Finite Group Databasebeta

← C47×#24457 #26064155

Subgroups — C47×#24457 #26064155

Order 12032.

1376 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#577C211yesmaximal, characteristic, complemented
2C2×C47×#471C211yesmaximal, characteristic, complemented
3C47×#3045C211yesmaximal, characteristic, complemented
4C2×C47×#453C211yesmaximal, characteristic, complemented
5C47×#3010C211yesmaximal, characteristic, complemented
6C47×#2897C211yesmaximal, characteristic, complemented
7C47×#2051C211yesmaximal, characteristic, complemented
8C47×#2046C211yesmaximal, characteristic, complemented
9C47×#2014C211yesmaximal, characteristic, complemented
10C47×#2002C211yesmaximal, characteristic, complemented
11C47×#1907C211yesmaximal, characteristic, complemented
12C47×#1882C211yesmaximal, characteristic, complemented
13C47×#1876C211yesmaximal, characteristic, complemented
14C47×#1866C211yesmaximal, characteristic, complemented
15C47×#1793C211yesmaximal, 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
26C2×#135×C47—21no—
27C2×#135×C47C2211yescharacteristic
28C22×SD16×C47—21no—
29C22×SD16×C47C2211yescharacteristic
30C22×SD16×C47C2211yescharacteristic, complemented
31C2×#131×C47C2211yescharacteristic
32C2×#131×C47C2211yescharacteristic
33C47×#535C2211yescharacteristic, complemented
34C2×#127×C47C2211yescharacteristic
35C47×#520C2211yescharacteristic
36C47×#471—24no—
37C47×#464—21no—
38C47×#463—21no—
39C47×#460—21no—
40C47×#459—21no—
41C47×#453—24no—
42C47×#449—21no—
43C47×#449—21no—
44C47×#448—21no—
45C47×#448—21no—
46C2×#108×C47C2211yescharacteristic, complemented
47C47×#424C2211yescharacteristic, complemented
48C2×#104×C47C2211yescharacteristic
49C2×#104×C47C2211yescharacteristic
50C2×#104×C47C2211yescharacteristic, complemented
51C47×#419C2211yescharacteristic, complemented
52C47×#418—21no—
53C47×#418C2211yescharacteristic
54C47×#417—21no—
55C47×#417C2211yescharacteristic
56C47×#417C2211yescharacteristic, complemented
57C47×#416—21no—
58C47×#416C2211yescharacteristic
59C2×#102×C47—21no—
60C2×#102×C47C2211yescharacteristic
61C2×#102×C47C2211yescharacteristic, complemented
62C2×#101×C47C2211yescharacteristic, complemented
63C2×#100×C47C2211yescharacteristic
64C2×#100×C47C2211yescharacteristic, complemented
65C47×#408C2211yescharacteristic, complemented
66C47×#391C2211yescharacteristic, complemented
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—22no—
742−1+4×C47—41no—
75H(5,𝔽2)×C47—22no—
76H(5,𝔽2)×C47—22no—
77H(5,𝔽2)×C47—41no—
78H(5,𝔽2)×C47D414yescomplemented
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×C47—41no—
94C22×D4×C47C2311yescharacteristic
95C22×D4×C47C2311yescharacteristic
96#137×C47—28no—
97#137×C47—22no—
98#137×C47D414yescomplemented
99AGL(1,ℤ/8)×C47—28no—
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)×C47—22no—
105AGL(1,ℤ/8)×C47—22no—
106#135×C47—28no—
107#135×C47—22no—
108#135×C47—22no—
109C2×Q16×C47—21no—
110C2×Q16×C47D411yescharacteristic, complemented
111C2×SD16×C47—28no—
112C2×SD16×C47—21no—
113C2×SD16×C47—22no—
114C2×SD16×C47—21no—
115C2×SD16×C47—22no—
116C2×SD16×C47—21no—
117C2×SD16×C47—22no—
118C2×SD16×C47—21no—
119C2×SD16×C47—21no—
120C2×SD16×C47—21no—
121C2×SD16×C47—21no—
122C2×SD16×C47—21no—
123C2×SD16×C47—41no—
124C2×SD16×C47D411yescharacteristic, complemented
125C2×SD16×C47D411yescharacteristic, complemented
126C2×D8×C47—21no—
127C2×D8×C47—21no—
128C2×D8×C47—21no—
129C2×D8×C47D411yescharacteristic, complemented
130#131×C47—22no—
131#131×C47—22no—
132#131×C47—22no—
133#131×C47—41no—
134C2×M16×C47—21no—
135C2×M16×C47—21no—
136C2×M16×C47C2311yescharacteristic
137C2×M16×C47C2311yescharacteristic
138C2×M16×C47C2311yescharacteristic
139C2×M16×C47C2311yescharacteristic
140C22×C8×C47—21no—
141C22×C8×C47—21no—
142C22×C8×C47C2311yescharacteristic
143C22×C8×C47C2311yescharacteristic
144#127×C47—22no—
145#127×C47—21no—
146#127×C47—41no—
147#124×C47—21no—
148#121×C47—21no—
149#121×C47—21no—
150#120×C47—41no—
151C4×Q8×C47—21no—
152C4×D4×C47—21no—
153C4×D4×C47—41no—
154#117×C47—21no—
155#117×C47C2311yescharacteristic
156C2×C4⋊C4×C47—21no—
157C2×C4⋊C4×C47C2311yescharacteristic
158C2×C42×C47C2311yescharacteristic
159#108×C47—22no—
160C4⋊C8×C47—21no—
161C4⋊C8×C47—21no—
162#104×C47—22no—
163#104×C47—22no—
164#104×C47—41no—
165#103×C47—21no—
166#103×C47—21no—
167#103×C47—21no—
168#103×C47—21no—
169#103×C47D411yescharacteristic, complemented
170#103×C47D411yescharacteristic, complemented
171#102×C47—21no—
172#102×C47—21no—
173#102×C47—21no—
174#102×C47—21no—
175#102×C47—21no—
176#102×C47—21no—
177#102×C47—21no—
178#102×C47—21no—
179#102×C47D411yescharacteristic, complemented
180#102×C47D411yescharacteristic, complemented
181#101×C47—22no—
182#100×C47—22no—
183#100×C47—22no—
184C22⋊C8×C47—21no—
185C22⋊C8×C47—21no—
186#95×C47—41no—
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—42no—
202#41×C47—44no—
203#41×C47—42no—
204#41×C47—42no—
205#41×C47—42no—
206#41×C47—44no—
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—21no—
215C2×Q8×C47—21no—
216C2×Q8×C47—21no—
217C2×Q8×C47—21no—
218C2×Q8×C47—41no—
219C2×Q8×C47—42no—
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—24no—
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—21no—
242C2×D4×C47—42no—
243C2×D4×C47—42no—
244C2×D4×C47—41no—
245C2×D4×C47—41no—
246C2×D4×C47—41no—
247C2×D4×C47—41no—
248C2×D4×C47—44no—
249C2×D4×C47—44no—
250C2×D4×C47—41no—
251C2×D4×C47—44no—
252C2×D4×C47—82no—
253C2×D4×C47—82no—
254C2×D4×C47C2×D411yescharacteristic
255C2×D4×C47C2×D412yes—
256C2×D4×C47C2×D411yescharacteristic
257C2×D4×C47C2×D411yescharacteristic
258C22×C4×C47—21no—
259C22×C4×C47—21no—
260C22×C4×C47—21no—
261C22×C4×C47—21no—
262C22×C4×C47—21no—
263C22×C4×C47—21no—
264C22×C4×C47—41no—
265C22×C4×C47—41no—
266C22×C4×C47—41no—
267C22×C4×C47—41no—
268C22×C4×C47C2411yescharacteristic
269Q16×C47—24no—
270Q16×C47—22no—
271SD16×C47—24no—
272SD16×C47—24no—
273SD16×C47—24no—
274SD16×C47—22no—
275SD16×C47—22no—
276SD16×C47—24no—
277SD16×C47—42no—
278SD16×C47—42no—
279SD16×C47—42no—
280SD16×C47—42no—
281D8×C47—24no—
282D8×C47—22no—
283D8×C47—42no—
284D8×C47—42no—
285M16×C47—24no—
286M16×C47—21no—
287M16×C47—21no—
288M16×C47—21no—
289M16×C47—21no—
290M16×C47—21no—
291M16×C47—21no—
292M16×C47—21no—
293M16×C47—42no—
294M16×C47C2×D412yes—
295C2×C8×C47—24no—
296C2×C8×C47—21no—
297C2×C8×C47—21no—
298C2×C8×C47—21no—
299C2×C8×C47—21no—
300C2×C8×C47—21no—
301C2×C8×C47—21no—
302C2×C8×C47—21no—
303C2×C8×C47—21no—
304C2×C8×C47—42no—
305C2×C8×C47C2×D411yescharacteristic
306C2×C8×C47C2×D411yescharacteristic
307C2×C8×C47C2×D411yescharacteristic
308C2×C8×C47C2×D411yescharacteristic
309C4⋊C4×C47—21no—
310C4⋊C4×C47—21no—
311C4⋊C4×C47—41no—
312C4⋊C4×C47C2×D411yescharacteristic
313C4⋊C4×C47C2×D411yescharacteristic
314C22⋊C4×C47—21no—
315C22⋊C4×C47—41no—
316C22⋊C4×C47—41no—
317C22⋊C4×C47—41no—
318C42×C47—21no—
319C42×C47—21no—
320C42×C47—21no—
321C42×C47—41no—
322C23×C47—21no—
323C23×C47—21no—
324C23×C47—21no—
325C23×C47—22no—
326C23×C47—44no—
327C23×C47—41no—
328C23×C47—41no—
329C23×C47—41no—
330C23×C47—41no—
331C23×C47—41no—
332C23×C47—81no—
333C23×C47—81no—
334C23×C47—81no—
335C23×C47—81no—
336C23×C47—161no—
337C23×C47—161no—
338C23×C47H(5,𝔽2)11yescharacteristic
339Q8×C47—21no—
340Q8×C47—21no—
341Q8×C47—22no—
342Q8×C47—21no—
343Q8×C47—22no—
344Q8×C47—21no—
345Q8×C47—44no—
346Q8×C47—41no—
347Q8×C47—41no—
348Q8×C47#12012yes—
349Q8×C47#12112yes—
350D4×C47—22no—
351D4×C47—22no—
352D4×C47—22no—
353D4×C47—22no—
354D4×C47—21no—
355D4×C47—22no—
356D4×C47—22no—
357D4×C47—21no—
358D4×C47—21no—
359D4×C47—21no—
360D4×C47—44no—
361D4×C47—44no—
362D4×C47—44no—
363D4×C47—41no—
364D4×C47—41no—
365D4×C47—41no—
366D4×C47—41no—
367D4×C47—41no—
368D4×C47—41no—
369D4×C47—41no—
370D4×C47—41no—
371D4×C47—88no—
372D4×C47—161no—
373D4×C47—161no—
374D4×C47#12012yes—
375D4×C47#12112yes—
376C2×C4×C47—21no—
377C2×C4×C47—21no—
378C2×C4×C47—22no—
379C2×C4×C47—22no—
380C2×C4×C47—22no—
381C2×C4×C47—22no—
382C2×C4×C47—22no—
383C2×C4×C47—21no—
384C2×C4×C47—21no—
385C2×C4×C47—21no—
386C2×C4×C47—22no—
387C2×C4×C47—44no—
388C2×C4×C47—44no—
389C2×C4×C47—41no—
390C2×C4×C47—44no—
391C2×C4×C47—41no—
392C2×C4×C47—41no—
393C2×C4×C47—41no—
394C2×C4×C47—41no—
395C2×C4×C47—41no—
396C2×C4×C47—41no—
397C2×C4×C47—81no—
398C2×C4×C47—161no—
399C2×C4×C47C22×D411yescharacteristic
400C2×C4×C47C22×D411yescharacteristic
401C2×C4×C47C22×D411yescharacteristic
402C2×C4×C47C22×D411yescharacteristic
403C2×C4×C47C2×#4111yescharacteristic
404C2×C4×C47H(5,𝔽2)11yescharacteristic
405C8×C47—21no—
406C8×C47—22no—
407C8×C47—21no—
408C8×C47—21no—
409C8×C47—21no—
410C8×C47—41no—
411C8×C47—41no—
412C8×C47—41no—
413#24457C4711yesmaximal, characteristic, direct product factor, Sylow
414C22×C47—21no—
415C22×C47—21no—
416C22×C47—22no—
417C22×C47—22no—
418C22×C47—41no—
419C22×C47—41no—
420C22×C47—41no—
421C22×C47—41no—
422C22×C47—41no—
423C22×C47—42no—
424C22×C47—41no—
425C22×C47—41no—
426C22×C47—82no—
427C22×C47—82no—
428C22×C47—81no—
429C22×C47—81no—
430C22×C47—81no—
431C22×C47—81no—
432C22×C47—81no—
433C22×C47—161no—
434C22×C47—161no—
435C22×C47—164no—
436C22×C47#53411yescharacteristic
437C22×C47D4211yescharacteristic
438C22×C47#54611yescharacteristic
439C4×C47—22no—
440C4×C47—22no—
441C4×C47—42no—
442C4×C47—41no—
443C4×C47—42no—
444C4×C47—41no—
445C4×C47—41no—
446C4×C47—81no—
447C4×C47C2×#12011yescharacteristic
448C4×C47C2×#12111yescharacteristic
449C4×C47D4211yescharacteristic
450C4×C47#54611yescharacteristic
451C2×#577C2×C4711yescharacteristic, complemented
452C2×#471C2×C4711yescharacteristic, complemented
453#3045C2×C4711yescharacteristic, complemented
454C2×#453C2×C4711yescharacteristic, complemented
455#3010C2×C4711yescharacteristic, complemented
456#2897C2×C4711yescharacteristic, complemented
457#2051C2×C4711yescharacteristic, complemented
458#2046C2×C4711yescharacteristic, complemented
459#2014C2×C4711yescharacteristic, complemented
460#2002C2×C4711yescharacteristic, complemented
461#1907C2×C4711yescharacteristic, complemented
462#1882C2×C4711yescharacteristic, complemented
463#1876C2×C4711yescharacteristic, complemented
464#1866C2×C4711yescharacteristic, complemented
465#1793C2×C4711yescharacteristic, complemented
466C2×C47—21no—
467C2×C47—21no—
468C2×C47—42no—
469C2×C47—42no—
470C2×C47—81no—
471C2×C47—82no—
472C2×C47—161no—
473C2×C47#241011yescharacteristic
474C2×C47#328811yescharacteristic
475C2×C47#329111yescharacteristic
476C2×2−1+4C22×C4711yescharacteristic
477C2×H(5,𝔽2)C22×C4711yescharacteristic
478#577—24no—
479#577—24no—
480C2×#137—21no—
481C2×#137C22×C4711yescharacteristic
482C2×AGL(1,ℤ/8)—21no—
483C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
484C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
485C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
486C2×#135—21no—
487C2×#135C22×C4711yescharacteristic
488C22×SD16—21no—
489C22×SD16C22×C4711yescharacteristic
490C22×SD16C22×C4711yescharacteristic, complemented
491C2×#131C22×C4711yescharacteristic
492C2×#131C22×C4711yescharacteristic
493#535C22×C4711yescharacteristic, complemented
494C2×#127C22×C4711yescharacteristic
495#520C22×C4711yescharacteristic
496#471—24no—
497#464—21no—
498#463—21no—
499#460—21no—
500#459—21no—
501#453—24no—
502#449—21no—
503#449—21no—
504#448—21no—
505#448—21no—
506C2×#108C22×C4711yescharacteristic, complemented
507#424C22×C4711yescharacteristic, complemented
508C2×#104C22×C4711yescharacteristic
509C2×#104C22×C4711yescharacteristic
510C2×#104C22×C4711yescharacteristic, complemented
511#419C22×C4711yescharacteristic, complemented
512#418—21no—
513#418C22×C4711yescharacteristic
514#417—21no—
515#417C22×C4711yescharacteristic
516#417C22×C4711yescharacteristic, complemented
517#416—21no—
518#416C22×C4711yescharacteristic
519C2×#102—21no—
520C2×#102C22×C4711yescharacteristic
521C2×#102C22×C4711yescharacteristic, complemented
522C2×#101C22×C4711yescharacteristic, complemented
523C2×#100C22×C4711yescharacteristic
524C2×#100C22×C4711yescharacteristic, complemented
525#408C22×C4711yescharacteristic, complemented
526#391C22×C4711yescharacteristic, complemented
527#343C22×C4711yescharacteristic, complemented
528#341C22×C4711yescharacteristic, complemented
529#339C22×C4711yescharacteristic, complemented
530#336C22×C4711yescharacteristic, complemented
531C47#2445711yescharacteristic, direct product factor, Sylow
5322−1+4—22no—
5332−1+4—22no—
5342−1+4—22no—
5352−1+4—41no—
536H(5,𝔽2)—22no—
537H(5,𝔽2)—22no—
538H(5,𝔽2)—41no—
539H(5,𝔽2)D4×C4714yescomplemented
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—41no—
545C2×#41C23×C4711yescharacteristic
546C2×#41C23×C4711yescharacteristic
547C2×#41C23×C4711yescharacteristic
548C22×Q8—21no—
549C22×Q8—21no—
550C22×Q8C23×C4711yescharacteristic
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4—41no—
555C22×D4C23×C4711yescharacteristic
556C22×D4C23×C4711yescharacteristic
557#137—28no—
558#137—22no—
559#137D4×C4714yescomplemented
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)—22no—
565AGL(1,ℤ/8)—22no—
566AGL(1,ℤ/8)—22no—
567#135—28no—
568#135—22no—
569#135—22no—
570C2×Q16—21no—
571C2×Q16D4×C4711yescharacteristic, complemented
572C2×SD16—28no—
573C2×SD16—21no—
574C2×SD16—22no—
575C2×SD16—21no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—21no—
579C2×SD16—21no—
580C2×SD16—21no—
581C2×SD16—21no—
582C2×SD16—21no—
583C2×SD16—21no—
584C2×SD16—41no—
585C2×SD16D4×C4711yescharacteristic, complemented
586C2×SD16D4×C4711yescharacteristic, complemented
587C2×D8—21no—
588C2×D8—21no—
589C2×D8—21no—
590C2×D8D4×C4711yescharacteristic, complemented
591#131—22no—
592#131—22no—
593#131—22no—
594#131—41no—
595C2×M16—21no—
596C2×M16—21no—
597C2×M16C23×C4711yescharacteristic
598C2×M16C23×C4711yescharacteristic
599C2×M16C23×C4711yescharacteristic
600C2×M16C23×C4711yescharacteristic
601C22×C8—21no—
602C22×C8—21no—
603C22×C8C23×C4711yescharacteristic
604C22×C8C23×C4711yescharacteristic
605#127—22no—
606#127—21no—
607#127—41no—
608#124—21no—
609#121—21no—
610#121—21no—
611#120—41no—
612C4×Q8—21no—
613C4×D4—21no—
614C4×D4—41no—
615#117—21no—
616#117C23×C4711yescharacteristic
617C2×C4⋊C4—21no—
618C2×C4⋊C4C23×C4711yescharacteristic
619C2×C42C23×C4711yescharacteristic
620#108—22no—
621C4⋊C8—21no—
622C4⋊C8—21no—
623#104—22no—
624#104—22no—
625#104—41no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103D4×C4711yescharacteristic, complemented
631#103D4×C4711yescharacteristic, complemented
632#102—21no—
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102D4×C4711yescharacteristic, complemented
641#102D4×C4711yescharacteristic, complemented
642#101—22no—
643#100—22no—
644#100—22no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647#95—41no—
648C24—21no—
649C24—21no—
650C24—41no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—24no—
656#41—24no—
657#41—24no—
658#41—21no—
659#41—21no—
660#41—21no—
661#41—21no—
662#41—42no—
663#41—44no—
664#41—42no—
665#41—42no—
666#41—42no—
667#41—44no—
668#41—42no—
669#41C2×D4×C4712yes—
670#41C2×D4×C4712yes—
671#41C2×D4×C4712yes—
672#41#41×C4712yes—
673C2×Q8—21no—
674C2×Q8—24no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—41no—
680C2×Q8—42no—
681C2×Q8—42no—
682C2×Q8—42no—
683C2×Q8C2×D4×C4712yes—
684C2×Q8C2×D4×C4711yescharacteristic
685C2×Q8C2×D4×C4711yescharacteristic
686C2×Q8C2×D4×C4711yescharacteristic
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—24no—
690C2×D4—24no—
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—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—41no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—41no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—41no—
712C2×D4—44no—
713C2×D4—82no—
714C2×D4—82no—
715C2×D4C2×D4×C4712yes—
716C2×D4C2×D4×C4711yescharacteristic
717C2×D4C2×D4×C4711yescharacteristic
718C2×D4C2×D4×C4711yescharacteristic
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—41no—
726C22×C4—41no—
727C22×C4—41no—
728C22×C4—41no—
729C22×C4C24×C4711yescharacteristic
730Q16—24no—
731Q16—22no—
732SD16—24no—
733SD16—24no—
734SD16—24no—
735SD16—22no—
736SD16—22no—
737SD16—24no—
738SD16—42no—
739SD16—42no—
740SD16—42no—
741SD16—42no—
742D8—24no—
743D8—22no—
744D8—42no—
745D8—42no—
746M16—24no—
747M16—21no—
748M16—21no—
749M16—21no—
750M16—21no—
751M16—21no—
752M16—21no—
753M16—21no—
754M16—42no—
755M16C2×D4×C4712yes—
756C2×C8—24no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—42no—
766C2×C8C2×D4×C4711yescharacteristic
767C2×C8C2×D4×C4711yescharacteristic
768C2×C8C2×D4×C4711yescharacteristic
769C2×C8C2×D4×C4711yescharacteristic
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—41no—
773C4⋊C4C2×D4×C4711yescharacteristic
774C4⋊C4C2×D4×C4711yescharacteristic
775C22⋊C4—21no—
776C22⋊C4—41no—
777C22⋊C4—41no—
778C22⋊C4—41no—
779C42—21no—
780C42—21no—
781C42—21no—
782C42—41no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—81no—
794C23—81no—
795C23—81no—
796C23—81no—
797C23—161no—
798C23—161no—
799C23H(5,𝔽2)×C4711yescharacteristic
800Q8—21no—
801Q8—21no—
802Q8—22no—
803Q8—21no—
804Q8—22no—
805Q8—21no—
806Q8—44no—
807Q8—41no—
808Q8—41no—
809Q8#120×C4712yes—
810Q8#121×C4712yes—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—21no—
816D4—22no—
817D4—22no—
818D4—21no—
819D4—21no—
820D4—21no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—88no—
833D4—161no—
834D4—161no—
835D4#120×C4712yes—
836D4#121×C4712yes—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—41no—
851C2×C4—44no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—81no—
859C2×C4—161no—
860C2×C4C22×D4×C4711yescharacteristic
861C2×C4C22×D4×C4711yescharacteristic
862C2×C4C22×D4×C4711yescharacteristic
863C2×C4C22×D4×C4711yescharacteristic
864C2×C4C2×#41×C4711yescharacteristic
865C2×C4H(5,𝔽2)×C4711yescharacteristic
866C8—21no—
867C8—22no—
868C8—21no—
869C8—21no—
870C8—21no—
871C8—41no—
872C8—41no—
873C8—41no—
874C22—21no—
875C22—21no—
876C22—22no—
877C22—22no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—42no—
886C22—82no—
887C22—82no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22—161no—
894C22—161no—
895C22—164no—
896C22C47×#53411yescharacteristic
897C22D42×C4711yescharacteristic
898C22C47×#54611yescharacteristic
899C4—22no—
900C4—22no—
901C4—42no—
902C4—41no—
903C4—41no—
904C4—41no—
905C4—42no—
906C4—81no—
907C4C2×#120×C4711yescharacteristic
908C4C2×#121×C4711yescharacteristic
909C4D42×C4711yescharacteristic
910C4C47×#54611yescharacteristic
911C2—21no—
912C2—21no—
913C2—42no—
914C2—42no—
915C2—81no—
916C2—82no—
917C2—161no—
918C2C47×#241011yescharacteristic
919C2C47×#328811yescharacteristic
920C2C47×#329111yescharacteristic
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×#471C2semidirect
3. C47×#3045C2semidirect
4. C2×C47×#453C2semidirect
5. C47×#3010C2semidirect
6. C47×#2897C2semidirect
7. C47×#2051C2semidirect
8. C47×#2046C2semidirect
9. C47×#2014C2semidirect
10. C47×#2002C2semidirect
11. C47×#1907C2semidirect
12. C47×#1882C2semidirect
13. C47×#1876C2semidirect
14. C47×#1866C2semidirect
15. C47×#1793C2semidirect
30. C22×SD16×C47C22semidirect
33. C47×#535C22semidirect
46. C2×#108×C47C22semidirect
47. C47×#424C22semidirect
50. C2×#104×C47C22semidirect
51. C47×#419C22semidirect
56. C47×#417C22semidirect
61. C2×#102×C47C22semidirect
62. C2×#101×C47C22semidirect
64. C2×#100×C47C22semidirect
65. C47×#408C22semidirect
66. C47×#391C22semidirect
67. C47×#343C22semidirect
68. C47×#341C22semidirect
69. C47×#339C22semidirect
70. C47×#336C22semidirect
78. H(5,𝔽2)×C47D4semidirect
98. #137×C47D4semidirect
110. C2×Q16×C47D4semidirect
124. C2×SD16×C47D4semidirect
125. C2×SD16×C47D4semidirect
129. C2×D8×C47D4semidirect
169. #103×C47D4semidirect
170. #103×C47D4semidirect
179. #102×C47D4semidirect
180. #102×C47D4semidirect
413. #24457C47direct (N × H)
451. C2×#577C2×C47semidirect
452. C2×#471C2×C47semidirect
453. #3045C2×C47semidirect
454. C2×#453C2×C47semidirect
455. #3010C2×C47semidirect
456. #2897C2×C47semidirect
457. #2051C2×C47semidirect
458. #2046C2×C47semidirect
459. #2014C2×C47semidirect
460. #2002C2×C47semidirect
461. #1907C2×C47semidirect
462. #1882C2×C47semidirect
463. #1876C2×C47semidirect
464. #1866C2×C47semidirect
465. #1793C2×C47semidirect
490. C22×SD16C22×C47semidirect
493. #535C22×C47semidirect
506. C2×#108C22×C47semidirect
507. #424C22×C47semidirect
510. C2×#104C22×C47semidirect
511. #419C22×C47semidirect
516. #417C22×C47semidirect
521. C2×#102C22×C47semidirect
522. C2×#101C22×C47semidirect
524. C2×#100C22×C47semidirect
525. #408C22×C47semidirect
526. #391C22×C47semidirect
527. #343C22×C47semidirect
528. #341C22×C47semidirect
529. #339C22×C47semidirect
530. #336C22×C47semidirect
531. C47#24457direct (N × H)
539. H(5,𝔽2)D4×C47semidirect
559. #137D4×C47semidirect
571. C2×Q16D4×C47semidirect
585. C2×SD16D4×C47semidirect
586. C2×SD16D4×C47semidirect
590. C2×D8D4×C47semidirect
630. #103D4×C47semidirect
631. #103D4×C47semidirect
640. #102D4×C47semidirect
641. #102D4×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×#4712
C47×#30452
C2×C47×#4532
C47×#30102
C47×#28972
C47×#20512
C47×#20462
C47×#20142
C47×#20022
C47×#19072
C47×#18822
C47×#18762
C47×#18662
C47×#17932
#2445747