Finite Group Databasebeta

← C47×#24754 #26064452

Subgroups — C47×#24754 #26064452

Order 12032.

1102 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×#466C211yesmaximal, characteristic
2C2×C47×#465C211yesmaximal, characteristic, complemented
3C2×C47×#463C211yesmaximal, characteristic, complemented
4C22×C4⋊C8×C47C211yesmaximal, characteristic, complemented
5C47×#2850C211yesmaximal, characteristic, complemented
6C4×#121×C47C211yesmaximal, characteristic, complemented
7C47×#2068C211yesmaximal, characteristic, complemented
8C47×#2065C211yesmaximal, characteristic, complemented
9C47×#2055C211yesmaximal, characteristic, complemented
10C47×#2054C211yesmaximal, characteristic, complemented
11C47×#1983C211yesmaximal, characteristic, complemented
12C47×#1949C211yesmaximal, characteristic, complemented
13C47×#1893C211yesmaximal, characteristic, complemented
14C47×#1892C211yesmaximal, characteristic, complemented
15C47×#1804C211yesmaximal, characteristic, complemented
16C22×SD16×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C23×C8×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C2×#124×C47C2211yescharacteristic
21C2×C22⋊Q8×C47C2211yescharacteristic
22C2×#121×C47C2211yescharacteristic
23C2×#121×C47C2211yescharacteristic
24C2×C4×D4×C47—21no—
25C2×C4×D4×C47C2211yescharacteristic
26C22×C42×C47C2211yescharacteristic
27C47×#466—24no—
28C47×#465—24no—
29C47×#463—24no—
30C2×#107×C47C2211yescharacteristic
31C2×#106×C47C2211yescharacteristic
32C2×C4⋊C8×C47—24no—
33C2×C4⋊C8×C47C2211yescharacteristic
34C2×C4⋊C8×C47C2211yescharacteristic
35C2×C4⋊C8×C47C2211yescharacteristic
36C2×C4⋊C8×C47C2211yescharacteristic
37C2×#103×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C47×#391C2211yescharacteristic
46C47×#390C2211yescharacteristic
47C47×#390C2211yescharacteristic
48C47×#389C2211yescharacteristic
49C47×#388—21no—
50C47×#388—21no—
51C47×#388—21no—
52C47×#386—21no—
53C47×#386—21no—
54C47×#386—21no—
55C47×#382C2211yescharacteristic
56C47×#380C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C22⋊C4×C47—21no—
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47C2311yescharacteristic
67C22×D4×C47C2311yescharacteristic
68C23×C4×C47—21no—
69C23×C4×C47D411yescharacteristic
70C23×C4×C47D411yescharacteristic
71C23×C4×C47C2311yescharacteristic
72C2×SD16×C47—22no—
73C2×SD16×C47—22no—
74C2×SD16×C47—41no—
75C2×D8×C47—22no—
76C2×D8×C47—22no—
77C2×D8×C47—41no—
78C22×C8×C47—22no—
79C22×C8×C47—22no—
80C22×C8×C47—22no—
81C22×C8×C47—22no—
82C22×C8×C47—41no—
83C22×C8×C47—41no—
84C22×C8×C47C2311yescharacteristic
85C22×C8×C47C2311yescharacteristic
86C22×C8×C47C2311yescharacteristic
87C22×C8×C47C2311yescharacteristic
88#124×C47—22no—
89#124×C47—22no—
90C22⋊Q8×C47—22no—
91C22⋊Q8×C47—22no—
92#121×C47—22no—
93#121×C47—22no—
94#121×C47—22no—
95#121×C47D414yes—
96C4×D4×C47—22no—
97C4×D4×C47—22no—
98C4×D4×C47—44no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
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×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×C42×C47—22no—
118C2×C42×C47—22no—
119C2×C42×C47—21no—
120C2×C42×C47D411yescharacteristic
121C2×C42×C47D411yescharacteristic
122C2×C42×C47C2311yescharacteristic
123C2×C42×C47C2311yescharacteristic
124#107×C47—22no—
125#106×C47—22no—
126C4⋊C8×C47—22no—
127C4⋊C8×C47—22no—
128C4⋊C8×C47—22no—
129C4⋊C8×C47D414yescomplemented
130#103×C47—22no—
131#103×C47—22no—
132#103×C47—41no—
133#102×C47—22no—
134#102×C47—22no—
135#102×C47—22no—
136#102×C47—22no—
137#102×C47—41no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47—21no—
143#95×C47—21no—
144#95×C47—21no—
145C24×C47—21no—
146C24×C47—21no—
147C24×C47C2×D411yescharacteristic
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×D4×C47—24no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
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—42no—
167C2×D4×C47—42no—
168C2×D4×C47—42no—
169C2×D4×C47—42no—
170C2×D4×C47—42no—
171C2×D4×C47C2×D412yes—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—22no—
180C22×C4×C47—21no—
181C22×C4×C47—22no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—41no—
188C22×C4×C47—42no—
189C22×C4×C47—42no—
190C22×C4×C47—42no—
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D412yes—
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47#4112yes—
198C22×C4×C47C2411yescharacteristic
199SD16×C47—44no—
200D8×C47—44no—
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×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—44no—
212C2×C8×C47—44no—
213C2×C8×C47C2×D412yes—
214C2×C8×C47C2×D412yes—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—42no—
225C4⋊C4×C47—42no—
226C4⋊C4×C47C2×D412yes—
227C22⋊C4×C47—24no—
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—42no—
235C22⋊C4×C47—42no—
236C22⋊C4×C47—42no—
237C22⋊C4×C47—42no—
238C42×C47—22no—
239C42×C47—22no—
240C42×C47—21no—
241C42×C47—21no—
242C42×C47—42no—
243C42×C47C2×D412yes—
244C42×C47#4112yes—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—22no—
250C23×C47—41no—
251C23×C47—41no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—41no—
263C23×C47#12112yes—
264C23×C47#13512yes—
265C23×C47AGL(1,ℤ/8)12yes—
266C23×C47C22×D411yescharacteristic
267Q8×C47—41no—
268Q8×C47—41no—
269Q8×C47—41no—
270Q8×C47—41no—
271D4×C47—22no—
272D4×C47—22no—
273D4×C47—48no—
274D4×C47—41no—
275D4×C47—41no—
276D4×C47—41no—
277D4×C47—41no—
278D4×C47—41no—
279D4×C47—41no—
280D4×C47—84no—
281C2×C4×C47—28no—
282C2×C4×C47—21no—
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—21no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—21no—
295C2×C4×C47—22no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—44no—
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—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—84no—
317C2×C4×C47#12112yes—
318C2×C4×C47#12112yes—
319C2×C4×C47#12112yes—
320C2×C4×C47#13512yes—
321C2×C4×C47C22×D411yescharacteristic
322C2×C4×C47C22×D411yescharacteristic
323C2×C4×C47C2×#4111yescharacteristic
324C2×C4×C47C2×#4111yescharacteristic
325C2×C4×C47H(5,𝔽2)11yescharacteristic
326C2×C4×C472−1+411yescharacteristic
327C8×C47—22no—
328C8×C47—22no—
329C8×C47—41no—
330C8×C47—41no—
331#24754C4711yesmaximal, characteristic, direct product factor, Sylow
332C22×C47—22no—
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47—42no—
339C22×C47—42no—
340C22×C47—42no—
341C22×C47—81no—
342C22×C47—81no—
343C22×C47—81no—
344C22×C47—81no—
345C22×C47—81no—
346C22×C47—81no—
347C22×C47—81no—
348C22×C47—81no—
349C22×C47—81no—
350C22×C47—81no—
351C22×C47—81no—
352C22×C47#46314yescomplemented
353C22×C47C2×#12111yescharacteristic
354C22×C47C2×#12111yescharacteristic
355C22×C47#53711yescharacteristic
356C22×C47C2×#13511yescharacteristic
357C22×C47C2×#13511yescharacteristic
358C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
359C22×C47#57511yescharacteristic
360C4×C47—22no—
361C4×C47—22no—
362C4×C47—22no—
363C4×C47—22no—
364C4×C47—42no—
365C4×C47—41no—
366C4×C47—81no—
367C4×C47—81no—
368C4×C47—81no—
369C4×C47—81no—
370C4×C47—81no—
371C4×C47D4211yescharacteristic
372C4×C47#54711yescharacteristic
373C4×C47#54811yescharacteristic
374C4×C47#55311yescharacteristic
375C2×#466C2×C4711yescharacteristic
376C2×#465C2×C4711yescharacteristic, complemented
377C2×#463C2×C4711yescharacteristic, complemented
378C22×C4⋊C8C2×C4711yescharacteristic, complemented
379#2850C2×C4711yescharacteristic, complemented
380C4×#121C2×C4711yescharacteristic, complemented
381#2068C2×C4711yescharacteristic, complemented
382#2065C2×C4711yescharacteristic, complemented
383#2055C2×C4711yescharacteristic, complemented
384#2054C2×C4711yescharacteristic, complemented
385#1983C2×C4711yescharacteristic, complemented
386#1949C2×C4711yescharacteristic, complemented
387#1893C2×C4711yescharacteristic, complemented
388#1892C2×C4711yescharacteristic, complemented
389#1804C2×C4711yescharacteristic, complemented
390C2×C47—24no—
391C2×C47—82no—
392C2×C47—161no—
393C2×C47#241611yescharacteristic
394C2×C47C2×#46311yescharacteristic
395C2×C47#303511yescharacteristic
396C2×C47#305011yescharacteristic
397C2×C47#305511yescharacteristic
398C2×C47#324711yescharacteristic
399C2×C47#325011yescharacteristic
400C22×SD16C22×C4711yescharacteristic
401C22×D8C22×C4711yescharacteristic
402C23×C8C22×C4711yescharacteristic
403C23×C8C22×C4711yescharacteristic
404C2×#124C22×C4711yescharacteristic
405C2×C22⋊Q8C22×C4711yescharacteristic
406C2×#121C22×C4711yescharacteristic
407C2×#121C22×C4711yescharacteristic
408C2×C4×D4—21no—
409C2×C4×D4C22×C4711yescharacteristic
410C22×C42C22×C4711yescharacteristic
411#466—24no—
412#465—24no—
413#463—24no—
414C2×#107C22×C4711yescharacteristic
415C2×#106C22×C4711yescharacteristic
416C2×C4⋊C8—24no—
417C2×C4⋊C8C22×C4711yescharacteristic
418C2×C4⋊C8C22×C4711yescharacteristic
419C2×C4⋊C8C22×C4711yescharacteristic
420C2×C4⋊C8C22×C4711yescharacteristic
421C2×#103C22×C4711yescharacteristic
422C2×#103C22×C4711yescharacteristic
423C2×#103C22×C4711yescharacteristic
424C2×#102C22×C4711yescharacteristic
425C2×#102C22×C4711yescharacteristic
426C2×#102C22×C4711yescharacteristic
427C2×#102C22×C4711yescharacteristic
428C2×#102C22×C4711yescharacteristic
429#391C22×C4711yescharacteristic
430#390C22×C4711yescharacteristic
431#390C22×C4711yescharacteristic
432#389C22×C4711yescharacteristic
433#388—21no—
434#388—21no—
435#388—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#382C22×C4711yescharacteristic
440#380C22×C4711yescharacteristic
441C4×C4⋊C4C22×C4711yescharacteristic
442C4×C22⋊C4—21no—
443#340C22×C4711yescharacteristic
444#340C22×C4711yescharacteristic
445#340C22×C4711yescharacteristic
446#340C22×C4711yescharacteristic
447C47#2475411yescharacteristic, direct product factor, Sylow
448C22×Q8C23×C4711yescharacteristic
449C22×D4—21no—
450C22×D4—21no—
451C22×D4C23×C4711yescharacteristic
452C22×D4C23×C4711yescharacteristic
453C23×C4—21no—
454C23×C4D4×C4711yescharacteristic
455C23×C4D4×C4711yescharacteristic
456C23×C4C23×C4711yescharacteristic
457C2×SD16—22no—
458C2×SD16—22no—
459C2×SD16—41no—
460C2×D8—22no—
461C2×D8—22no—
462C2×D8—41no—
463C22×C8—22no—
464C22×C8—22no—
465C22×C8—22no—
466C22×C8—22no—
467C22×C8—41no—
468C22×C8—41no—
469C22×C8C23×C4711yescharacteristic
470C22×C8C23×C4711yescharacteristic
471C22×C8C23×C4711yescharacteristic
472C22×C8C23×C4711yescharacteristic
473#124—22no—
474#124—22no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121D4×C4714yes—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—44no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4C23×C4711yescharacteristic
487C2×C4⋊C4C23×C4711yescharacteristic
488C2×C4⋊C4C23×C4711yescharacteristic
489C2×C4⋊C4C23×C4711yescharacteristic
490C2×C4⋊C4C23×C4711yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
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×C42—22no—
503C2×C42—22no—
504C2×C42—21no—
505C2×C42D4×C4711yescharacteristic
506C2×C42D4×C4711yescharacteristic
507C2×C42C23×C4711yescharacteristic
508C2×C42C23×C4711yescharacteristic
509#107—22no—
510#106—22no—
511C4⋊C8—22no—
512C4⋊C8—22no—
513C4⋊C8—22no—
514C4⋊C8D4×C4714yescomplemented
515#103—22no—
516#103—22no—
517#103—41no—
518#102—22no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—41no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530C24—21no—
531C24—21no—
532C24C2×D4×C4711yescharacteristic
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4C2×D4×C4712yes—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—41no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4C2×D4×C4711yescharacteristic
577C22×C4C2×D4×C4711yescharacteristic
578C22×C4C2×D4×C4711yescharacteristic
579C22×C4C2×D4×C4711yescharacteristic
580C22×C4C2×D4×C4712yes—
581C22×C4C2×D4×C4711yescharacteristic
582C22×C4#41×C4712yes—
583C22×C4C24×C4711yescharacteristic
584SD16—44no—
585D8—44no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—44no—
597C2×C8—44no—
598C2×C8C2×D4×C4712yes—
599C2×C8C2×D4×C4712yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
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⋊C4C2×D4×C4712yes—
612C22⋊C4—24no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C42—22no—
624C42—22no—
625C42—21no—
626C42—21no—
627C42—42no—
628C42C2×D4×C4712yes—
629C42#41×C4712yes—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—22no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23#121×C4712yes—
649C23#135×C4712yes—
650C23AGL(1,ℤ/8)×C4712yes—
651C23C22×D4×C4711yescharacteristic
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656D4—22no—
657D4—22no—
658D4—48no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—84no—
666C2×C4—28no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—44no—
684C2×C4—41no—
685C2×C4—41no—
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—84no—
702C2×C4#121×C4712yes—
703C2×C4#121×C4712yes—
704C2×C4#121×C4712yes—
705C2×C4#135×C4712yes—
706C2×C4C22×D4×C4711yescharacteristic
707C2×C4C22×D4×C4711yescharacteristic
708C2×C4C2×#41×C4711yescharacteristic
709C2×C4C2×#41×C4711yescharacteristic
710C2×C4H(5,𝔽2)×C4711yescharacteristic
711C2×C42−1+4×C4711yescharacteristic
712C8—22no—
713C8—22no—
714C8—41no—
715C8—41no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22C47×#46314yescomplemented
737C22C2×#121×C4711yescharacteristic
738C22C2×#121×C4711yescharacteristic
739C22C47×#53711yescharacteristic
740C22C2×#135×C4711yescharacteristic
741C22C2×#135×C4711yescharacteristic
742C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
743C22C47×#57511yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—42no—
749C4—41no—
750C4—81no—
751C4—81no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4D42×C4711yescharacteristic
756C4C47×#54711yescharacteristic
757C4C47×#54811yescharacteristic
758C4C47×#55311yescharacteristic
759C2—24no—
760C2—82no—
761C2—161no—
762C2C47×#241611yescharacteristic
763C2C2×C47×#46311yescharacteristic
764C2C47×#303511yescharacteristic
765C2C47×#305011yescharacteristic
766C2C47×#305511yescharacteristic
767C2C47×#324711yescharacteristic
768C2C47×#325011yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#466C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C22×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#465C2semidirect
3. C2×C47×#463C2semidirect
4. C22×C4⋊C8×C47C2semidirect
5. C47×#2850C2semidirect
6. C4×#121×C47C2semidirect
7. C47×#2068C2semidirect
8. C47×#2065C2semidirect
9. C47×#2055C2semidirect
10. C47×#2054C2semidirect
11. C47×#1983C2semidirect
12. C47×#1949C2semidirect
13. C47×#1893C2semidirect
14. C47×#1892C2semidirect
15. C47×#1804C2semidirect
129. C4⋊C8×C47D4semidirect
331. #24754C47direct (N × H)
352. C22×C47#463semidirect
376. C2×#465C2×C47semidirect
377. C2×#463C2×C47semidirect
378. C22×C4⋊C8C2×C47semidirect
379. #2850C2×C47semidirect
380. C4×#121C2×C47semidirect
381. #2068C2×C47semidirect
382. #2065C2×C47semidirect
383. #2055C2×C47semidirect
384. #2054C2×C47semidirect
385. #1983C2×C47semidirect
386. #1949C2×C47semidirect
387. #1893C2×C47semidirect
388. #1892C2×C47semidirect
389. #1804C2×C47semidirect
447. C47#24754direct (N × H)
514. C4⋊C8D4×C47semidirect
736. C22C47×#463semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4662
C2×C47×#4652
C2×C47×#4632
C22×C4⋊C8×C472
C47×#28502
C4×#121×C472
C47×#20682
C47×#20652
C47×#20552
C47×#20542
C47×#19832
C47×#19492
C47×#18932
C47×#18922
C47×#18042
#2475447