Finite Group Databasebeta

← C47×#22424 #26062122

Subgroups — C47×#22424 #26062122

Order 12032.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#546C211yesmaximal, characteristic
2C2×C47×#435C211yesmaximal, characteristic, complemented
3C2×C47×#418C211yesmaximal, characteristic, complemented
4C2×C47×#416C211yesmaximal, characteristic, complemented
5C47×#2354C211yesmaximal, characteristic, complemented
6C47×#1983C211yesmaximal, characteristic, complemented
7C47×#1959C211yesmaximal, characteristic, complemented
8C47×#1894C211yesmaximal, characteristic, complemented
9C47×#1893C211yesmaximal, characteristic, complemented
10C47×#1875C211yesmaximal, characteristic, complemented
11C47×#1873C211yesmaximal, characteristic, complemented
12C47×#1802C211yesmaximal, characteristic, complemented
13C47×#1788C211yesmaximal, characteristic, complemented
14C47×#1786C211yesmaximal, characteristic, complemented
15C47×#1762C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C23×D4×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C23×C8×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
31C2×#117×C47C2211yescharacteristic, complemented
32C22×C22⋊C4×C47—21no—
33C47×#435—24no—
34C2×C4⋊C8×C47C2211yescharacteristic, complemented
35C47×#418—24no—
36C47×#416—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×#97×C47C2211yescharacteristic, complemented
52C47×#390—21no—
53C47×#388—21no—
54C47×#388—21no—
55C47×#384C2211yescharacteristic, complemented
56C47×#380C2211yescharacteristic
57C47×#380C2211yescharacteristic, complemented
58C4×C4⋊C4×C47—21no—
59C4×C4⋊C4×C47C2211yescharacteristic, complemented
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×C414yes—
81C22×D4×C47D411yescharacteristic
82C22×D4×C47C2311yescharacteristic
83C22×D4×C47C2311yescharacteristic
84C23×C4×C47—21no—
85C23×C4×C47—21no—
86C23×C4×C47C2311yescharacteristic
87C23×C4×C47C2311yescharacteristic
88C2×M16×C47—22no—
89C2×M16×C47—22no—
90C2×M16×C47—41no—
91C22×C8×C47—22no—
92C22×C8×C47—22no—
93C22×C8×C47—41no—
94C22×C8×C47C2311yescharacteristic
95C22×C8×C47C2311yescharacteristic
96C22×C8×C47C2311yescharacteristic
97C22×C8×C47C2311yescharacteristic
98#124×C47—22no—
99#124×C47C2×C414yes—
100#123×C47—28no—
101C22⋊Q8×C47—22no—
102C22⋊Q8×C47C2×C414yes—
103#121×C47—22no—
104#121×C47—28no—
105#121×C47C2×C414yes—
106#120×C47—28no—
107C4×D4×C47—22no—
108C4×D4×C47C2×C414yes—
109C4×D4×C47C2×C414yes—
110C4×D4×C47D414yes—
111#117×C47—22no—
112#117×C47—22no—
113#117×C47—41no—
114#117×C47—41no—
115C2×C4⋊C4×C47—21no—
116C2×C4⋊C4×C47—21no—
117C2×C4⋊C4×C47—21no—
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×C47—21no—
134C2×C22⋊C4×C47D411yescharacteristic
135C2×C22⋊C4×C47D411yescharacteristic
136C2×C42×C47—21no—
137C2×C42×C47—21no—
138C2×C42×C47—21no—
139C2×C42×C47C2311yescharacteristic
140C4⋊C8×C47—22no—
141#103×C47—22no—
142#103×C47—22no—
143#103×C47—41no—
144#103×C47—41no—
145#102×C47—22no—
146#102×C47—22no—
147#102×C47—22no—
148#102×C47—22no—
149#102×C47—22no—
150#102×C47—41no—
151#102×C47—41no—
152#102×C47D414yescomplemented
153C22⋊C8×C47—22no—
154C22⋊C8×C47—22no—
155#97×C47—22no—
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—81no—
227C22×C4×C47—81no—
228C22×C4×C47C22×C412yes—
229C22×C4×C47C22×C412yes—
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2×D411yescharacteristic
232C22×C4×C47C2×D411yescharacteristic
233C22×C4×C47C2×D411yescharacteristic
234C22×C4×C47C2×D412yes—
235C22×C4×C47C2×D412yes—
236C22×C4×C47C2411yescharacteristic
237M16×C47—44no—
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—
250C2×C8×C47C2×D412yes—
251C4⋊C4×C47—24no—
252C4⋊C4×C47—21no—
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—42no—
261C4⋊C4×C47—81no—
262C4⋊C4×C47C22⋊C414yes—
263C4⋊C4×C47C22×C412yes—
264C4⋊C4×C47C2×D412yes—
265C22⋊C4×C47—24no—
266C22⋊C4×C47—24no—
267C22⋊C4×C47—24no—
268C22⋊C4×C47—24no—
269C22⋊C4×C47—24no—
270C22⋊C4×C47—42no—
271C22⋊C4×C47—42no—
272C22⋊C4×C47—81no—
273C22⋊C4×C47—81no—
274C22⋊C4×C47C22⋊C414yes—
275C22⋊C4×C47C22⋊C414yes—
276C42×C47—42no—
277C42×C47—42no—
278C42×C47—42no—
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×C47C2×C22⋊C412yes—
370C2×C4×C47C2×C22⋊C412yes—
371C2×C4×C47C2×C22⋊C412yes—
372C2×C4×C47C2×C22⋊C412yes—
373C2×C4×C47C23×C411yescharacteristic
374C2×C4×C47C22×D411yescharacteristic
375C2×C4×C47C22×D411yescharacteristic
376C2×C4×C47C2×#4111yescharacteristic
377C2×C4×C47H(5,𝔽2)11yescharacteristic
378C2×C4×C47H(5,𝔽2)11yescharacteristic
379C8×C47—22no—
380C8×C47—41no—
381C8×C47—41no—
382C8×C47—41no—
383#22424C4711yesmaximal, characteristic, direct product factor, Sylow
384C22×C47—22no—
385C22×C47—22no—
386C22×C47—24no—
387C22×C47—22no—
388C22×C47—22no—
389C22×C47—22no—
390C22×C47—22no—
391C22×C47—42no—
392C22×C47—42no—
393C22×C47—41no—
394C22×C47—41no—
395C22×C47—42no—
396C22×C47—41no—
397C22×C47—41no—
398C22×C47—42no—
399C22×C47—41no—
400C22×C47—41no—
401C22×C47—42no—
402C22×C47—41no—
403C22×C47—41no—
404C22×C47—42no—
405C22×C47—42no—
406C22×C47—42no—
407C22×C47—42no—
408C22×C47—816no—
409C22×C47—81no—
410C22×C47—81no—
411C22×C47—81no—
412C22×C47—81no—
413C22×C47C22×C22⋊C411yescharacteristic
414C22×C47D4211yescharacteristic
415C22×C47#54611yescharacteristic
416C22×C47#57511yescharacteristic
417C22×C47#57511yescharacteristic
418C22×C47#57611yescharacteristic
419C22×C47#57711yescharacteristic
420C4×C47—22no—
421C4×C47—22no—
422C4×C47—22no—
423C4×C47—22no—
424C4×C47—42no—
425C4×C47—42no—
426C4×C47—42no—
427C4×C47—81no—
428C4×C47—81no—
429C4×C47—81no—
430C4×C47C2×C4×D411yescharacteristic
431C4×C47#51811yescharacteristic
432C4×C47D4211yescharacteristic
433C4×C47#54611yescharacteristic
434C2×#546C2×C4711yescharacteristic
435C2×#435C2×C4711yescharacteristic, complemented
436C2×#418C2×C4711yescharacteristic, complemented
437C2×#416C2×C4711yescharacteristic, complemented
438#2354C2×C4711yescharacteristic, complemented
439#1983C2×C4711yescharacteristic, complemented
440#1959C2×C4711yescharacteristic, complemented
441#1894C2×C4711yescharacteristic, complemented
442#1893C2×C4711yescharacteristic, complemented
443#1875C2×C4711yescharacteristic, complemented
444#1873C2×C4711yescharacteristic, complemented
445#1802C2×C4711yescharacteristic, complemented
446#1788C2×C4711yescharacteristic, complemented
447#1786C2×C4711yescharacteristic, complemented
448#1762C2×C4711yescharacteristic, complemented
449C2×C47—42no—
450C2×C47—42no—
451C2×C47—44no—
452C2×C47—82no—
453C2×C47D4×C22⋊C411yescharacteristic
454C2×C47#289611yescharacteristic
455C2×C47#289711yescharacteristic
456C2×C47#326711yescharacteristic
457C2×C47#326811yescharacteristic
458C2×C47#331111yescharacteristic
459C2×C47#331911yescharacteristic
460C22×#41C22×C4711yescharacteristic
461C23×D4C22×C4711yescharacteristic
462C22×M16C22×C4711yescharacteristic
463C23×C8C22×C4711yescharacteristic, complemented
464#546—24no—
465#546C4×C4718yescomplemented
466C2×#124C22×C4711yescharacteristic
467C2×#123—21no—
468C2×C22⋊Q8C22×C4711yescharacteristic
469C2×#121—21no—
470C2×#121C22×C4711yescharacteristic
471C2×#120—21no—
472C2×C4×D4C22×C4711yescharacteristic
473C2×C4×D4C22×C4711yescharacteristic
474C2×#117C22×C4711yescharacteristic
475C2×#117C22×C4711yescharacteristic, complemented
476C22×C22⋊C4—21no—
477#435—24no—
478C2×C4⋊C8C22×C4711yescharacteristic, complemented
479#418—24no—
480#416—24no—
481C2×#103C22×C4711yescharacteristic, complemented
482C2×#103C22×C4711yescharacteristic, complemented
483C2×#103C22×C4711yescharacteristic, complemented
484C2×#103C22×C4711yescharacteristic, complemented
485C2×#102C22×C4711yescharacteristic
486C2×#102C22×C4711yescharacteristic
487C2×#102C22×C4711yescharacteristic
488C2×#102C22×C4711yescharacteristic
489C2×#102C22×C4711yescharacteristic
490C2×#102C22×C4711yescharacteristic
491C2×#102C22×C4711yescharacteristic
492C2×#102C22×C4711yescharacteristic
493C2×C22⋊C8C22×C4711yescharacteristic
494C2×C22⋊C8C22×C4711yescharacteristic, complemented
495C2×#97C22×C4711yescharacteristic, complemented
496#390—21no—
497#388—21no—
498#388—21no—
499#384C22×C4711yescharacteristic, complemented
500#380C22×C4711yescharacteristic
501#380C22×C4711yescharacteristic, complemented
502C4×C4⋊C4—21no—
503C4×C4⋊C4C22×C4711yescharacteristic, complemented
504#340C22×C4711yescharacteristic, complemented
505#340C22×C4711yescharacteristic, complemented
506#340C22×C4711yescharacteristic, complemented
507#340C22×C4711yescharacteristic, complemented
508C47#2242411yescharacteristic, direct product factor, Sylow
509C25—21no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×C4×C4714yes—
516C22×Q8C23×C4711yescharacteristic
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×C4×C4714yes—
526C22×D4D4×C4711yescharacteristic
527C22×D4C23×C4711yescharacteristic
528C22×D4C23×C4711yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C23×C4711yescharacteristic
532C23×C4C23×C4711yescharacteristic
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—41no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—41no—
539C22×C8C23×C4711yescharacteristic
540C22×C8C23×C4711yescharacteristic
541C22×C8C23×C4711yescharacteristic
542C22×C8C23×C4711yescharacteristic
543#124—22no—
544#124C2×C4×C4714yes—
545#123—28no—
546C22⋊Q8—22no—
547C22⋊Q8C2×C4×C4714yes—
548#121—22no—
549#121—28no—
550#121C2×C4×C4714yes—
551#120—28no—
552C4×D4—22no—
553C4×D4C2×C4×C4714yes—
554C4×D4C2×C4×C4714yes—
555C4×D4D4×C4714yes—
556#117—22no—
557#117—22no—
558#117—41no—
559#117—41no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4D4×C4711yescharacteristic
564C2×C4⋊C4C23×C4711yescharacteristic
565C2×C4⋊C4C23×C4711yescharacteristic
566C2×C4⋊C4C23×C4711yescharacteristic
567C2×C4⋊C4C23×C4711yescharacteristic
568C2×C4⋊C4C23×C4711yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—21no—
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×C42—21no—
584C2×C42C23×C4711yescharacteristic
585C4⋊C8—22no—
586#103—22no—
587#103—22no—
588#103—41no—
589#103—41no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—41no—
596#102—41no—
597#102D4×C4714yescomplemented
598C22⋊C8—22no—
599C22⋊C8—22no—
600#97—22no—
601#95—21no—
602#95—21no—
603#95—21no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×D4×C4711yescharacteristic
614C24C2×D4×C4711yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×C4×C4712yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊C4×C4714yes—
649C2×D4C22×C4×C4712yes—
650C2×D4C22×C4×C4712yes—
651C2×D4C2×D4×C4712yes—
652C2×D4#41×C4712yes—
653C22×C4—21no—
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—24no—
665C22×C4—24no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—81no—
672C22×C4—81no—
673C22×C4C22×C4×C4712yes—
674C22×C4C22×C4×C4712yes—
675C22×C4C2×D4×C4711yescharacteristic
676C22×C4C2×D4×C4711yescharacteristic
677C22×C4C2×D4×C4711yescharacteristic
678C22×C4C2×D4×C4711yescharacteristic
679C22×C4C2×D4×C4712yes—
680C22×C4C2×D4×C4712yes—
681C22×C4C24×C4711yescharacteristic
682M16—44no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—44no—
695C2×C8C2×D4×C4712yes—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—81no—
707C4⋊C4C22⋊C4×C4714yes—
708C4⋊C4C22×C4×C4712yes—
709C4⋊C4C2×D4×C4712yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—81no—
718C22⋊C4—81no—
719C22⋊C4C22⋊C4×C4714yes—
720C22⋊C4C22⋊C4×C4714yes—
721C42—42no—
722C42—42no—
723C42—42no—
724C42C22×C4×C4712yes—
725C42C2×D4×C4712yes—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—48no—
743C23—48no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23C2×C22⋊C4×C4712yes—
760C23C2×C22⋊C4×C4712yes—
761C23C22×D4×C4711yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—48no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4C4×D4×C4714yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
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—48no—
798C2×C4—41no—
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—84no—
814C2×C4C2×C22⋊C4×C4712yes—
815C2×C4C2×C22⋊C4×C4712yes—
816C2×C4C2×C22⋊C4×C4712yes—
817C2×C4C2×C22⋊C4×C4712yes—
818C2×C4C23×C4×C4711yescharacteristic
819C2×C4C22×D4×C4711yescharacteristic
820C2×C4C22×D4×C4711yescharacteristic
821C2×C4C2×#41×C4711yescharacteristic
822C2×C4H(5,𝔽2)×C4711yescharacteristic
823C2×C4H(5,𝔽2)×C4711yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C22—22no—
829C22—22no—
830C22—24no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—41no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C22×C22⋊C4×C4711yescharacteristic
858C22D42×C4711yescharacteristic
859C22C47×#54611yescharacteristic
860C22C47×#57511yescharacteristic
861C22C47×#57511yescharacteristic
862C22C47×#57611yescharacteristic
863C22C47×#57711yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4C2×C4×D4×C4711yescharacteristic
875C4C47×#51811yescharacteristic
876C4D42×C4711yescharacteristic
877C4C47×#54611yescharacteristic
878C2—42no—
879C2—42no—
880C2—44no—
881C2—82no—
882C2D4×C22⋊C4×C4711yescharacteristic
883C2C47×#289611yescharacteristic
884C2C47×#289711yescharacteristic
885C2C47×#326711yescharacteristic
886C2C47×#326811yescharacteristic
887C2C47×#331111yescharacteristic
888C2C47×#331911yescharacteristic
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×#435C2semidirect
3. C2×C47×#418C2semidirect
4. C2×C47×#416C2semidirect
5. C47×#2354C2semidirect
6. C47×#1983C2semidirect
7. C47×#1959C2semidirect
8. C47×#1894C2semidirect
9. C47×#1893C2semidirect
10. C47×#1875C2semidirect
11. C47×#1873C2semidirect
12. C47×#1802C2semidirect
13. C47×#1788C2semidirect
14. C47×#1786C2semidirect
15. C47×#1762C2semidirect
19. C23×C8×C47C22semidirect
21. C47×#546C4semidirect
31. C2×#117×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×#97×C47C22semidirect
55. C47×#384C22semidirect
57. C47×#380C22semidirect
59. C4×C4⋊C4×C47C22semidirect
60. C47×#340C22semidirect
61. C47×#340C22semidirect
62. C47×#340C22semidirect
63. C47×#340C22semidirect
152. #102×C47D4semidirect
383. #22424C47direct (N × H)
435. C2×#435C2×C47semidirect
436. C2×#418C2×C47semidirect
437. C2×#416C2×C47semidirect
438. #2354C2×C47semidirect
439. #1983C2×C47semidirect
440. #1959C2×C47semidirect
441. #1894C2×C47semidirect
442. #1893C2×C47semidirect
443. #1875C2×C47semidirect
444. #1873C2×C47semidirect
445. #1802C2×C47semidirect
446. #1788C2×C47semidirect
447. #1786C2×C47semidirect
448. #1762C2×C47semidirect
463. C23×C8C22×C47semidirect
465. #546C4×C47semidirect
475. C2×#117C22×C47semidirect
478. C2×C4⋊C8C22×C47semidirect
481. C2×#103C22×C47semidirect
482. C2×#103C22×C47semidirect
483. C2×#103C22×C47semidirect
484. C2×#103C22×C47semidirect
494. C2×C22⋊C8C22×C47semidirect
495. C2×#97C22×C47semidirect
499. #384C22×C47semidirect
501. #380C22×C47semidirect
503. C4×C4⋊C4C22×C47semidirect
504. #340C22×C47semidirect
505. #340C22×C47semidirect
506. #340C22×C47semidirect
507. #340C22×C47semidirect
508. C47#22424direct (N × H)
597. #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×#4352
C2×C47×#4182
C2×C47×#4162
C47×#23542
C47×#19832
C47×#19592
C47×#18942
C47×#18932
C47×#18752
C47×#18732
C47×#18022
C47×#17882
C47×#17862
C47×#17622
#2242447