Finite Group Databasebeta

← C47×#22874 #26062572

Subgroups — C47×#22874 #26062572

Order 12032.

1314 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×C4×SD16×C47C211yesmaximal, characteristic, complemented
3C22×#102×C47C211yesmaximal, characteristic
4C47×#2360C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C47C211yesmaximal, characteristic
6C47×#1968C211yesmaximal, characteristic, complemented
7C47×#1934C211yesmaximal, characteristic, complemented
8C47×#1926C211yesmaximal, characteristic, complemented
9C47×#1892C211yesmaximal, characteristic, complemented
10C47×#1880C211yesmaximal, characteristic, complemented
11C47×#1877C211yesmaximal, characteristic, complemented
12C47×#1864C211yesmaximal, characteristic, complemented
13C47×#1853C211yesmaximal, characteristic, complemented
14C4×#102×C47C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C47C211yesmaximal, 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
27C4×SD16×C47—24no—
28C2×#106×C47C2211yescharacteristic, complemented
29C2×#106×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×C4×C8×C47C2211yescharacteristic, complemented
41C2×C4×C8×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#106×C47—22no—
125#106×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
135C4×C8×C47—22no—
136C4×C8×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—42no—
238C22⋊C4×C47—42no—
239C22⋊C4×C47—42no—
240C22⋊C4×C47—42no—
241C22⋊C4×C47—42no—
242C22⋊C4×C47—81no—
243C22⋊C4×C47—81no—
244C22⋊C4×C47SD1614yescomplemented
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×C47C2×SD1612yes—
278C23×C47#13512yes—
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—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—21no—
306C2×C4×C47—22no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
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—84no—
328C2×C4×C47—84no—
329C2×C4×C47—84no—
330C2×C4×C47C4×D412yes—
331C2×C4×C47C2×SD1612yes—
332C2×C4×C47C2×SD1612yes—
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#22874C4711yesmaximal, 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×C47C4×SD1614yescomplemented
366C22×C47C2×C4×D411yescharacteristic
367C22×C47D4211yescharacteristic
368C22×C47#54611yescharacteristic
369C22×C47C22×SD1611yescharacteristic
370C22×C47C2×#13511yescharacteristic
371C22×C47#57611yescharacteristic
372C22×C47#57711yescharacteristic
373C4×C47—22no—
374C4×C47—22no—
375C4×C47—22no—
376C4×C47—42no—
377C4×C47—42no—
378C4×C47—41no—
379C4×C47—42no—
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×C4×SD16C2×C4711yescharacteristic, complemented
390C22×#102C2×C4711yescharacteristic
391#2360C2×C4711yescharacteristic, complemented
392D4×C22⋊C4C2×C4711yescharacteristic
393#1968C2×C4711yescharacteristic, complemented
394#1934C2×C4711yescharacteristic, complemented
395#1926C2×C4711yescharacteristic, complemented
396#1892C2×C4711yescharacteristic, complemented
397#1880C2×C4711yescharacteristic, complemented
398#1877C2×C4711yescharacteristic, complemented
399#1864C2×C4711yescharacteristic, complemented
400#1853C2×C4711yescharacteristic, complemented
401C4×#102C2×C4711yescharacteristic, complemented
402C8×C22⋊C4C2×C4711yescharacteristic, complemented
403C2×C47—24no—
404C2×C47—44no—
405C2×C47—82no—
406C2×C47#235811yescharacteristic
407C2×C47C2×C4×SD1611yescharacteristic
408C2×C47#294611yescharacteristic
409C2×C47#328011yescharacteristic
410C2×C47D4×SD1611yescharacteristic
411C2×C47#329511yescharacteristic
412C2×C47#329611yescharacteristic
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
424C4×SD16—24no—
425C2×#106C22×C4711yescharacteristic, complemented
426C2×#106C22×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×C4×C8C22×C4711yescharacteristic, complemented
438C2×C4×C8C22×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#2287411yescharacteristic, 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#106—22no—
523#106—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
533C4×C8—22no—
534C4×C8—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—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4SD16×C4714yescomplemented
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—
675C23C2×SD16×C4712yes—
676C23#135×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—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
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—84no—
726C2×C4—84no—
727C2×C4—84no—
728C2×C4C4×D4×C4712yes—
729C2×C4C2×SD16×C4712yes—
730C2×C4C2×SD16×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—
762C22C4×SD16×C4714yescomplemented
763C22C2×C4×D4×C4711yescharacteristic
764C22D42×C4711yescharacteristic
765C22C47×#54611yescharacteristic
766C22C22×SD16×C4711yescharacteristic
767C22C2×#135×C4711yescharacteristic
768C22C47×#57611yescharacteristic
769C22C47×#57711yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—41no—
774C4—42no—
775C4—42no—
776C4—41no—
777C4—42no—
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×C4×SD16×C4711yescharacteristic
790C2C47×#294611yescharacteristic
791C2C47×#328011yescharacteristic
792C2D4×SD16×C4711yescharacteristic
793C2C47×#329511yescharacteristic
794C2C47×#329611yescharacteristic
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×C4×SD16×C47C2semidirect
4. C47×#2360C2semidirect
6. C47×#1968C2semidirect
7. C47×#1934C2semidirect
8. C47×#1926C2semidirect
9. C47×#1892C2semidirect
10. C47×#1880C2semidirect
11. C47×#1877C2semidirect
12. C47×#1864C2semidirect
13. C47×#1853C2semidirect
14. C4×#102×C47C2semidirect
15. C8×C22⋊C4×C47C2semidirect
21. C2×C4×Q8×C47C22semidirect
26. C47×#450C4semidirect
28. C2×#106×C47C22semidirect
29. C2×#106×C47C22semidirect
30. C2×#103×C47C22semidirect
31. C2×#103×C47C22semidirect
40. C2×C4×C8×C47C22semidirect
41. C2×C4×C8×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
244. C22⋊C4×C47SD16semidirect
343. #22874C47direct (N × H)
365. C22×C47C4×SD16semidirect
389. C2×C4×SD16C2×C47semidirect
391. #2360C2×C47semidirect
393. #1968C2×C47semidirect
394. #1934C2×C47semidirect
395. #1926C2×C47semidirect
396. #1892C2×C47semidirect
397. #1880C2×C47semidirect
398. #1877C2×C47semidirect
399. #1864C2×C47semidirect
400. #1853C2×C47semidirect
401. C4×#102C2×C47semidirect
402. C8×C22⋊C4C2×C47semidirect
418. C2×C4×Q8C22×C47semidirect
423. #450C4×C47semidirect
425. C2×#106C22×C47semidirect
426. C2×#106C22×C47semidirect
427. C2×#103C22×C47semidirect
428. C2×#103C22×C47semidirect
437. C2×C4×C8C22×C47semidirect
438. C2×C4×C8C22×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#22874direct (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
642. C22⋊C4SD16×C47semidirect
762. C22C4×SD16×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4502
C2×C4×SD16×C472
C22×#102×C472
C47×#23602
D4×C22⋊C4×C472
C47×#19682
C47×#19342
C47×#19262
C47×#18922
C47×#18802
C47×#18772
C47×#18642
C47×#18532
C4×#102×C472
C8×C22⋊C4×C472
#2287447