Finite Group Databasebeta

← C47×#23850 #26063548

Subgroups — C47×#23850 #26063548

Order 12032.

1934 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C47C211yesmaximal, characteristic, complemented
2C2×C47×#546C211yesmaximal, characteristic, complemented
3C2×C47×#449C211yesmaximal, characteristic, complemented
4C2×C47×#450C211yesmaximal, characteristic, complemented
5C2×C47×#447C211yesmaximal, characteristic, complemented
6C47×#2407C211yesmaximal, characteristic, complemented
7C47×#2015C211yesmaximal, characteristic, complemented
8C47×#2012C211yesmaximal, characteristic, complemented
9C47×#2001C211yesmaximal, characteristic, complemented
10C47×#2000C211yesmaximal, characteristic, complemented
11C47×#1893C211yesmaximal, characteristic, complemented
12C47×#1879C211yesmaximal, characteristic, complemented
13C47×#1877C211yesmaximal, characteristic, complemented
14C47×#1869C211yesmaximal, characteristic, complemented
15C47×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic, complemented
18C23×D4×C47C2211yescharacteristic
19C2×#135×C47—24no—
20C2×#135×C47—24no—
21C2×#135×C47—24no—
22C22×Q16×C47C2211yescharacteristic, complemented
23C22×SD16×C47C2211yescharacteristic
24C22×SD16×C47C2211yescharacteristic
25C22×SD16×C47C2211yescharacteristic, complemented
26C22×D8×C47C2211yescharacteristic
27C22×D8×C47C2211yescharacteristic
28C23×C8×C47C2211yescharacteristic, complemented
29C47×#546—24no—
30C47×#546—24no—
31C2×#124×C47C2211yescharacteristic
32C2×#123×C47—21no—
33C2×C22⋊Q8×C47C2211yescharacteristic
34C2×C22⋊Q8×C47C2211yescharacteristic
35C2×#121×C47—21no—
36C2×#121×C47C2211yescharacteristic
37C2×#121×C47C2211yescharacteristic
38C2×#120×C47—21no—
39C2×C4×D4×C47C2211yescharacteristic
40C2×C4×D4×C47C2211yescharacteristic
41C22×C22⋊C4×C47—21no—
42C47×#450—24no—
43C47×#449—24no—
44C47×#447—24no—
45C2×#103×C47C2211yescharacteristic, complemented
46C2×#103×C47C2211yescharacteristic, complemented
47C2×#103×C47C2211yescharacteristic, complemented
48C2×#102×C47C2211yescharacteristic
49C2×#102×C47C2211yescharacteristic
50C2×#102×C47C2211yescharacteristic
51C2×#102×C47C2211yescharacteristic
52C2×#102×C47C2211yescharacteristic, complemented
53C2×C22⋊C8×C47C2211yescharacteristic
54C2×C22⋊C8×C47C2211yescharacteristic
55C2×C22⋊C8×C47C2211yescharacteristic, complemented
56C47×#394—21no—
57C47×#392—21no—
58C47×#391C2211yescharacteristic, complemented
59C47×#390C2211yescharacteristic, complemented
60C47×#386—21no—
61C47×#385—21no—
62C47×#380C2211yescharacteristic, complemented
63C47×#340C2211yescharacteristic, complemented
64C47×#340C2211yescharacteristic, complemented
65C47×#336C2211yescharacteristic, complemented
66C47×#336C2211yescharacteristic, complemented
67C25×C47—21no—
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—
79C2×#41×C47D414yescomplemented
80C22×Q8×C47C2311yescharacteristic
81C22×Q8×C47C2311yescharacteristic
82C22×D4×C47—21no—
83C22×D4×C47—21no—
84C22×D4×C47—22no—
85C22×D4×C47—22no—
86C22×D4×C47—22no—
87C22×D4×C47—22no—
88C22×D4×C47—21no—
89C22×D4×C47—21no—
90C22×D4×C47—21no—
91C22×D4×C47—41no—
92C22×D4×C47—41no—
93C22×D4×C47D411yescharacteristic
94C22×D4×C47C2311yescharacteristic
95C22×D4×C47C2311yescharacteristic
96C22×D4×C47C2311yescharacteristic
97C23×C4×C47—21no—
98C23×C4×C47—21no—
99C23×C4×C47—21no—
100C23×C4×C47C2311yescharacteristic
101C23×C4×C47C2311yescharacteristic
102#135×C47—232no—
103C2×Q16×C47—22no—
104C2×Q16×C47—22no—
105C2×Q16×C47—22no—
106C2×SD16×C47—22no—
107C2×SD16×C47—22no—
108C2×SD16×C47—22no—
109C2×SD16×C47—22no—
110C2×SD16×C47—22no—
111C2×SD16×C47—22no—
112C2×SD16×C47—22no—
113C2×SD16×C47—41no—
114C2×SD16×C47D414yescomplemented
115C2×D8×C47—22no—
116C2×D8×C47—22no—
117C2×D8×C47—22no—
118C2×D8×C47—22no—
119C2×D8×C47—41no—
120C2×D8×C47D414yescomplemented
121C22×C8×C47—22no—
122C22×C8×C47—22no—
123C22×C8×C47—22no—
124C22×C8×C47C2311yescharacteristic
125C22×C8×C47C2311yescharacteristic
126C22×C8×C47C2311yescharacteristic
127C22×C8×C47C2311yescharacteristic
128#124×C47—22no—
129#124×C47—22no—
130#123×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
140#120×C47—28no—
141C4×D4×C47—22no—
142C4×D4×C47—22no—
143C4×D4×C47—22no—
144C4×D4×C47—22no—
145C2×C4⋊C4×C47—21no—
146C2×C4⋊C4×C47—21no—
147C2×C4⋊C4×C47D411yescharacteristic
148C2×C4⋊C4×C47C2311yescharacteristic
149C2×C4⋊C4×C47C2311yescharacteristic
150C2×C4⋊C4×C47C2311yescharacteristic
151C2×C22⋊C4×C47—28no—
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×C47—21no—
162C2×C22⋊C4×C47D411yescharacteristic
163C2×C22⋊C4×C47D411yescharacteristic
164C2×C42×C47C2311yescharacteristic
165#103×C47—22no—
166#103×C47—41no—
167#103×C47—41no—
168#102×C47—22no—
169#102×C47—22no—
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—24no—
181C24×C47—21no—
182C24×C47—21no—
183C24×C47—42no—
184C24×C47—42no—
185C24×C47—42no—
186C24×C47—42no—
187C24×C47—81no—
188C24×C47—81no—
189C24×C47C2×D411yescharacteristic
190C24×C47C2×D411yescharacteristic
191#41×C47—28no—
192#41×C47—28no—
193#41×C47—44no—
194#41×C47—44no—
195#41×C47—44no—
196#41×C47—44no—
197#41×C47—44no—
198#41×C47—44no—
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—21no—
207C2×Q8×C47—21no—
208C2×Q8×C47—21no—
209C2×Q8×C47C2×D412yes—
210C2×Q8×C47C2×D412yes—
211C2×D4×C47—24no—
212C2×D4×C47—22no—
213C2×D4×C47—24no—
214C2×D4×C47—22no—
215C2×D4×C47—24no—
216C2×D4×C47—21no—
217C2×D4×C47—21no—
218C2×D4×C47—21no—
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—42no—
231C2×D4×C47—42no—
232C2×D4×C47—42no—
233C2×D4×C47—44no—
234C2×D4×C47—44no—
235C2×D4×C47—44no—
236C2×D4×C47—42no—
237C2×D4×C47—42no—
238C2×D4×C47—42no—
239C2×D4×C47—42no—
240C2×D4×C47—44no—
241C2×D4×C47—42no—
242C2×D4×C47—42no—
243C2×D4×C47—81no—
244C2×D4×C47—81no—
245C2×D4×C47—81no—
246C2×D4×C47C2×D412yes—
247C2×D4×C47C2×D412yes—
248C2×D4×C47C2×D412yes—
249C2×D4×C47C2×D412yes—
250C2×D4×C47C2×D412yes—
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—24no—
259C22×C4×C47—24no—
260C22×C4×C47—21no—
261C22×C4×C47—21no—
262C22×C4×C47—21no—
263C22×C4×C47—21no—
264C22×C4×C47—21no—
265C22×C4×C47—21no—
266C22×C4×C47—21no—
267C22×C4×C47—21no—
268C22×C4×C47—42no—
269C22×C4×C47—42no—
270C22×C4×C47—42no—
271C22×C4×C47—42no—
272C22×C4×C47—42no—
273C22×C4×C47—81no—
274C22×C4×C47—81no—
275C22×C4×C47C2×D411yescharacteristic
276C22×C4×C47C2×D411yescharacteristic
277C22×C4×C47C2×D411yescharacteristic
278C22×C4×C47C2×D411yescharacteristic
279C22×C4×C47C2×D412yes—
280C22×C4×C47C2×D412yes—
281C22×C4×C47C2411yescharacteristic
282Q16×C47—28no—
283SD16×C47—28no—
284SD16×C47—28no—
285SD16×C47—44no—
286D8×C47—28no—
287D8×C47—44no—
288C2×C8×C47—28no—
289C2×C8×C47—21no—
290C2×C8×C47—21no—
291C2×C8×C47—21no—
292C2×C8×C47—21no—
293C2×C8×C47—21no—
294C2×C8×C47—21no—
295C2×C8×C47—21no—
296C2×C8×C47—21no—
297C2×C8×C47—21no—
298C2×C8×C47—21no—
299C2×C8×C47C2×D412yes—
300C2×C8×C47C2×D412yes—
301C4⋊C4×C47—24no—
302C4⋊C4×C47—22no—
303C4⋊C4×C47—21no—
304C4⋊C4×C47—21no—
305C4⋊C4×C47—21no—
306C4⋊C4×C47—21no—
307C4⋊C4×C47—21no—
308C4⋊C4×C47—42no—
309C4⋊C4×C47C2×D412yes—
310C22⋊C4×C47—24no—
311C22⋊C4×C47—24no—
312C22⋊C4×C47—24no—
313C22⋊C4×C47—24no—
314C22⋊C4×C47—22no—
315C22⋊C4×C47—22no—
316C22⋊C4×C47—24no—
317C22⋊C4×C47—42no—
318C22⋊C4×C47—42no—
319C22⋊C4×C47—42no—
320C22⋊C4×C47—81no—
321C22⋊C4×C47—81no—
322C42×C47—21no—
323C42×C47—21no—
324C23×C47—21no—
325C23×C47—22no—
326C23×C47—21no—
327C23×C47—21no—
328C23×C47—21no—
329C23×C47—21no—
330C23×C47—22no—
331C23×C47—22no—
332C23×C47—21no—
333C23×C47—21no—
334C23×C47—21no—
335C23×C47—21no—
336C23×C47—21no—
337C23×C47—21no—
338C23×C47—21no—
339C23×C47—22no—
340C23×C47—22no—
341C23×C47—48no—
342C23×C47—48no—
343C23×C47—41no—
344C23×C47—41no—
345C23×C47—41no—
346C23×C47—41no—
347C23×C47—41no—
348C23×C47—41no—
349C23×C47—41no—
350C23×C47—41no—
351C23×C47—41no—
352C23×C47—41no—
353C23×C47—41no—
354C23×C47—41no—
355C23×C47—41no—
356C23×C47—41no—
357C23×C47—41no—
358C23×C47—41no—
359C23×C47—84no—
360C23×C47—84no—
361C23×C47—84no—
362C23×C47—84no—
363C23×C47—84no—
364C23×C47#12012yes—
365C23×C47#13512yescomplemented
366C23×C47C22×D411yescharacteristic
367Q8×C47—22no—
368Q8×C47—22no—
369Q8×C47—22no—
370Q8×C47—22no—
371Q8×C47—41no—
372Q8×C47—41no—
373Q8×C47—41no—
374Q8×C47—41no—
375D4×C47—22no—
376D4×C47—22no—
377D4×C47—22no—
378D4×C47—22no—
379D4×C47—22no—
380D4×C47—22no—
381D4×C47—22no—
382D4×C47—44no—
383D4×C47—48no—
384D4×C47—48no—
385D4×C47—48no—
386D4×C47—41no—
387D4×C47—41no—
388D4×C47—41no—
389D4×C47—41no—
390D4×C47—84no—
391D4×C47—84no—
392D4×C47#12014yes—
393C2×C4×C47—21no—
394C2×C4×C47—21no—
395C2×C4×C47—22no—
396C2×C4×C47—22no—
397C2×C4×C47—22no—
398C2×C4×C47—22no—
399C2×C4×C47—21no—
400C2×C4×C47—21no—
401C2×C4×C47—22no—
402C2×C4×C47—22no—
403C2×C4×C47—21no—
404C2×C4×C47—21no—
405C2×C4×C47—22no—
406C2×C4×C47—21no—
407C2×C4×C47—21no—
408C2×C4×C47—21no—
409C2×C4×C47—21no—
410C2×C4×C47—21no—
411C2×C4×C47—48no—
412C2×C4×C47—48no—
413C2×C4×C47—41no—
414C2×C4×C47—41no—
415C2×C4×C47—41no—
416C2×C4×C47—41no—
417C2×C4×C47—41no—
418C2×C4×C47—41no—
419C2×C4×C47—41no—
420C2×C4×C47—41no—
421C2×C4×C47—41no—
422C2×C4×C47—41no—
423C2×C4×C47—41no—
424C2×C4×C47—41no—
425C2×C4×C47—41no—
426C2×C4×C47—41no—
427C2×C4×C47—41no—
428C2×C4×C47—41no—
429C2×C4×C47—84no—
430C2×C4×C47#12012yes—
431C2×C4×C47C22×D411yescharacteristic
432C2×C4×C47C22×D411yescharacteristic
433C2×C4×C47C22×D411yescharacteristic
434C2×C4×C47C22×D411yescharacteristic
435C2×C4×C47H(5,𝔽2)11yescharacteristic
436C2×C4×C47H(5,𝔽2)11yescharacteristic
437C8×C47—22no—
438C8×C47—22no—
439C8×C47—41no—
440C8×C47—41no—
441#23850C4711yesmaximal, characteristic, direct product factor, Sylow
442C22×C47—22no—
443C22×C47—24no—
444C22×C47—22no—
445C22×C47—22no—
446C22×C47—22no—
447C22×C47—22no—
448C22×C47—22no—
449C22×C47—41no—
450C22×C47—42no—
451C22×C47—41no—
452C22×C47—41no—
453C22×C47—42no—
454C22×C47—42no—
455C22×C47—41no—
456C22×C47—41no—
457C22×C47—41no—
458C22×C47—42no—
459C22×C47—41no—
460C22×C47—42no—
461C22×C47—41no—
462C22×C47—42no—
463C22×C47—42no—
464C22×C47—42no—
465C22×C47—42no—
466C22×C47—42no—
467C22×C47—42no—
468C22×C47—42no—
469C22×C47—816no—
470C22×C47—81no—
471C22×C47—81no—
472C22×C47—81no—
473C22×C47—81no—
474C22×C47—81no—
475C22×C47—81no—
476C22×C47—81no—
477C22×C47—81no—
478C22×C47C2×#12011yescharacteristic
479C22×C47D4211yescharacteristic
480C22×C47D4211yescharacteristic
481C22×C47C2×#13511yescharacteristic
482C22×C47#57511yescharacteristic
483C22×C47#57611yescharacteristic
484C22×C47#57711yescharacteristic
485C4×C47—22no—
486C4×C47—41no—
487C4×C47—42no—
488C4×C47—42no—
489C4×C47—41no—
490C4×C47—41no—
491C4×C47—42no—
492C4×C47—81no—
493C4×C47—81no—
494C4×C47C2×#12011yescharacteristic
495C4×C47#53411yescharacteristic
496C4×C47D4211yescharacteristic
497C4×C47D4211yescharacteristic
498C22×#135C2×C4711yescharacteristic, complemented
499C2×#546C2×C4711yescharacteristic, complemented
500C2×#449C2×C4711yescharacteristic, complemented
501C2×#450C2×C4711yescharacteristic, complemented
502C2×#447C2×C4711yescharacteristic, complemented
503#2407C2×C4711yescharacteristic, complemented
504#2015C2×C4711yescharacteristic, complemented
505#2012C2×C4711yescharacteristic, complemented
506#2001C2×C4711yescharacteristic, complemented
507#2000C2×C4711yescharacteristic, complemented
508#1893C2×C4711yescharacteristic, complemented
509#1879C2×C4711yescharacteristic, complemented
510#1877C2×C4711yescharacteristic, complemented
511#1869C2×C4711yescharacteristic, complemented
512#1788C2×C4711yescharacteristic, complemented
513C2×C47—42no—
514C2×C47—42no—
515C2×C47—44no—
516C2×C47—82no—
517C2×C47—82no—
518C2×C47#240311yescharacteristic
519C2×C47#300211yescharacteristic
520C2×C47#301211yescharacteristic
521C2×C47#326711yescharacteristic
522C2×C47#326811yescharacteristic
523C2×C47#328011yescharacteristic
524C2×C47#328211yescharacteristic
525C22×#41C22×C4711yescharacteristic
526C22×#41C22×C4711yescharacteristic, complemented
527C23×D4C22×C4711yescharacteristic
528C2×#135—24no—
529C2×#135—24no—
530C2×#135—24no—
531C22×Q16C22×C4711yescharacteristic, complemented
532C22×SD16C22×C4711yescharacteristic
533C22×SD16C22×C4711yescharacteristic
534C22×SD16C22×C4711yescharacteristic, complemented
535C22×D8C22×C4711yescharacteristic
536C22×D8C22×C4711yescharacteristic
537C23×C8C22×C4711yescharacteristic, complemented
538#546—24no—
539#546—24no—
540C2×#124C22×C4711yescharacteristic
541C2×#123—21no—
542C2×C22⋊Q8C22×C4711yescharacteristic
543C2×C22⋊Q8C22×C4711yescharacteristic
544C2×#121—21no—
545C2×#121C22×C4711yescharacteristic
546C2×#121C22×C4711yescharacteristic
547C2×#120—21no—
548C2×C4×D4C22×C4711yescharacteristic
549C2×C4×D4C22×C4711yescharacteristic
550C22×C22⋊C4—21no—
551#450—24no—
552#449—24no—
553#447—24no—
554C2×#103C22×C4711yescharacteristic, complemented
555C2×#103C22×C4711yescharacteristic, complemented
556C2×#103C22×C4711yescharacteristic, complemented
557C2×#102C22×C4711yescharacteristic
558C2×#102C22×C4711yescharacteristic
559C2×#102C22×C4711yescharacteristic
560C2×#102C22×C4711yescharacteristic
561C2×#102C22×C4711yescharacteristic, complemented
562C2×C22⋊C8C22×C4711yescharacteristic
563C2×C22⋊C8C22×C4711yescharacteristic
564C2×C22⋊C8C22×C4711yescharacteristic, complemented
565#394—21no—
566#392—21no—
567#391C22×C4711yescharacteristic, complemented
568#390C22×C4711yescharacteristic, complemented
569#386—21no—
570#385—21no—
571#380C22×C4711yescharacteristic, complemented
572#340C22×C4711yescharacteristic, complemented
573#340C22×C4711yescharacteristic, complemented
574#336C22×C4711yescharacteristic, complemented
575#336C22×C4711yescharacteristic, complemented
576C47#2385011yescharacteristic, direct product factor, Sylow
577C25—21no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41D4×C4714yescomplemented
590C22×Q8C23×C4711yescharacteristic
591C22×Q8C23×C4711yescharacteristic
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—22no—
597C22×D4—22no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4—21no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4D4×C4711yescharacteristic
604C22×D4C23×C4711yescharacteristic
605C22×D4C23×C4711yescharacteristic
606C22×D4C23×C4711yescharacteristic
607C23×C4—21no—
608C23×C4—21no—
609C23×C4—21no—
610C23×C4C23×C4711yescharacteristic
611C23×C4C23×C4711yescharacteristic
612#135—232no—
613C2×Q16—22no—
614C2×Q16—22no—
615C2×Q16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—22no—
621C2×SD16—22no—
622C2×SD16—22no—
623C2×SD16—41no—
624C2×SD16D4×C4714yescomplemented
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—22no—
628C2×D8—22no—
629C2×D8—41no—
630C2×D8D4×C4714yescomplemented
631C22×C8—22no—
632C22×C8—22no—
633C22×C8—22no—
634C22×C8C23×C4711yescharacteristic
635C22×C8C23×C4711yescharacteristic
636C22×C8C23×C4711yescharacteristic
637C22×C8C23×C4711yescharacteristic
638#124—22no—
639#124—22no—
640#123—28no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—22no—
644C22⋊Q8—41no—
645#121—28no—
646#121—22no—
647#121—22no—
648#121—41no—
649#121D4×C4714yescomplemented
650#120—28no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4D4×C4711yescharacteristic
658C2×C4⋊C4C23×C4711yescharacteristic
659C2×C4⋊C4C23×C4711yescharacteristic
660C2×C4⋊C4C23×C4711yescharacteristic
661C2×C22⋊C4—28no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4D4×C4711yescharacteristic
673C2×C22⋊C4D4×C4711yescharacteristic
674C2×C42C23×C4711yescharacteristic
675#103—22no—
676#103—41no—
677#103—41no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—22no—
683C22⋊C8—22no—
684C22⋊C8—22no—
685C22⋊C8—22no—
686#95—21no—
687#95—21no—
688#95—21no—
689C24—21no—
690C24—24no—
691C24—21no—
692C24—21no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—81no—
698C24—81no—
699C24C2×D4×C4711yescharacteristic
700C24C2×D4×C4711yescharacteristic
701#41—28no—
702#41—28no—
703#41—44no—
704#41—44no—
705#41—44no—
706#41—44no—
707#41—44no—
708#41—44no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8C2×D4×C4712yes—
720C2×Q8C2×D4×C4712yes—
721C2×D4—24no—
722C2×D4—22no—
723C2×D4—24no—
724C2×D4—22no—
725C2×D4—24no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—44no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4C2×D4×C4712yes—
757C2×D4C2×D4×C4712yes—
758C2×D4C2×D4×C4712yes—
759C2×D4C2×D4×C4712yes—
760C2×D4C2×D4×C4712yes—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4C2×D4×C4711yescharacteristic
786C22×C4C2×D4×C4711yescharacteristic
787C22×C4C2×D4×C4711yescharacteristic
788C22×C4C2×D4×C4711yescharacteristic
789C22×C4C2×D4×C4712yes—
790C22×C4C2×D4×C4712yes—
791C22×C4C24×C4711yescharacteristic
792Q16—28no—
793SD16—28no—
794SD16—28no—
795SD16—44no—
796D8—28no—
797D8—44no—
798C2×C8—28no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8C2×D4×C4712yes—
810C2×C8C2×D4×C4712yes—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C4712yes—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—22no—
826C22⋊C4—24no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C22⋊C4—81no—
832C42—21no—
833C42—21no—
834C23—21no—
835C23—22no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—22no—
850C23—22no—
851C23—48no—
852C23—48no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—84no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23#120×C4712yes—
875C23#135×C4712yescomplemented
876C23C22×D4×C4711yescharacteristic
877Q8—22no—
878Q8—22no—
879Q8—22no—
880Q8—22no—
881Q8—41no—
882Q8—41no—
883Q8—41no—
884Q8—41no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—22no—
892D4—44no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—84no—
901D4—84no—
902D4#120×C4714yes—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—48no—
922C2×C4—48no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—84no—
940C2×C4#120×C4712yes—
941C2×C4C22×D4×C4711yescharacteristic
942C2×C4C22×D4×C4711yescharacteristic
943C2×C4C22×D4×C4711yescharacteristic
944C2×C4C22×D4×C4711yescharacteristic
945C2×C4H(5,𝔽2)×C4711yescharacteristic
946C2×C4H(5,𝔽2)×C4711yescharacteristic
947C8—22no—
948C8—22no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—24no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—41no—
959C22—42no—
960C22—41no—
961C22—41no—
962C22—42no—
963C22—42no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—42no—
968C22—41no—
969C22—42no—
970C22—41no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—81no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22C2×#120×C4711yescharacteristic
988C22D42×C4711yescharacteristic
989C22D42×C4711yescharacteristic
990C22C2×#135×C4711yescharacteristic
991C22C47×#57511yescharacteristic
992C22C47×#57611yescharacteristic
993C22C47×#57711yescharacteristic
994C4—22no—
995C4—41no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C4711yescharacteristic
1004C4C47×#53411yescharacteristic
1005C4D42×C4711yescharacteristic
1006C4D42×C4711yescharacteristic
1007C2—42no—
1008C2—42no—
1009C2—44no—
1010C2—82no—
1011C2—82no—
1012C2C47×#240311yescharacteristic
1013C2C47×#300211yescharacteristic
1014C2C47×#301211yescharacteristic
1015C2C47×#326711yescharacteristic
1016C2C47×#326811yescharacteristic
1017C2C47×#328011yescharacteristic
1018C2C47×#328211yescharacteristic
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×#135×C47C2semidirect
2. C2×C47×#546C2semidirect
3. C2×C47×#449C2semidirect
4. C2×C47×#450C2semidirect
5. C2×C47×#447C2semidirect
6. C47×#2407C2semidirect
7. C47×#2015C2semidirect
8. C47×#2012C2semidirect
9. C47×#2001C2semidirect
10. C47×#2000C2semidirect
11. C47×#1893C2semidirect
12. C47×#1879C2semidirect
13. C47×#1877C2semidirect
14. C47×#1869C2semidirect
15. C47×#1788C2semidirect
17. C22×#41×C47C22semidirect
22. C22×Q16×C47C22semidirect
25. C22×SD16×C47C22semidirect
28. C23×C8×C47C22semidirect
45. C2×#103×C47C22semidirect
46. C2×#103×C47C22semidirect
47. C2×#103×C47C22semidirect
52. C2×#102×C47C22semidirect
55. C2×C22⋊C8×C47C22semidirect
58. C47×#391C22semidirect
59. C47×#390C22semidirect
62. C47×#380C22semidirect
63. C47×#340C22semidirect
64. C47×#340C22semidirect
65. C47×#336C22semidirect
66. C47×#336C22semidirect
79. C2×#41×C47D4semidirect
114. C2×SD16×C47D4semidirect
120. C2×D8×C47D4semidirect
139. #121×C47D4semidirect
365. C23×C47#135semidirect
441. #23850C47direct (N × H)
498. C22×#135C2×C47semidirect
499. C2×#546C2×C47semidirect
500. C2×#449C2×C47semidirect
501. C2×#450C2×C47semidirect
502. C2×#447C2×C47semidirect
503. #2407C2×C47semidirect
504. #2015C2×C47semidirect
505. #2012C2×C47semidirect
506. #2001C2×C47semidirect
507. #2000C2×C47semidirect
508. #1893C2×C47semidirect
509. #1879C2×C47semidirect
510. #1877C2×C47semidirect
511. #1869C2×C47semidirect
512. #1788C2×C47semidirect
526. C22×#41C22×C47semidirect
531. C22×Q16C22×C47semidirect
534. C22×SD16C22×C47semidirect
537. C23×C8C22×C47semidirect
554. C2×#103C22×C47semidirect
555. C2×#103C22×C47semidirect
556. C2×#103C22×C47semidirect
561. C2×#102C22×C47semidirect
564. C2×C22⋊C8C22×C47semidirect
567. #391C22×C47semidirect
568. #390C22×C47semidirect
571. #380C22×C47semidirect
572. #340C22×C47semidirect
573. #340C22×C47semidirect
574. #336C22×C47semidirect
575. #336C22×C47semidirect
576. C47#23850direct (N × H)
589. C2×#41D4×C47semidirect
624. C2×SD16D4×C47semidirect
630. C2×D8D4×C47semidirect
649. #121D4×C47semidirect
875. C23#135×C47semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C472
C2×C47×#5462
C2×C47×#4492
C2×C47×#4502
C2×C47×#4472
C47×#24072
C47×#20152
C47×#20122
C47×#20012
C47×#20002
C47×#18932
C47×#18792
C47×#18772
C47×#18692
C47×#17882
#2385047