Finite Group Databasebeta

← D47×#3273 #27091378

Subgroups — D47×#3273 #27091378

Order 12032.

3042 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×AGL(1,ℤ/8)×D47C212yesmaximal, complemented
2#546×D47C212yesmaximal, complemented
3#20255000C211yesmaximal, characteristic, complemented
4#20254999C212yesmaximal, complemented
5#20254998C211yesmaximal, characteristic, complemented
6#20254997C211yesmaximal, characteristic, complemented
7#20254996C212yesmaximal, complemented
8#20254995C212yesmaximal, complemented
9#20254994C212yesmaximal, complemented
10#20254993C212yesmaximal, complemented
11#20254992C212yesmaximal, complemented
12#495×D47C211yesmaximal, characteristic, complemented
13#468×D47C212yesmaximal, complemented
14#463×D47C212yesmaximal, complemented
15#452×D47C212yesmaximal, complemented
16#447×D47C212yesmaximal, complemented
17C4×D8×D47C211yesmaximal, characteristic, complemented
18#436×D47C211yesmaximal, characteristic, complemented
19C47×#3273C211yesmaximal, characteristic, complemented
20C2×#41×D47C2212yes—
21C22×D4×D47C2212yescomplemented
22C2×#13094052C2212yescomplemented
23C2×#13094051C2212yescomplemented
24C2×#13094051C2212yescomplemented
25C2×#13094050C2212yescomplemented
26C2×#13094049C2212yescomplemented
27C2×#13094048C2212yescomplemented
28C2×#13094048C2212yescomplemented
29AGL(1,ℤ/8)×D47—216no—
30C2×Q16×D47C2211yescharacteristic, complemented
31C2×SD16×D47C2212yescomplemented
32C2×SD16×D47C2212yescomplemented
33C2×D8×D47C2212yes—
34C2×D8×D47C2211yescharacteristic
35C2×D8×D47C2211yescharacteristic
36C2×M16×D47C2212yescomplemented
37#15689770C2212yescomplemented
38#15689769C2212yescomplemented
39#15689768C2212yescomplemented
40#15689767C2212yescomplemented
41#15689766C2212yescomplemented
42#15689765—22no—
43#15689764C2212yescomplemented
44#15689763—22no—
45#15689762—22no—
46#15689761C2212yescomplemented
47#15689760—22no—
48#124×D47C2212yescomplemented
49#123×D47—22no—
50C22⋊Q8×D47C2212yescomplemented
51#121×D47—22no—
52#121×D47C2212yes—
53#120×D47—22no—
54C4×D4×D47C2211yescharacteristic
55C4×D4×D47C2212yescomplemented
56C2×C22⋊C4×D47—22no—
57#15689508C2211yescharacteristic, complemented
58#15689507C2211yescharacteristic, complemented
59#15689506C2211yescharacteristic, complemented
60#15689505C2212yescomplemented
61#15689504C2212yescomplemented
62#15689372C2212yescomplemented
63#15689371C2212yescomplemented
64#15689370C2212yescomplemented
65#15689369C2212yescomplemented
66#15689368C2212yescomplemented
67#15689367C2212yescomplemented
68#15689366C2212yescomplemented
69#15689341C2212yescomplemented
70#15689340C2212yescomplemented
71#15689339C2212yescomplemented
72#15689338C2212yescomplemented
73#15689337C2212yescomplemented
74#15689336C2212yescomplemented
75#15689335C2212yescomplemented
76#15689288C2212yescomplemented
77#15689287C2212yescomplemented
78#15689286C2212yescomplemented
79#15689285C2212yescomplemented
80#15689284C2212yescomplemented
81#15689283C2212yescomplemented
82#15689282C2212yescomplemented
83#15689259C2212yescomplemented
84#15689258C2212yescomplemented
85#15689258C2212yescomplemented
86#15689257C2212yescomplemented
87#15689256C2212yescomplemented
88#15689255C2212yescomplemented
89#15689255C2212yescomplemented
90C4×D376C2211yescharacteristic, complemented
91D8×Dic47C2211yescharacteristic, complemented
92#15689205C2211yescharacteristic, complemented
93C4×#10625334C2212yescomplemented
94#15689203C2212yescomplemented
95#15689202C2211yescharacteristic, complemented
96#15689201C2211yescharacteristic, complemented
97#15689200C2211yescharacteristic, complemented
98#15689199C2212yescomplemented
99#15689198C2212yescomplemented
100#107×D47C2211yescharacteristic, complemented
101C4⋊C8×D47C2211yescharacteristic, complemented
102#103×D47C2212yescomplemented
103#102×D47C2212yescomplemented
104#102×D47C2212yescomplemented
105C22⋊C8×D47C2212yescomplemented
106C4×C8×D47C2211yescharacteristic, complemented
107C2×AGL(1,ℤ/8)×C47C2212yescomplemented
108C47×#546C2212yescomplemented
109C47×#495C2211yescharacteristic, complemented
110C47×#468C2212yescomplemented
111C47×#463C2212yescomplemented
112C47×#452C2212yescomplemented
113C47×#447C2212yescomplemented
114C4×D8×C47C2211yescharacteristic, complemented
115C47×#436C2211yescharacteristic, complemented
116C24×D47—22no—
117C2×#10625354C2312yes—
118C2×#10625350—22no—
119C2×#10625350C2312yes—
120C2×#10625352—22no—
121C2×#10625352C2312yes—
122#41×D47—28no—
123#41×D47—44no—
124C2×Q8×D47C2312yes—
125C22×D188C2312yescomplemented
126C22×C22⋊D47—22no—
127C2×D4×D47—28no—
128C2×D4×D47—22no—
129C2×D4×D47—22no—
130C2×D4×D47—22no—
131C2×D4×D47—22no—
132C2×D4×D47—44no—
133C2×D4×D47D411yescharacteristic
134C2×D4×D47C2312yes—
135C2×D4×D47C2312yes—
136C2×D4×D47C2312yescomplemented
137C2×D4×D47C2312yescomplemented
138C22×C4×D47—22no—
139C22×C4×D47—22no—
140C22×C4×D47C2312yes—
141#13094052—28no—
142#13094051—28no—
143#13094051—28no—
144#13094050—28no—
145#13094049—28no—
146#13094048—28no—
147#13094048—28no—
148C2×Dic188C2311yescharacteristic, complemented
149C2×#10625337C2312yescomplemented
150Q16×D47—42no—
151C2×#10625325C2312yescomplemented
152C2×#10625325C2312yescomplemented
153C2×#10625335C2312yescomplemented
154C2×#10625335C2312yescomplemented
155C2×#10625336C2312yescomplemented
156C2×#10625336C2312yescomplemented
157SD16×D47—28no—
158SD16×D47—28no—
159C2×D376C2312yes—
160C2×D376C2311yescharacteristic
161C2×D376C2311yescharacteristic
162C2×#10625334C2312yes—
163C2×#10625334C2312yes—
164C2×#10625334C2312yes—
165C2×#10625334C2312yes—
166D8×D47—28no—
167D8×D47—42no—
168D8×D47D418yescomplemented
169C2×#10625329C2312yescomplemented
170C2×#10625324C2312yescomplemented
171C2×#10625324C2312yescomplemented
172M16×D47—28no—
173C2×C8×D47C2311yescharacteristic
174C2×C8×D47C2312yes—
175C2×C8×D47C2311yescharacteristic
176#13094013C2312yescomplemented
177#13094012C2312yescomplemented
178#13094011C2312yescomplemented
179#13094010—22no—
180#13094010—22no—
181#13094009—22no—
182#13094009—22no—
183#13094008—22no—
184#13094007—22no—
185#13094006—22no—
186#13094006—22no—
187#13094005—22no—
188#13094004C2312yescomplemented
189#13094003C2312yescomplemented
190#13094002—22no—
191#13094001—22no—
192#13094000C2312yescomplemented
193#13093999—22no—
194#13093999C2312yes—
195#13093998—22no—
196#13093998C2312yes—
197#13093997—22no—
198#13093997—22no—
199#13093997—22no—
200#13093996—22no—
201#13093996—22no—
202#13093996—22no—
203#13093995—22no—
204#13093995C2312yes—
205#13093994—22no—
206#13093994—22no—
207#13093994—22no—
208#13093993—22no—
209#13093992—22no—
210#13093992—22no—
211#13093992—22no—
212C4×D188C2311yescharacteristic
213C4×D188C2312yescomplemented
214D4×Dic47D411yescharacteristic
215D4×Dic47C2312yescomplemented
216#13093986D411yescharacteristic
217#13093986C2312yescomplemented
218C4×C22⋊D47—22no—
219C4×C22⋊D47C2312yes—
220(C22⋊D47)⋊C4—22no—
221(C22⋊D47)⋊C4D412yes—
222C4⋊C4×D47—22no—
223C4⋊C4×D47D411yescharacteristic
224C4⋊C4×D47C2312yes—
225C2×C22⋊Dic47—22no—
226C2×(C2×D47)⋊C4—22no—
227C2×(C2×D47)⋊C4—22no—
228C22⋊C4×D47—22no—
229C22⋊C4×D47—22no—
230C22⋊C4×D47—22no—
231C22⋊C4×D47—22no—
232C22⋊C4×D47—22no—
233C22⋊C4×D47—22no—
234C22⋊C4×D47—22no—
235C22⋊C4×D47—22no—
236C22⋊C4×D47—22no—
237C22⋊C4×D47D412yes—
238C42×D47C2311yescharacteristic
239#13093958C2311yescharacteristic, complemented
240#13093957C2312yescomplemented
241C4⋊(C47⋊C8)C2311yescharacteristic, complemented
242Dic47⋊C8C2312yescomplemented
243#13093949C2312yescomplemented
244#13093948C2312yescomplemented
245#13093947C2312yescomplemented
246#13093946C2312yescomplemented
247#13093946C2312yescomplemented
248#13093945C2312yescomplemented
249#13093945C2312yescomplemented
250#13093944C2312yescomplemented
251#13093944C2312yescomplemented
252C22⋊(C47⋊C8)C2312yescomplemented
253(C2×D47)⋊C8C2312yescomplemented
254(C2×D47)⋊C8C2312yescomplemented
255C4×C47⋊C8C2311yescharacteristic, complemented
256C8×Dic47C2311yescharacteristic, complemented
257C8×Dic47C2311yescharacteristic, complemented
258C2×#41×C47C2312yes—
259C22×D4×C47C2312yescomplemented
260AGL(1,ℤ/8)×C47—28no—
261C2×Q16×C47C2311yescharacteristic, complemented
262C2×SD16×C47C2312yescomplemented
263C2×SD16×C47C2312yescomplemented
264C2×D8×C47C2312yes—
265C2×D8×C47C2311yescharacteristic
266C2×D8×C47C2311yescharacteristic
267C2×M16×C47C2312yescomplemented
268#124×C47C2312yescomplemented
269#123×C47—22no—
270C22⋊Q8×C47C2312yescomplemented
271#121×C47—22no—
272#121×C47C2312yes—
273#120×C47—22no—
274C4×D4×C47C2311yescharacteristic
275C4×D4×C47C2312yescomplemented
276C2×C22⋊C4×C47—22no—
277#107×C47C2311yescharacteristic, complemented
278C4⋊C8×C47C2311yescharacteristic, complemented
279#103×C47C2312yescomplemented
280#102×C47C2312yescomplemented
281#102×C47C2312yescomplemented
282C22⋊C8×C47C2312yescomplemented
283C4×C8×C47C2311yescharacteristic, complemented
284C24×C47—22no—
285C23×D47—22no—
286C23×D47—22no—
287C23×D47—22no—
288C23×D47—22no—
289C23×D47—22no—
290C23×D47—48no—
291C23×D47—48no—
292C23×D47—84no—
293C23×D47C2×D412yes—
294#41×C47—24no—
295#41×C47—42no—
296C2×Q8×C47C2412yes—
297C2×D4×C47—24no—
298C2×D4×C47—22no—
299C2×D4×C47—22no—
300C2×D4×C47—22no—
301C2×D4×C47—42no—
302C2×D4×C47C2×D411yescharacteristic
303C2×D4×C47C2412yes—
304C2×D4×C47C2412yes—
305C22×C4×C47—22no—
306C22×C4×C47—22no—
307C22×C4×C47C2412yes—
308C2×C22⋊D47—22no—
309C2×C22⋊D47—22no—
310C2×C22⋊D47—22no—
311C2×C22⋊D47—22no—
312C2×C22⋊D47—22no—
313C2×C22⋊D47—22no—
314C2×C22⋊D47—22no—
315C2×C22⋊D47—22no—
316C2×C22⋊D47—48no—
317C2×C22⋊D47C2×D412yes—
318C22×Dic47—22no—
319C22×Dic47—22no—
320C22×Dic47C2×D412yes—
321#10625354—24no—
322#10625354—42no—
323Q8×D47—24no—
324Q8×D47—24no—
325#10625352—24no—
326#10625352—42no—
327#10625352—48no—
328D4×D47—24no—
329D4×D47—24no—
330D4×D47—24no—
331D4×D47—24no—
332D4×D47—24no—
333D4×D47—42no—
334D4×D47—42no—
335D4×D47—48no—
336D4×D47—42no—
337D4×D47—48no—
338D4×D47—48no—
339D4×D47—84no—
340D4×D47C2×D418yes—
341#10625350—24no—
342#10625350—42no—
343#10625350—48no—
344C2×D188—24no—
345C2×D188—22no—
346C2×D188—22no—
347C2×D188—22no—
348C2×D188—42no—
349C2×D188C2×D411yescharacteristic
350C2×D188C2412yes—
351C2×D188C2412yes—
352C2×C4×D47—24no—
353C2×C4×D47—24no—
354C2×C4×D47—22no—
355C2×C4×D47—22no—
356C2×C4×D47—22no—
357C2×C4×D47—22no—
358C2×C4×D47—22no—
359C2×C4×D47—22no—
360C2×C4×D47—48no—
361C2×C4×D47—84no—
362C2×C4×D47C2×D411yescharacteristic
363C2×C4×D47C2×D411yescharacteristic
364C2×C4×D47C2×D412yes—
365C2×C4×D47C2×D412yes—
366C2×C4×D47C2412yes—
367C2×C4×D47C2411yescharacteristic
368C2×Dic94—22no—
369C2×Dic94C2412yes—
370Q16×C47—41no—
371SD16×C47—24no—
372SD16×C47—24no—
373D8×C47—24no—
374D8×C47—41no—
375D8×C47C2×D414yescomplemented
376M16×C47—24no—
377C2×C8×C47C2412yes—
378C2×C8×C47C2411yescharacteristic
379C2×C8×C47C2411yescharacteristic
380C4⋊C4×C47—22no—
381C4⋊C4×C47C2×D411yescharacteristic
382C4⋊C4×C47C2412yes—
383C22⋊C4×C47—22no—
384C22⋊C4×C47—22no—
385C22⋊C4×C47—22no—
386C22⋊C4×C47—22no—
387C22⋊C4×C47—22no—
388C22⋊C4×C47C2×D412yes—
389C42×C47C2411yescharacteristic
390C22⋊Dic47—22no—
391C22⋊Dic47—22no—
392C22⋊Dic47—22no—
393C22⋊Dic47—22no—
394C22⋊Dic47—22no—
395C22⋊Dic47C2×D412yes—
396#10625337—42no—
397#10625336—24no—
398#10625336—24no—
399#10625335—24no—
400#10625335—24no—
401#10625334—24no—
402#10625334—24no—
403#10625334—42no—
404#10625334C2×D418yescomplemented
405(C2×D47)⋊C4—22no—
406(C2×D47)⋊C4—22no—
407(C2×D47)⋊C4—22no—
408(C2×D47)⋊C4—22no—
409(C2×D47)⋊C4—22no—
410(C2×D47)⋊C4—22no—
411(C2×D47)⋊C4—22no—
412(C2×D47)⋊C4—22no—
413(C2×D47)⋊C4—22no—
414(C2×D47)⋊C4—22no—
415(C2×D47)⋊C4C2×D412yes—
416(C2×D47)⋊C4C2×D412yes—
417C4⋊Dic47—22no—
418C4⋊Dic47C2×D411yescharacteristic
419C4⋊Dic47C2412yes—
420Dic47⋊C4—22no—
421Dic47⋊C4—22no—
422Dic47⋊C4—22no—
423Dic47⋊C4C2×D412yes—
424C4×Dic47C2×D411yescharacteristic
425C4×Dic47C2×D411yescharacteristic
426C4×Dic47C2411yescharacteristic
427#10625329—24no—
428C2×C47⋊C8C2411yescharacteristic
429C2×C47⋊C8C2412yes—
430C2×C47⋊C8C2411yescharacteristic
431Dic188—41no—
432D376—24no—
433D376—41no—
434D376C2×D414yescomplemented
435#10625325—24no—
436#10625325—24no—
437#10625324—24no—
438#10625324—24no—
439C8×D47—24no—
440C8×D47—22no—
441C8×D47C2×D414yes—
442C23×C47—22no—
443C23×C47—22no—
444C23×C47—44no—
445C23×C47—44no—
446C23×C47—82no—
447C23×C47C22×D412yes—
448C22×D47—22no—
449C22×D47—24no—
450C22×D47—28no—
451C22×D47—24no—
452C22×D47—24no—
453C22×D47—22no—
454C22×D47—44no—
455C22×D47—44no—
456C22×D47—44no—
457C22×D47—44no—
458C22×D47—44no—
459C22×D47—44no—
460C22×D47—44no—
461C22×D47—44no—
462C22×D47—44no—
463C22×D47—44no—
464C22×D47—44no—
465C22×D47—82no—
466C22×D47—82no—
467C22×D47—82no—
468C22×D47—832no—
469C22×D47C22×D412yes—
470C22×D47C22×D411yescharacteristic
471Q8×C47—22no—
472Q8×C47—22no—
473D4×C47—22no—
474D4×C47—22no—
475D4×C47—22no—
476D4×C47—41no—
477D4×C47—44no—
478D4×C47—44no—
479D4×C47—82no—
480D4×C47C22×D414yes—
481C2×C4×C47—22no—
482C2×C4×C47—22no—
483C2×C4×C47—22no—
484C2×C4×C47—22no—
485C2×C4×C47—44no—
486C2×C4×C47—82no—
487C2×C4×C47C22×D411yescharacteristic
488C2×C4×C47C22×D411yescharacteristic
489C2×C4×C47C22×D412yes—
490C2×C4×C47C2511yescharacteristic
491C22⋊D47—28no—
492C22⋊D47—42no—
493C22⋊D47—44no—
494C22⋊D47—44no—
495C22⋊D47—44no—
496C22⋊D47—44no—
497C22⋊D47—44no—
498C22⋊D47—82no—
499C22⋊D47—82no—
500C2×Dic47—24no—
501C2×Dic47—22no—
502C2×Dic47—22no—
503C2×Dic47—44no—
504C2×Dic47—82no—
505C2×Dic47C22×D411yescharacteristic
506C2×Dic47C22×D411yescharacteristic
507C2×Dic47C22×D412yes—
508C2×Dic47C22×D411yescharacteristic
509D188—22no—
510D188—22no—
511D188—22no—
512D188—41no—
513D188—44no—
514D188—44no—
515D188—82no—
516D188C22×D414yes—
517C4×D47—24no—
518C4×D47—22no—
519C4×D47—22no—
520C4×D47—22no—
521C4×D47—22no—
522C4×D47—24no—
523C4×D47—44no—
524C4×D47—44no—
525C4×D47—44no—
526C4×D47—44no—
527C4×D47—82no—
528C4×D47—82no—
529C4×D47C22×D412yes—
530C4×D47H(5,𝔽2)12yes—
531Dic94—22no—
532Dic94—22no—
533Dic94—44no—
534C8×C47—22no—
535C8×C47—21no—
536C8×C47C22×D412yes—
537C47⋊C8—22no—
538C47⋊C8—21no—
539C47⋊C8C22×D412yes—
540C2×#3273—471nomaximal, Sylow
541C22×C47—22no—
542C22×C47—24no—
543C22×C47—22no—
544C22×C47—22no—
545C22×C47—42no—
546C22×C47—42no—
547C22×C47—42no—
548C22×C47—42no—
549C22×C47—42no—
550C22×C47—88no—
551C22×C47C23×D411yescharacteristic
552C2×D47—22no—
553C2×D47—24no—
554C2×D47—22no—
555C2×D47—22no—
556C2×D47—42no—
557C2×D47—42no—
558C2×D47—48no—
559C2×D47—416no—
560C2×D47—42no—
561C2×D47—42no—
562C2×D47—42no—
563C2×D47—88no—
564C2×D47—88no—
565C2×D47—88no—
566C2×D47—88no—
567C2×D47D4212yes—
568C2×D47#57512yes—
569C2×D47#57612yes—
570C4×C47—22no—
571C4×C47—21no—
572C4×C47—21no—
573C4×C47—42no—
574C4×C47—42no—
575C4×C47C23×D411yescharacteristic
576C4×C47C2×H(5,𝔽2)11yescharacteristic
577Dic47—22no—
578Dic47—21no—
579Dic47—21no—
580Dic47—42no—
581Dic47—42no—
582Dic47D4212yes—
583C22×AGL(1,ℤ/8)—472no—
584C2×#546—472no—
585#3273—471no—
586#3273—472no—
587#3273—472no—
588#3273—472no—
589#3273—472no—
590#3273—471no—
591#3273—471no—
592#3273—472no—
593#3273—472no—
594#3273D4711yescharacteristic, direct product factor
595C2×#495—471no—
596C2×#468—472no—
597C2×#463—472no—
598C2×#452—472no—
599C2×#447—472no—
600C2×C4×D8—471no—
601C2×#436—471no—
602C2×C47—42no—
603C2×C47—44no—
604C2×C47—82no—
605C2×C47C2×D4211yescharacteristic
606C2×C47C2×#57511yescharacteristic
607C2×C47C2×#57611yescharacteristic
608D47—42no—
609D47—44no—
610D47—82no—
611D47#327314yesdirect product factor
612C22×#41—472no—
613C23×D4—472no—
614C2×AGL(1,ℤ/8)—472no—
615C2×AGL(1,ℤ/8)—472no—
616C2×AGL(1,ℤ/8)—472no—
617C2×AGL(1,ℤ/8)—472no—
618C2×AGL(1,ℤ/8)—472no—
619C2×AGL(1,ℤ/8)—472no—
620C2×AGL(1,ℤ/8)—472no—
621C2×AGL(1,ℤ/8)—9416no—
622C2×AGL(1,ℤ/8)C2×D4712yescomplemented
623C22×Q16—471no—
624C22×SD16—472no—
625C22×SD16—472no—
626C22×D8—471no—
627C22×D8—472no—
628C22×D8—471no—
629C22×M16—472no—
630#546—472no—
631#546—472no—
632#546—472no—
633#546—472no—
634#546—472no—
635#546—472no—
636#546—472no—
637#546—942no—
638#546—942no—
639#546—942no—
640#546—942no—
641#546C2×D4712yescomplemented
642C2×#124—472no—
643C2×#123—942no—
644C2×C22⋊Q8—472no—
645C2×#121—472no—
646C2×#121—942no—
647C2×#120—942no—
648C2×C4×D4—471no—
649C2×C4×D4—472no—
650C22×C22⋊C4—942no—
651#495—471no—
652#495—472no—
653#495—471no—
654#495—472no—
655#495—471no—
656#495C2×D4711yescharacteristic, complemented
657#468—472no—
658#468—472no—
659#468—472no—
660#468—472no—
661#468—472no—
662#468—472no—
663#468—472no—
664#468C2×D4712yescomplemented
665#463—472no—
666#463—472no—
667#463—472no—
668#463—472no—
669#463—472no—
670#463—472no—
671#463—472no—
672#463C2×D4712yescomplemented
673#452—472no—
674#452—472no—
675#452—472no—
676#452—472no—
677#452—472no—
678#452—472no—
679#452—472no—
680#452C2×D4712yescomplemented
681#447—472no—
682#447—472no—
683#447—472no—
684#447—472no—
685#447—472no—
686#447—472no—
687#447—472no—
688#447C2×D4712yescomplemented
689C4×D8—471no—
690C4×D8—472no—
691C4×D8—471no—
692C4×D8—472no—
693C4×D8—471no—
694C4×D8C2×D4711yescharacteristic, complemented
695#436—472no—
696#436—471no—
697#436—471no—
698#436—472no—
699#436—471no—
700#436C2×D4711yescharacteristic, complemented
701C2×#107—471no—
702C2×C4⋊C8—471no—
703C2×#103—472no—
704C2×#102—472no—
705C2×#102—472no—
706C2×C22⋊C8—472no—
707C2×C4×C8—471no—
708C47C2×#327311yescharacteristic, complemented, Sylow
709C25—942no—
710C2×#41—472no—
711C2×#41—472no—
712C2×#41—472no—
713C2×#41—942no—
714C2×#41—942no—
715C2×#41—948no—
716C2×#41—1884no—
717C2×#41C22×D4712yes—
718C22×Q8—472no—
719C22×D4—472no—
720C22×D4—471no—
721C22×D4—472no—
722C22×D4—472no—
723C22×D4—472no—
724C22×D4—472no—
725C22×D4—942no—
726C22×D4—942no—
727C22×D4—942no—
728C22×D4—948no—
729C22×D4—942no—
730C22×D4—942no—
731C22×D4—1884no—
732C22×D4C22×D4712yescomplemented
733C23×C4—472no—
734C23×C4—942no—
735C23×C4—942no—
736AGL(1,ℤ/8)—28no—
737AGL(1,ℤ/8)—948no—
738AGL(1,ℤ/8)—948no—
739AGL(1,ℤ/8)—948no—
740AGL(1,ℤ/8)—948no—
741AGL(1,ℤ/8)—948no—
742AGL(1,ℤ/8)—948no—
743AGL(1,ℤ/8)—948no—
744C2×Q16—472no—
745C2×Q16—471no—
746C2×Q16—1882no—
747C2×Q16C22×D4711yescharacteristic, complemented
748C2×SD16—472no—
749C2×SD16—472no—
750C2×SD16—472no—
751C2×SD16—472no—
752C2×SD16—472no—
753C2×SD16—472no—
754C2×SD16—948no—
755C2×SD16—948no—
756C2×SD16C22×D4712yescomplemented
757C2×SD16C22×D4712yescomplemented
758C2×D8—472no—
759C2×D8—478no—
760C2×D8—472no—
761C2×D8—472no—
762C2×D8—472no—
763C2×D8—471no—
764C2×D8—472no—
765C2×D8—471no—
766C2×D8—948no—
767C2×D8—1882no—
768C2×D8C22×D4712yes—
769C2×D8C22×D4711yescharacteristic
770C2×D8C22×D4711yescharacteristic
771C2×M16—472no—
772C2×M16—472no—
773C2×M16—472no—
774C2×M16—948no—
775C2×M16C22×D4712yescomplemented
776C22×C8—471no—
777C22×C8—472no—
778C22×C8—471no—
779#124—472no—
780#124—472no—
781#124—472no—
782#124—942no—
783#124—942no—
784#124C22×D4712yescomplemented
785#123—22no—
786#123—942no—
787#123—942no—
788#123—942no—
789#123—942no—
790#123—942no—
791#123—942no—
792#123—942no—
793C22⋊Q8—472no—
794C22⋊Q8—472no—
795C22⋊Q8—472no—
796C22⋊Q8—942no—
797C22⋊Q8—942no—
798C22⋊Q8C22×D4712yescomplemented
799#121—22no—
800#121—472no—
801#121—472no—
802#121—472no—
803#121—942no—
804#121—942no—
805#121—942no—
806#121—942no—
807#121—942no—
808#121—942no—
809#121—942no—
810#121—942no—
811#121—942no—
812#121C22×D4712yes—
813#120—22no—
814#120—942no—
815#120—942no—
816#120—942no—
817#120—942no—
818#120—942no—
819#120—942no—
820#120—942no—
821C4×D4—471no—
822C4×D4—472no—
823C4×D4—471no—
824C4×D4—472no—
825C4×D4—472no—
826C4×D4—472no—
827C4×D4—471no—
828C4×D4—472no—
829C4×D4—942no—
830C4×D4—942no—
831C4×D4C22×D4711yescharacteristic
832C4×D4C22×D4712yescomplemented
833C2×C4⋊C4—471no—
834C2×C4⋊C4—472no—
835C2×C4⋊C4—942no—
836C2×C22⋊C4—22no—
837C2×C22⋊C4—472no—
838C2×C22⋊C4—942no—
839C2×C22⋊C4—942no—
840C2×C22⋊C4—942no—
841C2×C22⋊C4—942no—
842C2×C22⋊C4—942no—
843C2×C22⋊C4—942no—
844C2×C22⋊C4—942no—
845C2×C22⋊C4—942no—
846C2×C22⋊C4—942no—
847C2×C22⋊C4—942no—
848C2×C22⋊C4—942no—
849C2×C22⋊C4—942no—
850C2×C42—471no—
851#107—471no—
852#107—472no—
853#107C22×D4711yescharacteristic, complemented
854C4⋊C8—472no—
855C4⋊C8—471no—
856C4⋊C8C22×D4711yescharacteristic, complemented
857#103—472no—
858#103—472no—
859#103—472no—
860#103C22×D4712yescomplemented
861#102—472no—
862#102—472no—
863#102—472no—
864#102—472no—
865#102—472no—
866#102—472no—
867#102C22×D4712yescomplemented
868#102C22×D4712yescomplemented
869C22⋊C8—472no—
870C22⋊C8—472no—
871C22⋊C8—472no—
872C22⋊C8C22×D4712yescomplemented
873C4×C8—471no—
874C4×C8—471no—
875C4×C8—471no—
876C4×C8C22×D4711yescharacteristic, complemented
877C24—22no—
878C24—472no—
879C24—942no—
880C24—942no—
881C24—942no—
882C24—942no—
883C24—942no—
884C24—3764no—
885C24—1888no—
886C24—1888no—
887#41—24no—
888#41—42no—
889#41—944no—
890#41—944no—
891#41—944no—
892#41—1882no—
893#41—1888no—
894#41—1882no—
895#41—1888no—
896#41—1882no—
897C2×Q8—472no—
898C2×Q8—942no—
899C2×Q8—944no—
900C2×Q8—944no—
901C2×Q8C23×D4712yes—
902C2×D4—24no—
903C2×D4—22no—
904C2×D4—22no—
905C2×D4—22no—
906C2×D4—42no—
907C2×D4—478no—
908C2×D4—472no—
909C2×D4—471no—
910C2×D4—472no—
911C2×D4—472no—
912C2×D4—944no—
913C2×D4—942no—
914C2×D4—942no—
915C2×D4—944no—
916C2×D4—944no—
917C2×D4—944no—
918C2×D4—942no—
919C2×D4—942no—
920C2×D4—942no—
921C2×D4—942no—
922C2×D4—944no—
923C2×D4—944no—
924C2×D4—942no—
925C2×D4—942no—
926C2×D4—942no—
927C2×D4—942no—
928C2×D4—942no—
929C2×D4—3764no—
930C2×D4—1882no—
931C2×D4—1882no—
932C2×D4—1882no—
933C2×D4—1888no—
934C2×D4—1882no—
935C2×D4—1888no—
936C2×D4—1888no—
937C2×D4—1888no—
938C2×D4D4×D4711yescharacteristic
939C2×D4C23×D4712yes—
940C2×D4C23×D4712yes—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—471no—
944C22×C4—472no—
945C22×C4—471no—
946C22×C4—471no—
947C22×C4—472no—
948C22×C4—472no—
949C22×C4—472no—
950C22×C4—944no—
951C22×C4—944no—
952C22×C4—942no—
953C22×C4—942no—
954C22×C4—942no—
955C22×C4—942no—
956C22×C4—942no—
957C22×C4—942no—
958C22×C4—942no—
959C22×C4—942no—
960C22×C4—3764no—
961C22×C4—1888no—
962C22×C4C23×D4712yes—
963Q16—41no—
964Q16—1881no—
965Q16—1882no—
966SD16—24no—
967SD16—24no—
968SD16—944no—
969SD16—944no—
970SD16—944no—
971SD16—944no—
972SD16—944no—
973SD16—944no—
974D8—24no—
975D8—41no—
976D8—478no—
977D8—474no—
978D8—944no—
979D8—944no—
980D8—944no—
981D8—1881no—
982D8—1882no—
983D8D4×D4714yescomplemented
984M16—24no—
985M16—944no—
986M16—944no—
987M16—944no—
988C2×C8—471no—
989C2×C8—474no—
990C2×C8—471no—
991C2×C8—472no—
992C2×C8—944no—
993C2×C8—942no—
994C2×C8C23×D4711yescharacteristic
995C2×C8C23×D4712yes—
996C2×C8C23×D4711yescharacteristic
997C4⋊C4—22no—
998C4⋊C4—472no—
999C4⋊C4—471no—
1000C4⋊C4—472no—
1001C4⋊C4—942no—
1002C4⋊C4—942no—
1003C4⋊C4—942no—
1004C4⋊C4—942no—
1005C4⋊C4D4×D4711yescharacteristic
1006C4⋊C4C23×D4712yes—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—472no—
1013C22⋊C4—472no—
1014C22⋊C4—472no—
1015C22⋊C4—942no—
1016C22⋊C4—942no—
1017C22⋊C4—942no—
1018C22⋊C4—942no—
1019C22⋊C4—942no—
1020C22⋊C4—942no—
1021C22⋊C4—942no—
1022C22⋊C4—942no—
1023C22⋊C4—942no—
1024C22⋊C4—942no—
1025C22⋊C4—942no—
1026C22⋊C4—942no—
1027C22⋊C4—942no—
1028C22⋊C4—942no—
1029C22⋊C4—942no—
1030C22⋊C4D4×D4712yes—
1031C42—471no—
1032C42—471no—
1033C42—471no—
1034C42C23×D4711yescharacteristic
1035C23—22no—
1036C23—22no—
1037C23—44no—
1038C23—44no—
1039C23—82no—
1040C23—471no—
1041C23—472no—
1042C23—944no—
1043C23—948no—
1044C23—944no—
1045C23—944no—
1046C23—942no—
1047C23—942no—
1048C23—3762no—
1049C23—3762no—
1050C23—3762no—
1051C23—37632no—
1052C23—1884no—
1053C23—1884no—
1054C23—1884no—
1055C23—1884no—
1056C23—1884no—
1057C23—1884no—
1058C23—1884no—
1059C23—1884no—
1060C23—1884no—
1061C23—1884no—
1062C23—1884no—
1063C23C2×D4×D4712yes—
1064Q8—22no—
1065Q8—22no—
1066Q8—942no—
1067Q8—942no—
1068Q8—1884no—
1069D4—22no—
1070D4—22no—
1071D4—22no—
1072D4—41no—
1073D4—44no—
1074D4—44no—
1075D4—82no—
1076D4—474no—
1077D4—948no—
1078D4—942no—
1079D4—942no—
1080D4—942no—
1081D4—3762no—
1082D4—3762no—
1083D4—3762no—
1084D4—1881no—
1085D4—1884no—
1086D4—1884no—
1087D4—1884no—
1088D4—1882no—
1089D4—1884no—
1090D4—1884no—
1091D4—1884no—
1092D4—1884no—
1093D4C2×D4×D4714yes—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—44no—
1099C2×C4—82no—
1100C2×C4—471no—
1101C2×C4—472no—
1102C2×C4—472no—
1103C2×C4—471no—
1104C2×C4—471no—
1105C2×C4—472no—
1106C2×C4—944no—
1107C2×C4—944no—
1108C2×C4—942no—
1109C2×C4—942no—
1110C2×C4—944no—
1111C2×C4—942no—
1112C2×C4—942no—
1113C2×C4—942no—
1114C2×C4—942no—
1115C2×C4—3762no—
1116C2×C4—3762no—
1117C2×C4—3762no—
1118C2×C4—1884no—
1119C2×C4—1884no—
1120C2×C4—1884no—
1121C2×C4—1884no—
1122C2×C4—1884no—
1123C2×C4C2×D4×D4711yescharacteristic
1124C2×C4C2×D4×D4711yescharacteristic
1125C2×C4C2×D4×D4712yes—
1126C2×C4C24×D4711yescharacteristic
1127C8—22no—
1128C8—21no—
1129C8—472no—
1130C8—942no—
1131C8—941no—
1132C8C2×D4×D4712yes—
1133C22—22no—
1134C22—24no—
1135C22—22no—
1136C22—22no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—88no—
1143C22—472no—
1144C22—472no—
1145C22—472no—
1146C22—942no—
1147C22—944no—
1148C22—942no—
1149C22—942no—
1150C22—3768no—
1151C22—3768no—
1152C22—3768no—
1153C22—3768no—
1154C22—1888no—
1155C22—18816no—
1156C22—1882no—
1157C22—1882no—
1158C22—1882no—
1159C22—1882no—
1160C22—1882no—
1161C22C22×D4×D4711yescharacteristic
1162C4—22no—
1163C4—21no—
1164C4—21no—
1165C4—42no—
1166C4—42no—
1167C4—472no—
1168C4—942no—
1169C4—941no—
1170C4—941no—
1171C4—1882no—
1172C4—1882no—
1173C4C22×D4×D4711yescharacteristic
1174C4H(5,𝔽2)×D4711yescharacteristic
1175C2—42no—
1176C2—44no—
1177C2—82no—
1178C2—474no—
1179C2—3762no—
1180C2—1882no—
1181C2—1884no—
1182C2D42×D4711yescharacteristic
1183C2#575×D4711yescharacteristic
1184C2#576×D4711yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3273C2
socleC22×C47C23×D4
hypercenter#3273D47
hypocenterC47C2×#3273
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3273

Complements

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

NH ≅ G/Ntype
1. C2×AGL(1,ℤ/8)×D47C2semidirect
2. #546×D47C2semidirect
3. #20255000C2semidirect
4. #20254999C2semidirect
5. #20254998C2semidirect
6. #20254997C2semidirect
7. #20254996C2semidirect
8. #20254995C2semidirect
9. #20254994C2semidirect
10. #20254993C2semidirect
11. #20254992C2semidirect
12. #495×D47C2semidirect
13. #468×D47C2semidirect
14. #463×D47C2semidirect
15. #452×D47C2semidirect
16. #447×D47C2semidirect
17. C4×D8×D47C2semidirect
18. #436×D47C2semidirect
19. C47×#3273C2semidirect
21. C22×D4×D47C22semidirect
22. C2×#13094052C22semidirect
23. C2×#13094051C22semidirect
24. C2×#13094051C22semidirect
25. C2×#13094050C22semidirect
26. C2×#13094049C22semidirect
27. C2×#13094048C22semidirect
28. C2×#13094048C22semidirect
30. C2×Q16×D47C22semidirect
31. C2×SD16×D47C22semidirect
32. C2×SD16×D47C22semidirect
36. C2×M16×D47C22semidirect
37. #15689770C22semidirect
38. #15689769C22semidirect
39. #15689768C22semidirect
40. #15689767C22semidirect
41. #15689766C22semidirect
43. #15689764C22semidirect
46. #15689761C22semidirect
48. #124×D47C22semidirect
50. C22⋊Q8×D47C22semidirect
55. C4×D4×D47C22semidirect
57. #15689508C22semidirect
58. #15689507C22semidirect
59. #15689506C22semidirect
60. #15689505C22semidirect
61. #15689504C22semidirect
62. #15689372C22semidirect
63. #15689371C22semidirect
64. #15689370C22semidirect
65. #15689369C22semidirect
66. #15689368C22semidirect
67. #15689367C22semidirect
68. #15689366C22semidirect
69. #15689341C22semidirect
70. #15689340C22semidirect
71. #15689339C22semidirect
72. #15689338C22semidirect
73. #15689337C22semidirect
74. #15689336C22semidirect
75. #15689335C22semidirect
76. #15689288C22semidirect
77. #15689287C22semidirect
78. #15689286C22semidirect
79. #15689285C22semidirect
80. #15689284C22semidirect
81. #15689283C22semidirect
82. #15689282C22semidirect
83. #15689259C22semidirect
84. #15689258C22semidirect
85. #15689258C22semidirect
86. #15689257C22semidirect
87. #15689256C22semidirect
88. #15689255C22semidirect
89. #15689255C22semidirect
90. C4×D376C22semidirect
91. D8×Dic47C22semidirect
92. #15689205C22semidirect
93. C4×#10625334C22semidirect
94. #15689203C22semidirect
95. #15689202C22semidirect
96. #15689201C22semidirect
97. #15689200C22semidirect
98. #15689199C22semidirect
99. #15689198C22semidirect
100. #107×D47C22semidirect
101. C4⋊C8×D47C22semidirect
102. #103×D47C22semidirect
103. #102×D47C22semidirect
104. #102×D47C22semidirect
105. C22⋊C8×D47C22semidirect
106. C4×C8×D47C22semidirect
107. C2×AGL(1,ℤ/8)×C47C22semidirect
108. C47×#546C22semidirect
109. C47×#495C22semidirect
110. C47×#468C22semidirect
111. C47×#463C22semidirect
112. C47×#452C22semidirect
113. C47×#447C22semidirect
114. C4×D8×C47C22semidirect
115. C47×#436C22semidirect
125. C22×D188C23semidirect
136. C2×D4×D47C23semidirect
137. C2×D4×D47C23semidirect
148. C2×Dic188C23semidirect
149. C2×#10625337C23semidirect
151. C2×#10625325C23semidirect
152. C2×#10625325C23semidirect
153. C2×#10625335C23semidirect
154. C2×#10625335C23semidirect
155. C2×#10625336C23semidirect
156. C2×#10625336C23semidirect
168. D8×D47D4semidirect
169. C2×#10625329C23semidirect
170. C2×#10625324C23semidirect
171. C2×#10625324C23semidirect
176. #13094013C23semidirect
177. #13094012C23semidirect
178. #13094011C23semidirect
188. #13094004C23semidirect
189. #13094003C23semidirect
192. #13094000C23semidirect
213. C4×D188C23semidirect
215. D4×Dic47C23semidirect
217. #13093986C23semidirect
239. #13093958C23semidirect
240. #13093957C23semidirect
241. C4⋊(C47⋊C8)C23semidirect
242. Dic47⋊C8C23semidirect
243. #13093949C23semidirect
244. #13093948C23semidirect
245. #13093947C23semidirect
246. #13093946C23semidirect
247. #13093946C23semidirect
248. #13093945C23semidirect
249. #13093945C23semidirect
250. #13093944C23semidirect
251. #13093944C23semidirect
252. C22⋊(C47⋊C8)C23semidirect
253. (C2×D47)⋊C8C23semidirect
254. (C2×D47)⋊C8C23semidirect
255. C4×C47⋊C8C23semidirect
256. C8×Dic47C23semidirect
257. C8×Dic47C23semidirect
259. C22×D4×C47C23semidirect
261. C2×Q16×C47C23semidirect
262. C2×SD16×C47C23semidirect
263. C2×SD16×C47C23semidirect
267. C2×M16×C47C23semidirect
268. #124×C47C23semidirect
270. C22⋊Q8×C47C23semidirect
275. C4×D4×C47C23semidirect
277. #107×C47C23semidirect
278. C4⋊C8×C47C23semidirect
279. #103×C47C23semidirect
280. #102×C47C23semidirect
281. #102×C47C23semidirect
282. C22⋊C8×C47C23semidirect
283. C4×C8×C47C23semidirect
375. D8×C47C2×D4semidirect
404. #10625334C2×D4semidirect
434. D376C2×D4semidirect
594. #3273D47direct (N × H)
611. D47#3273direct (N × H)
622. C2×AGL(1,ℤ/8)C2×D47semidirect
641. #546C2×D47semidirect
656. #495C2×D47semidirect
664. #468C2×D47semidirect
672. #463C2×D47semidirect
680. #452C2×D47semidirect
688. #447C2×D47semidirect
694. C4×D8C2×D47semidirect
700. #436C2×D47semidirect
708. C47C2×#3273semidirect
732. C22×D4C22×D47semidirect
747. C2×Q16C22×D47semidirect
756. C2×SD16C22×D47semidirect
757. C2×SD16C22×D47semidirect
775. C2×M16C22×D47semidirect
784. #124C22×D47semidirect
798. C22⋊Q8C22×D47semidirect
832. C4×D4C22×D47semidirect
853. #107C22×D47semidirect
856. C4⋊C8C22×D47semidirect
860. #103C22×D47semidirect
867. #102C22×D47semidirect
868. #102C22×D47semidirect
872. C22⋊C8C22×D47semidirect
876. C4×C8C22×D47semidirect
983. D8D4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×AGL(1,ℤ/8)×D472
#546×D472
#202550002
#202549992
#202549982
#202549972
#202549962
#202549952
#202549942
#202549932
#202549922
#495×D472
#468×D472
#463×D472
#452×D472
#447×D472
C4×D8×D472
#436×D472
C47×#32732
C2×#327347