Finite Group Databasebeta

← C47×#18012 #26057710

Subgroups — C47×#18012 #26057710

Order 12032.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3108C211yesmaximal, characteristic
2C47×#2969C211yesmaximal, characteristic
3Q8×M16×C47C211yesmaximal, characteristic, complemented
4C47×#1593C211yesmaximal, characteristic, complemented
5C47×#1590C211yesmaximal, characteristic, complemented
6C47×#1587C211yesmaximal, characteristic, complemented
7C47×#1585C211yesmaximal, characteristic, complemented
8C47×#1584C211yesmaximal, characteristic, complemented
9C47×#1583C211yesmaximal, characteristic, complemented
10C47×SD16⋊C8C211yesmaximal, characteristic, complemented
11C8×Q16×C47C211yesmaximal, characteristic, complemented
12C47×#1574C211yesmaximal, characteristic, complemented
13C47×#1495C211yesmaximal, characteristic
14C47×#1479C211yesmaximal, characteristic, complemented
15C47×#1453C211yesmaximal, characteristic, complemented
16C47×#529C2211yescharacteristic
17C2×C4×Q8×C47C2211yescharacteristic
18C47×#483C411yescharacteristic
19C47×#480C411yescharacteristic
20C47×#479C411yescharacteristic
21C47×#479C411yescharacteristic
22C47×#464C411yescharacteristic
23C47×#464C411yescharacteristic
24C47×#451C411yescharacteristic
25C47×#448C411yescharacteristic
26C47×#446—21no—
27C47×#446—21no—
28C47×#446C2211yescharacteristic
29C47×#446C2211yescharacteristic
30C47×#446C2211yescharacteristic
31C8×Q8×C47C2211yescharacteristic
32C8×Q8×C47C2211yescharacteristic
33C8×Q8×C47C2211yescharacteristic
34C4×Q16×C47C2211yescharacteristic
35C4×Q16×C47C2211yescharacteristic
36C4×SD16×C47C2211yescharacteristic
37C4×SD16×C47C2211yescharacteristic
38C47×#436—21no—
39C47×#436C2211yescharacteristic
40C47×#435—21no—
41C8×D4×C47C2211yescharacteristic
42C47×#433—21no—
43C47×#431C2211yescharacteristic
44C47×#431C2211yescharacteristic
45C47×#431C2211yescharacteristic
46C47×#423—21no—
47C47×#423C2211yescharacteristic
48C47×#405—21no—
49C4×M16×C47—21no—
50C4×M16×C47C2211yescharacteristic
51C47×#335C2211yescharacteristic
52C47×#335C2211yescharacteristic
53C47×#334C2211yescharacteristic
54C47×#334C2211yescharacteristic
55C47×Q8⋊C8C2211yescharacteristic
56C47×Q8⋊C8C2211yescharacteristic
57C47×Q8⋊C8C2211yescharacteristic
58C47×Q8⋊C8C2211yescharacteristic
59C47×Q8⋊C8C2211yescharacteristic
60C47×Q8⋊C8C2211yescharacteristic
61C47×D4⋊C8C2211yescharacteristic
62C47×D4⋊C8C2211yescharacteristic
63C47×#322C2211yescharacteristic
64C47×#322C2211yescharacteristic
65C47×#322C2211yescharacteristic
66C82×C47C2211yescharacteristic
67C22×Q8×C47C2×C411yescharacteristic
68C2×Q16×C47C2×C411yescharacteristic
69C2×Q16×C47C2×C411yescharacteristic
70C2×SD16×C47C2×C411yescharacteristic
71C2×SD16×C47C2×C411yescharacteristic
72C2×M16×C47—21no—
73C2×M16×C47—21no—
74C2×M16×C47D411yescharacteristic
75C2×M16×C47D411yescharacteristic
76C22×C8×C47—21no—
77#126×C47—21no—
78#125×C47C2×C411yescharacteristic
79#124×C47C2×C411yescharacteristic
80#123×C47—21no—
81C22⋊Q8×C47C2×C411yescharacteristic
82#121×C47C2×C411yescharacteristic
83C4×Q8×C47—21no—
84C4×Q8×C47—21no—
85C4×Q8×C47C2×C411yescharacteristic
86C4×Q8×C47C2×C411yescharacteristic
87C4×Q8×C47C2311yescharacteristic
88C4×Q8×C47C2311yescharacteristic
89C4×Q8×C47C2311yescharacteristic
90C4×D4×C47—21no—
91C4×D4×C47C2311yescharacteristic
92#117×C47—21no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47C2×C411yescharacteristic
95C2×C42×C47—21no—
96C2×C42×C47C2311yescharacteristic
97#107×C47C2×C411yescharacteristic
98#107×C47C2×C411yescharacteristic
99#106×C47C2×C411yescharacteristic
100#106×C47C2×C411yescharacteristic
101C4⋊C8×C47—21no—
102C4⋊C8×C47—21no—
103C4⋊C8×C47—21no—
104C4⋊C8×C47—21no—
105C4⋊C8×C47—21no—
106C4⋊C8×C47—21no—
107C4⋊C8×C47—21no—
108C4⋊C8×C47—21no—
109C4⋊C8×C47C2×C411yescharacteristic
110C4⋊C8×C47C2×C411yescharacteristic
111C4⋊C8×C47C2311yescharacteristic
112C4⋊C8×C47C2311yescharacteristic
113C4⋊C8×C47C2311yescharacteristic
114C4⋊C8×C47C2311yescharacteristic
115#103×C47C2×C411yescharacteristic
116#103×C47C2×C411yescharacteristic
117#103×C47C2×C411yescharacteristic
118#103×C47C2×C411yescharacteristic
119#103×C47C2×C411yescharacteristic
120#103×C47C2×C411yescharacteristic
121#102×C47C2×C411yescharacteristic
122#102×C47C2×C411yescharacteristic
123C22⋊C8×C47—21no—
124C22⋊C8×C47—21no—
125C22⋊C8×C47—21no—
126C22⋊C8×C47—21no—
127C22⋊C8×C47C2×C411yescharacteristic
128C22⋊C8×C47C2×C411yescharacteristic
129#97×C47—21no—
130#97×C47—21no—
131#97×C47—21no—
132#97×C47D411yescharacteristic
133#97×C47D411yescharacteristic
134C4×C8×C47—21no—
135C4×C8×C47—21no—
136C4×C8×C47—21no—
137C4×C8×C47—21no—
138C4×C8×C47C2311yescharacteristic
139C4×C8×C47C2311yescharacteristic
140C4×C8×C47C2311yescharacteristic
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47—21no—
145C2×Q8×C47—22no—
146C2×Q8×C47—41no—
147C2×Q8×C47C22×C411yescharacteristic
148C2×Q8×C47C22×C411yescharacteristic
149C2×Q8×C47C22×C411yescharacteristic
150C2×D4×C47—21no—
151C2×D4×C47C22×C411yescharacteristic
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47C22×C411yescharacteristic
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47#4111yescharacteristic
158Q16×C47—22no—
159Q16×C47—41no—
160SD16×C47—22no—
161SD16×C47—41no—
162M16×C47—22no—
163M16×C47—41no—
164M16×C47—42no—
165M16×C47—42no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—42no—
173C2×C8×C47C22×C411yescharacteristic
174C2×C8×C47C22×C411yescharacteristic
175C2×C8×C47C22×C411yescharacteristic
176C2×C8×C47C22×C411yescharacteristic
177C2×C8×C47C2×D411yescharacteristic
178C2×C8×C47C2×D411yescharacteristic
179C2×C8×C47C2×D411yescharacteristic
180C2×C8×C47C2×D411yescharacteristic
181C4⋊C4×C47—21no—
182C4⋊C4×C47—21no—
183C4⋊C4×C47—21no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47C22×C411yescharacteristic
191C4⋊C4×C47C22×C411yescharacteristic
192C4⋊C4×C47C22×C411yescharacteristic
193C4⋊C4×C47C22×C411yescharacteristic
194C22⋊C4×C47—21no—
195C22⋊C4×C47—21no—
196C22⋊C4×C47—21no—
197C22⋊C4×C47—21no—
198C22⋊C4×C47—21no—
199C42×C47—21no—
200C42×C47—21no—
201C42×C47—21no—
202C42×C47—21no—
203C42×C47—21no—
204C42×C47C22×C411yescharacteristic
205C42×C47C2×D411yescharacteristic
206C42×C47#4111yescharacteristic
207C42×C47C2411yescharacteristic
208C23×C47—21no—
209C23×C47C4×D411yescharacteristic
210Q8×C47—21no—
211Q8×C47—21no—
212Q8×C47—21no—
213Q8×C47—21no—
214Q8×C47—21no—
215Q8×C47—42no—
216Q8×C47#13112yes—
217D4×C47—21no—
218D4×C47—21no—
219D4×C47—81no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—41no—
232C2×C4×C47—42no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—81no—
236C2×C4×C47C4×D411yescharacteristic
237C2×C4×C47C4×D411yescharacteristic
238C2×C4×C47C4×D411yescharacteristic
239C2×C4×C47C23×C411yescharacteristic
240C2×C4×C47C22×D411yescharacteristic
241C2×C4×C47C2×#4111yescharacteristic
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—21no—
246C8×C47—21no—
247C8×C47—21no—
248C8×C47—21no—
249C8×C47—41no—
250C8×C47—41no—
251C8×C47—41no—
252C8×C47—41no—
253C8×C47—41no—
254C8×C47—41no—
255C8×C47#13712yes—
256#18012C4711yesmaximal, characteristic, direct product factor, Sylow
257C22×C47—21no—
258C22×C47—21no—
259C22×C47—21no—
260C22×C47—41no—
261C22×C47—41no—
262C22×C47—41no—
263C22×C47C2×C4×D411yescharacteristic
264C4×C47—21no—
265C4×C47—22no—
266C4×C47—21no—
267C4×C47—21no—
268C4×C47—21no—
269C4×C47—41no—
270C4×C47—41no—
271C4×C47—41no—
272C4×C47—41no—
273C4×C47—41no—
274C4×C47—41no—
275C4×C47C2×#13111yescharacteristic
276C4×C47#56811yescharacteristic
277C4×C47C2×#13711yescharacteristic
278C4×C47#57511yescharacteristic
279#3108C2×C4711yescharacteristic
280#2969C2×C4711yescharacteristic
281Q8×M16C2×C4711yescharacteristic, complemented
282#1593C2×C4711yescharacteristic, complemented
283#1590C2×C4711yescharacteristic, complemented
284#1587C2×C4711yescharacteristic, complemented
285#1585C2×C4711yescharacteristic, complemented
286#1584C2×C4711yescharacteristic, complemented
287#1583C2×C4711yescharacteristic, complemented
288SD16⋊C8C2×C4711yescharacteristic, complemented
289C8×Q16C2×C4711yescharacteristic, complemented
290#1574C2×C4711yescharacteristic, complemented
291#1495C2×C4711yescharacteristic
292#1479C2×C4711yescharacteristic, complemented
293#1453C2×C4711yescharacteristic, complemented
294C2×C47—41no—
295C2×C47—81no—
296C2×C47#293311yescharacteristic
297C2×C47C4×#13711yescharacteristic
298C2×C47#295711yescharacteristic
299#529C22×C4711yescharacteristic
300C2×C4×Q8C22×C4711yescharacteristic
301#483C4×C4711yescharacteristic
302#480C4×C4711yescharacteristic
303#479C4×C4711yescharacteristic
304#479C4×C4711yescharacteristic
305#464C4×C4711yescharacteristic
306#464C4×C4711yescharacteristic
307#451C4×C4711yescharacteristic
308#448C4×C4711yescharacteristic
309#446—21no—
310#446—21no—
311#446C22×C4711yescharacteristic
312#446C22×C4711yescharacteristic
313#446C22×C4711yescharacteristic
314C8×Q8C22×C4711yescharacteristic
315C8×Q8C22×C4711yescharacteristic
316C8×Q8C22×C4711yescharacteristic
317C4×Q16C22×C4711yescharacteristic
318C4×Q16C22×C4711yescharacteristic
319C4×SD16C22×C4711yescharacteristic
320C4×SD16C22×C4711yescharacteristic
321#436—21no—
322#436C22×C4711yescharacteristic
323#435—21no—
324C8×D4C22×C4711yescharacteristic
325#433—21no—
326#431C22×C4711yescharacteristic
327#431C22×C4711yescharacteristic
328#431C22×C4711yescharacteristic
329#423—21no—
330#423C22×C4711yescharacteristic
331#405—21no—
332C4×M16—21no—
333C4×M16C22×C4711yescharacteristic
334#335C22×C4711yescharacteristic
335#335C22×C4711yescharacteristic
336#334C22×C4711yescharacteristic
337#334C22×C4711yescharacteristic
338Q8⋊C8C22×C4711yescharacteristic
339Q8⋊C8C22×C4711yescharacteristic
340Q8⋊C8C22×C4711yescharacteristic
341Q8⋊C8C22×C4711yescharacteristic
342Q8⋊C8C22×C4711yescharacteristic
343Q8⋊C8C22×C4711yescharacteristic
344D4⋊C8C22×C4711yescharacteristic
345D4⋊C8C22×C4711yescharacteristic
346#322C22×C4711yescharacteristic
347#322C22×C4711yescharacteristic
348#322C22×C4711yescharacteristic
349C82C22×C4711yescharacteristic
350C47#1801211yescharacteristic, direct product factor, Sylow
351C22×Q8C2×C4×C4711yescharacteristic
352C2×Q16C2×C4×C4711yescharacteristic
353C2×Q16C2×C4×C4711yescharacteristic
354C2×SD16C2×C4×C4711yescharacteristic
355C2×SD16C2×C4×C4711yescharacteristic
356C2×M16—21no—
357C2×M16—21no—
358C2×M16D4×C4711yescharacteristic
359C2×M16D4×C4711yescharacteristic
360C22×C8—21no—
361#126—21no—
362#125C2×C4×C4711yescharacteristic
363#124C2×C4×C4711yescharacteristic
364#123—21no—
365C22⋊Q8C2×C4×C4711yescharacteristic
366#121C2×C4×C4711yescharacteristic
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8C2×C4×C4711yescharacteristic
370C4×Q8C2×C4×C4711yescharacteristic
371C4×Q8C23×C4711yescharacteristic
372C4×Q8C23×C4711yescharacteristic
373C4×Q8C23×C4711yescharacteristic
374C4×D4—21no—
375C4×D4C23×C4711yescharacteristic
376#117—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4C2×C4×C4711yescharacteristic
379C2×C42—21no—
380C2×C42C23×C4711yescharacteristic
381#107C2×C4×C4711yescharacteristic
382#107C2×C4×C4711yescharacteristic
383#106C2×C4×C4711yescharacteristic
384#106C2×C4×C4711yescharacteristic
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8C2×C4×C4711yescharacteristic
394C4⋊C8C2×C4×C4711yescharacteristic
395C4⋊C8C23×C4711yescharacteristic
396C4⋊C8C23×C4711yescharacteristic
397C4⋊C8C23×C4711yescharacteristic
398C4⋊C8C23×C4711yescharacteristic
399#103C2×C4×C4711yescharacteristic
400#103C2×C4×C4711yescharacteristic
401#103C2×C4×C4711yescharacteristic
402#103C2×C4×C4711yescharacteristic
403#103C2×C4×C4711yescharacteristic
404#103C2×C4×C4711yescharacteristic
405#102C2×C4×C4711yescharacteristic
406#102C2×C4×C4711yescharacteristic
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8C2×C4×C4711yescharacteristic
412C22⋊C8C2×C4×C4711yescharacteristic
413#97—21no—
414#97—21no—
415#97—21no—
416#97D4×C4711yescharacteristic
417#97D4×C4711yescharacteristic
418C4×C8—21no—
419C4×C8—21no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8C23×C4711yescharacteristic
423C4×C8C23×C4711yescharacteristic
424C4×C8C23×C4711yescharacteristic
425C4×C8C23×C4711yescharacteristic
426C4×C8C23×C4711yescharacteristic
427C4×C8C23×C4711yescharacteristic
428C2×Q8—21no—
429C2×Q8—22no—
430C2×Q8—41no—
431C2×Q8C22×C4×C4711yescharacteristic
432C2×Q8C22×C4×C4711yescharacteristic
433C2×Q8C22×C4×C4711yescharacteristic
434C2×D4—21no—
435C2×D4C22×C4×C4711yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4C22×C4×C4711yescharacteristic
440C22×C4C2×D4×C4711yescharacteristic
441C22×C4#41×C4711yescharacteristic
442Q16—22no—
443Q16—41no—
444SD16—22no—
445SD16—41no—
446M16—22no—
447M16—41no—
448M16—42no—
449M16—42no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—42no—
457C2×C8C22×C4×C4711yescharacteristic
458C2×C8C22×C4×C4711yescharacteristic
459C2×C8C22×C4×C4711yescharacteristic
460C2×C8C22×C4×C4711yescharacteristic
461C2×C8C2×D4×C4711yescharacteristic
462C2×C8C2×D4×C4711yescharacteristic
463C2×C8C2×D4×C4711yescharacteristic
464C2×C8C2×D4×C4711yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4C22×C4×C4711yescharacteristic
475C4⋊C4C22×C4×C4711yescharacteristic
476C4⋊C4C22×C4×C4711yescharacteristic
477C4⋊C4C22×C4×C4711yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42C22×C4×C4711yescharacteristic
489C42C2×D4×C4711yescharacteristic
490C42#41×C4711yescharacteristic
491C42C24×C4711yescharacteristic
492C23—21no—
493C23C4×D4×C4711yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—42no—
500Q8#131×C4712yes—
501D4—21no—
502D4—21no—
503D4—81no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—81no—
520C2×C4C4×D4×C4711yescharacteristic
521C2×C4C4×D4×C4711yescharacteristic
522C2×C4C4×D4×C4711yescharacteristic
523C2×C4C23×C4×C4711yescharacteristic
524C2×C4C22×D4×C4711yescharacteristic
525C2×C4C2×#41×C4711yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8#137×C4712yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×C4×D4×C4711yescharacteristic
547C4—21no—
548C4—22no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4C2×#131×C4711yescharacteristic
559C4C47×#56811yescharacteristic
560C4C2×#137×C4711yescharacteristic
561C4C47×#57511yescharacteristic
562C2—41no—
563C2—81no—
564C2C47×#293311yescharacteristic
565C2C4×#137×C4711yescharacteristic
566C2C47×#295711yescharacteristic
subgroupG/H
centerC2×C4×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC42C24×C47
socleC22×C47C2×C4×D4
prime radical#121×C47C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C4×M16×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. Q8×M16×C47C2semidirect
4. C47×#1593C2semidirect
5. C47×#1590C2semidirect
6. C47×#1587C2semidirect
7. C47×#1585C2semidirect
8. C47×#1584C2semidirect
9. C47×#1583C2semidirect
10. C47×SD16⋊C8C2semidirect
11. C8×Q16×C47C2semidirect
12. C47×#1574C2semidirect
14. C47×#1479C2semidirect
15. C47×#1453C2semidirect
256. #18012C47direct (N × H)
281. Q8×M16C2×C47semidirect
282. #1593C2×C47semidirect
283. #1590C2×C47semidirect
284. #1587C2×C47semidirect
285. #1585C2×C47semidirect
286. #1584C2×C47semidirect
287. #1583C2×C47semidirect
288. SD16⋊C8C2×C47semidirect
289. C8×Q16C2×C47semidirect
290. #1574C2×C47semidirect
292. #1479C2×C47semidirect
293. #1453C2×C47semidirect
350. C47#18012direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31082
C47×#29692
Q8×M16×C472
C47×#15932
C47×#15902
C47×#15872
C47×#15852
C47×#15842
C47×#15832
C47×SD16⋊C82
C8×Q16×C472
C47×#15742
C47×#14952
C47×#14792
C47×#14532
#1801247