Finite Group Databasebeta

← C47×#25334 #26065032

Subgroups — C47×#25334 #26065032

Order 12032.

928 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#489C211yesmaximal, characteristic, complemented
2C2×C47×#463C211yesmaximal, characteristic
3C47×#2542C211yesmaximal, characteristic, complemented
4C47×#2367C211yesmaximal, characteristic, complemented
5C47×#2072C211yesmaximal, characteristic, complemented
6C47×#2071C211yesmaximal, characteristic, complemented
7C47×#2055C211yesmaximal, characteristic, complemented
8C47×#2054C211yesmaximal, characteristic
9C47×#1987C211yesmaximal, characteristic, complemented
10C47×#1940C211yesmaximal, characteristic, complemented
11C47×#1880C211yesmaximal, characteristic, complemented
12C47×#1879C211yesmaximal, characteristic
13C47×#1803C211yesmaximal, characteristic, complemented
14C47×#1802C211yesmaximal, characteristic, complemented
15C47×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C2×C4⋊Q8×C47C2211yescharacteristic
19C2×#124×C47C2211yescharacteristic
20C2×C22⋊Q8×C47—21no—
21C2×C22⋊Q8×C47—21no—
22C2×C4×Q8×C47C2211yescharacteristic
23C2×C4×D4×C47C2211yescharacteristic
24C2×C4×D4×C47C2211yescharacteristic
25C47×#489—24no—
26C47×#463—24no—
27C2×C4⋊C8×C47C2211yescharacteristic
28C2×C4⋊C8×C47C2211yescharacteristic
29C2×C4⋊C8×C47C2211yescharacteristic
30C2×#103×C47C2211yescharacteristic
31C2×#103×C47C2211yescharacteristic
32C2×#103×C47C2211yescharacteristic
33C2×#102×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C2×#102×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×#97×C47C2211yescharacteristic
39C47×#399—21no—
40C47×#399—21no—
41C47×#391C2211yescharacteristic
42C47×#390C2211yescharacteristic
43C47×#390C2211yescharacteristic
44C47×#390C2211yescharacteristic
45C47×#388—21no—
46C47×#388—21no—
47C47×#385—21no—
48C47×#384C2211yescharacteristic
49C47×#384C2211yescharacteristic
50C4×C4⋊C4×C47C2211yescharacteristic
51C4×C4⋊C4×C47C2211yescharacteristic
52C4×C22⋊C4×C47—21no—
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C22×Q8×C47—21no—
62C22×Q8×C47C2311yescharacteristic
63C22×D4×C47C2311yescharacteristic
64C22×D4×C47C2311yescharacteristic
65C23×C4×C47—21no—
66C23×C4×C47—21no—
67C2×SD16×C47—22no—
68C2×SD16×C47—22no—
69C2×SD16×C47—41no—
70C2×D8×C47—22no—
71C2×D8×C47—22no—
72C2×D8×C47—41no—
73C22×C8×C47C2311yescharacteristic
74C22×C8×C47C2311yescharacteristic
75C22×C8×C47C2311yescharacteristic
76C22×C8×C47C2311yescharacteristic
77C4⋊Q8×C47—22no—
78C4⋊Q8×C47—22no—
79#124×C47—22no—
80#124×C47D414yes—
81C22⋊Q8×C47—44no—
82C22⋊Q8×C47—44no—
83C4×Q8×C47—22no—
84C4×Q8×C47—41no—
85C4×D4×C47—22no—
86C4×D4×C47—22no—
87C4×D4×C47—22no—
88C4×D4×C47—41no—
89C2×C4⋊C4×C47—21no—
90C2×C4⋊C4×C47—21no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47D411yescharacteristic
96C2×C4⋊C4×C47D411yescharacteristic
97C2×C4⋊C4×C47C2311yescharacteristic
98C2×C4⋊C4×C47C2311yescharacteristic
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C22⋊C4×C47—21no—
103C2×C22⋊C4×C47—21no—
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
107C2×C22⋊C4×C47—21no—
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C42×C47—21no—
113C2×C42×C47—21no—
114C2×C42×C47C2311yescharacteristic
115C2×C42×C47C2311yescharacteristic
116C2×C42×C47C2311yescharacteristic
117C4⋊C8×C47—22no—
118C4⋊C8×C47—41no—
119C4⋊C8×C47—41no—
120#103×C47—22no—
121#103×C47—22no—
122#103×C47—22no—
123#102×C47—22no—
124#102×C47—22no—
125#102×C47—22no—
126#102×C47—22no—
127#102×C47—22no—
128#97×C47—22no—
129#95×C47—21no—
130#95×C47—21no—
131#95×C47—21no—
132#95×C47D411yescharacteristic
133#95×C47D411yescharacteristic
134C24×C47—21no—
135C24×C47—21no—
136C2×Q8×C47—21no—
137C2×Q8×C47—21no—
138C2×Q8×C47—21no—
139C2×Q8×C47—21no—
140C2×Q8×C47—21no—
141C2×Q8×C47—42no—
142C2×Q8×C47—42no—
143C2×Q8×C47—42no—
144C2×Q8×C47C2×D412yes—
145C2×D4×C47—21no—
146C2×D4×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47C2×D412yes—
156C2×D4×C47#4112yes—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—42no—
164C22×C4×C47—42no—
165C22×C4×C47—42no—
166C22×C4×C47—42no—
167C22×C4×C47—42no—
168C22×C4×C47—81no—
169C22×C4×C47C2×D411yescharacteristic
170C22×C4×C47C2×D411yescharacteristic
171C22×C4×C47C2×D411yescharacteristic
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2×D411yescharacteristic
174C22×C4×C47C2×D411yescharacteristic
175C22×C4×C47C2411yescharacteristic
176SD16×C47—44no—
177D8×C47—44no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47—21no—
182C2×C8×C47—21no—
183C2×C8×C47—21no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C4⋊C4×C47—22no—
191C4⋊C4×C47—22no—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47—21no—
199C4⋊C4×C47—21no—
200C4⋊C4×C47—21no—
201C4⋊C4×C47—42no—
202C4⋊C4×C47—42no—
203C4⋊C4×C47—42no—
204C4⋊C4×C47—42no—
205C4⋊C4×C47—42no—
206C4⋊C4×C47—42no—
207C4⋊C4×C47#4112yes—
208C22⋊C4×C47—24no—
209C22⋊C4×C47—24no—
210C22⋊C4×C47—42no—
211C22⋊C4×C47—42no—
212C22⋊C4×C47—42no—
213C22⋊C4×C47—42no—
214C22⋊C4×C47—42no—
215C22⋊C4×C47—42no—
216C22⋊C4×C47—42no—
217C22⋊C4×C47—81no—
218C42×C47—21no—
219C42×C47—21no—
220C42×C47—21no—
221C42×C47—21no—
222C42×C47—42no—
223C42×C47—81no—
224C42×C47C2×D412yes—
225C42×C47#4112yes—
226C23×C47—22no—
227C23×C47—22no—
228C23×C47—41no—
229C23×C47—41no—
230C23×C47—41no—
231C23×C47—41no—
232C23×C47—41no—
233C23×C47—41no—
234C23×C47—41no—
235C23×C47—41no—
236C23×C47—41no—
237C23×C47—41no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47C22×D411yescharacteristic
241Q8×C47—22no—
242Q8×C47—22no—
243Q8×C47—41no—
244Q8×C47—41no—
245Q8×C47—84no—
246D4×C47—22no—
247D4×C47—22no—
248D4×C47—22no—
249D4×C47—22no—
250D4×C47—41no—
251D4×C47—41no—
252D4×C47—41no—
253D4×C47—41no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—22no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—22no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—84no—
287C2×C4×C47—84no—
288C2×C4×C47#12112yes—
289C2×C4×C47#12112yes—
290C2×C4×C47AGL(1,ℤ/8)12yes—
291C2×C4×C47AGL(1,ℤ/8)12yes—
292C2×C4×C47C22×D411yescharacteristic
293C2×C4×C47C2×#4111yescharacteristic
294C2×C4×C47C2×#4111yescharacteristic
295C2×C4×C47C2×#4111yescharacteristic
296C2×C4×C47H(5,𝔽2)11yescharacteristic
297C2×C4×C472−1+411yescharacteristic
298C8×C47—41no—
299C8×C47—41no—
300C8×C47—41no—
301C8×C47—41no—
302#25334C4711yesmaximal, characteristic, direct product factor, Sylow
303C22×C47—42no—
304C22×C47—42no—
305C22×C47—42no—
306C22×C47—42no—
307C22×C47—42no—
308C22×C47—42no—
309C22×C47—81no—
310C22×C47—81no—
311C22×C47—81no—
312C22×C47—81no—
313C22×C47—81no—
314C22×C47—81no—
315C22×C47—81no—
316C22×C47—81no—
317C22×C47C2×#12111yescharacteristic
318C22×C47#54611yescharacteristic
319C22×C47#54811yescharacteristic
320C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
322C22×C47#57711yescharacteristic
323C22×C47#57811yescharacteristic
324C4×C47—22no—
325C4×C47—22no—
326C4×C47—22no—
327C4×C47—22no—
328C4×C47—42no—
329C4×C47—41no—
330C4×C47—42no—
331C4×C47—41no—
332C4×C47—81no—
333C4×C47—81no—
334C4×C47—81no—
335C4×C47—81no—
336C4×C47#52911yescharacteristic
337C4×C47#54211yescharacteristic
338C4×C47#54611yescharacteristic
339C4×C47#54711yescharacteristic
340C2×#489C2×C4711yescharacteristic, complemented
341C2×#463C2×C4711yescharacteristic
342#2542C2×C4711yescharacteristic, complemented
343#2367C2×C4711yescharacteristic, complemented
344#2072C2×C4711yescharacteristic, complemented
345#2071C2×C4711yescharacteristic, complemented
346#2055C2×C4711yescharacteristic, complemented
347#2054C2×C4711yescharacteristic
348#1987C2×C4711yescharacteristic, complemented
349#1940C2×C4711yescharacteristic, complemented
350#1880C2×C4711yescharacteristic, complemented
351#1879C2×C4711yescharacteristic
352#1803C2×C4711yescharacteristic, complemented
353#1802C2×C4711yescharacteristic, complemented
354#1762C2×C4711yescharacteristic, complemented
355C2×C47—82no—
356C2×C47—82no—
357C2×C47#242711yescharacteristic
358C2×C47#303811yescharacteristic
359C2×C47#304611yescharacteristic
360C2×C47#330611yescharacteristic
361C2×C47#330811yescharacteristic
362C2×C47#336711yescharacteristic
363C2×C47#337311yescharacteristic
364C22×SD16C22×C4711yescharacteristic
365C22×D8C22×C4711yescharacteristic
366C2×C4⋊Q8C22×C4711yescharacteristic
367C2×#124C22×C4711yescharacteristic
368C2×C22⋊Q8—21no—
369C2×C22⋊Q8—21no—
370C2×C4×Q8C22×C4711yescharacteristic
371C2×C4×D4C22×C4711yescharacteristic
372C2×C4×D4C22×C4711yescharacteristic
373#489—24no—
374#463—24no—
375C2×C4⋊C8C22×C4711yescharacteristic
376C2×C4⋊C8C22×C4711yescharacteristic
377C2×C4⋊C8C22×C4711yescharacteristic
378C2×#103C22×C4711yescharacteristic
379C2×#103C22×C4711yescharacteristic
380C2×#103C22×C4711yescharacteristic
381C2×#102C22×C4711yescharacteristic
382C2×#102C22×C4711yescharacteristic
383C2×#102C22×C4711yescharacteristic
384C2×#102C22×C4711yescharacteristic
385C2×#102C22×C4711yescharacteristic
386C2×#97C22×C4711yescharacteristic
387#399—21no—
388#399—21no—
389#391C22×C4711yescharacteristic
390#390C22×C4711yescharacteristic
391#390C22×C4711yescharacteristic
392#390C22×C4711yescharacteristic
393#388—21no—
394#388—21no—
395#385—21no—
396#384C22×C4711yescharacteristic
397#384C22×C4711yescharacteristic
398C4×C4⋊C4C22×C4711yescharacteristic
399C4×C4⋊C4C22×C4711yescharacteristic
400C4×C22⋊C4—21no—
401#340C22×C4711yescharacteristic
402#340C22×C4711yescharacteristic
403#340C22×C4711yescharacteristic
404#340C22×C4711yescharacteristic
405#340C22×C4711yescharacteristic
406#340C22×C4711yescharacteristic
407#336C22×C4711yescharacteristic
408#336C22×C4711yescharacteristic
409C47#2533411yescharacteristic, direct product factor, Sylow
410C22×Q8—21no—
411C22×Q8C23×C4711yescharacteristic
412C22×D4C23×C4711yescharacteristic
413C22×D4C23×C4711yescharacteristic
414C23×C4—21no—
415C23×C4—21no—
416C2×SD16—22no—
417C2×SD16—22no—
418C2×SD16—41no—
419C2×D8—22no—
420C2×D8—22no—
421C2×D8—41no—
422C22×C8C23×C4711yescharacteristic
423C22×C8C23×C4711yescharacteristic
424C22×C8C23×C4711yescharacteristic
425C22×C8C23×C4711yescharacteristic
426C4⋊Q8—22no—
427C4⋊Q8—22no—
428#124—22no—
429#124D4×C4714yes—
430C22⋊Q8—44no—
431C22⋊Q8—44no—
432C4×Q8—22no—
433C4×Q8—41no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—41no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4D4×C4711yescharacteristic
445C2×C4⋊C4D4×C4711yescharacteristic
446C2×C4⋊C4C23×C4711yescharacteristic
447C2×C4⋊C4C23×C4711yescharacteristic
448C2×C4⋊C4C23×C4711yescharacteristic
449C2×C4⋊C4C23×C4711yescharacteristic
450C2×C4⋊C4C23×C4711yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42C23×C4711yescharacteristic
464C2×C42C23×C4711yescharacteristic
465C2×C42C23×C4711yescharacteristic
466C4⋊C8—22no—
467C4⋊C8—41no—
468C4⋊C8—41no—
469#103—22no—
470#103—22no—
471#103—22no—
472#102—22no—
473#102—22no—
474#102—22no—
475#102—22no—
476#102—22no—
477#97—22no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95D4×C4711yescharacteristic
482#95D4×C4711yescharacteristic
483C24—21no—
484C24—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8C2×D4×C4712yes—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4C2×D4×C4712yes—
505C2×D4#41×C4712yes—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—81no—
518C22×C4C2×D4×C4711yescharacteristic
519C22×C4C2×D4×C4711yescharacteristic
520C22×C4C2×D4×C4711yescharacteristic
521C22×C4C2×D4×C4711yescharacteristic
522C22×C4C2×D4×C4711yescharacteristic
523C22×C4C2×D4×C4711yescharacteristic
524C22×C4C24×C4711yescharacteristic
525SD16—44no—
526D8—44no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4#41×C4712yes—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—81no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C42—81no—
573C42C2×D4×C4712yes—
574C42#41×C4712yes—
575C23—22no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23C22×D4×C4711yescharacteristic
590Q8—22no—
591Q8—22no—
592Q8—41no—
593Q8—41no—
594Q8—84no—
595D4—22no—
596D4—22no—
597D4—22no—
598D4—22no—
599D4—41no—
600D4—41no—
601D4—41no—
602D4—41no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—84no—
636C2×C4—84no—
637C2×C4#121×C4712yes—
638C2×C4#121×C4712yes—
639C2×C4AGL(1,ℤ/8)×C4712yes—
640C2×C4AGL(1,ℤ/8)×C4712yes—
641C2×C4C22×D4×C4711yescharacteristic
642C2×C4C2×#41×C4711yescharacteristic
643C2×C4C2×#41×C4711yescharacteristic
644C2×C4C2×#41×C4711yescharacteristic
645C2×C4H(5,𝔽2)×C4711yescharacteristic
646C2×C42−1+4×C4711yescharacteristic
647C8—41no—
648C8—41no—
649C8—41no—
650C8—41no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22C2×#121×C4711yescharacteristic
666C22C47×#54611yescharacteristic
667C22C47×#54811yescharacteristic
668C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
669C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
670C22C47×#57711yescharacteristic
671C22C47×#57811yescharacteristic
672C4—22no—
673C4—22no—
674C4—22no—
675C4—22no—
676C4—41no—
677C4—42no—
678C4—41no—
679C4—42no—
680C4—81no—
681C4—81no—
682C4—81no—
683C4—81no—
684C4C47×#52911yescharacteristic
685C4C47×#54211yescharacteristic
686C4C47×#54611yescharacteristic
687C4C47×#54711yescharacteristic
688C2—82no—
689C2—82no—
690C2C47×#242711yescharacteristic
691C2C47×#303811yescharacteristic
692C2C47×#304611yescharacteristic
693C2C47×#330611yescharacteristic
694C2C47×#330811yescharacteristic
695C2C47×#336711yescharacteristic
696C2C47×#337311yescharacteristic
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
1. C2×C47×#489C2semidirect
3. C47×#2542C2semidirect
4. C47×#2367C2semidirect
5. C47×#2072C2semidirect
6. C47×#2071C2semidirect
7. C47×#2055C2semidirect
9. C47×#1987C2semidirect
10. C47×#1940C2semidirect
11. C47×#1880C2semidirect
13. C47×#1803C2semidirect
14. C47×#1802C2semidirect
15. C47×#1762C2semidirect
302. #25334C47direct (N × H)
340. C2×#489C2×C47semidirect
342. #2542C2×C47semidirect
343. #2367C2×C47semidirect
344. #2072C2×C47semidirect
345. #2071C2×C47semidirect
346. #2055C2×C47semidirect
348. #1987C2×C47semidirect
349. #1940C2×C47semidirect
350. #1880C2×C47semidirect
352. #1803C2×C47semidirect
353. #1802C2×C47semidirect
354. #1762C2×C47semidirect
409. C47#25334direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#4892
C2×C47×#4632
C47×#25422
C47×#23672
C47×#20722
C47×#20712
C47×#20552
C47×#20542
C47×#19872
C47×#19402
C47×#18802
C47×#18792
C47×#18032
C47×#18022
C47×#17622
#2533447