Finite Group Databasebeta

← #26218195

Subgroups — #26218195

Order 12032.

1704 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256591C211yesmaximal, characteristic, complemented
2C2×#15689140C211yesmaximal, characteristic, complemented
3C2×#15689140C211yesmaximal, characteristic, complemented
4C2×#15689097C211yesmaximal, characteristic, complemented
5#20243891C218yesmaximal, complemented
6C2×#15688895C211yesmaximal, characteristic, complemented
7#20243099C211yesmaximal, characteristic, complemented
8C2×C47×#575C211yesmaximal, characteristic
9C22×#10625329C2211yescharacteristic
10#15689606—22no—
11#15689606—22no—
12#15689601—21no—
13#15689598—22no—
14#15689598—21no—
15#41×Dic47—22no—
16#41×Dic47C2214yescomplemented
17C2×#13093983—22no—
18C2×#13093983C2211yescharacteristic
19C2×#13093983C2211yescharacteristic
20C2×#13093983C2211yescharacteristic
21#15689140—22no—
22#15689140—22no—
23#15689140—22no—
24#15689140C2214yescomplemented
25C2×#13093951—22no—
26C2×#13093951C2214yescomplemented
27#15689097—22no—
28#15689097C2214yescomplemented
29C2×#13093939—22no—
30#15688895C2214yescomplemented
31#15688884C2214yescomplemented
32C22×#41×C47C2211yescharacteristic
33C22×#41×C47C2211yescharacteristic
34C47×#575—22no—
35C47×#575—22no—
36C47×#575C414yescomplemented
37C47×#575C2214yes—
38C2×#137×C47—21no—
39C2×#137×C47C412yescomplemented
40C2×AGL(1,ℤ/8)×C47—21no—
41C2×AGL(1,ℤ/8)×C47C412yescomplemented
42C2×#135×C47—22no—
43C22×M16×C47C2211yescharacteristic
44C2×#10625329—21no—
45C2×#10625329—21no—
46C2×#10625329—21no—
47C2×#10625329—21no—
48C2×#10625329—21no—
49C2×#10625329C2312yes—
50C22×C47⋊C8—21no—
51Q8×Dic47—24no—
52Q8×Dic47—24no—
53D4×Dic47—28no—
54D4×Dic47—24no—
55D4×Dic47—24no—
56D4×Dic47—28no—
57#13093983—24no—
58#13093983—24no—
59#13093983—21no—
60#13093983—21no—
61#13093983—21no—
62#13093983—21no—
63#13093983—21no—
64#13093983—24no—
65#13093983—21no—
66#13093983—21no—
67#13093983D412yes—
68#13093983D412yes—
69#13093983D412yes—
70#13093983C2312yes—
71#13093983C2312yes—
72C2×C4⋊Dic47—24no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47—21no—
76C2×C22⋊Dic47—24no—
77C2×C22⋊Dic47—21no—
78C2×C22⋊Dic47—21no—
79C2×C22⋊Dic47D412yes—
80C2×C4×Dic47—21no—
81C2×C4×Dic47—24no—
82C2×C4×Dic47—21no—
83C2×C4×Dic47C2312yes—
84#13093951—28no—
85#13093951—28no—
86#13093939—28no—
87C2×#41×C47—21no—
88C2×#41×C47—21no—
89C2×#41×C47—21no—
90C2×#41×C47—21no—
91C2×#41×C47—21no—
92C2×#41×C47—21no—
93C2×#41×C47—21no—
94C2×#41×C47—21no—
95C2×#41×C47—21no—
96C2×#41×C47—21no—
97C2×#41×C47—21no—
98C2×#41×C47—21no—
99C2×#41×C47—21no—
100C2×#41×C47—21no—
101C2×#41×C47—21no—
102C2×#41×C47—21no—
103C2×#41×C47C2×C412yes—
104C2×#41×C47C2×C412yes—
105C2×#41×C47C2×C412yescomplemented
106C2×#41×C47D412yes—
107C2×#41×C47D412yes—
108C2×#41×C47D412yes—
109C2×#41×C47C2312yes—
110C2×#41×C47C2312yes—
111C22×Q8×C47C2×C411yescharacteristic, complemented
112C22×Q8×C47D411yescharacteristic
113C22×D4×C47—21no—
114C22×D4×C47—21no—
115C22×D4×C47C2×C411yescharacteristic, complemented
116C22×D4×C47D411yescharacteristic
117C23×C4×C47—21no—
118C23×C4×C47—21no—
119C23×C4×C47C2311yescharacteristic
120#137×C47—24no—
121#137×C47—24no—
122#137×C47—24no—
123#137×C47C2×C418yescomplemented
124AGL(1,ℤ/8)×C47—24no—
125AGL(1,ℤ/8)×C47—24no—
126AGL(1,ℤ/8)×C47—24no—
127AGL(1,ℤ/8)×C47C2×C418yescomplemented
128#135×C47—28no—
129#135×C47—28no—
130C2×Q16×C47—22no—
131C2×SD16×C47—22no—
132C2×SD16×C47—22no—
133C2×D8×C47—22no—
134C2×M16×C47—21no—
135C2×M16×C47—21no—
136C2×M16×C47—21no—
137C2×M16×C47C2×C412yescomplemented
138C2×M16×C47C2×C412yescomplemented
139C2×M16×C47C2312yes—
140C22×C8×C47—21no—
141C24×C47—21no—
142C24×C47—21no—
143C24×C47C2×D411yescharacteristic
144#41×C47—22no—
145#41×C47—22no—
146#41×C47—22no—
147#41×C47—22no—
148#41×C47—22no—
149#41×C47—22no—
150#41×C47—22no—
151#41×C47—22no—
152#41×C47—22no—
153#41×C47—22no—
154#41×C47—22no—
155#41×C47—22no—
156#41×C47—22no—
157#41×C47—22no—
158#41×C47—22no—
159#41×C47—22no—
160#41×C47—22no—
161#41×C47—22no—
162#41×C47—22no—
163#41×C47—22no—
164#41×C47—41no—
165#41×C47—41no—
166#41×C47—41no—
167#41×C47—41no—
168#41×C47—41no—
169#41×C47—41no—
170#41×C47—41no—
171#41×C47—41no—
172#41×C47C22⋊C414yes—
173#41×C47C22⋊C414yes—
174#41×C47C22×C414yes—
175#41×C47C2×D414yes—
176C2×Q8×C47—21no—
177C2×Q8×C47—21no—
178C2×Q8×C47—21no—
179C2×Q8×C47—21no—
180C2×Q8×C47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—21no—
184C2×Q8×C47C22⋊C412yes—
185C2×Q8×C47C22⋊C412yes—
186C2×Q8×C47C22×C412yes—
187C2×Q8×C47C2×D412yes—
188C2×D4×C47—22no—
189C2×D4×C47—22no—
190C2×D4×C47—22no—
191C2×D4×C47—22no—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47—22no—
196C2×D4×C47—21no—
197C2×D4×C47—21no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47—21no—
203C2×D4×C47—21no—
204C2×D4×C47—41no—
205C2×D4×C47—41no—
206C2×D4×C47—41no—
207C2×D4×C47—41no—
208C2×D4×C47C22⋊C412yes—
209C2×D4×C47C22⋊C412yes—
210C2×D4×C47C22×C412yes—
211C2×D4×C47C2×D412yes—
212C22×C4×C47—21no—
213C22×C4×C47—22no—
214C22×C4×C47—22no—
215C22×C4×C47—22no—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47—22no—
219C22×C4×C47—21no—
220C22×C4×C47—22no—
221C22×C4×C47—22no—
222C22×C4×C47—41no—
223C22×C4×C47—41no—
224C22×C4×C47—41no—
225C22×C4×C47—41no—
226C22×C4×C47C22×C411yescharacteristic
227C22×C4×C47C22×C411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2×D411yescharacteristic
232C22×C4×C47C2×D411yescharacteristic
233C22×C4×C47C2×D411yescharacteristic
234C22×C4×C47C2×D411yescharacteristic
235C22×C4×C47#4111yescharacteristic
236C22×C4×C47#4111yescharacteristic
237C22×C4×C47#4111yescharacteristic
238C22×C4×C47#4111yescharacteristic
239C22×C4×C47C2411yescharacteristic
240C22×Dic47—28no—
241C22×Dic47—22no—
242C22×Dic47—22no—
243C22×Dic47—41no—
244Q16×C47—28no—
245SD16×C47—28no—
246SD16×C47—28no—
247D8×C47—28no—
248M16×C47—22no—
249M16×C47—22no—
250M16×C47—22no—
251M16×C47C22×C414yes—
252C2×C8×C47—22no—
253C2×C8×C47—22no—
254C2×C8×C47—22no—
255C22⋊Dic47—28no—
256C22⋊Dic47—22no—
257C22⋊Dic47—22no—
258C22⋊Dic47—22no—
259C22⋊Dic47—22no—
260C22⋊Dic47—41no—
261C22⋊Dic47C2×D414yes—
262C4⋊Dic47—28no—
263C4⋊Dic47—22no—
264C4⋊Dic47—22no—
265C4⋊Dic47—22no—
266C4⋊Dic47—22no—
267C4⋊Dic47—22no—
268C4⋊Dic47—41no—
269C4×Dic47—28no—
270C4×Dic47—22no—
271C4×Dic47—22no—
272C4×Dic47—22no—
273C4×Dic47—22no—
274C4×Dic47—41no—
275C4×Dic47C2×D414yes—
276#10625329—22no—
277#10625329—22no—
278#10625329—41no—
279#10625329—41no—
280C2×C47⋊C8—22no—
281C2×C47⋊C8—41no—
282C2×C47⋊C8—41no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—22no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—81no—
290C23×C47—82no—
291C23×C47—82no—
292C23×C47C4×D411yescharacteristic
293C23×C47C4×D411yescharacteristic
294C23×C47#12011yescharacteristic
295C23×C47#12011yescharacteristic
296C23×C47#12111yescharacteristic
297C23×C47#12111yescharacteristic
298C23×C47C22×D411yescharacteristic
299Q8×C47—22no—
300Q8×C47—22no—
301Q8×C47—22no—
302Q8×C47—22no—
303Q8×C47—22no—
304Q8×C47—41no—
305Q8×C47—41no—
306Q8×C47C2×C22⋊C414yes—
307D4×C47—24no—
308D4×C47—24no—
309D4×C47—24no—
310D4×C47—24no—
311D4×C47—22no—
312D4×C47—22no—
313D4×C47—22no—
314D4×C47—22no—
315D4×C47—22no—
316D4×C47—42no—
317D4×C47—42no—
318D4×C47—42no—
319D4×C47—42no—
320D4×C47—41no—
321D4×C47—41no—
322D4×C47C2×C22⋊C414yes—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—24no—
327C2×C4×C47—24no—
328C2×C4×C47—24no—
329C2×C4×C47—24no—
330C2×C4×C47—22no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—42no—
334C2×C4×C47—42no—
335C2×C4×C47—42no—
336C2×C4×C47—42no—
337C2×C4×C47C2×C22⋊C411yescharacteristic
338C2×C4×C47C2×C22⋊C411yescharacteristic
339C2×C4×C47C2×C22⋊C411yescharacteristic
340C2×C4×C47C2×C22⋊C411yescharacteristic
341C2×C4×C47C4×D411yescharacteristic
342C2×C4×C47C4×D411yescharacteristic
343C2×C4×C47C4×D411yescharacteristic
344C2×C4×C47C4×D411yescharacteristic
345C2×C4×C47C4×D411yescharacteristic
346C2×C4×C47C4×D411yescharacteristic
347C2×C4×C47#12011yescharacteristic
348C2×C4×C47#12011yescharacteristic
349C2×C4×C47#12111yescharacteristic
350C2×C4×C47#12111yescharacteristic
351C2×C4×C47#12111yescharacteristic
352C2×C4×C47#12111yescharacteristic
353C2×C4×C47#12111yescharacteristic
354C2×C4×C47#12111yescharacteristic
355C2×C4×C47#12311yescharacteristic
356C2×C4×C47#12311yescharacteristic
357C2×C4×C47#12311yescharacteristic
358C2×C4×C47#12311yescharacteristic
359C2×C4×C47C23×C411yescharacteristic
360C2×C4×C47C22×D411yescharacteristic
361C2×C4×C47C22×D411yescharacteristic
362C2×C4×C47C22×D411yescharacteristic
363C2×C4×C47C2×#4111yescharacteristic
364C2×C4×C47C2×#4111yescharacteristic
365C2×Dic47—24no—
366C2×Dic47—24no—
367C2×Dic47—42no—
368C2×Dic47—82no—
369C2×Dic47—82no—
370C2×Dic47—88no—
371C2×Dic47—82no—
372C8×C47—24no—
373C47⋊C8—42no—
374#21000—471nomaximal, Sylow
375C22×C47—24no—
376C22×C47—41no—
377C22×C47—41no—
378C22×C47—41no—
379C22×C47—41no—
380C22×C47—41no—
381C22×C47—41no—
382C22×C47—41no—
383C22×C47—44no—
384C22×C47—42no—
385C22×C47—82no—
386C22×C47—82no—
387C22×C47—82no—
388C22×C47—82no—
389C22×C47—82no—
390C22×C47#38611yescharacteristic
391C22×C47#38611yescharacteristic
392C22×C47#38611yescharacteristic
393C22×C47#38611yescharacteristic
394C22×C47C2×C4×D411yescharacteristic
395C22×C47C2×#12011yescharacteristic
396C22×C47C2×#12111yescharacteristic
397C4×C47—24no—
398C4×C47—42no—
399C4×C47#38611yescharacteristic
400C4×C47#38611yescharacteristic
401C4×C47#38611yescharacteristic
402C4×C47#38611yescharacteristic
403C4×C47C22×C22⋊C411yescharacteristic
404C4×C47C2×C4×D411yescharacteristic
405C4×C47C2×#12111yescharacteristic
406C4×C47C2×#12311yescharacteristic
407Dic47—44no—
408Dic47—44no—
409Dic47—82no—
410C2×#575D4711yescharacteristic
411#3428—471no—
412C2×#421—471no—
413C2×#421—471no—
414C2×#410—471no—
415#1906—478no—
416C2×#344—471no—
417#1733—471no—
418C2×C47—21no—
419C2×C47—21no—
420C2×C47—21no—
421C2×C47—21no—
422C2×C47—21no—
423C2×C47—21no—
424C2×C47—21no—
425C2×C47—44no—
426C2×C47—82no—
427C2×C47C2×#38611yescharacteristic
428C22×#41C2×D4711yescharacteristic
429C22×#41C2×D4711yescharacteristic
430#575—22no—
431#575—22no—
432#575Dic4714yescomplemented
433#575C2×D4714yes—
434C2×#137—21no—
435C2×#137Dic4712yescomplemented
436C2×AGL(1,ℤ/8)—21no—
437C2×AGL(1,ℤ/8)Dic4712yescomplemented
438C2×#135—22no—
439C22×M16—471no—
440C22×M16C2×D4711yescharacteristic
441#520—942no—
442#520—942no—
443#519—941no—
444#518—942no—
445#518—941no—
446C4×#41—474no—
447C4×#41—942no—
448C2×#117—471no—
449C2×#117—471no—
450C2×#117—471no—
451C2×#117—942no—
452#421—474no—
453#421—942no—
454#421—942no—
455#421—942no—
456C2×#104—474no—
457C2×#104—942no—
458#410—474no—
459#410—942no—
460C2×#99—942no—
461#344—474no—
462#339—474no—
463C47#2100011yescharacteristic, complemented, Sylow
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41C2×Dic4712yes—
481C2×#41C2×Dic4712yes—
482C2×#41C2×Dic4712yescomplemented
483C2×#41C22⋊D4712yes—
484C2×#41C22⋊D4712yes—
485C2×#41C22⋊D4712yes—
486C2×#41C22×D4712yes—
487C2×#41C22×D4712yes—
488C22×Q8C2×Dic4711yescharacteristic, complemented
489C22×Q8C22⋊D4711yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4C2×Dic4711yescharacteristic, complemented
493C22×D4C22⋊D4711yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C22×D4711yescharacteristic
497#137—24no—
498#137—24no—
499#137—24no—
500#137C2×Dic4718yescomplemented
501AGL(1,ℤ/8)—24no—
502AGL(1,ℤ/8)—24no—
503AGL(1,ℤ/8)—24no—
504AGL(1,ℤ/8)C2×Dic4718yescomplemented
505#135—28no—
506#135—28no—
507C2×Q16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×D8—22no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—472no—
515C2×M16—941no—
516C2×M16—941no—
517C2×M16—941no—
518C2×M16—941no—
519C2×M16—941no—
520C2×M16C2×Dic4712yescomplemented
521C2×M16C2×Dic4712yescomplemented
522C2×M16C22×D4712yes—
523C22×C8—21no—
524C22×C8—941no—
525C4×Q8—944no—
526C4×Q8—944no—
527C4×D4—948no—
528C4×D4—948no—
529C4×D4—944no—
530C4×D4—944no—
531#117—472no—
532#117—472no—
533#117—472no—
534#117—472no—
535#117—472no—
536#117—944no—
537#117—944no—
538#117—944no—
539#117—941no—
540#117—941no—
541#117—941no—
542#117—941no—
543#117—941no—
544#117—941no—
545#117—941no—
546C2×C4⋊C4—944no—
547C2×C4⋊C4—941no—
548C2×C4⋊C4—941no—
549C2×C4⋊C4—941no—
550C2×C22⋊C4—472no—
551C2×C22⋊C4—944no—
552C2×C22⋊C4—941no—
553C2×C22⋊C4—941no—
554C2×C42—472no—
555C2×C42—944no—
556C2×C42—941no—
557C2×C42—941no—
558#104—948no—
559#104—948no—
560#99—948no—
561C24—21no—
562C24—21no—
563C24D4×D4711yescharacteristic
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—22no—
578#41—22no—
579#41—22no—
580#41—22no—
581#41—22no—
582#41—22no—
583#41—22no—
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41C22⋊Dic4714yes—
593#41C22⋊Dic4714yes—
594#41C22×Dic4714yes—
595#41C2×C22⋊D4714yes—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8C22⋊Dic4712yes—
605C2×Q8C22⋊Dic4712yes—
606C2×Q8C22×Dic4712yes—
607C2×Q8C2×C22⋊D4712yes—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—41no—
628C2×D4C22⋊Dic4712yes—
629C2×D4C22⋊Dic4712yes—
630C2×D4C22×Dic4712yes—
631C2×D4C2×C22⋊D4712yes—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—948no—
647C22×C4—942no—
648C22×C4—942no—
649C22×C4—1881no—
650C22×C4D4×D4711yescharacteristic
651C22×C4D4×D4711yescharacteristic
652C22×C4D4×D4711yescharacteristic
653C22×C4#1062535211yescharacteristic
654C22×C4#1062535211yescharacteristic
655C22×C4#1062535211yescharacteristic
656C22×C4#1062535211yescharacteristic
657C22×C4C22×Dic4711yescharacteristic
658C22×C4C22×Dic4711yescharacteristic
659C22×C4C2×C22⋊D4711yescharacteristic
660C22×C4C2×C22⋊D4711yescharacteristic
661C22×C4C2×C22⋊D4711yescharacteristic
662C22×C4C2×C22⋊D4711yescharacteristic
663C22×C4C23×D4711yescharacteristic
664Q16—28no—
665SD16—28no—
666SD16—28no—
667D8—28no—
668M16—22no—
669M16—22no—
670M16—22no—
671M16—942no—
672M16—942no—
673M16—1881no—
674M16—1881no—
675M16C22×Dic4714yes—
676C2×C8—22no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—942no—
680C2×C8—1881no—
681C2×C8—1881no—
682C4⋊C4—948no—
683C4⋊C4—942no—
684C4⋊C4—942no—
685C4⋊C4—942no—
686C4⋊C4—942no—
687C4⋊C4—942no—
688C4⋊C4—1881no—
689C22⋊C4—474no—
690C22⋊C4—948no—
691C22⋊C4—942no—
692C22⋊C4—942no—
693C22⋊C4—942no—
694C22⋊C4—942no—
695C22⋊C4—1881no—
696C42—474no—
697C42—948no—
698C42—942no—
699C42—942no—
700C42—942no—
701C42—942no—
702C42—1881no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—81no—
710C23—82no—
711C23—82no—
712C23D4×Dic4711yescharacteristic
713C23D4×Dic4711yescharacteristic
714C23#1309399211yescharacteristic
715C23#1309399211yescharacteristic
716C23#1309399611yescharacteristic
717C23#1309399611yescharacteristic
718C23C2×D4×D4711yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—41no—
725Q8—41no—
726Q8C2×C22⋊Dic4714yes—
727D4—24no—
728D4—24no—
729D4—24no—
730D4—24no—
731D4—22no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—41no—
741D4—41no—
742D4C2×C22⋊Dic4714yes—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—944no—
758C2×C4—944no—
759C2×C4—3762no—
760C2×C4—3762no—
761C2×C4—3762no—
762C2×C4—3768no—
763C2×C4—1882no—
764C2×C4C2×C22⋊Dic4711yescharacteristic
765C2×C4C2×C22⋊Dic4711yescharacteristic
766C2×C4C2×C22⋊Dic4711yescharacteristic
767C2×C4C2×C22⋊Dic4711yescharacteristic
768C2×C4D4×Dic4711yescharacteristic
769C2×C4D4×Dic4711yescharacteristic
770C2×C4D4×Dic4711yescharacteristic
771C2×C4D4×Dic4711yescharacteristic
772C2×C4D4×Dic4711yescharacteristic
773C2×C4D4×Dic4711yescharacteristic
774C2×C4#1309399211yescharacteristic
775C2×C4#1309399211yescharacteristic
776C2×C4#1309399611yescharacteristic
777C2×C4#1309399611yescharacteristic
778C2×C4#1309399611yescharacteristic
779C2×C4#1309399611yescharacteristic
780C2×C4#1309399611yescharacteristic
781C2×C4#1309399611yescharacteristic
782C2×C4#1309400511yescharacteristic
783C2×C4#1309400511yescharacteristic
784C2×C4#1309400511yescharacteristic
785C2×C4#1309400511yescharacteristic
786C2×C4C23×Dic4711yescharacteristic
787C2×C4C2×D4×D4711yescharacteristic
788C2×C4C22×C22⋊D4711yescharacteristic
789C2×C4C22×C22⋊D4711yescharacteristic
790C2×C4C2×#1062535211yescharacteristic
791C2×C4C2×#1062535211yescharacteristic
792C8—24no—
793C8—1882no—
794C22—24no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—44no—
803C22—42no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22#1568900311yescharacteristic
810C22#1568900311yescharacteristic
811C22#1568900311yescharacteristic
812C22#1568900311yescharacteristic
813C22C2×D4×Dic4711yescharacteristic
814C22C2×#1309399211yescharacteristic
815C22C2×#1309399611yescharacteristic
816C4—24no—
817C4—42no—
818C4—3762no—
819C4—1884no—
820C4—1884no—
821C4#1568900311yescharacteristic
822C4#1568900311yescharacteristic
823C4#1568900311yescharacteristic
824C4#1568900311yescharacteristic
825C4C22×C22⋊Dic4711yescharacteristic
826C4C2×D4×Dic4711yescharacteristic
827C4C2×#1309399611yescharacteristic
828C4C2×#1309400511yescharacteristic
829C2—21no—
830C2—21no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—21no—
835C2—21no—
836C2—44no—
837C2—82no—
838C2C2×#1568900311yescharacteristic
subgroupG/H
centerC4C2×#13093996
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#575C2
socleC2×C47C2×#386
cosocleC22×C4×C47C24
hypercenterC2×#575D47
hypocenterC47#21000
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. #20256591C2semidirect
2. C2×#15689140C2semidirect
3. C2×#15689140C2semidirect
4. C2×#15689097C2semidirect
5. #20243891C2semidirect
6. C2×#15688895C2semidirect
7. #20243099C2semidirect
16. #41×Dic47C22semidirect
24. #15689140C22semidirect
26. C2×#13093951C22semidirect
28. #15689097C22semidirect
30. #15688895C22semidirect
31. #15688884C22semidirect
36. C47×#575C4semidirect
39. C2×#137×C47C4semidirect
41. C2×AGL(1,ℤ/8)×C47C4semidirect
105. C2×#41×C47C2×C4semidirect
111. C22×Q8×C47C2×C4semidirect
115. C22×D4×C47C2×C4semidirect
123. #137×C47C2×C4semidirect
127. AGL(1,ℤ/8)×C47C2×C4semidirect
137. C2×M16×C47C2×C4semidirect
138. C2×M16×C47C2×C4semidirect
432. #575Dic47semidirect
435. C2×#137Dic47semidirect
437. C2×AGL(1,ℤ/8)Dic47semidirect
463. C47#21000semidirect
482. C2×#41C2×Dic47semidirect
488. C22×Q8C2×Dic47semidirect
492. C22×D4C2×Dic47semidirect
500. #137C2×Dic47semidirect
504. AGL(1,ℤ/8)C2×Dic47semidirect
520. C2×M16C2×Dic47semidirect
521. C2×M16C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
#202565912
C2×#156891402
C2×#156890972
#202438912
C2×#156888952
#202430992
C2×C47×#5752
#2100047