Finite Group Databasebeta

← C47×#23871 #26063569

Subgroups — C47×#23871 #26063569

Order 12032.

1782 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C47C211yesmaximal, characteristic, complemented
2C2×C47×#548C211yesmaximal, characteristic, complemented
3C2×C47×#452C211yesmaximal, characteristic, complemented
4C2×C47×#449C211yesmaximal, characteristic, complemented
5C2×C47×#449C211yesmaximal, characteristic, complemented
6C47×#2407C211yesmaximal, characteristic, complemented
7C47×#2015C211yesmaximal, characteristic, complemented
8C47×#2012C211yesmaximal, characteristic, complemented
9C47×#2001C211yesmaximal, characteristic, complemented
10C47×#2000C211yesmaximal, characteristic, complemented
11C47×#1895C211yesmaximal, characteristic, complemented
12C47×#1880C211yesmaximal, characteristic, complemented
13C47×#1878C211yesmaximal, characteristic, complemented
14C47×#1870C211yesmaximal, characteristic, complemented
15C47×#1787C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic
18C23×Q8×C47C2211yescharacteristic
19C2×#137×C47—24no—
20C2×#137×C47—24no—
21C2×#137×C47—24no—
22C22×Q16×C47C2211yescharacteristic
23C22×Q16×C47C2211yescharacteristic
24C22×SD16×C47C2211yescharacteristic
25C22×SD16×C47C2211yescharacteristic
26C22×SD16×C47C2211yescharacteristic
27C22×D8×C47C2211yescharacteristic
28C22×M16×C47C2211yescharacteristic
29C47×#548—24no—
30C47×#548—24no—
31C2×#124×C47—21no—
32C2×#124×C47C2211yescharacteristic
33C2×C22⋊Q8×C47—21no—
34C2×C22⋊Q8×C47C2211yescharacteristic
35C2×C22⋊Q8×C47C2211yescharacteristic
36C2×#121×C47—21no—
37C2×#121×C47C2211yescharacteristic
38C2×#121×C47C2211yescharacteristic
39C2×C4×Q8×C47C2211yescharacteristic
40C2×C4×D4×C47—21no—
41C2×C4×D4×C47C2211yescharacteristic
42C47×#452—24no—
43C47×#449—24no—
44C47×#449—24no—
45C2×#103×C47C2211yescharacteristic
46C2×#103×C47C2211yescharacteristic
47C2×#103×C47C2211yescharacteristic
48C2×#103×C47C2211yescharacteristic
49C2×#103×C47C2211yescharacteristic
50C2×#102×C47C2211yescharacteristic
51C2×#102×C47C2211yescharacteristic
52C2×#102×C47C2211yescharacteristic
53C2×C22⋊C8×C47C2211yescharacteristic
54C2×C22⋊C8×C47C2211yescharacteristic
55C2×C22⋊C8×C47C2211yescharacteristic
56C47×#394—21no—
57C47×#392—21no—
58C47×#391C2211yescharacteristic
59C47×#390C2211yescharacteristic
60C47×#386—21no—
61C47×#385—21no—
62C47×#380C2211yescharacteristic
63C47×#340C2211yescharacteristic
64C47×#340C2211yescharacteristic
65C47×#336C2211yescharacteristic
66C47×#336C2211yescharacteristic
67C2×#41×C47—22no—
68C2×#41×C47—22no—
69C2×#41×C47—22no—
70C2×#41×C47—22no—
71C2×#41×C47—22no—
72C2×#41×C47—22no—
73C2×#41×C47—22no—
74C2×#41×C47—22no—
75C2×#41×C47—41no—
76C2×#41×C47—41no—
77C2×#41×C47—41no—
78C2×#41×C47—41no—
79C22×Q8×C47—21no—
80C22×Q8×C47—22no—
81C22×Q8×C47—22no—
82C22×Q8×C47—22no—
83C22×Q8×C47—41no—
84C22×Q8×C47—41no—
85C22×Q8×C47D414yescomplemented
86C22×Q8×C47C2311yescharacteristic
87C22×Q8×C47C2311yescharacteristic
88C22×Q8×C47C2311yescharacteristic
89C22×D4×C47—21no—
90C22×D4×C47—21no—
91C22×D4×C47—21no—
92C22×D4×C47—21no—
93C22×D4×C47D411yescharacteristic
94C22×D4×C47C2311yescharacteristic
95C22×D4×C47C2311yescharacteristic
96C23×C4×C47—21no—
97C23×C4×C47—21no—
98C23×C4×C47—21no—
99C23×C4×C47C2311yescharacteristic
100C23×C4×C47C2311yescharacteristic
101#137×C47—232no—
102C2×Q16×C47—22no—
103C2×Q16×C47—22no—
104C2×Q16×C47—22no—
105C2×Q16×C47—22no—
106C2×Q16×C47—22no—
107C2×Q16×C47D414yescomplemented
108C2×SD16×C47—22no—
109C2×SD16×C47—22no—
110C2×SD16×C47—22no—
111C2×SD16×C47—22no—
112C2×SD16×C47—22no—
113C2×SD16×C47—22no—
114C2×SD16×C47—22no—
115C2×SD16×C47—41no—
116C2×SD16×C47D414yescomplemented
117C2×D8×C47—22no—
118C2×D8×C47—22no—
119C2×D8×C47—41no—
120C2×M16×C47—22no—
121C2×M16×C47—22no—
122C2×M16×C47—22no—
123C22×C8×C47C2311yescharacteristic
124C22×C8×C47C2311yescharacteristic
125C22×C8×C47C2311yescharacteristic
126C22×C8×C47C2311yescharacteristic
127#124×C47—28no—
128#124×C47—22no—
129#124×C47—22no—
130C22⋊Q8×C47—28no—
131C22⋊Q8×C47—22no—
132C22⋊Q8×C47—22no—
133C22⋊Q8×C47—22no—
134C22⋊Q8×C47—41no—
135#121×C47—28no—
136#121×C47—22no—
137#121×C47—22no—
138#121×C47—41no—
139#121×C47D414yescomplemented
140C4×Q8×C47—22no—
141C4×Q8×C47—22no—
142C4×D4×C47—28no—
143C4×D4×C47—22no—
144C4×D4×C47—22no—
145C2×C4⋊C4×C47—21no—
146C2×C4⋊C4×C47—21no—
147C2×C4⋊C4×C47—21no—
148C2×C4⋊C4×C47D411yescharacteristic
149C2×C4⋊C4×C47C2311yescharacteristic
150C2×C4⋊C4×C47C2311yescharacteristic
151C2×C4⋊C4×C47C2311yescharacteristic
152C2×C22⋊C4×C47—21no—
153C2×C22⋊C4×C47—21no—
154C2×C22⋊C4×C47—21no—
155C2×C22⋊C4×C47—21no—
156C2×C22⋊C4×C47—21no—
157C2×C22⋊C4×C47—21no—
158C2×C22⋊C4×C47—21no—
159C2×C22⋊C4×C47—21no—
160C2×C22⋊C4×C47—21no—
161C2×C22⋊C4×C47D411yescharacteristic
162C2×C22⋊C4×C47D411yescharacteristic
163C2×C42×C47—21no—
164C2×C42×C47C2311yescharacteristic
165#103×C47—22no—
166#103×C47—22no—
167#103×C47—22no—
168#103×C47—41no—
169#103×C47—41no—
170#102×C47—22no—
171#102×C47—22no—
172#102×C47—22no—
173C22⋊C8×C47—22no—
174C22⋊C8×C47—22no—
175C22⋊C8×C47—22no—
176#95×C47—21no—
177#95×C47—21no—
178#95×C47—21no—
179C24×C47—21no—
180C24×C47—21no—
181C24×C47C2×D411yescharacteristic
182C24×C47C2×D411yescharacteristic
183#41×C47—28no—
184#41×C47—44no—
185#41×C47—44no—
186#41×C47—44no—
187#41×C47—44no—
188#41×C47—44no—
189#41×C47—44no—
190#41×C47—44no—
191C2×Q8×C47—24no—
192C2×Q8×C47—21no—
193C2×Q8×C47—21no—
194C2×Q8×C47—21no—
195C2×Q8×C47—21no—
196C2×Q8×C47—21no—
197C2×Q8×C47—28no—
198C2×Q8×C47—21no—
199C2×Q8×C47—21no—
200C2×Q8×C47—21no—
201C2×Q8×C47—21no—
202C2×Q8×C47—21no—
203C2×Q8×C47—21no—
204C2×Q8×C47—21no—
205C2×Q8×C47—21no—
206C2×Q8×C47—42no—
207C2×Q8×C47—42no—
208C2×Q8×C47—44no—
209C2×Q8×C47—44no—
210C2×Q8×C47—44no—
211C2×Q8×C47C2×D412yes—
212C2×Q8×C47C2×D412yes—
213C2×Q8×C47C2×D412yes—
214C2×Q8×C47C2×D412yes—
215C2×Q8×C47C2×D412yes—
216C2×D4×C47—24no—
217C2×D4×C47—22no—
218C2×D4×C47—24no—
219C2×D4×C47—21no—
220C2×D4×C47—21no—
221C2×D4×C47—21no—
222C2×D4×C47—21no—
223C2×D4×C47—21no—
224C2×D4×C47—21no—
225C2×D4×C47—21no—
226C2×D4×C47—21no—
227C2×D4×C47—21no—
228C2×D4×C47—21no—
229C2×D4×C47—41no—
230C2×D4×C47—41no—
231C2×D4×C47—42no—
232C2×D4×C47—42no—
233C2×D4×C47—42no—
234C2×D4×C47—42no—
235C2×D4×C47—42no—
236C2×D4×C47—42no—
237C2×D4×C47—42no—
238C2×D4×C47—42no—
239C2×D4×C47—42no—
240C2×D4×C47—81no—
241C2×D4×C47C2×D412yes—
242C2×D4×C47C2×D412yes—
243C22×C4×C47—21no—
244C22×C4×C47—21no—
245C22×C4×C47—21no—
246C22×C4×C47—21no—
247C22×C4×C47—21no—
248C22×C4×C47—24no—
249C22×C4×C47—24no—
250C22×C4×C47—21no—
251C22×C4×C47—21no—
252C22×C4×C47—21no—
253C22×C4×C47—21no—
254C22×C4×C47—21no—
255C22×C4×C47—21no—
256C22×C4×C47—21no—
257C22×C4×C47—21no—
258C22×C4×C47—21no—
259C22×C4×C47—21no—
260C22×C4×C47—21no—
261C22×C4×C47—42no—
262C22×C4×C47—42no—
263C22×C4×C47—42no—
264C22×C4×C47—42no—
265C22×C4×C47—42no—
266C22×C4×C47—42no—
267C22×C4×C47—42no—
268C22×C4×C47C2×D411yescharacteristic
269C22×C4×C47C2×D411yescharacteristic
270C22×C4×C47C2×D411yescharacteristic
271C22×C4×C47C2×D411yescharacteristic
272C22×C4×C47C2×D412yes—
273C22×C4×C47C2×D412yes—
274C22×C4×C47C2411yescharacteristic
275Q16×C47—28no—
276Q16×C47—28no—
277SD16×C47—28no—
278SD16×C47—28no—
279SD16×C47—44no—
280D8×C47—44no—
281M16×C47—28no—
282C2×C8×C47—21no—
283C2×C8×C47—21no—
284C2×C8×C47—21no—
285C2×C8×C47—21no—
286C2×C8×C47—21no—
287C2×C8×C47—21no—
288C2×C8×C47—21no—
289C2×C8×C47—21no—
290C2×C8×C47—21no—
291C2×C8×C47—21no—
292C2×C8×C47C2×D412yes—
293C2×C8×C47C2×D412yes—
294C4⋊C4×C47—24no—
295C4⋊C4×C47—24no—
296C4⋊C4×C47—22no—
297C4⋊C4×C47—21no—
298C4⋊C4×C47—21no—
299C4⋊C4×C47—21no—
300C4⋊C4×C47—21no—
301C4⋊C4×C47—21no—
302C4⋊C4×C47—42no—
303C4⋊C4×C47C2×D412yes—
304C22⋊C4×C47—24no—
305C22⋊C4×C47—24no—
306C22⋊C4×C47—24no—
307C22⋊C4×C47—22no—
308C22⋊C4×C47—24no—
309C22⋊C4×C47—22no—
310C22⋊C4×C47—42no—
311C22⋊C4×C47—42no—
312C22⋊C4×C47—42no—
313C22⋊C4×C47—81no—
314C22⋊C4×C47—81no—
315C42×C47—24no—
316C42×C47—21no—
317C42×C47—21no—
318C23×C47—21no—
319C23×C47—21no—
320C23×C47—21no—
321C23×C47—21no—
322C23×C47—21no—
323C23×C47—21no—
324C23×C47—21no—
325C23×C47—22no—
326C23×C47—21no—
327C23×C47—22no—
328C23×C47—21no—
329C23×C47—21no—
330C23×C47—21no—
331C23×C47—21no—
332C23×C47—21no—
333C23×C47—41no—
334C23×C47—41no—
335C23×C47—41no—
336C23×C47—41no—
337C23×C47—41no—
338C23×C47—41no—
339C23×C47—41no—
340C23×C47—41no—
341C23×C47—41no—
342C23×C47—41no—
343C23×C47—41no—
344C23×C47—41no—
345C23×C47#12012yes—
346C23×C47C22×D411yescharacteristic
347Q8×C47—22no—
348Q8×C47—22no—
349Q8×C47—22no—
350Q8×C47—22no—
351Q8×C47—22no—
352Q8×C47—22no—
353Q8×C47—22no—
354Q8×C47—48no—
355Q8×C47—41no—
356Q8×C47—41no—
357Q8×C47—41no—
358Q8×C47—41no—
359Q8×C47#12014yes—
360D4×C47—22no—
361D4×C47—22no—
362D4×C47—22no—
363D4×C47—22no—
364D4×C47—48no—
365D4×C47—44no—
366D4×C47—48no—
367D4×C47—48no—
368D4×C47—41no—
369D4×C47—41no—
370D4×C47—41no—
371D4×C47—41no—
372D4×C47—84no—
373C2×C4×C47—22no—
374C2×C4×C47—21no—
375C2×C4×C47—21no—
376C2×C4×C47—22no—
377C2×C4×C47—22no—
378C2×C4×C47—22no—
379C2×C4×C47—22no—
380C2×C4×C47—22no—
381C2×C4×C47—22no—
382C2×C4×C47—21no—
383C2×C4×C47—21no—
384C2×C4×C47—22no—
385C2×C4×C47—22no—
386C2×C4×C47—21no—
387C2×C4×C47—21no—
388C2×C4×C47—22no—
389C2×C4×C47—21no—
390C2×C4×C47—21no—
391C2×C4×C47—21no—
392C2×C4×C47—21no—
393C2×C4×C47—21no—
394C2×C4×C47—48no—
395C2×C4×C47—48no—
396C2×C4×C47—48no—
397C2×C4×C47—41no—
398C2×C4×C47—41no—
399C2×C4×C47—41no—
400C2×C4×C47—41no—
401C2×C4×C47—41no—
402C2×C4×C47—41no—
403C2×C4×C47—41no—
404C2×C4×C47—41no—
405C2×C4×C47—41no—
406C2×C4×C47—41no—
407C2×C4×C47—41no—
408C2×C4×C47—41no—
409C2×C4×C47—41no—
410C2×C4×C47—41no—
411C2×C4×C47—41no—
412C2×C4×C47—41no—
413C2×C4×C47#12012yes—
414C2×C4×C47C22×D411yescharacteristic
415C2×C4×C47C22×D411yescharacteristic
416C2×C4×C47C22×D411yescharacteristic
417C2×C4×C47C22×D411yescharacteristic
418C2×C4×C47H(5,𝔽2)11yescharacteristic
419C2×C4×C47H(5,𝔽2)11yescharacteristic
420C8×C47—22no—
421C8×C47—22no—
422C8×C47—41no—
423C8×C47—41no—
424#23871C4711yesmaximal, characteristic, direct product factor, Sylow
425C22×C47—22no—
426C22×C47—22no—
427C22×C47—22no—
428C22×C47—41no—
429C22×C47—41no—
430C22×C47—41no—
431C22×C47—41no—
432C22×C47—42no—
433C22×C47—42no—
434C22×C47—41no—
435C22×C47—41no—
436C22×C47—42no—
437C22×C47—41no—
438C22×C47—42no—
439C22×C47—41no—
440C22×C47—42no—
441C22×C47—41no—
442C22×C47—41no—
443C22×C47—42no—
444C22×C47—41no—
445C22×C47—81no—
446C22×C47—81no—
447C22×C47—81no—
448C22×C47—81no—
449C22×C47—81no—
450C22×C47—81no—
451C22×C47—81no—
452C22×C47—81no—
453C22×C47C2×#12011yescharacteristic
454C22×C47D4211yescharacteristic
455C22×C47D4211yescharacteristic
456C22×C47#57511yescharacteristic
457C22×C47#57511yescharacteristic
458C22×C47#57711yescharacteristic
459C22×C47#57811yescharacteristic
460C4×C47—22no—
461C4×C47—24no—
462C4×C47—41no—
463C4×C47—42no—
464C4×C47—42no—
465C4×C47—41no—
466C4×C47—42no—
467C4×C47—41no—
468C4×C47—81no—
469C4×C47—81no—
470C4×C47C2×#12011yescharacteristic
471C4×C47#53411yescharacteristic
472C4×C47D4211yescharacteristic
473C4×C47D4211yescharacteristic
474C22×#137C2×C4711yescharacteristic, complemented
475C2×#548C2×C4711yescharacteristic, complemented
476C2×#452C2×C4711yescharacteristic, complemented
477C2×#449C2×C4711yescharacteristic, complemented
478C2×#449C2×C4711yescharacteristic, complemented
479#2407C2×C4711yescharacteristic, complemented
480#2015C2×C4711yescharacteristic, complemented
481#2012C2×C4711yescharacteristic, complemented
482#2001C2×C4711yescharacteristic, complemented
483#2000C2×C4711yescharacteristic, complemented
484#1895C2×C4711yescharacteristic, complemented
485#1880C2×C4711yescharacteristic, complemented
486#1878C2×C4711yescharacteristic, complemented
487#1870C2×C4711yescharacteristic, complemented
488#1787C2×C4711yescharacteristic, complemented
489C2×C47—42no—
490C2×C47—81no—
491C2×C47—82no—
492C2×C47—82no—
493C2×C47#240311yescharacteristic
494C2×C47#300511yescharacteristic
495C2×C47#301311yescharacteristic
496C2×C47#326911yescharacteristic
497C2×C47#327111yescharacteristic
498C2×C47#327511yescharacteristic
499C2×C47#327711yescharacteristic
500C22×#41C22×C4711yescharacteristic
501C22×#41C22×C4711yescharacteristic
502C23×Q8C22×C4711yescharacteristic
503C2×#137—24no—
504C2×#137—24no—
505C2×#137—24no—
506C22×Q16C22×C4711yescharacteristic
507C22×Q16C22×C4711yescharacteristic
508C22×SD16C22×C4711yescharacteristic
509C22×SD16C22×C4711yescharacteristic
510C22×SD16C22×C4711yescharacteristic
511C22×D8C22×C4711yescharacteristic
512C22×M16C22×C4711yescharacteristic
513#548—24no—
514#548—24no—
515C2×#124—21no—
516C2×#124C22×C4711yescharacteristic
517C2×C22⋊Q8—21no—
518C2×C22⋊Q8C22×C4711yescharacteristic
519C2×C22⋊Q8C22×C4711yescharacteristic
520C2×#121—21no—
521C2×#121C22×C4711yescharacteristic
522C2×#121C22×C4711yescharacteristic
523C2×C4×Q8C22×C4711yescharacteristic
524C2×C4×D4—21no—
525C2×C4×D4C22×C4711yescharacteristic
526#452—24no—
527#449—24no—
528#449—24no—
529C2×#103C22×C4711yescharacteristic
530C2×#103C22×C4711yescharacteristic
531C2×#103C22×C4711yescharacteristic
532C2×#103C22×C4711yescharacteristic
533C2×#103C22×C4711yescharacteristic
534C2×#102C22×C4711yescharacteristic
535C2×#102C22×C4711yescharacteristic
536C2×#102C22×C4711yescharacteristic
537C2×C22⋊C8C22×C4711yescharacteristic
538C2×C22⋊C8C22×C4711yescharacteristic
539C2×C22⋊C8C22×C4711yescharacteristic
540#394—21no—
541#392—21no—
542#391C22×C4711yescharacteristic
543#390C22×C4711yescharacteristic
544#386—21no—
545#385—21no—
546#380C22×C4711yescharacteristic
547#340C22×C4711yescharacteristic
548#340C22×C4711yescharacteristic
549#336C22×C4711yescharacteristic
550#336C22×C4711yescharacteristic
551C47#2387111yescharacteristic, direct product factor, Sylow
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—22no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—22no—
560C2×#41—41no—
561C2×#41—41no—
562C2×#41—41no—
563C2×#41—41no—
564C22×Q8—21no—
565C22×Q8—22no—
566C22×Q8—22no—
567C22×Q8—22no—
568C22×Q8—41no—
569C22×Q8—41no—
570C22×Q8D4×C4714yescomplemented
571C22×Q8C23×C4711yescharacteristic
572C22×Q8C23×C4711yescharacteristic
573C22×Q8C23×C4711yescharacteristic
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4D4×C4711yescharacteristic
579C22×D4C23×C4711yescharacteristic
580C22×D4C23×C4711yescharacteristic
581C23×C4—21no—
582C23×C4—21no—
583C23×C4—21no—
584C23×C4C23×C4711yescharacteristic
585C23×C4C23×C4711yescharacteristic
586#137—232no—
587C2×Q16—22no—
588C2×Q16—22no—
589C2×Q16—22no—
590C2×Q16—22no—
591C2×Q16—22no—
592C2×Q16D4×C4714yescomplemented
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—41no—
601C2×SD16D4×C4714yescomplemented
602C2×D8—22no—
603C2×D8—22no—
604C2×D8—41no—
605C2×M16—22no—
606C2×M16—22no—
607C2×M16—22no—
608C22×C8C23×C4711yescharacteristic
609C22×C8C23×C4711yescharacteristic
610C22×C8C23×C4711yescharacteristic
611C22×C8C23×C4711yescharacteristic
612#124—28no—
613#124—22no—
614#124—22no—
615C22⋊Q8—28no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—22no—
619C22⋊Q8—41no—
620#121—28no—
621#121—22no—
622#121—22no—
623#121—41no—
624#121D4×C4714yescomplemented
625C4×Q8—22no—
626C4×Q8—22no—
627C4×D4—28no—
628C4×D4—22no—
629C4×D4—22no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4D4×C4711yescharacteristic
634C2×C4⋊C4C23×C4711yescharacteristic
635C2×C4⋊C4C23×C4711yescharacteristic
636C2×C4⋊C4C23×C4711yescharacteristic
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4D4×C4711yescharacteristic
647C2×C22⋊C4D4×C4711yescharacteristic
648C2×C42—21no—
649C2×C42C23×C4711yescharacteristic
650#103—22no—
651#103—22no—
652#103—22no—
653#103—41no—
654#103—41no—
655#102—22no—
656#102—22no—
657#102—22no—
658C22⋊C8—22no—
659C22⋊C8—22no—
660C22⋊C8—22no—
661#95—21no—
662#95—21no—
663#95—21no—
664C24—21no—
665C24—21no—
666C24C2×D4×C4711yescharacteristic
667C24C2×D4×C4711yescharacteristic
668#41—28no—
669#41—44no—
670#41—44no—
671#41—44no—
672#41—44no—
673#41—44no—
674#41—44no—
675#41—44no—
676C2×Q8—24no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—21no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—28no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—42no—
692C2×Q8—42no—
693C2×Q8—44no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×Q8C2×D4×C4712yes—
697C2×Q8C2×D4×C4712yes—
698C2×Q8C2×D4×C4712yes—
699C2×Q8C2×D4×C4712yes—
700C2×Q8C2×D4×C4712yes—
701C2×D4—24no—
702C2×D4—22no—
703C2×D4—24no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—41no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—81no—
726C2×D4C2×D4×C4712yes—
727C2×D4C2×D4×C4712yes—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4C2×D4×C4711yescharacteristic
754C22×C4C2×D4×C4711yescharacteristic
755C22×C4C2×D4×C4711yescharacteristic
756C22×C4C2×D4×C4711yescharacteristic
757C22×C4C2×D4×C4712yes—
758C22×C4C2×D4×C4712yes—
759C22×C4C24×C4711yescharacteristic
760Q16—28no—
761Q16—28no—
762SD16—28no—
763SD16—28no—
764SD16—44no—
765D8—44no—
766M16—28no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8C2×D4×C4712yes—
778C2×C8C2×D4×C4712yes—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—42no—
788C4⋊C4C2×D4×C4712yes—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—24no—
792C22⋊C4—22no—
793C22⋊C4—24no—
794C22⋊C4—22no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C22⋊C4—81no—
799C22⋊C4—81no—
800C42—24no—
801C42—21no—
802C42—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—22no—
811C23—21no—
812C23—22no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23#120×C4712yes—
831C23C22×D4×C4711yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—22no—
838Q8—22no—
839Q8—48no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8#120×C4714yes—
845D4—22no—
846D4—22no—
847D4—22no—
848D4—22no—
849D4—48no—
850D4—44no—
851D4—48no—
852D4—48no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—41no—
857D4—84no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—48no—
880C2×C4—48no—
881C2×C4—48no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4#120×C4712yes—
899C2×C4C22×D4×C4711yescharacteristic
900C2×C4C22×D4×C4711yescharacteristic
901C2×C4C22×D4×C4711yescharacteristic
902C2×C4C22×D4×C4711yescharacteristic
903C2×C4H(5,𝔽2)×C4711yescharacteristic
904C2×C4H(5,𝔽2)×C4711yescharacteristic
905C8—22no—
906C8—22no—
907C8—41no—
908C8—41no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—42no—
917C22—42no—
918C22—41no—
919C22—41no—
920C22—42no—
921C22—41no—
922C22—42no—
923C22—41no—
924C22—42no—
925C22—41no—
926C22—41no—
927C22—42no—
928C22—41no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22C2×#120×C4711yescharacteristic
938C22D42×C4711yescharacteristic
939C22D42×C4711yescharacteristic
940C22C47×#57511yescharacteristic
941C22C47×#57511yescharacteristic
942C22C47×#57711yescharacteristic
943C22C47×#57811yescharacteristic
944C4—22no—
945C4—24no—
946C4—41no—
947C4—42no—
948C4—42no—
949C4—41no—
950C4—42no—
951C4—41no—
952C4—81no—
953C4—81no—
954C4C2×#120×C4711yescharacteristic
955C4C47×#53411yescharacteristic
956C4D42×C4711yescharacteristic
957C4D42×C4711yescharacteristic
958C2—42no—
959C2—81no—
960C2—82no—
961C2—82no—
962C2C47×#240311yescharacteristic
963C2C47×#300511yescharacteristic
964C2C47×#301311yescharacteristic
965C2C47×#326911yescharacteristic
966C2C47×#327111yescharacteristic
967C2C47×#327511yescharacteristic
968C2C47×#327711yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
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. C22×#137×C47C2semidirect
2. C2×C47×#548C2semidirect
3. C2×C47×#452C2semidirect
4. C2×C47×#449C2semidirect
5. C2×C47×#449C2semidirect
6. C47×#2407C2semidirect
7. C47×#2015C2semidirect
8. C47×#2012C2semidirect
9. C47×#2001C2semidirect
10. C47×#2000C2semidirect
11. C47×#1895C2semidirect
12. C47×#1880C2semidirect
13. C47×#1878C2semidirect
14. C47×#1870C2semidirect
15. C47×#1787C2semidirect
85. C22×Q8×C47D4semidirect
107. C2×Q16×C47D4semidirect
116. C2×SD16×C47D4semidirect
139. #121×C47D4semidirect
424. #23871C47direct (N × H)
474. C22×#137C2×C47semidirect
475. C2×#548C2×C47semidirect
476. C2×#452C2×C47semidirect
477. C2×#449C2×C47semidirect
478. C2×#449C2×C47semidirect
479. #2407C2×C47semidirect
480. #2015C2×C47semidirect
481. #2012C2×C47semidirect
482. #2001C2×C47semidirect
483. #2000C2×C47semidirect
484. #1895C2×C47semidirect
485. #1880C2×C47semidirect
486. #1878C2×C47semidirect
487. #1870C2×C47semidirect
488. #1787C2×C47semidirect
551. C47#23871direct (N × H)
570. C22×Q8D4×C47semidirect
592. C2×Q16D4×C47semidirect
601. C2×SD16D4×C47semidirect
624. #121D4×C47semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C472
C2×C47×#5482
C2×C47×#4522
C2×C47×#4492
C47×#24072
C47×#20152
C47×#20122
C47×#20012
C47×#20002
C47×#18952
C47×#18802
C47×#18782
C47×#18702
C47×#17872
#2387147