Finite Group Databasebeta

← C47×#25128 #26064826

Subgroups — C47×#25128 #26064826

Order 12032.

1292 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#468C211yesmaximal, characteristic, complemented
2C2×C47×#450C211yesmaximal, characteristic, complemented
3C2×C47×#435C211yesmaximal, characteristic, complemented
4C22×#102×C47C211yesmaximal, characteristic, complemented
5C47×#2417C211yesmaximal, characteristic, complemented
6C47×#2408C211yesmaximal, characteristic
7C47×#2067C211yesmaximal, characteristic, complemented
8C47×#2055C211yesmaximal, characteristic, complemented
9C47×#2033C211yesmaximal, characteristic, complemented
10C47×#2000C211yesmaximal, characteristic, complemented
11C47×#1973C211yesmaximal, characteristic, complemented
12C47×#1936C211yesmaximal, characteristic, complemented
13C47×#1895C211yesmaximal, characteristic, complemented
14C47×#1892C211yesmaximal, characteristic, complemented
15C47×#1852C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C22×M16×C47C2211yescharacteristic, complemented
20C23×C8×C47C2211yescharacteristic
21C2×C22⋊Q8×C47C2211yescharacteristic
22C2×C22⋊Q8×C47C2211yescharacteristic, complemented
23C2×#121×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×#120×C47—21no—
26C2×C4×D4×C47C2211yescharacteristic
27C22×C4⋊C4×C47C2211yescharacteristic
28C47×#468—24no—
29C47×#450—24no—
30C47×#435—24no—
31C2×#107×C47C2211yescharacteristic, complemented
32C2×#107×C47C2211yescharacteristic, complemented
33C2×C4⋊C8×C47C2211yescharacteristic, complemented
34C2×#103×C47C2211yescharacteristic, complemented
35C2×#103×C47C2211yescharacteristic, complemented
36C2×#102×C47—24no—
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×C22⋊C8×C47C2211yescharacteristic
44C2×C22⋊C8×C47C2211yescharacteristic, complemented
45C2×#97×C47C2211yescharacteristic, complemented
46C47×#398—21no—
47C47×#396—21no—
48C47×#394—21no—
49C47×#392—21no—
50C47×#391C2211yescharacteristic, complemented
51C47×#390C2211yescharacteristic
52C47×#390C2211yescharacteristic
53C47×#389C2211yescharacteristic, complemented
54C47×#386—21no—
55C47×#380—21no—
56C47×#380C2211yescharacteristic
57C47×#380C2211yescharacteristic, complemented
58C47×#379—21no—
59C47×#340C2211yescharacteristic, complemented
60C47×#340C2211yescharacteristic, complemented
61C47×#340C2211yescharacteristic, complemented
62C47×#340C2211yescharacteristic, complemented
63C25×C47—21no—
64C22×Q8×C47C2311yescharacteristic
65C22×D4×C47—22no—
66C22×D4×C47—22no—
67C22×D4×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47—22no—
70C22×D4×C47—21no—
71C22×D4×C47—22no—
72C22×D4×C47—41no—
73C22×D4×C47—41no—
74C22×D4×C47D411yescharacteristic
75C22×D4×C47C2311yescharacteristic
76C22×D4×C47C2311yescharacteristic
77C23×C4×C47—21no—
78C23×C4×C47C2311yescharacteristic
79C23×C4×C47C2311yescharacteristic
80C2×SD16×C47—22no—
81C2×SD16×C47—22no—
82C2×SD16×C47—22no—
83C2×SD16×C47—22no—
84C2×SD16×C47—41no—
85C2×SD16×C47—41no—
86C2×M16×C47—22no—
87C2×M16×C47—22no—
88C2×M16×C47—41no—
89C22×C8×C47—22no—
90C22×C8×C47—22no—
91C22×C8×C47—41no—
92C22×C8×C47C2311yescharacteristic
93C22×C8×C47C2311yescharacteristic
94C22×C8×C47C2311yescharacteristic
95C22×C8×C47C2311yescharacteristic
96C22⋊Q8×C47—22no—
97C22⋊Q8×C47—22no—
98C22⋊Q8×C47—22no—
99C22⋊Q8×C47—41no—
100#121×C47—22no—
101#121×C47—22no—
102#121×C47—41no—
103#121×C47—41no—
104#120×C47—44no—
105C4×D4×C47—22no—
106C4×D4×C47—22no—
107C2×C4⋊C4×C47—22no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47—21no—
112C2×C4⋊C4×C47—41no—
113C2×C4⋊C4×C47D411yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47—21no—
121C2×C22⋊C4×C47—21no—
122C2×C22⋊C4×C47—21no—
123C2×C22⋊C4×C47—21no—
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47D411yescharacteristic
130C2×C22⋊C4×C47D411yescharacteristic
131C2×C42×C47C2311yescharacteristic
132#107×C47—22no—
133#107×C47—41no—
134C4⋊C8×C47—22no—
135#103×C47—22no—
136#103×C47—41no—
137#102×C47—22no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47D414yescomplemented
143C22⋊C8×C47—22no—
144C22⋊C8×C47D414yescomplemented
145#97×C47—22no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47—21no—
149#95×C47—21no—
150#95×C47—21no—
151C24×C47—21no—
152C24×C47—21no—
153C24×C47—42no—
154C24×C47—42no—
155C24×C47—42no—
156C24×C47—42no—
157C24×C47—42no—
158C24×C47—81no—
159C24×C47—81no—
160C24×C47C2×D411yescharacteristic
161C24×C47C2×D411yescharacteristic
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×D4×C47—28no—
169C2×D4×C47—22no—
170C2×D4×C47—22no—
171C2×D4×C47—22no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47—21no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—21no—
182C2×D4×C47—44no—
183C2×D4×C47—44no—
184C2×D4×C47—42no—
185C2×D4×C47—42no—
186C2×D4×C47—44no—
187C2×D4×C47—42no—
188C2×D4×C47—42no—
189C2×D4×C47—42no—
190C2×D4×C47—42no—
191C2×D4×C47—42no—
192C2×D4×C47—81no—
193C2×D4×C47—81no—
194C2×D4×C47C2×D412yes—
195C2×D4×C47#4112yes—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—42no—
213C22×C4×C47—42no—
214C22×C4×C47—81no—
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D412yes—
220C22×C4×C47#4112yes—
221C22×C4×C47C2411yescharacteristic
222SD16×C47—44no—
223SD16×C47—44no—
224M16×C47—44no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47—21no—
231C2×C8×C47—21no—
232C2×C8×C47—21no—
233C2×C8×C47—21no—
234C2×C8×C47—44no—
235C2×C8×C47C2×D412yes—
236C2×C8×C47C2×D412yes—
237C2×C8×C47C2×D412yes—
238C4⋊C4×C47—22no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—42no—
249C4⋊C4×C47—42no—
250C4⋊C4×C47—42no—
251C4⋊C4×C47—81no—
252C4⋊C4×C47C2×D412yes—
253C22⋊C4×C47—22no—
254C22⋊C4×C47—22no—
255C22⋊C4×C47—42no—
256C22⋊C4×C47—42no—
257C22⋊C4×C47—42no—
258C22⋊C4×C47—42no—
259C22⋊C4×C47—42no—
260C22⋊C4×C47—42no—
261C22⋊C4×C47—42no—
262C22⋊C4×C47—81no—
263C22⋊C4×C47—81no—
264C22⋊C4×C47—81no—
265C42×C47—21no—
266C42×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—21no—
276C23×C47—21no—
277C23×C47—21no—
278C23×C47—21no—
279C23×C47—21no—
280C23×C47—48no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—41no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—84no—
294C23×C47—84no—
295C23×C47—84no—
296C23×C47—84no—
297C23×C47—84no—
298C23×C47—84no—
299C23×C47#12112yes—
300C23×C47AGL(1,ℤ/8)12yes—
301C23×C47#13712yes—
302C23×C47C22×D411yescharacteristic
303Q8×C47—41no—
304Q8×C47—41no—
305Q8×C47—41no—
306Q8×C47—41no—
307D4×C47—22no—
308D4×C47—22no—
309D4×C47—22no—
310D4×C47—22no—
311D4×C47—48no—
312D4×C47—44no—
313D4×C47—41no—
314D4×C47—41no—
315D4×C47—41no—
316D4×C47—41no—
317D4×C47—84no—
318D4×C47—84no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—21no—
328C2×C4×C47—21no—
329C2×C4×C47—22no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
332C2×C4×C47—21no—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—84no—
357C2×C4×C47#12112yes—
358C2×C4×C47C22×D411yescharacteristic
359C2×C4×C47C22×D411yescharacteristic
360C2×C4×C47C2×#4111yescharacteristic
361C2×C4×C47C2×#4111yescharacteristic
362C2×C4×C47H(5,𝔽2)11yescharacteristic
363C2×C4×C47H(5,𝔽2)11yescharacteristic
364C8×C47—22no—
365C8×C47—22no—
366C8×C47—22no—
367C8×C47—41no—
368#25128C4711yesmaximal, characteristic, direct product factor, Sylow
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—22no—
372C22×C47—22no—
373C22×C47—22no—
374C22×C47—22no—
375C22×C47—41no—
376C22×C47—42no—
377C22×C47—42no—
378C22×C47—41no—
379C22×C47—42no—
380C22×C47—41no—
381C22×C47—42no—
382C22×C47—41no—
383C22×C47—41no—
384C22×C47—42no—
385C22×C47—41no—
386C22×C47—42no—
387C22×C47—41no—
388C22×C47—816no—
389C22×C47—81no—
390C22×C47—81no—
391C22×C47—81no—
392C22×C47—81no—
393C22×C47—81no—
394C22×C47—81no—
395C22×C47—81no—
396C22×C47—81no—
397C22×C47#46814yescomplemented
398C22×C47C2×#12111yescharacteristic
399C22×C47D4211yescharacteristic
400C22×C47#54611yescharacteristic
401C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
402C22×C47C2×#13711yescharacteristic
403C22×C47#57611yescharacteristic
404C22×C47#57711yescharacteristic
405C4×C47—22no—
406C4×C47—41no—
407C4×C47—42no—
408C4×C47—41no—
409C4×C47—41no—
410C4×C47—81no—
411C4×C47—81no—
412C4×C47—81no—
413C4×C47—81no—
414C4×C47—81no—
415C4×C47#52511yescharacteristic
416C4×C47#53811yescharacteristic
417C4×C47D4211yescharacteristic
418C4×C47#54611yescharacteristic
419C2×#468C2×C4711yescharacteristic, complemented
420C2×#450C2×C4711yescharacteristic, complemented
421C2×#435C2×C4711yescharacteristic, complemented
422C22×#102C2×C4711yescharacteristic, complemented
423#2417C2×C4711yescharacteristic, complemented
424#2408C2×C4711yescharacteristic
425#2067C2×C4711yescharacteristic, complemented
426#2055C2×C4711yescharacteristic, complemented
427#2033C2×C4711yescharacteristic, complemented
428#2000C2×C4711yescharacteristic, complemented
429#1973C2×C4711yescharacteristic, complemented
430#1936C2×C4711yescharacteristic, complemented
431#1895C2×C4711yescharacteristic, complemented
432#1892C2×C4711yescharacteristic, complemented
433#1852C2×C4711yescharacteristic, complemented
434C2×C47—24no—
435C2×C47—81no—
436C2×C47—82no—
437C2×C47—82no—
438C2×C47#242411yescharacteristic
439C2×C47C2×#46811yescharacteristic
440C2×C47#306211yescharacteristic
441C2×C47#326411yescharacteristic
442C2×C47#326611yescharacteristic
443C2×C47#331011yescharacteristic
444C2×C47#331411yescharacteristic
445C23×D4C22×C4711yescharacteristic
446C22×SD16C22×C4711yescharacteristic
447C22×SD16C22×C4711yescharacteristic
448C22×M16C22×C4711yescharacteristic, complemented
449C23×C8C22×C4711yescharacteristic
450C2×C22⋊Q8C22×C4711yescharacteristic
451C2×C22⋊Q8C22×C4711yescharacteristic, complemented
452C2×#121C22×C4711yescharacteristic
453C2×#121C22×C4711yescharacteristic
454C2×#120—21no—
455C2×C4×D4C22×C4711yescharacteristic
456C22×C4⋊C4C22×C4711yescharacteristic
457#468—24no—
458#450—24no—
459#435—24no—
460C2×#107C22×C4711yescharacteristic, complemented
461C2×#107C22×C4711yescharacteristic, complemented
462C2×C4⋊C8C22×C4711yescharacteristic, complemented
463C2×#103C22×C4711yescharacteristic, complemented
464C2×#103C22×C4711yescharacteristic, complemented
465C2×#102—24no—
466C2×#102C22×C4711yescharacteristic
467C2×#102C22×C4711yescharacteristic
468C2×#102C22×C4711yescharacteristic
469C2×#102C22×C4711yescharacteristic
470C2×#102C22×C4711yescharacteristic
471C2×#102C22×C4711yescharacteristic
472C2×C22⋊C8C22×C4711yescharacteristic
473C2×C22⋊C8C22×C4711yescharacteristic, complemented
474C2×#97C22×C4711yescharacteristic, complemented
475#398—21no—
476#396—21no—
477#394—21no—
478#392—21no—
479#391C22×C4711yescharacteristic, complemented
480#390C22×C4711yescharacteristic
481#390C22×C4711yescharacteristic
482#389C22×C4711yescharacteristic, complemented
483#386—21no—
484#380—21no—
485#380C22×C4711yescharacteristic
486#380C22×C4711yescharacteristic, complemented
487#379—21no—
488#340C22×C4711yescharacteristic, complemented
489#340C22×C4711yescharacteristic, complemented
490#340C22×C4711yescharacteristic, complemented
491#340C22×C4711yescharacteristic, complemented
492C47#2512811yescharacteristic, direct product factor, Sylow
493C25—21no—
494C22×Q8C23×C4711yescharacteristic
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4D4×C4711yescharacteristic
505C22×D4C23×C4711yescharacteristic
506C22×D4C23×C4711yescharacteristic
507C23×C4—21no—
508C23×C4C23×C4711yescharacteristic
509C23×C4C23×C4711yescharacteristic
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—41no—
519C22×C8—22no—
520C22×C8—22no—
521C22×C8—41no—
522C22×C8C23×C4711yescharacteristic
523C22×C8C23×C4711yescharacteristic
524C22×C8C23×C4711yescharacteristic
525C22×C8C23×C4711yescharacteristic
526C22⋊Q8—22no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—22no—
531#121—22no—
532#121—41no—
533#121—41no—
534#120—44no—
535C4×D4—22no—
536C4×D4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4D4×C4711yescharacteristic
544C2×C4⋊C4C23×C4711yescharacteristic
545C2×C4⋊C4C23×C4711yescharacteristic
546C2×C4⋊C4C23×C4711yescharacteristic
547C2×C4⋊C4C23×C4711yescharacteristic
548C2×C4⋊C4C23×C4711yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4D4×C4711yescharacteristic
560C2×C22⋊C4D4×C4711yescharacteristic
561C2×C42C23×C4711yescharacteristic
562#107—22no—
563#107—41no—
564C4⋊C8—22no—
565#103—22no—
566#103—41no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102D4×C4714yescomplemented
573C22⋊C8—22no—
574C22⋊C8D4×C4714yescomplemented
575#97—22no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—21no—
580#95—21no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—81no—
589C24—81no—
590C24C2×D4×C4711yescharacteristic
591C24C2×D4×C4711yescharacteristic
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×D4—28no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—44no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—81no—
623C2×D4—81no—
624C2×D4C2×D4×C4712yes—
625C2×D4#41×C4712yes—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—81no—
645C22×C4C2×D4×C4711yescharacteristic
646C22×C4C2×D4×C4711yescharacteristic
647C22×C4C2×D4×C4711yescharacteristic
648C22×C4C2×D4×C4711yescharacteristic
649C22×C4C2×D4×C4712yes—
650C22×C4#41×C4712yes—
651C22×C4C24×C4711yescharacteristic
652SD16—44no—
653SD16—44no—
654M16—44no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—44no—
665C2×C8C2×D4×C4712yes—
666C2×C8C2×D4×C4712yes—
667C2×C8C2×D4×C4712yes—
668C4⋊C4—22no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—81no—
682C4⋊C4C2×D4×C4712yes—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—81no—
693C22⋊C4—81no—
694C22⋊C4—81no—
695C42—21no—
696C42—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—48no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23#121×C4712yes—
730C23AGL(1,ℤ/8)×C4712yes—
731C23#137×C4712yes—
732C23C22×D4×C4711yescharacteristic
733Q8—41no—
734Q8—41no—
735Q8—41no—
736Q8—41no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—48no—
742D4—44no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4—84no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—84no—
787C2×C4#121×C4712yes—
788C2×C4C22×D4×C4711yescharacteristic
789C2×C4C22×D4×C4711yescharacteristic
790C2×C4C2×#41×C4711yescharacteristic
791C2×C4C2×#41×C4711yescharacteristic
792C2×C4H(5,𝔽2)×C4711yescharacteristic
793C2×C4H(5,𝔽2)×C4711yescharacteristic
794C8—22no—
795C8—22no—
796C8—22no—
797C8—41no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—41no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—41no—
814C22—42no—
815C22—41no—
816C22—42no—
817C22—816no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22C47×#46814yescomplemented
827C22C2×#121×C4711yescharacteristic
828C22D42×C4711yescharacteristic
829C22C47×#54611yescharacteristic
830C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
831C22C2×#137×C4711yescharacteristic
832C22C47×#57611yescharacteristic
833C22C47×#57711yescharacteristic
834C4—22no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—42no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4—81no—
843C4—81no—
844C4C47×#52511yescharacteristic
845C4C47×#53811yescharacteristic
846C4D42×C4711yescharacteristic
847C4C47×#54611yescharacteristic
848C2—24no—
849C2—81no—
850C2—82no—
851C2—82no—
852C2C47×#242411yescharacteristic
853C2C2×C47×#46811yescharacteristic
854C2C47×#306211yescharacteristic
855C2C47×#326411yescharacteristic
856C2C47×#326611yescharacteristic
857C2C47×#331011yescharacteristic
858C2C47×#331411yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#2408C2
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×#450C2semidirect
3. C2×C47×#435C2semidirect
4. C22×#102×C47C2semidirect
5. C47×#2417C2semidirect
7. C47×#2067C2semidirect
8. C47×#2055C2semidirect
9. C47×#2033C2semidirect
10. C47×#2000C2semidirect
11. C47×#1973C2semidirect
12. C47×#1936C2semidirect
13. C47×#1895C2semidirect
14. C47×#1892C2semidirect
15. C47×#1852C2semidirect
19. C22×M16×C47C22semidirect
22. C2×C22⋊Q8×C47C22semidirect
31. C2×#107×C47C22semidirect
32. C2×#107×C47C22semidirect
33. C2×C4⋊C8×C47C22semidirect
34. C2×#103×C47C22semidirect
35. C2×#103×C47C22semidirect
44. C2×C22⋊C8×C47C22semidirect
45. C2×#97×C47C22semidirect
50. C47×#391C22semidirect
53. C47×#389C22semidirect
57. C47×#380C22semidirect
59. C47×#340C22semidirect
60. C47×#340C22semidirect
61. C47×#340C22semidirect
62. C47×#340C22semidirect
142. #102×C47D4semidirect
144. C22⋊C8×C47D4semidirect
368. #25128C47direct (N × H)
397. C22×C47#468semidirect
419. C2×#468C2×C47semidirect
420. C2×#450C2×C47semidirect
421. C2×#435C2×C47semidirect
422. C22×#102C2×C47semidirect
423. #2417C2×C47semidirect
425. #2067C2×C47semidirect
426. #2055C2×C47semidirect
427. #2033C2×C47semidirect
428. #2000C2×C47semidirect
429. #1973C2×C47semidirect
430. #1936C2×C47semidirect
431. #1895C2×C47semidirect
432. #1892C2×C47semidirect
433. #1852C2×C47semidirect
448. C22×M16C22×C47semidirect
451. C2×C22⋊Q8C22×C47semidirect
460. C2×#107C22×C47semidirect
461. C2×#107C22×C47semidirect
462. C2×C4⋊C8C22×C47semidirect
463. C2×#103C22×C47semidirect
464. C2×#103C22×C47semidirect
473. C2×C22⋊C8C22×C47semidirect
474. C2×#97C22×C47semidirect
479. #391C22×C47semidirect
482. #389C22×C47semidirect
486. #380C22×C47semidirect
488. #340C22×C47semidirect
489. #340C22×C47semidirect
490. #340C22×C47semidirect
491. #340C22×C47semidirect
492. C47#25128direct (N × H)
572. #102D4×C47semidirect
574. C22⋊C8D4×C47semidirect
826. C22C47×#468semidirect

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×#4502
C2×C47×#4352
C22×#102×C472
C47×#24172
C47×#24082
C47×#20672
C47×#20552
C47×#20332
C47×#20002
C47×#19732
C47×#19362
C47×#18952
C47×#18922
C47×#18522
#2512847