Finite Group Databasebeta

← #72287535

Subgroups — #72287535

Order 1024.

2525 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#33748C211yesmaximal, characteristic
2#6345722C211yesmaximal, characteristic, complemented
3#6345702C211yesmaximal, characteristic, complemented
4#484147C218yesmaximal, complemented
5#484097C218yesmaximal, complemented
6#483992C214yesmaximal, complemented
7#483961C214yesmaximal, complemented
8#483397C211yesmaximal, characteristic, complemented
9#481384C211yesmaximal, characteristic, complemented
10#481379C211yesmaximal, characteristic, complemented
11#479962C211yesmaximal, characteristic, complemented
12C2×#3169C2211yescharacteristic
13C2×#3169C2211yescharacteristic
14#60236—21no—
15#60144—21no—
16#33748C412yes—
17#33748C414yes—
18#33748C412yes—
19#33748C2214yes—
20#33748C2212yes—
21#33748C2212yes—
22C2×#2254C411yescharacteristic
23C2×#2246C411yescharacteristic
24C2×#2240C411yescharacteristic
25C2×#2240C411yescharacteristic
26C2×#2218C414yes—
27C2×#2177C2214yes—
28#33418C2211yescharacteristic
29C2×C4×M32C2211yescharacteristic
30#18091—22no—
31#18091C2214yescomplemented
32#18073—22no—
33#18073C2214yescomplemented
34#18064—22no—
35#18064C2214yes—
36#18044—22no—
37#18044C2214yes—
38#17981—22no—
39#17975—22no—
40#17962C2214yescomplemented
41#17962C2214yescomplemented
42#17793C2211yescharacteristic
43C2×#1566C2211yescharacteristic
44#17500—21no—
45#17485—21no—
46C2×#1451C2211yescharacteristic
47#12089C22116yescomplemented
48#12078C22116yescomplemented
49#12078C22116yescomplemented
50#12067C22116yescomplemented
51#12020C2212yescomplemented
52#12020C2212yescomplemented
53#12019C2214yes—
54#12000C2214yescomplemented
55#11680C2214yescomplemented
56#11680C2214yescomplemented
57#11667C2214yes—
58#11663C2214yes—
59#11654C2214yescomplemented
60#11652C2214yescomplemented
61#11414C2214yescomplemented
62#11413C2214yes—
63#11404C2212yescomplemented
64#11404C2212yescomplemented
65C2×#568—41no—
66C2×#532—21no—
67C2×#532—21no—
68C22×D16C2×C414yes—
69C22×M32C2×C412yes—
70#3169—21no—
71#3169—21no—
72#3169—21no—
73#3169—21no—
74#3169—21no—
75#3169—21no—
76#3169—21no—
77#3169—21no—
78#3169C2×C412yes—
79#3169C2×C412yes—
80#3169C2×C412yes—
81#3169C2×C412yes—
82#3169C2312yes—
83#3169C2312yes—
84#3169C2312yes—
85#3169C2312yes—
86C2×#500C2×C411yescharacteristic
87C2×#500C2×C411yescharacteristic
88C2×#493C2×C411yescharacteristic
89C2×#493C2×C411yescharacteristic
90C2×#486—21no—
91C2×#486—21no—
92C2×#466—21no—
93C2×#466—21no—
94C2×#466C2×C412yes—
95C2×#466C2×C412yes—
96#2981—42no—
97#2979—24no—
98#2975—41no—
99#2974—24no—
100#2972—41no—
101C2×C4×D8—21no—
102C2×C4×D8—21no—
103C2×C4×D8C2312yes—
104C2×C4×D8C2312yes—
105#2935—24no—
106#2935—42no—
107#2935—42no—
108D4×M16—24no—
109D4×M16—42no—
110#2932—42no—
111#2931—24no—
112#2931—24no—
113#2920—21no—
114C2×#431D411yescharacteristic
115C2×#423—21no—
116#2880—42no—
117#2879—41no—
118C2×C4×M16D411yescharacteristic
119C22×C4×C8C2311yescharacteristic
120#2254C2×C414yes—
121#2254C2×C412yes—
122#2254C2×C412yes—
123#2246C2×C412yes—
124#2246C2×C414yes—
125#2246C2×C412yes—
126#2240C2×C414yes—
127#2240C2×C414yes—
128#2240C2×C412yes—
129#2240C2×C412yes—
130#2240C2×C412yes—
131#2240C2×C412yes—
132#2218C2×C418yes—
133#2218C2×C418yes—
134#2218C2×C418yes—
135#2218C2×C418yes—
136#2177C2×C418yes—
137#2177C2×C418yes—
138#2177C2318yes—
139#2177C2318yes—
140#2163C2312yes—
141#2163C2312yes—
142#2162—21no—
143#2162—21no—
144C2×#367C2×C414yes—
145#2150—21no—
146C2×#357C2×C414yes—
147C2×#357C2×C414yes—
148#2112—21no—
149C4×M32C2×C411yescharacteristic
150C4×M32C2×C412yes—
151C4×M32C2×C411yescharacteristic
152C4×M32C2312yes—
153C4×M32C2311yescharacteristic
154C4×M32C2311yescharacteristic
155C4×M32C2312yes—
156C2×#346C2312yes—
157C2×C4×C16C2×C411yescharacteristic
158C2×C4×C16C2×C411yescharacteristic
159#1594—24no—
160#1594—24no—
161#1594C2318yes—
162#1594C2318yes—
163#1586—28no—
164#1586—28no—
165#1581—28no—
166#1581—28no—
167#1580—24no—
168#1580—24no—
169#1580C2318yes—
170#1580C2318yes—
171#1568—21no—
172#1568C2312yes—
173#1567—21no—
174#1566—21no—
175#1566—21no—
176#1566C2312yes—
177#1566C2312yes—
178#1566C2312yes—
179#1564—21no—
180#1564C2312yes—
181C2×#334—21no—
182C2×#334C2312yes—
183#1492—24no—
184#1492—24no—
185#1490—24no—
186#1486—24no—
187#1484—24no—
188#1480—24no—
189#1451D412yes—
190#1451D412yes—
191#1451C2312yes—
192#1451C2312yes—
193C2×#322D412yes—
194C2×#322C2312yes—
195#1368C2318yes—
196#1368C2318yes—
197#1333C23116yes—
198#1333C23116yes—
199#1313C2318yes—
200#1313C2318yes—
201C22×#41—41no—
202C22×#41—41no—
203C22×D8—21no—
204C22×D8—21no—
205C22×D8C22×C412yes—
206C22×D8C22×C412yes—
207#568—88no—
208C2×#131—44no—
209C2×#131—44no—
210C2×#131—44no—
211C22×M16—21no—
212C22×M16—44no—
213C22×M16—41no—
214C23×C8C22×C411yescharacteristic
215C23×C8#4111yescharacteristic
216#532—22no—
217#532—22no—
218#532—22no—
219#532—22no—
220#532—22no—
221#532—22no—
222#532—22no—
223#532—22no—
224#532—41no—
225#532—41no—
226#532—41no—
227#532—41no—
228#532—41no—
229#532—41no—
230#532—41no—
231#532—41no—
232C2×C4⋊Q8—21no—
233C2×C4⋊Q8—21no—
234C2×#127—21no—
235C2×#127—21no—
236C2×#124—41no—
237C2×#124—41no—
238C2×#121—22no—
239C2×#121—22no—
240C2×#121—41no—
241C2×#121—41no—
242C2×C4×D4—22no—
243C2×C4×D4—22no—
244C2×C4×D4—41no—
245C2×C4×D4—41no—
246C22×C42C2×D411yescharacteristic
247C2×D16—48no—
248C2×D16C22×C418yes—
249C2×D16C22×C418yes—
250C2×M32—22no—
251C2×M32—44no—
252C2×M32C22×C412yes—
253C2×M32C22×C412yes—
254C2×M32C22×C412yes—
255C2×M32C22×C412yes—
256C22×C16C22×C412yes—
257C22×C16C22×C412yes—
258#500—21no—
259#500—21no—
260#500—21no—
261#500—21no—
262#500C22×C412yes—
263#500C22×C412yes—
264#500C22×C412yes—
265#500C22×C412yes—
266#493—21no—
267#493—21no—
268#493—21no—
269#493—21no—
270#493C22×C412yes—
271#493C22×C412yes—
272#493C22×C412yes—
273#493C22×C412yes—
274#486—22no—
275#486—22no—
276#486—22no—
277#486—22no—
278#486—22no—
279#486—22no—
280#486—22no—
281#486—22no—
282#466—22no—
283#466—22no—
284#466—22no—
285#466—22no—
286#466—22no—
287#466—22no—
288#466—22no—
289#466—22no—
290#466—22no—
291#466—22no—
292#466—22no—
293#466—22no—
294#466C22×C414yes—
295#466C22×C414yes—
296#466C22×C414yes—
297#466C22×C414yes—
298C4×D8—22no—
299C4×D8—22no—
300C4×D8—22no—
301C4×D8—22no—
302C4×D8—22no—
303C4×D8—22no—
304C4×D8—22no—
305C4×D8—22no—
306C4×D8—22no—
307C4×D8—22no—
308C4×D8—22no—
309C4×D8—22no—
310C4×D8C22×C414yes—
311C4×D8C22×C414yes—
312C4×D8C2414yes—
313C4×D8C2414yes—
314#436—28no—
315#436—28no—
316#436—44no—
317#436—44no—
318#436—44no—
319#435—48no—
320#435—48no—
321#435—48no—
322C8×D4—28no—
323C8×D4—28no—
324C8×D4—44no—
325C8×D4—44no—
326C8×D4—44no—
327#432—22no—
328#432—41no—
329#431—21no—
330#431—21no—
331#431—22no—
332#431—41no—
333#431C2×D412yes—
334#431C2×D412yes—
335C2×#107—21no—
336C2×#107—21no—
337C2×#107C22×C412yes—
338C2×#107C22×C412yes—
339#423—22no—
340#423—22no—
341#423—22no—
342#423—41no—
343#423—41no—
344C2×C4⋊C8—21no—
345C2×C4⋊C8—22no—
346C2×C4⋊C8—41no—
347C2×#102—22no—
348C2×#102—22no—
349C2×#102—22no—
350C2×#102—22no—
351#408—48no—
352#408—44no—
353#408—44no—
354#408—44no—
355#407—44no—
356#407—44no—
357#407—41no—
358C2×C22⋊C8—21no—
359C2×C22⋊C8—44no—
360C4×M16—21no—
361C4×M16—21no—
362C4×M16—41no—
363C4×M16C2×D412yes—
364C4×M16C2×D412yes—
365C2×#97—21no—
366C2×C4×C8C22×C411yescharacteristic
367C2×C4×C8C22×C411yescharacteristic
368C2×C4×C8C22×C411yescharacteristic
369C2×C4×C8C2×D412yes—
370C2×C4×C8C2×D412yes—
371C2×C4×C8C2×D411yescharacteristic
372C2×C4×C8C2×D411yescharacteristic
373C2×C4×C8C2×D411yescharacteristic
374C2×C4×C8#4111yescharacteristic
375C2×C4×C8#4111yescharacteristic
376C2×C4×C8#4111yescharacteristic
377C2×C4×C8C2411yescharacteristic
378C2×C4×C8C2411yescharacteristic
379C2×C4×C8C2411yescharacteristic
380#367C22×C418yes—
381#367C22×C418yes—
382C4⋊C16—22no—
383C4⋊C16—22no—
384#357C22×C418yes—
385#357C22×C418yes—
386#357C22×C418yes—
387#357C22×C418yes—
388C22⋊C16—22no—
389C22⋊C16—22no—
390#346C22×C412yes—
391#346C22×C412yes—
392#346C2414yes—
393#346C2412yes—
394#346C2412yes—
395C4×C16—22no—
396C4×C16C22×C411yescharacteristic
397C4×C16C22×C411yescharacteristic
398C4×C16C22×C412yes—
399C4×C16C22×C411yescharacteristic
400C4×C16C22×C412yes—
401C4×C16C22×C411yescharacteristic
402#335—22no—
403#335—22no—
404#334—22no—
405#334—22no—
406#334—22no—
407#334—22no—
408#334C2414yes—
409#334C2414yes—
410D4⋊C8—28no—
411D4⋊C8—28no—
412D4⋊C8—28no—
413D4⋊C8—28no—
414#322C2×D414yes—
415#322C2×D414yes—
416#322C2×D414yes—
417#322C2414yes—
418C2×#41—42no—
419C2×#41—42no—
420C2×#41—42no—
421C2×#41—42no—
422C2×#41—42no—
423C2×#41—42no—
424C2×#41—42no—
425C2×#41—42no—
426C2×#41—84no—
427C2×#41—84no—
428C2×#41—164no—
429C22×Q8—41no—
430C22×Q8—41no—
431C22×D4—22no—
432C22×D4—22no—
433C22×D4—42no—
434C22×D4—42no—
435C22×D4—41no—
436C22×D4—41no—
437C22×D4—41no—
438C22×D4—41no—
439C23×C4—42no—
440C23×C4—42no—
441C23×C4C4×D411yescharacteristic
442C23×C4AGL(1,ℤ/8)11yescharacteristic
443C23×C4AGL(1,ℤ/8)11yescharacteristic
444C2×D8—22no—
445C2×D8—22no—
446C2×D8—22no—
447C2×D8—22no—
448C2×D8—22no—
449C2×D8—22no—
450C2×D8—44no—
451C2×D8—44no—
452C2×D8—82no—
453C2×D8—82no—
454C2×D8C23×C414yes—
455C2×D8C23×C414yes—
456#131—816no—
457#131—816no—
458#131—168no—
459C2×M16—22no—
460C2×M16—22no—
461C2×M16—48no—
462C2×M16—48no—
463C2×M16—44no—
464C2×M16—42no—
465C2×M16—42no—
466C2×M16—42no—
467C2×M16—816no—
468C2×M16—84no—
469C22×C8—22no—
470C22×C8—22no—
471C22×C8—42no—
472C22×C8—42no—
473C22×C8—48no—
474C22×C8—48no—
475C22×C8—42no—
476C22×C8C4×D411yescharacteristic
477C22×C8C4×D411yescharacteristic
478C22×C8C4×D411yescharacteristic
479C22×C8C4×D411yescharacteristic
480C22×C8C4×D411yescharacteristic
481C22×C8C4×D411yescharacteristic
482C22×C8C23×C411yescharacteristic
483C22×C8C23×C411yescharacteristic
484C22×C8C23×C411yescharacteristic
485C22×C8C2×#4111yescharacteristic
486C22×C8C2×#4111yescharacteristic
487C22×C8C2×#4111yescharacteristic
488C4⋊Q8—22no—
489C4⋊Q8—22no—
490C4⋊Q8—22no—
491C4⋊Q8—22no—
492C4⋊Q8—41no—
493C4⋊Q8—41no—
494C4⋊Q8—41no—
495C4⋊Q8—41no—
496#127—22no—
497#127—22no—
498#127—22no—
499#127—22no—
500#127—41no—
501#127—41no—
502#127—41no—
503#127—41no—
504#124—42no—
505#124—42no—
506#124—42no—
507#124—42no—
508#124—42no—
509#124—42no—
510#124—42no—
511#124—42no—
512#121—24no—
513#121—24no—
514#121—24no—
515#121—24no—
516#121—42no—
517#121—42no—
518#121—42no—
519#121—42no—
520#121—42no—
521#121—42no—
522#121—42no—
523#121—42no—
524#121—42no—
525#121—42no—
526#121—42no—
527#121—42no—
528C4×D4—24no—
529C4×D4—24no—
530C4×D4—24no—
531C4×D4—24no—
532C4×D4—42no—
533C4×D4—42no—
534C4×D4—42no—
535C4×D4—42no—
536C4×D4—42no—
537C4×D4—42no—
538C4×D4—42no—
539C4×D4—42no—
540C4×D4—42no—
541C4×D4—42no—
542C4×D4—42no—
543C4×D4—42no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—41no—
547C2×C4⋊C4—41no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C42C4×D411yescharacteristic
553C2×C42C4×D411yescharacteristic
554C2×C42C4×D411yescharacteristic
555C2×C42AGL(1,ℤ/8)11yescharacteristic
556C2×C42AGL(1,ℤ/8)11yescharacteristic
557C2×C42AGL(1,ℤ/8)11yescharacteristic
558C2×C42AGL(1,ℤ/8)11yescharacteristic
559C2×C42AGL(1,ℤ/8)11yescharacteristic
560C2×C42AGL(1,ℤ/8)11yescharacteristic
561C2×C42C22×D411yescharacteristic
562C2×C42C22×D411yescharacteristic
563C2×C42C22×D411yescharacteristic
564D16—216no—
565D16—48no—
566M32—24no—
567M32—24no—
568M32—42no—
569M32—42no—
570M32—44no—
571C2×C16—24no—
572C2×C16—24no—
573C2×C16—42no—
574C2×C16C23×C412yes—
575C2×C16C23×C412yes—
576C2×C16C23×C412yes—
577C2×C16C23×C412yes—
578#107—22no—
579#107—22no—
580#107—22no—
581#107—22no—
582#107—22no—
583#107—22no—
584#107C23×C414yes—
585#107C23×C414yes—
586C4⋊C8—22no—
587C4⋊C8—22no—
588C4⋊C8—24no—
589C4⋊C8—24no—
590C4⋊C8—42no—
591C4⋊C8—42no—
592C4⋊C8—42no—
593C4⋊C8—42no—
594#102—24no—
595#102—24no—
596#102—24no—
597#102—24no—
598#102—24no—
599#102—24no—
600#102—24no—
601#102—24no—
602C22⋊C8—22no—
603C22⋊C8—22no—
604C22⋊C8—48no—
605C22⋊C8—48no—
606C22⋊C8—48no—
607C22⋊C8—48no—
608C22⋊C8—42no—
609C22⋊C8—42no—
610#97—22no—
611#97—22no—
612#97—42no—
613C4×C8—22no—
614C4×C8—22no—
615C4×C8—42no—
616C4×C8C4×D411yescharacteristic
617C4×C8C4×D411yescharacteristic
618C4×C8C4×D411yescharacteristic
619C4×C8C4×D411yescharacteristic
620C4×C8C4×D411yescharacteristic
621C4×C8C4×D411yescharacteristic
622C4×C8C23×C411yescharacteristic
623C4×C8C23×C411yescharacteristic
624C4×C8C23×C411yescharacteristic
625C4×C8C22×D414yes—
626C4×C8C22×D414yes—
627C4×C8C22×D411yescharacteristic
628C4×C8C22×D411yescharacteristic
629C4×C8C22×D411yescharacteristic
630C4×C8C2×#4111yescharacteristic
631C4×C8C2×#4111yescharacteristic
632C4×C8C2×#4111yescharacteristic
633C4×C8C2511yescharacteristic
634C24—42no—
635C24—42no—
636C24#44211yescharacteristic
637#41—84no—
638#41—84no—
639#41—88no—
640#41—84no—
641#41—84no—
642#41—88no—
643#41—88no—
644#41—164no—
645#41—164no—
646#41—164no—
647C2×Q8—42no—
648C2×Q8—42no—
649C2×Q8—42no—
650C2×Q8—42no—
651C2×Q8—84no—
652C2×Q8—162no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—44no—
656C2×D4—44no—
657C2×D4—44no—
658C2×D4—44no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—82no—
670C2×D4—82no—
671C2×D4—82no—
672C2×D4—82no—
673C2×D4—88no—
674C2×D4—84no—
675C2×D4—84no—
676C2×D4—162no—
677C2×D4—162no—
678C2×D4—164no—
679C22×C4—24no—
680C22×C4—41no—
681C22×C4—41no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—84no—
690C22×C4—84no—
691C22×C4—164no—
692C22×C4#44211yescharacteristic
693C22×C4#44211yescharacteristic
694C22×C4#44211yescharacteristic
695C22×C4#44211yescharacteristic
696C22×C4#44211yescharacteristic
697C22×C4#44211yescharacteristic
698C22×C4#44211yescharacteristic
699C22×C4#44211yescharacteristic
700C22×C4#44211yescharacteristic
701C22×C4C2×C4×D411yescharacteristic
702C22×C4C2×C4×D411yescharacteristic
703C22×C4C2×C4×D411yescharacteristic
704C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
705C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
706C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
707C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
708C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
709C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
710D8—28no—
711D8—28no—
712D8—44no—
713D8—44no—
714D8—82no—
715D8—82no—
716D8—82no—
717D8—82no—
718M16—44no—
719M16—44no—
720M16—816no—
721M16—84no—
722M16—84no—
723M16—84no—
724M16—168no—
725C2×C8—22no—
726C2×C8—22no—
727C2×C8—22no—
728C2×C8—22no—
729C2×C8—22no—
730C2×C8—22no—
731C2×C8—24no—
732C2×C8—24no—
733C2×C8—41no—
734C2×C8—41no—
735C2×C8—41no—
736C2×C8—41no—
737C2×C8—41no—
738C2×C8—41no—
739C2×C8—44no—
740C2×C8—44no—
741C2×C8—44no—
742C2×C8—44no—
743C2×C8—816no—
744C2×C8—84no—
745C2×C8—168no—
746C2×C8C2×C4×D411yescharacteristic
747C2×C8C2×C4×D411yescharacteristic
748C2×C8C2×C4×D411yescharacteristic
749C2×C8C2×C4×D411yescharacteristic
750C2×C8C2×C4×D411yescharacteristic
751C2×C8C2×C4×D411yescharacteristic
752C2×C8C24×C411yescharacteristic
753C2×C8C22×#4111yescharacteristic
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—42no—
757C4⋊C4—42no—
758C4⋊C4—42no—
759C4⋊C4—42no—
760C4⋊C4—42no—
761C4⋊C4—42no—
762C22⋊C4—44no—
763C22⋊C4—44no—
764C22⋊C4—44no—
765C22⋊C4—44no—
766C22⋊C4—44no—
767C22⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C42#44211yescharacteristic
771C42#44211yescharacteristic
772C42#44211yescharacteristic
773C42#44211yescharacteristic
774C42#44211yescharacteristic
775C42#44211yescharacteristic
776C42C2×C4×D411yescharacteristic
777C42C2×C4×D411yescharacteristic
778C42C2×C4×D411yescharacteristic
779C42C2×AGL(1,ℤ/8)11yescharacteristic
780C42C2×AGL(1,ℤ/8)11yescharacteristic
781C42C2×AGL(1,ℤ/8)11yescharacteristic
782C42C2×AGL(1,ℤ/8)11yescharacteristic
783C42C2×AGL(1,ℤ/8)11yescharacteristic
784C42C2×AGL(1,ℤ/8)11yescharacteristic
785C42C23×D411yescharacteristic
786C16—22no—
787C16—22no—
788C16—22no—
789C16—44no—
790C16#56814yescomplemented
791C23—22no—
792C23—41no—
793C23—41no—
794C23—44no—
795C23—44no—
796C23—84no—
797C23—84no—
798C23—162no—
799C23—162no—
800C23—162no—
801C23—162no—
802C23C2×#44211yescharacteristic
803C23C2×#44211yescharacteristic
804C23C2×#44211yescharacteristic
805Q8—84no—
806Q8—84no—
807Q8—84no—
808Q8—162no—
809D4—44no—
810D4—44no—
811D4—44no—
812D4—44no—
813D4—88no—
814D4—88no—
815D4—88no—
816D4—84no—
817D4—84no—
818D4—84no—
819D4—84no—
820D4—84no—
821D4—84no—
822D4—162no—
823D4—162no—
824D4—162no—
825D4—162no—
826D4—164no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—84no—
850C2×C4—88no—
851C2×C4—84no—
852C2×C4—88no—
853C2×C4—84no—
854C2×C4—164no—
855C2×C4—162no—
856C2×C4AGL(1,ℤ/16)14yes—
857C2×C4C2×#44211yescharacteristic
858C2×C4C2×#44211yescharacteristic
859C2×C4C2×#44211yescharacteristic
860C2×C4C2×#44211yescharacteristic
861C2×C4C2×#44211yescharacteristic
862C2×C4C2×#44211yescharacteristic
863C2×C4C2×#44211yescharacteristic
864C2×C4C2×#44211yescharacteristic
865C2×C4C2×#44211yescharacteristic
866C2×C4C22×C4×D411yescharacteristic
867C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
868C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
869C8—21no—
870C8—21no—
871C8—21no—
872C8—21no—
873C8—21no—
874C8—21no—
875C8—44no—
876C8—44no—
877C8—84no—
878C8—84no—
879C8#295712yes—
880C8C2×#56812yes—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—21no—
889C22—82no—
890C22—84no—
891C22—84no—
892C22—84no—
893C22—84no—
894C22—84no—
895C22—84no—
896C22—324no—
897C22—324no—
898C22C2×AGL(1,ℤ/16)12yes—
899C22C22×#44211yescharacteristic
900C4—21no—
901C4—21no—
902C4—21no—
903C4—21no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—21no—
908C4—84no—
909C4—84no—
910C4C2×AGL(1,ℤ/16)12yes—
911C4C2×AGL(1,ℤ/16)12yes—
912C4#3347112yes—
913C4#6014411yescharacteristic
914C4C2×#295711yescharacteristic
915C2—22no—
916C2—41no—
917C2—41no—
918C2—164no—
919C2—164no—
920C2#634570211yescharacteristic
921C2C22×AGL(1,ℤ/16)11yescharacteristic
922C2C2×#3347111yescharacteristic
subgroupG/H
center, socleC22C22×#442
commutatorC2×C8C24×C4
Frattini, cosocleC4×C8C25
prime radicalC2×#33748C2
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. #6345722C2semidirect
3. #6345702C2semidirect
4. #484147C2semidirect
5. #484097C2semidirect
6. #483992C2semidirect
7. #483961C2semidirect
8. #483397C2semidirect
9. #481384C2semidirect
10. #481379C2semidirect
11. #479962C2semidirect
31. #18091C22semidirect
33. #18073C22semidirect
40. #17962C22semidirect
41. #17962C22semidirect
47. #12089C22semidirect
48. #12078C22semidirect
49. #12078C22semidirect
50. #12067C22semidirect
51. #12020C22semidirect
52. #12020C22semidirect
54. #12000C22semidirect
55. #11680C22semidirect
56. #11680C22semidirect
59. #11654C22semidirect
60. #11652C22semidirect
61. #11414C22semidirect
63. #11404C22semidirect
64. #11404C22semidirect
790. C16#568semidirect

Maximal subgroups

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

subgroupindex
C2×#337482
#63457222
#63457022
#4841472
#4840972
#4839922
#4839612
#4833972
#4813842
#4813792
#4799622