Finite Group Databasebeta

← C47×#24455 #26064153

Subgroups — C47×#24455 #26064153

Order 12032.

1480 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#548C211yesmaximal, characteristic, complemented
2C2×C47×#469C211yesmaximal, characteristic, complemented
3C2×C47×#449C211yesmaximal, characteristic, complemented
4C2×C47×#448C211yesmaximal, characteristic, complemented
5C2×C47×#419C211yesmaximal, characteristic, complemented
6C47×#2414C211yesmaximal, characteristic, complemented
7C47×#2042C211yesmaximal, characteristic, complemented
8C47×#2035C211yesmaximal, characteristic, complemented
9C47×#2012C211yesmaximal, characteristic, complemented
10C47×#2000C211yesmaximal, characteristic, complemented
11C47×#1880C211yesmaximal, characteristic, complemented
12C47×#1875C211yesmaximal, characteristic, complemented
13C47×#1870C211yesmaximal, characteristic, complemented
14C47×#1865C211yesmaximal, characteristic, complemented
15C47×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C23×Q8×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C22×SD16×C47C2211yescharacteristic
20C22×D8×C47C2211yescharacteristic
21C22×M16×C47C2211yescharacteristic
22C47×#548—24no—
23C47×#548—24no—
24C2×#124×C47—21no—
25C2×#124×C47C2211yescharacteristic
26C2×C22⋊Q8×C47—21no—
27C2×C22⋊Q8×C47C2211yescharacteristic
28C2×#121×C47—21no—
29C2×#121×C47C2211yescharacteristic
30C2×#121×C47C2211yescharacteristic
31C2×#121×C47C2211yescharacteristic
32C2×C4×Q8×C47C2211yescharacteristic
33C2×C4×D4×C47—21no—
34C2×C4×D4×C47C2211yescharacteristic
35C2×#117×C47C2211yescharacteristic
36C47×#469—24no—
37C47×#449—24no—
38C47×#448—24no—
39C2×#106×C47C2211yescharacteristic
40C47×#419—24no—
41C2×#103×C47C2211yescharacteristic
42C2×#103×C47C2211yescharacteristic
43C2×#103×C47C2211yescharacteristic
44C2×#103×C47C2211yescharacteristic
45C2×#103×C47C2211yescharacteristic
46C2×#103×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
54C47×#394—21no—
55C47×#392—21no—
56C47×#390—21no—
57C47×#390C2211yescharacteristic
58C47×#389C2211yescharacteristic
59C47×#388—21no—
60C47×#380C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C47×#336C2211yescharacteristic
64C47×#336C2211yescharacteristic
65C2×#41×C47—22no—
66C2×#41×C47—22no—
67C2×#41×C47—22no—
68C2×#41×C47—22no—
69C2×#41×C47—41no—
70C2×#41×C47—41no—
71C22×Q8×C47—21no—
72C22×Q8×C47—22no—
73C22×Q8×C47—22no—
74C22×Q8×C47—22no—
75C22×Q8×C47—41no—
76C22×Q8×C47—41no—
77C22×Q8×C47D414yescomplemented
78C22×Q8×C47C2311yescharacteristic
79C22×Q8×C47C2311yescharacteristic
80C22×D4×C47—21no—
81C22×D4×C47—21no—
82C22×D4×C47—21no—
83C22×D4×C47—21no—
84C22×D4×C47D411yescharacteristic
85C22×D4×C47C2311yescharacteristic
86C22×D4×C47C2311yescharacteristic
87C23×C4×C47—21no—
88C23×C4×C47—21no—
89C23×C4×C47C2311yescharacteristic
90C23×C4×C47C2311yescharacteristic
91C2×SD16×C47—22no—
92C2×SD16×C47—22no—
93C2×SD16×C47—22no—
94C2×SD16×C47—22no—
95C2×SD16×C47—41no—
96C2×SD16×C47—41no—
97C2×D8×C47—22no—
98C2×D8×C47—22no—
99C2×D8×C47—41no—
100C2×M16×C47—22no—
101C2×M16×C47—22no—
102C2×M16×C47—41no—
103C22×C8×C47C2311yescharacteristic
104C22×C8×C47C2311yescharacteristic
105C22×C8×C47C2311yescharacteristic
106C22×C8×C47C2311yescharacteristic
107#124×C47—28no—
108#124×C47—22no—
109#124×C47—22no—
110C22⋊Q8×C47—28no—
111C22⋊Q8×C47—22no—
112C22⋊Q8×C47—22no—
113#121×C47—28no—
114#121×C47—22no—
115#121×C47—22no—
116#121×C47—22no—
117#121×C47—22no—
118#121×C47—41no—
119#121×C47D414yescomplemented
120C4×Q8×C47—22no—
121C4×Q8×C47—22no—
122C4×D4×C47—28no—
123C4×D4×C47—22no—
124C4×D4×C47—22no—
125#117×C47—22no—
126#117×C47—41no—
127C2×C4⋊C4×C47—21no—
128C2×C4⋊C4×C47—21no—
129C2×C4⋊C4×C47—21no—
130C2×C4⋊C4×C47D411yescharacteristic
131C2×C4⋊C4×C47C2311yescharacteristic
132C2×C4⋊C4×C47C2311yescharacteristic
133C2×C4⋊C4×C47C2311yescharacteristic
134C2×C4⋊C4×C47C2311yescharacteristic
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×C47—21no—
145C2×C22⋊C4×C47D411yescharacteristic
146C2×C22⋊C4×C47D411yescharacteristic
147C2×C42×C47—21no—
148C2×C42×C47—21no—
149C2×C42×C47C2311yescharacteristic
150#106×C47—22no—
151#103×C47—22no—
152#103×C47—22no—
153#103×C47—22no—
154#103×C47—22no—
155#103×C47—22no—
156#103×C47D414yescomplemented
157#102×C47—22no—
158#102×C47—22no—
159#102×C47—22no—
160#102×C47—41no—
161C22⋊C8×C47—22no—
162C22⋊C8×C47—22no—
163C22⋊C8×C47—41no—
164#95×C47—21no—
165#95×C47—21no—
166C24×C47—21no—
167C24×C47—21no—
168C24×C47C2×D411yescharacteristic
169C24×C47C2×D411yescharacteristic
170#41×C47—44no—
171#41×C47—44no—
172#41×C47—44no—
173#41×C47—44no—
174C2×Q8×C47—24no—
175C2×Q8×C47—21no—
176C2×Q8×C47—21no—
177C2×Q8×C47—21no—
178C2×Q8×C47—21no—
179C2×Q8×C47—28no—
180C2×Q8×C47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—21no—
184C2×Q8×C47—42no—
185C2×Q8×C47—42no—
186C2×Q8×C47—44no—
187C2×Q8×C47—44no—
188C2×Q8×C47—44no—
189C2×Q8×C47C2×D412yes—
190C2×Q8×C47C2×D412yes—
191C2×Q8×C47C2×D412yes—
192C2×Q8×C47#4112yes—
193C2×D4×C47—24no—
194C2×D4×C47—22no—
195C2×D4×C47—24no—
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—21no—
205C2×D4×C47—21no—
206C2×D4×C47—21no—
207C2×D4×C47—41no—
208C2×D4×C47—41no—
209C2×D4×C47—42no—
210C2×D4×C47—42no—
211C2×D4×C47—42no—
212C2×D4×C47—42no—
213C2×D4×C47—42no—
214C2×D4×C47—42no—
215C2×D4×C47—42no—
216C2×D4×C47—81no—
217C2×D4×C47—81no—
218C2×D4×C47—81no—
219C2×D4×C47C2×D412yes—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—24no—
226C22×C4×C47—24no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
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—42no—
239C22×C4×C47—42no—
240C22×C4×C47—42no—
241C22×C4×C47—42no—
242C22×C4×C47C2×D411yescharacteristic
243C22×C4×C47C2×D411yescharacteristic
244C22×C4×C47C2×D411yescharacteristic
245C22×C4×C47C2×D411yescharacteristic
246C22×C4×C47C2×D412yes—
247C22×C4×C47C2×D412yes—
248C22×C4×C47C2411yescharacteristic
249SD16×C47—44no—
250SD16×C47—44no—
251D8×C47—44no—
252M16×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×C47C2×D412yes—
265C4⋊C4×C47—24no—
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—81no—
275C4⋊C4×C47C2×D412yes—
276C4⋊C4×C47C2×D412yes—
277C22⋊C4×C47—24no—
278C22⋊C4×C47—24no—
279C22⋊C4×C47—24no—
280C22⋊C4×C47—22no—
281C22⋊C4×C47—24no—
282C22⋊C4×C47—22no—
283C22⋊C4×C47—42no—
284C22⋊C4×C47—42no—
285C22⋊C4×C47—42no—
286C22⋊C4×C47—42no—
287C22⋊C4×C47—81no—
288C22⋊C4×C47—81no—
289C42×C47—24no—
290C42×C47—21no—
291C42×C47—21no—
292C42×C47—42no—
293C23×C47—21no—
294C23×C47—21no—
295C23×C47—21no—
296C23×C47—21no—
297C23×C47—21no—
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—41no—
308C23×C47—41no—
309C23×C47—41no—
310C23×C47—41no—
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#12012yes—
321C23×C47C22×D411yescharacteristic
322Q8×C47—22no—
323Q8×C47—22no—
324Q8×C47—22no—
325Q8×C47—22no—
326Q8×C47—22no—
327Q8×C47—48no—
328Q8×C47—41no—
329Q8×C47—41no—
330Q8×C47#12114yes—
331D4×C47—22no—
332D4×C47—22no—
333D4×C47—48no—
334D4×C47—44no—
335D4×C47—48no—
336D4×C47—41no—
337D4×C47—41no—
338D4×C47—41no—
339D4×C47—41no—
340D4×C47—41no—
341D4×C47—41no—
342D4×C47—84no—
343D4×C47—84no—
344C2×C4×C47—22no—
345C2×C4×C47—21no—
346C2×C4×C47—22no—
347C2×C4×C47—21no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—21no—
354C2×C4×C47—21no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—21no—
358C2×C4×C47—22no—
359C2×C4×C47—21no—
360C2×C4×C47—21no—
361C2×C4×C47—21no—
362C2×C4×C47—21no—
363C2×C4×C47—21no—
364C2×C4×C47—21no—
365C2×C4×C47—48no—
366C2×C4×C47—48no—
367C2×C4×C47—41no—
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#12012yes—
384C2×C4×C47C22×D411yescharacteristic
385C2×C4×C47C22×D411yescharacteristic
386C2×C4×C47C22×D411yescharacteristic
387C2×C4×C47C2×#4111yescharacteristic
388C2×C4×C47H(5,𝔽2)11yescharacteristic
389C2×C4×C47H(5,𝔽2)11yescharacteristic
390C8×C47—22no—
391C8×C47—41no—
392C8×C47—41no—
393C8×C47—41no—
394#24455C4711yesmaximal, characteristic, direct product factor, Sylow
395C22×C47—22no—
396C22×C47—22no—
397C22×C47—22no—
398C22×C47—41no—
399C22×C47—41no—
400C22×C47—41no—
401C22×C47—41no—
402C22×C47—42no—
403C22×C47—41no—
404C22×C47—41no—
405C22×C47—42no—
406C22×C47—41no—
407C22×C47—42no—
408C22×C47—41no—
409C22×C47—41no—
410C22×C47—41no—
411C22×C47—41no—
412C22×C47—81no—
413C22×C47—81no—
414C22×C47—81no—
415C22×C47—81no—
416C22×C47—81no—
417C22×C47—81no—
418C22×C47—81no—
419C22×C47—81no—
420C22×C47—81no—
421C22×C47—81no—
422C22×C47—81no—
423C22×C47C2×#12011yescharacteristic
424C22×C47D4211yescharacteristic
425C22×C47#54611yescharacteristic
426C22×C47#57511yescharacteristic
427C22×C47#57511yescharacteristic
428C22×C47#57711yescharacteristic
429C22×C47#57711yescharacteristic
430C4×C47—22no—
431C4×C47—24no—
432C4×C47—41no—
433C4×C47—42no—
434C4×C47—41no—
435C4×C47—42no—
436C4×C47—41no—
437C4×C47—42no—
438C4×C47—81no—
439C4×C47—81no—
440C4×C47C2×#12111yescharacteristic
441C4×C47#53411yescharacteristic
442C4×C47D4211yescharacteristic
443C4×C47#54611yescharacteristic
444C2×#548C2×C4711yescharacteristic, complemented
445C2×#469C2×C4711yescharacteristic, complemented
446C2×#449C2×C4711yescharacteristic, complemented
447C2×#448C2×C4711yescharacteristic, complemented
448C2×#419C2×C4711yescharacteristic, complemented
449#2414C2×C4711yescharacteristic, complemented
450#2042C2×C4711yescharacteristic, complemented
451#2035C2×C4711yescharacteristic, complemented
452#2012C2×C4711yescharacteristic, complemented
453#2000C2×C4711yescharacteristic, complemented
454#1880C2×C4711yescharacteristic, complemented
455#1875C2×C4711yescharacteristic, complemented
456#1870C2×C4711yescharacteristic, complemented
457#1865C2×C4711yescharacteristic, complemented
458#1788C2×C4711yescharacteristic, complemented
459C2×C47—42no—
460C2×C47—81no—
461C2×C47—82no—
462C2×C47—161no—
463C2×C47#241011yescharacteristic
464C2×C47#300511yescharacteristic
465C2×C47#301011yescharacteristic
466C2×C47#327111yescharacteristic
467C2×C47#327511yescharacteristic
468C2×C47#332111yescharacteristic
469C2×C47#332611yescharacteristic
470C22×#41C22×C4711yescharacteristic
471C23×Q8C22×C4711yescharacteristic
472C22×SD16C22×C4711yescharacteristic
473C22×SD16C22×C4711yescharacteristic
474C22×D8C22×C4711yescharacteristic
475C22×M16C22×C4711yescharacteristic
476#548—24no—
477#548—24no—
478C2×#124—21no—
479C2×#124C22×C4711yescharacteristic
480C2×C22⋊Q8—21no—
481C2×C22⋊Q8C22×C4711yescharacteristic
482C2×#121—21no—
483C2×#121C22×C4711yescharacteristic
484C2×#121C22×C4711yescharacteristic
485C2×#121C22×C4711yescharacteristic
486C2×C4×Q8C22×C4711yescharacteristic
487C2×C4×D4—21no—
488C2×C4×D4C22×C4711yescharacteristic
489C2×#117C22×C4711yescharacteristic
490#469—24no—
491#449—24no—
492#448—24no—
493C2×#106C22×C4711yescharacteristic
494#419—24no—
495C2×#103C22×C4711yescharacteristic
496C2×#103C22×C4711yescharacteristic
497C2×#103C22×C4711yescharacteristic
498C2×#103C22×C4711yescharacteristic
499C2×#103C22×C4711yescharacteristic
500C2×#103C22×C4711yescharacteristic
501C2×#102C22×C4711yescharacteristic
502C2×#102C22×C4711yescharacteristic
503C2×#102C22×C4711yescharacteristic
504C2×#102C22×C4711yescharacteristic
505C2×C22⋊C8C22×C4711yescharacteristic
506C2×C22⋊C8C22×C4711yescharacteristic
507C2×C22⋊C8C22×C4711yescharacteristic
508#394—21no—
509#392—21no—
510#390—21no—
511#390C22×C4711yescharacteristic
512#389C22×C4711yescharacteristic
513#388—21no—
514#380C22×C4711yescharacteristic
515#340C22×C4711yescharacteristic
516#340C22×C4711yescharacteristic
517#336C22×C4711yescharacteristic
518#336C22×C4711yescharacteristic
519C47#2445511yescharacteristic, direct product factor, Sylow
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—41no—
525C2×#41—41no—
526C22×Q8—21no—
527C22×Q8—22no—
528C22×Q8—22no—
529C22×Q8—22no—
530C22×Q8—41no—
531C22×Q8—41no—
532C22×Q8D4×C4714yescomplemented
533C22×Q8C23×C4711yescharacteristic
534C22×Q8C23×C4711yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4D4×C4711yescharacteristic
540C22×D4C23×C4711yescharacteristic
541C22×D4C23×C4711yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C23×C4711yescharacteristic
545C23×C4C23×C4711yescharacteristic
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—41no—
555C2×M16—22no—
556C2×M16—22no—
557C2×M16—41no—
558C22×C8C23×C4711yescharacteristic
559C22×C8C23×C4711yescharacteristic
560C22×C8C23×C4711yescharacteristic
561C22×C8C23×C4711yescharacteristic
562#124—28no—
563#124—22no—
564#124—22no—
565C22⋊Q8—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568#121—28no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—41no—
574#121D4×C4714yescomplemented
575C4×Q8—22no—
576C4×Q8—22no—
577C4×D4—28no—
578C4×D4—22no—
579C4×D4—22no—
580#117—22no—
581#117—41no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4D4×C4711yescharacteristic
586C2×C4⋊C4C23×C4711yescharacteristic
587C2×C4⋊C4C23×C4711yescharacteristic
588C2×C4⋊C4C23×C4711yescharacteristic
589C2×C4⋊C4C23×C4711yescharacteristic
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4D4×C4711yescharacteristic
601C2×C22⋊C4D4×C4711yescharacteristic
602C2×C42—21no—
603C2×C42—21no—
604C2×C42C23×C4711yescharacteristic
605#106—22no—
606#103—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103D4×C4714yescomplemented
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616C22⋊C8—22no—
617C22⋊C8—22no—
618C22⋊C8—41no—
619#95—21no—
620#95—21no—
621C24—21no—
622C24—21no—
623C24C2×D4×C4711yescharacteristic
624C24C2×D4×C4711yescharacteristic
625#41—44no—
626#41—44no—
627#41—44no—
628#41—44no—
629C2×Q8—24no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—28no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—42no—
640C2×Q8—42no—
641C2×Q8—44no—
642C2×Q8—44no—
643C2×Q8—44no—
644C2×Q8C2×D4×C4712yes—
645C2×Q8C2×D4×C4712yes—
646C2×Q8C2×D4×C4712yes—
647C2×Q8#41×C4712yes—
648C2×D4—24no—
649C2×D4—22no—
650C2×D4—24no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—41no—
663C2×D4—41no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4—81no—
674C2×D4C2×D4×C4712yes—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4C2×D4×C4711yescharacteristic
698C22×C4C2×D4×C4711yescharacteristic
699C22×C4C2×D4×C4711yescharacteristic
700C22×C4C2×D4×C4711yescharacteristic
701C22×C4C2×D4×C4712yes—
702C22×C4C2×D4×C4712yes—
703C22×C4C24×C4711yescharacteristic
704SD16—44no—
705SD16—44no—
706D8—44no—
707M16—44no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8C2×D4×C4712yes—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—22no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—81no—
730C4⋊C4C2×D4×C4712yes—
731C4⋊C4C2×D4×C4712yes—
732C22⋊C4—24no—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—22no—
736C22⋊C4—24no—
737C22⋊C4—22no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—81no—
743C22⋊C4—81no—
744C42—24no—
745C42—21no—
746C42—21no—
747C42—42no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23#120×C4712yes—
776C23C22×D4×C4711yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—22no—
782Q8—48no—
783Q8—41no—
784Q8—41no—
785Q8#121×C4714yes—
786D4—22no—
787D4—22no—
788D4—48no—
789D4—44no—
790D4—48no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—84no—
798D4—84no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—48no—
821C2×C4—48no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
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#120×C4712yes—
839C2×C4C22×D4×C4711yescharacteristic
840C2×C4C22×D4×C4711yescharacteristic
841C2×C4C22×D4×C4711yescharacteristic
842C2×C4C2×#41×C4711yescharacteristic
843C2×C4H(5,𝔽2)×C4711yescharacteristic
844C2×C4H(5,𝔽2)×C4711yescharacteristic
845C8—22no—
846C8—41no—
847C8—41no—
848C8—41no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—42no—
859C22—41no—
860C22—41no—
861C22—42no—
862C22—41no—
863C22—42no—
864C22—41no—
865C22—41no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22C2×#120×C4711yescharacteristic
878C22D42×C4711yescharacteristic
879C22C47×#54611yescharacteristic
880C22C47×#57511yescharacteristic
881C22C47×#57511yescharacteristic
882C22C47×#57711yescharacteristic
883C22C47×#57711yescharacteristic
884C4—22no—
885C4—24no—
886C4—41no—
887C4—42no—
888C4—41no—
889C4—42no—
890C4—41no—
891C4—42no—
892C4—81no—
893C4—81no—
894C4C2×#121×C4711yescharacteristic
895C4C47×#53411yescharacteristic
896C4D42×C4711yescharacteristic
897C4C47×#54611yescharacteristic
898C2—42no—
899C2—81no—
900C2—82no—
901C2—161no—
902C2C47×#241011yescharacteristic
903C2C47×#300511yescharacteristic
904C2C47×#301011yescharacteristic
905C2C47×#327111yescharacteristic
906C2C47×#327511yescharacteristic
907C2C47×#332111yescharacteristic
908C2C47×#332611yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
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
1. C2×C47×#548C2semidirect
2. C2×C47×#469C2semidirect
3. C2×C47×#449C2semidirect
4. C2×C47×#448C2semidirect
5. C2×C47×#419C2semidirect
6. C47×#2414C2semidirect
7. C47×#2042C2semidirect
8. C47×#2035C2semidirect
9. C47×#2012C2semidirect
10. C47×#2000C2semidirect
11. C47×#1880C2semidirect
12. C47×#1875C2semidirect
13. C47×#1870C2semidirect
14. C47×#1865C2semidirect
15. C47×#1788C2semidirect
77. C22×Q8×C47D4semidirect
119. #121×C47D4semidirect
156. #103×C47D4semidirect
394. #24455C47direct (N × H)
444. C2×#548C2×C47semidirect
445. C2×#469C2×C47semidirect
446. C2×#449C2×C47semidirect
447. C2×#448C2×C47semidirect
448. C2×#419C2×C47semidirect
449. #2414C2×C47semidirect
450. #2042C2×C47semidirect
451. #2035C2×C47semidirect
452. #2012C2×C47semidirect
453. #2000C2×C47semidirect
454. #1880C2×C47semidirect
455. #1875C2×C47semidirect
456. #1870C2×C47semidirect
457. #1865C2×C47semidirect
458. #1788C2×C47semidirect
519. C47#24455direct (N × H)
532. C22×Q8D4×C47semidirect
574. #121D4×C47semidirect
611. #103D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5482
C2×C47×#4692
C2×C47×#4492
C2×C47×#4482
C2×C47×#4192
C47×#24142
C47×#20422
C47×#20352
C47×#20122
C47×#20002
C47×#18802
C47×#18752
C47×#18702
C47×#18652
C47×#17882
#2445547