Finite Group Databasebeta

← C47×#29747 #26069445

Subgroups — C47×#29747 #26069445

Order 12032.

1024 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#468C211yesmaximal, characteristic, complemented
2C2×C47×#408C211yesmaximal, characteristic, complemented
3C47×#2616C211yesmaximal, characteristic, complemented
4C47×#2615C211yesmaximal, characteristic
5C47×#2076C211yesmaximal, characteristic, complemented
6C47×#2075C211yesmaximal, characteristic, complemented
7C47×#2036C211yesmaximal, characteristic, complemented
8C47×#2035C211yesmaximal, characteristic, complemented
9C47×#2034C211yesmaximal, characteristic, complemented
10C47×#2033C211yesmaximal, characteristic, complemented
11C47×#2000C211yesmaximal, characteristic, complemented
12C47×#2000C211yesmaximal, characteristic, complemented
13C47×#1893C211yesmaximal, characteristic, complemented
14C47×#1892C211yesmaximal, characteristic, complemented
15C47×#1809C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C2×C22⋊Q8×C47C2211yescharacteristic
21C2×C22⋊Q8×C47C2211yescharacteristic
22C2×C22⋊Q8×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×#121×C47C2211yescharacteristic
26C47×#468—24no—
27C2×#107×C47C2211yescharacteristic
28C2×#107×C47C2211yescharacteristic
29C2×#106×C47C2211yescharacteristic
30C2×#103×C47C2211yescharacteristic
31C2×#103×C47C2211yescharacteristic
32C2×#103×C47C2211yescharacteristic
33C2×#102×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C2×#102×C47C2211yescharacteristic
36C47×#408—24no—
37C2×C22⋊C8×C47C2211yescharacteristic
38C2×C22⋊C8×C47C2211yescharacteristic
39C2×C22⋊C8×C47C2211yescharacteristic
40C2×C22⋊C8×C47C2211yescharacteristic
41C47×#395—21no—
42C47×#394—21no—
43C47×#394—21no—
44C47×#394—21no—
45C47×#393—21no—
46C47×#392—21no—
47C47×#392—21no—
48C47×#392—21no—
49C47×#380C2211yescharacteristic
50C47×#380C2211yescharacteristic
51C47×#380C2211yescharacteristic
52C47×#380C2211yescharacteristic
53C47×#380C2211yescharacteristic
54C47×#380C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C2×#41×C47—22no—
62C2×#41×C47—22no—
63C2×#41×C47—41no—
64C2×#41×C47—41no—
65C2×#41×C47—41no—
66C2×#41×C47—41no—
67C22×Q8×C47D411yescharacteristic
68C22×Q8×C47C2311yescharacteristic
69C22×D4×C47—21no—
70C22×D4×C47—21no—
71C22×D4×C47—21no—
72C22×D4×C47D411yescharacteristic
73C22×D4×C47D411yescharacteristic
74C22×D4×C47D411yescharacteristic
75C22×D4×C47C2311yescharacteristic
76C23×C4×C47C2311yescharacteristic
77C23×C4×C47C2311yescharacteristic
78C23×C4×C47C2311yescharacteristic
79C2×SD16×C47—22no—
80C2×SD16×C47—41no—
81C2×SD16×C47—41no—
82C2×M16×C47—41no—
83C2×M16×C47—41no—
84C2×M16×C47D414yescomplemented
85C22×C8×C47—22no—
86C22×C8×C47—41no—
87C22×C8×C47—41no—
88C22×C8×C47C2311yescharacteristic
89C22×C8×C47C2311yescharacteristic
90C22×C8×C47C2311yescharacteristic
91C22×C8×C47C2311yescharacteristic
92C22⋊Q8×C47—22no—
93C22⋊Q8×C47—22no—
94C22⋊Q8×C47—41no—
95C22⋊Q8×C47—41no—
96C22⋊Q8×C47—41no—
97C22⋊Q8×C47—41no—
98#121×C47—22no—
99#121×C47—22no—
100#121×C47—41no—
101#121×C47—41no—
102#121×C47—41no—
103#121×C47—41no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
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—
125#107×C47—22no—
126#107×C47—41no—
127#106×C47—41no—
128#103×C47—22no—
129#103×C47—41no—
130#103×C47—41no—
131#102×C47—22no—
132#102×C47—41no—
133#102×C47—41no—
134C22⋊C8×C47—22no—
135C22⋊C8×C47—22no—
136C22⋊C8×C47—22no—
137C22⋊C8×C47—22no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47—21no—
143#95×C47—21no—
144C24×C47—21no—
145C24×C47C2×D411yescharacteristic
146C24×C47C2×D411yescharacteristic
147C24×C47C2×D411yescharacteristic
148#41×C47—44no—
149#41×C47—44no—
150#41×C47—44no—
151#41×C47—44no—
152C2×Q8×C47—22no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—41no—
160C2×Q8×C47—41no—
161C2×D4×C47—22no—
162C2×D4×C47—22no—
163C2×D4×C47—22no—
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—41no—
171C2×D4×C47—41no—
172C2×D4×C47—41no—
173C2×D4×C47—41no—
174C2×D4×C47—41no—
175C2×D4×C47—41no—
176C2×D4×C47—42no—
177C2×D4×C47—42no—
178C2×D4×C47—42no—
179C2×D4×C47—81no—
180C2×D4×C47—81no—
181C2×D4×C47—81no—
182C2×D4×C47—81no—
183C2×D4×C47—81no—
184C2×D4×C47—81no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
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—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D412yes—
212C22×C4×C47#4112yes—
213C22×C4×C47C2411yescharacteristic
214SD16×C47—44no—
215M16×C47—44no—
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—21no—
225C2×C8×C47—21no—
226C2×C8×C47—44no—
227C2×C8×C47C2×D412yes—
228C2×C8×C47C2×D412yes—
229C4⋊C4×C47—21no—
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—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—42no—
242C4⋊C4×C47—42no—
243C4⋊C4×C47—42no—
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—81no—
251C22⋊C4×C47—81no—
252C22⋊C4×C47—81no—
253C22⋊C4×C47—81no—
254C22⋊C4×C47—81no—
255C22⋊C4×C47—81no—
256C23×C47—21no—
257C23×C47—21no—
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—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47#12112yes—
284C23×C47C22×D411yescharacteristic
285Q8×C47—44no—
286Q8×C47—41no—
287Q8×C47—41no—
288Q8×C47—41no—
289Q8×C47—41no—
290D4×C47—44no—
291D4×C47—44no—
292D4×C47—44no—
293D4×C47—41no—
294D4×C47—41no—
295D4×C47—41no—
296D4×C47—41no—
297D4×C47—84no—
298D4×C47—84no—
299D4×C47—84no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
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—41no—
341C2×C4×C47#12112yes—
342C2×C4×C47C22×D411yescharacteristic
343C2×C4×C47C2×#4111yescharacteristic
344C2×C4×C47H(5,𝔽2)11yescharacteristic
345C2×C4×C47H(5,𝔽2)11yescharacteristic
346C2×C4×C47H(5,𝔽2)11yescharacteristic
347C2×C4×C47H(5,𝔽2)11yescharacteristic
348C8×C47—22no—
349C8×C47—22no—
350C8×C47—41no—
351C8×C47—41no—
352#29747C4711yesmaximal, characteristic, direct product factor, Sylow
353C22×C47—22no—
354C22×C47—22no—
355C22×C47—22no—
356C22×C47—41no—
357C22×C47—41no—
358C22×C47—41no—
359C22×C47—41no—
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—41no—
369C22×C47—41no—
370C22×C47—41no—
371C22×C47—41no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—81no—
375C22×C47—81no—
376C22×C47—81no—
377C22×C47—81no—
378C22×C47—81no—
379C22×C47—81no—
380C22×C47—81no—
381C22×C47C2×#12111yescharacteristic
382C22×C47#53411yescharacteristic
383C22×C47#53411yescharacteristic
384C22×C47#57611yescharacteristic
385C22×C47#57711yescharacteristic
386C22×C47#57711yescharacteristic
387C22×C47#57811yescharacteristic
388C4×C47—22no—
389C4×C47—41no—
390C4×C47—41no—
391C4×C47—81no—
392C4×C47—81no—
393C4×C47—81no—
394C4×C47—81no—
395C4×C47—81no—
396C4×C47—81no—
397C4×C47—81no—
398C4×C47#53411yescharacteristic
399C4×C47#53511yescharacteristic
400C4×C47#53811yescharacteristic
401C4×C47#53811yescharacteristic
402C2×#468C2×C4711yescharacteristic, complemented
403C2×#408C2×C4711yescharacteristic, complemented
404#2616C2×C4711yescharacteristic, complemented
405#2615C2×C4711yescharacteristic
406#2076C2×C4711yescharacteristic, complemented
407#2075C2×C4711yescharacteristic, complemented
408#2036C2×C4711yescharacteristic, complemented
409#2035C2×C4711yescharacteristic, complemented
410#2034C2×C4711yescharacteristic, complemented
411#2033C2×C4711yescharacteristic, complemented
412#2000C2×C4711yescharacteristic, complemented
413#2000C2×C4711yescharacteristic, complemented
414#1893C2×C4711yescharacteristic, complemented
415#1892C2×C4711yescharacteristic, complemented
416#1809C2×C4711yescharacteristic, complemented
417C2×C47—42no—
418C2×C47—81no—
419C2×C47—81no—
420C2×C47—161no—
421C2×C47#261711yescharacteristic
422C2×C47#306211yescharacteristic
423C2×C47#306311yescharacteristic
424C2×C47#319811yescharacteristic
425C2×C47#320011yescharacteristic
426C2×C47#320111yescharacteristic
427C2×C47#320311yescharacteristic
428C22×#41C22×C4711yescharacteristic
429C22×SD16C22×C4711yescharacteristic
430C22×M16C22×C4711yescharacteristic
431C23×C8C22×C4711yescharacteristic
432C2×C22⋊Q8C22×C4711yescharacteristic
433C2×C22⋊Q8C22×C4711yescharacteristic
434C2×C22⋊Q8C22×C4711yescharacteristic
435C2×#121C22×C4711yescharacteristic
436C2×#121C22×C4711yescharacteristic
437C2×#121C22×C4711yescharacteristic
438#468—24no—
439C2×#107C22×C4711yescharacteristic
440C2×#107C22×C4711yescharacteristic
441C2×#106C22×C4711yescharacteristic
442C2×#103C22×C4711yescharacteristic
443C2×#103C22×C4711yescharacteristic
444C2×#103C22×C4711yescharacteristic
445C2×#102C22×C4711yescharacteristic
446C2×#102C22×C4711yescharacteristic
447C2×#102C22×C4711yescharacteristic
448#408—24no—
449C2×C22⋊C8C22×C4711yescharacteristic
450C2×C22⋊C8C22×C4711yescharacteristic
451C2×C22⋊C8C22×C4711yescharacteristic
452C2×C22⋊C8C22×C4711yescharacteristic
453#395—21no—
454#394—21no—
455#394—21no—
456#394—21no—
457#393—21no—
458#392—21no—
459#392—21no—
460#392—21no—
461#380C22×C4711yescharacteristic
462#380C22×C4711yescharacteristic
463#380C22×C4711yescharacteristic
464#380C22×C4711yescharacteristic
465#380C22×C4711yescharacteristic
466#380C22×C4711yescharacteristic
467#340C22×C4711yescharacteristic
468#340C22×C4711yescharacteristic
469#340C22×C4711yescharacteristic
470#340C22×C4711yescharacteristic
471#340C22×C4711yescharacteristic
472#340C22×C4711yescharacteristic
473C47#2974711yescharacteristic, direct product factor, Sylow
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—41no—
477C2×#41—41no—
478C2×#41—41no—
479C2×#41—41no—
480C22×Q8D4×C4711yescharacteristic
481C22×Q8C23×C4711yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4D4×C4711yescharacteristic
486C22×D4D4×C4711yescharacteristic
487C22×D4D4×C4711yescharacteristic
488C22×D4C23×C4711yescharacteristic
489C23×C4C23×C4711yescharacteristic
490C23×C4C23×C4711yescharacteristic
491C23×C4C23×C4711yescharacteristic
492C2×SD16—22no—
493C2×SD16—41no—
494C2×SD16—41no—
495C2×M16—41no—
496C2×M16—41no—
497C2×M16D4×C4714yescomplemented
498C22×C8—22no—
499C22×C8—41no—
500C22×C8—41no—
501C22×C8C23×C4711yescharacteristic
502C22×C8C23×C4711yescharacteristic
503C22×C8C23×C4711yescharacteristic
504C22×C8C23×C4711yescharacteristic
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—41no—
508C22⋊Q8—41no—
509C22⋊Q8—41no—
510C22⋊Q8—41no—
511#121—22no—
512#121—22no—
513#121—41no—
514#121—41no—
515#121—41no—
516#121—41no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4C23×C4711yescharacteristic
521C2×C4⋊C4C23×C4711yescharacteristic
522C2×C4⋊C4C23×C4711yescharacteristic
523C2×C4⋊C4C23×C4711yescharacteristic
524C2×C4⋊C4C23×C4711yescharacteristic
525C2×C4⋊C4C23×C4711yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
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—
538#107—22no—
539#107—41no—
540#106—41no—
541#103—22no—
542#103—41no—
543#103—41no—
544#102—22no—
545#102—41no—
546#102—41no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—22no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557C24—21no—
558C24C2×D4×C4711yescharacteristic
559C24C2×D4×C4711yescharacteristic
560C24C2×D4×C4711yescharacteristic
561#41—44no—
562#41—44no—
563#41—44no—
564#41—44no—
565C2×Q8—22no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—41no—
573C2×Q8—41no—
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—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4—81no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
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—21no—
620C22×C4—21no—
621C22×C4C2×D4×C4711yescharacteristic
622C22×C4C2×D4×C4711yescharacteristic
623C22×C4C2×D4×C4711yescharacteristic
624C22×C4C2×D4×C4712yes—
625C22×C4#41×C4712yes—
626C22×C4C24×C4711yescharacteristic
627SD16—44no—
628M16—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—21no—
639C2×C8—44no—
640C2×C8C2×D4×C4712yes—
641C2×C8C2×D4×C4712yes—
642C4⋊C4—21no—
643C4⋊C4—21no—
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—21no—
653C4⋊C4—21no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—81no—
664C22⋊C4—81no—
665C22⋊C4—81no—
666C22⋊C4—81no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C23—21no—
670C23—21no—
671C23—21no—
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—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23#121×C4712yes—
697C23C22×D4×C4711yescharacteristic
698Q8—44no—
699Q8—41no—
700Q8—41no—
701Q8—41no—
702Q8—41no—
703D4—44no—
704D4—44no—
705D4—44no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—84no—
711D4—84no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
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#121×C4712yes—
755C2×C4C22×D4×C4711yescharacteristic
756C2×C4C2×#41×C4711yescharacteristic
757C2×C4H(5,𝔽2)×C4711yescharacteristic
758C2×C4H(5,𝔽2)×C4711yescharacteristic
759C2×C4H(5,𝔽2)×C4711yescharacteristic
760C2×C4H(5,𝔽2)×C4711yescharacteristic
761C8—22no—
762C8—22no—
763C8—41no—
764C8—41no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22C2×#121×C4711yescharacteristic
794C22C47×#53411yescharacteristic
795C22C47×#53411yescharacteristic
796C22C47×#57611yescharacteristic
797C22C47×#57711yescharacteristic
798C22C47×#57711yescharacteristic
799C22C47×#57811yescharacteristic
800C4—22no—
801C4—41no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4—81no—
810C4C47×#53411yescharacteristic
811C4C47×#53511yescharacteristic
812C4C47×#53811yescharacteristic
813C4C47×#53811yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—161no—
818C2C47×#261711yescharacteristic
819C2C47×#306211yescharacteristic
820C2C47×#306311yescharacteristic
821C2C47×#319811yescharacteristic
822C2C47×#320011yescharacteristic
823C2C47×#320111yescharacteristic
824C2C47×#320311yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C22×#41×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#468C2semidirect
2. C2×C47×#408C2semidirect
3. C47×#2616C2semidirect
5. C47×#2076C2semidirect
6. C47×#2075C2semidirect
7. C47×#2036C2semidirect
8. C47×#2035C2semidirect
9. C47×#2034C2semidirect
10. C47×#2033C2semidirect
11. C47×#2000C2semidirect
12. C47×#2000C2semidirect
13. C47×#1893C2semidirect
14. C47×#1892C2semidirect
15. C47×#1809C2semidirect
84. C2×M16×C47D4semidirect
352. #29747C47direct (N × H)
402. C2×#468C2×C47semidirect
403. C2×#408C2×C47semidirect
404. #2616C2×C47semidirect
406. #2076C2×C47semidirect
407. #2075C2×C47semidirect
408. #2036C2×C47semidirect
409. #2035C2×C47semidirect
410. #2034C2×C47semidirect
411. #2033C2×C47semidirect
412. #2000C2×C47semidirect
413. #2000C2×C47semidirect
414. #1893C2×C47semidirect
415. #1892C2×C47semidirect
416. #1809C2×C47semidirect
473. C47#29747direct (N × H)
497. C2×M16D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4682
C2×C47×#4082
C47×#26162
C47×#26152
C47×#20762
C47×#20752
C47×#20362
C47×#20352
C47×#20342
C47×#20332
C47×#20002
C47×#18932
C47×#18922
C47×#18092
#2974747