Finite Group Databasebeta

← C47×#24436 #26064134

Subgroups — C47×#24436 #26064134

Order 12032.

1582 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#546C211yesmaximal, characteristic
2C2×C47×#465C211yesmaximal, characteristic, complemented
3C2×C47×#452C211yesmaximal, characteristic, complemented
4C2×C47×#450C211yesmaximal, characteristic, complemented
5C2×C47×#416C211yesmaximal, characteristic, complemented
6C47×#2415C211yesmaximal, characteristic, complemented
7C47×#2042C211yesmaximal, characteristic, complemented
8C47×#2035C211yesmaximal, characteristic, complemented
9C47×#2015C211yesmaximal, characteristic, complemented
10C47×#2001C211yesmaximal, characteristic, complemented
11C47×#1877C211yesmaximal, characteristic, complemented
12C47×#1875C211yesmaximal, characteristic, complemented
13C47×#1869C211yesmaximal, characteristic, complemented
14C47×#1864C211yesmaximal, characteristic, complemented
15C47×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C23×D4×C47C2211yescharacteristic
18C22×Q16×C47C2211yescharacteristic, complemented
19C22×SD16×C47C2211yescharacteristic
20C22×SD16×C47C2211yescharacteristic
21C23×C8×C47C2211yescharacteristic, complemented
22C47×#546—24no—
23C47×#546—24no—
24C2×#124×C47C2211yescharacteristic
25C2×#123×C47—21no—
26C2×C22⋊Q8×C47C2211yescharacteristic
27C2×C22⋊Q8×C47C2211yescharacteristic
28C2×C22⋊Q8×C47C2211yescharacteristic, complemented
29C2×#121×C47—21no—
30C2×#121×C47C2211yescharacteristic
31C2×#120×C47—21no—
32C2×C4×D4×C47C2211yescharacteristic
33C2×C4×D4×C47C2211yescharacteristic
34C2×#117×C47C2211yescharacteristic, complemented
35C22×C22⋊C4×C47—21no—
36C47×#465—24no—
37C47×#452—24no—
38C47×#450—24no—
39C2×#106×C47C2211yescharacteristic, complemented
40C47×#416—24no—
41C2×#103×C47C2211yescharacteristic, complemented
42C2×#103×C47C2211yescharacteristic, complemented
43C2×#103×C47C2211yescharacteristic, complemented
44C2×#103×C47C2211yescharacteristic, complemented
45C2×#102×C47C2211yescharacteristic
46C2×#102×C47C2211yescharacteristic
47C2×#102×C47C2211yescharacteristic
48C2×#102×C47C2211yescharacteristic
49C2×#102×C47C2211yescharacteristic
50C2×#102×C47C2211yescharacteristic
51C2×C22⋊C8×C47C2211yescharacteristic
52C2×C22⋊C8×C47C2211yescharacteristic
53C2×C22⋊C8×C47C2211yescharacteristic, complemented
54C47×#397—21no—
55C47×#394—21no—
56C47×#391C2211yescharacteristic, complemented
57C47×#389—21no—
58C47×#389C2211yescharacteristic, complemented
59C47×#388—21no—
60C47×#380C2211yescharacteristic
61C47×#340C2211yescharacteristic, complemented
62C47×#340C2211yescharacteristic, complemented
63C47×#336C2211yescharacteristic, complemented
64C47×#336C2211yescharacteristic, complemented
65C25×C47—21no—
66C2×#41×C47—22no—
67C2×#41×C47—22no—
68C2×#41×C47—22no—
69C2×#41×C47—41no—
70C2×#41×C47—41no—
71C2×#41×C47D414yes—
72C22×Q8×C47C2311yescharacteristic
73C22×Q8×C47C2311yescharacteristic
74C22×D4×C47—21no—
75C22×D4×C47—21no—
76C22×D4×C47—22no—
77C22×D4×C47—22no—
78C22×D4×C47—22no—
79C22×D4×C47—22no—
80C22×D4×C47—21no—
81C22×D4×C47—41no—
82C22×D4×C47—41no—
83C22×D4×C47D411yescharacteristic
84C22×D4×C47C2311yescharacteristic
85C22×D4×C47C2311yescharacteristic
86C23×C4×C47—21no—
87C23×C4×C47—21no—
88C23×C4×C47C2311yescharacteristic
89C23×C4×C47C2311yescharacteristic
90C2×Q16×C47—22no—
91C2×Q16×C47—41no—
92C2×Q16×C47—41no—
93C2×SD16×C47—22no—
94C2×SD16×C47—22no—
95C2×SD16×C47—22no—
96C2×SD16×C47—22no—
97C2×SD16×C47—22no—
98C2×SD16×C47—41no—
99C22×C8×C47—22no—
100C22×C8×C47—22no—
101C22×C8×C47—41no—
102C22×C8×C47C2311yescharacteristic
103C22×C8×C47C2311yescharacteristic
104C22×C8×C47C2311yescharacteristic
105C22×C8×C47C2311yescharacteristic
106#124×C47—22no—
107#124×C47—22no—
108#123×C47—28no—
109C22⋊Q8×C47—22no—
110C22⋊Q8×C47—22no—
111C22⋊Q8×C47—22no—
112C22⋊Q8×C47—22no—
113C22⋊Q8×C47—22no—
114C22⋊Q8×C47—41no—
115#121×C47—28no—
116#121×C47—22no—
117#121×C47D414yes—
118#120×C47—28no—
119C4×D4×C47—22no—
120C4×D4×C47—22no—
121C4×D4×C47—22no—
122C4×D4×C47—22no—
123#117×C47—22no—
124#117×C47—41no—
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47—21no—
128C2×C4⋊C4×C47—21no—
129C2×C4⋊C4×C47D411yescharacteristic
130C2×C4⋊C4×C47C2311yescharacteristic
131C2×C4⋊C4×C47C2311yescharacteristic
132C2×C4⋊C4×C47C2311yescharacteristic
133C2×C4⋊C4×C47C2311yescharacteristic
134C2×C22⋊C4×C47—28no—
135C2×C22⋊C4×C47—21no—
136C2×C22⋊C4×C47—21no—
137C2×C22⋊C4×C47—21no—
138C2×C22⋊C4×C47—21no—
139C2×C22⋊C4×C47—21no—
140C2×C22⋊C4×C47—21no—
141C2×C22⋊C4×C47—21no—
142C2×C22⋊C4×C47—21no—
143C2×C22⋊C4×C47—21no—
144C2×C22⋊C4×C47D411yescharacteristic
145C2×C22⋊C4×C47D411yescharacteristic
146C2×C42×C47—21no—
147C2×C42×C47C2311yescharacteristic
148#106×C47—22no—
149#103×C47—22no—
150#103×C47—22no—
151#103×C47—22no—
152#103×C47—22no—
153#102×C47—22no—
154#102×C47—22no—
155#102×C47—22no—
156#102×C47—22no—
157#102×C47—41no—
158#102×C47D414yescomplemented
159C22⋊C8×C47—22no—
160C22⋊C8×C47—22no—
161C22⋊C8×C47—41no—
162#95×C47—21no—
163#95×C47—21no—
164#95×C47—21no—
165#95×C47—21no—
166C24×C47—21no—
167C24×C47—24no—
168C24×C47—21no—
169C24×C47—42no—
170C24×C47—42no—
171C24×C47—42no—
172C24×C47—42no—
173C24×C47—81no—
174C24×C47—81no—
175C24×C47C2×D411yescharacteristic
176C24×C47C2×D411yescharacteristic
177#41×C47—28no—
178#41×C47—44no—
179#41×C47—44no—
180#41×C47—44no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47—21no—
191C2×Q8×C47—21no—
192C2×Q8×C47C2×D412yes—
193C2×D4×C47—24no—
194C2×D4×C47—22no—
195C2×D4×C47—24no—
196C2×D4×C47—22no—
197C2×D4×C47—24no—
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—21no—
205C2×D4×C47—21no—
206C2×D4×C47—41no—
207C2×D4×C47—42no—
208C2×D4×C47—42no—
209C2×D4×C47—44no—
210C2×D4×C47—44no—
211C2×D4×C47—44no—
212C2×D4×C47—42no—
213C2×D4×C47—42no—
214C2×D4×C47—44no—
215C2×D4×C47—81no—
216C2×D4×C47—81no—
217C2×D4×C47C2×D412yes—
218C2×D4×C47C2×D412yes—
219C2×D4×C47C2×D412yes—
220C2×D4×C47#4112yes—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—24no—
229C22×C4×C47—24no—
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—21no—
239C22×C4×C47—42no—
240C22×C4×C47—42no—
241C22×C4×C47—81no—
242C22×C4×C47—81no—
243C22×C4×C47C2×D411yescharacteristic
244C22×C4×C47C2×D411yescharacteristic
245C22×C4×C47C2×D411yescharacteristic
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2×D412yes—
248C22×C4×C47C2×D412yes—
249C22×C4×C47C2411yescharacteristic
250Q16×C47—44no—
251SD16×C47—44no—
252SD16×C47—44no—
253C2×C8×C47—21no—
254C2×C8×C47—21no—
255C2×C8×C47—21no—
256C2×C8×C47—21no—
257C2×C8×C47—21no—
258C2×C8×C47—21no—
259C2×C8×C47—21no—
260C2×C8×C47—21no—
261C2×C8×C47—21no—
262C2×C8×C47—21no—
263C2×C8×C47—21no—
264C2×C8×C47—44no—
265C2×C8×C47C2×D412yes—
266C4⋊C4×C47—24no—
267C4⋊C4×C47—22no—
268C4⋊C4×C47—21no—
269C4⋊C4×C47—21no—
270C4⋊C4×C47—21no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47—21no—
273C4⋊C4×C47—21no—
274C4⋊C4×C47—42no—
275C4⋊C4×C47—42no—
276C4⋊C4×C47—42no—
277C4⋊C4×C47C2×D412yes—
278C4⋊C4×C47C2×D412yes—
279C22⋊C4×C47—24no—
280C22⋊C4×C47—24no—
281C22⋊C4×C47—24no—
282C22⋊C4×C47—24no—
283C22⋊C4×C47—22no—
284C22⋊C4×C47—22no—
285C22⋊C4×C47—24no—
286C22⋊C4×C47—42no—
287C22⋊C4×C47—42no—
288C22⋊C4×C47—42no—
289C22⋊C4×C47—42no—
290C42×C47—21no—
291C42×C47—21no—
292C42×C47—42no—
293C23×C47—21no—
294C23×C47—22no—
295C23×C47—21no—
296C23×C47—21no—
297C23×C47—22no—
298C23×C47—21no—
299C23×C47—21no—
300C23×C47—22no—
301C23×C47—21no—
302C23×C47—21no—
303C23×C47—21no—
304C23×C47—21no—
305C23×C47—21no—
306C23×C47—21no—
307C23×C47—21no—
308C23×C47—22no—
309C23×C47—48no—
310C23×C47—48no—
311C23×C47—41no—
312C23×C47—41no—
313C23×C47—41no—
314C23×C47—41no—
315C23×C47—41no—
316C23×C47—41no—
317C23×C47—41no—
318C23×C47—41no—
319C23×C47—41no—
320C23×C47—41no—
321C23×C47—84no—
322C23×C47—84no—
323C23×C47—84no—
324C23×C47—84no—
325C23×C47—84no—
326C23×C47#12012yes—
327C23×C47#13512yes—
328C23×C47C22×D411yescharacteristic
329Q8×C47—22no—
330Q8×C47—22no—
331Q8×C47—41no—
332Q8×C47—41no—
333Q8×C47—41no—
334Q8×C47—41no—
335Q8×C47—41no—
336Q8×C47—41no—
337D4×C47—22no—
338D4×C47—22no—
339D4×C47—22no—
340D4×C47—22no—
341D4×C47—22no—
342D4×C47—44no—
343D4×C47—48no—
344D4×C47—48no—
345D4×C47—41no—
346D4×C47—41no—
347D4×C47—84no—
348D4×C47#12114yes—
349C2×C4×C47—21no—
350C2×C4×C47—21no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—21no—
356C2×C4×C47—21no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—21no—
360C2×C4×C47—22no—
361C2×C4×C47—21no—
362C2×C4×C47—21no—
363C2×C4×C47—21no—
364C2×C4×C47—21no—
365C2×C4×C47—21no—
366C2×C4×C47—21no—
367C2×C4×C47—48no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—84no—
388C2×C4×C47#12012yes—
389C2×C4×C47C22×D411yescharacteristic
390C2×C4×C47C22×D411yescharacteristic
391C2×C4×C47C22×D411yescharacteristic
392C2×C4×C47C2×#4111yescharacteristic
393C2×C4×C47H(5,𝔽2)11yescharacteristic
394C2×C4×C47H(5,𝔽2)11yescharacteristic
395C8×C47—22no—
396C8×C47—41no—
397C8×C47—41no—
398C8×C47—41no—
399#24436C4711yesmaximal, characteristic, direct product factor, Sylow
400C22×C47—22no—
401C22×C47—24no—
402C22×C47—22no—
403C22×C47—22no—
404C22×C47—22no—
405C22×C47—22no—
406C22×C47—22no—
407C22×C47—41no—
408C22×C47—42no—
409C22×C47—42no—
410C22×C47—41no—
411C22×C47—41no—
412C22×C47—41no—
413C22×C47—42no—
414C22×C47—41no—
415C22×C47—42no—
416C22×C47—41no—
417C22×C47—42no—
418C22×C47—41no—
419C22×C47—41no—
420C22×C47—42no—
421C22×C47—42no—
422C22×C47—42no—
423C22×C47—42no—
424C22×C47—816no—
425C22×C47—81no—
426C22×C47—81no—
427C22×C47—81no—
428C22×C47—81no—
429C22×C47C2×#12011yescharacteristic
430C22×C47D4211yescharacteristic
431C22×C47#54611yescharacteristic
432C22×C47C2×#13511yescharacteristic
433C22×C47#57511yescharacteristic
434C22×C47#57711yescharacteristic
435C22×C47#57711yescharacteristic
436C4×C47—22no—
437C4×C47—41no—
438C4×C47—42no—
439C4×C47—41no—
440C4×C47—41no—
441C4×C47—42no—
442C4×C47—42no—
443C4×C47—81no—
444C4×C47—81no—
445C4×C47—81no—
446C4×C47C2×#12111yescharacteristic
447C4×C47#53411yescharacteristic
448C4×C47D4211yescharacteristic
449C4×C47#54611yescharacteristic
450C2×#546C2×C4711yescharacteristic
451C2×#465C2×C4711yescharacteristic, complemented
452C2×#452C2×C4711yescharacteristic, complemented
453C2×#450C2×C4711yescharacteristic, complemented
454C2×#416C2×C4711yescharacteristic, complemented
455#2415C2×C4711yescharacteristic, complemented
456#2042C2×C4711yescharacteristic, complemented
457#2035C2×C4711yescharacteristic, complemented
458#2015C2×C4711yescharacteristic, complemented
459#2001C2×C4711yescharacteristic, complemented
460#1877C2×C4711yescharacteristic, complemented
461#1875C2×C4711yescharacteristic, complemented
462#1869C2×C4711yescharacteristic, complemented
463#1864C2×C4711yescharacteristic, complemented
464#1786C2×C4711yescharacteristic, complemented
465C2×C47—42no—
466C2×C47—42no—
467C2×C47—44no—
468C2×C47—82no—
469C2×C47#241011yescharacteristic
470C2×C47#300211yescharacteristic
471C2×C47#300911yescharacteristic
472C2×C47#326711yescharacteristic
473C2×C47#328211yescharacteristic
474C2×C47#329611yescharacteristic
475C2×C47#331111yescharacteristic
476C22×#41C22×C4711yescharacteristic
477C23×D4C22×C4711yescharacteristic
478C22×Q16C22×C4711yescharacteristic, complemented
479C22×SD16C22×C4711yescharacteristic
480C22×SD16C22×C4711yescharacteristic
481C23×C8C22×C4711yescharacteristic, complemented
482#546—24no—
483#546—24no—
484C2×#124C22×C4711yescharacteristic
485C2×#123—21no—
486C2×C22⋊Q8C22×C4711yescharacteristic
487C2×C22⋊Q8C22×C4711yescharacteristic
488C2×C22⋊Q8C22×C4711yescharacteristic, complemented
489C2×#121—21no—
490C2×#121C22×C4711yescharacteristic
491C2×#120—21no—
492C2×C4×D4C22×C4711yescharacteristic
493C2×C4×D4C22×C4711yescharacteristic
494C2×#117C22×C4711yescharacteristic, complemented
495C22×C22⋊C4—21no—
496#465—24no—
497#452—24no—
498#450—24no—
499C2×#106C22×C4711yescharacteristic, complemented
500#416—24no—
501C2×#103C22×C4711yescharacteristic, complemented
502C2×#103C22×C4711yescharacteristic, complemented
503C2×#103C22×C4711yescharacteristic, complemented
504C2×#103C22×C4711yescharacteristic, complemented
505C2×#102C22×C4711yescharacteristic
506C2×#102C22×C4711yescharacteristic
507C2×#102C22×C4711yescharacteristic
508C2×#102C22×C4711yescharacteristic
509C2×#102C22×C4711yescharacteristic
510C2×#102C22×C4711yescharacteristic
511C2×C22⋊C8C22×C4711yescharacteristic
512C2×C22⋊C8C22×C4711yescharacteristic
513C2×C22⋊C8C22×C4711yescharacteristic, complemented
514#397—21no—
515#394—21no—
516#391C22×C4711yescharacteristic, complemented
517#389—21no—
518#389C22×C4711yescharacteristic, complemented
519#388—21no—
520#380C22×C4711yescharacteristic
521#340C22×C4711yescharacteristic, complemented
522#340C22×C4711yescharacteristic, complemented
523#336C22×C4711yescharacteristic, complemented
524#336C22×C4711yescharacteristic, complemented
525C47#2443611yescharacteristic, direct product factor, Sylow
526C25—21no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—41no—
531C2×#41—41no—
532C2×#41D4×C4714yes—
533C22×Q8C23×C4711yescharacteristic
534C22×Q8C23×C4711yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—22no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—21no—
542C22×D4—41no—
543C22×D4—41no—
544C22×D4D4×C4711yescharacteristic
545C22×D4C23×C4711yescharacteristic
546C22×D4C23×C4711yescharacteristic
547C23×C4—21no—
548C23×C4—21no—
549C23×C4C23×C4711yescharacteristic
550C23×C4C23×C4711yescharacteristic
551C2×Q16—22no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—41no—
560C22×C8—22no—
561C22×C8—22no—
562C22×C8—41no—
563C22×C8C23×C4711yescharacteristic
564C22×C8C23×C4711yescharacteristic
565C22×C8C23×C4711yescharacteristic
566C22×C8C23×C4711yescharacteristic
567#124—22no—
568#124—22no—
569#123—28no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—41no—
576#121—28no—
577#121—22no—
578#121D4×C4714yes—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—22no—
585#117—41no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4D4×C4711yescharacteristic
591C2×C4⋊C4C23×C4711yescharacteristic
592C2×C4⋊C4C23×C4711yescharacteristic
593C2×C4⋊C4C23×C4711yescharacteristic
594C2×C4⋊C4C23×C4711yescharacteristic
595C2×C22⋊C4—28no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4D4×C4711yescharacteristic
606C2×C22⋊C4D4×C4711yescharacteristic
607C2×C42—21no—
608C2×C42C23×C4711yescharacteristic
609#106—22no—
610#103—22no—
611#103—22no—
612#103—22no—
613#103—22no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—22no—
618#102—41no—
619#102D4×C4714yescomplemented
620C22⋊C8—22no—
621C22⋊C8—22no—
622C22⋊C8—41no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627C24—21no—
628C24—24no—
629C24—21no—
630C24—42no—
631C24—42no—
632C24—42no—
633C24—42no—
634C24—81no—
635C24—81no—
636C24C2×D4×C4711yescharacteristic
637C24C2×D4×C4711yescharacteristic
638#41—28no—
639#41—44no—
640#41—44no—
641#41—44no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8C2×D4×C4712yes—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—41no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—44no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4C2×D4×C4712yes—
679C2×D4C2×D4×C4712yes—
680C2×D4C2×D4×C4712yes—
681C2×D4#41×C4712yes—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—81no—
703C22×C4—81no—
704C22×C4C2×D4×C4711yescharacteristic
705C22×C4C2×D4×C4711yescharacteristic
706C22×C4C2×D4×C4711yescharacteristic
707C22×C4C2×D4×C4711yescharacteristic
708C22×C4C2×D4×C4712yes—
709C22×C4C2×D4×C4712yes—
710C22×C4C24×C4711yescharacteristic
711Q16—44no—
712SD16—44no—
713SD16—44no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—44no—
726C2×C8C2×D4×C4712yes—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4C2×D4×C4712yes—
739C4⋊C4C2×D4×C4712yes—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—24no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C42—21no—
752C42—21no—
753C42—42no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—48no—
771C23—48no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—84no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23—84no—
787C23#120×C4712yes—
788C23#135×C4712yes—
789C23C22×D4×C4711yescharacteristic
790Q8—22no—
791Q8—22no—
792Q8—41no—
793Q8—41no—
794Q8—41no—
795Q8—41no—
796Q8—41no—
797Q8—41no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—44no—
804D4—48no—
805D4—48no—
806D4—41no—
807D4—41no—
808D4—84no—
809D4#121×C4714yes—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—48no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—84no—
849C2×C4#120×C4712yes—
850C2×C4C22×D4×C4711yescharacteristic
851C2×C4C22×D4×C4711yescharacteristic
852C2×C4C22×D4×C4711yescharacteristic
853C2×C4C2×#41×C4711yescharacteristic
854C2×C4H(5,𝔽2)×C4711yescharacteristic
855C2×C4H(5,𝔽2)×C4711yescharacteristic
856C8—22no—
857C8—41no—
858C8—41no—
859C8—41no—
860C22—22no—
861C22—22no—
862C22—24no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—41no—
873C22—42no—
874C22—42no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—42no—
879C22—41no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—816no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22C2×#120×C4711yescharacteristic
890C22D42×C4711yescharacteristic
891C22C47×#54611yescharacteristic
892C22C2×#135×C4711yescharacteristic
893C22C47×#57511yescharacteristic
894C22C47×#57711yescharacteristic
895C22C47×#57711yescharacteristic
896C4—22no—
897C4—41no—
898C4—42no—
899C4—41no—
900C4—41no—
901C4—42no—
902C4—42no—
903C4—81no—
904C4—81no—
905C4—81no—
906C4C2×#121×C4711yescharacteristic
907C4C47×#53411yescharacteristic
908C4D42×C4711yescharacteristic
909C4C47×#54611yescharacteristic
910C2—42no—
911C2—42no—
912C2—44no—
913C2—82no—
914C2C47×#241011yescharacteristic
915C2C47×#300211yescharacteristic
916C2C47×#300911yescharacteristic
917C2C47×#326711yescharacteristic
918C2C47×#328211yescharacteristic
919C2C47×#329611yescharacteristic
920C2C47×#331111yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#546C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C4×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#465C2semidirect
3. C2×C47×#452C2semidirect
4. C2×C47×#450C2semidirect
5. C2×C47×#416C2semidirect
6. C47×#2415C2semidirect
7. C47×#2042C2semidirect
8. C47×#2035C2semidirect
9. C47×#2015C2semidirect
10. C47×#2001C2semidirect
11. C47×#1877C2semidirect
12. C47×#1875C2semidirect
13. C47×#1869C2semidirect
14. C47×#1864C2semidirect
15. C47×#1786C2semidirect
18. C22×Q16×C47C22semidirect
21. C23×C8×C47C22semidirect
28. C2×C22⋊Q8×C47C22semidirect
34. C2×#117×C47C22semidirect
39. C2×#106×C47C22semidirect
41. C2×#103×C47C22semidirect
42. C2×#103×C47C22semidirect
43. C2×#103×C47C22semidirect
44. C2×#103×C47C22semidirect
53. C2×C22⋊C8×C47C22semidirect
56. C47×#391C22semidirect
58. C47×#389C22semidirect
61. C47×#340C22semidirect
62. C47×#340C22semidirect
63. C47×#336C22semidirect
64. C47×#336C22semidirect
158. #102×C47D4semidirect
399. #24436C47direct (N × H)
451. C2×#465C2×C47semidirect
452. C2×#452C2×C47semidirect
453. C2×#450C2×C47semidirect
454. C2×#416C2×C47semidirect
455. #2415C2×C47semidirect
456. #2042C2×C47semidirect
457. #2035C2×C47semidirect
458. #2015C2×C47semidirect
459. #2001C2×C47semidirect
460. #1877C2×C47semidirect
461. #1875C2×C47semidirect
462. #1869C2×C47semidirect
463. #1864C2×C47semidirect
464. #1786C2×C47semidirect
478. C22×Q16C22×C47semidirect
481. C23×C8C22×C47semidirect
488. C2×C22⋊Q8C22×C47semidirect
494. C2×#117C22×C47semidirect
499. C2×#106C22×C47semidirect
501. C2×#103C22×C47semidirect
502. C2×#103C22×C47semidirect
503. C2×#103C22×C47semidirect
504. C2×#103C22×C47semidirect
513. C2×C22⋊C8C22×C47semidirect
516. #391C22×C47semidirect
518. #389C22×C47semidirect
521. #340C22×C47semidirect
522. #340C22×C47semidirect
523. #336C22×C47semidirect
524. #336C22×C47semidirect
525. C47#24436direct (N × H)
619. #102D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5462
C2×C47×#4652
C2×C47×#4522
C2×C47×#4502
C2×C47×#4162
C47×#24152
C47×#20422
C47×#20352
C47×#20152
C47×#20012
C47×#18772
C47×#18752
C47×#18692
C47×#18642
C47×#17862
#2443647