Finite Group Databasebeta

← C47×#25089 #26064787

Subgroups — C47×#25089 #26064787

Order 12032.

1078 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#467C211yesmaximal, characteristic, complemented
2C2×C47×#464C211yesmaximal, characteristic, complemented
3C2×C47×#452C211yesmaximal, characteristic
4C2×C47×#416C211yesmaximal, characteristic
5C47×#2432C211yesmaximal, characteristic
6C47×#2362C211yesmaximal, characteristic, complemented
7C47×#2068C211yesmaximal, characteristic, complemented
8C47×#2055C211yesmaximal, characteristic, complemented
9C47×#2042C211yesmaximal, characteristic, complemented
10C47×#2016C211yesmaximal, characteristic, complemented
11C47×#1981C211yesmaximal, characteristic, complemented
12C47×#1925C211yesmaximal, characteristic, complemented
13C47×#1878C211yesmaximal, characteristic, complemented
14C47×#1873C211yesmaximal, characteristic, complemented
15C47×#1850C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×Q16×C47C2211yescharacteristic
18C22×Q16×C47C2211yescharacteristic
19C22×SD16×C47C2211yescharacteristic
20C23×C8×C47C2211yescharacteristic
21C2×C4⋊Q8×C47C2211yescharacteristic
22C2×#124×C47C2211yescharacteristic
23C2×C22⋊Q8×C47C2211yescharacteristic
24C2×C22⋊Q8×C47C2211yescharacteristic
25C2×C4×Q8×C47C2211yescharacteristic
26C2×#117×C47C2211yescharacteristic
27C47×#467—24no—
28C47×#464—24no—
29C47×#452—24no—
30C2×#107×C47C2211yescharacteristic
31C2×C4⋊C8×C47C2211yescharacteristic
32C2×C4⋊C8×C47C2211yescharacteristic
33C47×#416—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×#394—21no—
46C47×#394—21no—
47C47×#391C2211yescharacteristic
48C47×#391C2211yescharacteristic
49C47×#390C2211yescharacteristic
50C47×#389C2211yescharacteristic
51C47×#388—21no—
52C47×#388—21no—
53C47×#387—21no—
54C47×#385—21no—
55C47×#385—21no—
56C4×C4⋊C4×C47—21no—
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C22⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C2×#41×C47—22no—
64C2×#41×C47—22no—
65C2×#41×C47—22no—
66C2×#41×C47—22no—
67C2×#41×C47—41no—
68C2×#41×C47—41no—
69C22×Q8×C47C2311yescharacteristic
70C22×Q8×C47C2311yescharacteristic
71C22×Q8×C47C2311yescharacteristic
72C22×D4×C47—21no—
73C22×D4×C47C2311yescharacteristic
74C23×C4×C47—21no—
75C23×C4×C47C2311yescharacteristic
76C2×Q16×C47—22no—
77C2×Q16×C47—22no—
78C2×Q16×C47—22no—
79C2×Q16×C47—22no—
80C2×Q16×C47—41no—
81C2×Q16×C47—41no—
82C2×SD16×C47—22no—
83C2×SD16×C47—22no—
84C2×SD16×C47—41no—
85C22×C8×C47—22no—
86C22×C8×C47—22no—
87C22×C8×C47—41no—
88C22×C8×C47C2311yescharacteristic
89C22×C8×C47C2311yescharacteristic
90C22×C8×C47C2311yescharacteristic
91C22×C8×C47C2311yescharacteristic
92C4⋊Q8×C47—22no—
93C4⋊Q8×C47—41no—
94#124×C47—22no—
95#124×C47—41no—
96C22⋊Q8×C47—22no—
97C22⋊Q8×C47—22no—
98C22⋊Q8×C47—22no—
99C22⋊Q8×C47D414yes—
100C4×Q8×C47—22no—
101C4×Q8×C47—41no—
102#117×C47—22no—
103#117×C47—41no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
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×C47—21no—
121C2×C22⋊C4×C47D411yescharacteristic
122C2×C22⋊C4×C47D411yescharacteristic
123C2×C42×C47—21no—
124C2×C42×C47—21no—
125C2×C42×C47—21no—
126C2×C42×C47C2311yescharacteristic
127C2×C42×C47C2311yescharacteristic
128#107×C47—22no—
129C4⋊C8×C47—22no—
130C4⋊C8×C47—41no—
131#103×C47—22no—
132#103×C47—22no—
133#103×C47—22no—
134#103×C47—22no—
135#103×C47—22no—
136#103×C47—22no—
137#103×C47—41no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47D414yes—
141C22⋊C8×C47—22no—
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
152#41×C47—28no—
153#41×C47—44no—
154#41×C47—44no—
155#41×C47—44no—
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—21no—
169C2×Q8×C47—21no—
170C2×Q8×C47—21no—
171C2×Q8×C47—21no—
172C2×Q8×C47C2×D412yes—
173C2×Q8×C47#4112yes—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47—21no—
178C2×D4×C47—21no—
179C2×D4×C47—42no—
180C2×D4×C47—42no—
181C2×D4×C47—42no—
182C2×D4×C47C2×D412yes—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
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—42no—
195C22×C4×C47—42no—
196C22×C4×C47—42no—
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D412yes—
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47#4112yes—
204C22×C4×C47C2411yescharacteristic
205Q16×C47—44no—
206Q16×C47—44no—
207SD16×C47—44no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47—21no—
217C2×C8×C47—21no—
218C2×C8×C47—21no—
219C2×C8×C47—44no—
220C2×C8×C47C2×D412yes—
221C4⋊C4×C47—24no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—42no—
229C4⋊C4×C47—42no—
230C4⋊C4×C47—42no—
231C4⋊C4×C47—42no—
232C4⋊C4×C47—42no—
233C4⋊C4×C47C2×D412yes—
234C4⋊C4×C47C2×D412yes—
235C22⋊C4×C47—24no—
236C22⋊C4×C47—22no—
237C22⋊C4×C47—41no—
238C22⋊C4×C47—42no—
239C22⋊C4×C47—42no—
240C22⋊C4×C47—42no—
241C22⋊C4×C47—42no—
242C22⋊C4×C47—42no—
243C22⋊C4×C47—42no—
244C42×C47—21no—
245C42×C47—21no—
246C42×C47—21no—
247C42×C47—21no—
248C42×C47—42no—
249C42×C47—42no—
250C42×C47—42no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—22no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—41no—
263C23×C47—41no—
264C23×C47#12112yes—
265C23×C47C22×D411yescharacteristic
266Q8×C47—22no—
267Q8×C47—22no—
268Q8×C47—22no—
269Q8×C47—22no—
270Q8×C47—41no—
271Q8×C47—41no—
272Q8×C47—41no—
273Q8×C47—41no—
274Q8×C47—41no—
275Q8×C47—41no—
276Q8×C47—41no—
277Q8×C47—41no—
278D4×C47—22no—
279D4×C47—22no—
280D4×C47—48no—
281D4×C47—41no—
282D4×C47—41no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—22no—
296C2×C4×C47—21no—
297C2×C4×C47—22no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—48no—
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—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#12112yes—
323C2×C4×C47#13512yes—
324C2×C4×C47C22×D411yescharacteristic
325C2×C4×C47C22×D411yescharacteristic
326C2×C4×C47C2×#4111yescharacteristic
327C2×C4×C47C2×#4111yescharacteristic
328C2×C4×C47H(5,𝔽2)11yescharacteristic
329C2×C4×C47H(5,𝔽2)11yescharacteristic
330C8×C47—22no—
331C8×C47—41no—
332C8×C47—41no—
333C8×C47—41no—
334#25089C4711yesmaximal, characteristic, direct product factor, Sylow
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—81no—
346C22×C47—81no—
347C22×C47—81no—
348C22×C47—81no—
349C22×C47C2×#12111yescharacteristic
350C22×C47D4211yescharacteristic
351C22×C47#54611yescharacteristic
352C22×C47C2×#13511yescharacteristic
353C22×C47#57511yescharacteristic
354C22×C47#57811yescharacteristic
355C22×C47#57811yescharacteristic
356C4×C47—22no—
357C4×C47—22no—
358C4×C47—42no—
359C4×C47—42no—
360C4×C47—41no—
361C4×C47—41no—
362C4×C47—42no—
363C4×C47—42no—
364C4×C47—41no—
365C4×C47—81no—
366C4×C47—81no—
367C4×C47—81no—
368C4×C47#52511yescharacteristic
369C4×C47#53811yescharacteristic
370C4×C47D4211yescharacteristic
371C4×C47#54611yescharacteristic
372C2×#467C2×C4711yescharacteristic, complemented
373C2×#464C2×C4711yescharacteristic, complemented
374C2×#452C2×C4711yescharacteristic
375C2×#416C2×C4711yescharacteristic
376#2432C2×C4711yescharacteristic
377#2362C2×C4711yescharacteristic, complemented
378#2068C2×C4711yescharacteristic, complemented
379#2055C2×C4711yescharacteristic, complemented
380#2042C2×C4711yescharacteristic, complemented
381#2016C2×C4711yescharacteristic, complemented
382#1981C2×C4711yescharacteristic, complemented
383#1925C2×C4711yescharacteristic, complemented
384#1878C2×C4711yescharacteristic, complemented
385#1873C2×C4711yescharacteristic, complemented
386#1850C2×C4711yescharacteristic, complemented
387C2×C47—42no—
388C2×C47—82no—
389C2×C47#242411yescharacteristic
390C2×C47#303511yescharacteristic
391C2×C47#304411yescharacteristic
392C2×C47#326911yescharacteristic
393C2×C47#328311yescharacteristic
394C2×C47#330011yescharacteristic
395C2×C47#331311yescharacteristic
396C22×#41C22×C4711yescharacteristic
397C22×Q16C22×C4711yescharacteristic
398C22×Q16C22×C4711yescharacteristic
399C22×SD16C22×C4711yescharacteristic
400C23×C8C22×C4711yescharacteristic
401C2×C4⋊Q8C22×C4711yescharacteristic
402C2×#124C22×C4711yescharacteristic
403C2×C22⋊Q8C22×C4711yescharacteristic
404C2×C22⋊Q8C22×C4711yescharacteristic
405C2×C4×Q8C22×C4711yescharacteristic
406C2×#117C22×C4711yescharacteristic
407#467—24no—
408#464—24no—
409#452—24no—
410C2×#107C22×C4711yescharacteristic
411C2×C4⋊C8C22×C4711yescharacteristic
412C2×C4⋊C8C22×C4711yescharacteristic
413#416—24no—
414C2×#103C22×C4711yescharacteristic
415C2×#103C22×C4711yescharacteristic
416C2×#103C22×C4711yescharacteristic
417C2×#103C22×C4711yescharacteristic
418C2×#103C22×C4711yescharacteristic
419C2×#103C22×C4711yescharacteristic
420C2×#103C22×C4711yescharacteristic
421C2×#102C22×C4711yescharacteristic
422C2×#102C22×C4711yescharacteristic
423C2×#102C22×C4711yescharacteristic
424C2×C22⋊C8C22×C4711yescharacteristic
425#394—21no—
426#394—21no—
427#391C22×C4711yescharacteristic
428#391C22×C4711yescharacteristic
429#390C22×C4711yescharacteristic
430#389C22×C4711yescharacteristic
431#388—21no—
432#388—21no—
433#387—21no—
434#385—21no—
435#385—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4C22×C4711yescharacteristic
438C4×C22⋊C4C22×C4711yescharacteristic
439#340C22×C4711yescharacteristic
440#340C22×C4711yescharacteristic
441#336C22×C4711yescharacteristic
442#336C22×C4711yescharacteristic
443C47#2508911yescharacteristic, direct product factor, Sylow
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—22no—
448C2×#41—41no—
449C2×#41—41no—
450C22×Q8C23×C4711yescharacteristic
451C22×Q8C23×C4711yescharacteristic
452C22×Q8C23×C4711yescharacteristic
453C22×D4—21no—
454C22×D4C23×C4711yescharacteristic
455C23×C4—21no—
456C23×C4C23×C4711yescharacteristic
457C2×Q16—22no—
458C2×Q16—22no—
459C2×Q16—22no—
460C2×Q16—22no—
461C2×Q16—41no—
462C2×Q16—41no—
463C2×SD16—22no—
464C2×SD16—22no—
465C2×SD16—41no—
466C22×C8—22no—
467C22×C8—22no—
468C22×C8—41no—
469C22×C8C23×C4711yescharacteristic
470C22×C8C23×C4711yescharacteristic
471C22×C8C23×C4711yescharacteristic
472C22×C8C23×C4711yescharacteristic
473C4⋊Q8—22no—
474C4⋊Q8—41no—
475#124—22no—
476#124—41no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8D4×C4714yes—
481C4×Q8—22no—
482C4×Q8—41no—
483#117—22no—
484#117—41no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4C23×C4711yescharacteristic
492C2×C4⋊C4C23×C4711yescharacteristic
493C2×C4⋊C4C23×C4711yescharacteristic
494C2×C4⋊C4C23×C4711yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4D4×C4711yescharacteristic
503C2×C22⋊C4D4×C4711yescharacteristic
504C2×C42—21no—
505C2×C42—21no—
506C2×C42—21no—
507C2×C42C23×C4711yescharacteristic
508C2×C42C23×C4711yescharacteristic
509#107—22no—
510C4⋊C8—22no—
511C4⋊C8—41no—
512#103—22no—
513#103—22no—
514#103—22no—
515#103—22no—
516#103—22no—
517#103—22no—
518#103—41no—
519#102—22no—
520#102—22no—
521#102D4×C4714yes—
522C22⋊C8—22no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95D4×C4711yescharacteristic
530#95D4×C4711yescharacteristic
531C24—21no—
532C24C2×D4×C4711yescharacteristic
533#41—28no—
534#41—44no—
535#41—44no—
536#41—44no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
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×Q8C2×D4×C4712yes—
554C2×Q8#41×C4712yes—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4C2×D4×C4712yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4C2×D4×C4711yescharacteristic
579C22×C4C2×D4×C4711yescharacteristic
580C22×C4C2×D4×C4711yescharacteristic
581C22×C4C2×D4×C4711yescharacteristic
582C22×C4C2×D4×C4712yes—
583C22×C4C2×D4×C4711yescharacteristic
584C22×C4#41×C4712yes—
585C22×C4C24×C4711yescharacteristic
586Q16—44no—
587Q16—44no—
588SD16—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—44no—
601C2×C8C2×D4×C4712yes—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4C2×D4×C4712yes—
615C4⋊C4C2×D4×C4712yes—
616C22⋊C4—24no—
617C22⋊C4—22no—
618C22⋊C4—41no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—42no—
630C42—42no—
631C42—42no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23#121×C4712yes—
646C23C22×D4×C4711yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—22no—
650Q8—22no—
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659D4—22no—
660D4—22no—
661D4—48no—
662D4—41no—
663D4—41no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—48no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
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#121×C4712yes—
704C2×C4#135×C4712yes—
705C2×C4C22×D4×C4711yescharacteristic
706C2×C4C22×D4×C4711yescharacteristic
707C2×C4C2×#41×C4711yescharacteristic
708C2×C4C2×#41×C4711yescharacteristic
709C2×C4H(5,𝔽2)×C4711yescharacteristic
710C2×C4H(5,𝔽2)×C4711yescharacteristic
711C8—22no—
712C8—41no—
713C8—41no—
714C8—41no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22C2×#121×C4711yescharacteristic
730C22D42×C4711yescharacteristic
731C22C47×#54611yescharacteristic
732C22C2×#135×C4711yescharacteristic
733C22C47×#57511yescharacteristic
734C22C47×#57811yescharacteristic
735C22C47×#57811yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—41no—
740C4—42no—
741C4—42no—
742C4—41no—
743C4—41no—
744C4—42no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4C47×#52511yescharacteristic
749C4C47×#53811yescharacteristic
750C4D42×C4711yescharacteristic
751C4C47×#54611yescharacteristic
752C2—42no—
753C2—82no—
754C2C47×#242411yescharacteristic
755C2C47×#303511yescharacteristic
756C2C47×#304411yescharacteristic
757C2C47×#326911yescharacteristic
758C2C47×#328311yescharacteristic
759C2C47×#330011yescharacteristic
760C2C47×#331311yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×#41×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
1. C2×C47×#467C2semidirect
2. C2×C47×#464C2semidirect
6. C47×#2362C2semidirect
7. C47×#2068C2semidirect
8. C47×#2055C2semidirect
9. C47×#2042C2semidirect
10. C47×#2016C2semidirect
11. C47×#1981C2semidirect
12. C47×#1925C2semidirect
13. C47×#1878C2semidirect
14. C47×#1873C2semidirect
15. C47×#1850C2semidirect
334. #25089C47direct (N × H)
372. C2×#467C2×C47semidirect
373. C2×#464C2×C47semidirect
377. #2362C2×C47semidirect
378. #2068C2×C47semidirect
379. #2055C2×C47semidirect
380. #2042C2×C47semidirect
381. #2016C2×C47semidirect
382. #1981C2×C47semidirect
383. #1925C2×C47semidirect
384. #1878C2×C47semidirect
385. #1873C2×C47semidirect
386. #1850C2×C47semidirect
443. C47#25089direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#4672
C2×C47×#4642
C2×C47×#4522
C2×C47×#4162
C47×#24322
C47×#23622
C47×#20682
C47×#20552
C47×#20422
C47×#20162
C47×#19812
C47×#19252
C47×#18782
C47×#18732
C47×#18502
#2508947