Finite Group Databasebeta

← C47×#22854 #26062552

Subgroups — C47×#22854 #26062552

Order 12032.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#450C211yesmaximal, characteristic
2C2×C47×#440C211yesmaximal, characteristic, complemented
3C22×#102×C47C211yesmaximal, characteristic
4C47×#2360C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C47C211yesmaximal, characteristic
6C47×#1973C211yesmaximal, characteristic, complemented
7C47×#1936C211yesmaximal, characteristic, complemented
8C47×#1925C211yesmaximal, characteristic, complemented
9C47×#1892C211yesmaximal, characteristic, complemented
10C47×#1880C211yesmaximal, characteristic, complemented
11C47×#1877C211yesmaximal, characteristic, complemented
12C47×#1862C211yesmaximal, characteristic, complemented
13C47×#1852C211yesmaximal, characteristic, complemented
14C47×#1762C211yesmaximal, characteristic, complemented
15C47×#1752C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C2×C22⋊Q8×C47C2211yescharacteristic
21C2×C4×Q8×C47C2211yescharacteristic, complemented
22C2×C4×D4×C47C2211yescharacteristic
23C2×C4×D4×C47C2211yescharacteristic
24C22×C4⋊C4×C47C2211yescharacteristic
25C22×C22⋊C4×C47—21no—
26C47×#450C418yescomplemented
27C47×#440—24no—
28C2×#107×C47C2211yescharacteristic, complemented
29C2×#107×C47C2211yescharacteristic, complemented
30C2×#103×C47C2211yescharacteristic, complemented
31C2×#103×C47C2211yescharacteristic, complemented
32C2×#102×C47—24no—
33C2×#102×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C2×#102×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×C22⋊C8×C47C2211yescharacteristic
40C2×#97×C47C2211yescharacteristic, complemented
41C2×#97×C47C2211yescharacteristic, complemented
42C47×#391C2211yescharacteristic, complemented
43C47×#390C2211yescharacteristic
44C47×#390C2211yescharacteristic
45C47×#389—21no—
46C47×#389C2211yescharacteristic, complemented
47C47×#387—21no—
48C47×#386—21no—
49C47×#386—21no—
50C47×#385—21no—
51C47×#380C2211yescharacteristic
52C47×#379—21no—
53C4×C4⋊C4×C47C2211yescharacteristic, complemented
54C4×C22⋊C4×C47—21no—
55C4×C22⋊C4×C47C2211yescharacteristic
56C47×#340C2211yescharacteristic, complemented
57C47×#340C2211yescharacteristic, complemented
58C47×#340C2211yescharacteristic, complemented
59C47×#340C2211yescharacteristic, complemented
60C47×#336C2211yescharacteristic, complemented
61C47×#336C2211yescharacteristic, complemented
62C25×C47—21no—
63C22×Q8×C47C2311yescharacteristic
64C22×D4×C47—22no—
65C22×D4×C47—22no—
66C22×D4×C47—21no—
67C22×D4×C47—22no—
68C22×D4×C47—41no—
69C22×D4×C47—41no—
70C22×D4×C47C2×C414yes—
71C22×D4×C47C2311yescharacteristic
72C22×D4×C47C2311yescharacteristic
73C23×C4×C47—21no—
74C23×C4×C47—21no—
75C23×C4×C47—21no—
76C23×C4×C47C2311yescharacteristic
77C2×SD16×C47—22no—
78C2×SD16×C47—22no—
79C2×SD16×C47—41no—
80C2×SD16×C47—41no—
81C2×SD16×C47C2×C414yescomplemented
82C2×SD16×C47C2×C414yescomplemented
83C22×C8×C47—22no—
84C22×C8×C47—22no—
85C22×C8×C47—41no—
86C22×C8×C47C2311yescharacteristic
87C22×C8×C47C2311yescharacteristic
88C22×C8×C47C2311yescharacteristic
89C22×C8×C47C2311yescharacteristic
90C22⋊Q8×C47—22no—
91C22⋊Q8×C47C2×C414yescomplemented
92C4×Q8×C47—22no—
93C4×Q8×C47—41no—
94C4×D4×C47—22no—
95C4×D4×C47—22no—
96C4×D4×C47—41no—
97C4×D4×C47—41no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—22no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—41no—
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—44no—
118C2×C22⋊C4×C47D411yescharacteristic
119C2×C22⋊C4×C47D411yescharacteristic
120C2×C42×C47—21no—
121C2×C42×C47—21no—
122C2×C42×C47C2311yescharacteristic
123C2×C42×C47C2311yescharacteristic
124#107×C47—22no—
125#107×C47—41no—
126#103×C47—22no—
127#103×C47—41no—
128#102×C47—22no—
129#102×C47—22no—
130#102×C47—22no—
131#102×C47C2×C414yescomplemented
132#102×C47C2×C414yescomplemented
133#102×C47D414yes—
134C22⋊C8×C47C2×C414yescomplemented
135#97×C47—22no—
136#97×C47—41no—
137#95×C47—21no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47D411yescharacteristic
143#95×C47D411yescharacteristic
144C24×C47—21no—
145C24×C47—21no—
146C24×C47—24no—
147C24×C47—42no—
148C24×C47—42no—
149C24×C47—42no—
150C24×C47—42no—
151C24×C47—81no—
152C24×C47—81no—
153C24×C47C2×D411yescharacteristic
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47C22×C412yes—
160C2×D4×C47—28no—
161C2×D4×C47—24no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—21no—
169C2×D4×C47—21no—
170C2×D4×C47—44no—
171C2×D4×C47—44no—
172C2×D4×C47—44no—
173C2×D4×C47—42no—
174C2×D4×C47—42no—
175C2×D4×C47C22×C412yes—
176C2×D4×C47C22×C412yes—
177C2×D4×C47C2×D412yes—
178C2×D4×C47#4112yes—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—42no—
190C22×C4×C47—42no—
191C22×C4×C47—42no—
192C22×C4×C47—42no—
193C22×C4×C47—42no—
194C22×C4×C47—42no—
195C22×C4×C47—81no—
196C22×C4×C47—81no—
197C22×C4×C47—81no—
198C22×C4×C47C22×C412yes—
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47#4112yes—
205C22×C4×C47C2411yescharacteristic
206SD16×C47—28no—
207SD16×C47—44no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47—21no—
217C2×C8×C47—44no—
218C2×C8×C47C22×C412yes—
219C2×C8×C47C22×C412yes—
220C2×C8×C47C2×D412yes—
221C4⋊C4×C47—24no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—42no—
231C4⋊C4×C47—42no—
232C4⋊C4×C47—81no—
233C4⋊C4×C47C22×C412yes—
234C4⋊C4×C47C2×D412yes—
235C22⋊C4×C47—24no—
236C22⋊C4×C47—22no—
237C22⋊C4×C47—22no—
238C22⋊C4×C47—42no—
239C22⋊C4×C47—42no—
240C22⋊C4×C47—42no—
241C22⋊C4×C47—42no—
242C22⋊C4×C47—42no—
243C22⋊C4×C47—81no—
244C22⋊C4×C47—81no—
245C42×C47—21no—
246C42×C47—21no—
247C42×C47—21no—
248C42×C47—21no—
249C42×C47—42no—
250C42×C47—81no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—22no—
256C23×C47—22no—
257C23×C47—22no—
258C23×C47—22no—
259C23×C47—48no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—41no—
263C23×C47—41no—
264C23×C47—41no—
265C23×C47—41no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—48no—
271C23×C47—84no—
272C23×C47—84no—
273C23×C47—84no—
274C23×C47—84no—
275C23×C47—84no—
276C23×C47C4×D412yes—
277C23×C47AGL(1,ℤ/8)12yes—
278C23×C47#13712yes—
279C23×C47C22×D411yescharacteristic
280Q8×C47—22no—
281Q8×C47—22no—
282Q8×C47—41no—
283Q8×C47—41no—
284D4×C47—22no—
285D4×C47—22no—
286D4×C47—22no—
287D4×C47—22no—
288D4×C47—22no—
289D4×C47—48no—
290D4×C47—41no—
291D4×C47—41no—
292D4×C47C4×D414yes—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—22no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47—84no—
330C2×C4×C47—84no—
331C2×C4×C47—84no—
332C2×C4×C47C4×D412yes—
333C2×C4×C47C23×C411yescharacteristic
334C2×C4×C47C22×D411yescharacteristic
335C2×C4×C47C2×#4111yescharacteristic
336C2×C4×C47C2×#4111yescharacteristic
337C2×C4×C47H(5,𝔽2)11yescharacteristic
338C2×C4×C47H(5,𝔽2)11yescharacteristic
339C8×C47—22no—
340C8×C47—22no—
341C8×C47—22no—
342C8×C47—41no—
343#22854C4711yesmaximal, characteristic, direct product factor, Sylow
344C22×C47—22no—
345C22×C47—22no—
346C22×C47—22no—
347C22×C47—22no—
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—24no—
351C22×C47—42no—
352C22×C47—42no—
353C22×C47—42no—
354C22×C47—42no—
355C22×C47—42no—
356C22×C47—42no—
357C22×C47—42no—
358C22×C47—42no—
359C22×C47—42no—
360C22×C47—816no—
361C22×C47—81no—
362C22×C47—81no—
363C22×C47—81no—
364C22×C47—81no—
365C22×C47#44014yescomplemented
366C22×C47C2×C4×D411yescharacteristic
367C22×C47D4211yescharacteristic
368C22×C47#54611yescharacteristic
369C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C47C2×#13711yescharacteristic
371C22×C47#57611yescharacteristic
372C22×C47#57711yescharacteristic
373C4×C47—22no—
374C4×C47—42no—
375C4×C47—42no—
376C4×C47—41no—
377C4×C47—42no—
378C4×C47—41no—
379C4×C47—41no—
380C4×C47—41no—
381C4×C47—81no—
382C4×C47—81no—
383C4×C47—81no—
384C4×C47C2×C4×D411yescharacteristic
385C4×C47#51811yescharacteristic
386C4×C47#54611yescharacteristic
387C4×C47#55111yescharacteristic
388C2×#450C2×C4711yescharacteristic
389C2×#440C2×C4711yescharacteristic, complemented
390C22×#102C2×C4711yescharacteristic
391#2360C2×C4711yescharacteristic, complemented
392D4×C22⋊C4C2×C4711yescharacteristic
393#1973C2×C4711yescharacteristic, complemented
394#1936C2×C4711yescharacteristic, complemented
395#1925C2×C4711yescharacteristic, complemented
396#1892C2×C4711yescharacteristic, complemented
397#1880C2×C4711yescharacteristic, complemented
398#1877C2×C4711yescharacteristic, complemented
399#1862C2×C4711yescharacteristic, complemented
400#1852C2×C4711yescharacteristic, complemented
401#1762C2×C4711yescharacteristic, complemented
402#1752C2×C4711yescharacteristic, complemented
403C2×C47—24no—
404C2×C47—44no—
405C2×C47—82no—
406C2×C47#235811yescharacteristic
407C2×C47C2×#44011yescharacteristic
408C2×C47#294611yescharacteristic
409C2×C47#326411yescharacteristic
410C2×C47#326611yescharacteristic
411C2×C47#331011yescharacteristic
412C2×C47#331411yescharacteristic
413C23×D4C22×C4711yescharacteristic
414C22×SD16C22×C4711yescharacteristic
415C22×SD16C22×C4711yescharacteristic
416C23×C8C22×C4711yescharacteristic
417C2×C22⋊Q8C22×C4711yescharacteristic
418C2×C4×Q8C22×C4711yescharacteristic, complemented
419C2×C4×D4C22×C4711yescharacteristic
420C2×C4×D4C22×C4711yescharacteristic
421C22×C4⋊C4C22×C4711yescharacteristic
422C22×C22⋊C4—21no—
423#450C4×C4718yescomplemented
424#440—24no—
425C2×#107C22×C4711yescharacteristic, complemented
426C2×#107C22×C4711yescharacteristic, complemented
427C2×#103C22×C4711yescharacteristic, complemented
428C2×#103C22×C4711yescharacteristic, complemented
429C2×#102—24no—
430C2×#102C22×C4711yescharacteristic
431C2×#102C22×C4711yescharacteristic
432C2×#102C22×C4711yescharacteristic
433C2×#102C22×C4711yescharacteristic
434C2×#102C22×C4711yescharacteristic
435C2×#102C22×C4711yescharacteristic
436C2×C22⋊C8C22×C4711yescharacteristic
437C2×#97C22×C4711yescharacteristic, complemented
438C2×#97C22×C4711yescharacteristic, complemented
439#391C22×C4711yescharacteristic, complemented
440#390C22×C4711yescharacteristic
441#390C22×C4711yescharacteristic
442#389—21no—
443#389C22×C4711yescharacteristic, complemented
444#387—21no—
445#386—21no—
446#386—21no—
447#385—21no—
448#380C22×C4711yescharacteristic
449#379—21no—
450C4×C4⋊C4C22×C4711yescharacteristic, complemented
451C4×C22⋊C4—21no—
452C4×C22⋊C4C22×C4711yescharacteristic
453#340C22×C4711yescharacteristic, complemented
454#340C22×C4711yescharacteristic, complemented
455#340C22×C4711yescharacteristic, complemented
456#340C22×C4711yescharacteristic, complemented
457#336C22×C4711yescharacteristic, complemented
458#336C22×C4711yescharacteristic, complemented
459C47#2285411yescharacteristic, direct product factor, Sylow
460C25—21no—
461C22×Q8C23×C4711yescharacteristic
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4C2×C4×C4714yes—
469C22×D4C23×C4711yescharacteristic
470C22×D4C23×C4711yescharacteristic
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—21no—
474C23×C4C23×C4711yescharacteristic
475C2×SD16—22no—
476C2×SD16—22no—
477C2×SD16—41no—
478C2×SD16—41no—
479C2×SD16C2×C4×C4714yescomplemented
480C2×SD16C2×C4×C4714yescomplemented
481C22×C8—22no—
482C22×C8—22no—
483C22×C8—41no—
484C22×C8C23×C4711yescharacteristic
485C22×C8C23×C4711yescharacteristic
486C22×C8C23×C4711yescharacteristic
487C22×C8C23×C4711yescharacteristic
488C22⋊Q8—22no—
489C22⋊Q8C2×C4×C4714yescomplemented
490C4×Q8—22no—
491C4×Q8—41no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—41no—
495C4×D4—41no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4C23×C4711yescharacteristic
503C2×C4⋊C4C23×C4711yescharacteristic
504C2×C4⋊C4C23×C4711yescharacteristic
505C2×C4⋊C4C23×C4711yescharacteristic
506C2×C4⋊C4C23×C4711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—44no—
516C2×C22⋊C4D4×C4711yescharacteristic
517C2×C22⋊C4D4×C4711yescharacteristic
518C2×C42—21no—
519C2×C42—21no—
520C2×C42C23×C4711yescharacteristic
521C2×C42C23×C4711yescharacteristic
522#107—22no—
523#107—41no—
524#103—22no—
525#103—41no—
526#102—22no—
527#102—22no—
528#102—22no—
529#102C2×C4×C4714yescomplemented
530#102C2×C4×C4714yescomplemented
531#102D4×C4714yes—
532C22⋊C8C2×C4×C4714yescomplemented
533#97—22no—
534#97—41no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95D4×C4711yescharacteristic
541#95D4×C4711yescharacteristic
542C24—21no—
543C24—21no—
544C24—24no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—81no—
550C24—81no—
551C24C2×D4×C4711yescharacteristic
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8C22×C4×C4712yes—
558C2×D4—28no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4C22×C4×C4712yes—
574C2×D4C22×C4×C4712yes—
575C2×D4C2×D4×C4712yes—
576C2×D4#41×C4712yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—81no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4C22×C4×C4712yes—
597C22×C4C2×D4×C4711yescharacteristic
598C22×C4C2×D4×C4711yescharacteristic
599C22×C4C2×D4×C4711yescharacteristic
600C22×C4C2×D4×C4711yescharacteristic
601C22×C4C2×D4×C4711yescharacteristic
602C22×C4#41×C4712yes—
603C22×C4C24×C4711yescharacteristic
604SD16—28no—
605SD16—44no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—44no—
616C2×C8C22×C4×C4712yes—
617C2×C8C22×C4×C4712yes—
618C2×C8C2×D4×C4712yes—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—81no—
631C4⋊C4C22×C4×C4712yes—
632C4⋊C4C2×D4×C4712yes—
633C22⋊C4—24no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—42no—
648C42—81no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—48no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—48no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23C4×D4×C4712yes—
675C23AGL(1,ℤ/8)×C4712yes—
676C23#137×C4712yes—
677C23C22×D4×C4711yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4C4×D4×C4714yes—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4C4×D4×C4712yes—
731C2×C4C23×C4×C4711yescharacteristic
732C2×C4C22×D4×C4711yescharacteristic
733C2×C4C2×#41×C4711yescharacteristic
734C2×C4C2×#41×C4711yescharacteristic
735C2×C4H(5,𝔽2)×C4711yescharacteristic
736C2×C4H(5,𝔽2)×C4711yescharacteristic
737C8—22no—
738C8—22no—
739C8—22no—
740C8—41no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—816no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22C47×#44014yescomplemented
763C22C2×C4×D4×C4711yescharacteristic
764C22D42×C4711yescharacteristic
765C22C47×#54611yescharacteristic
766C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
767C22C2×#137×C4711yescharacteristic
768C22C47×#57611yescharacteristic
769C22C47×#57711yescharacteristic
770C4—22no—
771C4—41no—
772C4—41no—
773C4—42no—
774C4—42no—
775C4—41no—
776C4—42no—
777C4—41no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4C2×C4×D4×C4711yescharacteristic
782C4C47×#51811yescharacteristic
783C4C47×#54611yescharacteristic
784C4C47×#55111yescharacteristic
785C2—24no—
786C2—44no—
787C2—82no—
788C2C47×#235811yescharacteristic
789C2C2×C47×#44011yescharacteristic
790C2C47×#294611yescharacteristic
791C2C47×#326411yescharacteristic
792C2C47×#326611yescharacteristic
793C2C47×#331011yescharacteristic
794C2C47×#331411yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
prime radicalC23×D4×C47C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C22⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#440C2semidirect
4. C47×#2360C2semidirect
6. C47×#1973C2semidirect
7. C47×#1936C2semidirect
8. C47×#1925C2semidirect
9. C47×#1892C2semidirect
10. C47×#1880C2semidirect
11. C47×#1877C2semidirect
12. C47×#1862C2semidirect
13. C47×#1852C2semidirect
14. C47×#1762C2semidirect
15. C47×#1752C2semidirect
21. C2×C4×Q8×C47C22semidirect
26. C47×#450C4semidirect
28. C2×#107×C47C22semidirect
29. C2×#107×C47C22semidirect
30. C2×#103×C47C22semidirect
31. C2×#103×C47C22semidirect
40. C2×#97×C47C22semidirect
41. C2×#97×C47C22semidirect
42. C47×#391C22semidirect
46. C47×#389C22semidirect
53. C4×C4⋊C4×C47C22semidirect
56. C47×#340C22semidirect
57. C47×#340C22semidirect
58. C47×#340C22semidirect
59. C47×#340C22semidirect
60. C47×#336C22semidirect
61. C47×#336C22semidirect
81. C2×SD16×C47C2×C4semidirect
82. C2×SD16×C47C2×C4semidirect
91. C22⋊Q8×C47C2×C4semidirect
131. #102×C47C2×C4semidirect
132. #102×C47C2×C4semidirect
134. C22⋊C8×C47C2×C4semidirect
343. #22854C47direct (N × H)
365. C22×C47#440semidirect
389. C2×#440C2×C47semidirect
391. #2360C2×C47semidirect
393. #1973C2×C47semidirect
394. #1936C2×C47semidirect
395. #1925C2×C47semidirect
396. #1892C2×C47semidirect
397. #1880C2×C47semidirect
398. #1877C2×C47semidirect
399. #1862C2×C47semidirect
400. #1852C2×C47semidirect
401. #1762C2×C47semidirect
402. #1752C2×C47semidirect
418. C2×C4×Q8C22×C47semidirect
423. #450C4×C47semidirect
425. C2×#107C22×C47semidirect
426. C2×#107C22×C47semidirect
427. C2×#103C22×C47semidirect
428. C2×#103C22×C47semidirect
437. C2×#97C22×C47semidirect
438. C2×#97C22×C47semidirect
439. #391C22×C47semidirect
443. #389C22×C47semidirect
450. C4×C4⋊C4C22×C47semidirect
453. #340C22×C47semidirect
454. #340C22×C47semidirect
455. #340C22×C47semidirect
456. #340C22×C47semidirect
457. #336C22×C47semidirect
458. #336C22×C47semidirect
459. C47#22854direct (N × H)
479. C2×SD16C2×C4×C47semidirect
480. C2×SD16C2×C4×C47semidirect
489. C22⋊Q8C2×C4×C47semidirect
529. #102C2×C4×C47semidirect
530. #102C2×C4×C47semidirect
532. C22⋊C8C2×C4×C47semidirect
762. C22C47×#440semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4502
C2×C47×#4402
C22×#102×C472
C47×#23602
D4×C22⋊C4×C472
C47×#19732
C47×#19362
C47×#19252
C47×#18922
C47×#18802
C47×#18772
C47×#18622
C47×#18522
C47×#17622
C47×#17522
#2285447