Finite Group Databasebeta

← C47×#21772 #26061470

Subgroups — C47×#21772 #26061470

Order 12032.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#537C211yesmaximal, characteristic
2C2×C47×#408C211yesmaximal, characteristic, complemented
3C47×#2311C211yesmaximal, characteristic, complemented
4C47×#1895C211yesmaximal, characteristic, complemented
5C47×#1894C211yesmaximal, characteristic, complemented
6C47×#1893C211yesmaximal, characteristic, complemented
7C47×#1892C211yesmaximal, characteristic, complemented
8C47×#1875C211yesmaximal, characteristic, complemented
9C47×#1874C211yesmaximal, characteristic, complemented
10C47×#1873C211yesmaximal, characteristic, complemented
11C47×#1872C211yesmaximal, characteristic, complemented
12C47×#1824C211yesmaximal, characteristic, complemented
13C47×#1823C211yesmaximal, characteristic, complemented
14C47×#1788C211yesmaximal, characteristic, complemented
15C47×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C47×#537—24no—
21C47×#537C418yescomplemented
22C2×C22⋊Q8×C47—21no—
23C2×C22⋊Q8×C47C2211yescharacteristic
24C2×C22⋊Q8×C47C2211yescharacteristic
25C2×#121×C47—21no—
26C2×#121×C47—21no—
27C2×#121×C47—21no—
28C2×#121×C47C2211yescharacteristic
29C2×#121×C47C2211yescharacteristic
30C2×#117×C47C2211yescharacteristic
31C22×C4⋊C4×C47C2211yescharacteristic
32C22×C4⋊C4×C47C2211yescharacteristic
33C2×#103×C47C2211yescharacteristic
34C2×#103×C47C2211yescharacteristic
35C2×#103×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C47×#408—24no—
42C2×C22⋊C8×C47C2211yescharacteristic
43C2×C22⋊C8×C47C2211yescharacteristic
44C2×C22⋊C8×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2211yescharacteristic
46C47×#391—21no—
47C47×#390—21no—
48C47×#386—21no—
49C47×#386—21no—
50C47×#380C2211yescharacteristic
51C47×#380C2211yescharacteristic
52C47×#380C2211yescharacteristic
53C47×#380C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C2×#41×C47—22no—
63C2×#41×C47—41no—
64C2×#41×C47—41no—
65C2×#41×C47—41no—
66C2×#41×C47—41no—
67C2×#41×C47—41no—
68C2×#41×C47—41no—
69C2×#41×C47—41no—
70C2×#41×C47—41no—
71C2×#41×C47C2×C414yes—
72C2×#41×C47C2×C414yescomplemented
73C2×#41×C47D414yes—
74C22×Q8×C47D411yescharacteristic
75C22×Q8×C47C2311yescharacteristic
76C22×D4×C47—21no—
77C22×D4×C47—21no—
78C22×D4×C47—21no—
79C22×D4×C47D411yescharacteristic
80C22×D4×C47D411yescharacteristic
81C22×D4×C47D411yescharacteristic
82C22×D4×C47C2311yescharacteristic
83C23×C4×C47—21no—
84C23×C4×C47—21no—
85C23×C4×C47—21no—
86C23×C4×C47C2311yescharacteristic
87C23×C4×C47C2311yescharacteristic
88C23×C4×C47C2311yescharacteristic
89C2×M16×C47—22no—
90C2×M16×C47—41no—
91C2×M16×C47—41no—
92C22×C8×C47—22no—
93C22×C8×C47—41no—
94C22×C8×C47—41no—
95C22×C8×C47C2311yescharacteristic
96C22×C8×C47C2311yescharacteristic
97C22×C8×C47C2311yescharacteristic
98C22×C8×C47C2311yescharacteristic
99C22⋊Q8×C47—28no—
100C22⋊Q8×C47—22no—
101C22⋊Q8×C47—22no—
102C22⋊Q8×C47C2×C414yes—
103C22⋊Q8×C47C2×C414yescomplemented
104#121×C47—28no—
105#121×C47—28no—
106#121×C47—28no—
107#121×C47—22no—
108#121×C47—22no—
109#121×C47C2×C414yes—
110#121×C47C2×C414yescomplemented
111#117×C47—41no—
112#117×C47—41no—
113C2×C4⋊C4×C47—21no—
114C2×C4⋊C4×C47—22no—
115C2×C4⋊C4×C47—21no—
116C2×C4⋊C4×C47—21no—
117C2×C4⋊C4×C47—21no—
118C2×C4⋊C4×C47—41no—
119C2×C4⋊C4×C47—41no—
120C2×C4⋊C4×C47C2×C414yescomplemented
121C2×C4⋊C4×C47C2311yescharacteristic
122C2×C4⋊C4×C47C2311yescharacteristic
123C2×C4⋊C4×C47C2311yescharacteristic
124C2×C4⋊C4×C47C2311yescharacteristic
125C2×C4⋊C4×C47C2311yescharacteristic
126C2×C4⋊C4×C47C2311yescharacteristic
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C22⋊C4×C47—21no—
135C2×C22⋊C4×C47—21no—
136C2×C42×C47—21no—
137#103×C47—41no—
138#103×C47—41no—
139#103×C47—41no—
140#103×C47—41no—
141#102×C47—41no—
142#102×C47—41no—
143#102×C47—41no—
144#102×C47—41no—
145C22⋊C8×C47—22no—
146C22⋊C8×C47—22no—
147C22⋊C8×C47—22no—
148C22⋊C8×C47—22no—
149#95×C47—21no—
150#95×C47—21no—
151#95×C47—21no—
152#95×C47—21no—
153C24×C47—21no—
154C24×C47C2×D411yescharacteristic
155C24×C47C2×D411yescharacteristic
156C24×C47C2×D411yescharacteristic
157#41×C47—44no—
158#41×C47—44no—
159#41×C47—44no—
160#41×C47—44no—
161#41×C47—44no—
162#41×C47—44no—
163#41×C47—44no—
164#41×C47—44no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×Q8×C47—21no—
169C2×Q8×C47—21no—
170C2×Q8×C47—41no—
171C2×Q8×C47—41no—
172C2×Q8×C47C22⋊C414yes—
173C2×Q8×C47C22×C412yes—
174C2×D4×C47—24no—
175C2×D4×C47—24no—
176C2×D4×C47—24no—
177C2×D4×C47—21no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—21no—
182C2×D4×C47—41no—
183C2×D4×C47—41no—
184C2×D4×C47—41no—
185C2×D4×C47—41no—
186C2×D4×C47—41no—
187C2×D4×C47—41no—
188C2×D4×C47—42no—
189C2×D4×C47—42no—
190C2×D4×C47—81no—
191C2×D4×C47—81no—
192C2×D4×C47—81no—
193C2×D4×C47—81no—
194C2×D4×C47C22⋊C414yes—
195C2×D4×C47C22⋊C414yes—
196C2×D4×C47C22⋊C414yes—
197C2×D4×C47C22×C412yes—
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—21no—
213C22×C4×C47—24no—
214C22×C4×C47—24no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—42no—
220C22×C4×C47—42no—
221C22×C4×C47—42no—
222C22×C4×C47—81no—
223C22×C4×C47—81no—
224C22×C4×C47—81no—
225C22×C4×C47—81no—
226C22×C4×C47C22×C412yes—
227C22×C4×C47C22×C412yes—
228C22×C4×C47C22×C412yes—
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2×D411yescharacteristic
232C22×C4×C47C2×D412yes—
233C22×C4×C47C2×D412yes—
234C22×C4×C47C2×D412yes—
235C22×C4×C47C2411yescharacteristic
236M16×C47—44no—
237C2×C8×C47—21no—
238C2×C8×C47—21no—
239C2×C8×C47—21no—
240C2×C8×C47—21no—
241C2×C8×C47—21no—
242C2×C8×C47—21no—
243C2×C8×C47—21no—
244C2×C8×C47—21no—
245C2×C8×C47—21no—
246C2×C8×C47—21no—
247C2×C8×C47—21no—
248C2×C8×C47—21no—
249C2×C8×C47—44no—
250C4⋊C4×C47—24no—
251C4⋊C4×C47—24no—
252C4⋊C4×C47—24no—
253C4⋊C4×C47—21no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47—21no—
257C4⋊C4×C47—21no—
258C4⋊C4×C47—21no—
259C4⋊C4×C47—21no—
260C4⋊C4×C47—21no—
261C4⋊C4×C47—21no—
262C4⋊C4×C47—21no—
263C4⋊C4×C47—42no—
264C4⋊C4×C47C22×C412yes—
265C4⋊C4×C47C22×C412yes—
266C22⋊C4×C47—24no—
267C22⋊C4×C47—24no—
268C22⋊C4×C47—24no—
269C22⋊C4×C47—24no—
270C22⋊C4×C47—42no—
271C22⋊C4×C47—81no—
272C22⋊C4×C47—81no—
273C22⋊C4×C47—81no—
274C22⋊C4×C47—81no—
275C42×C47—42no—
276C23×C47—21no—
277C23×C47—21no—
278C23×C47—21no—
279C23×C47—21no—
280C23×C47—21no—
281C23×C47—21no—
282C23×C47—21no—
283C23×C47—21no—
284C23×C47—21no—
285C23×C47—21no—
286C23×C47—21no—
287C23×C47—21no—
288C23×C47—21no—
289C23×C47—21no—
290C23×C47—21no—
291C23×C47—21no—
292C23×C47—21no—
293C23×C47—21no—
294C23×C47—22no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—41no—
298C23×C47—41no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47C2×C22⋊C412yes—
302C23×C47C2×C22⋊C412yes—
303C23×C47C2×C22⋊C412yes—
304C23×C47C22×D411yescharacteristic
305Q8×C47—22no—
306Q8×C47—22no—
307Q8×C47—44no—
308Q8×C47—41no—
309Q8×C47—41no—
310D4×C47—22no—
311D4×C47—22no—
312D4×C47—44no—
313D4×C47—44no—
314D4×C47—44no—
315D4×C47—48no—
316D4×C47—41no—
317D4×C47—41no—
318D4×C47—84no—
319D4×C47—84no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—48no—
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—41no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47—41no—
360C2×C4×C47—84no—
361C2×C4×C47—84no—
362C2×C4×C47C2×C22⋊C412yes—
363C2×C4×C47C2×C22⋊C412yes—
364C2×C4×C47C2×C22⋊C412yes—
365C2×C4×C47C23×C411yescharacteristic
366C2×C4×C47C22×D411yescharacteristic
367C2×C4×C47H(5,𝔽2)11yescharacteristic
368C2×C4×C47H(5,𝔽2)11yescharacteristic
369C2×C4×C47H(5,𝔽2)11yescharacteristic
370C2×C4×C47H(5,𝔽2)11yescharacteristic
371C8×C47—41no—
372C8×C47—41no—
373C8×C47—41no—
374C8×C47—41no—
375#21772C4711yesmaximal, characteristic, direct product factor, Sylow
376C22×C47—22no—
377C22×C47—22no—
378C22×C47—22no—
379C22×C47—22no—
380C22×C47—22no—
381C22×C47—22no—
382C22×C47—22no—
383C22×C47—22no—
384C22×C47—22no—
385C22×C47—41no—
386C22×C47—41no—
387C22×C47—41no—
388C22×C47—41no—
389C22×C47—41no—
390C22×C47—41no—
391C22×C47—41no—
392C22×C47—41no—
393C22×C47—41no—
394C22×C47—41no—
395C22×C47—41no—
396C22×C47—41no—
397C22×C47—42no—
398C22×C47—42no—
399C22×C47—42no—
400C22×C47—81no—
401C22×C47—81no—
402C22×C47—81no—
403C22×C47—81no—
404C22×C47C22×C22⋊C411yescharacteristic
405C22×C47#53411yescharacteristic
406C22×C47#53411yescharacteristic
407C22×C47#57611yescharacteristic
408C22×C47#57711yescharacteristic
409C22×C47#57711yescharacteristic
410C22×C47#57811yescharacteristic
411C4×C47—22no—
412C4×C47—22no—
413C4×C47—22no—
414C4×C47—42no—
415C4×C47—42no—
416C4×C47—42no—
417C4×C47—81no—
418C4×C47—81no—
419C4×C47—81no—
420C4×C47—81no—
421C4×C47#51811yescharacteristic
422C4×C47#51811yescharacteristic
423C4×C47#53411yescharacteristic
424C4×C47#53411yescharacteristic
425C2×#537C2×C4711yescharacteristic
426C2×#408C2×C4711yescharacteristic, complemented
427#2311C2×C4711yescharacteristic, complemented
428#1895C2×C4711yescharacteristic, complemented
429#1894C2×C4711yescharacteristic, complemented
430#1893C2×C4711yescharacteristic, complemented
431#1892C2×C4711yescharacteristic, complemented
432#1875C2×C4711yescharacteristic, complemented
433#1874C2×C4711yescharacteristic, complemented
434#1873C2×C4711yescharacteristic, complemented
435#1872C2×C4711yescharacteristic, complemented
436#1824C2×C4711yescharacteristic, complemented
437#1823C2×C4711yescharacteristic, complemented
438#1788C2×C4711yescharacteristic, complemented
439#1788C2×C4711yescharacteristic, complemented
440C2×C47—42no—
441C2×C47—42no—
442C2×C47—42no—
443C2×C47—82no—
444C2×C47#230811yescharacteristic
445C2×C47#289711yescharacteristic
446C2×C47#289811yescharacteristic
447C2×C47#319811yescharacteristic
448C2×C47#320111yescharacteristic
449C2×C47#320311yescharacteristic
450C2×C47#320411yescharacteristic
451C22×#41C22×C4711yescharacteristic
452C22×#41C22×C4711yescharacteristic
453C22×M16C22×C4711yescharacteristic
454C23×C8C22×C4711yescharacteristic
455#537—24no—
456#537C4×C4718yescomplemented
457C2×C22⋊Q8—21no—
458C2×C22⋊Q8C22×C4711yescharacteristic
459C2×C22⋊Q8C22×C4711yescharacteristic
460C2×#121—21no—
461C2×#121—21no—
462C2×#121—21no—
463C2×#121C22×C4711yescharacteristic
464C2×#121C22×C4711yescharacteristic
465C2×#117C22×C4711yescharacteristic
466C22×C4⋊C4C22×C4711yescharacteristic
467C22×C4⋊C4C22×C4711yescharacteristic
468C2×#103C22×C4711yescharacteristic
469C2×#103C22×C4711yescharacteristic
470C2×#103C22×C4711yescharacteristic
471C2×#103C22×C4711yescharacteristic
472C2×#102C22×C4711yescharacteristic
473C2×#102C22×C4711yescharacteristic
474C2×#102C22×C4711yescharacteristic
475C2×#102C22×C4711yescharacteristic
476#408—24no—
477C2×C22⋊C8C22×C4711yescharacteristic
478C2×C22⋊C8C22×C4711yescharacteristic
479C2×C22⋊C8C22×C4711yescharacteristic
480C2×C22⋊C8C22×C4711yescharacteristic
481#391—21no—
482#390—21no—
483#386—21no—
484#386—21no—
485#380C22×C4711yescharacteristic
486#380C22×C4711yescharacteristic
487#380C22×C4711yescharacteristic
488#380C22×C4711yescharacteristic
489#340C22×C4711yescharacteristic
490#340C22×C4711yescharacteristic
491#340C22×C4711yescharacteristic
492#340C22×C4711yescharacteristic
493#340C22×C4711yescharacteristic
494#340C22×C4711yescharacteristic
495#340C22×C4711yescharacteristic
496#340C22×C4711yescharacteristic
497C47#2177211yescharacteristic, direct product factor, Sylow
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41C2×C4×C4714yes—
508C2×#41C2×C4×C4714yescomplemented
509C2×#41D4×C4714yes—
510C22×Q8D4×C4711yescharacteristic
511C22×Q8C23×C4711yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C4711yescharacteristic
516C22×D4D4×C4711yescharacteristic
517C22×D4D4×C4711yescharacteristic
518C22×D4C23×C4711yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C4711yescharacteristic
523C23×C4C23×C4711yescharacteristic
524C23×C4C23×C4711yescharacteristic
525C2×M16—22no—
526C2×M16—41no—
527C2×M16—41no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C23×C4711yescharacteristic
532C22×C8C23×C4711yescharacteristic
533C22×C8C23×C4711yescharacteristic
534C22×C8C23×C4711yescharacteristic
535C22⋊Q8—28no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8C2×C4×C4714yes—
539C22⋊Q8C2×C4×C4714yescomplemented
540#121—28no—
541#121—28no—
542#121—28no—
543#121—22no—
544#121—22no—
545#121C2×C4×C4714yes—
546#121C2×C4×C4714yescomplemented
547#117—41no—
548#117—41no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4C2×C4×C4714yescomplemented
557C2×C4⋊C4C23×C4711yescharacteristic
558C2×C4⋊C4C23×C4711yescharacteristic
559C2×C4⋊C4C23×C4711yescharacteristic
560C2×C4⋊C4C23×C4711yescharacteristic
561C2×C4⋊C4C23×C4711yescharacteristic
562C2×C4⋊C4C23×C4711yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C42—21no—
573#103—41no—
574#103—41no—
575#103—41no—
576#103—41no—
577#102—41no—
578#102—41no—
579#102—41no—
580#102—41no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—22no—
584C22⋊C8—22no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24C2×D4×C4711yescharacteristic
591C24C2×D4×C4711yescharacteristic
592C24C2×D4×C4711yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—41no—
607C2×Q8—41no—
608C2×Q8C22⋊C4×C4714yes—
609C2×Q8C22×C4×C4712yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4C22⋊C4×C4714yes—
631C2×D4C22⋊C4×C4714yes—
632C2×D4C22⋊C4×C4714yes—
633C2×D4C22×C4×C4712yes—
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—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—81no—
659C22×C4—81no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C22×C4×C4712yes—
663C22×C4C22×C4×C4712yes—
664C22×C4C22×C4×C4712yes—
665C22×C4C2×D4×C4711yescharacteristic
666C22×C4C2×D4×C4711yescharacteristic
667C22×C4C2×D4×C4711yescharacteristic
668C22×C4C2×D4×C4712yes—
669C22×C4C2×D4×C4712yes—
670C22×C4C2×D4×C4712yes—
671C22×C4C24×C4711yescharacteristic
672M16—44no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—44no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—42no—
700C4⋊C4C22×C4×C4712yes—
701C4⋊C4C22×C4×C4712yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4—81no—
711C42—42no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×C22⋊C4×C4712yes—
738C23C2×C22⋊C4×C4712yes—
739C23C2×C22⋊C4×C4712yes—
740C23C22×D4×C4711yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—44no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—48no—
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—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—84no—
797C2×C4—84no—
798C2×C4C2×C22⋊C4×C4712yes—
799C2×C4C2×C22⋊C4×C4712yes—
800C2×C4C2×C22⋊C4×C4712yes—
801C2×C4C23×C4×C4711yescharacteristic
802C2×C4C22×D4×C4711yescharacteristic
803C2×C4H(5,𝔽2)×C4711yescharacteristic
804C2×C4H(5,𝔽2)×C4711yescharacteristic
805C2×C4H(5,𝔽2)×C4711yescharacteristic
806C2×C4H(5,𝔽2)×C4711yescharacteristic
807C8—41no—
808C8—41no—
809C8—41no—
810C8—41no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C22×C22⋊C4×C4711yescharacteristic
840C22C47×#53411yescharacteristic
841C22C47×#53411yescharacteristic
842C22C47×#57611yescharacteristic
843C22C47×#57711yescharacteristic
844C22C47×#57711yescharacteristic
845C22C47×#57811yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4C47×#51811yescharacteristic
857C4C47×#51811yescharacteristic
858C4C47×#53411yescharacteristic
859C4C47×#53411yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—82no—
864C2C47×#230811yescharacteristic
865C2C47×#289711yescharacteristic
866C2C47×#289811yescharacteristic
867C2C47×#319811yescharacteristic
868C2C47×#320111yescharacteristic
869C2C47×#320311yescharacteristic
870C2C47×#320411yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#537C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C22×#41×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#408C2semidirect
3. C47×#2311C2semidirect
4. C47×#1895C2semidirect
5. C47×#1894C2semidirect
6. C47×#1893C2semidirect
7. C47×#1892C2semidirect
8. C47×#1875C2semidirect
9. C47×#1874C2semidirect
10. C47×#1873C2semidirect
11. C47×#1872C2semidirect
12. C47×#1824C2semidirect
13. C47×#1823C2semidirect
14. C47×#1788C2semidirect
15. C47×#1788C2semidirect
21. C47×#537C4semidirect
72. C2×#41×C47C2×C4semidirect
103. C22⋊Q8×C47C2×C4semidirect
110. #121×C47C2×C4semidirect
120. C2×C4⋊C4×C47C2×C4semidirect
375. #21772C47direct (N × H)
426. C2×#408C2×C47semidirect
427. #2311C2×C47semidirect
428. #1895C2×C47semidirect
429. #1894C2×C47semidirect
430. #1893C2×C47semidirect
431. #1892C2×C47semidirect
432. #1875C2×C47semidirect
433. #1874C2×C47semidirect
434. #1873C2×C47semidirect
435. #1872C2×C47semidirect
436. #1824C2×C47semidirect
437. #1823C2×C47semidirect
438. #1788C2×C47semidirect
439. #1788C2×C47semidirect
456. #537C4×C47semidirect
497. C47#21772direct (N × H)
508. C2×#41C2×C4×C47semidirect
539. C22⋊Q8C2×C4×C47semidirect
546. #121C2×C4×C47semidirect
556. C2×C4⋊C4C2×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5372
C2×C47×#4082
C47×#23112
C47×#18952
C47×#18942
C47×#18932
C47×#18922
C47×#18752
C47×#18742
C47×#18732
C47×#18722
C47×#18242
C47×#18232
C47×#17882
#2177247