Finite Group Databasebeta

← C47×#17955 #26057653

Subgroups — C47×#17955 #26057653

Order 12032.

590 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3102C211yesmaximal, characteristic
2C47×#2993C211yesmaximal, characteristic, complemented
3C47×#2989C211yesmaximal, characteristic, complemented
4C47×#1594C211yesmaximal, characteristic, complemented
5C47×#1593C211yesmaximal, characteristic, complemented
6C47×#1590C211yesmaximal, characteristic, complemented
7C47×#1590C211yesmaximal, characteristic, complemented
8C47×#1587C211yesmaximal, characteristic, complemented
9C47×#1586C211yesmaximal, characteristic, complemented
10C47×#1583C211yesmaximal, characteristic, complemented
11C47×#1582C211yesmaximal, characteristic, complemented
12C47×#1570C211yesmaximal, characteristic, complemented
13C47×#1489C211yesmaximal, characteristic, complemented
14C47×#1483C211yesmaximal, characteristic, complemented
15C47×#1453C211yesmaximal, characteristic, complemented
16C47×#529C2211yescharacteristic
17C4×#41×C47C2211yescharacteristic
18C47×#485C411yescharacteristic
19C47×#482C411yescharacteristic
20C47×#479C411yescharacteristic
21C47×#478C411yescharacteristic
22C47×#464C411yescharacteristic
23C47×#463C411yescharacteristic
24C47×#452C411yescharacteristic
25C47×#449C411yescharacteristic
26C47×#446C2211yescharacteristic
27C47×#446C2211yescharacteristic
28C47×#446C2211yescharacteristic
29C8×Q8×C47C2211yescharacteristic
30C4×Q16×C47C2211yescharacteristic
31C4×SD16×C47C2211yescharacteristic
32C4×SD16×C47C2211yescharacteristic
33C4×D8×C47C2211yescharacteristic
34C47×#436—21no—
35C47×#436C2211yescharacteristic
36C47×#436C2211yescharacteristic
37C47×#436C2211yescharacteristic
38C47×#435—21no—
39C47×#435—21no—
40C47×#435—21no—
41C8×D4×C47C2211yescharacteristic
42C47×#433—21no—
43C47×#432—21no—
44C47×#431C2211yescharacteristic
45C47×#431C2211yescharacteristic
46C47×#424—21no—
47C47×#423—21no—
48C47×#423C2211yescharacteristic
49C2×C4⋊C8×C47C2211yescharacteristic
50C4×M16×C47C2211yescharacteristic
51C47×#334C2211yescharacteristic
52C47×#334C2211yescharacteristic
53C47×#334C2211yescharacteristic
54C47×#334C2211yescharacteristic
55C47×Q8⋊C8C2211yescharacteristic
56C47×Q8⋊C8C2211yescharacteristic
57C47×Q8⋊C8C2211yescharacteristic
58C47×Q8⋊C8C2211yescharacteristic
59C47×D4⋊C8C2211yescharacteristic
60C47×D4⋊C8C2211yescharacteristic
61C47×D4⋊C8C2211yescharacteristic
62C47×D4⋊C8C2211yescharacteristic
63C47×#322C2211yescharacteristic
64C47×#322C2211yescharacteristic
65C47×#322C2211yescharacteristic
66C82×C47C2211yescharacteristic
67C2×#41×C47C2×C411yescharacteristic
68C2×Q16×C47C2×C411yescharacteristic
69C2×SD16×C47C2×C411yescharacteristic
70C2×SD16×C47C2×C411yescharacteristic
71C2×D8×C47C2×C411yescharacteristic
72C2×M16×C47—21no—
73C2×M16×C47—21no—
74C2×M16×C47—21no—
75C2×M16×C47—21no—
76C2×M16×C47—21no—
77C22×C8×C47—21no—
78C22×C8×C47—21no—
79#126×C47—21no—
80#125×C47C2×C411yescharacteristic
81#124×C47C2×C411yescharacteristic
82#123×C47—21no—
83C22⋊Q8×C47C2×C411yescharacteristic
84#121×C47C2×C411yescharacteristic
85C4×Q8×C47C2×C411yescharacteristic
86C4×Q8×C47C2311yescharacteristic
87C4×Q8×C47C2311yescharacteristic
88C4×D4×C47—21no—
89C4×D4×C47—21no—
90C4×D4×C47—21no—
91C4×D4×C47C2×C411yescharacteristic
92C4×D4×C47C2311yescharacteristic
93C4×D4×C47C2311yescharacteristic
94#117×C47—21no—
95#117×C47—21no—
96#117×C47C2×C411yescharacteristic
97C2×C42×C47—21no—
98C2×C42×C47C2311yescharacteristic
99#107×C47C2×C411yescharacteristic
100#107×C47C2×C411yescharacteristic
101#106×C47C2×C411yescharacteristic
102#106×C47C2×C411yescharacteristic
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×C47D411yescharacteristic
112C4⋊C8×C47D411yescharacteristic
113C4⋊C8×C47C2311yescharacteristic
114C4⋊C8×C47C2311yescharacteristic
115C4⋊C8×C47C2311yescharacteristic
116C4⋊C8×C47C2311yescharacteristic
117#103×C47C2×C411yescharacteristic
118#103×C47C2×C411yescharacteristic
119#103×C47C2×C411yescharacteristic
120#103×C47C2×C411yescharacteristic
121#102×C47C2×C411yescharacteristic
122#102×C47C2×C411yescharacteristic
123#102×C47C2×C411yescharacteristic
124#102×C47C2×C411yescharacteristic
125C22⋊C8×C47—21no—
126C22⋊C8×C47—21no—
127C22⋊C8×C47—21no—
128C22⋊C8×C47—21no—
129C22⋊C8×C47C2×C411yescharacteristic
130C22⋊C8×C47C2×C411yescharacteristic
131C22⋊C8×C47D411yescharacteristic
132C22⋊C8×C47D411yescharacteristic
133#97×C47—21no—
134#97×C47—21no—
135#97×C47—21no—
136#97×C47—21no—
137C4×C8×C47—21no—
138C4×C8×C47C2311yescharacteristic
139C4×C8×C47C2311yescharacteristic
140C4×C8×C47C2311yescharacteristic
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144#41×C47—41no—
145#41×C47—41no—
146C2×Q8×C47C22×C411yescharacteristic
147C2×Q8×C47C22×C411yescharacteristic
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47C22×C411yescharacteristic
151C2×D4×C47C22×C411yescharacteristic
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47C22×C411yescharacteristic
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47#4111yescharacteristic
159Q16×C47—41no—
160SD16×C47—41no—
161SD16×C47—41no—
162D8×C47—41no—
163M16×C47—42no—
164M16×C47—81no—
165M16×C47—81no—
166M16×C47—81no—
167M16×C47—81no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—81no—
175C2×C8×C47—81no—
176C2×C8×C47C22×C411yescharacteristic
177C2×C8×C47C22×C411yescharacteristic
178C2×C8×C47C22×C411yescharacteristic
179C2×C8×C47C22×C411yescharacteristic
180C2×C8×C47C2×D411yescharacteristic
181C2×C8×C47C2×D411yescharacteristic
182C2×C8×C47C2×D411yescharacteristic
183C2×C8×C47C2×D411yescharacteristic
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—
199C22⋊C4×C47—21no—
200C22⋊C4×C47—21no—
201C22⋊C4×C47—21no—
202C42×C47—21no—
203C42×C47—21no—
204C42×C47—21no—
205C42×C47—21no—
206C42×C47C22×C411yescharacteristic
207C42×C47C2×D411yescharacteristic
208C42×C47#4111yescharacteristic
209C42×C47C2411yescharacteristic
210C23×C47—21no—
211C23×C47—21no—
212C23×C47C4×D411yescharacteristic
213Q8×C47—21no—
214Q8×C47—21no—
215Q8×C47—21no—
216Q8×C47—21no—
217D4×C47—21no—
218D4×C47—21no—
219D4×C47—21no—
220D4×C47—21no—
221D4×C47—42no—
222D4×C47—81no—
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—21no—
232C2×C4×C47—21no—
233C2×C4×C47—41no—
234C2×C4×C47—42no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—81no—
240C2×C4×C47C4×D411yescharacteristic
241C2×C4×C47C4×D411yescharacteristic
242C2×C4×C47C4×D411yescharacteristic
243C2×C4×C47C23×C411yescharacteristic
244C2×C4×C47C22×D411yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C8×C47—22no—
247C8×C47—21no—
248C8×C47—21no—
249C8×C47—21no—
250C8×C47—21no—
251C8×C47—21no—
252C8×C47—21no—
253C8×C47—21no—
254C8×C47—21no—
255C8×C47—41no—
256C8×C47—41no—
257C8×C47—41no—
258C8×C47—41no—
259C8×C47—41no—
260#17955C4711yesmaximal, characteristic, direct product factor, Sylow
261C22×C47—21no—
262C22×C47—21no—
263C22×C47—21no—
264C22×C47—41no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47—41no—
270C22×C47C2×C4×D411yescharacteristic
271C4×C47—21no—
272C4×C47—21no—
273C4×C47—21no—
274C4×C47—21no—
275C4×C47—41no—
276C4×C47—41no—
277C4×C47—41no—
278C4×C47—41no—
279C4×C47—41no—
280C4×C47—41no—
281C4×C47#56811yescharacteristic
282C4×C47#56811yescharacteristic
283C4×C47#57711yescharacteristic
284C4×C47#57711yescharacteristic
285#3102C2×C4711yescharacteristic
286#2993C2×C4711yescharacteristic, complemented
287#2989C2×C4711yescharacteristic, complemented
288#1594C2×C4711yescharacteristic, complemented
289#1593C2×C4711yescharacteristic, complemented
290#1590C2×C4711yescharacteristic, complemented
291#1590C2×C4711yescharacteristic, complemented
292#1587C2×C4711yescharacteristic, complemented
293#1586C2×C4711yescharacteristic, complemented
294#1583C2×C4711yescharacteristic, complemented
295#1582C2×C4711yescharacteristic, complemented
296#1570C2×C4711yescharacteristic, complemented
297#1489C2×C4711yescharacteristic, complemented
298#1483C2×C4711yescharacteristic, complemented
299#1453C2×C4711yescharacteristic, complemented
300C2×C47—41no—
301C2×C47—81no—
302C2×C47—81no—
303C2×C47#293011yescharacteristic
304C2×C47#295211yescharacteristic
305C2×C47#295611yescharacteristic
306#529C22×C4711yescharacteristic
307C4×#41C22×C4711yescharacteristic
308#485C4×C4711yescharacteristic
309#482C4×C4711yescharacteristic
310#479C4×C4711yescharacteristic
311#478C4×C4711yescharacteristic
312#464C4×C4711yescharacteristic
313#463C4×C4711yescharacteristic
314#452C4×C4711yescharacteristic
315#449C4×C4711yescharacteristic
316#446C22×C4711yescharacteristic
317#446C22×C4711yescharacteristic
318#446C22×C4711yescharacteristic
319C8×Q8C22×C4711yescharacteristic
320C4×Q16C22×C4711yescharacteristic
321C4×SD16C22×C4711yescharacteristic
322C4×SD16C22×C4711yescharacteristic
323C4×D8C22×C4711yescharacteristic
324#436—21no—
325#436C22×C4711yescharacteristic
326#436C22×C4711yescharacteristic
327#436C22×C4711yescharacteristic
328#435—21no—
329#435—21no—
330#435—21no—
331C8×D4C22×C4711yescharacteristic
332#433—21no—
333#432—21no—
334#431C22×C4711yescharacteristic
335#431C22×C4711yescharacteristic
336#424—21no—
337#423—21no—
338#423C22×C4711yescharacteristic
339C2×C4⋊C8C22×C4711yescharacteristic
340C4×M16C22×C4711yescharacteristic
341#334C22×C4711yescharacteristic
342#334C22×C4711yescharacteristic
343#334C22×C4711yescharacteristic
344#334C22×C4711yescharacteristic
345Q8⋊C8C22×C4711yescharacteristic
346Q8⋊C8C22×C4711yescharacteristic
347Q8⋊C8C22×C4711yescharacteristic
348Q8⋊C8C22×C4711yescharacteristic
349D4⋊C8C22×C4711yescharacteristic
350D4⋊C8C22×C4711yescharacteristic
351D4⋊C8C22×C4711yescharacteristic
352D4⋊C8C22×C4711yescharacteristic
353#322C22×C4711yescharacteristic
354#322C22×C4711yescharacteristic
355#322C22×C4711yescharacteristic
356C82C22×C4711yescharacteristic
357C47#1795511yescharacteristic, direct product factor, Sylow
358C2×#41C2×C4×C4711yescharacteristic
359C2×Q16C2×C4×C4711yescharacteristic
360C2×SD16C2×C4×C4711yescharacteristic
361C2×SD16C2×C4×C4711yescharacteristic
362C2×D8C2×C4×C4711yescharacteristic
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C22×C8—21no—
369C22×C8—21no—
370#126—21no—
371#125C2×C4×C4711yescharacteristic
372#124C2×C4×C4711yescharacteristic
373#123—21no—
374C22⋊Q8C2×C4×C4711yescharacteristic
375#121C2×C4×C4711yescharacteristic
376C4×Q8C2×C4×C4711yescharacteristic
377C4×Q8C23×C4711yescharacteristic
378C4×Q8C23×C4711yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4C2×C4×C4711yescharacteristic
383C4×D4C23×C4711yescharacteristic
384C4×D4C23×C4711yescharacteristic
385#117—21no—
386#117—21no—
387#117C2×C4×C4711yescharacteristic
388C2×C42—21no—
389C2×C42C23×C4711yescharacteristic
390#107C2×C4×C4711yescharacteristic
391#107C2×C4×C4711yescharacteristic
392#106C2×C4×C4711yescharacteristic
393#106C2×C4×C4711yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8C2×C4×C4711yescharacteristic
401C4⋊C8C2×C4×C4711yescharacteristic
402C4⋊C8D4×C4711yescharacteristic
403C4⋊C8D4×C4711yescharacteristic
404C4⋊C8C23×C4711yescharacteristic
405C4⋊C8C23×C4711yescharacteristic
406C4⋊C8C23×C4711yescharacteristic
407C4⋊C8C23×C4711yescharacteristic
408#103C2×C4×C4711yescharacteristic
409#103C2×C4×C4711yescharacteristic
410#103C2×C4×C4711yescharacteristic
411#103C2×C4×C4711yescharacteristic
412#102C2×C4×C4711yescharacteristic
413#102C2×C4×C4711yescharacteristic
414#102C2×C4×C4711yescharacteristic
415#102C2×C4×C4711yescharacteristic
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8C2×C4×C4711yescharacteristic
421C22⋊C8C2×C4×C4711yescharacteristic
422C22⋊C8D4×C4711yescharacteristic
423C22⋊C8D4×C4711yescharacteristic
424#97—21no—
425#97—21no—
426#97—21no—
427#97—21no—
428C4×C8—21no—
429C4×C8C23×C4711yescharacteristic
430C4×C8C23×C4711yescharacteristic
431C4×C8C23×C4711yescharacteristic
432C4×C8C23×C4711yescharacteristic
433C4×C8C23×C4711yescharacteristic
434C4×C8C23×C4711yescharacteristic
435#41—41no—
436#41—41no—
437C2×Q8C22×C4×C4711yescharacteristic
438C2×Q8C22×C4×C4711yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C22×C4×C4711yescharacteristic
442C2×D4C22×C4×C4711yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4C22×C4×C4711yescharacteristic
448C22×C4C2×D4×C4711yescharacteristic
449C22×C4#41×C4711yescharacteristic
450Q16—41no—
451SD16—41no—
452SD16—41no—
453D8—41no—
454M16—42no—
455M16—81no—
456M16—81no—
457M16—81no—
458M16—81no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—81no—
466C2×C8—81no—
467C2×C8C22×C4×C4711yescharacteristic
468C2×C8C22×C4×C4711yescharacteristic
469C2×C8C22×C4×C4711yescharacteristic
470C2×C8C22×C4×C4711yescharacteristic
471C2×C8C2×D4×C4711yescharacteristic
472C2×C8C2×D4×C4711yescharacteristic
473C2×C8C2×D4×C4711yescharacteristic
474C2×C8C2×D4×C4711yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4C22×C4×C4711yescharacteristic
482C4⋊C4C22×C4×C4711yescharacteristic
483C4⋊C4C22×C4×C4711yescharacteristic
484C4⋊C4C22×C4×C4711yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42C22×C4×C4711yescharacteristic
498C42C2×D4×C4711yescharacteristic
499C42#41×C4711yescharacteristic
500C42C24×C4711yescharacteristic
501C23—21no—
502C23—21no—
503C23C4×D4×C4711yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—21no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—21no—
512D4—42no—
513D4—81no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—81no—
531C2×C4C4×D4×C4711yescharacteristic
532C2×C4C4×D4×C4711yescharacteristic
533C2×C4C4×D4×C4711yescharacteristic
534C2×C4C23×C4×C4711yescharacteristic
535C2×C4C22×D4×C4711yescharacteristic
536C2×C4C2×#41×C4711yescharacteristic
537C8—22no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22C2×C4×D4×C4711yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4C47×#56811yescharacteristic
572C4C47×#56811yescharacteristic
573C4C47×#57711yescharacteristic
574C4C47×#57711yescharacteristic
575C2—41no—
576C2—81no—
577C2—81no—
578C2C47×#293011yescharacteristic
579C2C47×#295211yescharacteristic
580C2C47×#295611yescharacteristic
subgroupG/H
centerC2×C4×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC42C24×C47
socleC22×C47C2×C4×D4
prime radicalC47×#449C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C47×#431 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2993C2semidirect
3. C47×#2989C2semidirect
4. C47×#1594C2semidirect
5. C47×#1593C2semidirect
6. C47×#1590C2semidirect
7. C47×#1590C2semidirect
8. C47×#1587C2semidirect
9. C47×#1586C2semidirect
10. C47×#1583C2semidirect
11. C47×#1582C2semidirect
12. C47×#1570C2semidirect
13. C47×#1489C2semidirect
14. C47×#1483C2semidirect
15. C47×#1453C2semidirect
260. #17955C47direct (N × H)
286. #2993C2×C47semidirect
287. #2989C2×C47semidirect
288. #1594C2×C47semidirect
289. #1593C2×C47semidirect
290. #1590C2×C47semidirect
291. #1590C2×C47semidirect
292. #1587C2×C47semidirect
293. #1586C2×C47semidirect
294. #1583C2×C47semidirect
295. #1582C2×C47semidirect
296. #1570C2×C47semidirect
297. #1489C2×C47semidirect
298. #1483C2×C47semidirect
299. #1453C2×C47semidirect
357. C47#17955direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31022
C47×#29932
C47×#29892
C47×#15942
C47×#15932
C47×#15902
C47×#15872
C47×#15862
C47×#15832
C47×#15822
C47×#15702
C47×#14892
C47×#14832
C47×#14532
#1795547