Finite Group Databasebeta

← C47×#24786 #26064484

Subgroups — C47×#24786 #26064484

Order 12032.

990 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#468C211yesmaximal, characteristic, complemented
2C2×C47×#465C211yesmaximal, characteristic, complemented
3C2×C47×#435C211yesmaximal, characteristic, complemented
4C2×C47×#427C211yesmaximal, characteristic, complemented
5C47×#2415C211yesmaximal, characteristic, complemented
6C47×#2414C211yesmaximal, characteristic
7C47×#2066C211yesmaximal, characteristic, complemented
8C47×#2065C211yesmaximal, characteristic, complemented
9C47×#2035C211yesmaximal, characteristic, complemented
10C47×#2034C211yesmaximal, characteristic, complemented
11C47×#1973C211yesmaximal, characteristic, complemented
12C47×#1943C211yesmaximal, characteristic, complemented
13C47×#1875C211yesmaximal, characteristic, complemented
14C47×#1873C211yesmaximal, characteristic, complemented
15C47×#1809C211yesmaximal, characteristic, complemented
16C22×SD16×C47C2211yescharacteristic
17C22×M16×C47C2211yescharacteristic
18C23×C8×C47C2211yescharacteristic
19C2×C22⋊Q8×C47C2211yescharacteristic
20C2×C22⋊Q8×C47C2211yescharacteristic
21C2×#121×C47C2211yescharacteristic
22C2×#121×C47C2211yescharacteristic
23C2×C4×D4×C47C2211yescharacteristic
24C2×#117×C47C2211yescharacteristic
25C2×#117×C47C2211yescharacteristic
26C47×#468—24no—
27C47×#465—24no—
28C47×#435—24no—
29C47×#427—24no—
30C2×#107×C47C2211yescharacteristic
31C2×#107×C47C2211yescharacteristic
32C2×#106×C47C2211yescharacteristic
33C2×#106×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×C22⋊C8×C47C2211yescharacteristic
43C2×C22⋊C8×C47C2211yescharacteristic
44C2×#97×C47C2211yescharacteristic
45C47×#397—21no—
46C47×#394—21no—
47C47×#394—21no—
48C47×#392—21no—
49C47×#391C2211yescharacteristic
50C47×#390—21no—
51C47×#390C2211yescharacteristic
52C47×#389—21no—
53C47×#389C2211yescharacteristic
54C47×#389C2211yescharacteristic
55C47×#388—21no—
56C47×#388—21no—
57C47×#380C2211yescharacteristic
58C47×#380C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47D411yescharacteristic
67C22×D4×C47C2311yescharacteristic
68C23×C4×C47C2311yescharacteristic
69C23×C4×C47C2311yescharacteristic
70C2×SD16×C47—22no—
71C2×SD16×C47—22no—
72C2×SD16×C47—22no—
73C2×M16×C47—22no—
74C2×M16×C47—22no—
75C2×M16×C47—22no—
76C22×C8×C47—22no—
77C22×C8×C47—22no—
78C22×C8×C47D414yescomplemented
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C22⋊Q8×C47—22no—
84C22⋊Q8×C47—22no—
85C22⋊Q8×C47—22no—
86C22⋊Q8×C47—41no—
87#121×C47—22no—
88#121×C47—22no—
89#121×C47—22no—
90#121×C47—41no—
91C4×D4×C47—22no—
92C4×D4×C47—22no—
93#117×C47—22no—
94#117×C47—22no—
95#117×C47—41no—
96#117×C47—41no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47D411yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
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×C47D411yescharacteristic
119C2×C22⋊C4×C47D411yescharacteristic
120C2×C42×C47—21no—
121C2×C42×C47—21no—
122C2×C42×C47C2311yescharacteristic
123#107×C47—22no—
124#107×C47D414yescomplemented
125#106×C47—22no—
126#106×C47—22no—
127#106×C47—22no—
128C4⋊C8×C47—22no—
129#103×C47—22no—
130#103×C47—22no—
131#103×C47—41no—
132#102×C47—22no—
133#102×C47—22no—
134#102×C47—41no—
135C22⋊C8×C47—22no—
136C22⋊C8×C47—22no—
137#97×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
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×D4×C47—22no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—41no—
161C2×D4×C47—41no—
162C2×D4×C47—42no—
163C2×D4×C47—42no—
164C2×D4×C47—42no—
165C2×D4×C47—81no—
166C2×D4×C47—81no—
167C2×D4×C47—81no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D412yes—
190C22×C4×C47#4112yes—
191C22×C4×C47C2411yescharacteristic
192SD16×C47—44no—
193M16×C47—44no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—28no—
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×C47C2×D412yes—
204C2×C8×C47C2×D412yes—
205C2×C8×C47C2×D412yes—
206C2×C8×C47#4112yes—
207C4⋊C4×C47—22no—
208C4⋊C4×C47—21no—
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—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—42no—
219C4⋊C4×C47—42no—
220C4⋊C4×C47—42no—
221C4⋊C4×C47—81no—
222C4⋊C4×C47C2×D412yes—
223C4⋊C4×C47C2×D412yes—
224C22⋊C4×C47—22no—
225C22⋊C4×C47—22no—
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—
234C22⋊C4×C47—81no—
235C22⋊C4×C47—81no—
236C42×C47—21no—
237C42×C47—21no—
238C42×C47—42no—
239C42×C47—42no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47#12112yes—
261C23×C47C22×D411yescharacteristic
262Q8×C47—41no—
263Q8×C47—41no—
264Q8×C47—41no—
265Q8×C47—41no—
266D4×C47—44no—
267D4×C47—41no—
268D4×C47—41no—
269D4×C47—41no—
270D4×C47—41no—
271D4×C47—84no—
272D4×C47—84no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
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—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47#12112yes—
314C2×C4×C47C22×D411yescharacteristic
315C2×C4×C47C22×D411yescharacteristic
316C2×C4×C47C2×#4111yescharacteristic
317C2×C4×C47C2×#4111yescharacteristic
318C2×C4×C47H(5,𝔽2)11yescharacteristic
319C2×C4×C472−1+411yescharacteristic
320C8×C47—22no—
321C8×C47—41no—
322C8×C47—41no—
323C8×C47#12114yes—
324#24786C4711yesmaximal, characteristic, direct product factor, Sylow
325C22×C47—22no—
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—41no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47—41no—
334C22×C47—41no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—81no—
340C22×C47—81no—
341C22×C47—81no—
342C22×C47—81no—
343C22×C47—81no—
344C22×C47—81no—
345C22×C47—81no—
346C22×C47C2×#12111yescharacteristic
347C22×C47D4211yescharacteristic
348C22×C47#54711yescharacteristic
349C22×C47#57511yescharacteristic
350C22×C47#57511yescharacteristic
351C22×C47#57711yescharacteristic
352C22×C47#57711yescharacteristic
353C4×C47—22no—
354C4×C47—41no—
355C4×C47—42no—
356C4×C47—42no—
357C4×C47—41no—
358C4×C47—41no—
359C4×C47—81no—
360C4×C47—81no—
361C4×C47—81no—
362C4×C47—81no—
363C4×C47—81no—
364C4×C47C2×#12111yescharacteristic
365C4×C47#53711yescharacteristic
366C4×C47#54811yescharacteristic
367C4×C47#55311yescharacteristic
368C2×#468C2×C4711yescharacteristic, complemented
369C2×#465C2×C4711yescharacteristic, complemented
370C2×#435C2×C4711yescharacteristic, complemented
371C2×#427C2×C4711yescharacteristic, complemented
372#2415C2×C4711yescharacteristic, complemented
373#2414C2×C4711yescharacteristic
374#2066C2×C4711yescharacteristic, complemented
375#2065C2×C4711yescharacteristic, complemented
376#2035C2×C4711yescharacteristic, complemented
377#2034C2×C4711yescharacteristic, complemented
378#1973C2×C4711yescharacteristic, complemented
379#1943C2×C4711yescharacteristic, complemented
380#1875C2×C4711yescharacteristic, complemented
381#1873C2×C4711yescharacteristic, complemented
382#1809C2×C4711yescharacteristic, complemented
383C2×C47—42no—
384C2×C47—81no—
385C2×C47—161no—
386C2×C47#241611yescharacteristic
387C2×C47#305411yescharacteristic
388C2×C47#305711yescharacteristic
389C2×C47#326711yescharacteristic
390C2×C47#327111yescharacteristic
391C2×C47#334811yescharacteristic
392C2×C47#335011yescharacteristic
393C22×SD16C22×C4711yescharacteristic
394C22×M16C22×C4711yescharacteristic
395C23×C8C22×C4711yescharacteristic
396C2×C22⋊Q8C22×C4711yescharacteristic
397C2×C22⋊Q8C22×C4711yescharacteristic
398C2×#121C22×C4711yescharacteristic
399C2×#121C22×C4711yescharacteristic
400C2×C4×D4C22×C4711yescharacteristic
401C2×#117C22×C4711yescharacteristic
402C2×#117C22×C4711yescharacteristic
403#468—24no—
404#465—24no—
405#435—24no—
406#427—24no—
407C2×#107C22×C4711yescharacteristic
408C2×#107C22×C4711yescharacteristic
409C2×#106C22×C4711yescharacteristic
410C2×#106C22×C4711yescharacteristic
411C2×#106C22×C4711yescharacteristic
412C2×C4⋊C8C22×C4711yescharacteristic
413C2×#103C22×C4711yescharacteristic
414C2×#103C22×C4711yescharacteristic
415C2×#103C22×C4711yescharacteristic
416C2×#102C22×C4711yescharacteristic
417C2×#102C22×C4711yescharacteristic
418C2×#102C22×C4711yescharacteristic
419C2×C22⋊C8C22×C4711yescharacteristic
420C2×C22⋊C8C22×C4711yescharacteristic
421C2×#97C22×C4711yescharacteristic
422#397—21no—
423#394—21no—
424#394—21no—
425#392—21no—
426#391C22×C4711yescharacteristic
427#390—21no—
428#390C22×C4711yescharacteristic
429#389—21no—
430#389C22×C4711yescharacteristic
431#389C22×C4711yescharacteristic
432#388—21no—
433#388—21no—
434#380C22×C4711yescharacteristic
435#380C22×C4711yescharacteristic
436#340C22×C4711yescharacteristic
437#340C22×C4711yescharacteristic
438#340C22×C4711yescharacteristic
439#340C22×C4711yescharacteristic
440C47#2478611yescharacteristic, direct product factor, Sylow
441C22×Q8C23×C4711yescharacteristic
442C22×D4—21no—
443C22×D4—21no—
444C22×D4D4×C4711yescharacteristic
445C22×D4C23×C4711yescharacteristic
446C23×C4C23×C4711yescharacteristic
447C23×C4C23×C4711yescharacteristic
448C2×SD16—22no—
449C2×SD16—22no—
450C2×SD16—22no—
451C2×M16—22no—
452C2×M16—22no—
453C2×M16—22no—
454C22×C8—22no—
455C22×C8—22no—
456C22×C8D4×C4714yescomplemented
457C22×C8C23×C4711yescharacteristic
458C22×C8C23×C4711yescharacteristic
459C22×C8C23×C4711yescharacteristic
460C22×C8C23×C4711yescharacteristic
461C22⋊Q8—22no—
462C22⋊Q8—22no—
463C22⋊Q8—22no—
464C22⋊Q8—41no—
465#121—22no—
466#121—22no—
467#121—22no—
468#121—41no—
469C4×D4—22no—
470C4×D4—22no—
471#117—22no—
472#117—22no—
473#117—41no—
474#117—41no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4D4×C4711yescharacteristic
480C2×C4⋊C4C23×C4711yescharacteristic
481C2×C4⋊C4C23×C4711yescharacteristic
482C2×C4⋊C4C23×C4711yescharacteristic
483C2×C4⋊C4C23×C4711yescharacteristic
484C2×C4⋊C4C23×C4711yescharacteristic
485C2×C4⋊C4C23×C4711yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4D4×C4711yescharacteristic
497C2×C22⋊C4D4×C4711yescharacteristic
498C2×C42—21no—
499C2×C42—21no—
500C2×C42C23×C4711yescharacteristic
501#107—22no—
502#107D4×C4714yescomplemented
503#106—22no—
504#106—22no—
505#106—22no—
506C4⋊C8—22no—
507#103—22no—
508#103—22no—
509#103—41no—
510#102—22no—
511#102—22no—
512#102—41no—
513C22⋊C8—22no—
514C22⋊C8—22no—
515#97—22no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522C24—21no—
523C24C2×D4×C4711yescharacteristic
524C24C2×D4×C4711yescharacteristic
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×D4—22no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—41no—
539C2×D4—41no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—81no—
544C2×D4—81no—
545C2×D4—81no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4C2×D4×C4711yescharacteristic
564C22×C4C2×D4×C4711yescharacteristic
565C22×C4C2×D4×C4711yescharacteristic
566C22×C4C2×D4×C4711yescharacteristic
567C22×C4C2×D4×C4712yes—
568C22×C4#41×C4712yes—
569C22×C4C24×C4711yescharacteristic
570SD16—44no—
571M16—44no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—28no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8C2×D4×C4712yes—
582C2×C8C2×D4×C4712yes—
583C2×C8C2×D4×C4712yes—
584C2×C8#41×C4712yes—
585C4⋊C4—22no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—81no—
600C4⋊C4C2×D4×C4712yes—
601C4⋊C4C2×D4×C4712yes—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C42—21no—
615C42—21no—
616C42—42no—
617C42—42no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23#121×C4712yes—
639C23C22×D4×C4711yescharacteristic
640Q8—41no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644D4—44no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—84no—
650D4—84no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4#121×C4712yes—
692C2×C4C22×D4×C4711yescharacteristic
693C2×C4C22×D4×C4711yescharacteristic
694C2×C4C2×#41×C4711yescharacteristic
695C2×C4C2×#41×C4711yescharacteristic
696C2×C4H(5,𝔽2)×C4711yescharacteristic
697C2×C42−1+4×C4711yescharacteristic
698C8—22no—
699C8—41no—
700C8—41no—
701C8#121×C4714yes—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22C2×#121×C4711yescharacteristic
724C22D42×C4711yescharacteristic
725C22C47×#54711yescharacteristic
726C22C47×#57511yescharacteristic
727C22C47×#57511yescharacteristic
728C22C47×#57711yescharacteristic
729C22C47×#57711yescharacteristic
730C4—22no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—42no—
735C4—42no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4C2×#121×C4711yescharacteristic
742C4C47×#53711yescharacteristic
743C4C47×#54811yescharacteristic
744C4C47×#55311yescharacteristic
745C2—42no—
746C2—81no—
747C2—161no—
748C2C47×#241611yescharacteristic
749C2C47×#305411yescharacteristic
750C2C47×#305711yescharacteristic
751C2C47×#326711yescharacteristic
752C2C47×#327111yescharacteristic
753C2C47×#334811yescharacteristic
754C2C47×#335011yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#2414C2
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×#468C2semidirect
2. C2×C47×#465C2semidirect
3. C2×C47×#435C2semidirect
4. C2×C47×#427C2semidirect
5. C47×#2415C2semidirect
7. C47×#2066C2semidirect
8. C47×#2065C2semidirect
9. C47×#2035C2semidirect
10. C47×#2034C2semidirect
11. C47×#1973C2semidirect
12. C47×#1943C2semidirect
13. C47×#1875C2semidirect
14. C47×#1873C2semidirect
15. C47×#1809C2semidirect
78. C22×C8×C47D4semidirect
124. #107×C47D4semidirect
324. #24786C47direct (N × H)
368. C2×#468C2×C47semidirect
369. C2×#465C2×C47semidirect
370. C2×#435C2×C47semidirect
371. C2×#427C2×C47semidirect
372. #2415C2×C47semidirect
374. #2066C2×C47semidirect
375. #2065C2×C47semidirect
376. #2035C2×C47semidirect
377. #2034C2×C47semidirect
378. #1973C2×C47semidirect
379. #1943C2×C47semidirect
380. #1875C2×C47semidirect
381. #1873C2×C47semidirect
382. #1809C2×C47semidirect
440. C47#24786direct (N × H)
456. C22×C8D4×C47semidirect
502. #107D4×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×#4652
C2×C47×#4352
C2×C47×#4272
C47×#24152
C47×#24142
C47×#20662
C47×#20652
C47×#20352
C47×#20342
C47×#19732
C47×#19432
C47×#18752
C47×#18732
C47×#18092
#2478647