Finite Group Databasebeta

← C47×#22427 #26062125

Subgroups — C47×#22427 #26062125

Order 12032.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#546C211yesmaximal, characteristic
2C2×C47×#436C211yesmaximal, characteristic, complemented
3C2×C47×#417C211yesmaximal, characteristic, complemented
4C2×C47×#418C211yesmaximal, characteristic, complemented
5C47×#2352C211yesmaximal, characteristic, complemented
6C47×#1983C211yesmaximal, characteristic, complemented
7C47×#1958C211yesmaximal, characteristic, complemented
8C47×#1895C211yesmaximal, characteristic, complemented
9C47×#1894C211yesmaximal, characteristic, complemented
10C47×#1874C211yesmaximal, characteristic, complemented
11C47×#1873C211yesmaximal, characteristic, complemented
12C47×#1804C211yesmaximal, characteristic, complemented
13C47×#1788C211yesmaximal, characteristic, complemented
14C47×#1786C211yesmaximal, characteristic, complemented
15C4×#102×C47C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C23×D4×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C22×M16×C47C2211yescharacteristic, complemented
20C47×#546—24no—
21C47×#546C418yescomplemented
22C2×#124×C47C2211yescharacteristic
23C2×#123×C47—21no—
24C2×C22⋊Q8×C47C2211yescharacteristic
25C2×#121×C47—21no—
26C2×#121×C47C2211yescharacteristic
27C2×#120×C47—21no—
28C2×C4×D4×C47C2211yescharacteristic
29C2×C4×D4×C47C2211yescharacteristic
30C2×#117×C47C2211yescharacteristic
31C22×C4⋊C4×C47C2211yescharacteristic, complemented
32C22×C22⋊C4×C47—21no—
33C47×#436—24no—
34C2×C4⋊C8×C47C2211yescharacteristic, complemented
35C47×#418—24no—
36C47×#417—24no—
37C2×#103×C47C2211yescharacteristic, complemented
38C2×#103×C47C2211yescharacteristic, complemented
39C2×#103×C47C2211yescharacteristic, complemented
40C2×#103×C47C2211yescharacteristic, complemented
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×#102×C47C2211yescharacteristic
46C2×#102×C47C2211yescharacteristic
47C2×#102×C47C2211yescharacteristic
48C2×#102×C47C2211yescharacteristic
49C2×C22⋊C8×C47C2211yescharacteristic
50C2×C22⋊C8×C47C2211yescharacteristic, complemented
51C2×C4×C8×C47C2211yescharacteristic, complemented
52C47×#388—21no—
53C47×#387—21no—
54C47×#386—21no—
55C47×#382C2211yescharacteristic, complemented
56C47×#380C2211yescharacteristic
57C47×#380C2211yescharacteristic, complemented
58C4×C4⋊C4×C47C2211yescharacteristic, complemented
59C4×C22⋊C4×C47—21no—
60C47×#340C2211yescharacteristic, complemented
61C47×#340C2211yescharacteristic, complemented
62C47×#340C2211yescharacteristic, complemented
63C47×#340C2211yescharacteristic, complemented
64C25×C47—21no—
65C2×#41×C47—22no—
66C2×#41×C47—22no—
67C2×#41×C47—22no—
68C2×#41×C47—41no—
69C2×#41×C47—41no—
70C2×#41×C47C2×C414yes—
71C22×Q8×C47C2311yescharacteristic
72C22×D4×C47—22no—
73C22×D4×C47—22no—
74C22×D4×C47—21no—
75C22×D4×C47—21no—
76C22×D4×C47—21no—
77C22×D4×C47—22no—
78C22×D4×C47—41no—
79C22×D4×C47—41no—
80C22×D4×C47C2×C414yescomplemented
81C22×D4×C47D411yescharacteristic
82C22×D4×C47C2311yescharacteristic
83C22×D4×C47C2311yescharacteristic
84C23×C4×C47—21no—
85C23×C4×C47—21no—
86C23×C4×C47—21no—
87C23×C4×C47C2311yescharacteristic
88C23×C4×C47C2311yescharacteristic
89C2×M16×C47—22no—
90C2×M16×C47—22no—
91C2×M16×C47—22no—
92C2×M16×C47—22no—
93C2×M16×C47—41no—
94C2×M16×C47—41no—
95C22×C8×C47C2311yescharacteristic
96C22×C8×C47C2311yescharacteristic
97C22×C8×C47C2311yescharacteristic
98C22×C8×C47C2311yescharacteristic
99#124×C47—22no—
100#124×C47C2×C414yescomplemented
101#123×C47—28no—
102C22⋊Q8×C47—22no—
103C22⋊Q8×C47C2×C414yescomplemented
104#121×C47—22no—
105#121×C47—28no—
106#121×C47C2×C414yes—
107#120×C47—28no—
108C4×D4×C47—22no—
109C4×D4×C47C2×C414yes—
110C4×D4×C47C2×C414yescomplemented
111C4×D4×C47D414yes—
112#117×C47—22no—
113#117×C47—41no—
114C2×C4⋊C4×C47—21no—
115C2×C4⋊C4×C47—22no—
116C2×C4⋊C4×C47—21no—
117C2×C4⋊C4×C47—41no—
118C2×C4⋊C4×C47D411yescharacteristic
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C4⋊C4×C47C2311yescharacteristic
121C2×C4⋊C4×C47C2311yescharacteristic
122C2×C4⋊C4×C47C2311yescharacteristic
123C2×C4⋊C4×C47C2311yescharacteristic
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×C47—28no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47D411yescharacteristic
134C2×C22⋊C4×C47D411yescharacteristic
135C2×C42×C47—21no—
136C2×C42×C47—21no—
137C2×C42×C47C2311yescharacteristic
138C4⋊C8×C47—22no—
139#103×C47—22no—
140#103×C47—22no—
141#103×C47—41no—
142#103×C47—41no—
143#102×C47—22no—
144#102×C47—22no—
145#102×C47—22no—
146#102×C47—22no—
147#102×C47—22no—
148#102×C47—41no—
149#102×C47—41no—
150#102×C47D414yescomplemented
151C22⋊C8×C47—22no—
152C22⋊C8×C47—22no—
153C4×C8×C47—22no—
154#95×C47—21no—
155#95×C47—21no—
156#95×C47—21no—
157#95×C47—21no—
158#95×C47—21no—
159C24×C47—21no—
160C24×C47—21no—
161C24×C47—24no—
162C24×C47—42no—
163C24×C47—42no—
164C24×C47—42no—
165C24×C47—42no—
166C24×C47—81no—
167C24×C47—81no—
168C24×C47C2×D411yescharacteristic
169C24×C47C2×D411yescharacteristic
170#41×C47—28no—
171#41×C47—44no—
172#41×C47—44no—
173#41×C47—44no—
174C2×Q8×C47—21no—
175C2×Q8×C47—21no—
176C2×Q8×C47—21no—
177C2×Q8×C47—21no—
178C2×Q8×C47—21no—
179C2×Q8×C47C22×C412yes—
180C2×D4×C47—28no—
181C2×D4×C47—24no—
182C2×D4×C47—24no—
183C2×D4×C47—24no—
184C2×D4×C47—21no—
185C2×D4×C47—21no—
186C2×D4×C47—21no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—44no—
193C2×D4×C47—44no—
194C2×D4×C47—44no—
195C2×D4×C47—41no—
196C2×D4×C47—41no—
197C2×D4×C47—42no—
198C2×D4×C47—42no—
199C2×D4×C47—42no—
200C2×D4×C47—42no—
201C2×D4×C47—81no—
202C2×D4×C47—81no—
203C2×D4×C47C22⋊C414yes—
204C2×D4×C47C22×C412yes—
205C2×D4×C47C22×C412yes—
206C2×D4×C47C2×D412yes—
207C2×D4×C47#4112yes—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—24no—
220C22×C4×C47—24no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—42no—
225C22×C4×C47—42no—
226C22×C4×C47—42no—
227C22×C4×C47—42no—
228C22×C4×C47—81no—
229C22×C4×C47—81no—
230C22×C4×C47—81no—
231C22×C4×C47C22×C412yes—
232C22×C4×C47C22×C412yes—
233C22×C4×C47C2×D411yescharacteristic
234C22×C4×C47C2×D411yescharacteristic
235C22×C4×C47C2×D411yescharacteristic
236C22×C4×C47C2×D411yescharacteristic
237C22×C4×C47C2×D412yes—
238C22×C4×C47C2×D412yes—
239C22×C4×C47C2411yescharacteristic
240M16×C47—44no—
241M16×C47—44no—
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—21no—
250C2×C8×C47—21no—
251C2×C8×C47—21no—
252C2×C8×C47—21no—
253C2×C8×C47C2×D412yes—
254C4⋊C4×C47—24no—
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⋊C414yes—
265C4⋊C4×C47C22×C412yes—
266C4⋊C4×C47C2×D412yes—
267C22⋊C4×C47—24no—
268C22⋊C4×C47—24no—
269C22⋊C4×C47—24no—
270C22⋊C4×C47—24no—
271C22⋊C4×C47—24no—
272C22⋊C4×C47—42no—
273C22⋊C4×C47—42no—
274C22⋊C4×C47—81no—
275C22⋊C4×C47C22⋊C414yes—
276C22⋊C4×C47C22⋊C414yes—
277C42×C47—42no—
278C42×C47—81no—
279C42×C47C22×C412yes—
280C42×C47C2×D412yes—
281C23×C47—22no—
282C23×C47—21no—
283C23×C47—21no—
284C23×C47—22no—
285C23×C47—21no—
286C23×C47—21no—
287C23×C47—22no—
288C23×C47—21no—
289C23×C47—21no—
290C23×C47—21no—
291C23×C47—21no—
292C23×C47—21no—
293C23×C47—21no—
294C23×C47—21no—
295C23×C47—21no—
296C23×C47—22no—
297C23×C47—48no—
298C23×C47—48no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47—41no—
308C23×C47—41no—
309C23×C47—84no—
310C23×C47—84no—
311C23×C47—84no—
312C23×C47—84no—
313C23×C47—84no—
314C23×C47C2×C22⋊C412yes—
315C23×C47C2×C22⋊C412yes—
316C23×C47C22×D411yescharacteristic
317Q8×C47—22no—
318Q8×C47—22no—
319Q8×C47—41no—
320Q8×C47—41no—
321D4×C47—22no—
322D4×C47—22no—
323D4×C47—22no—
324D4×C47—22no—
325D4×C47—22no—
326D4×C47—44no—
327D4×C47—48no—
328D4×C47—48no—
329D4×C47—41no—
330D4×C47—41no—
331D4×C47—84no—
332D4×C47C4×D414yes—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—21no—
339C2×C4×C47—21no—
340C2×C4×C47—21no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—48no—
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—41no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—84no—
369C2×C4×C47—84no—
370C2×C4×C47C2×C22⋊C412yes—
371C2×C4×C47C2×C22⋊C412yes—
372C2×C4×C47C2×C22⋊C412yes—
373C2×C4×C47C2×C22⋊C412yes—
374C2×C4×C47C23×C411yescharacteristic
375C2×C4×C47C22×D411yescharacteristic
376C2×C4×C47C22×D411yescharacteristic
377C2×C4×C47C2×#4111yescharacteristic
378C2×C4×C47H(5,𝔽2)11yescharacteristic
379C2×C4×C47H(5,𝔽2)11yescharacteristic
380C8×C47—22no—
381C8×C47—41no—
382C8×C47—41no—
383C8×C47—41no—
384#22427C4711yesmaximal, characteristic, direct product factor, Sylow
385C22×C47—22no—
386C22×C47—22no—
387C22×C47—24no—
388C22×C47—22no—
389C22×C47—22no—
390C22×C47—22no—
391C22×C47—22no—
392C22×C47—42no—
393C22×C47—42no—
394C22×C47—41no—
395C22×C47—41no—
396C22×C47—42no—
397C22×C47—41no—
398C22×C47—41no—
399C22×C47—42no—
400C22×C47—41no—
401C22×C47—41no—
402C22×C47—42no—
403C22×C47—41no—
404C22×C47—41no—
405C22×C47—42no—
406C22×C47—42no—
407C22×C47—42no—
408C22×C47—42no—
409C22×C47—816no—
410C22×C47—81no—
411C22×C47—81no—
412C22×C47—81no—
413C22×C47—81no—
414C22×C47C22×C22⋊C411yescharacteristic
415C22×C47D4211yescharacteristic
416C22×C47#54611yescharacteristic
417C22×C47#57511yescharacteristic
418C22×C47#57511yescharacteristic
419C22×C47#57611yescharacteristic
420C22×C47#57711yescharacteristic
421C4×C47—22no—
422C4×C47—22no—
423C4×C47—22no—
424C4×C47—22no—
425C4×C47—42no—
426C4×C47—42no—
427C4×C47—42no—
428C4×C47—81no—
429C4×C47—81no—
430C4×C47—81no—
431C4×C47C2×C4×D411yescharacteristic
432C4×C47#51811yescharacteristic
433C4×C47D4211yescharacteristic
434C4×C47#54611yescharacteristic
435C2×#546C2×C4711yescharacteristic
436C2×#436C2×C4711yescharacteristic, complemented
437C2×#417C2×C4711yescharacteristic, complemented
438C2×#418C2×C4711yescharacteristic, complemented
439#2352C2×C4711yescharacteristic, complemented
440#1983C2×C4711yescharacteristic, complemented
441#1958C2×C4711yescharacteristic, complemented
442#1895C2×C4711yescharacteristic, complemented
443#1894C2×C4711yescharacteristic, complemented
444#1874C2×C4711yescharacteristic, complemented
445#1873C2×C4711yescharacteristic, complemented
446#1804C2×C4711yescharacteristic, complemented
447#1788C2×C4711yescharacteristic, complemented
448#1786C2×C4711yescharacteristic, complemented
449C4×#102C2×C4711yescharacteristic, complemented
450C2×C47—42no—
451C2×C47—42no—
452C2×C47—44no—
453C2×C47—82no—
454C2×C47D4×C22⋊C411yescharacteristic
455C2×C47#289611yescharacteristic
456C2×C47#289711yescharacteristic
457C2×C47#327311yescharacteristic
458C2×C47#327511yescharacteristic
459C2×C47#332211yescharacteristic
460C2×C47#332311yescharacteristic
461C22×#41C22×C4711yescharacteristic
462C23×D4C22×C4711yescharacteristic
463C22×M16C22×C4711yescharacteristic
464C22×M16C22×C4711yescharacteristic, complemented
465#546—24no—
466#546C4×C4718yescomplemented
467C2×#124C22×C4711yescharacteristic
468C2×#123—21no—
469C2×C22⋊Q8C22×C4711yescharacteristic
470C2×#121—21no—
471C2×#121C22×C4711yescharacteristic
472C2×#120—21no—
473C2×C4×D4C22×C4711yescharacteristic
474C2×C4×D4C22×C4711yescharacteristic
475C2×#117C22×C4711yescharacteristic
476C22×C4⋊C4C22×C4711yescharacteristic, complemented
477C22×C22⋊C4—21no—
478#436—24no—
479C2×C4⋊C8C22×C4711yescharacteristic, complemented
480#418—24no—
481#417—24no—
482C2×#103C22×C4711yescharacteristic, complemented
483C2×#103C22×C4711yescharacteristic, complemented
484C2×#103C22×C4711yescharacteristic, complemented
485C2×#103C22×C4711yescharacteristic, complemented
486C2×#102C22×C4711yescharacteristic
487C2×#102C22×C4711yescharacteristic
488C2×#102C22×C4711yescharacteristic
489C2×#102C22×C4711yescharacteristic
490C2×#102C22×C4711yescharacteristic
491C2×#102C22×C4711yescharacteristic
492C2×#102C22×C4711yescharacteristic
493C2×#102C22×C4711yescharacteristic
494C2×C22⋊C8C22×C4711yescharacteristic
495C2×C22⋊C8C22×C4711yescharacteristic, complemented
496C2×C4×C8C22×C4711yescharacteristic, complemented
497#388—21no—
498#387—21no—
499#386—21no—
500#382C22×C4711yescharacteristic, complemented
501#380C22×C4711yescharacteristic
502#380C22×C4711yescharacteristic, complemented
503C4×C4⋊C4C22×C4711yescharacteristic, complemented
504C4×C22⋊C4—21no—
505#340C22×C4711yescharacteristic, complemented
506#340C22×C4711yescharacteristic, complemented
507#340C22×C4711yescharacteristic, complemented
508#340C22×C4711yescharacteristic, complemented
509C47#2242711yescharacteristic, direct product factor, Sylow
510C25—21no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41C2×C4×C4714yes—
517C22×Q8C23×C4711yescharacteristic
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×C4×C4714yescomplemented
527C22×D4D4×C4711yescharacteristic
528C22×D4C23×C4711yescharacteristic
529C22×D4C23×C4711yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C23×C4711yescharacteristic
534C23×C4C23×C4711yescharacteristic
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—22no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16—41no—
541C22×C8C23×C4711yescharacteristic
542C22×C8C23×C4711yescharacteristic
543C22×C8C23×C4711yescharacteristic
544C22×C8C23×C4711yescharacteristic
545#124—22no—
546#124C2×C4×C4714yescomplemented
547#123—28no—
548C22⋊Q8—22no—
549C22⋊Q8C2×C4×C4714yescomplemented
550#121—22no—
551#121—28no—
552#121C2×C4×C4714yes—
553#120—28no—
554C4×D4—22no—
555C4×D4C2×C4×C4714yes—
556C4×D4C2×C4×C4714yescomplemented
557C4×D4D4×C4714yes—
558#117—22no—
559#117—41no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4D4×C4711yescharacteristic
565C2×C4⋊C4C23×C4711yescharacteristic
566C2×C4⋊C4C23×C4711yescharacteristic
567C2×C4⋊C4C23×C4711yescharacteristic
568C2×C4⋊C4C23×C4711yescharacteristic
569C2×C4⋊C4C23×C4711yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—28no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4D4×C4711yescharacteristic
580C2×C22⋊C4D4×C4711yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42C23×C4711yescharacteristic
584C4⋊C8—22no—
585#103—22no—
586#103—22no—
587#103—41no—
588#103—41no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—41no—
595#102—41no—
596#102D4×C4714yescomplemented
597C22⋊C8—22no—
598C22⋊C8—22no—
599C4×C8—22no—
600#95—21no—
601#95—21no—
602#95—21no—
603#95—21no—
604#95—21no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—81no—
613C24—81no—
614C24C2×D4×C4711yescharacteristic
615C24C2×D4×C4711yescharacteristic
616#41—28no—
617#41—44no—
618#41—44no—
619#41—44no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C22×C4×C4712yes—
626C2×D4—28no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—24no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—41no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—81no—
648C2×D4—81no—
649C2×D4C22⋊C4×C4714yes—
650C2×D4C22×C4×C4712yes—
651C2×D4C22×C4×C4712yes—
652C2×D4C2×D4×C4712yes—
653C2×D4#41×C4712yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—81no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4C22×C4×C4712yes—
678C22×C4C22×C4×C4712yes—
679C22×C4C2×D4×C4711yescharacteristic
680C22×C4C2×D4×C4711yescharacteristic
681C22×C4C2×D4×C4711yescharacteristic
682C22×C4C2×D4×C4711yescharacteristic
683C22×C4C2×D4×C4712yes—
684C22×C4C2×D4×C4712yes—
685C22×C4C24×C4711yescharacteristic
686M16—44no—
687M16—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8C2×D4×C4712yes—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—42no—
710C4⋊C4C22⋊C4×C4714yes—
711C4⋊C4C22×C4×C4712yes—
712C4⋊C4C2×D4×C4712yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—81no—
721C22⋊C4C22⋊C4×C4714yes—
722C22⋊C4C22⋊C4×C4714yes—
723C42—42no—
724C42—81no—
725C42C22×C4×C4712yes—
726C42C2×D4×C4712yes—
727C23—22no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—48no—
744C23—48no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23C2×C22⋊C4×C4712yes—
761C23C2×C22⋊C4×C4712yes—
762C23C22×D4×C4711yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—44no—
773D4—48no—
774D4—48no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4C4×D4×C4714yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—48no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4C2×C22⋊C4×C4712yes—
817C2×C4C2×C22⋊C4×C4712yes—
818C2×C4C2×C22⋊C4×C4712yes—
819C2×C4C2×C22⋊C4×C4712yes—
820C2×C4C23×C4×C4711yescharacteristic
821C2×C4C22×D4×C4711yescharacteristic
822C2×C4C22×D4×C4711yescharacteristic
823C2×C4C2×#41×C4711yescharacteristic
824C2×C4H(5,𝔽2)×C4711yescharacteristic
825C2×C4H(5,𝔽2)×C4711yescharacteristic
826C8—22no—
827C8—41no—
828C8—41no—
829C8—41no—
830C22—22no—
831C22—22no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—41no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—41no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—816no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22C22×C22⋊C4×C4711yescharacteristic
860C22D42×C4711yescharacteristic
861C22C47×#54611yescharacteristic
862C22C47×#57511yescharacteristic
863C22C47×#57511yescharacteristic
864C22C47×#57611yescharacteristic
865C22C47×#57711yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4C2×C4×D4×C4711yescharacteristic
877C4C47×#51811yescharacteristic
878C4D42×C4711yescharacteristic
879C4C47×#54611yescharacteristic
880C2—42no—
881C2—42no—
882C2—44no—
883C2—82no—
884C2D4×C22⋊C4×C4711yescharacteristic
885C2C47×#289611yescharacteristic
886C2C47×#289711yescharacteristic
887C2C47×#327311yescharacteristic
888C2C47×#327511yescharacteristic
889C2C47×#332211yescharacteristic
890C2C47×#332311yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#546C2
LCSG ▷ C2×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
2. C2×C47×#436C2semidirect
3. C2×C47×#417C2semidirect
4. C2×C47×#418C2semidirect
5. C47×#2352C2semidirect
6. C47×#1983C2semidirect
7. C47×#1958C2semidirect
8. C47×#1895C2semidirect
9. C47×#1894C2semidirect
10. C47×#1874C2semidirect
11. C47×#1873C2semidirect
12. C47×#1804C2semidirect
13. C47×#1788C2semidirect
14. C47×#1786C2semidirect
15. C4×#102×C47C2semidirect
19. C22×M16×C47C22semidirect
21. C47×#546C4semidirect
31. C22×C4⋊C4×C47C22semidirect
34. C2×C4⋊C8×C47C22semidirect
37. C2×#103×C47C22semidirect
38. C2×#103×C47C22semidirect
39. C2×#103×C47C22semidirect
40. C2×#103×C47C22semidirect
50. C2×C22⋊C8×C47C22semidirect
51. C2×C4×C8×C47C22semidirect
55. C47×#382C22semidirect
57. C47×#380C22semidirect
58. C4×C4⋊C4×C47C22semidirect
60. C47×#340C22semidirect
61. C47×#340C22semidirect
62. C47×#340C22semidirect
63. C47×#340C22semidirect
80. C22×D4×C47C2×C4semidirect
100. #124×C47C2×C4semidirect
103. C22⋊Q8×C47C2×C4semidirect
110. C4×D4×C47C2×C4semidirect
150. #102×C47D4semidirect
384. #22427C47direct (N × H)
436. C2×#436C2×C47semidirect
437. C2×#417C2×C47semidirect
438. C2×#418C2×C47semidirect
439. #2352C2×C47semidirect
440. #1983C2×C47semidirect
441. #1958C2×C47semidirect
442. #1895C2×C47semidirect
443. #1894C2×C47semidirect
444. #1874C2×C47semidirect
445. #1873C2×C47semidirect
446. #1804C2×C47semidirect
447. #1788C2×C47semidirect
448. #1786C2×C47semidirect
449. C4×#102C2×C47semidirect
464. C22×M16C22×C47semidirect
466. #546C4×C47semidirect
476. C22×C4⋊C4C22×C47semidirect
479. C2×C4⋊C8C22×C47semidirect
482. C2×#103C22×C47semidirect
483. C2×#103C22×C47semidirect
484. C2×#103C22×C47semidirect
485. C2×#103C22×C47semidirect
495. C2×C22⋊C8C22×C47semidirect
496. C2×C4×C8C22×C47semidirect
500. #382C22×C47semidirect
502. #380C22×C47semidirect
503. C4×C4⋊C4C22×C47semidirect
505. #340C22×C47semidirect
506. #340C22×C47semidirect
507. #340C22×C47semidirect
508. #340C22×C47semidirect
509. C47#22427direct (N × H)
526. C22×D4C2×C4×C47semidirect
546. #124C2×C4×C47semidirect
549. C22⋊Q8C2×C4×C47semidirect
556. C4×D4C2×C4×C47semidirect
596. #102D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5462
C2×C47×#4362
C2×C47×#4172
C2×C47×#4182
C47×#23522
C47×#19832
C47×#19582
C47×#18952
C47×#18942
C47×#18742
C47×#18732
C47×#18042
C47×#17882
C47×#17862
C4×#102×C472
#2242747