Finite Group Databasebeta

← #72287149

Subgroups — #72287149

Order 1024.

2536 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#7623099C211yesmaximal, characteristic
2#6345702C211yesmaximal, characteristic, complemented
3C2×#18065C211yesmaximal, characteristic, complemented
4#484106C218yesmaximal, complemented
5#484053C218yesmaximal, complemented
6#483922C214yesmaximal, complemented
7#483875C214yesmaximal, complemented
8#483446C211yesmaximal, characteristic, complemented
9#481379C211yesmaximal, characteristic, complemented
10#481282C211yesmaximal, characteristic, complemented
11#479974C211yesmaximal, characteristic, complemented
12C2×#3169C2211yescharacteristic
13C2×#2990—21no—
14C2×C4×#135C2211yescharacteristic
15#60144—21no—
16#33675C2214yes—
17#33672C2212yes—
18#33669C2212yes—
19#33666C414yes—
20#33663C412yes—
21#33660C412yes—
22#33648C412yes—
23#33629C412yes—
24#33582C412yes—
25#33520C412yes—
26C4×#509C2214yes—
27#33418C2211yescharacteristic
28#33418C2211yescharacteristic
29#18073—22no—
30#18073C2214yescomplemented
31#18065—22no—
32#18065—22no—
33#18065C2214yes—
34#18065C2214yescomplemented
35#18044—22no—
36#18044C2214yescomplemented
37#17981—22no—
38#17962C2214yes—
39C2×#1593C2212yescomplemented
40C2×#1582—22no—
41C2×#1580C2212yescomplemented
42C2×#1566C2211yescharacteristic
43C2×#1566C2211yescharacteristic
44#17485—21no—
45C2×#1489—21no—
46C2×#1451C2211yescharacteristic
47#12087C22116yescomplemented
48#12078C22116yescomplemented
49#12077C22116yescomplemented
50#12067C22116yescomplemented
51#12030C2214yescomplemented
52#12030C2214yescomplemented
53#12020C2214yescomplemented
54#11680C2214yescomplemented
55#11666C2214yes—
56#11664C2212yescomplemented
57#11663C2212yescomplemented
58#11663C2214yescomplemented
59#11654C2214yes—
60#11598C2214yescomplemented
61#11415C2214yescomplemented
62#11414C2214yescomplemented
63#11414C2214yescomplemented
64C22×#135C2×C411yescharacteristic
65C2×#568—41no—
66C2×#532—21no—
67C2×C4×#41—21no—
68C2×#509C2×C414yes—
69#3169—21no—
70#3169—21no—
71#3169—21no—
72#3169—21no—
73#3169C2×C412yes—
74#3169C2×C412yes—
75#3169C2312yes—
76#3169C2312yes—
77C2×#500C2×C411yescharacteristic
78C2×#493C2×C411yescharacteristic
79C2×#486—21no—
80C2×#466—21no—
81C2×#466C2×C412yes—
82#2990—24no—
83#2990—24no—
84#2990—42no—
85#2990—42no—
86C2×#446—22no—
87C4×#135—21no—
88C4×#135—21no—
89C4×#135—21no—
90C4×#135—21no—
91C4×#135C2×C412yes—
92C4×#135C2×C412yes—
93C4×#135C2312yes—
94C4×#135C2312yes—
95C2×C4×Q16C2×C411yescharacteristic
96C2×C4×Q16C2311yescharacteristic
97C2×C4×SD16—21no—
98C2×C4×SD16—21no—
99C2×C4×D8—21no—
100C2×C4×D8C2×C411yescharacteristic
101C2×C4×D8C2312yes—
102C2×C4×D8C2311yescharacteristic
103#2935—24no—
104#2935—42no—
105D4×M16—24no—
106D4×M16—42no—
107#2932—42no—
108#2931—24no—
109C2×#435—42no—
110C2×C8×D4—22no—
111C2×#432—41no—
112C2×#431D411yescharacteristic
113C2×#427C2×C411yescharacteristic
114C2×#423—21no—
115C2×#423—21no—
116C22×C4⋊C8—41no—
117C2×#416—21no—
118#2879—41no—
119C2×C4×M16D411yescharacteristic
120C22×C4×C8C2311yescharacteristic
121#2234C2×C418yes—
122#2233C2×C414yes—
123#2232C2×C414yes—
124#2227C2×C414yes—
125#2226C2×C414yes—
126#2225C2×C414yes—
127#2224C2×C414yes—
128#2207C2×C414yes—
129#2207C2×C414yes—
130#2206C2×C414yes—
131#2206C2×C414yes—
132#2186C2×C418yes—
133#2185C2×C414yes—
134#2184C2×C414yes—
135#2177C2318yes—
136#2175C2318yes—
137C4×SD32C2×C418yes—
138C4×D16C2×C418yes—
139#2163C2312yes—
140#2163C2312yes—
141#2163C2312yes—
142#2163C2312yes—
143#2162—21no—
144#2162—21no—
145#2162C2×C412yes—
146#2162C2×C412yes—
147#2159C2×C414yes—
148#2150—21no—
149#2150C2×C412yes—
150#2140C2×C414yes—
151#2139C2×C414yes—
152#2112—21no—
153#2112C2×C412yes—
154C4×M32C2312yes—
155C4×M32C2312yes—
156#1594—24no—
157#1594C2318yes—
158#1593—24no—
159#1593C2318yes—
160#1586—28no—
161#1586—28no—
162#1582—28no—
163#1582—28no—
164#1580—24no—
165#1580—24no—
166#1580C2318yes—
167#1580C2318yes—
168#1566—21no—
169#1566—21no—
170#1566—21no—
171#1566—21no—
172#1566C2312yes—
173#1566C2312yes—
174#1566C2312yes—
175#1566C2312yes—
176C2×#334—21no—
177C2×#334—21no—
178C2×#334C2312yes—
179C2×#334C2312yes—
180#1492—24no—
181#1489—24no—
182#1489—24no—
183#1486—24no—
184#1480—24no—
185C2×Q8⋊C8—22no—
186C2×D4⋊C8—22no—
187#1451D412yes—
188#1451D412yes—
189#1451C2312yes—
190#1451C2312yes—
191C2×#322D412yes—
192C2×#322C2312yes—
193#1368C23116yes—
194#1334C2318yes—
195#1333C2318yes—
196#1333C23116yes—
197#1313C2318yes—
198#1313C2318yes—
199C22×#41—21no—
200C22×#41—41no—
201C2×#135—21no—
202C2×#135—21no—
203C2×#135—44no—
204C2×#135C22×C412yes—
205C2×#135C22×C412yes—
206C22×Q16C22×C411yescharacteristic
207C22×SD16—21no—
208C22×D8—21no—
209C22×D8C22×C411yescharacteristic
210C22×D8C22×C412yes—
211#568—88no—
212C2×#131—44no—
213C2×#131—44no—
214C22×M16—21no—
215C22×M16—44no—
216C22×M16—41no—
217C22×M16—41no—
218C23×C8—42no—
219C23×C8C22×C411yescharacteristic
220C23×C8#4111yescharacteristic
221#532—22no—
222#532—22no—
223#532—22no—
224#532—22no—
225#532—41no—
226#532—41no—
227#532—41no—
228#532—41no—
229C2×C4⋊Q8—21no—
230C2×#127—21no—
231C2×#124—41no—
232C2×#121—22no—
233C2×#121—41no—
234C4×#41—22no—
235C4×#41—22no—
236C4×#41—22no—
237C4×#41—22no—
238C4×#41—41no—
239C4×#41—41no—
240C4×#41—41no—
241C4×#41—41no—
242C2×C4×Q8—21no—
243C2×C4×Q8—21no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—22no—
247C2×C4×D4—41no—
248C2×C4×D4—41no—
249C2×C4×D4—41no—
250C2×#117—21no—
251C2×#117—41no—
252C22×C42—41no—
253C22×C42C2×D411yescharacteristic
254#509—48no—
255C2×SD32C22×C418yes—
256C2×D16C22×C418yes—
257C2×M32—22no—
258C2×M32C22×C414yes—
259#500—21no—
260#500—21no—
261#500C22×C412yes—
262#500C22×C412yes—
263#493—21no—
264#493—21no—
265#493C22×C412yes—
266#493C22×C412yes—
267#486—22no—
268#486—22no—
269#486—22no—
270#486—22no—
271#466—22no—
272#466—22no—
273#466—22no—
274#466—22no—
275#466—22no—
276#466—22no—
277#466C22×C414yes—
278#466C22×C414yes—
279#446—28no—
280#446—44no—
281C4×Q16—21no—
282C4×Q16—21no—
283C4×Q16—21no—
284C4×Q16—21no—
285C4×Q16C22×C412yes—
286C4×Q16C22×C412yes—
287C4×Q16C22×C412yes—
288C4×Q16C2412yes—
289C4×SD16—22no—
290C4×SD16—22no—
291C4×SD16—22no—
292C4×SD16—22no—
293C4×SD16—22no—
294C4×SD16—22no—
295C4×SD16—22no—
296C4×SD16—22no—
297C4×D8—22no—
298C4×D8—22no—
299C4×D8—21no—
300C4×D8—21no—
301C4×D8—21no—
302C4×D8—22no—
303C4×D8—22no—
304C4×D8—22no—
305C4×D8—22no—
306C4×D8—21no—
307C4×D8C22×C414yes—
308C4×D8C22×C412yes—
309C4×D8C22×C412yes—
310C4×D8C22×C412yes—
311C4×D8C2412yes—
312C4×D8C2414yes—
313#436—28no—
314#436—44no—
315#435—48no—
316#435—48no—
317#435—48no—
318#435—48no—
319C8×D4—28no—
320C8×D4—28no—
321C8×D4—44no—
322C8×D4—44no—
323#432—44no—
324#432—44no—
325#431—21no—
326#431—21no—
327#431C2×D412yes—
328#431C2×D412yes—
329#427—21no—
330#427—21no—
331#427C22×C412yes—
332#427C22×C412yes—
333C2×#107—21no—
334C2×#107C22×C412yes—
335C2×#107C22×C411yescharacteristic
336C2×#107C22×C411yescharacteristic
337C2×#106—21no—
338#423—22no—
339#423—22no—
340#423—22no—
341#423—22no—
342#423—41no—
343#423—41no—
344#423—41no—
345#423—41no—
346C2×C4⋊C8—21no—
347C2×C4⋊C8—22no—
348C2×C4⋊C8—22no—
349C2×C4⋊C8—44no—
350C2×C4⋊C8—44no—
351C2×C4⋊C8—42no—
352C2×C4⋊C8—41no—
353C2×C4⋊C8—41no—
354#416—22no—
355#416—22no—
356#416—22no—
357#416—22no—
358C2×#103—21no—
359C2×#103—21no—
360C2×#102—22no—
361C2×#102—21no—
362C2×#102—22no—
363C2×#102—21no—
364#408—44no—
365#408—44no—
366#407—44no—
367C2×C22⋊C8—21no—
368C2×C22⋊C8—42no—
369C4×M16—21no—
370C4×M16—21no—
371C4×M16C2×D412yes—
372C4×M16C2×D412yes—
373C2×#97—21no—
374C2×#97—42no—
375C2×C4×C8C22×C411yescharacteristic
376C2×C4×C8C22×C411yescharacteristic
377C2×C4×C8C22×C411yescharacteristic
378C2×C4×C8C2×D412yes—
379C2×C4×C8C2×D412yes—
380C2×C4×C8C2×D411yescharacteristic
381C2×C4×C8C2×D411yescharacteristic
382C2×C4×C8C2×D411yescharacteristic
383C2×C4×C8#4111yescharacteristic
384C2×C4×C8#4111yescharacteristic
385C2×C4×C8#4111yescharacteristic
386C2×C4×C8C2411yescharacteristic
387C2×C4×C8C2411yescharacteristic
388C2×C4×C8C2411yescharacteristic
389#367C22×C418yes—
390#366C22×C418yes—
391C4⋊C16—22no—
392C4⋊C16—22no—
393C4⋊C16C22×C414yes—
394C4⋊C16C22×C414yes—
395#358C22×C418yes—
396#357C22×C418yes—
397#357C22×C418yes—
398#357C22×C418yes—
399C22⋊C16—22no—
400C22⋊C16—22no—
401C22⋊C16C22×C414yes—
402C22⋊C16C22×C414yes—
403#346C2414yes—
404#346C2414yes—
405C4×C16—22no—
406C4×C16C22×C414yes—
407#334—22no—
408#334—22no—
409#334—22no—
410#334—22no—
411#334—22no—
412#334—22no—
413#334C2414yes—
414#334C2414yes—
415Q8⋊C8—28no—
416D4⋊C8—28no—
417D4⋊C8—28no—
418D4⋊C8—28no—
419#322C2×D414yes—
420#322C2×D414yes—
421#322C2×D414yes—
422#322C2414yes—
423C2×#41—22no—
424C2×#41—22no—
425C2×#41—42no—
426C2×#41—42no—
427C2×#41—41no—
428C2×#41—41no—
429C2×#41—42no—
430C2×#41—42no—
431C2×#41—44no—
432C2×#41—84no—
433C2×#41—84no—
434C2×#41—82no—
435C22×Q8—21no—
436C22×Q8—41no—
437C22×D4—21no—
438C22×D4—22no—
439C22×D4—41no—
440C22×D4—42no—
441C22×D4—41no—
442C22×D4—41no—
443C23×C4—41no—
444C23×C4—42no—
445C23×C4—41no—
446C23×C4—41no—
447C23×C4C4×D411yescharacteristic
448C23×C4AGL(1,ℤ/8)11yescharacteristic
449C23×C4AGL(1,ℤ/8)11yescharacteristic
450#135—24no—
451#135—24no—
452#135—42no—
453#135—42no—
454#135—44no—
455#135—44no—
456C2×Q16—21no—
457C2×Q16—42no—
458C2×Q16C23×C412yes—
459C2×SD16—22no—
460C2×SD16—22no—
461C2×SD16—44no—
462C2×D8—24no—
463C2×D8—21no—
464C2×D8—22no—
465C2×D8—22no—
466C2×D8—22no—
467C2×D8—44no—
468C2×D8—82no—
469C2×D8C23×C414yes—
470C2×D8C23×C412yes—
471#131—816no—
472#131—816no—
473C2×M16—22no—
474C2×M16—22no—
475C2×M16—48no—
476C2×M16—44no—
477C2×M16—42no—
478C2×M16—42no—
479C2×M16—42no—
480C2×M16—42no—
481C2×M16—816no—
482C2×M16—84no—
483C2×M16—162no—
484C22×C8—22no—
485C22×C8—22no—
486C22×C8—42no—
487C22×C8—48no—
488C22×C8—48no—
489C22×C8—42no—
490C22×C8—42no—
491C22×C8—81no—
492C22×C8—164no—
493C22×C8C4×D411yescharacteristic
494C22×C8C4×D411yescharacteristic
495C22×C8C4×D411yescharacteristic
496C22×C8C4×D411yescharacteristic
497C22×C8C4×D411yescharacteristic
498C22×C8C4×D411yescharacteristic
499C22×C8C23×C411yescharacteristic
500C22×C8C23×C411yescharacteristic
501C22×C8C23×C411yescharacteristic
502C22×C8C2×#4111yescharacteristic
503C22×C8C2×#4111yescharacteristic
504C22×C8C2×#4111yescharacteristic
505C4⋊Q8—22no—
506C4⋊Q8—22no—
507C4⋊Q8—41no—
508C4⋊Q8—41no—
509#127—22no—
510#127—22no—
511#127—41no—
512#127—41no—
513#124—42no—
514#124—42no—
515#124—42no—
516#124—42no—
517#121—24no—
518#121—24no—
519#121—42no—
520#121—42no—
521#121—42no—
522#121—42no—
523#121—42no—
524#121—42no—
525C4×Q8—22no—
526C4×Q8—22no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×Q8—41no—
532C4×Q8—41no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536C4×D4—24no—
537C4×D4—22no—
538C4×D4—24no—
539C4×D4—42no—
540C4×D4—42no—
541C4×D4—42no—
542C4×D4—42no—
543C4×D4—42no—
544C4×D4—42no—
545C4×D4—42no—
546C4×D4—42no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—42no—
550C4×D4—42no—
551C4×D4—42no—
552C4×D4—42no—
553C4×D4—41no—
554C4×D4—41no—
555C4×D4—42no—
556C4×D4—42no—
557#117—22no—
558#117—22no—
559#117—41no—
560#117—41no—
561#117—42no—
562#117—42no—
563#117—42no—
564#117—42no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4—41no—
570C2×C4⋊C4—41no—
571C2×C22⋊C4—41no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—41no—
575C2×C22⋊C4—42no—
576C2×C42—41no—
577C2×C42—41no—
578C2×C42—41no—
579C2×C42—42no—
580C2×C42—42no—
581C2×C42—42no—
582C2×C42—42no—
583C2×C42C4×D411yescharacteristic
584C2×C42C4×D411yescharacteristic
585C2×C42C4×D411yescharacteristic
586C2×C42AGL(1,ℤ/8)11yescharacteristic
587C2×C42AGL(1,ℤ/8)11yescharacteristic
588C2×C42AGL(1,ℤ/8)11yescharacteristic
589C2×C42AGL(1,ℤ/8)11yescharacteristic
590C2×C42AGL(1,ℤ/8)11yescharacteristic
591C2×C42AGL(1,ℤ/8)11yescharacteristic
592C2×C42C22×D411yescharacteristic
593C2×C42C22×D411yescharacteristic
594C2×C42C22×D411yescharacteristic
595SD32—48no—
596D16—216no—
597M32—44no—
598M32—82no—
599C2×C16—24no—
600C2×C16C23×C418yes—
601#107—22no—
602#107—22no—
603#107—21no—
604#107—21no—
605#107—22no—
606#107C23×C412yes—
607#107C23×C412yes—
608#107C23×C414yes—
609#106—22no—
610#106—22no—
611C4⋊C8—22no—
612C4⋊C8—22no—
613C4⋊C8—24no—
614C4⋊C8—24no—
615C4⋊C8—48no—
616C4⋊C8—42no—
617C4⋊C8—42no—
618C4⋊C8—42no—
619C4⋊C8—42no—
620C4⋊C8—42no—
621C4⋊C8—42no—
622#103—22no—
623#103—22no—
624#103—22no—
625#103—22no—
626#102—22no—
627#102—22no—
628#102—22no—
629#102—24no—
630#102—24no—
631#102—24no—
632#102—22no—
633#102—24no—
634C22⋊C8—22no—
635C22⋊C8—22no—
636C22⋊C8—48no—
637C22⋊C8—48no—
638C22⋊C8—48no—
639#97—22no—
640#97—22no—
641#97—48no—
642C4×C8—22no—
643C4×C8—22no—
644C4×C8C4×D411yescharacteristic
645C4×C8C4×D411yescharacteristic
646C4×C8C4×D411yescharacteristic
647C4×C8C4×D411yescharacteristic
648C4×C8C4×D411yescharacteristic
649C4×C8C4×D411yescharacteristic
650C4×C8C23×C411yescharacteristic
651C4×C8C23×C411yescharacteristic
652C4×C8C23×C411yescharacteristic
653C4×C8C22×D414yes—
654C4×C8C22×D414yes—
655C4×C8C22×D411yescharacteristic
656C4×C8C22×D411yescharacteristic
657C4×C8C22×D411yescharacteristic
658C4×C8C2×#4111yescharacteristic
659C4×C8C2×#4111yescharacteristic
660C4×C8C2×#4111yescharacteristic
661C4×C8C2511yescharacteristic
662C24—41no—
663C24—42no—
664C24#44211yescharacteristic
665#41—44no—
666#41—44no—
667#41—82no—
668#41—82no—
669#41—84no—
670#41—84no—
671#41—84no—
672#41—84no—
673#41—88no—
674#41—84no—
675#41—84no—
676#41—88no—
677C2×Q8—22no—
678C2×Q8—42no—
679C2×Q8—42no—
680C2×Q8—41no—
681C2×Q8—42no—
682C2×Q8—42no—
683C2×Q8—84no—
684C2×D4—24no—
685C2×D4—22no—
686C2×D4—24no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—41no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—82no—
699C2×D4—82no—
700C2×D4—84no—
701C2×D4—88no—
702C2×D4—84no—
703C2×D4—162no—
704C22×C4—24no—
705C22×C4—41no—
706C22×C4—41no—
707C22×C4—42no—
708C22×C4—41no—
709C22×C4—41no—
710C22×C4—41no—
711C22×C4—42no—
712C22×C4—42no—
713C22×C4—42no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—44no—
718C22×C4—42no—
719C22×C4—44no—
720C22×C4—82no—
721C22×C4—84no—
722C22×C4—82no—
723C22×C4—84no—
724C22×C4—84no—
725C22×C4—84no—
726C22×C4#44211yescharacteristic
727C22×C4#44211yescharacteristic
728C22×C4#44211yescharacteristic
729C22×C4#44211yescharacteristic
730C22×C4#44211yescharacteristic
731C22×C4#44211yescharacteristic
732C22×C4#44211yescharacteristic
733C22×C4#44211yescharacteristic
734C22×C4#44211yescharacteristic
735C22×C4C2×C4×D411yescharacteristic
736C22×C4C2×C4×D411yescharacteristic
737C22×C4C2×C4×D411yescharacteristic
738C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
739C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
740C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
741C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
742C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
743C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
744Q16—22no—
745Q16—22no—
746Q16—42no—
747SD16—44no—
748SD16—44no—
749D8—24no—
750D8—22no—
751D8—28no—
752D8—44no—
753D8—82no—
754D8—82no—
755D8#56814yescomplemented
756M16—44no—
757M16—44no—
758M16—816no—
759M16—84no—
760M16—84no—
761M16—162no—
762M16—162no—
763C2×C8—22no—
764C2×C8—22no—
765C2×C8—22no—
766C2×C8—24no—
767C2×C8—24no—
768C2×C8—41no—
769C2×C8—41no—
770C2×C8—41no—
771C2×C8—41no—
772C2×C8—41no—
773C2×C8—41no—
774C2×C8—41no—
775C2×C8—41no—
776C2×C8—41no—
777C2×C8—44no—
778C2×C8—44no—
779C2×C8—44no—
780C2×C8—44no—
781C2×C8—816no—
782C2×C8—84no—
783C2×C8—84no—
784C2×C8—168no—
785C2×C8C2×C4×D411yescharacteristic
786C2×C8C2×C4×D411yescharacteristic
787C2×C8C2×C4×D411yescharacteristic
788C2×C8C2×C4×D411yescharacteristic
789C2×C8C2×C4×D411yescharacteristic
790C2×C8C2×C4×D411yescharacteristic
791C2×C8C24×C411yescharacteristic
792C2×C8C22×#4111yescharacteristic
793C4⋊C4—24no—
794C4⋊C4—22no—
795C4⋊C4—22no—
796C4⋊C4—41no—
797C4⋊C4—41no—
798C4⋊C4—42no—
799C4⋊C4—42no—
800C4⋊C4—42no—
801C4⋊C4—42no—
802C4⋊C4—42no—
803C4⋊C4—42no—
804C4⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4—42no—
808C22⋊C4—42no—
809C22⋊C4—42no—
810C22⋊C4—44no—
811C22⋊C4—44no—
812C22⋊C4—44no—
813C22⋊C4—42no—
814C22⋊C4—44no—
815C42—42no—
816C42—42no—
817C42—42no—
818C42—42no—
819C42—42no—
820C42—42no—
821C42#44211yescharacteristic
822C42#44211yescharacteristic
823C42#44211yescharacteristic
824C42#44211yescharacteristic
825C42#44211yescharacteristic
826C42#44211yescharacteristic
827C42C2×C4×D411yescharacteristic
828C42C2×C4×D411yescharacteristic
829C42C2×C4×D411yescharacteristic
830C42C2×AGL(1,ℤ/8)11yescharacteristic
831C42C2×AGL(1,ℤ/8)11yescharacteristic
832C42C2×AGL(1,ℤ/8)11yescharacteristic
833C42C2×AGL(1,ℤ/8)11yescharacteristic
834C42C2×AGL(1,ℤ/8)11yescharacteristic
835C42C2×AGL(1,ℤ/8)11yescharacteristic
836C42C23×D411yescharacteristic
837C16—28no—
838C16—44no—
839C23—22no—
840C23—41no—
841C23—41no—
842C23—44no—
843C23—42no—
844C23—44no—
845C23—82no—
846C23—84no—
847C23—82no—
848C23—162no—
849C23—162no—
850C23C2×#44211yescharacteristic
851C23C2×#44211yescharacteristic
852C23C2×#44211yescharacteristic
853Q8—42no—
854Q8—42no—
855Q8—82no—
856Q8—84no—
857Q8—84no—
858D4—24no—
859D4—44no—
860D4—42no—
861D4—44no—
862D4—44no—
863D4—84no—
864D4—84no—
865D4—84no—
866D4—88no—
867D4—88no—
868D4—84no—
869D4—84no—
870D4—162no—
871D4—162no—
872C2×C4—22no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—44no—
896C2×C4—84no—
897C2×C4—84no—
898C2×C4—84no—
899C2×C4—82no—
900C2×C4—82no—
901C2×C4—84no—
902C2×C4—82no—
903C2×C4—82no—
904C2×C4—84no—
905C2×C4—82no—
906C2×C4—84no—
907C2×C4—84no—
908C2×C4—88no—
909C2×C4—84no—
910C2×C4AGL(1,ℤ/16)14yes—
911C2×C4C2×#44211yescharacteristic
912C2×C4C2×#44211yescharacteristic
913C2×C4C2×#44211yescharacteristic
914C2×C4C2×#44211yescharacteristic
915C2×C4C2×#44211yescharacteristic
916C2×C4C2×#44211yescharacteristic
917C2×C4C2×#44211yescharacteristic
918C2×C4C2×#44211yescharacteristic
919C2×C4C2×#44211yescharacteristic
920C2×C4C22×C4×D411yescharacteristic
921C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
922C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
923C8—21no—
924C8—21no—
925C8—21no—
926C8—21no—
927C8—21no—
928C8—21no—
929C8—21no—
930C8—44no—
931C8—44no—
932C8—84no—
933C8—84no—
934C8C2×#56812yes—
935C22—21no—
936C22—21no—
937C22—21no—
938C22—21no—
939C22—21no—
940C22—21no—
941C22—21no—
942C22—21no—
943C22—44no—
944C22—82no—
945C22—88no—
946C22—82no—
947C22—82no—
948C22—84no—
949C22—84no—
950C22—84no—
951C22—324no—
952C22C2×AGL(1,ℤ/16)12yes—
953C22C22×#44211yescharacteristic
954C4—21no—
955C4—21no—
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—21no—
961C4—21no—
962C4—82no—
963C4—82no—
964C4—84no—
965C4—82no—
966C4C2×AGL(1,ℤ/16)12yes—
967C4C2×AGL(1,ℤ/16)12yes—
968C4#3346912yes—
969C4#6014111yescharacteristic
970C4#6018211yescharacteristic
971C2—22no—
972C2—41no—
973C2—41no—
974C2—84no—
975C2—164no—
976C2#634528711yescharacteristic
977C2C22×AGL(1,ℤ/16)11yescharacteristic
978C2C2×#3346911yescharacteristic
subgroupG/H
center, socleC22C22×#442
commutatorC2×C8C24×C4
Frattini, cosocleC4×C8C25
prime radical#7623099C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#1451 ◁ G
LECSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #6345702C2semidirect
3. C2×#18065C2semidirect
4. #484106C2semidirect
5. #484053C2semidirect
6. #483922C2semidirect
7. #483875C2semidirect
8. #483446C2semidirect
9. #481379C2semidirect
10. #481282C2semidirect
11. #479974C2semidirect
30. #18073C22semidirect
34. #18065C22semidirect
36. #18044C22semidirect
39. C2×#1593C22semidirect
41. C2×#1580C22semidirect
47. #12087C22semidirect
48. #12078C22semidirect
49. #12077C22semidirect
50. #12067C22semidirect
51. #12030C22semidirect
52. #12030C22semidirect
53. #12020C22semidirect
54. #11680C22semidirect
56. #11664C22semidirect
57. #11663C22semidirect
58. #11663C22semidirect
60. #11598C22semidirect
61. #11415C22semidirect
62. #11414C22semidirect
63. #11414C22semidirect
755. D8#568semidirect

Maximal subgroups

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

subgroupindex
#76230992
#63457022
C2×#180652
#4841062
#4840532
#4839222
#4838752
#4834462
#4813792
#4812822
#4799742