Finite Group Databasebeta

← C47×#24460 #26064158

Subgroups — C47×#24460 #26064158

Order 12032.

1352 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#577C211yesmaximal, characteristic, complemented
2C2×C47×#472C211yesmaximal, characteristic, complemented
3C47×#3045C211yesmaximal, characteristic, complemented
4C2×C47×#454C211yesmaximal, characteristic, complemented
5C47×#3008C211yesmaximal, characteristic, complemented
6C47×#2898C211yesmaximal, characteristic, complemented
7C47×#2052C211yesmaximal, characteristic, complemented
8C47×#2046C211yesmaximal, characteristic, complemented
9C47×#2012C211yesmaximal, characteristic, complemented
10C47×#2004C211yesmaximal, characteristic, complemented
11C47×#1907C211yesmaximal, characteristic, complemented
12C47×#1883C211yesmaximal, characteristic, complemented
13C47×#1876C211yesmaximal, characteristic, complemented
14C47×#1866C211yesmaximal, characteristic, complemented
15C47×#1792C211yesmaximal, characteristic, complemented
16C2×2−1+4×C47C2211yescharacteristic
17C2×H(5,𝔽2)×C47C2211yescharacteristic
18C47×#577—24no—
19C47×#577—24no—
20C2×#137×C47—21no—
21C2×#137×C47C2211yescharacteristic
22C2×AGL(1,ℤ/8)×C47—21no—
23C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
24C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C47C2211yescharacteristic, complemented
26C2×#135×C47—21no—
27C2×#135×C47C2211yescharacteristic
28C22×SD16×C47—21no—
29C22×SD16×C47C2211yescharacteristic
30C22×D8×C47C2211yescharacteristic
31C2×#131×C47C2211yescharacteristic
32C2×#131×C47C2211yescharacteristic, complemented
33C47×#535C2211yescharacteristic
34C2×#124×C47C2211yescharacteristic, complemented
35C47×#520C2211yescharacteristic, complemented
36C47×#472—24no—
37C47×#464—21no—
38C47×#463—21no—
39C47×#460—21no—
40C47×#459—21no—
41C47×#454—24no—
42C47×#449—21no—
43C47×#449—21no—
44C47×#447—21no—
45C47×#447—21no—
46C2×#108×C47C2211yescharacteristic, complemented
47C47×#424C2211yescharacteristic, complemented
48C2×#104×C47C2211yescharacteristic
49C2×#104×C47C2211yescharacteristic
50C2×#104×C47C2211yescharacteristic, complemented
51C47×#419—21no—
52C47×#419C2211yescharacteristic, complemented
53C47×#418C2211yescharacteristic
54C47×#417—21no—
55C47×#417C2211yescharacteristic
56C47×#417C2211yescharacteristic
57C47×#416—21no—
58C47×#416C2211yescharacteristic
59C2×#103×C47—21no—
60C2×#103×C47C2211yescharacteristic, complemented
61C2×#102×C47C2211yescharacteristic, complemented
62C2×#101×C47C2211yescharacteristic, complemented
63C2×#100×C47C2211yescharacteristic
64C2×#100×C47C2211yescharacteristic, complemented
65C47×#408C2211yescharacteristic
66C47×#390C2211yescharacteristic
67C47×#343C2211yescharacteristic, complemented
68C47×#341C2211yescharacteristic, complemented
69C47×#339C2211yescharacteristic, complemented
70C47×#336C2211yescharacteristic, complemented
712−1+4×C47—22no—
722−1+4×C47—22no—
732−1+4×C47—41no—
742−1+4×C47D414yescomplemented
75H(5,𝔽2)×C47—22no—
76H(5,𝔽2)×C47—22no—
77H(5,𝔽2)×C47—22no—
78H(5,𝔽2)×C47—41no—
79C2×#41×C47—21no—
80C2×#41×C47—21no—
81C2×#41×C47—21no—
82C2×#41×C47—21no—
83C2×#41×C47—41no—
84C2×#41×C47C2311yescharacteristic
85C2×#41×C47C2311yescharacteristic
86C2×#41×C47C2311yescharacteristic
87C22×Q8×C47—21no—
88C22×Q8×C47—21no—
89C22×Q8×C47C2311yescharacteristic
90C22×D4×C47—21no—
91C22×D4×C47—21no—
92C22×D4×C47—41no—
93C22×D4×C47C2311yescharacteristic
94C22×D4×C47C2311yescharacteristic
95#137×C47—28no—
96#137×C47—22no—
97#137×C47—22no—
98AGL(1,ℤ/8)×C47—28no—
99AGL(1,ℤ/8)×C47—22no—
100AGL(1,ℤ/8)×C47—22no—
101AGL(1,ℤ/8)×C47—22no—
102AGL(1,ℤ/8)×C47—22no—
103AGL(1,ℤ/8)×C47—22no—
104AGL(1,ℤ/8)×C47D414yescomplemented
105#135×C47—28no—
106#135×C47—22no—
107#135×C47—22no—
108C2×Q16×C47—21no—
109C2×Q16×C47D411yescharacteristic
110C2×SD16×C47—28no—
111C2×SD16×C47—21no—
112C2×SD16×C47—22no—
113C2×SD16×C47—21no—
114C2×SD16×C47—22no—
115C2×SD16×C47—21no—
116C2×SD16×C47—21no—
117C2×SD16×C47—21no—
118C2×SD16×C47—21no—
119C2×SD16×C47D411yescharacteristic
120C2×SD16×C47D411yescharacteristic
121C2×D8×C47—21no—
122C2×D8×C47—21no—
123C2×D8×C47—22no—
124C2×D8×C47—21no—
125C2×D8×C47—21no—
126C2×D8×C47—21no—
127C2×D8×C47—41no—
128C2×D8×C47D411yescharacteristic
129#131×C47—22no—
130#131×C47—22no—
131#131×C47—22no—
132#131×C47—41no—
133C2×M16×C47—21no—
134C2×M16×C47—21no—
135C2×M16×C47C2311yescharacteristic
136C2×M16×C47C2311yescharacteristic
137C2×M16×C47C2311yescharacteristic
138C2×M16×C47C2311yescharacteristic
139C22×C8×C47—21no—
140C22×C8×C47—21no—
141C22×C8×C47C2311yescharacteristic
142C22×C8×C47C2311yescharacteristic
143#127×C47—21no—
144#124×C47—22no—
145#124×C47—21no—
146#124×C47—41no—
147#121×C47—21no—
148#121×C47—21no—
149#120×C47—41no—
150C4×Q8×C47—21no—
151C4×D4×C47—21no—
152C4×D4×C47—41no—
153#117×C47—21no—
154#117×C47C2311yescharacteristic
155C2×C4⋊C4×C47—21no—
156C2×C4⋊C4×C47C2311yescharacteristic
157C2×C22⋊C4×C47—41no—
158C2×C22⋊C4×C47—41no—
159C2×C42×C47C2311yescharacteristic
160#108×C47—22no—
161C4⋊C8×C47—21no—
162C4⋊C8×C47—21no—
163#104×C47—22no—
164#104×C47—22no—
165#104×C47—41no—
166#103×C47—21no—
167#103×C47—21no—
168#103×C47—21no—
169#103×C47—21no—
170#103×C47—21no—
171#103×C47—21no—
172#103×C47D411yescharacteristic
173#103×C47D411yescharacteristic
174#102×C47—21no—
175#102×C47—21no—
176#102×C47—21no—
177#102×C47—21no—
178#102×C47—21no—
179#102×C47—21no—
180#102×C47D411yescharacteristic
181#102×C47D411yescharacteristic
182#101×C47—22no—
183#100×C47—22no—
184#100×C47—22no—
185C22⋊C8×C47—21no—
186C22⋊C8×C47—21no—
187C24×C47—21no—
188C24×C47—21no—
189C24×C47—41no—
190#41×C47—21no—
191#41×C47—21no—
192#41×C47—21no—
193#41×C47—21no—
194#41×C47—24no—
195#41×C47—24no—
196#41×C47—24no—
197#41×C47—21no—
198#41×C47—21no—
199#41×C47—21no—
200#41×C47—21no—
201#41×C47—44no—
202#41×C47—42no—
203#41×C47—42no—
204#41×C47—42no—
205#41×C47—44no—
206#41×C47—42no—
207#41×C47—42no—
208#41×C47C2×D412yes—
209#41×C47C2×D412yes—
210#41×C47C2×D412yes—
211#41×C47#4112yes—
212C2×Q8×C47—21no—
213C2×Q8×C47—24no—
214C2×Q8×C47—24no—
215C2×Q8×C47—21no—
216C2×Q8×C47—21no—
217C2×Q8×C47—21no—
218C2×Q8×C47—21no—
219C2×Q8×C47—41no—
220C2×Q8×C47—42no—
221C2×Q8×C47—42no—
222C2×Q8×C47C2×D411yescharacteristic
223C2×Q8×C47C2×D412yes—
224C2×Q8×C47C2×D411yescharacteristic
225C2×Q8×C47C2×D411yescharacteristic
226C2×D4×C47—21no—
227C2×D4×C47—21no—
228C2×D4×C47—24no—
229C2×D4×C47—21no—
230C2×D4×C47—21no—
231C2×D4×C47—21no—
232C2×D4×C47—21no—
233C2×D4×C47—21no—
234C2×D4×C47—21no—
235C2×D4×C47—21no—
236C2×D4×C47—21no—
237C2×D4×C47—21no—
238C2×D4×C47—21no—
239C2×D4×C47—21no—
240C2×D4×C47—21no—
241C2×D4×C47—42no—
242C2×D4×C47—41no—
243C2×D4×C47—41no—
244C2×D4×C47—41no—
245C2×D4×C47—41no—
246C2×D4×C47—42no—
247C2×D4×C47—44no—
248C2×D4×C47—44no—
249C2×D4×C47—41no—
250C2×D4×C47—42no—
251C2×D4×C47C2×D411yescharacteristic
252C2×D4×C47C2×D412yes—
253C2×D4×C47C2×D411yescharacteristic
254C2×D4×C47C2×D411yescharacteristic
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—41no—
262C22×C4×C47—41no—
263C22×C4×C47—41no—
264C22×C4×C47—41no—
265C22×C4×C47C2411yescharacteristic
266Q16×C47—24no—
267Q16×C47—22no—
268SD16×C47—24no—
269SD16×C47—24no—
270SD16×C47—24no—
271SD16×C47—22no—
272SD16×C47—24no—
273SD16×C47—22no—
274SD16×C47—42no—
275SD16×C47—42no—
276D8×C47—24no—
277D8×C47—22no—
278D8×C47—42no—
279D8×C47—42no—
280D8×C47—42no—
281D8×C47—42no—
282M16×C47—24no—
283M16×C47—21no—
284M16×C47—21no—
285M16×C47—21no—
286M16×C47—21no—
287M16×C47—21no—
288M16×C47—21no—
289M16×C47—21no—
290M16×C47—42no—
291M16×C47C2×D412yes—
292C2×C8×C47—24no—
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×C47—21no—
300C2×C8×C47—21no—
301C2×C8×C47—42no—
302C2×C8×C47C2×D411yescharacteristic
303C2×C8×C47C2×D411yescharacteristic
304C2×C8×C47C2×D411yescharacteristic
305C2×C8×C47C2×D411yescharacteristic
306C4⋊C4×C47—21no—
307C4⋊C4×C47—21no—
308C4⋊C4×C47—41no—
309C4⋊C4×C47C2×D411yescharacteristic
310C4⋊C4×C47C2×D411yescharacteristic
311C22⋊C4×C47—21no—
312C22⋊C4×C47—41no—
313C22⋊C4×C47—41no—
314C22⋊C4×C47—41no—
315C22⋊C4×C47—44no—
316C22⋊C4×C47—82no—
317C42×C47—21no—
318C42×C47—21no—
319C42×C47—21no—
320C42×C47—41no—
321C23×C47—21no—
322C23×C47—21no—
323C23×C47—21no—
324C23×C47—22no—
325C23×C47—44no—
326C23×C47—41no—
327C23×C47—41no—
328C23×C47—41no—
329C23×C47—41no—
330C23×C47—41no—
331C23×C47—81no—
332C23×C47—81no—
333C23×C47—81no—
334C23×C47—81no—
335C23×C47—161no—
336C23×C47—161no—
337C23×C47H(5,𝔽2)11yescharacteristic
338Q8×C47—21no—
339Q8×C47—21no—
340Q8×C47—22no—
341Q8×C47—21no—
342Q8×C47—22no—
343Q8×C47—21no—
344Q8×C47—44no—
345Q8×C47—41no—
346Q8×C47—41no—
347Q8×C47#12012yes—
348Q8×C47#12112yes—
349D4×C47—22no—
350D4×C47—22no—
351D4×C47—22no—
352D4×C47—22no—
353D4×C47—22no—
354D4×C47—21no—
355D4×C47—21no—
356D4×C47—22no—
357D4×C47—21no—
358D4×C47—21no—
359D4×C47—44no—
360D4×C47—44no—
361D4×C47—44no—
362D4×C47—41no—
363D4×C47—41no—
364D4×C47—41no—
365D4×C47—41no—
366D4×C47—41no—
367D4×C47—41no—
368D4×C47—41no—
369D4×C47—41no—
370D4×C47—161no—
371D4×C47—161no—
372D4×C47#12012yes—
373D4×C47#12112yes—
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—21no—
382C2×C4×C47—21no—
383C2×C4×C47—21no—
384C2×C4×C47—44no—
385C2×C4×C47—44no—
386C2×C4×C47—44no—
387C2×C4×C47—41no—
388C2×C4×C47—41no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—41no—
393C2×C4×C47—41no—
394C2×C4×C47—41no—
395C2×C4×C47—81no—
396C2×C4×C47—161no—
397C2×C4×C47C22×D411yescharacteristic
398C2×C4×C47C22×D411yescharacteristic
399C2×C4×C47C22×D411yescharacteristic
400C2×C4×C47C22×D411yescharacteristic
401C2×C4×C47C2×#4111yescharacteristic
402C2×C4×C47H(5,𝔽2)11yescharacteristic
403C8×C47—21no—
404C8×C47—22no—
405C8×C47—21no—
406C8×C47—21no—
407C8×C47—21no—
408C8×C47—41no—
409C8×C47—41no—
410C8×C47—41no—
411#24460C4711yesmaximal, characteristic, direct product factor, Sylow
412C22×C47—21no—
413C22×C47—21no—
414C22×C47—22no—
415C22×C47—22no—
416C22×C47—41no—
417C22×C47—41no—
418C22×C47—41no—
419C22×C47—41no—
420C22×C47—41no—
421C22×C47—42no—
422C22×C47—41no—
423C22×C47—41no—
424C22×C47—82no—
425C22×C47—82no—
426C22×C47—81no—
427C22×C47—81no—
428C22×C47—81no—
429C22×C47—81no—
430C22×C47—81no—
431C22×C47—161no—
432C22×C47—161no—
433C22×C47—164no—
434C22×C47#53411yescharacteristic
435C22×C47D4211yescharacteristic
436C22×C47#54611yescharacteristic
437C4×C47—22no—
438C4×C47—22no—
439C4×C47—41no—
440C4×C47—42no—
441C4×C47—41no—
442C4×C47—41no—
443C4×C47—81no—
444C4×C47—81no—
445C4×C47C2×#12011yescharacteristic
446C4×C47C2×#12111yescharacteristic
447C4×C47D4211yescharacteristic
448C4×C47#54611yescharacteristic
449C2×#577C2×C4711yescharacteristic, complemented
450C2×#472C2×C4711yescharacteristic, complemented
451#3045C2×C4711yescharacteristic, complemented
452C2×#454C2×C4711yescharacteristic, complemented
453#3008C2×C4711yescharacteristic, complemented
454#2898C2×C4711yescharacteristic, complemented
455#2052C2×C4711yescharacteristic, complemented
456#2046C2×C4711yescharacteristic, complemented
457#2012C2×C4711yescharacteristic, complemented
458#2004C2×C4711yescharacteristic, complemented
459#1907C2×C4711yescharacteristic, complemented
460#1883C2×C4711yescharacteristic, complemented
461#1876C2×C4711yescharacteristic, complemented
462#1866C2×C4711yescharacteristic, complemented
463#1792C2×C4711yescharacteristic, complemented
464C2×C47—21no—
465C2×C47—21no—
466C2×C47—42no—
467C2×C47—42no—
468C2×C47—81no—
469C2×C47—82no—
470C2×C47—161no—
471C2×C47#241011yescharacteristic
472C2×C47#328811yescharacteristic
473C2×C47#329011yescharacteristic
474C2×2−1+4C22×C4711yescharacteristic
475C2×H(5,𝔽2)C22×C4711yescharacteristic
476#577—24no—
477#577—24no—
478C2×#137—21no—
479C2×#137C22×C4711yescharacteristic
480C2×AGL(1,ℤ/8)—21no—
481C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
482C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
483C2×AGL(1,ℤ/8)C22×C4711yescharacteristic, complemented
484C2×#135—21no—
485C2×#135C22×C4711yescharacteristic
486C22×SD16—21no—
487C22×SD16C22×C4711yescharacteristic
488C22×D8C22×C4711yescharacteristic
489C2×#131C22×C4711yescharacteristic
490C2×#131C22×C4711yescharacteristic, complemented
491#535C22×C4711yescharacteristic
492C2×#124C22×C4711yescharacteristic, complemented
493#520C22×C4711yescharacteristic, complemented
494#472—24no—
495#464—21no—
496#463—21no—
497#460—21no—
498#459—21no—
499#454—24no—
500#449—21no—
501#449—21no—
502#447—21no—
503#447—21no—
504C2×#108C22×C4711yescharacteristic, complemented
505#424C22×C4711yescharacteristic, complemented
506C2×#104C22×C4711yescharacteristic
507C2×#104C22×C4711yescharacteristic
508C2×#104C22×C4711yescharacteristic, complemented
509#419—21no—
510#419C22×C4711yescharacteristic, complemented
511#418C22×C4711yescharacteristic
512#417—21no—
513#417C22×C4711yescharacteristic
514#417C22×C4711yescharacteristic
515#416—21no—
516#416C22×C4711yescharacteristic
517C2×#103—21no—
518C2×#103C22×C4711yescharacteristic, complemented
519C2×#102C22×C4711yescharacteristic, complemented
520C2×#101C22×C4711yescharacteristic, complemented
521C2×#100C22×C4711yescharacteristic
522C2×#100C22×C4711yescharacteristic, complemented
523#408C22×C4711yescharacteristic
524#390C22×C4711yescharacteristic
525#343C22×C4711yescharacteristic, complemented
526#341C22×C4711yescharacteristic, complemented
527#339C22×C4711yescharacteristic, complemented
528#336C22×C4711yescharacteristic, complemented
529C47#2446011yescharacteristic, direct product factor, Sylow
5302−1+4—22no—
5312−1+4—22no—
5322−1+4—41no—
5332−1+4D4×C4714yescomplemented
534H(5,𝔽2)—22no—
535H(5,𝔽2)—22no—
536H(5,𝔽2)—22no—
537H(5,𝔽2)—41no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—41no—
543C2×#41C23×C4711yescharacteristic
544C2×#41C23×C4711yescharacteristic
545C2×#41C23×C4711yescharacteristic
546C22×Q8—21no—
547C22×Q8—21no—
548C22×Q8C23×C4711yescharacteristic
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—41no—
552C22×D4C23×C4711yescharacteristic
553C22×D4C23×C4711yescharacteristic
554#137—28no—
555#137—22no—
556#137—22no—
557AGL(1,ℤ/8)—28no—
558AGL(1,ℤ/8)—22no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—22no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)D4×C4714yescomplemented
564#135—28no—
565#135—22no—
566#135—22no—
567C2×Q16—21no—
568C2×Q16D4×C4711yescharacteristic
569C2×SD16—28no—
570C2×SD16—21no—
571C2×SD16—22no—
572C2×SD16—21no—
573C2×SD16—22no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16D4×C4711yescharacteristic
579C2×SD16D4×C4711yescharacteristic
580C2×D8—21no—
581C2×D8—22no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—21no—
585C2×D8—21no—
586C2×D8—41no—
587C2×D8D4×C4711yescharacteristic
588#131—22no—
589#131—22no—
590#131—22no—
591#131—41no—
592C2×M16—21no—
593C2×M16—21no—
594C2×M16C23×C4711yescharacteristic
595C2×M16C23×C4711yescharacteristic
596C2×M16C23×C4711yescharacteristic
597C2×M16C23×C4711yescharacteristic
598C22×C8—21no—
599C22×C8—21no—
600C22×C8C23×C4711yescharacteristic
601C22×C8C23×C4711yescharacteristic
602#127—21no—
603#124—22no—
604#124—21no—
605#124—41no—
606#121—21no—
607#121—21no—
608#120—41no—
609C4×Q8—21no—
610C4×D4—21no—
611C4×D4—41no—
612#117—21no—
613#117C23×C4711yescharacteristic
614C2×C4⋊C4—21no—
615C2×C4⋊C4C23×C4711yescharacteristic
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C42C23×C4711yescharacteristic
619#108—22no—
620C4⋊C8—21no—
621C4⋊C8—21no—
622#104—22no—
623#104—22no—
624#104—41no—
625#103—21no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103—21no—
631#103D4×C4711yescharacteristic
632#103D4×C4711yescharacteristic
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102D4×C4711yescharacteristic
640#102D4×C4711yescharacteristic
641#101—22no—
642#100—22no—
643#100—22no—
644C22⋊C8—21no—
645C22⋊C8—21no—
646C24—21no—
647C24—21no—
648C24—41no—
649#41—21no—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—24no—
654#41—24no—
655#41—24no—
656#41—21no—
657#41—21no—
658#41—21no—
659#41—21no—
660#41—44no—
661#41—42no—
662#41—42no—
663#41—42no—
664#41—44no—
665#41—42no—
666#41—42no—
667#41C2×D4×C4712yes—
668#41C2×D4×C4712yes—
669#41C2×D4×C4712yes—
670#41#41×C4712yes—
671C2×Q8—21no—
672C2×Q8—24no—
673C2×Q8—24no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—41no—
679C2×Q8—42no—
680C2×Q8—42no—
681C2×Q8C2×D4×C4712yes—
682C2×Q8C2×D4×C4711yescharacteristic
683C2×Q8C2×D4×C4711yescharacteristic
684C2×Q8C2×D4×C4711yescharacteristic
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—24no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—42no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—42no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—41no—
709C2×D4—42no—
710C2×D4C2×D4×C4712yes—
711C2×D4C2×D4×C4711yescharacteristic
712C2×D4C2×D4×C4711yescharacteristic
713C2×D4C2×D4×C4711yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—41no—
724C22×C4C24×C4711yescharacteristic
725Q16—24no—
726Q16—22no—
727SD16—24no—
728SD16—24no—
729SD16—24no—
730SD16—22no—
731SD16—24no—
732SD16—22no—
733SD16—42no—
734SD16—42no—
735D8—24no—
736D8—22no—
737D8—42no—
738D8—42no—
739D8—42no—
740D8—42no—
741M16—24no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—21no—
749M16—42no—
750M16C2×D4×C4712yes—
751C2×C8—24no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—42no—
761C2×C8C2×D4×C4711yescharacteristic
762C2×C8C2×D4×C4711yescharacteristic
763C2×C8C2×D4×C4711yescharacteristic
764C2×C8C2×D4×C4711yescharacteristic
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—41no—
768C4⋊C4C2×D4×C4711yescharacteristic
769C4⋊C4C2×D4×C4711yescharacteristic
770C22⋊C4—21no—
771C22⋊C4—41no—
772C22⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—44no—
775C22⋊C4—82no—
776C42—21no—
777C42—21no—
778C42—21no—
779C42—41no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—44no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—81no—
791C23—81no—
792C23—81no—
793C23—81no—
794C23—161no—
795C23—161no—
796C23H(5,𝔽2)×C4711yescharacteristic
797Q8—21no—
798Q8—21no—
799Q8—22no—
800Q8—21no—
801Q8—22no—
802Q8—21no—
803Q8—44no—
804Q8—41no—
805Q8—41no—
806Q8#120×C4712yes—
807Q8#121×C4712yes—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—21no—
814D4—21no—
815D4—22no—
816D4—21no—
817D4—21no—
818D4—44no—
819D4—44no—
820D4—44no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—161no—
830D4—161no—
831D4#120×C4712yes—
832D4#121×C4712yes—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—81no—
855C2×C4—161no—
856C2×C4C22×D4×C4711yescharacteristic
857C2×C4C22×D4×C4711yescharacteristic
858C2×C4C22×D4×C4711yescharacteristic
859C2×C4C22×D4×C4711yescharacteristic
860C2×C4C2×#41×C4711yescharacteristic
861C2×C4H(5,𝔽2)×C4711yescharacteristic
862C8—21no—
863C8—22no—
864C8—21no—
865C8—21no—
866C8—21no—
867C8—41no—
868C8—41no—
869C8—41no—
870C22—21no—
871C22—21no—
872C22—22no—
873C22—22no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—42no—
882C22—82no—
883C22—82no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—161no—
890C22—161no—
891C22—164no—
892C22C47×#53411yescharacteristic
893C22D42×C4711yescharacteristic
894C22C47×#54611yescharacteristic
895C4—22no—
896C4—22no—
897C4—41no—
898C4—41no—
899C4—41no—
900C4—42no—
901C4—81no—
902C4—81no—
903C4C2×#120×C4711yescharacteristic
904C4C2×#121×C4711yescharacteristic
905C4D42×C4711yescharacteristic
906C4C47×#54611yescharacteristic
907C2—21no—
908C2—21no—
909C2—42no—
910C2—42no—
911C2—81no—
912C2—82no—
913C2—161no—
914C2C47×#241011yescharacteristic
915C2C47×#328811yescharacteristic
916C2C47×#329011yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#577C2semidirect
2. C2×C47×#472C2semidirect
3. C47×#3045C2semidirect
4. C2×C47×#454C2semidirect
5. C47×#3008C2semidirect
6. C47×#2898C2semidirect
7. C47×#2052C2semidirect
8. C47×#2046C2semidirect
9. C47×#2012C2semidirect
10. C47×#2004C2semidirect
11. C47×#1907C2semidirect
12. C47×#1883C2semidirect
13. C47×#1876C2semidirect
14. C47×#1866C2semidirect
15. C47×#1792C2semidirect
25. C2×AGL(1,ℤ/8)×C47C22semidirect
32. C2×#131×C47C22semidirect
34. C2×#124×C47C22semidirect
35. C47×#520C22semidirect
46. C2×#108×C47C22semidirect
47. C47×#424C22semidirect
50. C2×#104×C47C22semidirect
52. C47×#419C22semidirect
60. C2×#103×C47C22semidirect
61. C2×#102×C47C22semidirect
62. C2×#101×C47C22semidirect
64. C2×#100×C47C22semidirect
67. C47×#343C22semidirect
68. C47×#341C22semidirect
69. C47×#339C22semidirect
70. C47×#336C22semidirect
74. 2−1+4×C47D4semidirect
104. AGL(1,ℤ/8)×C47D4semidirect
411. #24460C47direct (N × H)
449. C2×#577C2×C47semidirect
450. C2×#472C2×C47semidirect
451. #3045C2×C47semidirect
452. C2×#454C2×C47semidirect
453. #3008C2×C47semidirect
454. #2898C2×C47semidirect
455. #2052C2×C47semidirect
456. #2046C2×C47semidirect
457. #2012C2×C47semidirect
458. #2004C2×C47semidirect
459. #1907C2×C47semidirect
460. #1883C2×C47semidirect
461. #1876C2×C47semidirect
462. #1866C2×C47semidirect
463. #1792C2×C47semidirect
483. C2×AGL(1,ℤ/8)C22×C47semidirect
490. C2×#131C22×C47semidirect
492. C2×#124C22×C47semidirect
493. #520C22×C47semidirect
504. C2×#108C22×C47semidirect
505. #424C22×C47semidirect
508. C2×#104C22×C47semidirect
510. #419C22×C47semidirect
518. C2×#103C22×C47semidirect
519. C2×#102C22×C47semidirect
520. C2×#101C22×C47semidirect
522. C2×#100C22×C47semidirect
525. #343C22×C47semidirect
526. #341C22×C47semidirect
527. #339C22×C47semidirect
528. #336C22×C47semidirect
529. C47#24460direct (N × H)
533. 2−1+4D4×C47semidirect
563. 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×#5772
C2×C47×#4722
C47×#30452
C2×C47×#4542
C47×#30082
C47×#28982
C47×#20522
C47×#20462
C47×#20122
C47×#20042
C47×#19072
C47×#18832
C47×#18762
C47×#18662
C47×#17922
#2446047