Finite Group Databasebeta

← #7645663

Subgroups — #7645663

Order 512.

4762 conjugacy classes of subgroups.

The subgroup lattice has 1385 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42190C214yesmaximal, complemented
2#42159C214yesmaximal, complemented
3#42010C214yesmaximal, complemented
4#41965C214yesmaximal, complemented
5#38469C214yesmaximal, complemented
6#38465C214yesmaximal, complemented
7#38403C214yesmaximal, complemented
8#38401C214yesmaximal, complemented
9#37507C214yesmaximal, complemented
10#36998C214yesmaximal, complemented
11#36824C214yesmaximal, complemented
12#35456C211yesmaximal, characteristic, complemented
13#35448C211yesmaximal, characteristic
14#35368C211yesmaximal, characteristic, complemented
15#35359C211yesmaximal, characteristic
16#35097C211yesmaximal, characteristic
17#35097C211yesmaximal, characteristic
18#35090C211yesmaximal, characteristic, complemented
19#35090C211yesmaximal, characteristic, complemented
20#35059C214yesmaximal, complemented
21#34995C211yesmaximal, characteristic
22#34994C211yesmaximal, characteristic, complemented
23C2×#2484C211yesmaximal, characteristic, complemented
24C2×#2413C211yesmaximal, characteristic
25#34199C211yesmaximal, characteristic
26C2×#2344C211yesmaximal, characteristic, complemented
27#34052C211yesmaximal, characteristic, complemented
28C2×#543C2211yescharacteristic
29C22×#123C2211yescharacteristic
30C22×#123C2211yescharacteristic
31C2×#518C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C23×C4⋊C4C2211yescharacteristic
37#2855C2214yes—
38#2855C2214yescomplemented
39#2853C2212yes—
40#2853C2212yes—
41#2853C2214yes—
42#2852C2214yes—
43#2851C2214yescomplemented
44#2839C2214yescomplemented
45#2839C2214yescomplemented
46#2838C2214yescomplemented
47#2836C2214yescomplemented
48#2810C2214yescomplemented
49#2809C2214yescomplemented
50#2807C2214yescomplemented
51#2805C2214yescomplemented
52#2802C2214yescomplemented
53#2802C2214yescomplemented
54#2798C2214yescomplemented
55#2794C2214yescomplemented
56#2793C2214yescomplemented
57#2792C2214yescomplemented
58#2791C2214yescomplemented
59#2791C2214yescomplemented
60#2790C2214yescomplemented
61#2789C2214yescomplemented
62#2787C2214yescomplemented
63#2783C2214yescomplemented
64#2783C2214yescomplemented
65#2777C2214yescomplemented
66#2776C2214yescomplemented
67#2776C2214yescomplemented
68#2775C2214yescomplemented
69#2773C2214yescomplemented
70#2771C2214yescomplemented
71#2769C2214yescomplemented
72#2767C2214yescomplemented
73#2767C2214yescomplemented
74#2765C2214yescomplemented
75#2744C2214yescomplemented
76#2726C2214yescomplemented
77#2721C2214yescomplemented
78#2720C2214yescomplemented
79#2689C2214yescomplemented
80#2667C2214yescomplemented
81#2666C2214yescomplemented
82#2666C2214yescomplemented
83#2664C2214yescomplemented
84#2655C2214yescomplemented
85#2655C2214yescomplemented
86#2655C2214yescomplemented
87#2655C2214yescomplemented
88#2654C2214yescomplemented
89#2654C2214yescomplemented
90#2652C2214yescomplemented
91#2650C2214yescomplemented
92#2646C2214yescomplemented
93#2643C2214yes—
94#2627C2214yes—
95#2627C2214yescomplemented
96#2623C2214yes—
97#2623C2212yes—
98#2623C2212yes—
99#2596C2214yescomplemented
100#2594C2214yescomplemented
101#2590C2214yescomplemented
102#2590C2214yescomplemented
103#2588C2214yescomplemented
104#2588C2214yescomplemented
105#2585C2214yescomplemented
106#2585C2214yescomplemented
107#2577C2214yescomplemented
108#2575C2214yescomplemented
109#2573C2214yescomplemented
110#2569C2214yescomplemented
111#2564C2214yes—
112#2556C2214yescomplemented
113#2510C2214yes—
114#2505C2214yes—
115#2505C2214yes—
116#2505C2214yescomplemented
117#2505C2214yescomplemented
118#2498C2214yes—
119#2498C2214yes—
120#2498C2214yes—
121#2498C2214yes—
122#2493C2214yes—
123#2493C2214yes—
124#2493C2214yes—
125#2493C2214yescomplemented
126#2493C2214yescomplemented
127#2493C2214yescomplemented
128#2493C2214yescomplemented
129#2484C2212yes—
130#2484C2214yes—
131#2484C2212yes—
132#2484C2214yes—
133#2484C2214yes—
134#2484C2214yes—
135#2484C2212yescomplemented
136#2484C2212yescomplemented
137#2484C2212yescomplemented
138#2484C2212yescomplemented
139#2483C2214yes—
140#2482C2212yes—
141#2482C2214yes—
142#2482C2212yes—
143#2481C2214yes—
144#2480C2214yes—
145#2473C2214yes—
146#2473C2214yes—
147#2473C2214yescomplemented
148#2473C2214yescomplemented
149#2450C2214yes—
150#2449C2214yes—
151#2442C2214yescomplemented
152#2438C2214yes—
153#2438C2214yes—
154#2438C2214yes—
155#2438C2214yescomplemented
156#2438C2214yescomplemented
157#2438C2214yescomplemented
158#2438C2214yescomplemented
159#2438C2214yescomplemented
160#2438C2214yescomplemented
161#2437C2214yes—
162#2419C2214yes—
163#2419C2214yes—
164#2419C2214yes—
165#2419C2214yes—
166#2417C2214yes—
167#2413C2214yes—
168#2413C2212yes—
169#2413C2212yes—
170#2413C2214yes—
171#2413C2212yes—
172#2413C2212yes—
173C2×#400C2212yescomplemented
174C2×#398C2212yes—
175C2×#398C2212yescomplemented
176C2×#396C2212yes—
177#2359C2214yes—
178#2359C2214yes—
179#2344C2214yes—
180#2344C2214yes—
181#2344C2212yes—
182#2344C2212yes—
183#2344C2214yescomplemented
184#2344C2214yescomplemented
185#2342C2212yes—
186#2342C2212yes—
187#2336C2214yescomplemented
188#2336C2214yescomplemented
189#2334C2214yescomplemented
190#2332C2214yescomplemented
191#2322C2214yes—
192#2317C2214yes—
193#2317C2214yescomplemented
194#2316C2212yescomplemented
195#2316C2212yescomplemented
196#2315C2211yescharacteristic
197#2315C2211yescharacteristic
198#2315C2211yescharacteristic
199#2315C2211yescharacteristic
200#2315C2211yescharacteristic
201#2315C2211yescharacteristic
202#2315C2211yescharacteristic
203#2315C2211yescharacteristic
204#2315C2211yescharacteristic
205#2315C2211yescharacteristic
206#2308C2211yescharacteristic
207#2308C2211yescharacteristic
208#2308C2211yescharacteristic
209C4×#123C2214yes—
210#2296C2214yes—
211#2296C2214yescomplemented
212C2×#389C2212yes—
213C2×#389C2212yescomplemented
214C2×#388C2212yes—
215C2×#387C2212yescomplemented
216C2×#387C2212yescomplemented
217C2×#387C2212yescomplemented
218C2×#387C2212yescomplemented
219C2×#386C2211yescharacteristic
220C2×#385C2211yescharacteristic
221C2×#385C2211yescharacteristic
222C2×#385C2211yescharacteristic
223#2285C2212yescomplemented
224#2285C2212yescomplemented
225C2×#381C2211yescharacteristic
226C2×#381C2211yescharacteristic
227C2×#381C2211yescharacteristic
228C2×#381C2211yescharacteristic
229C2×#381C2211yescharacteristic
230C2×#381C2211yescharacteristic
231C2×#380C2211yescharacteristic
232#2273C2211yescharacteristic
233C2×C4×C4⋊C4C2212yescomplemented
234C2×C4×C22⋊C4C2211yescharacteristic
235C23×D4C2311yescharacteristic
236C24×C4C2311yescharacteristic
237C24×C4C2311yescharacteristic
238C24×C4C2311yescharacteristic
239#543—44no—
240C2×#126C2314yes—
241C2×#125C2314yes—
242C2×#125C2314yes—
243C2×#123—28no—
244C2×#123—44no—
245C2×#123C2312yes—
246C2×#123C2312yes—
247C2×#123C2312yes—
248C2×#123C2312yes—
249C2×#123C2312yes—
250C2×#123C2312yes—
251C2×#123C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256#518—44no—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×#117—28no—
260C2×#117—44no—
261C2×#117—44no—
262C2×#117—44no—
263C2×#117C2312yes—
264C2×#117C2312yes—
265C2×#117C2312yes—
266C2×#117C2312yes—
267C2×#117C2312yes—
268C2×#117C2312yes—
269C2×#117C2312yes—
270C2×#117C2312yes—
271C2×#117C2312yes—
272C2×#117C2314yes—
273C2×#117C2312yes—
274C2×#117C2312yes—
275C2×#117C2314yes—
276C2×#117C2312yes—
277C2×#117C2312yes—
278C22×C4⋊C4—28no—
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2312yes—
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2312yes—
294C22×C4⋊C4C2312yes—
295C22×C4⋊C4C2312yes—
296C22×C4⋊C4C2312yes—
297C22×C4⋊C4C2312yes—
298C22×C4⋊C4C2312yes—
299C22×C22⋊C4C2311yescharacteristic
300C22×C22⋊C4C2311yescharacteristic
301C22×C22⋊C4C2311yescharacteristic
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2311yescharacteristic
304C22×C22⋊C4C2311yescharacteristic
305C22×C22⋊C4C2311yescharacteristic
306C22×C22⋊C4C2311yescharacteristic
307C22×C22⋊C4C2311yescharacteristic
308C22×C22⋊C4C2311yescharacteristic
309C22×C22⋊C4C2311yescharacteristic
310C22×C22⋊C4C2311yescharacteristic
311C22×C22⋊C4C2311yescharacteristic
312C22×C22⋊C4C2312yes—
313C22×C22⋊C4C2312yes—
314C22×C22⋊C4C2312yes—
315C22×C42C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2312yes—
318C22×C42C2312yes—
319C22×C42C2312yes—
320C22×C42C2312yes—
321#401C2314yes—
322#401C2314yes—
323#401C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#393C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
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#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
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#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#387C2314yes—
526#387C2314yes—
527#386C2312yes—
528#386C2314yes—
529#386C2314yes—
530#386C2312yes—
531#386C2312yes—
532#386C2312yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2312yes—
537#386C2312yes—
538#385C2314yes—
539#385C2314yes—
540#385C2312yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2312yes—
553#385C2314yes—
554#385C2312yes—
555#385C2312yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2312yes—
561#385C2312yes—
562#385C2314yes—
563#385C2312yes—
564#385C2312yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2312yes—
570#385C2312yes—
571#385C2312yes—
572#385C2312yes—
573#385C2312yes—
574#385C2312yes—
575#385C2314yes—
576#385C2314yes—
577#384C2314yes—
578#384C2314yes—
579#383C2314yes—
580#383C2314yes—
581#383C2314yes—
582#382C2314yes—
583#382C2314yes—
584#382C2314yes—
585#382C2314yes—
586#381C2312yes—
587#381C2312yes—
588#381C2312yes—
589#381C2314yes—
590#381C2314yes—
591#381C2312yes—
592#381C2312yes—
593#381C2312yes—
594#381C2312yes—
595#381C2312yes—
596#381C2312yes—
597#381C2312yes—
598#381C2312yes—
599#381C2312yes—
600#381C2314yes—
601#381C2312yes—
602#381C2314yes—
603#381C2312yes—
604#381C2312yes—
605#381C2312yes—
606#381C2314yes—
607#381C2314yes—
608#381C2312yes—
609#381C2314yes—
610#380C2312yes—
611#380C2314yes—
612#380C2312yes—
613#380C2314yes—
614#380C2312yes—
615#380C2312yes—
616#380C2312yes—
617#380C2312yes—
618#380C2312yes—
619#380C2312yes—
620#380C2314yes—
621#380C2314yes—
622#380C2312yes—
623#380C2312yes—
624#380C2314yes—
625#380C2314yes—
626#380C2314yes—
627#380C2314yes—
628#379C2312yes—
629#379C2312yes—
630#379C2312yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2314yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2312yes—
646C4×C22⋊C4C2312yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C2×#95C2312yes—
650C2×#95C2312yes—
651C2×#95C2312yes—
652C2×#95C2312yes—
653C2×#95C2312yes—
654C2×#95C2312yes—
655C2×#95C2312yes—
656C2×#95C2312yes—
657C2×#95C2312yes—
658C2×#95C2312yes—
659C2×#95C2312yes—
660C2×#95C2312yes—
661C2×#95C2312yes—
662C2×#95C2312yes—
663C2×#95C2312yes—
664C2×#95C2312yes—
665C2×#95C2312yes—
666C2×#95C2312yes—
667C25C2411yescharacteristic
668C25C2411yescharacteristic
669C22×Q8C2414yes—
670C22×D4—24no—
671C22×D4—24no—
672C22×D4—24no—
673C22×D4C2412yes—
674C22×D4C2412yes—
675C23×C4—24no—
676C23×C4—24no—
677C23×C4—24no—
678C23×C4—24no—
679C23×C4—24no—
680C23×C4—24no—
681C23×C4—44no—
682C23×C4#4118yes—
683C23×C4C2412yes—
684C23×C4C2411yescharacteristic
685C23×C4C2411yescharacteristic
686C23×C4C2411yescharacteristic
687C23×C4C2412yes—
688C23×C4C2411yescharacteristic
689C23×C4C2412yes—
690C23×C4C2412yes—
691C23×C4C2411yescharacteristic
692C23×C4C2411yescharacteristic
693C23×C4C2411yescharacteristic
694C23×C4C2411yescharacteristic
695C23×C4C2411yescharacteristic
696C23×C4C2411yescharacteristic
697C23×C4C2411yescharacteristic
698C23×C4C2412yes—
699C23×C4C2412yes—
700C23×C4C2411yescharacteristic
701C23×C4C2411yescharacteristic
702C23×C4C2411yescharacteristic
703C23×C4C2412yes—
704C23×C4C2412yes—
705C23×C4C2412yes—
706C23×C4C2412yes—
707C23×C4C2412yes—
708C23×C4C2411yescharacteristic
709C23×C4C2411yescharacteristic
710C23×C4C2412yes—
711C23×C4C2411yescharacteristic
712C23×C4C2414yes—
713#126—48no—
714#125—48no—
715#125—48no—
716#123—28no—
717#123—28no—
718#123—28no—
719#123—28no—
720#123—44no—
721#123—44no—
722#123—48no—
723C22⋊Q8—48no—
724C22⋊Q8—48no—
725C22⋊Q8—48no—
726C22⋊Q8—48no—
727C4×D4—48no—
728C4×D4—48no—
729#117—28no—
730#117—28no—
731#117—28no—
732#117—28no—
733#117—44no—
734#117—44no—
735#117—44no—
736#117—44no—
737#117—48no—
738#117—48no—
739#117—44no—
740#117—44no—
741#117—44no—
742#117—44no—
743#117—44no—
744C2×C4⋊C4—24no—
745C2×C4⋊C4—24no—
746C2×C4⋊C4—28no—
747C2×C4⋊C4—28no—
748C2×C4⋊C4—28no—
749C2×C4⋊C4—28no—
750C2×C4⋊C4—24no—
751C2×C4⋊C4—24no—
752C2×C4⋊C4—24no—
753C2×C4⋊C4—24no—
754C2×C4⋊C4—24no—
755C2×C4⋊C4—24no—
756C2×C4⋊C4—44no—
757C2×C4⋊C4—44no—
758C2×C4⋊C4—44no—
759C2×C4⋊C4—44no—
760C2×C4⋊C4—44no—
761C2×C4⋊C4—44no—
762C2×C4⋊C4—44no—
763C2×C4⋊C4—44no—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C22⋊C4—24no—
821C2×C22⋊C4—24no—
822C2×C22⋊C4—24no—
823C2×C22⋊C4—24no—
824C2×C22⋊C4—24no—
825C2×C22⋊C4—24no—
826C2×C22⋊C4—24no—
827C2×C22⋊C4—24no—
828C2×C22⋊C4—24no—
829C2×C22⋊C4—24no—
830C2×C22⋊C4—24no—
831C2×C22⋊C4—24no—
832C2×C22⋊C4—24no—
833C2×C22⋊C4—44no—
834C2×C22⋊C4—44no—
835C2×C22⋊C4—44no—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C42—24no—
874C2×C42—24no—
875C2×C42—44no—
876C2×C42—44no—
877C2×C42—44no—
878C2×C42—44no—
879C2×C42C2412yes—
880C2×C42C2412yes—
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894#95C2414yes—
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#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958C24—22no—
959C24—22no—
960C24—22no—
961C24—42no—
962C24—42no—
963C24—42no—
964C24—42no—
965C24C2×#4114yes—
966C24H(5,𝔽2)14yes—
967C242−1+414yes—
968C24C2512yes—
969C24C2511yescharacteristic
970C24C2511yescharacteristic
971C24C2511yescharacteristic
972C2×Q8—44no—
973C2×Q8—44no—
974C2×Q8—44no—
975C2×D4—24no—
976C2×D4—24no—
977C2×D4—24no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—24no—
981C2×D4—416no—
982C22×C4—232no—
983C22×C4—22no—
984C22×C4—22no—
985C22×C4—22no—
986C22×C4—22no—
987C22×C4—22no—
988C22×C4—22no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—22no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—24no—
999C22×C4—22no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—24no—
1003C22×C4—24no—
1004C22×C4—22no—
1005C22×C4—24no—
1006C22×C4—22no—
1007C22×C4—24no—
1008C22×C4—24no—
1009C22×C4—22no—
1010C22×C4—22no—
1011C22×C4—24no—
1012C22×C4—24no—
1013C22×C4—22no—
1014C22×C4—24no—
1015C22×C4—22no—
1016C22×C4—22no—
1017C22×C4—22no—
1018C22×C4—22no—
1019C22×C4—22no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—22no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4—42no—
1052C22×C4—42no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—416no—
1060C22×C4—416no—
1061C22×C4C2×#4114yes—
1062C22×C4C2×#4114yes—
1063C22×C4C2×#4114yes—
1064C22×C4C2×#4114yes—
1065C22×C4C2×#4114yes—
1066C22×C4C2×#4114yes—
1067C22×C4C2514yes—
1068C22×C4C2514yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2514yes—
1077C22×C4C2514yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2514yes—
1082C22×C4C2514yes—
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2511yescharacteristic
1086C22×C4C2511yescharacteristic
1087C22×C4C2511yescharacteristic
1088C22×C4C2511yescharacteristic
1089C22×C4C2512yes—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C22⋊C4—24no—
1147C22⋊C4—24no—
1148C22⋊C4—24no—
1149C22⋊C4—24no—
1150C22⋊C4—24no—
1151C22⋊C4—24no—
1152C22⋊C4—24no—
1153C22⋊C4—24no—
1154C22⋊C4—24no—
1155C22⋊C4—24no—
1156C22⋊C4—24no—
1157C22⋊C4—24no—
1158C22⋊C4—24no—
1159C22⋊C4—24no—
1160C22⋊C4—24no—
1161C22⋊C4—24no—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—24no—
1166C22⋊C4—24no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—24no—
1172C22⋊C4—28no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C42—24no—
1184C42—24no—
1185C42—24no—
1186C42—24no—
1187C42—28no—
1188C42—44no—
1189C42—44no—
1190C42—44no—
1191C42—44no—
1192C42—44no—
1193C42—44no—
1194C42—44no—
1195C42—44no—
1196C42—44no—
1197C42—44no—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—22no—
1202C23—22no—
1203C23—22no—
1204C23—22no—
1205C23—22no—
1206C23—22no—
1207C23—24no—
1208C23—24no—
1209C23—44no—
1210C23—44no—
1211C23—48no—
1212C23—48no—
1213C23—44no—
1214C23—82no—
1215C23—82no—
1216C23—84no—
1217C23—84no—
1218C23#539116yes—
1219C23C22×#4112yes—
1220C23C22×#4112yes—
1221C23C22×#4112yes—
1222C23C2×H(5,𝔽2)12yes—
1223C23C2×H(5,𝔽2)12yes—
1224C23C2×H(5,𝔽2)12yes—
1225C23C2×2−1+412yes—
1226C23C2×2−1+412yes—
1227C23C2×2−1+412yes—
1228C23C2611yescharacteristic
1229Q8—164no—
1230D4—48no—
1231D4—48no—
1232C2×C4—28no—
1233C2×C4—22no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—22no—
1243C2×C4—28no—
1244C2×C4—28no—
1245C2×C4—28no—
1246C2×C4—28no—
1247C2×C4—28no—
1248C2×C4—28no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
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—48no—
1298C2×C4—48no—
1299C2×C4—48no—
1300C2×C4—48no—
1301C2×C4—44no—
1302C2×C4—48no—
1303C2×C4—44no—
1304C2×C4—44no—
1305C2×C4—48no—
1306C2×C4—44no—
1307C2×C4—82no—
1308C2×C4—82no—
1309C2×C4—82no—
1310C2×C4—82no—
1311C2×C4—82no—
1312C2×C4—82no—
1313C2×C4—84no—
1314C2×C4—84no—
1315C2×C4—84no—
1316C2×C4—84no—
1317C2×C4—84no—
1318C2×C4—84no—
1319C2×C4—164no—
1320C2×C4C22×#4112yes—
1321C2×C4C22×#4112yes—
1322C2×C4C22×#4112yes—
1323C2×C4C22×#4112yes—
1324C2×C4#58514yes—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—22no—
1329C22—22no—
1330C22—22no—
1331C22—24no—
1332C22—24no—
1333C22—24no—
1334C22—24no—
1335C22—24no—
1336C22—24no—
1337C22—416no—
1338C22—42no—
1339C22—42no—
1340C22—44no—
1341C22—44no—
1342C22—42no—
1343C22—164no—
1344C22C2×#53914yes—
1345C22C2×#53914yes—
1346C22C2×#53914yes—
1347C22C23×#4111yescharacteristic
1348C22C22×H(5,𝔽2)11yescharacteristic
1349C22C22×2−1+411yescharacteristic
1350C22C2×#58512yes—
1351C222−1+612yes—
1352C4—24no—
1353C4—22no—
1354C4—22no—
1355C4—22no—
1356C4—22no—
1357C4—42no—
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—42no—
1362C4—42no—
1363C4—42no—
1364C4—44no—
1365C4—44no—
1366C4—44no—
1367C4—44no—
1368C4—44no—
1369C4—44no—
1370C4—44no—
1371C4—44no—
1372C4—42no—
1373C4—42no—
1374C4—42no—
1375C2—24no—
1376C2—24no—
1377C2—24no—
1378C2—82no—
1379C2C22×#53911yescharacteristic
1380C2#6281411yescharacteristic
1381C2#6286011yescharacteristic
1382C2#6290112yes—
1383C2#6290412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42190C2semidirect
2. #42159C2semidirect
3. #42010C2semidirect
4. #41965C2semidirect
5. #38469C2semidirect
6. #38465C2semidirect
7. #38403C2semidirect
8. #38401C2semidirect
9. #37507C2semidirect
10. #36998C2semidirect
11. #36824C2semidirect
12. #35456C2semidirect
14. #35368C2semidirect
18. #35090C2semidirect
19. #35090C2semidirect
20. #35059C2semidirect
22. #34994C2semidirect
23. C2×#2484C2semidirect
26. C2×#2344C2semidirect
27. #34052C2semidirect
38. #2855C22semidirect
43. #2851C22semidirect
44. #2839C22semidirect
45. #2839C22semidirect
46. #2838C22semidirect
47. #2836C22semidirect
48. #2810C22semidirect
49. #2809C22semidirect
50. #2807C22semidirect
51. #2805C22semidirect
52. #2802C22semidirect
53. #2802C22semidirect
54. #2798C22semidirect
55. #2794C22semidirect
56. #2793C22semidirect
57. #2792C22semidirect
58. #2791C22semidirect
59. #2791C22semidirect
60. #2790C22semidirect
61. #2789C22semidirect
62. #2787C22semidirect
63. #2783C22semidirect
64. #2783C22semidirect
65. #2777C22semidirect
66. #2776C22semidirect
67. #2776C22semidirect
68. #2775C22semidirect
69. #2773C22semidirect
70. #2771C22semidirect
71. #2769C22semidirect
72. #2767C22semidirect
73. #2767C22semidirect
74. #2765C22semidirect
75. #2744C22semidirect
76. #2726C22semidirect
77. #2721C22semidirect
78. #2720C22semidirect
79. #2689C22semidirect
80. #2667C22semidirect
81. #2666C22semidirect
82. #2666C22semidirect
83. #2664C22semidirect
84. #2655C22semidirect
85. #2655C22semidirect
86. #2655C22semidirect
87. #2655C22semidirect
88. #2654C22semidirect
89. #2654C22semidirect
90. #2652C22semidirect
91. #2650C22semidirect
92. #2646C22semidirect
95. #2627C22semidirect
99. #2596C22semidirect
100. #2594C22semidirect
101. #2590C22semidirect
102. #2590C22semidirect
103. #2588C22semidirect
104. #2588C22semidirect
105. #2585C22semidirect
106. #2585C22semidirect
107. #2577C22semidirect
108. #2575C22semidirect
109. #2573C22semidirect
110. #2569C22semidirect
112. #2556C22semidirect
116. #2505C22semidirect
117. #2505C22semidirect
125. #2493C22semidirect
126. #2493C22semidirect
127. #2493C22semidirect
128. #2493C22semidirect
135. #2484C22semidirect
136. #2484C22semidirect
137. #2484C22semidirect
138. #2484C22semidirect
147. #2473C22semidirect
148. #2473C22semidirect
151. #2442C22semidirect
155. #2438C22semidirect
156. #2438C22semidirect
157. #2438C22semidirect
158. #2438C22semidirect
159. #2438C22semidirect
160. #2438C22semidirect
173. C2×#400C22semidirect
175. C2×#398C22semidirect
183. #2344C22semidirect
184. #2344C22semidirect
187. #2336C22semidirect
188. #2336C22semidirect
189. #2334C22semidirect
190. #2332C22semidirect
193. #2317C22semidirect
194. #2316C22semidirect
195. #2316C22semidirect
211. #2296C22semidirect
213. C2×#389C22semidirect
215. C2×#387C22semidirect
216. C2×#387C22semidirect
217. C2×#387C22semidirect
218. C2×#387C22semidirect
223. #2285C22semidirect
224. #2285C22semidirect
233. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#421902
#421592
#420102
#419652
#384692
#384652
#384032
#384012
#375072
#369982
#368242
#354562
#354482
#353682
#353592
#350972
#350902
#350592
#349952
#349942
C2×#24842
C2×#24132
#341992
C2×#23442
#340522