Finite Group Databasebeta

← C47×#24738 #26064436

Subgroups — C47×#24738 #26064436

Order 12032.

1094 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#463C211yesmaximal, characteristic, complemented
2C2×C47×#463C211yesmaximal, characteristic, complemented
3C2×C47×#459C211yesmaximal, characteristic
4C2×C47×#442C211yesmaximal, characteristic, complemented
5C47×#2544C211yesmaximal, characteristic, complemented
6D4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
7C47×#2066C211yesmaximal, characteristic, complemented
8C47×#2065C211yesmaximal, characteristic, complemented
9C47×#2042C211yesmaximal, characteristic, complemented
10C47×#2041C211yesmaximal, characteristic, complemented
11C47×#1959C211yesmaximal, characteristic, complemented
12C47×#1940C211yesmaximal, characteristic, complemented
13C47×#1879C211yesmaximal, characteristic, complemented
14C47×#1877C211yesmaximal, characteristic, complemented
15C47×#1802C211yesmaximal, characteristic, complemented
16C22×SD16×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C22×D8×C47C2211yescharacteristic
19C2×#127×C47C2211yescharacteristic
20C2×#124×C47C2211yescharacteristic
21C2×#124×C47C2211yescharacteristic
22C2×C4×D4×C47C2211yescharacteristic
23C2×C4×D4×C47C2211yescharacteristic
24C2×C4×D4×C47C2211yescharacteristic
25C2×C4×D4×C47C2211yescharacteristic
26C22×C4⋊C4×C47—21no—
27C47×#463—24no—
28C47×#463—24no—
29C47×#459—24no—
30C47×#442—24no—
31C2×#106×C47C2211yescharacteristic
32C2×C4⋊C8×C47C2211yescharacteristic
33C2×C4⋊C8×C47C2211yescharacteristic
34C2×C4⋊C8×C47C2211yescharacteristic
35C2×#103×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#103×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×#97×C47C2211yescharacteristic
46C47×#394—21no—
47C47×#394—21no—
48C47×#391C2211yescharacteristic
49C47×#390C2211yescharacteristic
50C47×#389C2211yescharacteristic
51C47×#389C2211yescharacteristic
52C47×#386—21no—
53C47×#386—21no—
54C47×#385—21no—
55C47×#385—21no—
56C47×#384C2211yescharacteristic
57C47×#380—21no—
58C4×C4⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47C2311yescharacteristic
67C22×D4×C47C2311yescharacteristic
68C22×D4×C47C2311yescharacteristic
69C23×C4×C47—21no—
70C23×C4×C47—21no—
71C23×C4×C47—21no—
72C23×C4×C47—21no—
73C2×SD16×C47—22no—
74C2×SD16×C47—22no—
75C2×SD16×C47—22no—
76C2×D8×C47—22no—
77C2×D8×C47—22no—
78C2×D8×C47—22no—
79C2×D8×C47—22no—
80C2×D8×C47—22no—
81C2×D8×C47D414yes—
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84C22×C8×C47C2311yescharacteristic
85C22×C8×C47C2311yescharacteristic
86#127×C47—22no—
87#127×C47—41no—
88#124×C47—22no—
89#124×C47—22no—
90#124×C47—22no—
91#124×C47—41no—
92C4×D4×C47—22no—
93C4×D4×C47—22no—
94C4×D4×C47—22no—
95C4×D4×C47—22no—
96C4×D4×C47—22no—
97C4×D4×C47—41no—
98C4×D4×C47—41no—
99C4×D4×C47D414yescomplemented
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—44no—
105C2×C4⋊C4×C47D411yescharacteristic
106C2×C4⋊C4×C47D411yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
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×C47—21no—
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47—21no—
121C2×C42×C47C2311yescharacteristic
122C2×C42×C47C2311yescharacteristic
123C2×C42×C47C2311yescharacteristic
124#106×C47—22no—
125C4⋊C8×C47—22no—
126C4⋊C8×C47—22no—
127C4⋊C8×C47—22no—
128#103×C47—22no—
129#103×C47—22no—
130#103×C47—41no—
131#102×C47—22no—
132#102×C47—22no—
133#102×C47—22no—
134#102×C47—22no—
135#102×C47—22no—
136#102×C47—22no—
137#102×C47—41no—
138#97×C47—22no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47—21no—
143#95×C47D411yescharacteristic
144#95×C47D411yescharacteristic
145C24×C47—21no—
146C24×C47—21no—
147C24×C47—21no—
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—21no—
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—21no—
167C2×D4×C47—21no—
168C2×D4×C47—42no—
169C2×D4×C47—42no—
170C2×D4×C47—42no—
171C2×D4×C47—42no—
172C2×D4×C47—81no—
173C2×D4×C47—81no—
174C2×D4×C47C2×D412yes—
175C2×D4×C47C2×D412yes—
176C2×D4×C47C2×D412yes—
177C2×D4×C47#4112yes—
178C22×C4×C47—21no—
179C22×C4×C47—24no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—42no—
185C22×C4×C47—42no—
186C22×C4×C47—42no—
187C22×C4×C47—42no—
188C22×C4×C47—42no—
189C22×C4×C47—42no—
190C22×C4×C47—42no—
191C22×C4×C47—81no—
192C22×C4×C47—81no—
193C22×C4×C47—81no—
194C22×C4×C47—81no—
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2411yescharacteristic
202SD16×C47—44no—
203D8×C47—28no—
204D8×C47—44no—
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—21no—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47C2×D412yes—
217C4⋊C4×C47—22no—
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—21no—
225C4⋊C4×C47—41no—
226C4⋊C4×C47—42no—
227C4⋊C4×C47—42no—
228C4⋊C4×C47—42no—
229C4⋊C4×C47—81no—
230C4⋊C4×C47C2×D412yes—
231C22⋊C4×C47—24no—
232C22⋊C4×C47—42no—
233C22⋊C4×C47—42no—
234C22⋊C4×C47—42no—
235C22⋊C4×C47—42no—
236C22⋊C4×C47—42no—
237C22⋊C4×C47—42no—
238C22⋊C4×C47—42no—
239C22⋊C4×C47—81no—
240C22⋊C4×C47—81no—
241C42×C47—21no—
242C42×C47—21no—
243C42×C47—21no—
244C42×C47—21no—
245C42×C47C2×D412yes—
246C42×C47#4112yes—
247C23×C47—22no—
248C23×C47—22no—
249C23×C47—22no—
250C23×C47—22no—
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—41no—
264C23×C47—41no—
265C23×C47—41no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47C22×D411yescharacteristic
269Q8×C47—41no—
270Q8×C47—41no—
271Q8×C47—41no—
272Q8×C47—41no—
273D4×C47—22no—
274D4×C47—22no—
275D4×C47—22no—
276D4×C47—22no—
277D4×C47—22no—
278D4×C47—41no—
279D4×C47—41no—
280D4×C47—41no—
281D4×C47—41no—
282D4×C47—41no—
283D4×C47—41no—
284D4×C47—84no—
285D4×C47—84no—
286D4×C47#12114yes—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—22no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—48no—
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—41no—
317C2×C4×C47—41no—
318C2×C4×C47—84no—
319C2×C4×C47—84no—
320C2×C4×C47—84no—
321C2×C4×C47#12112yes—
322C2×C4×C47#12112yes—
323C2×C4×C47AGL(1,ℤ/8)12yes—
324C2×C4×C47C22×D411yescharacteristic
325C2×C4×C47C22×D411yescharacteristic
326C2×C4×C47C2×#4111yescharacteristic
327C2×C4×C47C2×#4111yescharacteristic
328C2×C4×C47H(5,𝔽2)11yescharacteristic
329C2×C4×C472−1+411yescharacteristic
330C8×C47—22no—
331C8×C47—41no—
332C8×C47—41no—
333C8×C47—41no—
334#24738C4711yesmaximal, characteristic, direct product factor, Sylow
335C22×C47—24no—
336C22×C47—42no—
337C22×C47—42no—
338C22×C47—42no—
339C22×C47—42no—
340C22×C47—42no—
341C22×C47—42no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—81no—
346C22×C47—81no—
347C22×C47—81no—
348C22×C47—81no—
349C22×C47—81no—
350C22×C47—81no—
351C22×C47—81no—
352C22×C47—81no—
353C22×C47—81no—
354C22×C47—81no—
355C22×C47—81no—
356C22×C47C2×#12111yescharacteristic
357C22×C47D4211yescharacteristic
358C22×C47#54811yescharacteristic
359C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C47#57511yescharacteristic
361C22×C47#57611yescharacteristic
362C22×C47#57711yescharacteristic
363C4×C47—22no—
364C4×C47—22no—
365C4×C47—22no—
366C4×C47—41no—
367C4×C47—41no—
368C4×C47—41no—
369C4×C47—42no—
370C4×C47—81no—
371C4×C47—81no—
372C4×C47—81no—
373C4×C47—81no—
374C4×C47C2×#12111yescharacteristic
375C4×C47#53711yescharacteristic
376C4×C47#54711yescharacteristic
377C4×C47#55311yescharacteristic
378C2×#463C2×C4711yescharacteristic, complemented
379C2×#463C2×C4711yescharacteristic, complemented
380C2×#459C2×C4711yescharacteristic
381C2×#442C2×C4711yescharacteristic, complemented
382#2544C2×C4711yescharacteristic, complemented
383D4×C4⋊C4C2×C4711yescharacteristic, complemented
384#2066C2×C4711yescharacteristic, complemented
385#2065C2×C4711yescharacteristic, complemented
386#2042C2×C4711yescharacteristic, complemented
387#2041C2×C4711yescharacteristic, complemented
388#1959C2×C4711yescharacteristic, complemented
389#1940C2×C4711yescharacteristic, complemented
390#1879C2×C4711yescharacteristic, complemented
391#1877C2×C4711yescharacteristic, complemented
392#1802C2×C4711yescharacteristic, complemented
393C2×C47—44no—
394C2×C47—82no—
395C2×C47—161no—
396C2×C47#241611yescharacteristic
397C2×C47#303611yescharacteristic
398C2×C47#304511yescharacteristic
399C2×C47#326411yescharacteristic
400C2×C47#326711yescharacteristic
401C2×C47#337011yescharacteristic
402C2×C47#337311yescharacteristic
403C22×SD16C22×C4711yescharacteristic
404C22×D8C22×C4711yescharacteristic
405C22×D8C22×C4711yescharacteristic
406C2×#127C22×C4711yescharacteristic
407C2×#124C22×C4711yescharacteristic
408C2×#124C22×C4711yescharacteristic
409C2×C4×D4C22×C4711yescharacteristic
410C2×C4×D4C22×C4711yescharacteristic
411C2×C4×D4C22×C4711yescharacteristic
412C2×C4×D4C22×C4711yescharacteristic
413C22×C4⋊C4—21no—
414#463—24no—
415#463—24no—
416#459—24no—
417#442—24no—
418C2×#106C22×C4711yescharacteristic
419C2×C4⋊C8C22×C4711yescharacteristic
420C2×C4⋊C8C22×C4711yescharacteristic
421C2×C4⋊C8C22×C4711yescharacteristic
422C2×#103C22×C4711yescharacteristic
423C2×#103C22×C4711yescharacteristic
424C2×#103C22×C4711yescharacteristic
425C2×#102C22×C4711yescharacteristic
426C2×#102C22×C4711yescharacteristic
427C2×#102C22×C4711yescharacteristic
428C2×#102C22×C4711yescharacteristic
429C2×#102C22×C4711yescharacteristic
430C2×#102C22×C4711yescharacteristic
431C2×#102C22×C4711yescharacteristic
432C2×#97C22×C4711yescharacteristic
433#394—21no—
434#394—21no—
435#391C22×C4711yescharacteristic
436#390C22×C4711yescharacteristic
437#389C22×C4711yescharacteristic
438#389C22×C4711yescharacteristic
439#386—21no—
440#386—21no—
441#385—21no—
442#385—21no—
443#384C22×C4711yescharacteristic
444#380—21no—
445C4×C4⋊C4C22×C4711yescharacteristic
446#340C22×C4711yescharacteristic
447#340C22×C4711yescharacteristic
448#336C22×C4711yescharacteristic
449#336C22×C4711yescharacteristic
450C47#2473811yescharacteristic, direct product factor, Sylow
451C22×Q8C23×C4711yescharacteristic
452C22×D4—21no—
453C22×D4—21no—
454C22×D4C23×C4711yescharacteristic
455C22×D4C23×C4711yescharacteristic
456C22×D4C23×C4711yescharacteristic
457C23×C4—21no—
458C23×C4—21no—
459C23×C4—21no—
460C23×C4—21no—
461C2×SD16—22no—
462C2×SD16—22no—
463C2×SD16—22no—
464C2×D8—22no—
465C2×D8—22no—
466C2×D8—22no—
467C2×D8—22no—
468C2×D8—22no—
469C2×D8D4×C4714yes—
470C22×C8C23×C4711yescharacteristic
471C22×C8C23×C4711yescharacteristic
472C22×C8C23×C4711yescharacteristic
473C22×C8C23×C4711yescharacteristic
474#127—22no—
475#127—41no—
476#124—22no—
477#124—22no—
478#124—22no—
479#124—41no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—41no—
486C4×D4—41no—
487C4×D4D4×C4714yescomplemented
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—44no—
493C2×C4⋊C4D4×C4711yescharacteristic
494C2×C4⋊C4D4×C4711yescharacteristic
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⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C42C23×C4711yescharacteristic
510C2×C42C23×C4711yescharacteristic
511C2×C42C23×C4711yescharacteristic
512#106—22no—
513C4⋊C8—22no—
514C4⋊C8—22no—
515C4⋊C8—22no—
516#103—22no—
517#103—22no—
518#103—41no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—41no—
526#97—22no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95D4×C4711yescharacteristic
532#95D4×C4711yescharacteristic
533C24—21no—
534C24—21no—
535C24—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—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—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—81no—
561C2×D4—81no—
562C2×D4C2×D4×C4712yes—
563C2×D4C2×D4×C4712yes—
564C2×D4C2×D4×C4712yes—
565C2×D4#41×C4712yes—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4C2×D4×C4711yescharacteristic
584C22×C4C2×D4×C4711yescharacteristic
585C22×C4C2×D4×C4711yescharacteristic
586C22×C4C2×D4×C4711yescharacteristic
587C22×C4C2×D4×C4711yescharacteristic
588C22×C4C2×D4×C4711yescharacteristic
589C22×C4C24×C4711yescharacteristic
590SD16—44no—
591D8—28no—
592D8—44no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8C2×D4×C4712yes—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—41no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—81no—
618C4⋊C4C2×D4×C4712yes—
619C22⋊C4—24no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42C2×D4×C4712yes—
634C42#41×C4712yes—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23C22×D4×C4711yescharacteristic
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661D4—22no—
662D4—22no—
663D4—22no—
664D4—22no—
665D4—22no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—84no—
673D4—84no—
674D4#121×C4714yes—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—48no—
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—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—84no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4#121×C4712yes—
710C2×C4#121×C4712yes—
711C2×C4AGL(1,ℤ/8)×C4712yes—
712C2×C4C22×D4×C4711yescharacteristic
713C2×C4C22×D4×C4711yescharacteristic
714C2×C4C2×#41×C4711yescharacteristic
715C2×C4C2×#41×C4711yescharacteristic
716C2×C4H(5,𝔽2)×C4711yescharacteristic
717C2×C42−1+4×C4711yescharacteristic
718C8—22no—
719C8—41no—
720C8—41no—
721C8—41no—
722C22—24no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22C2×#121×C4711yescharacteristic
744C22D42×C4711yescharacteristic
745C22C47×#54811yescharacteristic
746C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
747C22C47×#57511yescharacteristic
748C22C47×#57611yescharacteristic
749C22C47×#57711yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—42no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—81no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4C2×#121×C4711yescharacteristic
762C4C47×#53711yescharacteristic
763C4C47×#54711yescharacteristic
764C4C47×#55311yescharacteristic
765C2—44no—
766C2—82no—
767C2—161no—
768C2C47×#241611yescharacteristic
769C2C47×#303611yescharacteristic
770C2C47×#304511yescharacteristic
771C2C47×#326411yescharacteristic
772C2C47×#326711yescharacteristic
773C2C47×#337011yescharacteristic
774C2C47×#337311yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#459C2
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×#463C2semidirect
2. C2×C47×#463C2semidirect
4. C2×C47×#442C2semidirect
5. C47×#2544C2semidirect
6. D4×C4⋊C4×C47C2semidirect
7. C47×#2066C2semidirect
8. C47×#2065C2semidirect
9. C47×#2042C2semidirect
10. C47×#2041C2semidirect
11. C47×#1959C2semidirect
12. C47×#1940C2semidirect
13. C47×#1879C2semidirect
14. C47×#1877C2semidirect
15. C47×#1802C2semidirect
99. C4×D4×C47D4semidirect
334. #24738C47direct (N × H)
378. C2×#463C2×C47semidirect
379. C2×#463C2×C47semidirect
381. C2×#442C2×C47semidirect
382. #2544C2×C47semidirect
383. D4×C4⋊C4C2×C47semidirect
384. #2066C2×C47semidirect
385. #2065C2×C47semidirect
386. #2042C2×C47semidirect
387. #2041C2×C47semidirect
388. #1959C2×C47semidirect
389. #1940C2×C47semidirect
390. #1879C2×C47semidirect
391. #1877C2×C47semidirect
392. #1802C2×C47semidirect
450. C47#24738direct (N × H)
487. C4×D4D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4632
C2×C47×#4592
C2×C47×#4422
C47×#25442
D4×C4⋊C4×C472
C47×#20662
C47×#20652
C47×#20422
C47×#20412
C47×#19592
C47×#19402
C47×#18792
C47×#18772
C47×#18022
#2473847