Finite Group Databasebeta

← #9040093

Subgroups — #9040093

Order 512.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58268C214yesmaximal, complemented
2#55974C214yesmaximal, complemented
3#53715C214yesmaximal, complemented
4#53626C214yesmaximal, complemented
5#53598C214yesmaximal, complemented
6#53594C214yesmaximal, complemented
7#52054C211yesmaximal, characteristic
8#51992C212yesmaximal, complemented
9#51978C211yesmaximal, characteristic
10#51326C212yesmaximal, complemented
11#50720C212yesmaximal, complemented
12#50692C212yesmaximal, complemented
13#48163C214yesmaximal, complemented
14#47855C214yesmaximal, complemented
15#42886C212yesmaximal, complemented
16#42333C212yesmaximal, complemented
17#41305C214yesmaximal, complemented
18#40680C214yesmaximal, complemented
19#36966C212yesmaximal, complemented
20#36829C212yesmaximal, complemented
21#36813C212yesmaximal, complemented
22#35749C212yesmaximal, complemented
23#35677C211yesmaximal, characteristic
24C2×#563C2211yescharacteristic
25C2×#563C2212yes—
26C2×#559C2211yescharacteristic
27C2×#557C2212yescomplemented
28C2×#543C2212yes—
29C2×#536C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C2×#519C2211yescharacteristic
33#2855C2214yes—
34#2838C2214yescomplemented
35#2837C2214yescomplemented
36#2837C2214yescomplemented
37#2836C2214yescomplemented
38#2831C2214yescomplemented
39#2831C2214yescomplemented
40#2830C2214yescomplemented
41#2820C2214yescomplemented
42#2806C2214yescomplemented
43#2802C2214yescomplemented
44#2800C2214yes—
45#2799C2214yescomplemented
46#2798C2214yescomplemented
47#2796C2214yescomplemented
48#2793C2214yescomplemented
49#2790C2214yescomplemented
50#2788C2214yescomplemented
51#2786C2214yes—
52#2786C2214yescomplemented
53#2780C2214yescomplemented
54#2779C2214yescomplemented
55#2776C2214yescomplemented
56#2774C2214yescomplemented
57#2751C2214yescomplemented
58#2751C2214yescomplemented
59#2748C2212yes—
60#2745C2214yes—
61#2743C2214yes—
62#2743C2214yescomplemented
63#2740C2214yes—
64#2740C2214yescomplemented
65#2739C2214yescomplemented
66#2738C2214yes—
67#2737C2214yescomplemented
68#2735C2214yes—
69#2735C2214yes—
70#2731C2212yes—
71#2729C2214yescomplemented
72#2728C2214yescomplemented
73#2725C2214yescomplemented
74#2724C2212yes—
75#2724C2212yes—
76#2723C2214yescomplemented
77#2721C2214yescomplemented
78#2720C2214yescomplemented
79#2718C2214yes—
80#2717C2212yes—
81#2717C2212yes—
82#2713C2214yescomplemented
83#2713C2214yescomplemented
84#2709C2212yes—
85#2709C2212yes—
86#2704C2214yescomplemented
87#2702C2214yescomplemented
88#2700C2214yes—
89#2700C2214yes—
90#2700C2214yes—
91#2700C2214yes—
92#2700C2214yes—
93#2698C2214yes—
94#2694C2214yes—
95#2694C2214yescomplemented
96#2692C2214yescomplemented
97#2690C2214yescomplemented
98#2689C2214yes—
99#2689C2214yescomplemented
100#2687C2214yes—
101#2686C2214yes—
102#2685C2214yes—
103#2684C2214yes—
104#2681C2214yes—
105#2677C2214yescomplemented
106#2677C2214yescomplemented
107#2674C2214yes—
108#2674C2214yes—
109#2674C2214yes—
110#2674C2214yes—
111#2674C2214yescomplemented
112#2667C2214yescomplemented
113#2665C2214yescomplemented
114#2663C2214yes—
115#2655C2214yescomplemented
116#2654C2214yescomplemented
117#2653C2214yescomplemented
118#2653C2214yescomplemented
119#2652C2214yescomplemented
120#2651C2214yes—
121#2650C2214yescomplemented
122#2641C2212yes—
123#2634C2212yescomplemented
124#2634C2212yescomplemented
125#2633C2214yescomplemented
126#2632C2212yes—
127#2632C2214yescomplemented
128#2626C2214yes—
129#2621C2212yes—
130#2611C2212yes—
131#2611C2212yes—
132#2607C2212yescomplemented
133#2605C2212yescomplemented
134#2599C2212yes—
135#2599C2212yes—
136#2597C2214yescomplemented
137#2596C2214yescomplemented
138#2595C2214yes—
139#2594C2214yescomplemented
140#2593C2214yescomplemented
141#2589C2214yescomplemented
142#2588C2214yescomplemented
143#2584C2212yescomplemented
144#2583C2212yescomplemented
145#2581C2212yescomplemented
146#2561C2214yes—
147#2560C2214yescomplemented
148#2560C2214yescomplemented
149#2559C2214yes—
150#2558C2214yes—
151#2556C2214yescomplemented
152#2556C2214yescomplemented
153#2551C2214yescomplemented
154#2548C2212yes—
155#2548C2212yes—
156#2546C2212yescomplemented
157#2545C2212yes—
158#2545C2212yes—
159#2536C2214yescomplemented
160#2532C2214yescomplemented
161#2526C2214yescomplemented
162#2525C2214yescomplemented
163#2521C2214yescomplemented
164#2516C2214yescomplemented
165#2516C2214yescomplemented
166#2515C2214yescomplemented
167#2492C2214yescomplemented
168#2489C2214yescomplemented
169#2483C2212yes—
170#2483C2212yes—
171#2480C2214yes—
172#2480C2214yes—
173#2478C2214yes—
174#2475C2214yes—
175#2475C2214yes—
176#2472C2214yes—
177#2469C2214yescomplemented
178#2469C2214yescomplemented
179#2465C2214yescomplemented
180#2462C2214yescomplemented
181#2462C2214yescomplemented
182#2454C2214yescomplemented
183#2452C2214yescomplemented
184#2448C2214yescomplemented
185#2448C2214yescomplemented
186#2446C2214yescomplemented
187#2443C2214yes—
188#2440C2214yescomplemented
189#2434C2214yes—
190#2432C2212yes—
191#2429C2214yescomplemented
192#2426C2214yes—
193#2426C2214yes—
194#2418C2214yes—
195#2411C2214yes—
196#2411C2214yes—
197#2406C2212yes—
198#2405C2212yes—
199#2405C2212yes—
200#2399C2212yescomplemented
201#2399C2212yescomplemented
202#2396C2212yes—
203#2380C2211yescharacteristic
204#2376C2212yes—
205#2374C2212yes—
206#2374C2212yes—
207#2372C2211yescharacteristic
208#2365C2214yescomplemented
209#2362C2214yes—
210#2356C2212yescomplemented
211#2336C2212yescomplemented
212#2332C2212yescomplemented
213#2320C2212yescomplemented
214#2313C2212yescomplemented
215#2312C2212yes—
216#2309C2211yescharacteristic
217#2297C2211yescharacteristic
218#2296C2211yescharacteristic
219C22×#41C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×D4C2311yescharacteristic
222#563—48no—
223#563—44no—
224#559—44no—
225#557—48no—
226#543—48no—
227#536—44no—
228#535—44no—
229C2×C4⋊Q8C2314yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2314yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×#127C2311yescharacteristic
236C2×#127C2311yescharacteristic
237C2×#126C2314yes—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#125C2312yes—
241C2×#125C2314yes—
242C2×#125C2312yes—
243C2×#125C2314yes—
244C2×#125C2314yes—
245C2×#124—44no—
246C2×#124C2311yescharacteristic
247C2×#124C2314yes—
248C2×#124C2314yes—
249C2×#124C2312yes—
250C2×#124C2312yes—
251C2×#124C2312yes—
252C2×#124C2311yescharacteristic
253C2×#124C2312yes—
254C2×#123C2312yes—
255C2×#123C2312yes—
256C2×#123C2312yes—
257C2×#123C2312yes—
258C2×#123C2312yes—
259C2×#123C2312yes—
260C2×#123C2312yes—
261C2×#123C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×#121C2314yes—
273C2×#120C2314yes—
274#519—44no—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2314yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×D4C2314yes—
284C2×#117C2311yescharacteristic
285C2×#117C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C2×#117C2312yes—
288C2×#117C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2312yes—
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294C22×C42C2311yescharacteristic
295#401C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2312yes—
304#400C2312yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2312yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#399C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2312yes—
323#399C2314yes—
324#398C2312yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2312yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2312yes—
337#398C2312yes—
338#398C2312yes—
339#398C2312yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2312yes—
364#397C2312yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#395C2312yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2312yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2312yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
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#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2312yes—
425#393C2314yes—
426#393C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2312yes—
440#391C2312yes—
441#390C2314yes—
442#390C2314yes—
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#390C2312yes—
447#390C2314yes—
448#390C2314yes—
449#390C2312yes—
450#390C2314yes—
451#390C2314yes—
452#390C2312yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#388C2314yes—
472#388C2314yes—
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#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2312yes—
552#386C2314yes—
553#386C2312yes—
554#386C2312yes—
555#386C2312yes—
556#386C2312yes—
557#386C2312yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
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#385C2314yes—
579#384C2314yes—
580#383C2314yes—
581#383C2312yes—
582#383C2312yes—
583#382C2314yes—
584#382C2312yes—
585#381C2314yes—
586#381C2314yes—
587#381C2314yes—
588#381C2312yes—
589#381C2314yes—
590#381C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#379C2314yes—
598#379C2314yes—
599#379C2314yes—
600#379C2312yes—
601#379C2312yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2312yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2312yes—
618C4×C22⋊C4C2312yes—
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2314yes—
621#376C2312yes—
622#376C2312yes—
623C25C2412yes—
624C2×#41—42no—
625C2×#41—42no—
626C2×#41—42no—
627C22×Q8—24no—
628C22×Q8—42no—
629C22×Q8—42no—
630C22×Q8C2412yes—
631C22×Q8C2412yes—
632C22×Q8C2412yes—
633C22×Q8C2414yes—
634C22×Q8C2411yescharacteristic
635C22×Q8C2412yes—
636C22×Q8C2414yes—
637C22×D4—42no—
638C22×D4—42no—
639C22×D4—42no—
640C22×D4C2414yes—
641C22×D4C2412yes—
642C22×D4C2412yes—
643C22×D4C2411yescharacteristic
644C22×D4C2411yescharacteristic
645C22×D4C2411yescharacteristic
646C22×D4C2414yes—
647C23×C4C2411yescharacteristic
648C23×C4C2411yescharacteristic
649C23×C4C2412yes—
650C23×C4C2412yes—
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2412yes—
655C23×C4C2412yes—
656C23×C4C2412yes—
657C23×C4C2411yescharacteristic
658C4⋊Q8—44no—
659C4⋊Q8—48no—
660C4⋊Q8—44no—
661C4⋊Q8—48no—
662C4⋊Q8—48no—
663C4⋊Q8—44no—
664#127—24no—
665#127—42no—
666#126—48no—
667#126—48no—
668#126—48no—
669#125—28no—
670#125—44no—
671#125—48no—
672#125—48no—
673#125—48no—
674#124—24no—
675#124—42no—
676#124—48no—
677#124—44no—
678#124—48no—
679#124—44no—
680#124—44no—
681#124—44no—
682#123—28no—
683#123—44no—
684#123—44no—
685#123—44no—
686#123—44no—
687#123—44no—
688#123—44no—
689#123—44no—
690C22⋊Q8—216no—
691C22⋊Q8—48no—
692C22⋊Q8—48no—
693C22⋊Q8—48no—
694C22⋊Q8—48no—
695C22⋊Q8—48no—
696C22⋊Q8—48no—
697C22⋊Q8—48no—
698C22⋊Q8—48no—
699C22⋊Q8—44no—
700#121—48no—
701#120—48no—
702C4×Q8—28no—
703C4×Q8—28no—
704C4×Q8—44no—
705C4×Q8—44no—
706C4×Q8—48no—
707C4×Q8—44no—
708C4×Q8—44no—
709C4×Q8—44no—
710C4×D4—48no—
711#117—24no—
712#117—44no—
713#117—44no—
714#117—42no—
715#117—42no—
716C2×C4⋊C4—44no—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C22⋊C4—28no—
767C2×C22⋊C4—44no—
768C2×C22⋊C4—44no—
769C2×C22⋊C4—44no—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C42—42no—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2411yescharacteristic
819C2×C42C2414yes—
820C2×C42C2411yescharacteristic
821C2×C42C2411yescharacteristic
822C2×C42C2412yes—
823C2×C42C2412yes—
824C2×C42C2412yes—
825C2×C42C2414yes—
826C2×C42C2414yes—
827C2×C42C2412yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2414yes—
831C2×C42C2412yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2414yes—
836C2×C42C2411yescharacteristic
837#95C2412yes—
838#95C2412yes—
839#95C2414yes—
840#95C2412yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2412yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891C24—24no—
892C24—44no—
893C24—42no—
894C24—42no—
895C24—44no—
896C24C2512yes—
897C24C2512yes—
898C24C2512yes—
899C24C2511yescharacteristic
900#41—88no—
901C2×Q8—24no—
902C2×Q8—24no—
903C2×Q8—24no—
904C2×Q8—24no—
905C2×Q8—28no—
906C2×Q8—22no—
907C2×Q8—24no—
908C2×Q8—42no—
909C2×Q8—42no—
910C2×Q8—44no—
911C2×Q8—44no—
912C2×Q8—41no—
913C2×Q8—44no—
914C2×Q8—41no—
915C2×Q8—44no—
916C2×Q8—42no—
917C2×Q8—42no—
918C2×Q8—42no—
919C2×Q8—44no—
920C2×Q8—44no—
921C2×Q8—416no—
922C2×D4—24no—
923C2×D4—28no—
924C2×D4—22no—
925C2×D4—22no—
926C2×D4—22no—
927C2×D4—24no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—41no—
931C2×D4—41no—
932C2×D4—42no—
933C2×D4—41no—
934C2×D4—41no—
935C2×D4—41no—
936C2×D4—44no—
937C2×D4—44no—
938C2×D4—41no—
939C2×D4—42no—
940C2×D4—44no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—88no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—24no—
949C22×C4—24no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—41no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4H(5,𝔽2)14yes—
973C22×C4C2514yes—
974C22×C4C2514yes—
975C22×C4C2512yes—
976C22×C4C2514yes—
977C22×C4C2514yes—
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2512yes—
981C22×C4C2512yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2514yes—
987C22×C4C2514yes—
988C22×C4C2512yes—
989C22×C4C2511yescharacteristic
990C22×C4C2512yes—
991C22×C4C2511yescharacteristic
992C4⋊C4—24no—
993C4⋊C4—24no—
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—24no—
997C4⋊C4—28no—
998C4⋊C4—24no—
999C4⋊C4—28no—
1000C4⋊C4—24no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—42no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—24no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—24no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—42no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—42no—
1079C22⋊C4—44no—
1080C22⋊C4—42no—
1081C22⋊C4—44no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C42—22no—
1087C42—24no—
1088C42—24no—
1089C42—28no—
1090C42—42no—
1091C42—42no—
1092C42—44no—
1093C42—44no—
1094C42—44no—
1095C42—42no—
1096C42—41no—
1097C42—41no—
1098C42—42no—
1099C42—42no—
1100C42—44no—
1101C42—44no—
1102C42—42no—
1103C42—44no—
1104C42—42no—
1105C42—44no—
1106C42H(5,𝔽2)14yes—
1107C23—21no—
1108C23—21no—
1109C23—24no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—24no—
1120C23—24no—
1121C23—24no—
1122C23—24no—
1123C23—24no—
1124C23—24no—
1125C23—48no—
1126C23—84no—
1127C23—84no—
1128C23—164no—
1129C23—164no—
1130C23C2×H(5,𝔽2)12yes—
1131C23C2611yescharacteristic
1132Q8—48no—
1133Q8—48no—
1134Q8—48no—
1135Q8—88no—
1136Q8—82no—
1137Q8—162no—
1138Q8—164no—
1139D4—88no—
1140D4—84no—
1141D4—82no—
1142D4—82no—
1143D4—82no—
1144D4—84no—
1145D4—164no—
1146C2×C4—28no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—22no—
1152C2×C4—21no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—44no—
1197C2×C4—44no—
1198C2×C4—84no—
1199C2×C4—84no—
1200C2×C4—84no—
1201C2×C4—162no—
1202C2×C4—162no—
1203C2×C4—162no—
1204C2×C4—162no—
1205C2×C4—162no—
1206C2×C4C2×H(5,𝔽2)14yes—
1207C2×C4C2×H(5,𝔽2)12yes—
1208C2×C4C2×H(5,𝔽2)14yes—
1209C2×C4#58512yes—
1210C22—22no—
1211C22—24no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—44no—
1228C22—44no—
1229C22—168no—
1230C22C22×H(5,𝔽2)11yescharacteristic
1231C22C22×H(5,𝔽2)11yescharacteristic
1232C22C2×#58511yescharacteristic
1233C222−1+614yes—
1234C4—22no—
1235C4—22no—
1236C4—24no—
1237C4—24no—
1238C4—42no—
1239C4—42no—
1240C4—44no—
1241C4—44no—
1242C4—42no—
1243C4—42no—
1244C4—44no—
1245C4—44no—
1246C4—44no—
1247C4—44no—
1248C4—44no—
1249C4—42no—
1250C4—44no—
1251C4—44no—
1252C4—44no—
1253C2—42no—
1254C2—82no—
1255C2—82no—
1256C2—82no—
1257C2#6281811yescharacteristic
1258C2#6288712yes—
1259C2#6288712yes—
1260C2#6289112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#535C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58268C2semidirect
2. #55974C2semidirect
3. #53715C2semidirect
4. #53626C2semidirect
5. #53598C2semidirect
6. #53594C2semidirect
8. #51992C2semidirect
10. #51326C2semidirect
11. #50720C2semidirect
12. #50692C2semidirect
13. #48163C2semidirect
14. #47855C2semidirect
15. #42886C2semidirect
16. #42333C2semidirect
17. #41305C2semidirect
18. #40680C2semidirect
19. #36966C2semidirect
20. #36829C2semidirect
21. #36813C2semidirect
22. #35749C2semidirect
27. C2×#557C22semidirect
34. #2838C22semidirect
35. #2837C22semidirect
36. #2837C22semidirect
37. #2836C22semidirect
38. #2831C22semidirect
39. #2831C22semidirect
40. #2830C22semidirect
41. #2820C22semidirect
42. #2806C22semidirect
43. #2802C22semidirect
45. #2799C22semidirect
46. #2798C22semidirect
47. #2796C22semidirect
48. #2793C22semidirect
49. #2790C22semidirect
50. #2788C22semidirect
52. #2786C22semidirect
53. #2780C22semidirect
54. #2779C22semidirect
55. #2776C22semidirect
56. #2774C22semidirect
57. #2751C22semidirect
58. #2751C22semidirect
62. #2743C22semidirect
64. #2740C22semidirect
65. #2739C22semidirect
67. #2737C22semidirect
71. #2729C22semidirect
72. #2728C22semidirect
73. #2725C22semidirect
76. #2723C22semidirect
77. #2721C22semidirect
78. #2720C22semidirect
82. #2713C22semidirect
83. #2713C22semidirect
86. #2704C22semidirect
87. #2702C22semidirect
95. #2694C22semidirect
96. #2692C22semidirect
97. #2690C22semidirect
99. #2689C22semidirect
105. #2677C22semidirect
106. #2677C22semidirect
111. #2674C22semidirect
112. #2667C22semidirect
113. #2665C22semidirect
115. #2655C22semidirect
116. #2654C22semidirect
117. #2653C22semidirect
118. #2653C22semidirect
119. #2652C22semidirect
121. #2650C22semidirect
123. #2634C22semidirect
124. #2634C22semidirect
125. #2633C22semidirect
127. #2632C22semidirect
132. #2607C22semidirect
133. #2605C22semidirect
136. #2597C22semidirect
137. #2596C22semidirect
139. #2594C22semidirect
140. #2593C22semidirect
141. #2589C22semidirect
142. #2588C22semidirect
143. #2584C22semidirect
144. #2583C22semidirect
145. #2581C22semidirect
147. #2560C22semidirect
148. #2560C22semidirect
151. #2556C22semidirect
152. #2556C22semidirect
153. #2551C22semidirect
156. #2546C22semidirect
159. #2536C22semidirect
160. #2532C22semidirect
161. #2526C22semidirect
162. #2525C22semidirect
163. #2521C22semidirect
164. #2516C22semidirect
165. #2516C22semidirect
166. #2515C22semidirect
167. #2492C22semidirect
168. #2489C22semidirect
177. #2469C22semidirect
178. #2469C22semidirect
179. #2465C22semidirect
180. #2462C22semidirect
181. #2462C22semidirect
182. #2454C22semidirect
183. #2452C22semidirect
184. #2448C22semidirect
185. #2448C22semidirect
186. #2446C22semidirect
188. #2440C22semidirect
191. #2429C22semidirect
200. #2399C22semidirect
201. #2399C22semidirect
208. #2365C22semidirect
210. #2356C22semidirect
211. #2336C22semidirect
212. #2332C22semidirect
213. #2320C22semidirect
214. #2313C22semidirect

Maximal subgroups

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

subgroupindex
#582682
#559742
#537152
#536262
#535982
#535942
#520542
#519922
#519782
#513262
#507202
#506922
#481632
#478552
#428862
#423332
#413052
#406802
#369662
#368292
#368132
#357492
#356772