Finite Group Databasebeta

← #8957952

Subgroups — #8957952

Order 512.

5306 conjugacy classes of subgroups.

The subgroup lattice has 1394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58388C212yesmaximal, complemented
2#58295C214yesmaximal, complemented
3#57628C214yesmaximal, complemented
4#55702C212yesmaximal, complemented
5#51975C214yesmaximal, complemented
6#51898C214yesmaximal, complemented
7#51751C214yesmaximal, complemented
8#51040C212yesmaximal, complemented
9#50167C212yesmaximal, complemented
10#48796C212yesmaximal, complemented
11#47068C214yesmaximal, complemented
12#44428C214yesmaximal, complemented
13#43418C214yesmaximal, complemented
14#42595C214yesmaximal, complemented
15#41827C214yesmaximal, complemented
16#41381C212yesmaximal, complemented
17#37753C212yesmaximal, complemented
18#37745C212yesmaximal, complemented
19#36706C211yesmaximal, characteristic, complemented
20#36004C212yesmaximal, complemented
21#35857C212yesmaximal, complemented
22#35565C211yesmaximal, characteristic, complemented
23#35351C211yesmaximal, characteristic, complemented
24C2×#562C2214yescomplemented
25C2×#555C2212yes—
26C2×#544C2212yescomplemented
27C2×#538C2211yescharacteristic
28C2×#537C2211yescharacteristic
29C2×#537C2212yescomplemented
30C2×#535C2212yes—
31C2×#525C2212yes—
32C22×#121C2211yescharacteristic
33C2×#518C2211yescharacteristic
34#2848C2211yescharacteristic
35#2847C2211yescharacteristic
36#2838C2214yescomplemented
37#2834C2212yescomplemented
38#2826C2212yescomplemented
39#2825C2214yescomplemented
40#2825C2214yescomplemented
41#2821C2212yescomplemented
42#2813C2212yescomplemented
43#2778C2214yescomplemented
44#2761C2214yescomplemented
45#2761C2214yescomplemented
46#2760C2212yescomplemented
47#2760C2214yescomplemented
48#2752C2212yescomplemented
49#2751C2214yescomplemented
50#2749C2214yescomplemented
51#2749C2214yescomplemented
52#2740C2214yescomplemented
53#2738C2214yescomplemented
54#2732C2214yescomplemented
55#2730C2214yescomplemented
56#2729C2214yescomplemented
57#2711C2214yescomplemented
58#2711C2214yescomplemented
59#2711C2214yescomplemented
60#2709C2214yescomplemented
61#2709C2214yescomplemented
62#2709C2214yescomplemented
63#2708C2214yescomplemented
64#2707C2214yes—
65#2703C2214yescomplemented
66#2703C2214yescomplemented
67#2700C2214yescomplemented
68#2699C2214yes—
69#2694C2214yescomplemented
70#2694C2214yescomplemented
71#2692C2214yescomplemented
72#2692C2214yescomplemented
73#2692C2214yescomplemented
74#2691C2214yes—
75#2688C2214yescomplemented
76#2688C2214yescomplemented
77#2687C2214yes—
78#2686C2214yes—
79#2684C2214yes—
80#2678C2214yes—
81#2677C2212yescomplemented
82#2677C2214yescomplemented
83#2676C2214yes—
84#2676C2214yescomplemented
85#2676C2214yescomplemented
86#2676C2214yescomplemented
87#2675C2214yes—
88#2675C2212yescomplemented
89#2674C2214yes—
90#2674C2214yescomplemented
91#2674C2214yescomplemented
92#2673C2214yescomplemented
93#2673C2214yescomplemented
94#2671C2214yes—
95#2671C2214yes—
96#2671C2214yescomplemented
97#2670C2214yes—
98#2668C2214yes—
99#2665C2212yes—
100#2661C2214yescomplemented
101#2661C2214yescomplemented
102#2658C2212yescomplemented
103#2656C2212yescomplemented
104#2655C2214yescomplemented
105#2640C2214yescomplemented
106#2639C2214yescomplemented
107#2639C2212yescomplemented
108#2639C2212yescomplemented
109#2635C2212yes—
110#2631C2214yescomplemented
111#2631C2212yescomplemented
112#2627C2212yescomplemented
113#2626C2211yescharacteristic
114#2624C2212yes—
115#2624C2212yescomplemented
116#2618C2212yescomplemented
117#2617C2211yescharacteristic
118#2610C2214yescomplemented
119#2610C2214yescomplemented
120#2607C2212yescomplemented
121#2603C2212yescomplemented
122#2600C2212yescomplemented
123#2598C2214yescomplemented
124#2597C2214yescomplemented
125#2579C2212yes—
126#2577C2214yescomplemented
127#2576C2214yes—
128#2557C2214yescomplemented
129#2556C2214yescomplemented
130#2556C2214yescomplemented
131#2555C2214yescomplemented
132#2544C2214yescomplemented
133#2541C2214yes—
134#2541C2214yes—
135#2540C2214yes—
136#2540C2214yes—
137#2540C2214yescomplemented
138#2539C2212yes—
139#2539C2212yes—
140#2534C2214yes—
141#2527C2214yes—
142#2526C2214yescomplemented
143#2520C2214yescomplemented
144#2514C2214yescomplemented
145#2498C2212yescomplemented
146#2491C2214yescomplemented
147#2491C2214yescomplemented
148#2484C2212yes—
149#2483C2212yes—
150#2482C2212yes—
151#2479C2214yescomplemented
152#2477C2214yes—
153#2477C2214yescomplemented
154#2476C2214yescomplemented
155#2475C2214yes—
156#2472C2214yes—
157#2472C2214yes—
158#2472C2214yes—
159#2471C2214yescomplemented
160#2471C2214yescomplemented
161#2471C2214yescomplemented
162#2464C2214yescomplemented
163#2461C2214yescomplemented
164#2460C2214yescomplemented
165#2459C2214yescomplemented
166#2452C2214yescomplemented
167#2452C2214yescomplemented
168#2450C2214yescomplemented
169#2449C2214yescomplemented
170#2447C2214yescomplemented
171#2444C2214yes—
172#2444C2214yes—
173#2444C2214yescomplemented
174#2443C2214yes—
175#2443C2214yes—
176#2443C2214yescomplemented
177#2438C2214yescomplemented
178#2433C2212yes—
179#2433C2212yes—
180#2432C2214yes—
181#2431C2214yescomplemented
182#2431C2214yescomplemented
183#2430C2214yes—
184#2430C2214yescomplemented
185#2428C2214yescomplemented
186#2428C2214yescomplemented
187#2424C2214yes—
188#2424C2214yes—
189#2420C2214yescomplemented
190#2411C2214yes—
191#2410C2212yes—
192#2410C2212yes—
193#2408C2212yes—
194#2407C2214yescomplemented
195#2405C2212yes—
196#2404C2214yes—
197#2401C2214yescomplemented
198#2395C2212yes—
199#2392C2214yescomplemented
200#2377C2212yes—
201#2371C2214yescomplemented
202#2368C2214yescomplemented
203#2366C2214yescomplemented
204#2364C2214yescomplemented
205#2363C2214yescomplemented
206#2359C2214yescomplemented
207#2353C2212yes—
208#2347C2212yes—
209#2339C2214yescomplemented
210#2333C2214yescomplemented
211#2329C2212yescomplemented
212#2328C2214yescomplemented
213#2325C2212yescomplemented
214#2315C2211yescharacteristic
215#2308C2211yescharacteristic
216#2308C2212yes—
217C2×#385C2212yes—
218#2274C2211yescharacteristic
219C22×#41C2312yes—
220C22×#41C2314yes—
221C23×D4C2311yescharacteristic
222C23×D4C2311yescharacteristic
223C23×D4C2311yescharacteristic
224C24×C4C2311yescharacteristic
225#562—416no—
226#555—48no—
227#544—48no—
228#538—44no—
229#537—44no—
230#537—48no—
231#535—48no—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2314yes—
234C2×C4⋊Q8C2314yes—
235C2×#127C2314yes—
236C2×#127C2314yes—
237C2×#127C2314yes—
238C2×#126C2312yes—
239C2×#125C2314yes—
240C2×#125C2314yes—
241C2×#124C2314yes—
242C2×#124C2314yes—
243C2×#124C2312yes—
244C2×#124C2314yes—
245C2×#124C2314yes—
246C2×#124C2314yes—
247C2×#124C2314yes—
248#525—48no—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2312yes—
255C2×#123C2314yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×#121—44no—
268C2×#121C2312yes—
269C2×#121C2314yes—
270C2×#121C2312yes—
271C2×#121C2314yes—
272C2×#121C2311yescharacteristic
273C2×#121C2312yes—
274C2×#121C2312yes—
275C2×#121C2314yes—
276C2×#121C2312yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2312yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×#121C2314yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#121C2312yes—
290C2×#121C2314yes—
291C2×#120C2314yes—
292C2×#120C2312yes—
293C2×#120C2314yes—
294C2×#120C2314yes—
295C2×#120C2312yes—
296C2×#120C2312yes—
297#518—44no—
298C2×C4×D4C2312yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2314yes—
307C2×#117C2312yes—
308C2×#117C2312yes—
309C2×#117C2314yes—
310C2×#117C2314yes—
311C2×#117C2312yes—
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2312yes—
315C22×C22⋊C4C2311yescharacteristic
316C22×C22⋊C4C2312yes—
317C22×C22⋊C4C2312yes—
318C22×C22⋊C4C2311yescharacteristic
319C22×C22⋊C4C2312yes—
320C22×C22⋊C4C2312yes—
321#401C2314yes—
322#401C2314yes—
323#400C2312yes—
324#400C2312yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#399C2312yes—
332#399C2312yes—
333#399C2312yes—
334#399C2312yes—
335#399C2314yes—
336#399C2312yes—
337#399C2312yes—
338#399C2312yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2312yes—
343#399C2312yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2312yes—
351#398C2314yes—
352#398C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2312yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2312yes—
367#397C2314yes—
368#397C2312yes—
369#397C2312yes—
370#397C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2312yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2312yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#392C2312yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#392C2312yes—
433#392C2312yes—
434#392C2314yes—
435#392C2312yes—
436#392C2312yes—
437#392C2314yes—
438#392C2314yes—
439#392C2312yes—
440#392C2314yes—
441#392C2314yes—
442#392C2314yes—
443#392C2314yes—
444#392C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2314yes—
460#390C2314yes—
461#390C2314yes—
462#390C2314yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2314yes—
467#390C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2312yes—
528#386C2314yes—
529#386C2312yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#385C2312yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2312yes—
564#385C2312yes—
565#385C2312yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#383C2312yes—
579#383C2314yes—
580#382C2314yes—
581#381C2314yes—
582#381C2312yes—
583#381C2314yes—
584#381C2314yes—
585#381C2314yes—
586#381C2312yes—
587#381C2312yes—
588#381C2314yes—
589#380C2312yes—
590#380C2311yescharacteristic
591#380C2311yescharacteristic
592#380C2312yes—
593#380C2312yes—
594#380C2312yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#379C2314yes—
599#379C2312yes—
600#379C2312yes—
601#379C2312yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618#376C2314yes—
619#376C2312yes—
620C2×#95C2312yes—
621C2×#95C2312yes—
622C2×#95C2314yes—
623C2×#95C2312yes—
624C25C2411yescharacteristic
625C25C2411yescharacteristic
626C25C2411yescharacteristic
627C2×#41—44no—
628C2×#41—44no—
629C2×#41—48no—
630C2×#41—44no—
631C2×#41—48no—
632C2×#41—84no—
633C22×Q8C2412yes—
634C22×Q8C2414yes—
635C22×Q8C2414yes—
636C22×Q8C2411yescharacteristic
637C22×D4—24no—
638C22×D4—44no—
639C22×D4—42no—
640C22×D4—42no—
641C22×D4—44no—
642C22×D4—44no—
643C22×D4C2414yes—
644C22×D4C2414yes—
645C22×D4C2412yes—
646C22×D4C2414yes—
647C22×D4C2414yes—
648C22×D4C2414yes—
649C22×D4C2412yes—
650C22×D4C2414yes—
651C22×D4C2414yes—
652C22×D4C2412yes—
653C22×D4C2414yes—
654C22×D4C2414yes—
655C22×D4C2412yes—
656C22×D4C2414yes—
657C22×D4C2412yes—
658C22×D4C2414yes—
659C22×D4C2414yes—
660C22×D4C2411yescharacteristic
661C22×D4C2414yes—
662C22×D4C2412yes—
663C22×D4C2414yes—
664C23×C4—44no—
665C23×C4—42no—
666C23×C4C2411yescharacteristic
667C23×C4C2411yescharacteristic
668C23×C4C2412yes—
669C23×C4C2411yescharacteristic
670C23×C4C2412yes—
671C23×C4C2412yes—
672C23×C4C2412yes—
673C23×C4C2412yes—
674C23×C4C2414yes—
675C23×C4C2414yes—
676C23×C4C2412yes—
677C23×C4C2412yes—
678C23×C4C2412yes—
679C23×C4C2412yes—
680C23×C4C2414yes—
681C23×C4C2414yes—
682C23×C4C2414yes—
683C23×C4C2411yescharacteristic
684C4⋊Q8—48no—
685C4⋊Q8—44no—
686C4⋊Q8—48no—
687#127—48no—
688#127—48no—
689#127—48no—
690#126—44no—
691#125—216no—
692#125—48no—
693#124—48no—
694#124—44no—
695#124—48no—
696#124—48no—
697#124—48no—
698#124—48no—
699#124—84no—
700#123—48no—
701#123—44no—
702#123—48no—
703#123—48no—
704#123—48no—
705#123—48no—
706#123—48no—
707C22⋊Q8—28no—
708C22⋊Q8—216no—
709C22⋊Q8—42no—
710C22⋊Q8—48no—
711C22⋊Q8—48no—
712C22⋊Q8—48no—
713C22⋊Q8—48no—
714C22⋊Q8—48no—
715C22⋊Q8—44no—
716C22⋊Q8—48no—
717C22⋊Q8—44no—
718#121—28no—
719#121—28no—
720#121—216no—
721#121—48no—
722#121—44no—
723#121—44no—
724#121—48no—
725#121—48no—
726#121—48no—
727#121—48no—
728#121—48no—
729#121—48no—
730#121—48no—
731#121—48no—
732#121—48no—
733#121—48no—
734#121—44no—
735#121—48no—
736#121—44no—
737#121—48no—
738#121—44no—
739#121—42no—
740#121—84no—
741#120—48no—
742#120—48no—
743#120—48no—
744#120—44no—
745#120—82no—
746#120—82no—
747C4×D4—28no—
748C4×D4—48no—
749C4×D4—48no—
750C4×D4—48no—
751C4×D4—48no—
752C4×D4—44no—
753C4×D4—84no—
754C4×D4—84no—
755C4×D4—84no—
756#117—28no—
757#117—28no—
758#117—48no—
759#117—48no—
760#117—44no—
761C2×C4⋊C4—24no—
762C2×C4⋊C4—44no—
763C2×C4⋊C4—44no—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C22⋊C4—24no—
800C2×C22⋊C4—44no—
801C2×C22⋊C4—44no—
802C2×C22⋊C4—44no—
803C2×C22⋊C4—42no—
804C2×C22⋊C4—82no—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2414yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2412yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875#95C2414yes—
876#95C2412yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2412yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2412yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2412yes—
893#95C2412yes—
894#95C2412yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2412yes—
909#95C2414yes—
910#95C2414yes—
911#95C2412yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919C24—22no—
920C24—24no—
921C24—22no—
922C24—22no—
923C24—41no—
924C24—42no—
925C24—41no—
926C24—42no—
927C24—41no—
928C24—41no—
929C24—42no—
930C24—42no—
931C24—41no—
932C24—42no—
933C24—41no—
934C24C2512yes—
935C24C2512yes—
936C24C2512yes—
937C24C2514yes—
938C24C2511yescharacteristic
939C24C2512yes—
940#41—816no—
941#41—832no—
942C2×Q8—28no—
943C2×Q8—24no—
944C2×Q8—42no—
945C2×Q8—42no—
946C2×Q8—44no—
947C2×Q8—44no—
948C2×Q8—44no—
949C2×Q8—41no—
950C2×Q8—42no—
951C2×Q8—44no—
952C2×Q8—44no—
953C2×D4—28no—
954C2×D4—28no—
955C2×D4—24no—
956C2×D4—28no—
957C2×D4—28no—
958C2×D4—28no—
959C2×D4—28no—
960C2×D4—28no—
961C2×D4—28no—
962C2×D4—24no—
963C2×D4—28no—
964C2×D4—28no—
965C2×D4—24no—
966C2×D4—28no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—42no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—42no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—42no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—42no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—42no—
992C2×D4—42no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—41no—
997C2×D4—42no—
998C2×D4—44no—
999C2×D4—42no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—416no—
1012C2×D4—88no—
1013C2×D4—88no—
1014C22×C4—22no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—22no—
1019C22×C4—22no—
1020C22×C4—24no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—28no—
1024C22×C4—28no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—42no—
1030C22×C4—44no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—42no—
1043C22×C4—44no—
1044C22×C4—42no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4—44no—
1052C22×C4—42no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—88no—
1062C22×C4H(5,𝔽2)14yes—
1063C22×C4C2514yes—
1064C22×C4C2512yes—
1065C22×C4C2514yes—
1066C22×C4C2514yes—
1067C22×C4C2512yes—
1068C22×C4C2514yes—
1069C22×C4C2514yes—
1070C22×C4C2512yes—
1071C22×C4C2514yes—
1072C22×C4C2512yes—
1073C22×C4C2514yes—
1074C22×C4C2514yes—
1075C22×C4C2511yescharacteristic
1076C22×C4C2511yescharacteristic
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—41no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—41no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4H(5,𝔽2)18yes—
1115C22⋊C4—28no—
1116C22⋊C4—24no—
1117C22⋊C4—28no—
1118C22⋊C4—24no—
1119C22⋊C4—24no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—24no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—42no—
1134C22⋊C4—42no—
1135C22⋊C4—42no—
1136C22⋊C4—42no—
1137C22⋊C4—44no—
1138C22⋊C4—42no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—42no—
1157C22⋊C4—42no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—42no—
1167C22⋊C4—42no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C42—28no—
1176C42—28no—
1177C42—28no—
1178C42—24no—
1179C42—44no—
1180C42—44no—
1181C42—44no—
1182C42—44no—
1183C42—44no—
1184C42—44no—
1185C23—28no—
1186C23—22no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23—21no—
1193C23—22no—
1194C23—22no—
1195C23—21no—
1196C23—22no—
1197C23—24no—
1198C23—22no—
1199C23—24no—
1200C23—24no—
1201C23—24no—
1202C23—24no—
1203C23—22no—
1204C23—24no—
1205C23—24no—
1206C23—24no—
1207C23—24no—
1208C23—24no—
1209C23—24no—
1210C23—22no—
1211C23—24no—
1212C23—22no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—24no—
1217C23—22no—
1218C23—44no—
1219C23—44no—
1220C23—82no—
1221C23—82no—
1222C23—84no—
1223C23—84no—
1224C23—82no—
1225C23—82no—
1226C23—82no—
1227C23—82no—
1228C23—162no—
1229C23—162no—
1230C23—162no—
1231C23—162no—
1232C23C2×H(5,𝔽2)12yes—
1233C23#58514yes—
1234C23C2611yescharacteristic
1235Q8—84no—
1236Q8—88no—
1237Q8—161no—
1238Q8—164no—
1239D4—416no—
1240D4—416no—
1241D4—84no—
1242D4—88no—
1243D4—88no—
1244D4—88no—
1245D4—84no—
1246D4—84no—
1247D4—88no—
1248D4—88no—
1249D4—88no—
1250D4—88no—
1251D4—88no—
1252D4—162no—
1253D4—162no—
1254D4—161no—
1255D4—164no—
1256D4—162no—
1257D4—164no—
1258D4—164no—
1259D4—164no—
1260C2×C4—28no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—21no—
1278C2×C4—24no—
1279C2×C4—21no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—44no—
1304C2×C4—48no—
1305C2×C4—48no—
1306C2×C4—84no—
1307C2×C4—84no—
1308C2×C4—84no—
1309C2×C4—88no—
1310C2×C4—88no—
1311C2×C4—82no—
1312C2×C4—82no—
1313C2×C4—88no—
1314C2×C4—88no—
1315C2×C4—162no—
1316C2×C4—162no—
1317C2×C4—162no—
1318C2×C4—162no—
1319C2×C4—164no—
1320C2×C4C2×H(5,𝔽2)14yes—
1321C2×C4C2×H(5,𝔽2)18yes—
1322C2×C4C2×H(5,𝔽2)14yes—
1323C22—22no—
1324C22—24no—
1325C22—22no—
1326C22—22no—
1327C22—24no—
1328C22—24no—
1329C22—42no—
1330C22—42no—
1331C22—42no—
1332C22—42no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22—44no—
1339C22—44no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—44no—
1344C22—42no—
1345C22—42no—
1346C22—42no—
1347C22—44no—
1348C22—44no—
1349C22—44no—
1350C22—44no—
1351C22—44no—
1352C22—44no—
1353C22—44no—
1354C22—44no—
1355C22—44no—
1356C22—44no—
1357C22—88no—
1358C22—164no—
1359C22—164no—
1360C22C22×H(5,𝔽2)11yescharacteristic
1361C22C22×H(5,𝔽2)12yes—
1362C22C2×#58512yes—
1363C22H(7,𝔽2)11yescharacteristic
1364C222−1+611yescharacteristic
1365C4—24no—
1366C4—24no—
1367C4—28no—
1368C4—42no—
1369C4—42no—
1370C4—41no—
1371C4—41no—
1372C4—44no—
1373C4—44no—
1374C4—42no—
1375C4—42no—
1376C4—44no—
1377C4—44no—
1378C4—44no—
1379C4—44no—
1380C4—44no—
1381C4—44no—
1382C2—44no—
1383C2—42no—
1384C2—82no—
1385C2—84no—
1386C2—82no—
1387C2—82no—
1388C2#6282011yescharacteristic
1389C2#6283211yescharacteristic
1390C2#6287511yescharacteristic
1391C2#6291812yes—
1392C2#6291912yes—
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. #58388C2semidirect
2. #58295C2semidirect
3. #57628C2semidirect
4. #55702C2semidirect
5. #51975C2semidirect
6. #51898C2semidirect
7. #51751C2semidirect
8. #51040C2semidirect
9. #50167C2semidirect
10. #48796C2semidirect
11. #47068C2semidirect
12. #44428C2semidirect
13. #43418C2semidirect
14. #42595C2semidirect
15. #41827C2semidirect
16. #41381C2semidirect
17. #37753C2semidirect
18. #37745C2semidirect
19. #36706C2semidirect
20. #36004C2semidirect
21. #35857C2semidirect
22. #35565C2semidirect
23. #35351C2semidirect
24. C2×#562C22semidirect
26. C2×#544C22semidirect
29. C2×#537C22semidirect
36. #2838C22semidirect
37. #2834C22semidirect
38. #2826C22semidirect
39. #2825C22semidirect
40. #2825C22semidirect
41. #2821C22semidirect
42. #2813C22semidirect
43. #2778C22semidirect
44. #2761C22semidirect
45. #2761C22semidirect
46. #2760C22semidirect
47. #2760C22semidirect
48. #2752C22semidirect
49. #2751C22semidirect
50. #2749C22semidirect
51. #2749C22semidirect
52. #2740C22semidirect
53. #2738C22semidirect
54. #2732C22semidirect
55. #2730C22semidirect
56. #2729C22semidirect
57. #2711C22semidirect
58. #2711C22semidirect
59. #2711C22semidirect
60. #2709C22semidirect
61. #2709C22semidirect
62. #2709C22semidirect
63. #2708C22semidirect
65. #2703C22semidirect
66. #2703C22semidirect
67. #2700C22semidirect
69. #2694C22semidirect
70. #2694C22semidirect
71. #2692C22semidirect
72. #2692C22semidirect
73. #2692C22semidirect
75. #2688C22semidirect
76. #2688C22semidirect
81. #2677C22semidirect
82. #2677C22semidirect
84. #2676C22semidirect
85. #2676C22semidirect
86. #2676C22semidirect
88. #2675C22semidirect
90. #2674C22semidirect
91. #2674C22semidirect
92. #2673C22semidirect
93. #2673C22semidirect
96. #2671C22semidirect
100. #2661C22semidirect
101. #2661C22semidirect
102. #2658C22semidirect
103. #2656C22semidirect
104. #2655C22semidirect
105. #2640C22semidirect
106. #2639C22semidirect
107. #2639C22semidirect
108. #2639C22semidirect
110. #2631C22semidirect
111. #2631C22semidirect
112. #2627C22semidirect
115. #2624C22semidirect
116. #2618C22semidirect
118. #2610C22semidirect
119. #2610C22semidirect
120. #2607C22semidirect
121. #2603C22semidirect
122. #2600C22semidirect
123. #2598C22semidirect
124. #2597C22semidirect
126. #2577C22semidirect
128. #2557C22semidirect
129. #2556C22semidirect
130. #2556C22semidirect
131. #2555C22semidirect
132. #2544C22semidirect
137. #2540C22semidirect
142. #2526C22semidirect
143. #2520C22semidirect
144. #2514C22semidirect
145. #2498C22semidirect
146. #2491C22semidirect
147. #2491C22semidirect
151. #2479C22semidirect
153. #2477C22semidirect
154. #2476C22semidirect
159. #2471C22semidirect
160. #2471C22semidirect
161. #2471C22semidirect
162. #2464C22semidirect
163. #2461C22semidirect
164. #2460C22semidirect
165. #2459C22semidirect
166. #2452C22semidirect
167. #2452C22semidirect
168. #2450C22semidirect
169. #2449C22semidirect
170. #2447C22semidirect
173. #2444C22semidirect
176. #2443C22semidirect
177. #2438C22semidirect
181. #2431C22semidirect
182. #2431C22semidirect
184. #2430C22semidirect
185. #2428C22semidirect
186. #2428C22semidirect
189. #2420C22semidirect
194. #2407C22semidirect
197. #2401C22semidirect
199. #2392C22semidirect
201. #2371C22semidirect
202. #2368C22semidirect
203. #2366C22semidirect
204. #2364C22semidirect
205. #2363C22semidirect
206. #2359C22semidirect
209. #2339C22semidirect
210. #2333C22semidirect
211. #2329C22semidirect
212. #2328C22semidirect
213. #2325C22semidirect

Maximal subgroups

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

subgroupindex
#583882
#582952
#576282
#557022
#519752
#518982
#517512
#510402
#501672
#487962
#470682
#444282
#434182
#425952
#418272
#413812
#377532
#377452
#367062
#360042
#358572
#355652
#353512