Finite Group Databasebeta

← #8094731

Subgroups — #8094731

Order 512.

4772 conjugacy classes of subgroups.

The subgroup lattice has 1296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52953C212yesmaximal, complemented
2#52952C212yesmaximal, complemented
3#52948C214yesmaximal, complemented
4#52887C212yesmaximal, complemented
5#52886C212yesmaximal, complemented
6#52872C214yesmaximal, complemented
7#52375C214yesmaximal, complemented
8#52348C214yesmaximal, complemented
9#46335C212yesmaximal, complemented
10#46325C212yesmaximal, complemented
11#46205C211yesmaximal, characteristic, complemented
12#46099C211yesmaximal, characteristic, complemented
13#45976C212yesmaximal, complemented
14#45686C214yesmaximal, complemented
15#45607C214yesmaximal, complemented
16#45597C214yesmaximal, complemented
17#45481C214yesmaximal, complemented
18#35466C212yesmaximal, complemented
19#35457C214yesmaximal, complemented
20#35098C212yesmaximal, complemented
21#35095C214yesmaximal, complemented
22#34971C212yesmaximal, complemented
23C2×#2545C211yesmaximal, characteristic, complemented
24C2×#563C2212yescomplemented
25C2×#562C2212yes—
26C2×#538C2212yes—
27C22×C4⋊Q8C2211yescharacteristic
28C22×#124C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C2×C4×#41C2212yes—
31C22×C4×Q8C2211yescharacteristic
32#2854C2214yescomplemented
33#2853C2214yescomplemented
34#2852C2214yes—
35#2852C2214yescomplemented
36#2851C2212yes—
37#2850C2212yes—
38#2850C2214yescomplemented
39#2841C2214yescomplemented
40#2841C2214yescomplemented
41#2838C2214yescomplemented
42#2837C2214yescomplemented
43#2836C2214yescomplemented
44#2833C2212yescomplemented
45#2832C2212yescomplemented
46#2831C2214yescomplemented
47#2831C2214yescomplemented
48#2830C2212yes—
49#2830C2214yescomplemented
50#2830C2214yescomplemented
51#2829C2214yescomplemented
52#2828C2212yes—
53#2827C2214yescomplemented
54#2827C2214yescomplemented
55#2826C2214yescomplemented
56#2825C2214yescomplemented
57#2821C2214yescomplemented
58#2820C2212yes—
59#2819C2212yes—
60#2814C2214yescomplemented
61#2813C2214yescomplemented
62#2811C2211yescharacteristic, complemented
63#2809C2211yescharacteristic, complemented
64#2805C2212yescomplemented
65#2804C2212yescomplemented
66#2797C2214yes—
67#2784C2212yes—
68#2784C2214yescomplemented
69#2783C2214yescomplemented
70#2780C2214yescomplemented
71#2768C2214yescomplemented
72#2763C2214yescomplemented
73#2762C2214yescomplemented
74#2757C2214yescomplemented
75#2750C2214yescomplemented
76#2749C2214yes—
77#2749C2214yescomplemented
78#2748C2214yescomplemented
79#2740C2214yescomplemented
80#2739C2214yescomplemented
81#2737C2214yes—
82#2734C2211yescharacteristic, complemented
83#2734C2212yescomplemented
84#2733C2211yescharacteristic, complemented
85#2731C2212yescomplemented
86#2730C2214yes—
87#2729C2214yescomplemented
88#2716C2214yescomplemented
89#2714C2214yes—
90#2713C2214yescomplemented
91#2713C2214yescomplemented
92#2712C2214yescomplemented
93#2710C2214yes—
94#2705C2214yescomplemented
95#2704C2214yescomplemented
96#2700C2214yes—
97#2699C2212yes—
98#2694C2214yescomplemented
99#2693C2214yescomplemented
100#2692C2214yescomplemented
101#2691C2214yes—
102#2691C2214yescomplemented
103#2686C2214yes—
104#2677C2214yescomplemented
105#2676C2214yes—
106#2674C2214yescomplemented
107#2672C2214yes—
108#2637C2214yescomplemented
109#2635C2214yescomplemented
110#2632C2214yescomplemented
111#2630C2214yescomplemented
112#2627C2212yes—
113#2623C2214yes—
114#2618C2212yes—
115#2599C2214yescomplemented
116#2599C2214yescomplemented
117#2581C2212yescomplemented
118#2581C2212yescomplemented
119#2578C2214yescomplemented
120#2577C2214yescomplemented
121#2576C2214yescomplemented
122#2575C2214yescomplemented
123#2572C2214yescomplemented
124#2561C2212yes—
125#2560C2214yescomplemented
126#2558C2214yescomplemented
127#2557C2214yes—
128#2557C2214yes—
129#2555C2214yes—
130#2555C2214yes—
131#2553C2214yescomplemented
132#2545C2212yes—
133#2545C2212yes—
134#2545C2214yes—
135#2545C2214yes—
136#2545C2212yes—
137#2545C2212yes—
138#2539C2212yes—
139#2536C2212yescomplemented
140#2536C2212yescomplemented
141#2531C2214yescomplemented
142#2530C2214yescomplemented
143#2527C2214yescomplemented
144#2526C2214yescomplemented
145#2525C2214yescomplemented
146#2524C2214yescomplemented
147#2522C2214yescomplemented
148#2521C2214yes—
149#2521C2214yes—
150#2521C2214yescomplemented
151#2520C2214yescomplemented
152#2519C2214yescomplemented
153#2516C2214yescomplemented
154#2515C2214yescomplemented
155#2515C2214yescomplemented
156#2515C2214yescomplemented
157#2495C2214yescomplemented
158#2493C2214yes—
159#2491C2214yes—
160#2491C2214yes—
161#2489C2214yescomplemented
162#2488C2214yes—
163#2486C2214yes—
164#2484C2212yes—
165#2484C2212yes—
166#2483C2214yes—
167#2481C2214yes—
168#2479C2214yescomplemented
169#2476C2214yescomplemented
170#2474C2214yescomplemented
171#2473C2214yes—
172#2471C2214yescomplemented
173#2469C2214yescomplemented
174#2464C2214yescomplemented
175#2461C2214yescomplemented
176#2458C2214yescomplemented
177#2449C2214yes—
178#2443C2214yes—
179#2438C2214yes—
180#2437C2214yes—
181#2436C2212yes—
182#2434C2212yes—
183#2430C2214yes—
184#2424C2214yes—
185#2418C2214yes—
186#2412C2214yes—
187#2412C2214yes—
188#2412C2214yes—
189#2411C2214yes—
190#2410C2214yes—
191#2409C2214yes—
192#2406C2212yes—
193#2406C2212yes—
194#2404C2214yes—
195#2399C2212yescomplemented
196#2399C2212yescomplemented
197#2398C2212yescomplemented
198#2398C2212yescomplemented
199C2×#396C2214yes—
200#2381C2212yescomplemented
201#2381C2212yescomplemented
202#2379C2212yes—
203#2379C2212yescomplemented
204#2377C2214yes—
205#2329C2212yes—
206#2325C2212yes—
207#2321C2214yes—
208#2318C2214yes—
209C4×C22⋊Q8C2214yescomplemented
210C4×C22⋊Q8C2214yescomplemented
211C4×#123C2214yes—
212C4×#123C2214yes—
213C2×#391C2211yescharacteristic
214C2×#390C2211yescharacteristic
215C2×#388C2214yes—
216#2283C2212yes—
217#2273C2212yes—
218C2×C4×C4⋊C4C2211yescharacteristic
219C22×#41C2312yes—
220C23×Q8C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222C23×D4C2311yescharacteristic
223#563—48no—
224#562—48no—
225#538—48no—
226C2×C4⋊Q8—44no—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#125C2312yes—
237C2×#125C2314yes—
238C2×#124—44no—
239C2×#124—44no—
240C2×#124C2312yes—
241C2×#124C2312yes—
242C2×#124C2312yes—
243C2×#124C2314yes—
244C2×#124C2312yes—
245C2×#124C2312yes—
246C2×#124C2312yes—
247C2×#124C2312yes—
248C2×#124C2314yes—
249C2×#124C2312yes—
250C2×#124C2312yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×#121C2312yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2312yes—
269C2×#120C2314yes—
270C2×#120C2314yes—
271C4×#41—48no—
272C2×C4×Q8—44no—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2312yes—
283C2×#117C2314yes—
284C2×#117C2312yes—
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2314yes—
288C22×C4⋊C4C2311yescharacteristic
289C22×C22⋊C4C2312yes—
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2314yes—
292C22×C22⋊C4C2314yes—
293C22×C22⋊C4C2314yes—
294C22×C42C2312yes—
295C22×C42C2311yescharacteristic
296C22×C42C2311yescharacteristic
297C22×C42C2314yes—
298C22×C42C2311yescharacteristic
299#401C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2312yes—
304#400C2314yes—
305#400C2314yes—
306#400C2312yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2312yes—
315#400C2312yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2312yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2312yes—
337#398C2314yes—
338#398C2314yes—
339#398C2312yes—
340#398C2312yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
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#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2312yes—
380#395C2312yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2312yes—
385#395C2312yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2312yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2312yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2312yes—
409#394C2312yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2311yescharacteristic
431#391C2311yescharacteristic
432#391C2314yes—
433#391C2314yes—
434#391C2312yes—
435#391C2311yescharacteristic
436#391C2312yes—
437#391C2311yescharacteristic
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2314yes—
442#390C2314yes—
443#390C2312yes—
444#390C2314yes—
445#390C2314yes—
446#390C2314yes—
447#390C2314yes—
448#390C2312yes—
449#390C2314yes—
450#390C2314yes—
451#390C2312yes—
452#390C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
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#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#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
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#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#383C2314yes—
570#383C2314yes—
571#383C2314yes—
572#383C2314yes—
573#382C2312yes—
574#382C2312yes—
575#382C2314yes—
576#382C2314yes—
577#382C2312yes—
578#382C2312yes—
579#381C2314yes—
580#381C2314yes—
581#381C2314yes—
582#381C2314yes—
583#381C2314yes—
584#381C2314yes—
585#381C2312yes—
586#381C2312yes—
587#380C2314yes—
588#380C2314yes—
589#380C2312yes—
590#380C2312yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#379C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2312yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2312yes—
618#376C2312yes—
619#376C2312yes—
620C2×#95C2312yes—
621C2×#95C2314yes—
622C25C2412yes—
623C2×#41—44no—
624C2×#41—48no—
625C22×Q8—24no—
626C22×Q8—42no—
627C22×Q8—42no—
628C22×Q8—42no—
629C22×Q8—42no—
630C22×Q8—42no—
631C22×Q8C2412yes—
632C22×Q8C2411yescharacteristic
633C22×Q8C2411yescharacteristic
634C22×Q8C2412yes—
635C22×Q8C2411yescharacteristic
636C22×Q8C2412yes—
637C22×Q8C2412yes—
638C22×Q8C2412yes—
639C22×Q8C2411yescharacteristic
640C22×D4—42no—
641C22×D4—42no—
642C22×D4—42no—
643C22×D4C2414yes—
644C22×D4C2412yes—
645C22×D4C2412yes—
646C22×D4C2412yes—
647C22×D4C2414yes—
648C22×D4C2414yes—
649C22×D4C2414yes—
650C22×D4C2414yes—
651C22×D4C2412yes—
652C22×D4C2412yes—
653C23×C4C2411yescharacteristic
654C23×C4C2412yes—
655C23×C4C2411yescharacteristic
656C23×C4C2412yes—
657C23×C4C2412yes—
658C23×C4C2412yes—
659C23×C4C2412yes—
660C23×C4C2414yes—
661C23×C4C2414yes—
662C23×C4C2414yes—
663C23×C4C2414yes—
664C23×C4C2414yes—
665C23×C4C2411yescharacteristic
666C4⋊Q8—28no—
667C4⋊Q8—44no—
668C4⋊Q8—44no—
669C4⋊Q8—44no—
670C4⋊Q8—44no—
671C4⋊Q8—44no—
672#126—48no—
673#126—48no—
674#126—48no—
675#125—44no—
676#125—48no—
677#124—28no—
678#124—44no—
679#124—48no—
680#124—44no—
681#124—48no—
682#124—44no—
683#124—44no—
684#124—44no—
685#124—44no—
686#124—44no—
687#124—44no—
688#123—48no—
689#123—48no—
690#123—48no—
691#123—48no—
692#123—48no—
693#123—48no—
694C22⋊Q8—216no—
695C22⋊Q8—44no—
696C22⋊Q8—44no—
697C22⋊Q8—48no—
698C22⋊Q8—48no—
699C22⋊Q8—48no—
700#121—48no—
701#121—48no—
702#121—48no—
703#121—48no—
704#121—44no—
705#121—44no—
706#120—48no—
707#120—48no—
708C4×Q8—44no—
709C4×Q8—44no—
710C4×Q8—44no—
711C4×Q8—44no—
712C4×Q8—44no—
713C4×Q8—44no—
714C4×D4—216no—
715C4×D4—44no—
716C4×D4—44no—
717C4×D4—48no—
718#117—48no—
719#117—44no—
720C2×C4⋊C4—48no—
721C2×C4⋊C4—44no—
722C2×C4⋊C4—42no—
723C2×C4⋊C4—44no—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C22⋊C4—28no—
770C2×C22⋊C4—48no—
771C2×C22⋊C4—48no—
772C2×C22⋊C4—48no—
773C2×C22⋊C4—44no—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
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×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C42—28no—
820C2×C42—24no—
821C2×C42—48no—
822C2×C42—42no—
823C2×C42—42no—
824C2×C42C2412yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2414yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2411yescharacteristic
836C2×C42C2411yescharacteristic
837C2×C42C2412yes—
838C2×C42C2412yes—
839C2×C42C2412yes—
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2414yes—
843C2×C42C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2412yes—
851#95C2414yes—
852#95C2414yes—
853#95C2412yes—
854#95C2412yes—
855#95C2412yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
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—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896C24—24no—
897C24—28no—
898C24—42no—
899C24—42no—
900C24—44no—
901C24C2514yes—
902C24C2514yes—
903C24C2511yescharacteristic
904#41—432no—
905C2×Q8—24no—
906C2×Q8—22no—
907C2×Q8—24no—
908C2×Q8—24no—
909C2×Q8—22no—
910C2×Q8—22no—
911C2×Q8—41no—
912C2×Q8—42no—
913C2×Q8—41no—
914C2×Q8—42no—
915C2×Q8—41no—
916C2×Q8—41no—
917C2×Q8—44no—
918C2×Q8—41no—
919C2×Q8—42no—
920C2×Q8—41no—
921C2×Q8—41no—
922C2×Q8—41no—
923C2×Q8—42no—
924C2×Q8—42no—
925C2×Q8—42no—
926C2×Q8—42no—
927C2×Q8—42no—
928C2×Q8—42no—
929C2×Q8—42no—
930C2×Q8—416no—
931C2×Q8—88no—
932C2×Q8H(5,𝔽2)14yes—
933C2×D4—28no—
934C2×D4—28no—
935C2×D4—28no—
936C2×D4—24no—
937C2×D4—24no—
938C2×D4—42no—
939C2×D4—44no—
940C2×D4—42no—
941C2×D4—42no—
942C2×D4—42no—
943C2×D4—42no—
944C2×D4—44no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—42no—
949C2×D4—44no—
950C2×D4—44no—
951C2×D4—42no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—42no—
955C2×D4—42no—
956C2×D4—42no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—42no—
961C2×D4—44no—
962C2×D4—88no—
963C22×C4—22no—
964C22×C4—22no—
965C22×C4—22no—
966C22×C4—22no—
967C22×C4—24no—
968C22×C4—24no—
969C22×C4—24no—
970C22×C4—28no—
971C22×C4—24no—
972C22×C4—24no—
973C22×C4—24no—
974C22×C4—24no—
975C22×C4—28no—
976C22×C4—28no—
977C22×C4—42no—
978C22×C4—44no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—42no—
985C22×C4—44no—
986C22×C4—42no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4H(5,𝔽2)14yes—
999C22×C4C2514yes—
1000C22×C4C2514yes—
1001C22×C4C2514yes—
1002C22×C4C2512yes—
1003C22×C4C2512yes—
1004C22×C4C2514yes—
1005C22×C4C2514yes—
1006C22×C4C2512yes—
1007C22×C4C2514yes—
1008C22×C4C2512yes—
1009C22×C4C2514yes—
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2514yes—
1015C22×C4C2512yes—
1016C22×C4C2511yescharacteristic
1017C22×C4C2512yes—
1018C22×C4C2511yescharacteristic
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—41no—
1031C4⋊C4—42no—
1032C4⋊C4—41no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—42no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—42no—
1042C4⋊C4—44no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—42no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—42no—
1052C4⋊C4—44no—
1053C4⋊C4—42no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C42—24no—
1110C42—24no—
1111C42—24no—
1112C42—24no—
1113C42—24no—
1114C42—24no—
1115C42—28no—
1116C42—24no—
1117C42—24no—
1118C42—44no—
1119C42—44no—
1120C42—41no—
1121C42—41no—
1122C42—42no—
1123C42—44no—
1124C42—44no—
1125C42—42no—
1126C42—42no—
1127C42—42no—
1128C42—42no—
1129C23—21no—
1130C23—21no—
1131C23—22no—
1132C23—24no—
1133C23—24no—
1134C23—24no—
1135C23—24no—
1136C23—24no—
1137C23—24no—
1138C23—24no—
1139C23—24no—
1140C23—24no—
1141C23—24no—
1142C23—24no—
1143C23—24no—
1144C23—24no—
1145C23—24no—
1146C23—48no—
1147C23—84no—
1148C23—84no—
1149C23—88no—
1150C23—88no—
1151C23C2×H(5,𝔽2)12yes—
1152C23#58514yes—
1153C23C2611yescharacteristic
1154Q8—44no—
1155Q8—48no—
1156Q8—44no—
1157Q8—48no—
1158Q8—84no—
1159Q8—82no—
1160Q8—82no—
1161Q8—162no—
1162Q8—162no—
1163D4—48no—
1164D4—416no—
1165D4—84no—
1166D4—84no—
1167D4—162no—
1168D4—164no—
1169D4—164no—
1170D4—162no—
1171D4—164no—
1172D4—164no—
1173C2×C4—28no—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—22no—
1179C2×C4—21no—
1180C2×C4—24no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—44no—
1227C2×C4—48no—
1228C2×C4—48no—
1229C2×C4—416no—
1230C2×C4—44no—
1231C2×C4—48no—
1232C2×C4—88no—
1233C2×C4—88no—
1234C2×C4—84no—
1235C2×C4—84no—
1236C2×C4—164no—
1237C2×C4—164no—
1238C2×C4C2×H(5,𝔽2)14yes—
1239C2×C4C2×H(5,𝔽2)12yes—
1240C2×C4C2×H(5,𝔽2)14yes—
1241C2×C4#58512yes—
1242C22—22no—
1243C22—22no—
1244C22—24no—
1245C22—24no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—168no—
1261C22#352914yes—
1262C22C22×H(5,𝔽2)11yescharacteristic
1263C22C22×H(5,𝔽2)11yescharacteristic
1264C22C2×#58511yescharacteristic
1265C22C2×#58512yes—
1266C222−1+612yes—
1267C4—22no—
1268C4—22no—
1269C4—24no—
1270C4—24no—
1271C4—42no—
1272C4—42no—
1273C4—44no—
1274C4—42no—
1275C4—44no—
1276C4—44no—
1277C4—42no—
1278C4—42no—
1279C4—44no—
1280C4—44no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—44no—
1285C4—44no—
1286C4—44no—
1287C2—24no—
1288C2—84no—
1289C2—84no—
1290C2C2×#352911yescharacteristic
1291C2#6281811yescharacteristic
1292C2#6287111yescharacteristic
1293C2#6291912yes—
1294C2#6296412yes—
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. #52953C2semidirect
2. #52952C2semidirect
3. #52948C2semidirect
4. #52887C2semidirect
5. #52886C2semidirect
6. #52872C2semidirect
7. #52375C2semidirect
8. #52348C2semidirect
9. #46335C2semidirect
10. #46325C2semidirect
11. #46205C2semidirect
12. #46099C2semidirect
13. #45976C2semidirect
14. #45686C2semidirect
15. #45607C2semidirect
16. #45597C2semidirect
17. #45481C2semidirect
18. #35466C2semidirect
19. #35457C2semidirect
20. #35098C2semidirect
21. #35095C2semidirect
22. #34971C2semidirect
23. C2×#2545C2semidirect
24. C2×#563C22semidirect
32. #2854C22semidirect
33. #2853C22semidirect
35. #2852C22semidirect
38. #2850C22semidirect
39. #2841C22semidirect
40. #2841C22semidirect
41. #2838C22semidirect
42. #2837C22semidirect
43. #2836C22semidirect
44. #2833C22semidirect
45. #2832C22semidirect
46. #2831C22semidirect
47. #2831C22semidirect
49. #2830C22semidirect
50. #2830C22semidirect
51. #2829C22semidirect
53. #2827C22semidirect
54. #2827C22semidirect
55. #2826C22semidirect
56. #2825C22semidirect
57. #2821C22semidirect
60. #2814C22semidirect
61. #2813C22semidirect
62. #2811C22semidirect
63. #2809C22semidirect
64. #2805C22semidirect
65. #2804C22semidirect
68. #2784C22semidirect
69. #2783C22semidirect
70. #2780C22semidirect
71. #2768C22semidirect
72. #2763C22semidirect
73. #2762C22semidirect
74. #2757C22semidirect
75. #2750C22semidirect
77. #2749C22semidirect
78. #2748C22semidirect
79. #2740C22semidirect
80. #2739C22semidirect
82. #2734C22semidirect
83. #2734C22semidirect
84. #2733C22semidirect
85. #2731C22semidirect
87. #2729C22semidirect
88. #2716C22semidirect
90. #2713C22semidirect
91. #2713C22semidirect
92. #2712C22semidirect
94. #2705C22semidirect
95. #2704C22semidirect
98. #2694C22semidirect
99. #2693C22semidirect
100. #2692C22semidirect
102. #2691C22semidirect
104. #2677C22semidirect
106. #2674C22semidirect
108. #2637C22semidirect
109. #2635C22semidirect
110. #2632C22semidirect
111. #2630C22semidirect
115. #2599C22semidirect
116. #2599C22semidirect
117. #2581C22semidirect
118. #2581C22semidirect
119. #2578C22semidirect
120. #2577C22semidirect
121. #2576C22semidirect
122. #2575C22semidirect
123. #2572C22semidirect
125. #2560C22semidirect
126. #2558C22semidirect
131. #2553C22semidirect
139. #2536C22semidirect
140. #2536C22semidirect
141. #2531C22semidirect
142. #2530C22semidirect
143. #2527C22semidirect
144. #2526C22semidirect
145. #2525C22semidirect
146. #2524C22semidirect
147. #2522C22semidirect
150. #2521C22semidirect
151. #2520C22semidirect
152. #2519C22semidirect
153. #2516C22semidirect
154. #2515C22semidirect
155. #2515C22semidirect
156. #2515C22semidirect
157. #2495C22semidirect
161. #2489C22semidirect
168. #2479C22semidirect
169. #2476C22semidirect
170. #2474C22semidirect
172. #2471C22semidirect
173. #2469C22semidirect
174. #2464C22semidirect
175. #2461C22semidirect
176. #2458C22semidirect
195. #2399C22semidirect
196. #2399C22semidirect
197. #2398C22semidirect
198. #2398C22semidirect
200. #2381C22semidirect
201. #2381C22semidirect
203. #2379C22semidirect
209. C4×C22⋊Q8C22semidirect
210. C4×C22⋊Q8C22semidirect

Maximal subgroups

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

subgroupindex
#529532
#529522
#529482
#528872
#528862
#528722
#523752
#523482
#463352
#463252
#462052
#460992
#459762
#456862
#456072
#455972
#454812
#354662
#354572
#350982
#350952
#349712
C2×#25452