Finite Group Databasebeta

← #8893500

Subgroups — #8893500

Order 512.

4702 conjugacy classes of subgroups.

The subgroup lattice has 1335 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57825C214yesmaximal, complemented
2#55612C212yesmaximal, complemented
3#54955C214yesmaximal, complemented
4#53977C212yesmaximal, complemented
5#49310C214yesmaximal, complemented
6#48769C214yesmaximal, complemented
7#48114C214yesmaximal, complemented
8#47664C214yesmaximal, complemented
9#47141C214yesmaximal, complemented
10#46857C212yesmaximal, complemented
11#46555C214yesmaximal, complemented
12#46429C212yesmaximal, complemented
13#46354C212yesmaximal, complemented
14#38521C214yesmaximal, complemented
15#38328C214yesmaximal, complemented
16#37949C212yesmaximal, complemented
17#37940C212yesmaximal, complemented
18#37418C212yesmaximal, complemented
19#36707C211yesmaximal, characteristic, complemented
20#35644C211yesmaximal, characteristic, complemented
21#35441C212yesmaximal, complemented
22#35408C212yesmaximal, complemented
23#35377C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic, complemented
25C2×#537C2212yes—
26C2×#537C2211yescharacteristic, complemented
27C2×#534C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29#2850C2212yescomplemented
30#2850C2212yescomplemented
31#2847C2211yescharacteristic
32#2847C2211yescharacteristic
33#2833C2212yescomplemented
34#2832C2214yescomplemented
35#2831C2214yescomplemented
36#2826C2214yescomplemented
37#2819C2212yescomplemented
38#2816C2212yes—
39#2799C2214yescomplemented
40#2782C2212yescomplemented
41#2778C2214yes—
42#2778C2214yescomplemented
43#2769C2212yescomplemented
44#2764C2214yescomplemented
45#2764C2214yescomplemented
46#2764C2214yescomplemented
47#2762C2214yescomplemented
48#2761C2214yescomplemented
49#2759C2214yescomplemented
50#2756C2214yes—
51#2756C2214yes—
52#2754C2214yescomplemented
53#2751C2214yescomplemented
54#2751C2214yescomplemented
55#2751C2214yescomplemented
56#2749C2214yescomplemented
57#2746C2214yescomplemented
58#2739C2214yescomplemented
59#2738C2214yescomplemented
60#2737C2214yescomplemented
61#2737C2214yescomplemented
62#2733C2214yescomplemented
63#2733C2212yescomplemented
64#2730C2214yes—
65#2729C2214yescomplemented
66#2728C2212yescomplemented
67#2728C2214yescomplemented
68#2728C2214yescomplemented
69#2712C2214yescomplemented
70#2712C2214yescomplemented
71#2711C2214yescomplemented
72#2711C2214yescomplemented
73#2708C2214yes—
74#2700C2214yescomplemented
75#2699C2214yes—
76#2699C2214yescomplemented
77#2699C2214yescomplemented
78#2697C2214yescomplemented
79#2696C2214yes—
80#2692C2214yes—
81#2692C2214yescomplemented
82#2692C2214yescomplemented
83#2688C2214yes—
84#2688C2214yes—
85#2688C2214yescomplemented
86#2688C2214yescomplemented
87#2688C2214yescomplemented
88#2688C2214yescomplemented
89#2687C2214yes—
90#2686C2214yes—
91#2681C2214yescomplemented
92#2677C2214yescomplemented
93#2676C2214yescomplemented
94#2676C2214yescomplemented
95#2672C2214yescomplemented
96#2670C2214yescomplemented
97#2669C2214yes—
98#2668C2214yes—
99#2659C2212yescomplemented
100#2654C2214yescomplemented
101#2649C2214yes—
102#2648C2214yescomplemented
103#2646C2212yescomplemented
104#2631C2214yes—
105#2621C2212yescomplemented
106#2619C2212yescomplemented
107#2618C2211yescharacteristic, complemented
108#2618C2211yescharacteristic, complemented
109#2617C2212yescomplemented
110#2617C2212yescomplemented
111#2610C2214yescomplemented
112#2609C2212yescomplemented
113#2607C2212yescomplemented
114#2605C2214yescomplemented
115#2598C2214yescomplemented
116#2595C2214yescomplemented
117#2595C2214yescomplemented
118#2595C2214yescomplemented
119#2591C2212yes—
120#2591C2212yes—
121#2578C2214yes—
122#2578C2214yescomplemented
123#2575C2214yescomplemented
124#2572C2214yescomplemented
125#2572C2214yescomplemented
126#2572C2214yescomplemented
127#2572C2212yescomplemented
128#2561C2212yes—
129#2561C2212yes—
130#2557C2214yescomplemented
131#2557C2214yescomplemented
132#2556C2214yescomplemented
133#2555C2214yes—
134#2544C2214yescomplemented
135#2539C2212yes—
136#2532C2214yescomplemented
137#2532C2214yescomplemented
138#2531C2214yes—
139#2524C2214yescomplemented
140#2523C2214yescomplemented
141#2523C2214yescomplemented
142#2518C2214yescomplemented
143#2516C2214yescomplemented
144#2516C2214yescomplemented
145#2510C2214yescomplemented
146#2504C2212yes—
147#2504C2212yescomplemented
148#2503C2212yescomplemented
149#2503C2212yescomplemented
150#2503C2212yescomplemented
151#2492C2214yescomplemented
152#2492C2214yescomplemented
153#2492C2214yescomplemented
154#2491C2214yescomplemented
155#2489C2214yescomplemented
156#2489C2214yescomplemented
157#2488C2214yes—
158#2488C2214yes—
159#2482C2214yescomplemented
160#2477C2214yescomplemented
161#2476C2214yescomplemented
162#2476C2214yescomplemented
163#2474C2214yescomplemented
164#2474C2214yescomplemented
165#2474C2214yescomplemented
166#2473C2214yescomplemented
167#2472C2214yes—
168#2472C2214yes—
169#2472C2214yes—
170#2472C2214yes—
171#2472C2214yescomplemented
172#2472C2214yescomplemented
173#2471C2214yescomplemented
174#2464C2214yes—
175#2464C2214yes—
176#2459C2214yescomplemented
177#2459C2214yescomplemented
178#2459C2214yescomplemented
179#2457C2214yescomplemented
180#2447C2214yescomplemented
181#2443C2214yes—
182#2436C2212yes—
183#2436C2212yescomplemented
184#2432C2212yescomplemented
185#2432C2214yescomplemented
186#2432C2212yescomplemented
187#2431C2212yes—
188#2431C2212yescomplemented
189#2418C2214yes—
190#2410C2214yes—
191#2408C2214yes—
192#2406C2212yescomplemented
193#2404C2214yes—
194#2404C2212yes—
195#2377C2214yes—
196#2363C2214yes—
197#2358C2214yescomplemented
198#2353C2214yescomplemented
199#2337C2214yescomplemented
200#2337C2214yescomplemented
201#2337C2214yescomplemented
202#2337C2214yescomplemented
203#2333C2212yes—
204#2332C2212yescomplemented
205#2325C2212yescomplemented
206#2325C2212yescomplemented
207#2315C2212yescomplemented
208#2313C2211yescharacteristic, complemented
209#2312C2212yescomplemented
210#2310C2212yescomplemented
211#2308C2212yes—
212C4×#123C2214yescomplemented
213#2297C2212yescomplemented
214#2290C2214yescomplemented
215C2×#386C2212yes—
216#2280C2212yes—
217#2274C2211yescharacteristic, complemented
218#2273C2211yescharacteristic
219C22×#41C2312yes—
220C22×#41C2312yes—
221C23×Q8C2311yescharacteristic
222C23×D4C2312yes—
223C24×C4C2311yescharacteristic
224#544—44no—
225#537—44no—
226#537—48no—
227#534—44no—
228C2×C4⋊Q8C2314yes—
229C2×C4⋊Q8C2312yes—
230C2×#127C2312yes—
231C2×#125C2314yes—
232C2×#124C2314yes—
233C2×#124C2314yes—
234C2×#124C2314yes—
235C2×#124C2314yes—
236C2×#124C2314yes—
237C2×#124C2312yes—
238C2×#124C2312yes—
239C2×#124C2314yes—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×#123C2312yes—
243C2×#123C2312yes—
244C2×C22⋊Q8—44no—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2312yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×#121C2312yes—
256C2×#121C2312yes—
257C2×#121C2312yes—
258C2×#121C2312yes—
259C2×#121C2311yescharacteristic
260C2×#121C2311yescharacteristic
261C2×#121C2312yes—
262C2×#121C2312yes—
263C2×#121C2314yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2312yes—
269C2×#121C2312yes—
270C2×#120C2314yes—
271C2×#120C2314yes—
272C2×#120C2312yes—
273C2×#120C2312yes—
274C2×#120C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×#117C2312yes—
279C2×#117C2312yes—
280C2×#117C2314yes—
281C2×#117C2312yes—
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2312yes—
286C22×C22⋊C4C2311yescharacteristic
287C22×C22⋊C4C2311yescharacteristic
288C22×C22⋊C4C2312yes—
289C22×C22⋊C4C2312yes—
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2314yes—
292C22×C42C2312yes—
293#401C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2312yes—
299#400C2314yes—
300#400C2314yes—
301#400C2312yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#399C2314yes—
311#399C2314yes—
312#399C2314yes—
313#399C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2312yes—
318#398C2314yes—
319#398C2312yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#395C2314yes—
350#395C2314yes—
351#395C2314yes—
352#395C2314yes—
353#394C2314yes—
354#394C2314yes—
355#394C2314yes—
356#394C2312yes—
357#394C2312yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2312yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2312yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#393C2314yes—
381#393C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2314yes—
386#393C2314yes—
387#393C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#392C2314yes—
394#392C2314yes—
395#392C2314yes—
396#392C2314yes—
397#392C2314yes—
398#392C2314yes—
399#392C2314yes—
400#392C2314yes—
401#392C2314yes—
402#392C2314yes—
403#392C2314yes—
404#392C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2312yes—
412#391C2314yes—
413#391C2312yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2312yes—
424#390C2314yes—
425#390C2312yes—
426#390C2312yes—
427#390C2314yes—
428#390C2314yes—
429#390C2314yes—
430#390C2314yes—
431#390C2314yes—
432#390C2314yes—
433#390C2312yes—
434#390C2312yes—
435#390C2314yes—
436#390C2314yes—
437#389C2314yes—
438#389C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
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#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2312yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2312yes—
521#386C2314yes—
522#386C2312yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2312yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#383C2314yes—
558#383C2314yes—
559#383C2314yes—
560#383C2314yes—
561#383C2314yes—
562#383C2314yes—
563#382C2312yes—
564#382C2312yes—
565#382C2312yes—
566#382C2312yes—
567#382C2312yes—
568#382C2312yes—
569#381C2312yes—
570#381C2314yes—
571#381C2314yes—
572#381C2314yes—
573#381C2314yes—
574#381C2314yes—
575#381C2314yes—
576#381C2314yes—
577#381C2314yes—
578#381C2314yes—
579#380C2312yes—
580#380C2312yes—
581#380C2311yescharacteristic
582#380C2311yescharacteristic
583#380C2312yes—
584#380C2314yes—
585#380C2312yes—
586#380C2314yes—
587#380C2312yes—
588#380C2312yes—
589#380C2314yes—
590#379C2314yes—
591#379C2314yes—
592#379C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C22⋊C4C2312yes—
599C4×C22⋊C4C2312yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2312yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616#376C2314yes—
617C2×#95C2312yes—
618C2×#95C2312yes—
619C25C2411yescharacteristic
620C25C2412yes—
621C2×#41—28no—
622C2×#41—44no—
623C2×#41—82no—
624C2×#41—82no—
625C2×#41—82no—
626C2×#41—82no—
627C22×Q8—42no—
628C22×Q8—44no—
629C22×Q8C2412yes—
630C22×Q8C2414yes—
631C22×Q8C2412yes—
632C22×Q8C2412yes—
633C22×Q8C2414yes—
634C22×D4—44no—
635C22×D4—44no—
636C22×D4—44no—
637C22×D4C2414yes—
638C22×D4C2414yes—
639C22×D4C2412yes—
640C22×D4C2412yes—
641C22×D4C2412yes—
642C22×D4C2414yes—
643C22×D4C2412yes—
644C22×D4C2414yes—
645C22×D4C2414yes—
646C22×D4C2412yes—
647C22×D4C2414yes—
648C22×D4C2414yes—
649C22×D4C2414yes—
650C22×D4C2411yescharacteristic
651C22×D4C2411yescharacteristic
652C22×D4C2412yes—
653C23×C4—44no—
654C23×C4—42no—
655C23×C4C2411yescharacteristic
656C23×C4C2411yescharacteristic
657C23×C4C2411yescharacteristic
658C23×C4C2411yescharacteristic
659C23×C4C2412yes—
660C23×C4C2412yes—
661C23×C4C2411yescharacteristic
662C23×C4C2412yes—
663C23×C4C2412yes—
664C23×C4C2412yes—
665C23×C4C2412yes—
666C23×C4C2412yes—
667C23×C4C2414yes—
668C23×C4C2414yes—
669C23×C4C2414yes—
670C23×C4C2414yes—
671C23×C4C2411yescharacteristic
672C4⋊Q8—48no—
673C4⋊Q8—82no—
674#127—82no—
675#125—48no—
676#124—48no—
677#124—48no—
678#124—48no—
679#124—48no—
680#124—82no—
681#124—82no—
682#124—84no—
683#124—84no—
684#123—48no—
685#123—48no—
686#123—82no—
687#123—82no—
688C22⋊Q8—28no—
689C22⋊Q8—44no—
690C22⋊Q8—48no—
691C22⋊Q8—48no—
692C22⋊Q8—48no—
693C22⋊Q8—44no—
694C22⋊Q8—44no—
695C22⋊Q8—44no—
696C22⋊Q8—84no—
697C22⋊Q8—84no—
698#121—28no—
699#121—44no—
700#121—44no—
701#121—48no—
702#121—48no—
703#121—48no—
704#121—48no—
705#121—48no—
706#121—44no—
707#121—44no—
708#121—44no—
709#121—44no—
710#121—44no—
711#121—42no—
712#121—42no—
713#120—48no—
714#120—48no—
715#120—82no—
716#120—82no—
717#120—84no—
718C4×D4—48no—
719C4×D4—48no—
720C4×D4—84no—
721#117—44no—
722#117—44no—
723#117—84no—
724#117—82no—
725C2×C4⋊C4—24no—
726C2×C4⋊C4—24no—
727C2×C4⋊C4—44no—
728C2×C4⋊C4—42no—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C22⋊C4—24no—
765C2×C22⋊C4—44no—
766C2×C22⋊C4—44no—
767C2×C22⋊C4—44no—
768C2×C22⋊C4—42no—
769C2×C22⋊C4—84no—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C42—82no—
825C2×C42C2414yes—
826C2×C42C2412yes—
827C2×C42C2414yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2414yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2412yes—
836C2×C42C2414yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2412yes—
847#95C2414yes—
848#95C2414yes—
849#95C2412yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
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#95C2412yes—
876#95C2414yes—
877#95C2412yes—
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—22no—
892C24—24no—
893C24—24no—
894C24—42no—
895C24—42no—
896C24—41no—
897C24—41no—
898C24—42no—
899C24—42no—
900C24—42no—
901C24—42no—
902C24—42no—
903C24C2514yes—
904C24C2512yes—
905C24C2512yes—
906C24C2511yescharacteristic
907C24C2512yes—
908#41—816no—
909#41—816no—
910C2×Q8—24no—
911C2×Q8—24no—
912C2×Q8—28no—
913C2×Q8—44no—
914C2×Q8—42no—
915C2×Q8—42no—
916C2×Q8—42no—
917C2×Q8—42no—
918C2×Q8—44no—
919C2×Q8—42no—
920C2×Q8—42no—
921C2×Q8—44no—
922C2×Q8—44no—
923C2×Q8—44no—
924C2×Q8—42no—
925C2×Q8—88no—
926C2×D4—28no—
927C2×D4—24no—
928C2×D4—24no—
929C2×D4—28no—
930C2×D4—28no—
931C2×D4—28no—
932C2×D4—24no—
933C2×D4—24no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4—44no—
938C2×D4—44no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—42no—
946C2×D4—42no—
947C2×D4—44no—
948C2×D4—42no—
949C2×D4—42no—
950C2×D4—44no—
951C2×D4—42no—
952C2×D4—42no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—42no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—42no—
961C2×D4—41no—
962C2×D4—41no—
963C2×D4—44no—
964C2×D4—44no—
965C2×D4—42no—
966C2×D4—42no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—816no—
971C22×C4—22no—
972C22×C4—24no—
973C22×C4—22no—
974C22×C4—22no—
975C22×C4—22no—
976C22×C4—22no—
977C22×C4—24no—
978C22×C4—24no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—24no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—41no—
985C22×C4—41no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—44no—
998C22×C4—42no—
999C22×C4—44no—
1000C22×C4—41no—
1001C22×C4—41no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—42no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—42no—
1015C22×C4—44no—
1016C22×C4—42no—
1017C22×C4—88no—
1018C22×C4H(5,𝔽2)14yes—
1019C22×C4C2514yes—
1020C22×C4C2512yes—
1021C22×C4C2512yes—
1022C22×C4C2514yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2511yescharacteristic
1025C22×C4C2514yes—
1026C22×C4C2514yes—
1027C22×C4C2514yes—
1028C22×C4C2514yes—
1029C22×C4C2514yes—
1030C22×C4C2512yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C4⋊C4—24no—
1038C4⋊C4—24no—
1039C4⋊C4—28no—
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—28no—
1043C4⋊C4—44no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—42no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—28no—
1081C22⋊C4—28no—
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—42no—
1103C22⋊C4—42no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C42—28no—
1127C42—44no—
1128C42—42no—
1129C42—42no—
1130C42—44no—
1131C42—42no—
1132C42—42no—
1133C42—42no—
1134C42—44no—
1135C42—44no—
1136C42—44no—
1137C42—44no—
1138C42—44no—
1139C42—42no—
1140C23—28no—
1141C23—22no—
1142C23—22no—
1143C23—22no—
1144C23—22no—
1145C23—22no—
1146C23—22no—
1147C23—22no—
1148C23—22no—
1149C23—21no—
1150C23—21no—
1151C23—24no—
1152C23—22no—
1153C23—22no—
1154C23—24no—
1155C23—24no—
1156C23—24no—
1157C23—24no—
1158C23—24no—
1159C23—24no—
1160C23—24no—
1161C23—24no—
1162C23—24no—
1163C23—22no—
1164C23—22no—
1165C23—24no—
1166C23—22no—
1167C23—22no—
1168C23—48no—
1169C23—82no—
1170C23—82no—
1171C23—84no—
1172C23—84no—
1173C23—84no—
1174C23—84no—
1175C23—162no—
1176C23—162no—
1177C23—162no—
1178C23—162no—
1179C23C2×H(5,𝔽2)12yes—
1180C23#58514yes—
1181C23C2611yescharacteristic
1182Q8—88no—
1183Q8—84no—
1184Q8—84no—
1185Q8—162no—
1186Q8—164no—
1187D4—84no—
1188D4—84no—
1189D4—88no—
1190D4—88no—
1191D4—88no—
1192D4—88no—
1193D4—84no—
1194D4—84no—
1195D4—88no—
1196D4—88no—
1197D4—161no—
1198D4—161no—
1199D4—162no—
1200D4—162no—
1201D4—164no—
1202D4—164no—
1203C2×C4—28no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—44no—
1253C2×C4—48no—
1254C2×C4—48no—
1255C2×C4—84no—
1256C2×C4—84no—
1257C2×C4—82no—
1258C2×C4—82no—
1259C2×C4—84no—
1260C2×C4—82no—
1261C2×C4—82no—
1262C2×C4—88no—
1263C2×C4—88no—
1264C2×C4—88no—
1265C2×C4—164no—
1266C2×C4—162no—
1267C2×C4—162no—
1268C2×C4C2×H(5,𝔽2)14yes—
1269C2×C4#58514yes—
1270C22—22no—
1271C22—24no—
1272C22—22no—
1273C22—22no—
1274C22—24no—
1275C22—24no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—44no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—44no—
1288C22—42no—
1289C22—42no—
1290C22—44no—
1291C22—44no—
1292C22—44no—
1293C22—44no—
1294C22—44no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—44no—
1299C22—88no—
1300C22—168no—
1301C22C22×H(5,𝔽2)11yescharacteristic
1302C22C2×#58512yes—
1303C22C2×#58512yes—
1304C22H(7,𝔽2)11yescharacteristic
1305C22H(7,𝔽2)11yescharacteristic
1306C4—24no—
1307C4—24no—
1308C4—41no—
1309C4—41no—
1310C4—44no—
1311C4—42no—
1312C4—42no—
1313C4—44no—
1314C4—42no—
1315C4—42no—
1316C4—44no—
1317C4—42no—
1318C4—44no—
1319C4—44no—
1320C4—44no—
1321C4—44no—
1322C4—44no—
1323C4—44no—
1324C2—42no—
1325C2—44no—
1326C2—82no—
1327C2—82no—
1328C2—84no—
1329C2#6282411yescharacteristic
1330C2#6282411yescharacteristic
1331C2#6286211yescharacteristic
1332C2#6291012yes—
1333C2#6293512yes—
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. #57825C2semidirect
2. #55612C2semidirect
3. #54955C2semidirect
4. #53977C2semidirect
5. #49310C2semidirect
6. #48769C2semidirect
7. #48114C2semidirect
8. #47664C2semidirect
9. #47141C2semidirect
10. #46857C2semidirect
11. #46555C2semidirect
12. #46429C2semidirect
13. #46354C2semidirect
14. #38521C2semidirect
15. #38328C2semidirect
16. #37949C2semidirect
17. #37940C2semidirect
18. #37418C2semidirect
19. #36707C2semidirect
20. #35644C2semidirect
21. #35441C2semidirect
22. #35408C2semidirect
23. #35377C2semidirect
24. C2×#544C22semidirect
26. C2×#537C22semidirect
29. #2850C22semidirect
30. #2850C22semidirect
33. #2833C22semidirect
34. #2832C22semidirect
35. #2831C22semidirect
36. #2826C22semidirect
37. #2819C22semidirect
39. #2799C22semidirect
40. #2782C22semidirect
42. #2778C22semidirect
43. #2769C22semidirect
44. #2764C22semidirect
45. #2764C22semidirect
46. #2764C22semidirect
47. #2762C22semidirect
48. #2761C22semidirect
49. #2759C22semidirect
52. #2754C22semidirect
53. #2751C22semidirect
54. #2751C22semidirect
55. #2751C22semidirect
56. #2749C22semidirect
57. #2746C22semidirect
58. #2739C22semidirect
59. #2738C22semidirect
60. #2737C22semidirect
61. #2737C22semidirect
62. #2733C22semidirect
63. #2733C22semidirect
65. #2729C22semidirect
66. #2728C22semidirect
67. #2728C22semidirect
68. #2728C22semidirect
69. #2712C22semidirect
70. #2712C22semidirect
71. #2711C22semidirect
72. #2711C22semidirect
74. #2700C22semidirect
76. #2699C22semidirect
77. #2699C22semidirect
78. #2697C22semidirect
81. #2692C22semidirect
82. #2692C22semidirect
85. #2688C22semidirect
86. #2688C22semidirect
87. #2688C22semidirect
88. #2688C22semidirect
91. #2681C22semidirect
92. #2677C22semidirect
93. #2676C22semidirect
94. #2676C22semidirect
95. #2672C22semidirect
96. #2670C22semidirect
99. #2659C22semidirect
100. #2654C22semidirect
102. #2648C22semidirect
103. #2646C22semidirect
105. #2621C22semidirect
106. #2619C22semidirect
107. #2618C22semidirect
108. #2618C22semidirect
109. #2617C22semidirect
110. #2617C22semidirect
111. #2610C22semidirect
112. #2609C22semidirect
113. #2607C22semidirect
114. #2605C22semidirect
115. #2598C22semidirect
116. #2595C22semidirect
117. #2595C22semidirect
118. #2595C22semidirect
122. #2578C22semidirect
123. #2575C22semidirect
124. #2572C22semidirect
125. #2572C22semidirect
126. #2572C22semidirect
127. #2572C22semidirect
130. #2557C22semidirect
131. #2557C22semidirect
132. #2556C22semidirect
134. #2544C22semidirect
136. #2532C22semidirect
137. #2532C22semidirect
139. #2524C22semidirect
140. #2523C22semidirect
141. #2523C22semidirect
142. #2518C22semidirect
143. #2516C22semidirect
144. #2516C22semidirect
145. #2510C22semidirect
147. #2504C22semidirect
148. #2503C22semidirect
149. #2503C22semidirect
150. #2503C22semidirect
151. #2492C22semidirect
152. #2492C22semidirect
153. #2492C22semidirect
154. #2491C22semidirect
155. #2489C22semidirect
156. #2489C22semidirect
159. #2482C22semidirect
160. #2477C22semidirect
161. #2476C22semidirect
162. #2476C22semidirect
163. #2474C22semidirect
164. #2474C22semidirect
165. #2474C22semidirect
166. #2473C22semidirect
171. #2472C22semidirect
172. #2472C22semidirect
173. #2471C22semidirect
176. #2459C22semidirect
177. #2459C22semidirect
178. #2459C22semidirect
179. #2457C22semidirect
180. #2447C22semidirect
183. #2436C22semidirect
184. #2432C22semidirect
185. #2432C22semidirect
186. #2432C22semidirect
188. #2431C22semidirect
192. #2406C22semidirect
197. #2358C22semidirect
198. #2353C22semidirect
199. #2337C22semidirect
200. #2337C22semidirect
201. #2337C22semidirect
202. #2337C22semidirect
204. #2332C22semidirect
205. #2325C22semidirect
206. #2325C22semidirect
207. #2315C22semidirect
208. #2313C22semidirect
209. #2312C22semidirect
210. #2310C22semidirect
212. C4×#123C22semidirect
213. #2297C22semidirect
214. #2290C22semidirect
217. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#578252
#556122
#549552
#539772
#493102
#487692
#481142
#476642
#471412
#468572
#465552
#464292
#463542
#385212
#383282
#379492
#379402
#374182
#367072
#356442
#354412
#354082
#353772