Finite Group Databasebeta

← C47×#23876 #26063574

Subgroups — C47×#23876 #26063574

Order 12032.

2012 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C47C211yesmaximal, characteristic, complemented
2C47×#3488C211yesmaximal, characteristic, complemented
3C2×C47×#453C212yesmaximal, complemented
4C47×#3003C211yesmaximal, characteristic, complemented
5C47×#2433C211yesmaximal, characteristic, complemented
6C47×#2006C212yesmaximal, complemented
7C47×#2002C212yesmaximal, complemented
8C47×#1900C211yesmaximal, characteristic, complemented
9C47×#1883C212yesmaximal, complemented
10C47×#1871C211yesmaximal, characteristic, complemented
11C47×#1789C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C47C2211yescharacteristic, complemented
13C22×#41×C47C2211yescharacteristic
14C23×D4×C47C2211yescharacteristic, complemented
15C2×AGL(1,ℤ/8)×C47—21no—
16C2×AGL(1,ℤ/8)×C47—21no—
17C2×AGL(1,ℤ/8)×C47—28no—
18C2×AGL(1,ℤ/8)×C47C2212yes—
19C2×AGL(1,ℤ/8)×C47C2212yescomplemented
20C2×AGL(1,ℤ/8)×C47C2212yescomplemented
21C22×SD16×C47—21no—
22C22×D8×C47—21no—
23C22×M16×C47C2211yescharacteristic, complemented
24C47×#550—21no—
25C47×#548—21no—
26C47×#546—21no—
27C47×#546—22no—
28D42×C47—22no—
29D42×C47—21no—
30C47×#537—21no—
31C47×#537C2211yescharacteristic, complemented
32C47×#535—21no—
33C47×#535C2211yescharacteristic, complemented
34C2×#127×C47C2212yescomplemented
35C47×#525—21no—
36C47×#525C2211yescharacteristic
37C2×#121×C47—21no—
38C2×#121×C47C2211yescharacteristic
39C2×#120×C47—22no—
40C47×#520C2211yescharacteristic, complemented
41C47×#453—28no—
42C47×#450—21no—
43C47×#450—21no—
44C47×#447—21no—
45C47×#447—21no—
46C2×#104×C47C2212yescomplemented
47C2×#104×C47C2212yescomplemented
48C2×#104×C47C2212yescomplemented
49C47×#418C2212yescomplemented
50C2×#100×C47C2212yescomplemented
51C47×#407C2211yescharacteristic, complemented
52C47×#392—22no—
53C47×#390C2212yescomplemented
54C4×C22⋊C4×C47C2211yescharacteristic, complemented
55C47×#343C2212yescomplemented
56C47×#339C2212yescomplemented
57C25×C47—21no—
58H(5,𝔽2)×C47—24no—
59H(5,𝔽2)×C47—42no—
60C2×#41×C47—21no—
61C2×#41×C47—21no—
62C2×#41×C47—21no—
63C2×#41×C47—21no—
64C2×#41×C47—24no—
65C2×#41×C47—42no—
66C2×#41×C47D411yescharacteristic, complemented
67C2×#41×C47D411yescharacteristic, complemented
68C2×#41×C47C2311yescharacteristic
69C2×#41×C47C2311yescharacteristic
70C2×#41×C47C2311yescharacteristic
71C22×Q8×C47D411yescharacteristic, complemented
72C22×D4×C47—24no—
73C22×D4×C47—21no—
74C22×D4×C47—22no—
75C22×D4×C47—22no—
76C22×D4×C47—21no—
77C22×D4×C47—21no—
78C22×D4×C47—24no—
79C22×D4×C47—21no—
80C22×D4×C47—21no—
81C22×D4×C47—21no—
82C22×D4×C47—21no—
83C22×D4×C47—21no—
84C22×D4×C47—42no—
85C22×D4×C47D412yes—
86C22×D4×C47D411yescharacteristic, complemented
87C22×D4×C47C2311yescharacteristic
88C22×D4×C47C2312yes—
89C23×C4×C47—21no—
90C23×C4×C47C2311yescharacteristic
91AGL(1,ℤ/8)×C47—28no—
92AGL(1,ℤ/8)×C47—28no—
93AGL(1,ℤ/8)×C47—24no—
94AGL(1,ℤ/8)×C47—24no—
95AGL(1,ℤ/8)×C47—24no—
96AGL(1,ℤ/8)×C47—24no—
97AGL(1,ℤ/8)×C47—42no—
98AGL(1,ℤ/8)×C47D418yescomplemented
99C2×SD16×C47—28no—
100C2×SD16×C47—22no—
101C2×SD16×C47—22no—
102C2×SD16×C47—22no—
103C2×D8×C47—28no—
104C2×D8×C47—22no—
105C2×D8×C47—22no—
106C2×D8×C47—22no—
107C2×M16×C47—21no—
108C2×M16×C47—24no—
109C2×M16×C47C2312yes—
110C2×M16×C47C2312yes—
111C22×C8×C47—21no—
112#127×C47—22no—
113#127×C47—21no—
114#127×C47—24no—
115#127×C47—42no—
116#124×C47—22no—
117#124×C47—21no—
118#123×C47—22no—
119#123×C47—21no—
120C22⋊Q8×C47—22no—
121C22⋊Q8×C47—21no—
122C22⋊Q8×C47—21no—
123C22⋊Q8×C47D411yescharacteristic, complemented
124C22⋊Q8×C47D411yescharacteristic, complemented
125#121×C47—22no—
126#121×C47—22no—
127#121×C47—22no—
128#121×C47—22no—
129#121×C47—22no—
130#121×C47—21no—
131#121×C47—21no—
132#121×C47—21no—
133#121×C47—21no—
134#121×C47—21no—
135#121×C47—21no—
136#121×C47—22no—
137#121×C47—21no—
138#121×C47—21no—
139#121×C47D411yescharacteristic, complemented
140#121×C47D411yescharacteristic, complemented
141#120×C47—22no—
142#120×C47—22no—
143#120×C47—22no—
144#120×C47—21no—
145#120×C47—22no—
146#120×C47—48no—
147C4×Q8×C47—21no—
148C4×D4×C47—22no—
149C4×D4×C47—22no—
150C4×D4×C47—21no—
151C4×D4×C47—22no—
152C4×D4×C47—21no—
153C4×D4×C47—21no—
154#117×C47—21no—
155#117×C47C2311yescharacteristic
156C2×C4⋊C4×C47—21no—
157C2×C4⋊C4×C47C2311yescharacteristic
158C2×C22⋊C4×C47—22no—
159C2×C22⋊C4×C47—21no—
160C2×C22⋊C4×C47—24no—
161C2×C22⋊C4×C47D412yes—
162C2×C42×C47C2312yes—
163#104×C47—24no—
164#104×C47—24no—
165#104×C47—42no—
166#102×C47—22no—
167#102×C47—22no—
168#100×C47—24no—
169C22⋊C8×C47—21no—
170C22⋊C8×C47—21no—
171#95×C47—21no—
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—21no—
175C24×C47—44no—
176C24×C47—44no—
177C24×C47—41no—
178C24×C47—41no—
179C24×C47—82no—
180C24×C47C2×D411yescharacteristic
181C24×C47C2×D412yes—
182#41×C47—22no—
183#41×C47—22no—
184#41×C47—22no—
185#41×C47—22no—
186#41×C47—22no—
187#41×C47—22no—
188#41×C47—22no—
189#41×C47—44no—
190#41×C47—41no—
191#41×C47—41no—
192#41×C47—44no—
193#41×C47—44no—
194#41×C47—42no—
195#41×C47—42no—
196#41×C47C2×D414yes—
197C2×Q8×C47—21no—
198C2×Q8×C47—22no—
199C2×Q8×C47—41no—
200C2×Q8×C47C2×D411yescharacteristic
201C2×Q8×C47C2×D411yescharacteristic
202C2×Q8×C47C2×D411yescharacteristic
203C2×D4×C47—21no—
204C2×D4×C47—24no—
205C2×D4×C47—24no—
206C2×D4×C47—22no—
207C2×D4×C47—22no—
208C2×D4×C47—22no—
209C2×D4×C47—22no—
210C2×D4×C47—21no—
211C2×D4×C47—21no—
212C2×D4×C47—21no—
213C2×D4×C47—21no—
214C2×D4×C47—21no—
215C2×D4×C47—22no—
216C2×D4×C47—22no—
217C2×D4×C47—22no—
218C2×D4×C47—21no—
219C2×D4×C47—22no—
220C2×D4×C47—21no—
221C2×D4×C47—22no—
222C2×D4×C47—22no—
223C2×D4×C47—22no—
224C2×D4×C47—21no—
225C2×D4×C47—21no—
226C2×D4×C47—22no—
227C2×D4×C47—22no—
228C2×D4×C47—22no—
229C2×D4×C47—22no—
230C2×D4×C47—41no—
231C2×D4×C47—44no—
232C2×D4×C47—44no—
233C2×D4×C47—44no—
234C2×D4×C47—44no—
235C2×D4×C47—42no—
236C2×D4×C47—42no—
237C2×D4×C47—48no—
238C2×D4×C47—44no—
239C2×D4×C47—48no—
240C2×D4×C47—42no—
241C2×D4×C47—42no—
242C2×D4×C47—44no—
243C2×D4×C47—48no—
244C2×D4×C47—41no—
245C2×D4×C47—41no—
246C2×D4×C47—84no—
247C2×D4×C47—84no—
248C2×D4×C47C2×D411yescharacteristic
249C2×D4×C47C2×D411yescharacteristic
250C2×D4×C47C2×D411yescharacteristic
251C2×D4×C47C2×D414yescomplemented
252C22×C4×C47—21no—
253C22×C4×C47—22no—
254C22×C4×C47—22no—
255C22×C4×C47—22no—
256C22×C4×C47—21no—
257C22×C4×C47—22no—
258C22×C4×C47—22no—
259C22×C4×C47—21no—
260C22×C4×C47—21no—
261C22×C4×C47—21no—
262C22×C4×C47—21no—
263C22×C4×C47—44no—
264C22×C4×C47C2×D411yescharacteristic
265C22×C4×C47C2×D411yescharacteristic
266C22×C4×C47C2×D411yescharacteristic
267C22×C4×C47C2×D411yescharacteristic
268C22×C4×C47C2×D411yescharacteristic
269C22×C4×C47C2×D412yes—
270C22×C4×C47C2411yescharacteristic
271SD16×C47—28no—
272SD16×C47—28no—
273SD16×C47—44no—
274D8×C47—28no—
275D8×C47—28no—
276D8×C47—44no—
277M16×C47—24no—
278M16×C47—22no—
279M16×C47—22no—
280M16×C47—22no—
281M16×C47C2×D414yescomplemented
282C2×C8×C47—24no—
283C2×C8×C47—22no—
284C2×C8×C47—22no—
285C4⋊C4×C47—22no—
286C4⋊C4×C47—22no—
287C4⋊C4×C47—21no—
288C4⋊C4×C47—21no—
289C4⋊C4×C47—21no—
290C4⋊C4×C47—21no—
291C4⋊C4×C47C2×D411yescharacteristic
292C4⋊C4×C47C2×D411yescharacteristic
293C22⋊C4×C47—22no—
294C22⋊C4×C47—22no—
295C22⋊C4×C47—24no—
296C22⋊C4×C47—22no—
297C22⋊C4×C47—22no—
298C22⋊C4×C47—22no—
299C22⋊C4×C47—21no—
300C22⋊C4×C47—21no—
301C22⋊C4×C47—21no—
302C22⋊C4×C47—21no—
303C22⋊C4×C47—22no—
304C22⋊C4×C47—22no—
305C22⋊C4×C47—21no—
306C22⋊C4×C47—48no—
307C42×C47—22no—
308C42×C47—21no—
309C42×C47—22no—
310C42×C47—22no—
311C23×C47—21no—
312C23×C47—22no—
313C23×C47—22no—
314C23×C47—22no—
315C23×C47—21no—
316C23×C47—21no—
317C23×C47—24no—
318C23×C47—24no—
319C23×C47—41no—
320C23×C47—42no—
321C23×C47—44no—
322C23×C47—44no—
323C23×C47—44no—
324C23×C47—44no—
325C23×C47—44no—
326C23×C47—42no—
327C23×C47—42no—
328C23×C47—42no—
329C23×C47—42no—
330C23×C47—42no—
331C23×C47—81no—
332C23×C47—82no—
333C23×C47—82no—
334C23×C47—82no—
335C23×C47—82no—
336C23×C47—82no—
337C23×C47—816no—
338C23×C47—82no—
339C23×C47#12011yescharacteristic
340C23×C47#12011yescharacteristic
341C23×C47C22×D411yescharacteristic
342Q8×C47—21no—
343Q8×C47—21no—
344Q8×C47—21no—
345Q8×C47—22no—
346Q8×C47—42no—
347Q8×C47#12012yescomplemented
348D4×C47—24no—
349D4×C47—21no—
350D4×C47—24no—
351D4×C47—21no—
352D4×C47—21no—
353D4×C47—22no—
354D4×C47—24no—
355D4×C47—42no—
356D4×C47—42no—
357D4×C47—44no—
358D4×C47—44no—
359D4×C47—44no—
360D4×C47—42no—
361D4×C47—44no—
362D4×C47—42no—
363D4×C47—42no—
364D4×C47—44no—
365D4×C47—42no—
366D4×C47—41no—
367D4×C47—42no—
368D4×C47—41no—
369D4×C47—42no—
370D4×C47—42no—
371D4×C47—81no—
372D4×C47—82no—
373D4×C47—82no—
374D4×C47—82no—
375D4×C47—82no—
376D4×C47—816no—
377D4×C47#12012yescomplemented
378C2×C4×C47—21no—
379C2×C4×C47—22no—
380C2×C4×C47—21no—
381C2×C4×C47—21no—
382C2×C4×C47—21no—
383C2×C4×C47—21no—
384C2×C4×C47—22no—
385C2×C4×C47—22no—
386C2×C4×C47—24no—
387C2×C4×C47—24no—
388C2×C4×C47—21no—
389C2×C4×C47—22no—
390C2×C4×C47—21no—
391C2×C4×C47—21no—
392C2×C4×C47—21no—
393C2×C4×C47—42no—
394C2×C4×C47—42no—
395C2×C4×C47—42no—
396C2×C4×C47—44no—
397C2×C4×C47—42no—
398C2×C4×C47—42no—
399C2×C4×C47—41no—
400C2×C4×C47—41no—
401C2×C4×C47—42no—
402C2×C4×C47—42no—
403C2×C4×C47—82no—
404C2×C4×C47#12011yescharacteristic
405C2×C4×C47#12011yescharacteristic
406C2×C4×C47C22×D411yescharacteristic
407C2×C4×C47C22×D412yes—
408C2×C4×C47C22×D411yescharacteristic
409C2×C4×C47H(5,𝔽2)12yes—
410C8×C47—24no—
411C8×C47—42no—
412#23876C4711yesmaximal, characteristic, direct product factor, Sylow
413C22×C47—21no—
414C22×C47—21no—
415C22×C47—21no—
416C22×C47—21no—
417C22×C47—21no—
418C22×C47—22no—
419C22×C47—21no—
420C22×C47—21no—
421C22×C47—44no—
422C22×C47—48no—
423C22×C47—41no—
424C22×C47—41no—
425C22×C47—41no—
426C22×C47—41no—
427C22×C47—42no—
428C22×C47—44no—
429C22×C47—42no—
430C22×C47—41no—
431C22×C47—41no—
432C22×C47—41no—
433C22×C47—42no—
434C22×C47—41no—
435C22×C47—84no—
436C22×C47—84no—
437C22×C47—84no—
438C22×C47—88no—
439C22×C47—88no—
440C22×C47—82no—
441C22×C47—82no—
442C22×C47—164no—
443C22×C47#45312yescomplemented
444C22×C47C2×#12011yescharacteristic
445C22×C47D4212yes—
446C4×C47—21no—
447C4×C47—21no—
448C4×C47—22no—
449C4×C47—44no—
450C4×C47—41no—
451C4×C47—41no—
452C4×C47—42no—
453C4×C47—41no—
454C4×C47—41no—
455C4×C47C2×#12011yescharacteristic
456C4×C47#53411yescharacteristic
457C4×C47D4212yes—
458C22×AGL(1,ℤ/8)C2×C4711yescharacteristic, complemented
459#3488C2×C4711yescharacteristic, complemented
460C2×#453C2×C4712yescomplemented
461#3003C2×C4711yescharacteristic, complemented
462#2433C2×C4711yescharacteristic, complemented
463#2006C2×C4712yescomplemented
464#2002C2×C4712yescomplemented
465#1900C2×C4711yescharacteristic, complemented
466#1883C2×C4712yescomplemented
467#1871C2×C4711yescharacteristic, complemented
468#1789C2×C4711yescharacteristic, complemented
469C2×C47—22no—
470C2×C47—22no—
471C2×C47—41no—
472C2×C47—42no—
473C2×C47—81no—
474C2×C47—84no—
475C2×C47—82no—
476C2×C47—81no—
477C2×C47#240311yescharacteristic
478C2×C47C2×#45311yescharacteristic
479C2×C47#302111yescharacteristic
480C2×H(5,𝔽2)C22×C4711yescharacteristic, complemented
481C22×#41C22×C4711yescharacteristic
482C23×D4C22×C4711yescharacteristic, complemented
483C2×AGL(1,ℤ/8)—21no—
484C2×AGL(1,ℤ/8)—21no—
485C2×AGL(1,ℤ/8)—28no—
486C2×AGL(1,ℤ/8)C22×C4712yes—
487C2×AGL(1,ℤ/8)C22×C4712yescomplemented
488C2×AGL(1,ℤ/8)C22×C4712yescomplemented
489C22×SD16—21no—
490C22×D8—21no—
491C22×M16C22×C4711yescharacteristic, complemented
492#550—21no—
493#548—21no—
494#546—21no—
495#546—22no—
496D42—22no—
497D42—21no—
498#537—21no—
499#537C22×C4711yescharacteristic, complemented
500#535—21no—
501#535C22×C4711yescharacteristic, complemented
502C2×#127C22×C4712yescomplemented
503#525—21no—
504#525C22×C4711yescharacteristic
505C2×#121—21no—
506C2×#121C22×C4711yescharacteristic
507C2×#120—22no—
508#520C22×C4711yescharacteristic, complemented
509#453—28no—
510#450—21no—
511#450—21no—
512#447—21no—
513#447—21no—
514C2×#104C22×C4712yescomplemented
515C2×#104C22×C4712yescomplemented
516C2×#104C22×C4712yescomplemented
517#418C22×C4712yescomplemented
518C2×#100C22×C4712yescomplemented
519#407C22×C4711yescharacteristic, complemented
520#392—22no—
521#390C22×C4712yescomplemented
522C4×C22⋊C4C22×C4711yescharacteristic, complemented
523#343C22×C4712yescomplemented
524#339C22×C4712yescomplemented
525C47#2387611yescharacteristic, direct product factor, Sylow
526C25—21no—
527H(5,𝔽2)—24no—
528H(5,𝔽2)—42no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—21no—
533C2×#41—24no—
534C2×#41—42no—
535C2×#41D4×C4711yescharacteristic, complemented
536C2×#41D4×C4711yescharacteristic, complemented
537C2×#41C23×C4711yescharacteristic
538C2×#41C23×C4711yescharacteristic
539C2×#41C23×C4711yescharacteristic
540C22×Q8D4×C4711yescharacteristic, complemented
541C22×D4—24no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—24no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—42no—
554C22×D4D4×C4712yes—
555C22×D4D4×C4711yescharacteristic, complemented
556C22×D4C23×C4711yescharacteristic
557C22×D4C23×C4712yes—
558C23×C4—21no—
559C23×C4C23×C4711yescharacteristic
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—28no—
562AGL(1,ℤ/8)—24no—
563AGL(1,ℤ/8)—24no—
564AGL(1,ℤ/8)—24no—
565AGL(1,ℤ/8)—24no—
566AGL(1,ℤ/8)—42no—
567AGL(1,ℤ/8)D4×C4718yescomplemented
568C2×SD16—28no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×D8—28no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×M16—21no—
577C2×M16—24no—
578C2×M16C23×C4712yes—
579C2×M16C23×C4712yes—
580C22×C8—21no—
581#127—22no—
582#127—21no—
583#127—24no—
584#127—42no—
585#124—22no—
586#124—21no—
587#123—22no—
588#123—21no—
589C22⋊Q8—22no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8D4×C4711yescharacteristic, complemented
593C22⋊Q8D4×C4711yescharacteristic, complemented
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—22no—
606#121—21no—
607#121—21no—
608#121D4×C4711yescharacteristic, complemented
609#121D4×C4711yescharacteristic, complemented
610#120—22no—
611#120—22no—
612#120—22no—
613#120—21no—
614#120—22no—
615#120—48no—
616C4×Q8—21no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—21no—
620C4×D4—22no—
621C4×D4—21no—
622C4×D4—21no—
623#117—21no—
624#117C23×C4711yescharacteristic
625C2×C4⋊C4—21no—
626C2×C4⋊C4C23×C4711yescharacteristic
627C2×C22⋊C4—22no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4D4×C4712yes—
631C2×C42C23×C4712yes—
632#104—24no—
633#104—24no—
634#104—42no—
635#102—22no—
636#102—22no—
637#100—24no—
638C22⋊C8—21no—
639C22⋊C8—21no—
640#95—21no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—44no—
645C24—44no—
646C24—41no—
647C24—41no—
648C24—82no—
649C24C2×D4×C4711yescharacteristic
650C24C2×D4×C4712yes—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—44no—
659#41—41no—
660#41—41no—
661#41—44no—
662#41—44no—
663#41—42no—
664#41—42no—
665#41C2×D4×C4714yes—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—41no—
669C2×Q8C2×D4×C4711yescharacteristic
670C2×Q8C2×D4×C4711yescharacteristic
671C2×Q8C2×D4×C4711yescharacteristic
672C2×D4—21no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—41no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—48no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—84no—
716C2×D4—84no—
717C2×D4C2×D4×C4711yescharacteristic
718C2×D4C2×D4×C4711yescharacteristic
719C2×D4C2×D4×C4711yescharacteristic
720C2×D4C2×D4×C4714yescomplemented
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—44no—
733C22×C4C2×D4×C4711yescharacteristic
734C22×C4C2×D4×C4711yescharacteristic
735C22×C4C2×D4×C4711yescharacteristic
736C22×C4C2×D4×C4711yescharacteristic
737C22×C4C2×D4×C4711yescharacteristic
738C22×C4C2×D4×C4712yes—
739C22×C4C24×C4711yescharacteristic
740SD16—28no—
741SD16—28no—
742SD16—44no—
743D8—28no—
744D8—28no—
745D8—44no—
746M16—24no—
747M16—22no—
748M16—22no—
749M16—22no—
750M16C2×D4×C4714yescomplemented
751C2×C8—24no—
752C2×C8—22no—
753C2×C8—22no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4C2×D4×C4711yescharacteristic
761C4⋊C4C2×D4×C4711yescharacteristic
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—24no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—21no—
775C22⋊C4—48no—
776C42—22no—
777C42—21no—
778C42—22no—
779C42—22no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—24no—
787C23—24no—
788C23—41no—
789C23—42no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—81no—
801C23—82no—
802C23—82no—
803C23—82no—
804C23—82no—
805C23—82no—
806C23—816no—
807C23—82no—
808C23#120×C4711yescharacteristic
809C23#120×C4711yescharacteristic
810C23C22×D4×C4711yescharacteristic
811Q8—21no—
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—42no—
816Q8#120×C4712yescomplemented
817D4—24no—
818D4—21no—
819D4—24no—
820D4—21no—
821D4—21no—
822D4—22no—
823D4—24no—
824D4—42no—
825D4—42no—
826D4—44no—
827D4—44no—
828D4—44no—
829D4—42no—
830D4—44no—
831D4—44no—
832D4—42no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—42no—
837D4—41no—
838D4—42no—
839D4—42no—
840D4—81no—
841D4—82no—
842D4—82no—
843D4—82no—
844D4—82no—
845D4—816no—
846D4#120×C4712yescomplemented
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—44no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—82no—
873C2×C4#120×C4711yescharacteristic
874C2×C4#120×C4711yescharacteristic
875C2×C4C22×D4×C4711yescharacteristic
876C2×C4C22×D4×C4712yes—
877C2×C4C22×D4×C4711yescharacteristic
878C2×C4H(5,𝔽2)×C4712yes—
879C8—24no—
880C8—42no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—22no—
887C22—21no—
888C22—21no—
889C22—44no—
890C22—48no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—42no—
896C22—44no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—84no—
904C22—84no—
905C22—84no—
906C22—88no—
907C22—88no—
908C22—82no—
909C22—82no—
910C22—164no—
911C22C47×#45312yescomplemented
912C22C2×#120×C4711yescharacteristic
913C22D42×C4712yes—
914C4—21no—
915C4—21no—
916C4—22no—
917C4—44no—
918C4—41no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—41no—
923C4C2×#120×C4711yescharacteristic
924C4C47×#53411yescharacteristic
925C4D42×C4712yes—
926C2—22no—
927C2—22no—
928C2—41no—
929C2—42no—
930C2—84no—
931C2—81no—
932C2—82no—
933C2—81no—
934C2C47×#240311yescharacteristic
935C2C2×C47×#45311yescharacteristic
936C2C47×#302111yescharacteristic
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. C22×AGL(1,ℤ/8)×C47C2semidirect
2. C47×#3488C2semidirect
3. C2×C47×#453C2semidirect
4. C47×#3003C2semidirect
5. C47×#2433C2semidirect
6. C47×#2006C2semidirect
7. C47×#2002C2semidirect
8. C47×#1900C2semidirect
9. C47×#1883C2semidirect
10. C47×#1871C2semidirect
11. C47×#1789C2semidirect
12. C2×H(5,𝔽2)×C47C22semidirect
14. C23×D4×C47C22semidirect
19. C2×AGL(1,ℤ/8)×C47C22semidirect
20. C2×AGL(1,ℤ/8)×C47C22semidirect
23. C22×M16×C47C22semidirect
31. C47×#537C22semidirect
33. C47×#535C22semidirect
34. C2×#127×C47C22semidirect
40. C47×#520C22semidirect
46. C2×#104×C47C22semidirect
47. C2×#104×C47C22semidirect
48. C2×#104×C47C22semidirect
49. C47×#418C22semidirect
50. C2×#100×C47C22semidirect
51. C47×#407C22semidirect
53. C47×#390C22semidirect
54. C4×C22⋊C4×C47C22semidirect
55. C47×#343C22semidirect
56. C47×#339C22semidirect
66. C2×#41×C47D4semidirect
67. C2×#41×C47D4semidirect
71. C22×Q8×C47D4semidirect
86. C22×D4×C47D4semidirect
98. AGL(1,ℤ/8)×C47D4semidirect
123. C22⋊Q8×C47D4semidirect
124. C22⋊Q8×C47D4semidirect
139. #121×C47D4semidirect
140. #121×C47D4semidirect
251. C2×D4×C47C2×D4semidirect
281. M16×C47C2×D4semidirect
347. Q8×C47#120semidirect
377. D4×C47#120semidirect
412. #23876C47direct (N × H)
443. C22×C47#453semidirect
458. C22×AGL(1,ℤ/8)C2×C47semidirect
459. #3488C2×C47semidirect
460. C2×#453C2×C47semidirect
461. #3003C2×C47semidirect
462. #2433C2×C47semidirect
463. #2006C2×C47semidirect
464. #2002C2×C47semidirect
465. #1900C2×C47semidirect
466. #1883C2×C47semidirect
467. #1871C2×C47semidirect
468. #1789C2×C47semidirect
480. C2×H(5,𝔽2)C22×C47semidirect
482. C23×D4C22×C47semidirect
487. C2×AGL(1,ℤ/8)C22×C47semidirect
488. C2×AGL(1,ℤ/8)C22×C47semidirect
491. C22×M16C22×C47semidirect
499. #537C22×C47semidirect
501. #535C22×C47semidirect
502. C2×#127C22×C47semidirect
508. #520C22×C47semidirect
514. C2×#104C22×C47semidirect
515. C2×#104C22×C47semidirect
516. C2×#104C22×C47semidirect
517. #418C22×C47semidirect
518. C2×#100C22×C47semidirect
519. #407C22×C47semidirect
521. #390C22×C47semidirect
522. C4×C22⋊C4C22×C47semidirect
523. #343C22×C47semidirect
524. #339C22×C47semidirect
525. C47#23876direct (N × H)
535. C2×#41D4×C47semidirect
536. C2×#41D4×C47semidirect
540. C22×Q8D4×C47semidirect
555. C22×D4D4×C47semidirect
567. AGL(1,ℤ/8)D4×C47semidirect
592. C22⋊Q8D4×C47semidirect
593. C22⋊Q8D4×C47semidirect
608. #121D4×C47semidirect
609. #121D4×C47semidirect
720. C2×D4C2×D4×C47semidirect
750. M16C2×D4×C47semidirect
816. Q8#120×C47semidirect
846. D4#120×C47semidirect
911. C22C47×#453semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C472
C47×#34882
C2×C47×#4532
C47×#30032
C47×#24332
C47×#20062
C47×#20022
C47×#19002
C47×#18832
C47×#18712
C47×#17892
#2387647