Finite Group Databasebeta

← C47×#24740 #26064438

Subgroups — C47×#24740 #26064438

Order 12032.

1030 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#463C211yesmaximal, characteristic
2C2×C47×#463C211yesmaximal, characteristic
3C2×C47×#461C211yesmaximal, characteristic, complemented
4C2×C47×#440C211yesmaximal, characteristic, complemented
5C47×#2545C211yesmaximal, characteristic, complemented
6D4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
7C47×#2068C211yesmaximal, characteristic, complemented
8C47×#2067C211yesmaximal, characteristic, complemented
9C47×#2043C211yesmaximal, characteristic, complemented
10C47×#2042C211yesmaximal, characteristic, complemented
11C47×#1959C211yesmaximal, characteristic, complemented
12C47×#1940C211yesmaximal, characteristic, complemented
13C47×#1879C211yesmaximal, characteristic
14C47×#1877C211yesmaximal, characteristic, complemented
15C47×#1803C211yesmaximal, characteristic, complemented
16C22×SD16×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×D8×C47C2211yescharacteristic
19C2×C4⋊Q8×C47C2211yescharacteristic
20C2×#124×C47C2211yescharacteristic
21C2×#124×C47C2211yescharacteristic
22C2×C4×Q8×C47C2211yescharacteristic
23C2×C4×D4×C47C2211yescharacteristic
24C2×C4×D4×C47C2211yescharacteristic
25C2×C4×D4×C47C2211yescharacteristic
26C22×C4⋊C4×C47—21no—
27C47×#463—24no—
28C47×#463—24no—
29C47×#461—24no—
30C47×#440—24no—
31C2×#107×C47C2211yescharacteristic
32C2×C4⋊C8×C47C2211yescharacteristic
33C2×C4⋊C8×C47C2211yescharacteristic
34C2×C4⋊C8×C47C2211yescharacteristic
35C2×#103×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#103×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#103×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×#97×C47C2211yescharacteristic
46C47×#396—21no—
47C47×#396—21no—
48C47×#391C2211yescharacteristic
49C47×#390C2211yescharacteristic
50C47×#389C2211yescharacteristic
51C47×#389C2211yescharacteristic
52C47×#388—21no—
53C47×#388—21no—
54C47×#385—21no—
55C47×#385—21no—
56C47×#384C2211yescharacteristic
57C47×#380—21no—
58C4×C4⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×Q8×C47C2311yescharacteristic
65C22×D4×C47C2311yescharacteristic
66C22×D4×C47C2311yescharacteristic
67C23×C4×C47—21no—
68C23×C4×C47—21no—
69C23×C4×C47—21no—
70C2×SD16×C47—22no—
71C2×SD16×C47—22no—
72C2×SD16×C47—22no—
73C2×SD16×C47—22no—
74C2×SD16×C47—22no—
75C2×SD16×C47D414yes—
76C2×D8×C47—22no—
77C2×D8×C47—22no—
78C2×D8×C47—22no—
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C4⋊Q8×C47—22no—
84C4⋊Q8×C47—41no—
85#124×C47—22no—
86#124×C47—22no—
87#124×C47—22no—
88#124×C47—41no—
89C4×Q8×C47—22no—
90C4×Q8×C47—22no—
91C4×D4×C47—22no—
92C4×D4×C47—22no—
93C4×D4×C47—22no—
94C4×D4×C47—41no—
95C4×D4×C47—41no—
96C4×D4×C47D414yes—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—44no—
105C2×C4⋊C4×C47D411yescharacteristic
106C2×C4⋊C4×C47D411yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
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×C42×C47—21no—
121C2×C42×C47C2311yescharacteristic
122C2×C42×C47C2311yescharacteristic
123C2×C42×C47C2311yescharacteristic
124#107×C47—22no—
125C4⋊C8×C47—22no—
126C4⋊C8×C47—22no—
127C4⋊C8×C47—22no—
128#103×C47—22no—
129#103×C47—22no—
130#103×C47—22no—
131#103×C47—22no—
132#103×C47—22no—
133#103×C47—41no—
134#102×C47—22no—
135#102×C47—22no—
136#102×C47—22no—
137#102×C47—41no—
138#97×C47—22no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47—21no—
143#95×C47D411yescharacteristic
144#95×C47D411yescharacteristic
145C24×C47—21no—
146C24×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47C2×D412yes—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47C2×D412yes—
169C2×D4×C47C2×D412yes—
170C2×D4×C47#4112yes—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—24no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—42no—
179C22×C4×C47—42no—
180C22×C4×C47—42no—
181C22×C4×C47—42no—
182C22×C4×C47—42no—
183C22×C4×C47—42no—
184C22×C4×C47—81no—
185C22×C4×C47—81no—
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2411yescharacteristic
193SD16×C47—28no—
194SD16×C47—44no—
195D8×C47—44no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47C2×D412yes—
208C4⋊C4×C47—22no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47—21no—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—41no—
217C4⋊C4×C47—42no—
218C4⋊C4×C47—42no—
219C4⋊C4×C47—42no—
220C4⋊C4×C47—42no—
221C4⋊C4×C47—42no—
222C4⋊C4×C47—42no—
223C4⋊C4×C47—81no—
224C4⋊C4×C47C2×D412yes—
225C22⋊C4×C47—24no—
226C22⋊C4×C47—42no—
227C22⋊C4×C47—42no—
228C22⋊C4×C47—42no—
229C22⋊C4×C47—42no—
230C22⋊C4×C47—42no—
231C22⋊C4×C47—42no—
232C22⋊C4×C47—42no—
233C22⋊C4×C47—42no—
234C42×C47—21no—
235C42×C47—21no—
236C42×C47—21no—
237C42×C47—21no—
238C42×C47—42no—
239C42×C47C2×D412yes—
240C42×C47#4112yes—
241C23×C47—22no—
242C23×C47—22no—
243C23×C47—22no—
244C23×C47—41no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47—41no—
248C23×C47—41no—
249C23×C47—41no—
250C23×C47—41no—
251C23×C47—41no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47C22×D411yescharacteristic
256Q8×C47—22no—
257Q8×C47—22no—
258Q8×C47—41no—
259Q8×C47—41no—
260Q8×C47—41no—
261Q8×C47—41no—
262Q8×C47—41no—
263Q8×C47—41no—
264D4×C47—22no—
265D4×C47—22no—
266D4×C47—22no—
267D4×C47—41no—
268D4×C47—41no—
269D4×C47—41no—
270D4×C47—41no—
271D4×C47#12114yes—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—22no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—22no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—48no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—84no—
307C2×C4×C47—84no—
308C2×C4×C47#12112yes—
309C2×C4×C47#12112yes—
310C2×C4×C47AGL(1,ℤ/8)12yes—
311C2×C4×C47C22×D411yescharacteristic
312C2×C4×C47C22×D411yescharacteristic
313C2×C4×C47C2×#4111yescharacteristic
314C2×C4×C47C2×#4111yescharacteristic
315C2×C4×C47H(5,𝔽2)11yescharacteristic
316C2×C4×C472−1+411yescharacteristic
317C8×C47—22no—
318C8×C47—41no—
319C8×C47—41no—
320C8×C47—41no—
321#24740C4711yesmaximal, characteristic, direct product factor, Sylow
322C22×C47—24no—
323C22×C47—42no—
324C22×C47—42no—
325C22×C47—42no—
326C22×C47—42no—
327C22×C47—42no—
328C22×C47—42no—
329C22×C47—81no—
330C22×C47—81no—
331C22×C47—81no—
332C22×C47—81no—
333C22×C47—81no—
334C22×C47—81no—
335C22×C47—81no—
336C22×C47C2×#12111yescharacteristic
337C22×C47D4211yescharacteristic
338C22×C47#54811yescharacteristic
339C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C47#57511yescharacteristic
341C22×C47#57711yescharacteristic
342C22×C47#57811yescharacteristic
343C4×C47—22no—
344C4×C47—22no—
345C4×C47—22no—
346C4×C47—42no—
347C4×C47—41no—
348C4×C47—41no—
349C4×C47—41no—
350C4×C47—42no—
351C4×C47—81no—
352C4×C47—81no—
353C4×C47—81no—
354C4×C47—81no—
355C4×C47C2×#12111yescharacteristic
356C4×C47#53711yescharacteristic
357C4×C47#54711yescharacteristic
358C4×C47#55311yescharacteristic
359C2×#463C2×C4711yescharacteristic
360C2×#463C2×C4711yescharacteristic
361C2×#461C2×C4711yescharacteristic, complemented
362C2×#440C2×C4711yescharacteristic, complemented
363#2545C2×C4711yescharacteristic, complemented
364D4×C4⋊C4C2×C4711yescharacteristic, complemented
365#2068C2×C4711yescharacteristic, complemented
366#2067C2×C4711yescharacteristic, complemented
367#2043C2×C4711yescharacteristic, complemented
368#2042C2×C4711yescharacteristic, complemented
369#1959C2×C4711yescharacteristic, complemented
370#1940C2×C4711yescharacteristic, complemented
371#1879C2×C4711yescharacteristic
372#1877C2×C4711yescharacteristic, complemented
373#1803C2×C4711yescharacteristic, complemented
374C2×C47—44no—
375C2×C47—161no—
376C2×C47#241611yescharacteristic
377C2×C47#303611yescharacteristic
378C2×C47#304611yescharacteristic
379C2×C47#326511yescharacteristic
380C2×C47#326911yescharacteristic
381C2×C47#336711yescharacteristic
382C2×C47#337611yescharacteristic
383C22×SD16C22×C4711yescharacteristic
384C22×SD16C22×C4711yescharacteristic
385C22×D8C22×C4711yescharacteristic
386C2×C4⋊Q8C22×C4711yescharacteristic
387C2×#124C22×C4711yescharacteristic
388C2×#124C22×C4711yescharacteristic
389C2×C4×Q8C22×C4711yescharacteristic
390C2×C4×D4C22×C4711yescharacteristic
391C2×C4×D4C22×C4711yescharacteristic
392C2×C4×D4C22×C4711yescharacteristic
393C22×C4⋊C4—21no—
394#463—24no—
395#463—24no—
396#461—24no—
397#440—24no—
398C2×#107C22×C4711yescharacteristic
399C2×C4⋊C8C22×C4711yescharacteristic
400C2×C4⋊C8C22×C4711yescharacteristic
401C2×C4⋊C8C22×C4711yescharacteristic
402C2×#103C22×C4711yescharacteristic
403C2×#103C22×C4711yescharacteristic
404C2×#103C22×C4711yescharacteristic
405C2×#103C22×C4711yescharacteristic
406C2×#103C22×C4711yescharacteristic
407C2×#103C22×C4711yescharacteristic
408C2×#102C22×C4711yescharacteristic
409C2×#102C22×C4711yescharacteristic
410C2×#102C22×C4711yescharacteristic
411C2×#102C22×C4711yescharacteristic
412C2×#97C22×C4711yescharacteristic
413#396—21no—
414#396—21no—
415#391C22×C4711yescharacteristic
416#390C22×C4711yescharacteristic
417#389C22×C4711yescharacteristic
418#389C22×C4711yescharacteristic
419#388—21no—
420#388—21no—
421#385—21no—
422#385—21no—
423#384C22×C4711yescharacteristic
424#380—21no—
425C4×C4⋊C4C22×C4711yescharacteristic
426#340C22×C4711yescharacteristic
427#340C22×C4711yescharacteristic
428#336C22×C4711yescharacteristic
429#336C22×C4711yescharacteristic
430C47#2474011yescharacteristic, direct product factor, Sylow
431C22×Q8C23×C4711yescharacteristic
432C22×Q8C23×C4711yescharacteristic
433C22×D4C23×C4711yescharacteristic
434C22×D4C23×C4711yescharacteristic
435C23×C4—21no—
436C23×C4—21no—
437C23×C4—21no—
438C2×SD16—22no—
439C2×SD16—22no—
440C2×SD16—22no—
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16D4×C4714yes—
444C2×D8—22no—
445C2×D8—22no—
446C2×D8—22no—
447C22×C8C23×C4711yescharacteristic
448C22×C8C23×C4711yescharacteristic
449C22×C8C23×C4711yescharacteristic
450C22×C8C23×C4711yescharacteristic
451C4⋊Q8—22no—
452C4⋊Q8—41no—
453#124—22no—
454#124—22no—
455#124—22no—
456#124—41no—
457C4×Q8—22no—
458C4×Q8—22no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—41no—
463C4×D4—41no—
464C4×D4D4×C4714yes—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—44no—
473C2×C4⋊C4D4×C4711yescharacteristic
474C2×C4⋊C4D4×C4711yescharacteristic
475C2×C4⋊C4C23×C4711yescharacteristic
476C2×C4⋊C4C23×C4711yescharacteristic
477C2×C4⋊C4C23×C4711yescharacteristic
478C2×C4⋊C4C23×C4711yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C42—21no—
489C2×C42C23×C4711yescharacteristic
490C2×C42C23×C4711yescharacteristic
491C2×C42C23×C4711yescharacteristic
492#107—22no—
493C4⋊C8—22no—
494C4⋊C8—22no—
495C4⋊C8—22no—
496#103—22no—
497#103—22no—
498#103—22no—
499#103—22no—
500#103—22no—
501#103—41no—
502#102—22no—
503#102—22no—
504#102—22no—
505#102—41no—
506#97—22no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95D4×C4711yescharacteristic
512#95D4×C4711yescharacteristic
513C24—21no—
514C24—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8C2×D4×C4712yes—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4C2×D4×C4712yes—
537C2×D4C2×D4×C4712yes—
538C2×D4#41×C4712yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4C2×D4×C4711yescharacteristic
555C22×C4C2×D4×C4711yescharacteristic
556C22×C4C2×D4×C4711yescharacteristic
557C22×C4C2×D4×C4711yescharacteristic
558C22×C4C2×D4×C4711yescharacteristic
559C22×C4C2×D4×C4711yescharacteristic
560C22×C4C24×C4711yescharacteristic
561SD16—28no—
562SD16—44no—
563D8—44no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8C2×D4×C4712yes—
576C4⋊C4—22no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—41no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—81no—
592C4⋊C4C2×D4×C4712yes—
593C22⋊C4—24no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—42no—
607C42C2×D4×C4712yes—
608C42#41×C4712yes—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23C22×D4×C4711yescharacteristic
624Q8—22no—
625Q8—22no—
626Q8—41no—
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—41no—
636D4—41no—
637D4—41no—
638D4—41no—
639D4#121×C4714yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—48no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—84no—
675C2×C4—84no—
676C2×C4#121×C4712yes—
677C2×C4#121×C4712yes—
678C2×C4AGL(1,ℤ/8)×C4712yes—
679C2×C4C22×D4×C4711yescharacteristic
680C2×C4C22×D4×C4711yescharacteristic
681C2×C4C2×#41×C4711yescharacteristic
682C2×C4C2×#41×C4711yescharacteristic
683C2×C4H(5,𝔽2)×C4711yescharacteristic
684C2×C42−1+4×C4711yescharacteristic
685C8—22no—
686C8—41no—
687C8—41no—
688C8—41no—
689C22—24no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22C2×#121×C4711yescharacteristic
704C22D42×C4711yescharacteristic
705C22C47×#54811yescharacteristic
706C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
707C22C47×#57511yescharacteristic
708C22C47×#57711yescharacteristic
709C22C47×#57811yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—42no—
714C4—42no—
715C4—41no—
716C4—41no—
717C4—41no—
718C4—81no—
719C4—81no—
720C4—81no—
721C4—81no—
722C4C2×#121×C4711yescharacteristic
723C4C47×#53711yescharacteristic
724C4C47×#54711yescharacteristic
725C4C47×#55311yescharacteristic
726C2—44no—
727C2—161no—
728C2C47×#241611yescharacteristic
729C2C47×#303611yescharacteristic
730C2C47×#304611yescharacteristic
731C2C47×#326511yescharacteristic
732C2C47×#326911yescharacteristic
733C2C47×#336711yescharacteristic
734C2C47×#337611yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×D8×C47C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C4⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C47×#461C2semidirect
4. C2×C47×#440C2semidirect
5. C47×#2545C2semidirect
6. D4×C4⋊C4×C47C2semidirect
7. C47×#2068C2semidirect
8. C47×#2067C2semidirect
9. C47×#2043C2semidirect
10. C47×#2042C2semidirect
11. C47×#1959C2semidirect
12. C47×#1940C2semidirect
14. C47×#1877C2semidirect
15. C47×#1803C2semidirect
321. #24740C47direct (N × H)
361. C2×#461C2×C47semidirect
362. C2×#440C2×C47semidirect
363. #2545C2×C47semidirect
364. D4×C4⋊C4C2×C47semidirect
365. #2068C2×C47semidirect
366. #2067C2×C47semidirect
367. #2043C2×C47semidirect
368. #2042C2×C47semidirect
369. #1959C2×C47semidirect
370. #1940C2×C47semidirect
372. #1877C2×C47semidirect
373. #1803C2×C47semidirect
430. C47#24740direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#4632
C2×C47×#4612
C2×C47×#4402
C47×#25452
D4×C4⋊C4×C472
C47×#20682
C47×#20672
C47×#20432
C47×#20422
C47×#19592
C47×#19402
C47×#18792
C47×#18772
C47×#18032
#2474047