23—21no—
1321C23—24no—
1322C23—22no—
1323C23—24no—
1324C23—22no—
1325C23—22no—
1326C23—24no—
1327C23—22no—
1328C23—24no—
1329C23—22no—
1330C23—24no—
1331C23—22no—
1332C23—24no—
1333C23—22no—
1334C23—24no—
1335C23C2×2−1+412yes—
1336C23C2611yescharacteristic
1337Q8—44no—
1338Q8—48no—
1339Q8—84no—
1340Q8—88no—
1341Q8—84no—
1342Q8—88no—
1343D4—48no—
1344D4—44no—
1345D4—48no—
1346D4—84no—
1347D4—84no—
1348D4—88no—
1349D4—88no—
1350D4—88no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—22no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—22no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—22no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—22no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—21no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—24no—
1385C2×C4—24no—
1386C2×C4—24no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—24no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—22no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—24no—
1403C2×C4—22no—
1404C2×C4—21no—
1405C2×C4—22no—
1406C2×C4—24no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—24no—
1411C2×C4—24no—
1412C2×C4—22no—
1413C2×C4—24no—
1414C2×C4—22no—
1415C2×C4—24no—
1416C2×C4—24no—
1417C2×C4—24no—
1418C2×C4—24no—
1419C2×C4—24no—
1420C2×C4—24no—
1421C2×C4—44no—
1422C2×C4—44no—
1423C2×C4—48no—
1424C2×C4—44no—
1425C2×C4—44no—
1426C2×C4—44no—
1427C2×C4—44no—
1428C2×C4—44no—
1429C2×C4—48no—
1430C2×C4—88no—
1431C2×C4—88no—
1432C2×C4—84no—
1433C2×C4—88no—
1434C2×C4C22×#4114yes—
1435C2×C4C22×#4112yes—
1436C2×C4C22×#4112yes—
1437C2×C4C22×#4112yes—
1438C2×C4C22×#4114yes—
1439C2×C4C2×H(5,𝔽2)12yes—
1440C2×C4C2×H(5,𝔽2)12yes—
1441C2×C4C2×H(5,𝔽2)12yes—
1442C2×C4C2×2−1+412yes—
1443C2×C4C2×2−1+412yes—
1444C2×C4#58512yes—
1445C2×C4#58512yes—
1446C2×C4#58512yes—
1447C2×C4#58512yes—
1448C22—22no—
1449C22—22no—
1450C22—22no—
1451C22—41no—
1452C22—41no—
1453C22—41no—
1454C22—41no—
1455C22—42no—
1456C22—44no—
1457C22—44no—
1458C22—42no—
1459C22—42no—
1460C22—44no—
1461C22—42no—
1462C22—44no—
1463C22—42no—
1464C22—44no—
1465C22—42no—
1466C22—44no—
1467C22—44no—
1468C22—42no—
1469C22C23×#4111yescharacteristic
1470C22C22×H(5,𝔽2)11yescharacteristic
1471C22C22×2−1+411yescharacteristic
1472C22C2×#58511yescharacteristic
1473C22C2×#58511yescharacteristic
1474C22C2×#58511yescharacteristic
1475C22C2×#58511yescharacteristic
1476C4—22no—
1477C4—22no—
1478C4—22no—
1479C4—22no—
1480C4—24no—
1481C4—22no—
1482C4—22no—
1483C4—24no—
1484C4—22no—
1485C4—22no—
1486C4—22no—
1487C4—41no—
1488C4—42no—
1489C4—44no—
1490C4—44no—
1491C4—44no—
1492C4—42no—
1493C4—44no—
1494C4—41no—
1495C4—42no—
1496C4—44no—
1497C4—44no—
1498C4—41no—
1499C4—42no—
1500C4—42no—
1501C4—41no—
1502C4—44no—
1503C4#356814yes—
1504C2—42no—
1505C2—82no—
1506C2—84no—
1507C2C2×#356811yescharacteristic
1508C2#6274811yescharacteristic
1509C2#6279311yescharacteristic
1510C2#6280011yescharacteristic
1511C2#6280511yescharacteristic
1512C2#6282311yescharacteristic
1513C2#6283511yescharacteristic
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. #59714C2semidirect
2. #59478C2semidirect
3. #59188C2semidirect
4. #46158C2semidirect
5. #46016C2semidirect
6. #46006C2semidirect
7. #45998C2semidirect
8. #45984C2semidirect
9. #45975C2semidirect
10. #40127C2semidirect
11. #40118C2semidirect
12. #40076C2semidirect
13. #40047C2semidirect
14. #39708C2semidirect
15. #39582C2semidirect
16. #38673C2semidirect
17. #38493C2semidirect
18. #38435C2semidirect
19. #38003C2semidirect
20. #37599C2semidirect
21. #37056C2semidirect
22. #36635C2semidirect
23. #36631C2semidirect
24. #36473C2semidirect
25. #36379C2semidirect
26. #36371C2semidirect
27. #36368C2semidirect
28. #35177C2semidirect
29. #35038C2semidirect
30. #34528C2semidirect
31. C4×#529C2semidirect
786. #125#41semidirect

Maximal subgroups

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

subgroupindex
#597142
#594782
#591882
#461582
#460162
#460062
#459982
#459842
#459752
#401272
#401182
#400762
#400472
#397082
#395822
#386732
#384932
#384352
#380032
#375992
#370562
#366352
#366312
#364732
#363792
#363712
#363682
#351772
#350382
#345282
C4×#5292