Finite Group Databasebeta

← C47×#25388 #26065086

Subgroups — C47×#25388 #26065086

Order 12032.

1116 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#466C211yesmaximal, characteristic, complemented
2C2×C47×#465C211yesmaximal, characteristic, complemented
3C2×C47×#463C211yesmaximal, characteristic, complemented
4C2×C8×D4×C47C211yesmaximal, characteristic, complemented
5C47×#2540C211yesmaximal, characteristic, complemented
6C47×#2535C211yesmaximal, characteristic, complemented
7C47×#2036C211yesmaximal, characteristic, complemented
8C47×#2034C211yesmaximal, characteristic, complemented
9C47×#2000C211yesmaximal, characteristic, complemented
10C47×#1999C211yesmaximal, characteristic, complemented
11C47×#1958C211yesmaximal, characteristic, complemented
12C47×#1949C211yesmaximal, characteristic, complemented
13C47×#1893C211yesmaximal, characteristic, complemented
14C47×#1892C211yesmaximal, characteristic, complemented
15C4×#102×C47C211yesmaximal, characteristic, complemented
16C22×SD16×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C23×C8×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C2×#124×C47C2211yescharacteristic
21C2×C22⋊Q8×C47C2211yescharacteristic
22C2×C22⋊Q8×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×#121×C47C2211yescharacteristic
26C2×#121×C47C2211yescharacteristic
27C2×C4×D4×C47C2211yescharacteristic
28C2×C4×D4×C47C2211yescharacteristic
29C47×#466—24no—
30C47×#465—24no—
31C47×#463—24no—
32C8×D4×C47—24no—
33C2×#107×C47C2211yescharacteristic
34C2×#106×C47C2211yescharacteristic
35C2×C4⋊C8×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#103×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×C22⋊C8×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2211yescharacteristic
46C2×C4×C8×C47C2211yescharacteristic
47C47×#399—21no—
48C47×#397—21no—
49C47×#392—21no—
50C47×#392—21no—
51C47×#390—21no—
52C47×#390—21no—
53C47×#386—21no—
54C47×#386—21no—
55C47×#382C2211yescharacteristic
56C47×#380C2211yescharacteristic
57C47×#380C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47—21no—
67C22×D4×C47—21no—
68C22×D4×C47D411yescharacteristic
69C22×D4×C47C2311yescharacteristic
70C22×D4×C47C2311yescharacteristic
71C23×C4×C47—21no—
72C23×C4×C47C2311yescharacteristic
73C23×C4×C47C2311yescharacteristic
74C2×SD16×C47—22no—
75C2×SD16×C47—22no—
76C2×SD16×C47—41no—
77C2×D8×C47—22no—
78C2×D8×C47—22no—
79C2×D8×C47—41no—
80C22×C8×C47—22no—
81C22×C8×C47—22no—
82C22×C8×C47—22no—
83C22×C8×C47—22no—
84C22×C8×C47—41no—
85C22×C8×C47—41no—
86C22×C8×C47C2311yescharacteristic
87C22×C8×C47C2311yescharacteristic
88C22×C8×C47C2311yescharacteristic
89C22×C8×C47C2311yescharacteristic
90#124×C47—22no—
91#124×C47—22no—
92C22⋊Q8×C47—22no—
93C22⋊Q8×C47—22no—
94C22⋊Q8×C47—41no—
95C22⋊Q8×C47—41no—
96#121×C47—22no—
97#121×C47—22no—
98#121×C47—22no—
99#121×C47—22no—
100#121×C47—41no—
101#121×C47—41no—
102#121×C47—41no—
103#121×C47—41no—
104C4×D4×C47—22no—
105C4×D4×C47—22no—
106C4×D4×C47—22no—
107C4×D4×C47—22no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47D411yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47—21no—
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47—21no—
121C2×C22⋊C4×C47—21no—
122C2×C22⋊C4×C47—21no—
123C2×C22⋊C4×C47—21no—
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47—21no—
127C2×C22⋊C4×C47D411yescharacteristic
128C2×C22⋊C4×C47D411yescharacteristic
129C2×C42×C47—21no—
130C2×C42×C47C2311yescharacteristic
131#107×C47—22no—
132#106×C47—22no—
133C4⋊C8×C47D414yescomplemented
134#103×C47—22no—
135#103×C47—22no—
136#103×C47—41no—
137#102×C47—22no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—41no—
141#102×C47D414yescomplemented
142C22⋊C8×C47—22no—
143C22⋊C8×C47—22no—
144C4×C8×C47—22no—
145#95×C47—21no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47—21no—
149#95×C47—21no—
150C24×C47—21no—
151C24×C47—21no—
152C24×C47C2×D411yescharacteristic
153C24×C47C2×D411yescharacteristic
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×D4×C47—22no—
161C2×D4×C47—22no—
162C2×D4×C47—22no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—21no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—42no—
175C2×D4×C47—42no—
176C2×D4×C47—42no—
177C2×D4×C47—42no—
178C2×D4×C47—42no—
179C2×D4×C47—42no—
180C2×D4×C47—42no—
181C2×D4×C47—42no—
182C2×D4×C47—81no—
183C2×D4×C47—81no—
184C2×D4×C47—81no—
185C2×D4×C47—81no—
186C2×D4×C47C2×D412yes—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—42no—
206C22×C4×C47—81no—
207C22×C4×C47—81no—
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2411yescharacteristic
213SD16×C47—44no—
214D8×C47—44no—
215C2×C8×C47—21no—
216C2×C8×C47—21no—
217C2×C8×C47—21no—
218C2×C8×C47—21no—
219C2×C8×C47—21no—
220C2×C8×C47—21no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—44no—
225C2×C8×C47—44no—
226C2×C8×C47C2×D412yes—
227C2×C8×C47C2×D412yes—
228C2×C8×C47C2×D412yes—
229C4⋊C4×C47—22no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—42no—
239C4⋊C4×C47—42no—
240C4⋊C4×C47C2×D412yes—
241C4⋊C4×C47#4112yes—
242C22⋊C4×C47—22no—
243C22⋊C4×C47—22no—
244C22⋊C4×C47—42no—
245C22⋊C4×C47—42no—
246C22⋊C4×C47—42no—
247C22⋊C4×C47—42no—
248C22⋊C4×C47—42no—
249C22⋊C4×C47—42no—
250C22⋊C4×C47—42no—
251C22⋊C4×C47—42no—
252C22⋊C4×C47—42no—
253C22⋊C4×C47—81no—
254C22⋊C4×C47—81no—
255C42×C47—81no—
256C42×C47C2×D412yes—
257C42×C47#4112yes—
258C23×C47—21no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—22no—
271C23×C47—41no—
272C23×C47—41no—
273C23×C47—41no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47#13512yes—
285C23×C47#13512yes—
286C23×C47C22×D411yescharacteristic
287Q8×C47—41no—
288Q8×C47—41no—
289Q8×C47—41no—
290Q8×C47—41no—
291D4×C47—28no—
292D4×C47—22no—
293D4×C47—22no—
294D4×C47—41no—
295D4×C47—41no—
296D4×C47—41no—
297D4×C47—41no—
298D4×C47—41no—
299D4×C47—41no—
300D4×C47—84no—
301D4×C47—84no—
302D4×C47—84no—
303D4×C47—84no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—22no—
312C2×C4×C47—21no—
313C2×C4×C47—22no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—84no—
341C2×C4×C47#12112yes—
342C2×C4×C47#12112yes—
343C2×C4×C47C22×D411yescharacteristic
344C2×C4×C47C22×D411yescharacteristic
345C2×C4×C47C2×#4111yescharacteristic
346C2×C4×C47C2×#4111yescharacteristic
347C2×C4×C47H(5,𝔽2)11yescharacteristic
348C2×C4×C47H(5,𝔽2)11yescharacteristic
349C8×C47—22no—
350C8×C47—22no—
351C8×C47—22no—
352C8×C47—41no—
353#25388C4711yesmaximal, characteristic, direct product factor, Sylow
354C22×C47—22no—
355C22×C47—22no—
356C22×C47—22no—
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—41no—
367C22×C47—41no—
368C22×C47—42no—
369C22×C47—42no—
370C22×C47—42no—
371C22×C47—81no—
372C22×C47—81no—
373C22×C47—81no—
374C22×C47—81no—
375C22×C47—81no—
376C22×C47—81no—
377C22×C47—81no—
378C22×C47—81no—
379C22×C47—81no—
380C22×C47—81no—
381C22×C47—81no—
382C22×C47C2×#12111yescharacteristic
383C22×C47D4211yescharacteristic
384C22×C47#54611yescharacteristic
385C22×C47C2×#13511yescharacteristic
386C22×C47C2×#13511yescharacteristic
387C22×C47#57611yescharacteristic
388C22×C47#57711yescharacteristic
389C4×C47—22no—
390C4×C47—22no—
391C4×C47—41no—
392C4×C47—41no—
393C4×C47—42no—
394C4×C47—42no—
395C4×C47—81no—
396C4×C47—81no—
397C4×C47—81no—
398C4×C47—81no—
399C4×C47#53211yescharacteristic
400C4×C47#54011yescharacteristic
401C4×C47D4211yescharacteristic
402C4×C47#55011yescharacteristic
403C2×#466C2×C4711yescharacteristic, complemented
404C2×#465C2×C4711yescharacteristic, complemented
405C2×#463C2×C4711yescharacteristic, complemented
406C2×C8×D4C2×C4711yescharacteristic, complemented
407#2540C2×C4711yescharacteristic, complemented
408#2535C2×C4711yescharacteristic, complemented
409#2036C2×C4711yescharacteristic, complemented
410#2034C2×C4711yescharacteristic, complemented
411#2000C2×C4711yescharacteristic, complemented
412#1999C2×C4711yescharacteristic, complemented
413#1958C2×C4711yescharacteristic, complemented
414#1949C2×C4711yescharacteristic, complemented
415#1893C2×C4711yescharacteristic, complemented
416#1892C2×C4711yescharacteristic, complemented
417C4×#102C2×C4711yescharacteristic, complemented
418C2×C47—42no—
419C2×C47—42no—
420C2×C47—82no—
421C2×C47—161no—
422C2×C47#242811yescharacteristic
423C2×C47#305011yescharacteristic
424C2×C47#306211yescharacteristic
425C2×C47#328011yescharacteristic
426C2×C47#328211yescharacteristic
427C2×C47#329711yescharacteristic
428C2×C47#330111yescharacteristic
429C22×SD16C22×C4711yescharacteristic
430C22×D8C22×C4711yescharacteristic
431C23×C8C22×C4711yescharacteristic
432C23×C8C22×C4711yescharacteristic
433C2×#124C22×C4711yescharacteristic
434C2×C22⋊Q8C22×C4711yescharacteristic
435C2×C22⋊Q8C22×C4711yescharacteristic
436C2×#121C22×C4711yescharacteristic
437C2×#121C22×C4711yescharacteristic
438C2×#121C22×C4711yescharacteristic
439C2×#121C22×C4711yescharacteristic
440C2×C4×D4C22×C4711yescharacteristic
441C2×C4×D4C22×C4711yescharacteristic
442#466—24no—
443#465—24no—
444#463—24no—
445C8×D4—24no—
446C2×#107C22×C4711yescharacteristic
447C2×#106C22×C4711yescharacteristic
448C2×C4⋊C8C22×C4711yescharacteristic
449C2×#103C22×C4711yescharacteristic
450C2×#103C22×C4711yescharacteristic
451C2×#103C22×C4711yescharacteristic
452C2×#102C22×C4711yescharacteristic
453C2×#102C22×C4711yescharacteristic
454C2×#102C22×C4711yescharacteristic
455C2×#102C22×C4711yescharacteristic
456C2×#102C22×C4711yescharacteristic
457C2×C22⋊C8C22×C4711yescharacteristic
458C2×C22⋊C8C22×C4711yescharacteristic
459C2×C4×C8C22×C4711yescharacteristic
460#399—21no—
461#397—21no—
462#392—21no—
463#392—21no—
464#390—21no—
465#390—21no—
466#386—21no—
467#386—21no—
468#382C22×C4711yescharacteristic
469#380C22×C4711yescharacteristic
470#380C22×C4711yescharacteristic
471C4×C4⋊C4C22×C4711yescharacteristic
472#340C22×C4711yescharacteristic
473#340C22×C4711yescharacteristic
474#340C22×C4711yescharacteristic
475#340C22×C4711yescharacteristic
476C47#2538811yescharacteristic, direct product factor, Sylow
477C22×Q8C23×C4711yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4D4×C4711yescharacteristic
483C22×D4C23×C4711yescharacteristic
484C22×D4C23×C4711yescharacteristic
485C23×C4—21no—
486C23×C4C23×C4711yescharacteristic
487C23×C4C23×C4711yescharacteristic
488C2×SD16—22no—
489C2×SD16—22no—
490C2×SD16—41no—
491C2×D8—22no—
492C2×D8—22no—
493C2×D8—41no—
494C22×C8—22no—
495C22×C8—22no—
496C22×C8—22no—
497C22×C8—22no—
498C22×C8—41no—
499C22×C8—41no—
500C22×C8C23×C4711yescharacteristic
501C22×C8C23×C4711yescharacteristic
502C22×C8C23×C4711yescharacteristic
503C22×C8C23×C4711yescharacteristic
504#124—22no—
505#124—22no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—41no—
509C22⋊Q8—41no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—41no—
515#121—41no—
516#121—41no—
517#121—41no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4D4×C4711yescharacteristic
525C2×C4⋊C4C23×C4711yescharacteristic
526C2×C4⋊C4C23×C4711yescharacteristic
527C2×C4⋊C4C23×C4711yescharacteristic
528C2×C4⋊C4C23×C4711yescharacteristic
529C2×C4⋊C4C23×C4711yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4D4×C4711yescharacteristic
542C2×C22⋊C4D4×C4711yescharacteristic
543C2×C42—21no—
544C2×C42C23×C4711yescharacteristic
545#107—22no—
546#106—22no—
547C4⋊C8D4×C4714yescomplemented
548#103—22no—
549#103—22no—
550#103—41no—
551#102—22no—
552#102—22no—
553#102—22no—
554#102—41no—
555#102D4×C4714yescomplemented
556C22⋊C8—22no—
557C22⋊C8—22no—
558C4×C8—22no—
559#95—21no—
560#95—21no—
561#95—21no—
562#95—21no—
563#95—21no—
564C24—21no—
565C24—21no—
566C24C2×D4×C4711yescharacteristic
567C24C2×D4×C4711yescharacteristic
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—81no—
597C2×D4—81no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4C2×D4×C4712yes—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—42no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4C2×D4×C4711yescharacteristic
623C22×C4C2×D4×C4711yescharacteristic
624C22×C4C2×D4×C4711yescharacteristic
625C22×C4C2×D4×C4711yescharacteristic
626C22×C4C24×C4711yescharacteristic
627SD16—44no—
628D8—44no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—44no—
639C2×C8—44no—
640C2×C8C2×D4×C4712yes—
641C2×C8C2×D4×C4712yes—
642C2×C8C2×D4×C4712yes—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4C2×D4×C4712yes—
655C4⋊C4#41×C4712yes—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C42—81no—
670C42C2×D4×C4712yes—
671C42#41×C4712yes—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—22no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23#135×C4712yes—
699C23#135×C4712yes—
700C23C22×D4×C4711yescharacteristic
701Q8—41no—
702Q8—41no—
703Q8—41no—
704Q8—41no—
705D4—28no—
706D4—22no—
707D4—22no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—84no—
715D4—84no—
716D4—84no—
717D4—84no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—84no—
755C2×C4#121×C4712yes—
756C2×C4#121×C4712yes—
757C2×C4C22×D4×C4711yescharacteristic
758C2×C4C22×D4×C4711yescharacteristic
759C2×C4C2×#41×C4711yescharacteristic
760C2×C4C2×#41×C4711yescharacteristic
761C2×C4H(5,𝔽2)×C4711yescharacteristic
762C2×C4H(5,𝔽2)×C4711yescharacteristic
763C8—22no—
764C8—22no—
765C8—22no—
766C8—41no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×#121×C4711yescharacteristic
796C22D42×C4711yescharacteristic
797C22C47×#54611yescharacteristic
798C22C2×#135×C4711yescharacteristic
799C22C2×#135×C4711yescharacteristic
800C22C47×#57611yescharacteristic
801C22C47×#57711yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—41no—
806C4—41no—
807C4—42no—
808C4—81no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4C47×#53211yescharacteristic
813C4C47×#54011yescharacteristic
814C4D42×C4711yescharacteristic
815C4C47×#55011yescharacteristic
816C2—42no—
817C2—42no—
818C2—82no—
819C2—161no—
820C2C47×#242811yescharacteristic
821C2C47×#305011yescharacteristic
822C2C47×#306211yescharacteristic
823C2C47×#328011yescharacteristic
824C2C47×#328211yescharacteristic
825C2C47×#329711yescharacteristic
826C2C47×#330111yescharacteristic
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×#466C2semidirect
2. C2×C47×#465C2semidirect
3. C2×C47×#463C2semidirect
4. C2×C8×D4×C47C2semidirect
5. C47×#2540C2semidirect
6. C47×#2535C2semidirect
7. C47×#2036C2semidirect
8. C47×#2034C2semidirect
9. C47×#2000C2semidirect
10. C47×#1999C2semidirect
11. C47×#1958C2semidirect
12. C47×#1949C2semidirect
13. C47×#1893C2semidirect
14. C47×#1892C2semidirect
15. C4×#102×C47C2semidirect
133. C4⋊C8×C47D4semidirect
141. #102×C47D4semidirect
353. #25388C47direct (N × H)
403. C2×#466C2×C47semidirect
404. C2×#465C2×C47semidirect
405. C2×#463C2×C47semidirect
406. C2×C8×D4C2×C47semidirect
407. #2540C2×C47semidirect
408. #2535C2×C47semidirect
409. #2036C2×C47semidirect
410. #2034C2×C47semidirect
411. #2000C2×C47semidirect
412. #1999C2×C47semidirect
413. #1958C2×C47semidirect
414. #1949C2×C47semidirect
415. #1893C2×C47semidirect
416. #1892C2×C47semidirect
417. C4×#102C2×C47semidirect
476. C47#25388direct (N × H)
547. C4⋊C8D4×C47semidirect
555. #102D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4662
C2×C47×#4652
C2×C47×#4632
C2×C8×D4×C472
C47×#25402
C47×#25352
C47×#20362
C47×#20342
C47×#20002
C47×#19992
C47×#19582
C47×#19492
C47×#18932
C47×#18922
C4×#102×C472
#2538847