Finite Group Databasebeta

← D47×#3092 #27084051

Subgroups — D47×#3092 #27084051

Order 12032.

2650 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×D47C211yesmaximal, characteristic
2C22×C4⋊C4×D47C211yesmaximal, characteristic, complemented
3#20253315C212yesmaximal, complemented
4#20253314C212yesmaximal, complemented
5#20253313C211yesmaximal, characteristic, complemented
6#20253312C212yesmaximal, complemented
7#20253311C211yesmaximal, characteristic, complemented
8#20253310C212yesmaximal, complemented
9#20253309C212yesmaximal, complemented
10#20253308C211yesmaximal, characteristic, complemented
11#20253307C212yesmaximal, complemented
12#484×D47C212yesmaximal, complemented
13#481×D47C212yesmaximal, complemented
14#483×D47C212yesmaximal, complemented
15#480×D47C212yesmaximal, complemented
16#428×D47C212yesmaximal, complemented
17#417×D47C212yesmaximal, complemented
18#407×D47C211yesmaximal, characteristic, complemented
19C47×#3092C211yesmaximal, characteristic, complemented
20C2×#41×D47C2211yescharacteristic
21C23×C4×D47—21no—
22C23×C4×D47C2211yescharacteristic
23C2×M16×D47C2212yes—
24#15689636C2211yescharacteristic
25#15689636C2211yescharacteristic
26#15689635C2211yescharacteristic
27#15689634C2211yescharacteristic
28#15689633C2211yescharacteristic
29#15689633C2211yescharacteristic
30#15689632—21no—
31#15689632—21no—
32#15689631—21no—
33#15689630C2211yescharacteristic
34#15689629—21no—
35#123×D47—21no—
36C22⋊Q8×D47C2211yescharacteristic
37C22⋊Q8×D47C2211yescharacteristic
38#121×D47C2211yescharacteristic
39#121×D47C2211yescharacteristic
40#120×D47—21no—
41C4×D4×D47—21no—
42C4×D4×D47—21no—
43#117×D47C2211yescharacteristic
44C22×C4⋊Dic47C2211yescharacteristic, complemented
45C22×Dic47⋊C4—21no—
46C2×C4⋊C4×D47—21no—
47C2×C4⋊C4×D47—21no—
48C2×C4⋊C4×D47—21no—
49C2×C4⋊C4×D47—21no—
50C2×C4⋊C4×D47—21no—
51C2×C4⋊C4×D47—21no—
52C2×C4⋊C4×D47C2212yes—
53C2×C4⋊C4×D47C2212yes—
54C2×C4⋊C4×D47C2212yes—
55C2×C4⋊C4×D47C2212yescomplemented
56C2×C4⋊C4×D47C2212yescomplemented
57C2×C4⋊C4×D47C2212yescomplemented
58#15689460C2214yescomplemented
59#15689459C2212yescomplemented
60#15689458C2212yescomplemented
61#15689457C2214yescomplemented
62#15689456C2212yescomplemented
63#15689455C2214yescomplemented
64#15689454C2212yescomplemented
65#15689453C2212yescomplemented
66#15689452C2214yescomplemented
67#15689451C2212yescomplemented
68#15689443C2214yescomplemented
69#15689442C2212yescomplemented
70#15689441C2212yescomplemented
71#15689440C2214yescomplemented
72#15689439C2212yescomplemented
73#15689438C2214yescomplemented
74#15689437C2212yescomplemented
75#15689436C2212yescomplemented
76#15689435C2214yescomplemented
77#15689434C2212yescomplemented
78#15689166C2212yescomplemented
79#15689165C2212yescomplemented
80#15689164C2214yescomplemented
81#15689163C2212yescomplemented
82#15689162C2214yescomplemented
83#107×D47C2214yescomplemented
84#106×D47C2214yescomplemented
85#15689125C2212yescomplemented
86#15689124C2212yescomplemented
87#15689123C2214yescomplemented
88#15689122C2212yescomplemented
89#15689121C2214yescomplemented
90#103×D47C2214yescomplemented
91#102×D47C2214yescomplemented
92#15689087C2211yescharacteristic, complemented
93#15689086C2212yescomplemented
94#15689085C2212yescomplemented
95#15689085C2212yescomplemented
96C22⋊C8×D47C2212yes—
97C22⋊C8×D47C2212yes—
98C47×#525C2211yescharacteristic
99C22×C4⋊C4×C47C2211yescharacteristic, complemented
100C47×#484C2212yescomplemented
101C47×#483C2212yescomplemented
102C47×#481C2212yescomplemented
103C47×#480C2212yescomplemented
104C47×#428C2212yescomplemented
105C47×#417C2212yescomplemented
106C47×#407C2211yescharacteristic, complemented
107C24×D47D411yescharacteristic
108C2×#10625354C2311yescharacteristic
109C2×#10625350—21no—
110C2×#10625350C2311yescharacteristic
111C2×#10625352—21no—
112C2×#10625352C2311yescharacteristic
113#41×D47—28no—
114C2×Q8×D47C2311yescharacteristic
115C2×D4×D47—21no—
116C2×D4×D47—21no—
117C2×D4×D47—21no—
118C2×D4×D47C2311yescharacteristic
119C23×Dic47—21no—
120C23×Dic47D411yescharacteristic
121C22×C4×D47—28no—
122C22×C4×D47—22no—
123C22×C4×D47—22no—
124C22×C4×D47—22no—
125C22×C4×D47—22no—
126C22×C4×D47—22no—
127C22×C4×D47—22no—
128C22×C4×D47—21no—
129C22×C4×D47—48no—
130C22×C4×D47D411yescharacteristic
131C22×C4×D47D411yescharacteristic
132C22×C4×D47D411yescharacteristic
133C22×C4×D47D411yescharacteristic
134C22×C4×D47D411yescharacteristic
135C22×C4×D47D411yescharacteristic
136C22×C4×D47C2311yescharacteristic
137C22×C4×D47C2311yescharacteristic
138C22×C4×D47C2311yescharacteristic
139C22×C4×D47C2311yescharacteristic
140C22×C4×D47C2311yescharacteristic
141C22×C4×D47C2311yescharacteristic
142C2×#10625329C2312yes—
143C2×#10625324C2314yes—
144M16×D47—28no—
145C2×C8×D47C2314yes—
146#13094009—21no—
147#13094009—21no—
148#13094008—21no—
149#13094007—21no—
150#13094006—21no—
151#13094006—21no—
152#13094005—21no—
153#13094004C2311yescharacteristic
154#13094004C2311yescharacteristic
155#13094003C2311yescharacteristic
156#13094003C2311yescharacteristic
157#13094002—21no—
158#13094002—21no—
159#13094001—21no—
160#13094001—21no—
161#13094000C2311yescharacteristic
162#13094000C2311yescharacteristic
163#13093999C2311yescharacteristic
164#13093999C2311yescharacteristic
165#13093998C2311yescharacteristic
166#13093998C2311yescharacteristic
167#13093997—21no—
168#13093997—21no—
169#13093996—21no—
170#13093996—21no—
171#13093995C2311yescharacteristic
172#13093995C2311yescharacteristic
173#13093994—21no—
174#13093994—21no—
175#13093994—21no—
176#13093993—21no—
177#13093992—21no—
178#13093992—21no—
179#13093992—21no—
180C4×D188—21no—
181C4×D188—21no—
182D4×Dic47—21no—
183D4×Dic47—21no—
184#13093986—21no—
185#13093986—21no—
186C4×C22⋊D47—21no—
187C4×C22⋊D47—21no—
188C4×C22⋊D47—21no—
189C4×C22⋊D47—21no—
190(C22⋊D47)⋊C4—21no—
191(C22⋊D47)⋊C4—21no—
192(C22⋊D47)⋊C4—21no—
193(C22⋊D47)⋊C4—21no—
194#13093983C2311yescharacteristic
195#13093982C2311yescharacteristic
196#13093982C2311yescharacteristic
197#13093981—21no—
198#13093980—21no—
199C2×C4⋊Dic47—21no—
200C2×C4⋊Dic47—21no—
201C2×C4⋊Dic47—21no—
202C2×C4⋊Dic47C2312yes—
203C2×C4⋊Dic47C2312yes—
204C2×C4⋊Dic47C2312yes—
205C2×Dic47⋊C4—22no—
206C2×Dic47⋊C4—22no—
207C2×Dic47⋊C4—22no—
208C2×Dic47⋊C4—22no—
209C2×Dic47⋊C4—22no—
210C2×Dic47⋊C4—22no—
211C4⋊C4×D47—22no—
212C4⋊C4×D47—22no—
213C4⋊C4×D47—22no—
214C4⋊C4×D47—22no—
215C4⋊C4×D47—22no—
216C4⋊C4×D47—22no—
217C4⋊C4×D47—22no—
218C4⋊C4×D47—22no—
219C4⋊C4×D47—22no—
220C4⋊C4×D47—22no—
221C4⋊C4×D47—22no—
222C4⋊C4×D47—22no—
223C4⋊C4×D47—21no—
224C4⋊C4×D47—21no—
225C4⋊C4×D47C2314yes—
226C4⋊C4×D47C2314yes—
227C4⋊C4×D47C2314yes—
228C4⋊C4×D47C2314yes—
229C4⋊C4×D47C2311yescharacteristic
230C4⋊C4×D47C2311yescharacteristic
231C22⋊C4×D47—21no—
232C22⋊C4×D47—21no—
233C22⋊C4×D47—21no—
234C22⋊C4×D47—21no—
235C22⋊C4×D47—21no—
236C42×D47—21no—
237#13093958C2314yescomplemented
238#13093957C2314yescomplemented
239#13093957C2314yescomplemented
240#13093956C2314yescomplemented
241#13093955C2314yescomplemented
242#13093955C2314yescomplemented
243#13093949C2314yescomplemented
244#13093948C2314yescomplemented
245#13093947C2314yescomplemented
246#13093946C2314yescomplemented
247#13093945C2314yescomplemented
248#13093944C2314yescomplemented
249C22⋊(C47⋊C8)C2312yes—
250C22⋊(C47⋊C8)C2312yes—
251(C2×D47)⋊C8C2314yes—
252(C2×D47)⋊C8C2314yes—
253C2×#41×C47C2311yescharacteristic
254C23×C4×C47—21no—
255C23×C4×C47C2311yescharacteristic
256C2×M16×C47C2312yes—
257#123×C47—21no—
258C22⋊Q8×C47C2311yescharacteristic
259C22⋊Q8×C47C2311yescharacteristic
260#121×C47C2311yescharacteristic
261#121×C47C2311yescharacteristic
262#120×C47—21no—
263C4×D4×C47—21no—
264C4×D4×C47—21no—
265#117×C47C2311yescharacteristic
266C2×C4⋊C4×C47—21no—
267C2×C4⋊C4×C47—21no—
268C2×C4⋊C4×C47—21no—
269C2×C4⋊C4×C47C2312yes—
270C2×C4⋊C4×C47C2312yes—
271C2×C4⋊C4×C47C2312yes—
272#107×C47C2314yescomplemented
273#106×C47C2314yescomplemented
274#103×C47C2314yescomplemented
275#102×C47C2314yescomplemented
276C22⋊C8×C47C2312yes—
277C22⋊C8×C47C2312yes—
278C24×C47C2×D411yescharacteristic
279C23×D47—24no—
280C23×D47—24no—
281C23×D47—24no—
282C23×D47—21no—
283C23×D47C2×D411yescharacteristic
284C23×D47C2×D411yescharacteristic
285C23×D47C2×D411yescharacteristic
286C23×D47C2×D411yescharacteristic
287C23×D47C2×D411yescharacteristic
288C23×D47C2×D411yescharacteristic
289#41×C47—24no—
290C2×Q8×C47C2411yescharacteristic
291C2×D4×C47—21no—
292C2×D4×C47—21no—
293C2×D4×C47—21no—
294C2×D4×C47C2411yescharacteristic
295C22×C4×C47—24no—
296C22×C4×C47—22no—
297C22×C4×C47—22no—
298C22×C4×C47—22no—
299C22×C4×C47—21no—
300C22×C4×C47—44no—
301C22×C4×C47C2×D411yescharacteristic
302C22×C4×C47C2×D411yescharacteristic
303C22×C4×C47C2×D411yescharacteristic
304C22×C4×C47C2411yescharacteristic
305C22×C4×C47C2411yescharacteristic
306C22×C4×C47C2411yescharacteristic
307C2×C22⋊D47—21no—
308C2×C22⋊D47—21no—
309C2×C22⋊D47—21no—
310C2×C22⋊D47—21no—
311C2×C22⋊D47—21no—
312C2×C22⋊D47—21no—
313C2×C22⋊D47—21no—
314C22×Dic47—24no—
315C22×Dic47—22no—
316C22×Dic47—22no—
317C22×Dic47—22no—
318C22×Dic47—21no—
319C22×Dic47—44no—
320C22×Dic47C2×D411yescharacteristic
321C22×Dic47C2×D411yescharacteristic
322C22×Dic47C2×D411yescharacteristic
323C22×Dic47C2×D411yescharacteristic
324C22×Dic47C2×D411yescharacteristic
325C22×Dic47C2×D411yescharacteristic
326#10625354—24no—
327Q8×D47—24no—
328#10625352—24no—
329#10625352—44no—
330D4×D47—24no—
331D4×D47—44no—
332D4×D47—44no—
333D4×D47—44no—
334#10625350—24no—
335#10625350—44no—
336C2×D188—21no—
337C2×D188—21no—
338C2×D188—21no—
339C2×D188C2411yescharacteristic
340C2×C4×D47—24no—
341C2×C4×D47—24no—
342C2×C4×D47—24no—
343C2×C4×D47—24no—
344C2×C4×D47—24no—
345C2×C4×D47—24no—
346C2×C4×D47—24no—
347C2×C4×D47—24no—
348C2×C4×D47—24no—
349C2×C4×D47—24no—
350C2×C4×D47—24no—
351C2×C4×D47—21no—
352C2×C4×D47—21no—
353C2×C4×D47—21no—
354C2×C4×D47—24no—
355C2×C4×D47—24no—
356C2×C4×D47—24no—
357C2×C4×D47—24no—
358C2×C4×D47—21no—
359C2×C4×D47—21no—
360C2×C4×D47—48no—
361C2×C4×D47—48no—
362C2×C4×D47—48no—
363C2×C4×D47—48no—
364C2×C4×D47—48no—
365C2×C4×D47—48no—
366C2×C4×D47—44no—
367C2×C4×D47C2×D411yescharacteristic
368C2×C4×D47C2×D411yescharacteristic
369C2×C4×D47C2×D411yescharacteristic
370C2×C4×D47C2×D411yescharacteristic
371C2×C4×D47C2×D411yescharacteristic
372C2×C4×D47C2×D411yescharacteristic
373C2×C4×D47C2×D411yescharacteristic
374C2×C4×D47C2×D411yescharacteristic
375C2×C4×D47C2×D411yescharacteristic
376C2×C4×D47C2×D411yescharacteristic
377C2×C4×D47C2×D411yescharacteristic
378C2×C4×D47C2×D411yescharacteristic
379C2×C4×D47#4118yes—
380C2×C4×D47C2411yescharacteristic
381C2×C4×D47C2411yescharacteristic
382C2×C4×D47C2411yescharacteristic
383C2×C4×D47C2411yescharacteristic
384C2×Dic94—21no—
385C2×Dic94C2411yescharacteristic
386M16×C47—24no—
387C2×C8×C47C2414yes—
388C4⋊C4×C47—22no—
389C4⋊C4×C47—22no—
390C4⋊C4×C47—22no—
391C4⋊C4×C47—21no—
392C4⋊C4×C47—21no—
393C4⋊C4×C47C2414yes—
394C4⋊C4×C47C2411yescharacteristic
395C4⋊C4×C47C2411yescharacteristic
396C22⋊C4×C47—21no—
397C22⋊C4×C47—21no—
398C22⋊C4×C47—21no—
399C22⋊C4×C47—21no—
400C22⋊C4×C47—21no—
401C42×C47—21no—
402C22⋊Dic47—21no—
403C22⋊Dic47—21no—
404C22⋊Dic47—21no—
405C22⋊Dic47—21no—
406C22⋊Dic47—21no—
407(C2×D47)⋊C4—21no—
408(C2×D47)⋊C4—21no—
409(C2×D47)⋊C4—21no—
410(C2×D47)⋊C4—21no—
411(C2×D47)⋊C4—21no—
412(C2×D47)⋊C4—21no—
413(C2×D47)⋊C4—21no—
414(C2×D47)⋊C4—21no—
415(C2×D47)⋊C4—21no—
416(C2×D47)⋊C4—21no—
417C4⋊Dic47—22no—
418C4⋊Dic47—22no—
419C4⋊Dic47—22no—
420C4⋊Dic47—21no—
421C4⋊Dic47—21no—
422C4⋊Dic47C2414yes—
423C4⋊Dic47C2411yescharacteristic
424C4⋊Dic47C2411yescharacteristic
425Dic47⋊C4—21no—
426Dic47⋊C4—21no—
427Dic47⋊C4—24no—
428Dic47⋊C4—24no—
429Dic47⋊C4—24no—
430Dic47⋊C4—24no—
431Dic47⋊C4—21no—
432Dic47⋊C4—21no—
433Dic47⋊C4—21no—
434Dic47⋊C4—21no—
435C4×Dic47—21no—
436C4×Dic47—21no—
437C4×Dic47—21no—
438#10625329—24no—
439C2×C47⋊C8C2414yes—
440#10625324—28no—
441C8×D47—28no—
442C23×C47—22no—
443C23×C47—22no—
444C23×C47—22no—
445C23×C47—21no—
446C23×C47C22×D411yescharacteristic
447C23×C47C22×D411yescharacteristic
448C23×C47C22×D411yescharacteristic
449C22×D47—232no—
450C22×D47—22no—
451C22×D47—22no—
452C22×D47—22no—
453C22×D47—22no—
454C22×D47—22no—
455C22×D47—22no—
456C22×D47—22no—
457C22×D47—22no—
458C22×D47—22no—
459C22×D47—22no—
460C22×D47—22no—
461C22×D47—22no—
462C22×D47—22no—
463C22×D47—22no—
464C22×D47—22no—
465C22×D47—21no—
466C22×D47—42no—
467C22×D47—42no—
468C22×D47—42no—
469C22×D47#12314yes—
470C22×D47AGL(1,ℤ/8)14yes—
471C22×D47#13714yes—
472C22×D47C22×D411yescharacteristic
473C22×D47C22×D411yescharacteristic
474C22×D47C22×D411yescharacteristic
475C22×D47C22×D411yescharacteristic
476Q8×C47—22no—
477D4×C47—22no—
478D4×C47—42no—
479D4×C47—42no—
480D4×C47—42no—
481C2×C4×C47—22no—
482C2×C4×C47—22no—
483C2×C4×C47—22no—
484C2×C4×C47—22no—
485C2×C4×C47—22no—
486C2×C4×C47—21no—
487C2×C4×C47—21no—
488C2×C4×C47—24no—
489C2×C4×C47—21no—
490C2×C4×C47—44no—
491C2×C4×C47—44no—
492C2×C4×C47—44no—
493C2×C4×C47—42no—
494C2×C4×C47C22×D411yescharacteristic
495C2×C4×C47C22×D411yescharacteristic
496C2×C4×C47C22×D411yescharacteristic
497C2×C4×C47C2×#4114yes—
498C2×C4×C47C2511yescharacteristic
499C22⋊D47—42no—
500C22⋊D47—42no—
501C22⋊D47—42no—
502C22⋊D47—42no—
503C22⋊D47—42no—
504C22⋊D47—42no—
505C22⋊D47—42no—
506C2×Dic47—22no—
507C2×Dic47—22no—
508C2×Dic47—22no—
509C2×Dic47—22no—
510C2×Dic47—22no—
511C2×Dic47—21no—
512C2×Dic47—21no—
513C2×Dic47—24no—
514C2×Dic47—21no—
515C2×Dic47—44no—
516C2×Dic47—44no—
517C2×Dic47—44no—
518C2×Dic47—42no—
519C2×Dic47#12314yes—
520C2×Dic47C22×D411yescharacteristic
521C2×Dic47C22×D411yescharacteristic
522C2×Dic47C22×D411yescharacteristic
523C2×Dic47C22×D411yescharacteristic
524D188—22no—
525D188—42no—
526D188—42no—
527D188—42no—
528C4×D47—22no—
529C4×D47—22no—
530C4×D47—22no—
531C4×D47—22no—
532C4×D47—22no—
533C4×D47—22no—
534C4×D47—22no—
535C4×D47—22no—
536C4×D47—22no—
537C4×D47—22no—
538C4×D47—22no—
539C4×D47—22no—
540C4×D47—48no—
541C4×D47—48no—
542C4×D47—42no—
543C4×D47—48no—
544C4×D47—48no—
545C4×D47—42no—
546C4×D47—42no—
547C4×D47—42no—
548C4×D47—42no—
549C4×D47#12314yes—
550C4×D47#12314yes—
551C4×D47C2×#4114yes—
552C4×D47C2×#4114yes—
553Dic94—22no—
554Dic94—42no—
555C8×C47—24no—
556C47⋊C8—24no—
557C2×#3092—471nomaximal, Sylow
558C22×C47—28no—
559C22×C47—21no—
560C22×C47—21no—
561C22×C47—21no—
562C22×C47—21no—
563C22×C47—21no—
564C22×C47—21no—
565C22×C47—41no—
566C22×C47—41no—
567C22×C47—41no—
568C22×C47C2×#12312yes—
569C22×C47C2×AGL(1,ℤ/8)12yes—
570C22×C47C2×#13712yes—
571C22×C47C23×D411yescharacteristic
572C2×D47—28no—
573C2×D47—28no—
574C2×D47—28no—
575C2×D47—21no—
576C2×D47—21no—
577C2×D47—21no—
578C2×D47—21no—
579C2×D47—21no—
580C2×D47—21no—
581C2×D47—28no—
582C2×D47—28no—
583C2×D47—28no—
584C2×D47—41no—
585C2×D47—41no—
586C2×D47—41no—
587C2×D47—84no—
588C2×D47C2×#12312yes—
589C2×D47C2×#12312yes—
590C2×D47C2×AGL(1,ℤ/8)12yes—
591C2×D47C2×AGL(1,ℤ/8)12yes—
592C2×D47C2×#13712yes—
593C2×D47C2×#13712yes—
594C4×C47—21no—
595C4×C47—21no—
596C4×C47—41no—
597C4×C47—44no—
598C4×C47—41no—
599C4×C47—41no—
600C4×C47C2×#12312yes—
601C4×C47C22×#4112yes—
602Dic47—21no—
603Dic47—21no—
604Dic47—41no—
605Dic47—44no—
606Dic47—41no—
607Dic47—41no—
608Dic47C2×#12312yes—
609Dic47C2×#12312yes—
610C2×#525—471no—
611C23×C4⋊C4—471no—
612#3092—472no—
613#3092—472no—
614#3092—472no—
615#3092—472no—
616#3092—472no—
617#3092—472no—
618#3092—471no—
619#3092—471no—
620#3092—471no—
621#3092D4711yescharacteristic, direct product factor
622C2×#484—472no—
623C2×#481—472no—
624C2×#483—472no—
625C2×#480—472no—
626C2×#428—472no—
627C2×#417—472no—
628C2×#407—471no—
629C2×C47—22no—
630C2×C47—22no—
631C2×C47—22no—
632C2×C47—81no—
633C2×C47C22×#12311yescharacteristic
634C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
635C2×C47C22×#13711yescharacteristic
636D47—22no—
637D47—22no—
638D47—22no—
639D47—81no—
640D47#309214yesdirect product factor
641C22×#41—471no—
642C24×C4—471no—
643C24×C4—941no—
644C22×M16—472no—
645#525—471no—
646#525—471no—
647#525—471no—
648#525—471no—
649#525—471no—
650#525—471no—
651#525—471no—
652#525—941no—
653#525—941no—
654#525—941no—
655#525—941no—
656#525C2×D4711yescharacteristic
657C2×#123—941no—
658C2×C22⋊Q8—471no—
659C2×C22⋊Q8—471no—
660C2×#121—471no—
661C2×#121—471no—
662C2×#120—941no—
663C2×C4×D4—941no—
664C2×C4×D4—941no—
665C2×#117—471no—
666C22×C4⋊C4—471no—
667C22×C4⋊C4—472no—
668C22×C4⋊C4—472no—
669C22×C4⋊C4—472no—
670C22×C4⋊C4—472no—
671C22×C4⋊C4—472no—
672C22×C4⋊C4—472no—
673C22×C4⋊C4—941no—
674C22×C4⋊C4—941no—
675C22×C4⋊C4—941no—
676C22×C4⋊C4—941no—
677C22×C4⋊C4—941no—
678C22×C4⋊C4—941no—
679C22×C4⋊C4—941no—
680C22×C4⋊C4C2×D4711yescharacteristic, complemented
681#484—472no—
682#484—472no—
683#484—474no—
684#484—474no—
685#484—472no—
686#484C2×D4712yescomplemented
687#483—472no—
688#483—472no—
689#483—474no—
690#483—474no—
691#483—472no—
692#483C2×D4712yescomplemented
693#481—472no—
694#481—472no—
695#481—474no—
696#481—474no—
697#481—472no—
698#481C2×D4712yescomplemented
699#480—472no—
700#480—472no—
701#480—474no—
702#480—474no—
703#480—472no—
704#480C2×D4712yescomplemented
705#428—472no—
706#428—472no—
707#428—472no—
708#428—474no—
709#428—474no—
710#428C2×D4712yescomplemented
711C2×#107—474no—
712C2×#106—474no—
713#417—472no—
714#417—472no—
715#417—472no—
716#417—474no—
717#417—474no—
718#417C2×D4712yescomplemented
719C2×#103—474no—
720C2×#102—474no—
721#407—471no—
722#407—472no—
723#407—472no—
724#407—472no—
725#407C2×D4711yescharacteristic, complemented
726C2×C22⋊C8—472no—
727C2×C22⋊C8—472no—
728C47C2×#309211yescharacteristic, complemented, Sylow
729C25—471no—
730C2×#41—471no—
731C2×#41—471no—
732C2×#41—471no—
733C2×#41—941no—
734C2×#41—941no—
735C2×#41—948no—
736C2×#41C22×D4711yescharacteristic
737C22×Q8—471no—
738C22×D4—471no—
739C22×D4—941no—
740C22×D4—941no—
741C22×D4—941no—
742C23×C4—21no—
743C23×C4—471no—
744C23×C4—471no—
745C23×C4—471no—
746C23×C4—471no—
747C23×C4—471no—
748C23×C4—471no—
749C23×C4—471no—
750C23×C4—471no—
751C23×C4—471no—
752C23×C4—471no—
753C23×C4—471no—
754C23×C4—471no—
755C23×C4—471no—
756C23×C4—948no—
757C23×C4—941no—
758C23×C4—942no—
759C23×C4—942no—
760C23×C4—942no—
761C23×C4—942no—
762C23×C4—942no—
763C23×C4—942no—
764C23×C4—941no—
765C23×C4—1888no—
766C23×C4C22×D4711yescharacteristic
767C2×M16—472no—
768C2×M16—474no—
769C2×M16—948no—
770C2×M16C22×D4712yes—
771C22×C8—474no—
772#123—21no—
773#123—941no—
774#123—941no—
775#123—941no—
776#123—941no—
777#123—941no—
778#123—941no—
779#123—941no—
780C22⋊Q8—471no—
781C22⋊Q8—471no—
782C22⋊Q8—471no—
783C22⋊Q8—471no—
784C22⋊Q8—471no—
785C22⋊Q8—471no—
786C22⋊Q8—941no—
787C22⋊Q8—941no—
788C22⋊Q8—941no—
789C22⋊Q8—941no—
790C22⋊Q8C22×D4711yescharacteristic
791C22⋊Q8C22×D4711yescharacteristic
792#121—471no—
793#121—471no—
794#121—471no—
795#121—471no—
796#121—471no—
797#121—471no—
798#121—941no—
799#121—941no—
800#121—941no—
801#121—941no—
802#121C22×D4711yescharacteristic
803#121C22×D4711yescharacteristic
804#120—21no—
805#120—941no—
806#120—941no—
807#120—941no—
808#120—941no—
809#120—941no—
810#120—941no—
811#120—941no—
812C4×D4—21no—
813C4×D4—21no—
814C4×D4—941no—
815C4×D4—941no—
816C4×D4—941no—
817C4×D4—941no—
818C4×D4—941no—
819C4×D4—941no—
820C4×D4—941no—
821C4×D4—941no—
822C4×D4—941no—
823C4×D4—941no—
824C4×D4—941no—
825C4×D4—941no—
826C4×D4—941no—
827C4×D4—941no—
828#117—471no—
829#117—471no—
830#117—471no—
831#117—941no—
832#117—941no—
833#117C22×D4711yescharacteristic
834C2×C4⋊C4—21no—
835C2×C4⋊C4—21no—
836C2×C4⋊C4—21no—
837C2×C4⋊C4—472no—
838C2×C4⋊C4—472no—
839C2×C4⋊C4—472no—
840C2×C4⋊C4—474no—
841C2×C4⋊C4—474no—
842C2×C4⋊C4—474no—
843C2×C4⋊C4—474no—
844C2×C4⋊C4—471no—
845C2×C4⋊C4—471no—
846C2×C4⋊C4—942no—
847C2×C4⋊C4—942no—
848C2×C4⋊C4—942no—
849C2×C4⋊C4—942no—
850C2×C4⋊C4—942no—
851C2×C4⋊C4—942no—
852C2×C4⋊C4—942no—
853C2×C4⋊C4—942no—
854C2×C4⋊C4—942no—
855C2×C4⋊C4—942no—
856C2×C4⋊C4—942no—
857C2×C4⋊C4—942no—
858C2×C4⋊C4—941no—
859C2×C4⋊C4—941no—
860C2×C4⋊C4—942no—
861C2×C4⋊C4—942no—
862C2×C4⋊C4—942no—
863C2×C4⋊C4—942no—
864C2×C4⋊C4—942no—
865C2×C4⋊C4—942no—
866C2×C4⋊C4—941no—
867C2×C4⋊C4—941no—
868C2×C4⋊C4—941no—
869C2×C4⋊C4C22×D4712yes—
870C2×C4⋊C4C22×D4712yes—
871C2×C4⋊C4C22×D4712yes—
872C2×C22⋊C4—941no—
873C2×C22⋊C4—941no—
874C2×C22⋊C4—941no—
875C2×C22⋊C4—941no—
876C2×C22⋊C4—941no—
877C2×C42—941no—
878#107—474no—
879#107—474no—
880#107—474no—
881#107C22×D4714yescomplemented
882#106—474no—
883#106—474no—
884#106—474no—
885#106C22×D4714yescomplemented
886#103—474no—
887#103—474no—
888#103—474no—
889#103C22×D4714yescomplemented
890#102—474no—
891#102—474no—
892#102—474no—
893#102C22×D4714yescomplemented
894C22⋊C8—472no—
895C22⋊C8—472no—
896C22⋊C8—474no—
897C22⋊C8—474no—
898C22⋊C8C22×D4712yes—
899C22⋊C8C22×D4712yes—
900C24—471no—
901C24—471no—
902C24—471no—
903C24—471no—
904C24—471no—
905C24—471no—
906C24—944no—
907C24—944no—
908C24—944no—
909C24—941no—
910C24D4×D4711yescharacteristic
911#41—24no—
912#41—944no—
913#41—944no—
914#41—944no—
915#41—1884no—
916#41—1884no—
917C2×Q8—471no—
918C2×Q8—941no—
919C2×Q8—944no—
920C2×Q8C23×D4711yescharacteristic
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—471no—
925C2×D4—941no—
926C2×D4—941no—
927C2×D4—941no—
928C2×D4—944no—
929C2×D4—941no—
930C2×D4—941no—
931C2×D4—941no—
932C2×D4—941no—
933C2×D4—941no—
934C2×D4—941no—
935C2×D4—941no—
936C2×D4—1884no—
937C2×D4—1884no—
938C2×D4—1884no—
939C2×D4C23×D4711yescharacteristic
940C22×C4—24no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—21no—
945C22×C4—44no—
946C22×C4—471no—
947C22×C4—471no—
948C22×C4—471no—
949C22×C4—478no—
950C22×C4—471no—
951C22×C4—471no—
952C22×C4—471no—
953C22×C4—471no—
954C22×C4—471no—
955C22×C4—471no—
956C22×C4—471no—
957C22×C4—471no—
958C22×C4—471no—
959C22×C4—471no—
960C22×C4—471no—
961C22×C4—471no—
962C22×C4—471no—
963C22×C4—471no—
964C22×C4—471no—
965C22×C4—471no—
966C22×C4—471no—
967C22×C4—471no—
968C22×C4—471no—
969C22×C4—944no—
970C22×C4—944no—
971C22×C4—944no—
972C22×C4—944no—
973C22×C4—944no—
974C22×C4—944no—
975C22×C4—944no—
976C22×C4—944no—
977C22×C4—944no—
978C22×C4—941no—
979C22×C4—944no—
980C22×C4—941no—
981C22×C4—941no—
982C22×C4—941no—
983C22×C4—944no—
984C22×C4—944no—
985C22×C4—944no—
986C22×C4—944no—
987C22×C4—944no—
988C22×C4—941no—
989C22×C4—944no—
990C22×C4—942no—
991C22×C4—942no—
992C22×C4—942no—
993C22×C4—941no—
994C22×C4—1884no—
995C22×C4—1888no—
996C22×C4—1888no—
997C22×C4—1888no—
998C22×C4—1888no—
999C22×C4—1888no—
1000C22×C4—1888no—
1001C22×C4—1884no—
1002C22×C4D4×D4711yescharacteristic
1003C22×C4D4×D4711yescharacteristic
1004C22×C4D4×D4711yescharacteristic
1005C22×C4C23×D4711yescharacteristic
1006C22×C4C23×D4711yescharacteristic
1007C22×C4C23×D4711yescharacteristic
1008M16—24no—
1009M16—948no—
1010M16—944no—
1011C2×C8—474no—
1012C2×C8—948no—
1013C2×C8C23×D4714yes—
1014C4⋊C4—22no—
1015C4⋊C4—22no—
1016C4⋊C4—22no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—474no—
1020C4⋊C4—471no—
1021C4⋊C4—471no—
1022C4⋊C4—944no—
1023C4⋊C4—944no—
1024C4⋊C4—944no—
1025C4⋊C4—944no—
1026C4⋊C4—941no—
1027C4⋊C4—941no—
1028C4⋊C4—941no—
1029C4⋊C4—941no—
1030C4⋊C4—941no—
1031C4⋊C4—941no—
1032C4⋊C4—941no—
1033C4⋊C4—941no—
1034C4⋊C4—942no—
1035C4⋊C4—942no—
1036C4⋊C4—942no—
1037C4⋊C4C23×D4714yes—
1038C4⋊C4C23×D4711yescharacteristic
1039C4⋊C4C23×D4711yescharacteristic
1040C22⋊C4—21no—
1041C22⋊C4—21no—
1042C22⋊C4—21no—
1043C22⋊C4—21no—
1044C22⋊C4—21no—
1045C22⋊C4—941no—
1046C22⋊C4—941no—
1047C22⋊C4—941no—
1048C22⋊C4—941no—
1049C22⋊C4—941no—
1050C22⋊C4—941no—
1051C22⋊C4—941no—
1052C22⋊C4—941no—
1053C22⋊C4—941no—
1054C22⋊C4—941no—
1055C22⋊C4—941no—
1056C22⋊C4—941no—
1057C22⋊C4—941no—
1058C22⋊C4—941no—
1059C22⋊C4—941no—
1060C42—21no—
1061C42—941no—
1062C42—941no—
1063C42—941no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—21no—
1068C23—471no—
1069C23—474no—
1070C23—474no—
1071C23—474no—
1072C23—471no—
1073C23—471no—
1074C23—471no—
1075C23—942no—
1076C23—942no—
1077C23—942no—
1078C23—942no—
1079C23—942no—
1080C23—942no—
1081C23—942no—
1082C23—942no—
1083C23—942no—
1084C23—942no—
1085C23—942no—
1086C23—942no—
1087C23—9432no—
1088C23—942no—
1089C23—942no—
1090C23—942no—
1091C23—941no—
1092C23—1882no—
1093C23—1882no—
1094C23—1882no—
1095C23C2×D4×D4711yescharacteristic
1096C23C2×D4×D4711yescharacteristic
1097C23C2×D4×D4711yescharacteristic
1098Q8—22no—
1099Q8—942no—
1100Q8—1882no—
1101D4—22no—
1102D4—42no—
1103D4—42no—
1104D4—42no—
1105D4—942no—
1106D4—1882no—
1107D4—1882no—
1108D4—1882no—
1109D4—1882no—
1110D4—1882no—
1111D4—1882no—
1112D4—1882no—
1113D4—1882no—
1114D4—1882no—
1115D4—1882no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—24no—
1125C2×C4—44no—
1126C2×C4—44no—
1127C2×C4—44no—
1128C2×C4—42no—
1129C2×C4—474no—
1130C2×C4—471no—
1131C2×C4—471no—
1132C2×C4—474no—
1133C2×C4—474no—
1134C2×C4—474no—
1135C2×C4—474no—
1136C2×C4—471no—
1137C2×C4—471no—
1138C2×C4—942no—
1139C2×C4—942no—
1140C2×C4—942no—
1141C2×C4—942no—
1142C2×C4—942no—
1143C2×C4—942no—
1144C2×C4—942no—
1145C2×C4—942no—
1146C2×C4—942no—
1147C2×C4—942no—
1148C2×C4—942no—
1149C2×C4—942no—
1150C2×C4—942no—
1151C2×C4—942no—
1152C2×C4—942no—
1153C2×C4—942no—
1154C2×C4—942no—
1155C2×C4—941no—
1156C2×C4—941no—
1157C2×C4—941no—
1158C2×C4—944no—
1159C2×C4—1882no—
1160C2×C4—1888no—
1161C2×C4—1888no—
1162C2×C4—1882no—
1163C2×C4—1882no—
1164C2×C4—1882no—
1165C2×C4—1888no—
1166C2×C4—1888no—
1167C2×C4—1882no—
1168C2×C4—1884no—
1169C2×C4—1884no—
1170C2×C4—1884no—
1171C2×C4—1882no—
1172C2×C4C2×D4×D4711yescharacteristic
1173C2×C4C2×D4×D4711yescharacteristic
1174C2×C4C2×D4×D4711yescharacteristic
1175C2×C4#41×D4714yes—
1176C2×C4C24×D4711yescharacteristic
1177C8—24no—
1178C8—944no—
1179C22—28no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—472no—
1190C22—472no—
1191C22—472no—
1192C22—472no—
1193C22—472no—
1194C22—472no—
1195C22—948no—
1196C22—948no—
1197C22—948no—
1198C22—948no—
1199C22—948no—
1200C22—948no—
1201C22—941no—
1202C22—941no—
1203C22—941no—
1204C22—941no—
1205C22—941no—
1206C22—941no—
1207C22—3764no—
1208C22—1881no—
1209C22—1881no—
1210C22—1881no—
1211C22#123×D4712yes—
1212C22AGL(1,ℤ/8)×D4712yes—
1213C22#137×D4712yes—
1214C22C22×D4×D4711yescharacteristic
1215C4—21no—
1216C4—21no—
1217C4—44no—
1218C4—41no—
1219C4—41no—
1220C4—41no—
1221C4—472no—
1222C4—472no—
1223C4—941no—
1224C4—941no—
1225C4—1884no—
1226C4—1881no—
1227C4—1881no—
1228C4—1881no—
1229C4#123×D4712yes—
1230C4C2×#41×D4712yes—
1231C2—22no—
1232C2—22no—
1233C2—22no—
1234C2—81no—
1235C2—474no—
1236C2—942no—
1237C2—942no—
1238C2—942no—
1239C2—3761no—
1240C2C2×#123×D4711yescharacteristic
1241C2C2×AGL(1,ℤ/8)×D4711yescharacteristic
1242C2C2×#137×D4711yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3092C2
socleC22×C47C23×D4
prime radical#525×D47C2
hypercenter#3092D47
hypocenterC47C2×#3092
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3092

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D47C2semidirect
3. #20253315C2semidirect
4. #20253314C2semidirect
5. #20253313C2semidirect
6. #20253312C2semidirect
7. #20253311C2semidirect
8. #20253310C2semidirect
9. #20253309C2semidirect
10. #20253308C2semidirect
11. #20253307C2semidirect
12. #484×D47C2semidirect
13. #481×D47C2semidirect
14. #483×D47C2semidirect
15. #480×D47C2semidirect
16. #428×D47C2semidirect
17. #417×D47C2semidirect
18. #407×D47C2semidirect
19. C47×#3092C2semidirect
44. C22×C4⋊Dic47C22semidirect
55. C2×C4⋊C4×D47C22semidirect
56. C2×C4⋊C4×D47C22semidirect
57. C2×C4⋊C4×D47C22semidirect
58. #15689460C22semidirect
59. #15689459C22semidirect
60. #15689458C22semidirect
61. #15689457C22semidirect
62. #15689456C22semidirect
63. #15689455C22semidirect
64. #15689454C22semidirect
65. #15689453C22semidirect
66. #15689452C22semidirect
67. #15689451C22semidirect
68. #15689443C22semidirect
69. #15689442C22semidirect
70. #15689441C22semidirect
71. #15689440C22semidirect
72. #15689439C22semidirect
73. #15689438C22semidirect
74. #15689437C22semidirect
75. #15689436C22semidirect
76. #15689435C22semidirect
77. #15689434C22semidirect
78. #15689166C22semidirect
79. #15689165C22semidirect
80. #15689164C22semidirect
81. #15689163C22semidirect
82. #15689162C22semidirect
83. #107×D47C22semidirect
84. #106×D47C22semidirect
85. #15689125C22semidirect
86. #15689124C22semidirect
87. #15689123C22semidirect
88. #15689122C22semidirect
89. #15689121C22semidirect
90. #103×D47C22semidirect
91. #102×D47C22semidirect
92. #15689087C22semidirect
93. #15689086C22semidirect
94. #15689085C22semidirect
95. #15689085C22semidirect
99. C22×C4⋊C4×C47C22semidirect
100. C47×#484C22semidirect
101. C47×#483C22semidirect
102. C47×#481C22semidirect
103. C47×#480C22semidirect
104. C47×#428C22semidirect
105. C47×#417C22semidirect
106. C47×#407C22semidirect
237. #13093958C23semidirect
238. #13093957C23semidirect
239. #13093957C23semidirect
240. #13093956C23semidirect
241. #13093955C23semidirect
242. #13093955C23semidirect
243. #13093949C23semidirect
244. #13093948C23semidirect
245. #13093947C23semidirect
246. #13093946C23semidirect
247. #13093945C23semidirect
248. #13093944C23semidirect
272. #107×C47C23semidirect
273. #106×C47C23semidirect
274. #103×C47C23semidirect
275. #102×C47C23semidirect
621. #3092D47direct (N × H)
640. D47#3092direct (N × H)
680. C22×C4⋊C4C2×D47semidirect
686. #484C2×D47semidirect
692. #483C2×D47semidirect
698. #481C2×D47semidirect
704. #480C2×D47semidirect
710. #428C2×D47semidirect
718. #417C2×D47semidirect
725. #407C2×D47semidirect
728. C47C2×#3092semidirect
881. #107C22×D47semidirect
885. #106C22×D47semidirect
889. #103C22×D47semidirect
893. #102C22×D47semidirect

Maximal subgroups

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

subgroupindex
#525×D472
C22×C4⋊C4×D472
#202533152
#202533142
#202533132
#202533122
#202533112
#202533102
#202533092
#202533082
#202533072
#484×D472
#481×D472
#483×D472
#480×D472
#428×D472
#417×D472
#407×D472
C47×#30922
C2×#309247