Finite Group Databasebeta

← C47×#25086 #26064784

Subgroups — C47×#25086 #26064784

Order 12032.

1108 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#465C211yesmaximal, characteristic
2C2×C47×#464C211yesmaximal, characteristic, complemented
3C2×C47×#451C211yesmaximal, characteristic, complemented
4C22×#103×C47C211yesmaximal, characteristic, complemented
5C47×#2436C211yesmaximal, characteristic
6C47×#2360C211yesmaximal, characteristic, complemented
7C47×#2066C211yesmaximal, characteristic, complemented
8C47×#2056C211yesmaximal, characteristic, complemented
9C47×#2042C211yesmaximal, characteristic, complemented
10C47×#2015C211yesmaximal, characteristic, complemented
11C47×#1983C211yesmaximal, characteristic, complemented
12C47×#1927C211yesmaximal, characteristic, complemented
13C47×#1878C211yesmaximal, characteristic, complemented
14C47×#1874C211yesmaximal, characteristic
15C47×#1850C211yesmaximal, characteristic, complemented
16C23×Q8×C47C2211yescharacteristic
17C22×Q16×C47C2211yescharacteristic
18C22×Q16×C47C2211yescharacteristic
19C22×SD16×C47C2211yescharacteristic
20C23×C8×C47C2211yescharacteristic
21C2×#124×C47C2211yescharacteristic
22C2×#124×C47C2211yescharacteristic
23C2×C22⋊Q8×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×C4×Q8×C47C2211yescharacteristic
26C22×C4⋊C4×C47C2211yescharacteristic
27C47×#465—24no—
28C47×#464—24no—
29C47×#451—24no—
30C2×#106×C47C2211yescharacteristic
31C2×C4⋊C8×C47C2211yescharacteristic
32C2×C4⋊C8×C47C2211yescharacteristic
33C2×#103×C47—24no—
34C2×#103×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×C22⋊C8×C47C2211yescharacteristic
45C47×#393—21no—
46C47×#393—21no—
47C47×#391C2211yescharacteristic
48C47×#391C2211yescharacteristic
49C47×#391C2211yescharacteristic
50C47×#389—21no—
51C47×#389C2211yescharacteristic
52C47×#387—21no—
53C47×#386—21no—
54C47×#386—21no—
55C47×#385—21no—
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C22⋊C4×C47—21no—
58C4×C22⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Q8×C47—21no—
64C22×Q8×C47—22no—
65C22×Q8×C47—22no—
66C22×Q8×C47—22no—
67C22×Q8×C47—22no—
68C22×Q8×C47—41no—
69C22×Q8×C47—41no—
70C22×Q8×C47C2311yescharacteristic
71C22×Q8×C47C2311yescharacteristic
72C22×Q8×C47C2311yescharacteristic
73C22×D4×C47—21no—
74C22×D4×C47C2311yescharacteristic
75C23×C4×C47—21no—
76C23×C4×C47—21no—
77C23×C4×C47C2311yescharacteristic
78C2×Q16×C47—22no—
79C2×Q16×C47—22no—
80C2×Q16×C47—22no—
81C2×Q16×C47—22no—
82C2×Q16×C47—41no—
83C2×Q16×C47—41no—
84C2×SD16×C47—22no—
85C2×SD16×C47—22no—
86C2×SD16×C47—41no—
87C22×C8×C47—22no—
88C22×C8×C47—22no—
89C22×C8×C47—41no—
90C22×C8×C47C2311yescharacteristic
91C22×C8×C47C2311yescharacteristic
92C22×C8×C47C2311yescharacteristic
93C22×C8×C47C2311yescharacteristic
94#124×C47—22no—
95#124×C47—22no—
96#124×C47—41no—
97#124×C47—41no—
98C22⋊Q8×C47—22no—
99C22⋊Q8×C47D414yes—
100#121×C47—22no—
101#121×C47—22no—
102C4×Q8×C47—22no—
103C4×Q8×C47—41no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—22no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—41no—
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
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×C47D411yescharacteristic
121C2×C22⋊C4×C47D411yescharacteristic
122C2×C42×C47—21no—
123C2×C42×C47—21no—
124C2×C42×C47C2311yescharacteristic
125C2×C42×C47C2311yescharacteristic
126#106×C47—22no—
127C4⋊C8×C47—22no—
128C4⋊C8×C47—41no—
129#103×C47—22no—
130#103×C47—22no—
131#103×C47—22no—
132#103×C47—22no—
133#103×C47—22no—
134#103×C47—22no—
135#103×C47D414yescomplemented
136#102×C47—22no—
137#102×C47—22no—
138#102×C47—41no—
139C22⋊C8×C47—22no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47—21no—
143#95×C47—21no—
144#95×C47—21no—
145#95×C47—21no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47D411yescharacteristic
149#95×C47D411yescharacteristic
150C24×C47—21no—
151C24×C47C2×D411yescharacteristic
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—28no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×Q8×C47—42no—
169C2×Q8×C47—42no—
170C2×Q8×C47—44no—
171C2×Q8×C47—44no—
172C2×Q8×C47—44no—
173C2×Q8×C47—42no—
174C2×Q8×C47C2×D412yes—
175C2×Q8×C47C2×D412yes—
176C2×Q8×C47#4112yes—
177C2×D4×C47—21no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—21no—
182C2×D4×C47—21no—
183C2×D4×C47—42no—
184C2×D4×C47—42no—
185C2×D4×C47—42no—
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—42no—
198C22×C4×C47—42no—
199C22×C4×C47—42no—
200C22×C4×C47—42no—
201C22×C4×C47—42no—
202C22×C4×C47—81no—
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D412yes—
209C22×C4×C47#4112yes—
210C22×C4×C47C2411yescharacteristic
211Q16×C47—44no—
212Q16×C47—44no—
213SD16×C47—44no—
214C2×C8×C47—21no—
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—21no—
225C2×C8×C47—44no—
226C2×C8×C47C2×D412yes—
227C4⋊C4×C47—24no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—42no—
235C4⋊C4×C47—42no—
236C4⋊C4×C47—81no—
237C4⋊C4×C47C2×D412yes—
238C4⋊C4×C47C2×D412yes—
239C22⋊C4×C47—24no—
240C22⋊C4×C47—22no—
241C22⋊C4×C47—22no—
242C22⋊C4×C47—42no—
243C22⋊C4×C47—42no—
244C22⋊C4×C47—42no—
245C22⋊C4×C47—42no—
246C22⋊C4×C47—42no—
247C42×C47—21no—
248C42×C47—21no—
249C42×C47—21no—
250C42×C47—21no—
251C42×C47—42no—
252C42×C47—81no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—41no—
263C23×C47—41no—
264C23×C47#12112yes—
265C23×C47#13512yes—
266C23×C47#13712yes—
267C23×C47C22×D411yescharacteristic
268Q8×C47—22no—
269Q8×C47—22no—
270Q8×C47—22no—
271Q8×C47—22no—
272Q8×C47—22no—
273Q8×C47—22no—
274Q8×C47—48no—
275Q8×C47—41no—
276Q8×C47—41no—
277Q8×C47—41no—
278Q8×C47—41no—
279Q8×C47—41no—
280Q8×C47—41no—
281D4×C47—41no—
282D4×C47—41no—
283D4×C47—41no—
284D4×C47—41no—
285D4×C47—84no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—22no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—48no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
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—84no—
327C2×C4×C47#12112yes—
328C2×C4×C47C22×D411yescharacteristic
329C2×C4×C47C22×D411yescharacteristic
330C2×C4×C47C2×#4111yescharacteristic
331C2×C4×C47C2×#4111yescharacteristic
332C2×C4×C47H(5,𝔽2)11yescharacteristic
333C2×C4×C47H(5,𝔽2)11yescharacteristic
334C8×C47—22no—
335C8×C47—41no—
336C8×C47—41no—
337C8×C47—41no—
338#25086C4711yesmaximal, characteristic, direct product factor, Sylow
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—81no—
346C22×C47—81no—
347C22×C47—81no—
348C22×C47—81no—
349C22×C47—81no—
350C22×C47—81no—
351C22×C47—81no—
352C22×C47#46414yescomplemented
353C22×C47C2×#12111yescharacteristic
354C22×C47D4211yescharacteristic
355C22×C47#54611yescharacteristic
356C22×C47C2×#13511yescharacteristic
357C22×C47C2×#13711yescharacteristic
358C22×C47#57711yescharacteristic
359C22×C47#57811yescharacteristic
360C4×C47—22no—
361C4×C47—42no—
362C4×C47—42no—
363C4×C47—42no—
364C4×C47—41no—
365C4×C47—41no—
366C4×C47—42no—
367C4×C47—41no—
368C4×C47—42no—
369C4×C47—41no—
370C4×C47—81no—
371C4×C47—81no—
372C4×C47#52511yescharacteristic
373C4×C47#53811yescharacteristic
374C4×C47D4211yescharacteristic
375C4×C47#54611yescharacteristic
376C2×#465C2×C4711yescharacteristic
377C2×#464C2×C4711yescharacteristic, complemented
378C2×#451C2×C4711yescharacteristic, complemented
379C22×#103C2×C4711yescharacteristic, complemented
380#2436C2×C4711yescharacteristic
381#2360C2×C4711yescharacteristic, complemented
382#2066C2×C4711yescharacteristic, complemented
383#2056C2×C4711yescharacteristic, complemented
384#2042C2×C4711yescharacteristic, complemented
385#2015C2×C4711yescharacteristic, complemented
386#1983C2×C4711yescharacteristic, complemented
387#1927C2×C4711yescharacteristic, complemented
388#1878C2×C4711yescharacteristic, complemented
389#1874C2×C4711yescharacteristic
390#1850C2×C4711yescharacteristic, complemented
391C2×C47—24no—
392C2×C47—161no—
393C2×C47#242411yescharacteristic
394C2×C47C2×#46411yescharacteristic
395C2×C47#304611yescharacteristic
396C2×C47#327011yescharacteristic
397C2×C47#328211yescharacteristic
398C2×C47#330011yescharacteristic
399C2×C47#331611yescharacteristic
400C23×Q8C22×C4711yescharacteristic
401C22×Q16C22×C4711yescharacteristic
402C22×Q16C22×C4711yescharacteristic
403C22×SD16C22×C4711yescharacteristic
404C23×C8C22×C4711yescharacteristic
405C2×#124C22×C4711yescharacteristic
406C2×#124C22×C4711yescharacteristic
407C2×C22⋊Q8C22×C4711yescharacteristic
408C2×#121C22×C4711yescharacteristic
409C2×C4×Q8C22×C4711yescharacteristic
410C22×C4⋊C4C22×C4711yescharacteristic
411#465—24no—
412#464—24no—
413#451—24no—
414C2×#106C22×C4711yescharacteristic
415C2×C4⋊C8C22×C4711yescharacteristic
416C2×C4⋊C8C22×C4711yescharacteristic
417C2×#103—24no—
418C2×#103C22×C4711yescharacteristic
419C2×#103C22×C4711yescharacteristic
420C2×#103C22×C4711yescharacteristic
421C2×#103C22×C4711yescharacteristic
422C2×#103C22×C4711yescharacteristic
423C2×#103C22×C4711yescharacteristic
424C2×#103C22×C4711yescharacteristic
425C2×#102C22×C4711yescharacteristic
426C2×#102C22×C4711yescharacteristic
427C2×#102C22×C4711yescharacteristic
428C2×C22⋊C8C22×C4711yescharacteristic
429#393—21no—
430#393—21no—
431#391C22×C4711yescharacteristic
432#391C22×C4711yescharacteristic
433#391C22×C4711yescharacteristic
434#389—21no—
435#389C22×C4711yescharacteristic
436#387—21no—
437#386—21no—
438#386—21no—
439#385—21no—
440C4×C4⋊C4C22×C4711yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4C22×C4711yescharacteristic
443#340C22×C4711yescharacteristic
444#340C22×C4711yescharacteristic
445#336C22×C4711yescharacteristic
446#336C22×C4711yescharacteristic
447C47#2508611yescharacteristic, direct product factor, Sylow
448C22×Q8—21no—
449C22×Q8—22no—
450C22×Q8—22no—
451C22×Q8—22no—
452C22×Q8—22no—
453C22×Q8—41no—
454C22×Q8—41no—
455C22×Q8C23×C4711yescharacteristic
456C22×Q8C23×C4711yescharacteristic
457C22×Q8C23×C4711yescharacteristic
458C22×D4—21no—
459C22×D4C23×C4711yescharacteristic
460C23×C4—21no—
461C23×C4—21no—
462C23×C4C23×C4711yescharacteristic
463C2×Q16—22no—
464C2×Q16—22no—
465C2×Q16—22no—
466C2×Q16—22no—
467C2×Q16—41no—
468C2×Q16—41no—
469C2×SD16—22no—
470C2×SD16—22no—
471C2×SD16—41no—
472C22×C8—22no—
473C22×C8—22no—
474C22×C8—41no—
475C22×C8C23×C4711yescharacteristic
476C22×C8C23×C4711yescharacteristic
477C22×C8C23×C4711yescharacteristic
478C22×C8C23×C4711yescharacteristic
479#124—22no—
480#124—22no—
481#124—41no—
482#124—41no—
483C22⋊Q8—22no—
484C22⋊Q8D4×C4714yes—
485#121—22no—
486#121—22no—
487C4×Q8—22no—
488C4×Q8—41no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—41no—
495C2×C4⋊C4C23×C4711yescharacteristic
496C2×C4⋊C4C23×C4711yescharacteristic
497C2×C4⋊C4C23×C4711yescharacteristic
498C2×C4⋊C4C23×C4711yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4D4×C4711yescharacteristic
506C2×C22⋊C4D4×C4711yescharacteristic
507C2×C42—21no—
508C2×C42—21no—
509C2×C42C23×C4711yescharacteristic
510C2×C42C23×C4711yescharacteristic
511#106—22no—
512C4⋊C8—22no—
513C4⋊C8—41no—
514#103—22no—
515#103—22no—
516#103—22no—
517#103—22no—
518#103—22no—
519#103—22no—
520#103D4×C4714yescomplemented
521#102—22no—
522#102—22no—
523#102—41no—
524C22⋊C8—22no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95D4×C4711yescharacteristic
534#95D4×C4711yescharacteristic
535C24—21no—
536C24C2×D4×C4711yescharacteristic
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—28no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—42no—
554C2×Q8—42no—
555C2×Q8—44no—
556C2×Q8—44no—
557C2×Q8—44no—
558C2×Q8—42no—
559C2×Q8C2×D4×C4712yes—
560C2×Q8C2×D4×C4712yes—
561C2×Q8#41×C4712yes—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4C2×D4×C4711yescharacteristic
589C22×C4C2×D4×C4711yescharacteristic
590C22×C4C2×D4×C4711yescharacteristic
591C22×C4C2×D4×C4711yescharacteristic
592C22×C4C2×D4×C4711yescharacteristic
593C22×C4C2×D4×C4712yes—
594C22×C4#41×C4712yes—
595C22×C4C24×C4711yescharacteristic
596Q16—44no—
597Q16—44no—
598SD16—44no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—44no—
611C2×C8C2×D4×C4712yes—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—81no—
622C4⋊C4C2×D4×C4712yes—
623C4⋊C4C2×D4×C4712yes—
624C22⋊C4—24no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—42no—
637C42—81no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23#121×C4712yes—
650C23#135×C4712yes—
651C23#137×C4712yes—
652C23C22×D4×C4711yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—48no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—84no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—48no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—84no—
712C2×C4#121×C4712yes—
713C2×C4C22×D4×C4711yescharacteristic
714C2×C4C22×D4×C4711yescharacteristic
715C2×C4C2×#41×C4711yescharacteristic
716C2×C4C2×#41×C4711yescharacteristic
717C2×C4H(5,𝔽2)×C4711yescharacteristic
718C2×C4H(5,𝔽2)×C4711yescharacteristic
719C8—22no—
720C8—41no—
721C8—41no—
722C8—41no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22C47×#46414yescomplemented
737C22C2×#121×C4711yescharacteristic
738C22D42×C4711yescharacteristic
739C22C47×#54611yescharacteristic
740C22C2×#135×C4711yescharacteristic
741C22C2×#137×C4711yescharacteristic
742C22C47×#57711yescharacteristic
743C22C47×#57811yescharacteristic
744C4—22no—
745C4—41no—
746C4—42no—
747C4—41no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—42no—
754C4—81no—
755C4—81no—
756C4C47×#52511yescharacteristic
757C4C47×#53811yescharacteristic
758C4D42×C4711yescharacteristic
759C4C47×#54611yescharacteristic
760C2—24no—
761C2—161no—
762C2C47×#242411yescharacteristic
763C2C2×C47×#46411yescharacteristic
764C2C47×#304611yescharacteristic
765C2C47×#327011yescharacteristic
766C2C47×#328211yescharacteristic
767C2C47×#330011yescharacteristic
768C2C47×#331611yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×#121×C47C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C22⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#464C2semidirect
3. C2×C47×#451C2semidirect
4. C22×#103×C47C2semidirect
6. C47×#2360C2semidirect
7. C47×#2066C2semidirect
8. C47×#2056C2semidirect
9. C47×#2042C2semidirect
10. C47×#2015C2semidirect
11. C47×#1983C2semidirect
12. C47×#1927C2semidirect
13. C47×#1878C2semidirect
15. C47×#1850C2semidirect
135. #103×C47D4semidirect
338. #25086C47direct (N × H)
352. C22×C47#464semidirect
377. C2×#464C2×C47semidirect
378. C2×#451C2×C47semidirect
379. C22×#103C2×C47semidirect
381. #2360C2×C47semidirect
382. #2066C2×C47semidirect
383. #2056C2×C47semidirect
384. #2042C2×C47semidirect
385. #2015C2×C47semidirect
386. #1983C2×C47semidirect
387. #1927C2×C47semidirect
388. #1878C2×C47semidirect
390. #1850C2×C47semidirect
447. C47#25086direct (N × H)
520. #103D4×C47semidirect
736. C22C47×#464semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4652
C2×C47×#4642
C2×C47×#4512
C22×#103×C472
C47×#24362
C47×#23602
C47×#20662
C47×#20562
C47×#20422
C47×#20152
C47×#19832
C47×#19272
C47×#18782
C47×#18742
C47×#18502
#2508647