Finite Group Databasebeta

← C47×#23881 #26063579

Subgroups — C47×#23881 #26063579

Order 12032.

1714 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#575C211yesmaximal, characteristic, complemented
2C47×#3489C211yesmaximal, characteristic, complemented
3C2×C47×#456C211yesmaximal, characteristic, complemented
4C2×C47×#454C211yesmaximal, characteristic, complemented
5C47×#3005C211yesmaximal, characteristic, complemented
6C47×#2432C211yesmaximal, characteristic, complemented
7C47×#2007C211yesmaximal, characteristic, complemented
8C47×#2006C211yesmaximal, characteristic, complemented
9C47×#2005C211yesmaximal, characteristic, complemented
10C47×#2003C211yesmaximal, characteristic, complemented
11C47×#1901C211yesmaximal, characteristic, complemented
12C47×#1883C211yesmaximal, characteristic, complemented
13C47×#1882C211yesmaximal, characteristic, complemented
14C47×#1871C211yesmaximal, characteristic, complemented
15C47×#1789C211yesmaximal, characteristic, complemented
16C2×2−1+4×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic
18C22×#41×C47C2211yescharacteristic
19C47×#575—24no—
20C47×#575—24no—
21C2×#137×C47—21no—
22C2×#137×C47C2211yescharacteristic
23C2×#137×C47C2211yescharacteristic
24C2×#137×C47C2211yescharacteristic, complemented
25C2×AGL(1,ℤ/8)×C47—21no—
26C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C47C2211yescharacteristic, complemented
29C2×#135×C47—21no—
30C2×#135×C47—21no—
31C22×M16×C47C2211yescharacteristic
32D4×Q8×C47—21no—
33C47×#548—21no—
34C47×#547—21no—
35C47×#547—22no—
36C47×#546—21no—
37C47×#546—22no—
38C47×#537—21no—
39C47×#537C2211yescharacteristic
40C47×#536—21no—
41C47×#536C2211yescharacteristic
42C2×C4⋊Q8×C47C2211yescharacteristic, complemented
43C2×#124×C47C2211yescharacteristic, complemented
44C47×#525—21no—
45C47×#525C2211yescharacteristic
46C2×C22⋊Q8×C47—21no—
47C2×C22⋊Q8×C47C2211yescharacteristic
48C47×#520C2211yescharacteristic
49C47×#456—24no—
50C47×#454—24no—
51C47×#452—21no—
52C47×#452—21no—
53C47×#449—21no—
54C47×#449—21no—
55C2×#104×C47C2211yescharacteristic
56C2×#104×C47C2211yescharacteristic
57C2×#104×C47C2211yescharacteristic
58C2×#104×C47C2211yescharacteristic
59C2×#104×C47C2211yescharacteristic, complemented
60C2×#104×C47C2211yescharacteristic, complemented
61C47×#419C2211yescharacteristic, complemented
62C47×#418C2211yescharacteristic, complemented
63C2×#101×C47C2211yescharacteristic, complemented
64C2×#101×C47C2211yescharacteristic, complemented
65C47×#407C2211yescharacteristic
66C47×#394—22no—
67C47×#391C2211yescharacteristic, complemented
68C47×#390C2211yescharacteristic, complemented
69C47×#385—22no—
70C4×C22⋊C4×C47C2211yescharacteristic
71C47×#343C2211yescharacteristic, complemented
72C47×#343C2211yescharacteristic, complemented
73C47×#339C2211yescharacteristic, complemented
74C47×#339C2211yescharacteristic, complemented
752−1+4×C47—22no—
762−1+4×C47—22no—
772−1+4×C47—41no—
782−1+4×C47—41no—
79C2×#41×C47—21no—
80C2×#41×C47—21no—
81C2×#41×C47—21no—
82C2×#41×C47—22no—
83C2×#41×C47—21no—
84C2×#41×C47—22no—
85C2×#41×C47—22no—
86C2×#41×C47—22no—
87C2×#41×C47—22no—
88C2×#41×C47—21no—
89C2×#41×C47—21no—
90C2×#41×C47—21no—
91C2×#41×C47—21no—
92C2×#41×C47—41no—
93C2×#41×C47—41no—
94C2×#41×C47—41no—
95C2×#41×C47—41no—
96C2×#41×C47D411yescharacteristic
97C2×#41×C47D411yescharacteristic
98C2×#41×C47C2311yescharacteristic
99C2×#41×C47C2311yescharacteristic
100C2×#41×C47C2311yescharacteristic
101C22×Q8×C47—21no—
102C22×Q8×C47—21no—
103C22×Q8×C47D411yescharacteristic
104C22×Q8×C47C2311yescharacteristic
105C22×Q8×C47C2311yescharacteristic
106C22×D4×C47—21no—
107C22×D4×C47—21no—
108C22×D4×C47D411yescharacteristic
109C22×D4×C47C2311yescharacteristic
110C23×C4×C47—21no—
111C23×C4×C47—21no—
112C23×C4×C47C2311yescharacteristic
113#137×C47—28no—
114#137×C47—22no—
115#137×C47—22no—
116#137×C47—22no—
117#137×C47—22no—
118#137×C47—41no—
119#137×C47D414yescomplemented
120AGL(1,ℤ/8)×C47—28no—
121AGL(1,ℤ/8)×C47—22no—
122AGL(1,ℤ/8)×C47—22no—
123AGL(1,ℤ/8)×C47—22no—
124AGL(1,ℤ/8)×C47—22no—
125AGL(1,ℤ/8)×C47—41no—
126AGL(1,ℤ/8)×C47D414yescomplemented
127#135×C47—28no—
128#135×C47—28no—
129C2×Q16×C47—21no—
130C2×Q16×C47—21no—
131C2×Q16×C47—21no—
132C2×SD16×C47—21no—
133C2×SD16×C47—21no—
134C2×SD16×C47—21no—
135C2×SD16×C47—21no—
136C2×SD16×C47—21no—
137C2×SD16×C47—21no—
138C2×D8×C47—21no—
139C2×D8×C47—21no—
140C2×D8×C47—21no—
141C2×M16×C47—21no—
142C2×M16×C47—22no—
143C2×M16×C47—22no—
144C2×M16×C47C2311yescharacteristic
145C2×M16×C47C2311yescharacteristic
146C2×M16×C47C2311yescharacteristic
147C2×M16×C47C2311yescharacteristic
148C22×C8×C47—21no—
149C4⋊Q8×C47—22no—
150C4⋊Q8×C47—21no—
151C4⋊Q8×C47—22no—
152C4⋊Q8×C47—41no—
153#124×C47—22no—
154#124×C47—21no—
155#124×C47—22no—
156#124×C47—41no—
157#123×C47—22no—
158#123×C47—22no—
159#123×C47—22no—
160#123×C47—21no—
161#123×C47—22no—
162C22⋊Q8×C47—22no—
163C22⋊Q8×C47—22no—
164C22⋊Q8×C47—22no—
165C22⋊Q8×C47—21no—
166C22⋊Q8×C47—21no—
167C22⋊Q8×C47—21no—
168C22⋊Q8×C47—21no—
169C22⋊Q8×C47—21no—
170C22⋊Q8×C47—21no—
171C22⋊Q8×C47—21no—
172C22⋊Q8×C47—21no—
173C22⋊Q8×C47D411yescharacteristic
174C22⋊Q8×C47D411yescharacteristic
175#121×C47—22no—
176#121×C47—22no—
177#121×C47—22no—
178#121×C47—21no—
179#121×C47—21no—
180#121×C47—22no—
181#121×C47D411yescharacteristic
182#121×C47D411yescharacteristic
183#120×C47—22no—
184#120×C47—21no—
185C4×Q8×C47—21no—
186C4×D4×C47—22no—
187C4×D4×C47—22no—
188C4×D4×C47—21no—
189C4×D4×C47—22no—
190C4×D4×C47—21no—
191C4×D4×C47—21no—
192#117×C47—21no—
193#117×C47C2311yescharacteristic
194C2×C4⋊C4×C47—22no—
195C2×C4⋊C4×C47—21no—
196C2×C4⋊C4×C47—22no—
197C2×C4⋊C4×C47D412yes—
198C2×C4⋊C4×C47C2311yescharacteristic
199C2×C22⋊C4×C47—22no—
200C2×C22⋊C4×C47—21no—
201C2×C22⋊C4×C47—22no—
202C2×C22⋊C4×C47—22no—
203C2×C22⋊C4×C47D412yes—
204C2×C42×C47C2311yescharacteristic
205C2×C42×C47C2311yescharacteristic
206#104×C47—22no—
207#104×C47—22no—
208#104×C47—22no—
209#104×C47—22no—
210#104×C47—41no—
211#104×C47—41no—
212#103×C47—21no—
213#103×C47—21no—
214#102×C47—21no—
215#102×C47—21no—
216#101×C47—22no—
217#101×C47—22no—
218C22⋊C8×C47—21no—
219C22⋊C8×C47—21no—
220#95×C47—21no—
221#95×C47—22no—
222C24×C47—21no—
223C24×C47—21no—
224C24×C47C2×D411yescharacteristic
225#41×C47—21no—
226#41×C47—21no—
227#41×C47—24no—
228#41×C47—24no—
229#41×C47—22no—
230#41×C47—22no—
231#41×C47—21no—
232#41×C47—21no—
233#41×C47—21no—
234#41×C47—21no—
235#41×C47—21no—
236#41×C47—21no—
237#41×C47—21no—
238#41×C47—21no—
239#41×C47—42no—
240#41×C47—42no—
241#41×C47—41no—
242#41×C47—41no—
243#41×C47—42no—
244#41×C47—42no—
245#41×C47—42no—
246#41×C47—42no—
247#41×C47—42no—
248#41×C47—42no—
249#41×C47—44no—
250#41×C47—44no—
251#41×C47—42no—
252#41×C47—42no—
253#41×C47—42no—
254#41×C47—42no—
255#41×C47—42no—
256#41×C47—42no—
257#41×C47C2×D412yes—
258#41×C47C2×D412yes—
259C2×Q8×C47—22no—
260C2×Q8×C47—21no—
261C2×Q8×C47—21no—
262C2×Q8×C47—21no—
263C2×Q8×C47—21no—
264C2×Q8×C47—21no—
265C2×Q8×C47—21no—
266C2×Q8×C47—21no—
267C2×Q8×C47—21no—
268C2×Q8×C47—22no—
269C2×Q8×C47—21no—
270C2×Q8×C47—21no—
271C2×Q8×C47—21no—
272C2×Q8×C47—21no—
273C2×Q8×C47—41no—
274C2×Q8×C47—42no—
275C2×Q8×C47—42no—
276C2×Q8×C47—42no—
277C2×Q8×C47—42no—
278C2×Q8×C47C2×D411yescharacteristic
279C2×Q8×C47C2×D411yescharacteristic
280C2×Q8×C47C2×D412yes—
281C2×Q8×C47C2×D411yescharacteristic
282C2×D4×C47—21no—
283C2×D4×C47—22no—
284C2×D4×C47—22no—
285C2×D4×C47—21no—
286C2×D4×C47—21no—
287C2×D4×C47—21no—
288C2×D4×C47—21no—
289C2×D4×C47—21no—
290C2×D4×C47—22no—
291C2×D4×C47—21no—
292C2×D4×C47—21no—
293C2×D4×C47—21no—
294C2×D4×C47—21no—
295C2×D4×C47—21no—
296C2×D4×C47—21no—
297C2×D4×C47—21no—
298C2×D4×C47—41no—
299C2×D4×C47—42no—
300C2×D4×C47—42no—
301C2×D4×C47—42no—
302C2×D4×C47—42no—
303C2×D4×C47—41no—
304C2×D4×C47—41no—
305C2×D4×C47C2×D411yescharacteristic
306C2×D4×C47C2×D411yescharacteristic
307C2×D4×C47C2×D412yes—
308C2×D4×C47C2×D411yescharacteristic
309C22×C4×C47—21no—
310C22×C4×C47—21no—
311C22×C4×C47—21no—
312C22×C4×C47—21no—
313C22×C4×C47—21no—
314C22×C4×C47—22no—
315C22×C4×C47—22no—
316C22×C4×C47—21no—
317C22×C4×C47—21no—
318C22×C4×C47—21no—
319C22×C4×C47—22no—
320C22×C4×C47—21no—
321C22×C4×C47—21no—
322C22×C4×C47—21no—
323C22×C4×C47—21no—
324C22×C4×C47—21no—
325C22×C4×C47—42no—
326C22×C4×C47—42no—
327C22×C4×C47—42no—
328C22×C4×C47—42no—
329C22×C4×C47—41no—
330C22×C4×C47—41no—
331C22×C4×C47C2×D412yes—
332C22×C4×C47C2×D411yescharacteristic
333C22×C4×C47C2×D411yescharacteristic
334C22×C4×C47C2×D411yescharacteristic
335C22×C4×C47C2×D411yescharacteristic
336C22×C4×C47C2×D411yescharacteristic
337C22×C4×C47C2×D412yes—
338C22×C4×C47C2411yescharacteristic
339Q16×C47—24no—
340Q16×C47—24no—
341Q16×C47—42no—
342SD16×C47—24no—
343SD16×C47—24no—
344SD16×C47—24no—
345SD16×C47—24no—
346SD16×C47—42no—
347SD16×C47—42no—
348D8×C47—24no—
349D8×C47—24no—
350D8×C47—42no—
351M16×C47—24no—
352M16×C47—21no—
353M16×C47—21no—
354M16×C47—21no—
355M16×C47—21no—
356M16×C47—21no—
357M16×C47—21no—
358M16×C47C2×D412yes—
359M16×C47C2×D412yes—
360C2×C8×C47—24no—
361C2×C8×C47—21no—
362C2×C8×C47—21no—
363C2×C8×C47—21no—
364C2×C8×C47—21no—
365C4⋊C4×C47—22no—
366C4⋊C4×C47—22no—
367C4⋊C4×C47—22no—
368C4⋊C4×C47—22no—
369C4⋊C4×C47—21no—
370C4⋊C4×C47—22no—
371C4⋊C4×C47—22no—
372C4⋊C4×C47—21no—
373C4⋊C4×C47—21no—
374C4⋊C4×C47—21no—
375C4⋊C4×C47—44no—
376C4⋊C4×C47C2×D411yescharacteristic
377C4⋊C4×C47C2×D411yescharacteristic
378C22⋊C4×C47—22no—
379C22⋊C4×C47—22no—
380C22⋊C4×C47—22no—
381C22⋊C4×C47—22no—
382C22⋊C4×C47—22no—
383C22⋊C4×C47—21no—
384C22⋊C4×C47—22no—
385C22⋊C4×C47—22no—
386C22⋊C4×C47—21no—
387C22⋊C4×C47—21no—
388C22⋊C4×C47—21no—
389C22⋊C4×C47—21no—
390C22⋊C4×C47—44no—
391C22⋊C4×C47—44no—
392C22⋊C4×C47—42no—
393C42×C47—22no—
394C42×C47—21no—
395C42×C47—21no—
396C42×C47—21no—
397C42×C47—21no—
398C42×C47—21no—
399C23×C47—21no—
400C23×C47—21no—
401C23×C47—21no—
402C23×C47—21no—
403C23×C47—21no—
404C23×C47—22no—
405C23×C47—41no—
406C23×C47—41no—
407C23×C47—42no—
408C23×C47—42no—
409C23×C47—42no—
410C23×C47—42no—
411C23×C47—41no—
412C23×C47—41no—
413C23×C47—81no—
414C23×C47#12011yescharacteristic
415C23×C47#12011yescharacteristic
416C23×C47C22×D411yescharacteristic
417Q8×C47—21no—
418Q8×C47—21no—
419Q8×C47—22no—
420Q8×C47—21no—
421Q8×C47—21no—
422Q8×C47—22no—
423Q8×C47—21no—
424Q8×C47—42no—
425Q8×C47—44no—
426Q8×C47—41no—
427Q8×C47—41no—
428Q8×C47—41no—
429Q8×C47—41no—
430Q8×C47—41no—
431Q8×C47—41no—
432Q8×C47#12012yes—
433D4×C47—22no—
434D4×C47—22no—
435D4×C47—21no—
436D4×C47—22no—
437D4×C47—21no—
438D4×C47—21no—
439D4×C47—21no—
440D4×C47—22no—
441D4×C47—21no—
442D4×C47—42no—
443D4×C47—42no—
444D4×C47—42no—
445D4×C47—42no—
446D4×C47—44no—
447D4×C47—44no—
448D4×C47—44no—
449D4×C47—41no—
450D4×C47—41no—
451D4×C47—41no—
452D4×C47—41no—
453D4×C47—41no—
454D4×C47—41no—
455D4×C47—81no—
456D4×C47—82no—
457D4×C47#12012yes—
458C2×C4×C47—21no—
459C2×C4×C47—21no—
460C2×C4×C47—21no—
461C2×C4×C47—21no—
462C2×C4×C47—21no—
463C2×C4×C47—21no—
464C2×C4×C47—21no—
465C2×C4×C47—21no—
466C2×C4×C47—21no—
467C2×C4×C47—21no—
468C2×C4×C47—21no—
469C2×C4×C47—22no—
470C2×C4×C47—22no—
471C2×C4×C47—22no—
472C2×C4×C47—21no—
473C2×C4×C47—22no—
474C2×C4×C47—21no—
475C2×C4×C47—21no—
476C2×C4×C47—22no—
477C2×C4×C47—21no—
478C2×C4×C47—22no—
479C2×C4×C47—22no—
480C2×C4×C47—22no—
481C2×C4×C47—42no—
482C2×C4×C47—42no—
483C2×C4×C47—42no—
484C2×C4×C47—44no—
485C2×C4×C47—44no—
486C2×C4×C47—44no—
487C2×C4×C47—41no—
488C2×C4×C47—44no—
489C2×C4×C47—41no—
490C2×C4×C47—41no—
491C2×C4×C47—41no—
492C2×C4×C47—41no—
493C2×C4×C47—41no—
494C2×C4×C47—41no—
495C2×C4×C47—41no—
496C2×C4×C47—42no—
497C2×C4×C47—41no—
498C2×C4×C47—41no—
499C2×C4×C47—41no—
500C2×C4×C47—82no—
501C2×C4×C47#12011yescharacteristic
502C2×C4×C47#12011yescharacteristic
503C2×C4×C47C22×D411yescharacteristic
504C2×C4×C47C22×D411yescharacteristic
505C2×C4×C47C22×D411yescharacteristic
506C2×C4×C47C22×D411yescharacteristic
507C2×C4×C47H(5,𝔽2)11yescharacteristic
508C2×C4×C47H(5,𝔽2)11yescharacteristic
509C8×C47—22no—
510C8×C47—22no—
511C8×C47—41no—
512C8×C47—41no—
513#23881C4711yesmaximal, characteristic, direct product factor, Sylow
514C22×C47—21no—
515C22×C47—21no—
516C22×C47—21no—
517C22×C47—21no—
518C22×C47—22no—
519C22×C47—21no—
520C22×C47—21no—
521C22×C47—21no—
522C22×C47—21no—
523C22×C47—44no—
524C22×C47—41no—
525C22×C47—41no—
526C22×C47—41no—
527C22×C47—41no—
528C22×C47—42no—
529C22×C47—41no—
530C22×C47—41no—
531C22×C47—41no—
532C22×C47—41no—
533C22×C47—81no—
534C22×C47—81no—
535C22×C47—82no—
536C22×C47—84no—
537C22×C47—81no—
538C22×C47—81no—
539C22×C47C2×#12011yescharacteristic
540C22×C47D4211yescharacteristic
541C22×C47D4211yescharacteristic
542C4×C47—21no—
543C4×C47—21no—
544C4×C47—22no—
545C4×C47—42no—
546C4×C47—42no—
547C4×C47—41no—
548C4×C47—42no—
549C4×C47—41no—
550C4×C47—42no—
551C4×C47—41no—
552C4×C47—41no—
553C4×C47—81no—
554C4×C47C2×#12011yescharacteristic
555C4×C47#53411yescharacteristic
556C4×C47D4211yescharacteristic
557C4×C47D4211yescharacteristic
558C2×#575C2×C4711yescharacteristic, complemented
559#3489C2×C4711yescharacteristic, complemented
560C2×#456C2×C4711yescharacteristic, complemented
561C2×#454C2×C4711yescharacteristic, complemented
562#3005C2×C4711yescharacteristic, complemented
563#2432C2×C4711yescharacteristic, complemented
564#2007C2×C4711yescharacteristic, complemented
565#2006C2×C4711yescharacteristic, complemented
566#2005C2×C4711yescharacteristic, complemented
567#2003C2×C4711yescharacteristic, complemented
568#1901C2×C4711yescharacteristic, complemented
569#1883C2×C4711yescharacteristic, complemented
570#1882C2×C4711yescharacteristic, complemented
571#1871C2×C4711yescharacteristic, complemented
572#1789C2×C4711yescharacteristic, complemented
573C2×C47—21no—
574C2×C47—21no—
575C2×C47—41no—
576C2×C47—41no—
577C2×C47—42no—
578C2×C47—81no—
579C2×C47—82no—
580C2×C47—81no—
581C2×C47#240311yescharacteristic
582C2×C47#301811yescharacteristic
583C2×C47#302011yescharacteristic
584C2×2−1+4C22×C4711yescharacteristic
585C22×#41C22×C4711yescharacteristic
586C22×#41C22×C4711yescharacteristic
587#575—24no—
588#575—24no—
589C2×#137—21no—
590C2×#137C22×C4711yescharacteristic
591C2×#137C22×C4711yescharacteristic
592C2×#137C22×C4711yescharacteristic, complemented
593C2×AGL(1,ℤ/8)—21no—
594C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
595C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
596C2×AGL(1,ℤ/8)C22×C4711yescharacteristic, complemented
597C2×#135—21no—
598C2×#135—21no—
599C22×M16C22×C4711yescharacteristic
600D4×Q8—21no—
601#548—21no—
602#547—21no—
603#547—22no—
604#546—21no—
605#546—22no—
606#537—21no—
607#537C22×C4711yescharacteristic
608#536—21no—
609#536C22×C4711yescharacteristic
610C2×C4⋊Q8C22×C4711yescharacteristic, complemented
611C2×#124C22×C4711yescharacteristic, complemented
612#525—21no—
613#525C22×C4711yescharacteristic
614C2×C22⋊Q8—21no—
615C2×C22⋊Q8C22×C4711yescharacteristic
616#520C22×C4711yescharacteristic
617#456—24no—
618#454—24no—
619#452—21no—
620#452—21no—
621#449—21no—
622#449—21no—
623C2×#104C22×C4711yescharacteristic
624C2×#104C22×C4711yescharacteristic
625C2×#104C22×C4711yescharacteristic
626C2×#104C22×C4711yescharacteristic
627C2×#104C22×C4711yescharacteristic, complemented
628C2×#104C22×C4711yescharacteristic, complemented
629#419C22×C4711yescharacteristic, complemented
630#418C22×C4711yescharacteristic, complemented
631C2×#101C22×C4711yescharacteristic, complemented
632C2×#101C22×C4711yescharacteristic, complemented
633#407C22×C4711yescharacteristic
634#394—22no—
635#391C22×C4711yescharacteristic, complemented
636#390C22×C4711yescharacteristic, complemented
637#385—22no—
638C4×C22⋊C4C22×C4711yescharacteristic
639#343C22×C4711yescharacteristic, complemented
640#343C22×C4711yescharacteristic, complemented
641#339C22×C4711yescharacteristic, complemented
642#339C22×C4711yescharacteristic, complemented
643C47#2388111yescharacteristic, direct product factor, Sylow
6442−1+4—22no—
6452−1+4—22no—
6462−1+4—41no—
6472−1+4—41no—
648C2×#41—21no—
649C2×#41—21no—
650C2×#41—21no—
651C2×#41—22no—
652C2×#41—21no—
653C2×#41—22no—
654C2×#41—22no—
655C2×#41—22no—
656C2×#41—22no—
657C2×#41—21no—
658C2×#41—21no—
659C2×#41—21no—
660C2×#41—21no—
661C2×#41—41no—
662C2×#41—41no—
663C2×#41—41no—
664C2×#41—41no—
665C2×#41D4×C4711yescharacteristic
666C2×#41D4×C4711yescharacteristic
667C2×#41C23×C4711yescharacteristic
668C2×#41C23×C4711yescharacteristic
669C2×#41C23×C4711yescharacteristic
670C22×Q8—21no—
671C22×Q8—21no—
672C22×Q8D4×C4711yescharacteristic
673C22×Q8C23×C4711yescharacteristic
674C22×Q8C23×C4711yescharacteristic
675C22×D4—21no—
676C22×D4—21no—
677C22×D4D4×C4711yescharacteristic
678C22×D4C23×C4711yescharacteristic
679C23×C4—21no—
680C23×C4—21no—
681C23×C4C23×C4711yescharacteristic
682#137—28no—
683#137—22no—
684#137—22no—
685#137—22no—
686#137—22no—
687#137—41no—
688#137D4×C4714yescomplemented
689AGL(1,ℤ/8)—28no—
690AGL(1,ℤ/8)—22no—
691AGL(1,ℤ/8)—22no—
692AGL(1,ℤ/8)—22no—
693AGL(1,ℤ/8)—22no—
694AGL(1,ℤ/8)—41no—
695AGL(1,ℤ/8)D4×C4714yescomplemented
696#135—28no—
697#135—28no—
698C2×Q16—21no—
699C2×Q16—21no—
700C2×Q16—21no—
701C2×SD16—21no—
702C2×SD16—21no—
703C2×SD16—21no—
704C2×SD16—21no—
705C2×SD16—21no—
706C2×SD16—21no—
707C2×D8—21no—
708C2×D8—21no—
709C2×D8—21no—
710C2×M16—21no—
711C2×M16—22no—
712C2×M16—22no—
713C2×M16C23×C4711yescharacteristic
714C2×M16C23×C4711yescharacteristic
715C2×M16C23×C4711yescharacteristic
716C2×M16C23×C4711yescharacteristic
717C22×C8—21no—
718C4⋊Q8—22no—
719C4⋊Q8—21no—
720C4⋊Q8—22no—
721C4⋊Q8—41no—
722#124—22no—
723#124—21no—
724#124—22no—
725#124—41no—
726#123—22no—
727#123—22no—
728#123—22no—
729#123—21no—
730#123—22no—
731C22⋊Q8—22no—
732C22⋊Q8—22no—
733C22⋊Q8—22no—
734C22⋊Q8—21no—
735C22⋊Q8—21no—
736C22⋊Q8—21no—
737C22⋊Q8—21no—
738C22⋊Q8—21no—
739C22⋊Q8—21no—
740C22⋊Q8—21no—
741C22⋊Q8—21no—
742C22⋊Q8D4×C4711yescharacteristic
743C22⋊Q8D4×C4711yescharacteristic
744#121—22no—
745#121—22no—
746#121—22no—
747#121—21no—
748#121—21no—
749#121—22no—
750#121D4×C4711yescharacteristic
751#121D4×C4711yescharacteristic
752#120—22no—
753#120—21no—
754C4×Q8—21no—
755C4×D4—22no—
756C4×D4—22no—
757C4×D4—21no—
758C4×D4—22no—
759C4×D4—21no—
760C4×D4—21no—
761#117—21no—
762#117C23×C4711yescharacteristic
763C2×C4⋊C4—22no—
764C2×C4⋊C4—21no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4D4×C4712yes—
767C2×C4⋊C4C23×C4711yescharacteristic
768C2×C22⋊C4—22no—
769C2×C22⋊C4—21no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4D4×C4712yes—
773C2×C42C23×C4711yescharacteristic
774C2×C42C23×C4711yescharacteristic
775#104—22no—
776#104—22no—
777#104—22no—
778#104—22no—
779#104—41no—
780#104—41no—
781#103—21no—
782#103—21no—
783#102—21no—
784#102—21no—
785#101—22no—
786#101—22no—
787C22⋊C8—21no—
788C22⋊C8—21no—
789#95—21no—
790#95—22no—
791C24—21no—
792C24—21no—
793C24C2×D4×C4711yescharacteristic
794#41—21no—
795#41—21no—
796#41—24no—
797#41—24no—
798#41—22no—
799#41—22no—
800#41—21no—
801#41—21no—
802#41—21no—
803#41—21no—
804#41—21no—
805#41—21no—
806#41—21no—
807#41—21no—
808#41—42no—
809#41—42no—
810#41—41no—
811#41—41no—
812#41—42no—
813#41—42no—
814#41—42no—
815#41—42no—
816#41—42no—
817#41—42no—
818#41—44no—
819#41—44no—
820#41—42no—
821#41—42no—
822#41—42no—
823#41—42no—
824#41—42no—
825#41—42no—
826#41C2×D4×C4712yes—
827#41C2×D4×C4712yes—
828C2×Q8—22no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—22no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—41no—
843C2×Q8—42no—
844C2×Q8—42no—
845C2×Q8—42no—
846C2×Q8—42no—
847C2×Q8C2×D4×C4711yescharacteristic
848C2×Q8C2×D4×C4711yescharacteristic
849C2×Q8C2×D4×C4712yes—
850C2×Q8C2×D4×C4711yescharacteristic
851C2×D4—21no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—22no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4C2×D4×C4711yescharacteristic
875C2×D4C2×D4×C4711yescharacteristic
876C2×D4C2×D4×C4712yes—
877C2×D4C2×D4×C4711yescharacteristic
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—22no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4C2×D4×C4712yes—
901C22×C4C2×D4×C4711yescharacteristic
902C22×C4C2×D4×C4711yescharacteristic
903C22×C4C2×D4×C4711yescharacteristic
904C22×C4C2×D4×C4711yescharacteristic
905C22×C4C2×D4×C4711yescharacteristic
906C22×C4C2×D4×C4712yes—
907C22×C4C24×C4711yescharacteristic
908Q16—24no—
909Q16—24no—
910Q16—42no—
911SD16—24no—
912SD16—24no—
913SD16—24no—
914SD16—24no—
915SD16—42no—
916SD16—42no—
917D8—24no—
918D8—24no—
919D8—42no—
920M16—24no—
921M16—21no—
922M16—21no—
923M16—21no—
924M16—21no—
925M16—21no—
926M16—21no—
927M16C2×D4×C4712yes—
928M16C2×D4×C4712yes—
929C2×C8—24no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—21no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—44no—
945C4⋊C4C2×D4×C4711yescharacteristic
946C4⋊C4C2×D4×C4711yescharacteristic
947C22⋊C4—22no—
948C22⋊C4—22no—
949C22⋊C4—22no—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—21no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—21no—
956C22⋊C4—21no—
957C22⋊C4—21no—
958C22⋊C4—21no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—42no—
962C42—22no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—22no—
974C23—41no—
975C23—41no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—41no—
981C23—41no—
982C23—81no—
983C23#120×C4711yescharacteristic
984C23#120×C4711yescharacteristic
985C23C22×D4×C4711yescharacteristic
986Q8—21no—
987Q8—21no—
988Q8—22no—
989Q8—21no—
990Q8—21no—
991Q8—22no—
992Q8—21no—
993Q8—42no—
994Q8—44no—
995Q8—41no—
996Q8—41no—
997Q8—41no—
998Q8—41no—
999Q8—41no—
1000Q8—41no—
1001Q8#120×C4712yes—
1002D4—22no—
1003D4—22no—
1004D4—21no—
1005D4—22no—
1006D4—21no—
1007D4—21no—
1008D4—21no—
1009D4—22no—
1010D4—21no—
1011D4—42no—
1012D4—42no—
1013D4—42no—
1014D4—42no—
1015D4—44no—
1016D4—44no—
1017D4—44no—
1018D4—41no—
1019D4—41no—
1020D4—41no—
1021D4—41no—
1022D4—41no—
1023D4—41no—
1024D4—81no—
1025D4—82no—
1026D4#120×C4712yes—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—41no—
1057C2×C4—44no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—42no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—82no—
1070C2×C4#120×C4711yescharacteristic
1071C2×C4#120×C4711yescharacteristic
1072C2×C4C22×D4×C4711yescharacteristic
1073C2×C4C22×D4×C4711yescharacteristic
1074C2×C4C22×D4×C4711yescharacteristic
1075C2×C4C22×D4×C4711yescharacteristic
1076C2×C4H(5,𝔽2)×C4711yescharacteristic
1077C2×C4H(5,𝔽2)×C4711yescharacteristic
1078C8—22no—
1079C8—22no—
1080C8—41no—
1081C8—41no—
1082C22—21no—
1083C22—21no—
1084C22—21no—
1085C22—21no—
1086C22—22no—
1087C22—21no—
1088C22—21no—
1089C22—21no—
1090C22—21no—
1091C22—44no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—81no—
1102C22—81no—
1103C22—82no—
1104C22—84no—
1105C22—81no—
1106C22—81no—
1107C22C2×#120×C4711yescharacteristic
1108C22D42×C4711yescharacteristic
1109C22D42×C4711yescharacteristic
1110C4—21no—
1111C4—21no—
1112C4—22no—
1113C4—42no—
1114C4—42no—
1115C4—41no—
1116C4—42no—
1117C4—41no—
1118C4—42no—
1119C4—41no—
1120C4—41no—
1121C4—81no—
1122C4C2×#120×C4711yescharacteristic
1123C4C47×#53411yescharacteristic
1124C4D42×C4711yescharacteristic
1125C4D42×C4711yescharacteristic
1126C2—21no—
1127C2—21no—
1128C2—41no—
1129C2—41no—
1130C2—42no—
1131C2—82no—
1132C2—81no—
1133C2—81no—
1134C2C47×#240311yescharacteristic
1135C2C47×#301811yescharacteristic
1136C2C47×#302011yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#575C2semidirect
2. C47×#3489C2semidirect
3. C2×C47×#456C2semidirect
4. C2×C47×#454C2semidirect
5. C47×#3005C2semidirect
6. C47×#2432C2semidirect
7. C47×#2007C2semidirect
8. C47×#2006C2semidirect
9. C47×#2005C2semidirect
10. C47×#2003C2semidirect
11. C47×#1901C2semidirect
12. C47×#1883C2semidirect
13. C47×#1882C2semidirect
14. C47×#1871C2semidirect
15. C47×#1789C2semidirect
24. C2×#137×C47C22semidirect
28. C2×AGL(1,ℤ/8)×C47C22semidirect
42. C2×C4⋊Q8×C47C22semidirect
43. C2×#124×C47C22semidirect
59. C2×#104×C47C22semidirect
60. C2×#104×C47C22semidirect
61. C47×#419C22semidirect
62. C47×#418C22semidirect
63. C2×#101×C47C22semidirect
64. C2×#101×C47C22semidirect
67. C47×#391C22semidirect
68. C47×#390C22semidirect
71. C47×#343C22semidirect
72. C47×#343C22semidirect
73. C47×#339C22semidirect
74. C47×#339C22semidirect
119. #137×C47D4semidirect
126. AGL(1,ℤ/8)×C47D4semidirect
513. #23881C47direct (N × H)
558. C2×#575C2×C47semidirect
559. #3489C2×C47semidirect
560. C2×#456C2×C47semidirect
561. C2×#454C2×C47semidirect
562. #3005C2×C47semidirect
563. #2432C2×C47semidirect
564. #2007C2×C47semidirect
565. #2006C2×C47semidirect
566. #2005C2×C47semidirect
567. #2003C2×C47semidirect
568. #1901C2×C47semidirect
569. #1883C2×C47semidirect
570. #1882C2×C47semidirect
571. #1871C2×C47semidirect
572. #1789C2×C47semidirect
592. C2×#137C22×C47semidirect
596. C2×AGL(1,ℤ/8)C22×C47semidirect
610. C2×C4⋊Q8C22×C47semidirect
611. C2×#124C22×C47semidirect
627. C2×#104C22×C47semidirect
628. C2×#104C22×C47semidirect
629. #419C22×C47semidirect
630. #418C22×C47semidirect
631. C2×#101C22×C47semidirect
632. C2×#101C22×C47semidirect
635. #391C22×C47semidirect
636. #390C22×C47semidirect
639. #343C22×C47semidirect
640. #343C22×C47semidirect
641. #339C22×C47semidirect
642. #339C22×C47semidirect
643. C47#23881direct (N × H)
688. #137D4×C47semidirect
695. AGL(1,ℤ/8)D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5752
C47×#34892
C2×C47×#4562
C2×C47×#4542
C47×#30052
C47×#24322
C47×#20072
C47×#20062
C47×#20052
C47×#20032
C47×#19012
C47×#18832
C47×#18822
C47×#18712
C47×#17892
#2388147