Finite Group Databasebeta

← C47×#19253 #26058951

Subgroups — C47×#19253 #26058951

Order 12032.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3247C211yesmaximal, characteristic
2C47×#3233C211yesmaximal, characteristic, complemented
3C47×#3182C211yesmaximal, characteristic, complemented
4C47×#2969C211yesmaximal, characteristic, complemented
5C47×#1704C211yesmaximal, characteristic, complemented
6C47×#1698C211yesmaximal, characteristic, complemented
7C47×#1695C211yesmaximal, characteristic, complemented
8C47×#1685C211yesmaximal, characteristic, complemented
9C47×#1683C211yesmaximal, characteristic, complemented
10C47×#1677C211yesmaximal, characteristic, complemented
11C47×#1676C211yesmaximal, characteristic, complemented
12C47×#1666C211yesmaximal, characteristic, complemented
13C47×#1565C211yesmaximal, characteristic, complemented
14C47×#1543C211yesmaximal, characteristic, complemented
15C47×#1542C211yesmaximal, characteristic, complemented
16C47×#533C2211yescharacteristic
17C47×#532C2211yescharacteristic
18C47×#529C2211yescharacteristic
19C47×#500C2211yescharacteristic
20C47×#499—21no—
21C47×#492C2211yescharacteristic
22C47×#488—21no—
23C47×#487C2211yescharacteristic
24C47×#486C2211yescharacteristic
25C47×#485—21no—
26C47×#482—21no—
27C47×#478—21no—
28C47×#477C2211yescharacteristic
29C47×#477C2211yescharacteristic
30C47×#476C2211yescharacteristic
31C47×#476C2211yescharacteristic
32C47×#475C2211yescharacteristic
33C47×#474C2211yescharacteristic
34C47×#468—21no—
35C47×#468—21no—
36C47×#466—21no—
37C47×#465—21no—
38C47×#463—21no—
39C47×#460C2211yescharacteristic
40C47×#459C2211yescharacteristic
41C47×#446C2211yescharacteristic
42C8×Q8×C47C2211yescharacteristic
43C47×#440—21no—
44C47×#440—21no—
45C47×#436—21no—
46C47×#436C2211yescharacteristic
47C47×#435—21no—
48C8×D4×C47C2211yescharacteristic
49C47×#433—21no—
50C47×#431C2211yescharacteristic
51C47×#431C2211yescharacteristic
52C2×C4⋊C8×C47C2211yescharacteristic
53C47×#405—21no—
54C4×M16×C47C2211yescharacteristic
55C47×#335C2211yescharacteristic
56C47×#335C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#334C2211yescharacteristic
59C47×#333C2211yescharacteristic
60C47×#333C2211yescharacteristic
61C47×#333C2211yescharacteristic
62C47×#333C2211yescharacteristic
63C47×#332C2211yescharacteristic
64C47×#332C2211yescharacteristic
65C47×#331C2211yescharacteristic
66C47×#331C2211yescharacteristic
67C2×#41×C47—21no—
68C2×SD16×C47—21no—
69C2×SD16×C47—21no—
70C2×SD16×C47—21no—
71C2×D8×C47—21no—
72C2×M16×C47—21no—
73C2×M16×C47D411yescharacteristic
74C2×M16×C47D411yescharacteristic
75C22×C8×C47—21no—
76C22×C8×C47—21no—
77C4⋊Q8×C47C2311yescharacteristic
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80#127×C47C2311yescharacteristic
81#126×C47—21no—
82#125×C47—21no—
83#125×C47D411yescharacteristic
84#124×C47—21no—
85#124×C47D411yescharacteristic
86#123×C47—21no—
87C22⋊Q8×C47—21no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47D411yescharacteristic
90#121×C47—21no—
91#121×C47—21no—
92#121×C47D411yescharacteristic
93C4×Q8×C47—21no—
94C4×Q8×C47—21no—
95C4×Q8×C47C2311yescharacteristic
96C4×D4×C47—21no—
97C4×D4×C47—21no—
98C4×D4×C47—21no—
99C4×D4×C47C2311yescharacteristic
100#117×C47—21no—
101#117×C47—21no—
102C2×C42×C47C2311yescharacteristic
103#107×C47—21no—
104#107×C47—21no—
105#107×C47—21no—
106#107×C47—21no—
107#107×C47—21no—
108#106×C47—21no—
109#106×C47—21no—
110#106×C47—21no—
111C4⋊C8×C47—21no—
112C4⋊C8×C47—21no—
113C4⋊C8×C47—21no—
114C4⋊C8×C47C2311yescharacteristic
115C4⋊C8×C47C2311yescharacteristic
116C4⋊C8×C47C2311yescharacteristic
117C4⋊C8×C47C2311yescharacteristic
118C4⋊C8×C47C2311yescharacteristic
119C4⋊C8×C47C2311yescharacteristic
120#103×C47—21no—
121#103×C47—21no—
122#103×C47—21no—
123#103×C47—21no—
124#103×C47—21no—
125#102×C47—21no—
126#102×C47—21no—
127#102×C47—21no—
128#102×C47—21no—
129#102×C47—21no—
130#102×C47—21no—
131#102×C47—21no—
132C22⋊C8×C47—21no—
133C22⋊C8×C47—21no—
134C22⋊C8×C47—21no—
135C22⋊C8×C47—21no—
136#97×C47—21no—
137#97×C47D411yescharacteristic
138#97×C47D411yescharacteristic
139C4×C8×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144#41×C47—82no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47C2×D411yescharacteristic
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—41no—
154C2×D4×C47C2×D411yescharacteristic
155C22×C4×C47—21no—
156C22×C4×C47—41no—
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47C2×D411yescharacteristic
159C22×C4×C47#4111yescharacteristic
160SD16×C47—42no—
161SD16×C47—42no—
162SD16×C47—81no—
163D8×C47—81no—
164M16×C47—22no—
165M16×C47—41no—
166M16×C47—42no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—42no—
174C2×C8×C47—81no—
175C2×C8×C47C2×D411yescharacteristic
176C2×C8×C47C2×D411yescharacteristic
177C2×C8×C47C2×D411yescharacteristic
178C2×C8×C47C2×D411yescharacteristic
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
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—41no—
190C4⋊C4×C47—41no—
191C4⋊C4×C47C2×D411yescharacteristic
192C4⋊C4×C47C2×D411yescharacteristic
193C22⋊C4×C47—21no—
194C22⋊C4×C47—21no—
195C22⋊C4×C47—21no—
196C22⋊C4×C47—21no—
197C22⋊C4×C47—21no—
198C22⋊C4×C47—41no—
199C22⋊C4×C47—41no—
200C22⋊C4×C47—41no—
201C42×C47—21no—
202C42×C47—41no—
203C42×C47C2×D411yescharacteristic
204C42×C47C2×D411yescharacteristic
205C42×C47#4111yescharacteristic
206C42×C47C2411yescharacteristic
207C23×C47—21no—
208C23×C47—41no—
209C23×C47#12111yescharacteristic
210Q8×C47—21no—
211Q8×C47—21no—
212Q8×C47—41no—
213Q8×C47—41no—
214Q8×C47—81no—
215Q8×C47—81no—
216D4×C47—21no—
217D4×C47—21no—
218D4×C47—41no—
219D4×C47—41no—
220D4×C47—41no—
221D4×C47—41no—
222D4×C47—81no—
223D4×C47—81no—
224D4×C47—82no—
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—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—82no—
239C2×C4×C47#12111yescharacteristic
240C2×C4×C47#12111yescharacteristic
241C2×C4×C47#12111yescharacteristic
242C2×C4×C47C22×D411yescharacteristic
243C2×C4×C47C22×D411yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C8×C47—21no—
246C8×C47—21no—
247C8×C47—21no—
248C8×C47—41no—
249C8×C47—41no—
250C8×C47—41no—
251C8×C47—41no—
252C8×C47—41no—
253C8×C47—41no—
254C8×C47#13512yes—
255#19253C4711yesmaximal, characteristic, direct product factor, Sylow
256C22×C47—21no—
257C22×C47—21no—
258C22×C47—21no—
259C22×C47—41no—
260C22×C47—41no—
261C22×C47—41no—
262C22×C47—81no—
263C22×C47—81no—
264C22×C47—81no—
265C22×C47C2×#12111yescharacteristic
266C4×C47—21no—
267C4×C47—21no—
268C4×C47—21no—
269C4×C47—21no—
270C4×C47—41no—
271C4×C47—41no—
272C4×C47—41no—
273C4×C47—81no—
274C4×C47—81no—
275C4×C47—81no—
276C4×C47C2×#13511yescharacteristic
277C4×C47#57511yescharacteristic
278C4×C47#57711yescharacteristic
279C4×C47#57811yescharacteristic
280#3247C2×C4711yescharacteristic
281#3233C2×C4711yescharacteristic, complemented
282#3182C2×C4711yescharacteristic, complemented
283#2969C2×C4711yescharacteristic, complemented
284#1704C2×C4711yescharacteristic, complemented
285#1698C2×C4711yescharacteristic, complemented
286#1695C2×C4711yescharacteristic, complemented
287#1685C2×C4711yescharacteristic, complemented
288#1683C2×C4711yescharacteristic, complemented
289#1677C2×C4711yescharacteristic, complemented
290#1676C2×C4711yescharacteristic, complemented
291#1666C2×C4711yescharacteristic, complemented
292#1565C2×C4711yescharacteristic, complemented
293#1543C2×C4711yescharacteristic, complemented
294#1542C2×C4711yescharacteristic, complemented
295C2×C47—41no—
296C2×C47—81no—
297C2×C47—161no—
298C2×C47#303511yescharacteristic
299C2×C47#306311yescharacteristic
300C2×C47#306811yescharacteristic
301#533C22×C4711yescharacteristic
302#532C22×C4711yescharacteristic
303#529C22×C4711yescharacteristic
304#500C22×C4711yescharacteristic
305#499—21no—
306#492C22×C4711yescharacteristic
307#488—21no—
308#487C22×C4711yescharacteristic
309#486C22×C4711yescharacteristic
310#485—21no—
311#482—21no—
312#478—21no—
313#477C22×C4711yescharacteristic
314#477C22×C4711yescharacteristic
315#476C22×C4711yescharacteristic
316#476C22×C4711yescharacteristic
317#475C22×C4711yescharacteristic
318#474C22×C4711yescharacteristic
319#468—21no—
320#468—21no—
321#466—21no—
322#465—21no—
323#463—21no—
324#460C22×C4711yescharacteristic
325#459C22×C4711yescharacteristic
326#446C22×C4711yescharacteristic
327C8×Q8C22×C4711yescharacteristic
328#440—21no—
329#440—21no—
330#436—21no—
331#436C22×C4711yescharacteristic
332#435—21no—
333C8×D4C22×C4711yescharacteristic
334#433—21no—
335#431C22×C4711yescharacteristic
336#431C22×C4711yescharacteristic
337C2×C4⋊C8C22×C4711yescharacteristic
338#405—21no—
339C4×M16C22×C4711yescharacteristic
340#335C22×C4711yescharacteristic
341#335C22×C4711yescharacteristic
342#334C22×C4711yescharacteristic
343#334C22×C4711yescharacteristic
344#333C22×C4711yescharacteristic
345#333C22×C4711yescharacteristic
346#333C22×C4711yescharacteristic
347#333C22×C4711yescharacteristic
348#332C22×C4711yescharacteristic
349#332C22×C4711yescharacteristic
350#331C22×C4711yescharacteristic
351#331C22×C4711yescharacteristic
352C47#1925311yescharacteristic, direct product factor, Sylow
353C2×#41—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×D8—21no—
358C2×M16—21no—
359C2×M16D4×C4711yescharacteristic
360C2×M16D4×C4711yescharacteristic
361C22×C8—21no—
362C22×C8—21no—
363C4⋊Q8C23×C4711yescharacteristic
364C4⋊Q8C23×C4711yescharacteristic
365C4⋊Q8C23×C4711yescharacteristic
366#127C23×C4711yescharacteristic
367#126—21no—
368#125—21no—
369#125D4×C4711yescharacteristic
370#124—21no—
371#124D4×C4711yescharacteristic
372#123—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8D4×C4711yescharacteristic
376#121—21no—
377#121—21no—
378#121D4×C4711yescharacteristic
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8C23×C4711yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4C23×C4711yescharacteristic
386#117—21no—
387#117—21no—
388C2×C42C23×C4711yescharacteristic
389#107—21no—
390#107—21no—
391#107—21no—
392#107—21no—
393#107—21no—
394#106—21no—
395#106—21no—
396#106—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8C23×C4711yescharacteristic
401C4⋊C8C23×C4711yescharacteristic
402C4⋊C8C23×C4711yescharacteristic
403C4⋊C8C23×C4711yescharacteristic
404C4⋊C8C23×C4711yescharacteristic
405C4⋊C8C23×C4711yescharacteristic
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422#97—21no—
423#97D4×C4711yescharacteristic
424#97D4×C4711yescharacteristic
425C4×C8—21no—
426C4×C8—21no—
427C4×C8—21no—
428C4×C8C23×C4711yescharacteristic
429C4×C8C23×C4711yescharacteristic
430#41—82no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8C2×D4×C4711yescharacteristic
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—41no—
440C2×D4C2×D4×C4711yescharacteristic
441C22×C4—21no—
442C22×C4—41no—
443C22×C4C2×D4×C4711yescharacteristic
444C22×C4C2×D4×C4711yescharacteristic
445C22×C4#41×C4711yescharacteristic
446SD16—42no—
447SD16—42no—
448SD16—81no—
449D8—81no—
450M16—22no—
451M16—41no—
452M16—42no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—42no—
460C2×C8—81no—
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⋊C4—21no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4C2×D4×C4711yescharacteristic
478C4⋊C4C2×D4×C4711yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C42—21no—
488C42—41no—
489C42C2×D4×C4711yescharacteristic
490C42C2×D4×C4711yescharacteristic
491C42#41×C4711yescharacteristic
492C42C24×C4711yescharacteristic
493C23—21no—
494C23—41no—
495C23#121×C4711yescharacteristic
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—81no—
502D4—21no—
503D4—21no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—81no—
509D4—81no—
510D4—82no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—82no—
525C2×C4#121×C4711yescharacteristic
526C2×C4#121×C4711yescharacteristic
527C2×C4#121×C4711yescharacteristic
528C2×C4C22×D4×C4711yescharacteristic
529C2×C4C22×D4×C4711yescharacteristic
530C2×C4C2×#41×C4711yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8#135×C4712yes—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22C2×#121×C4711yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4C2×#135×C4711yescharacteristic
562C4C47×#57511yescharacteristic
563C4C47×#57711yescharacteristic
564C4C47×#57811yescharacteristic
565C2—41no—
566C2—81no—
567C2—161no—
568C2C47×#303511yescharacteristic
569C2C47×#306311yescharacteristic
570C2C47×#306811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3247C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#3233C2semidirect
3. C47×#3182C2semidirect
4. C47×#2969C2semidirect
5. C47×#1704C2semidirect
6. C47×#1698C2semidirect
7. C47×#1695C2semidirect
8. C47×#1685C2semidirect
9. C47×#1683C2semidirect
10. C47×#1677C2semidirect
11. C47×#1676C2semidirect
12. C47×#1666C2semidirect
13. C47×#1565C2semidirect
14. C47×#1543C2semidirect
15. C47×#1542C2semidirect
255. #19253C47direct (N × H)
281. #3233C2×C47semidirect
282. #3182C2×C47semidirect
283. #2969C2×C47semidirect
284. #1704C2×C47semidirect
285. #1698C2×C47semidirect
286. #1695C2×C47semidirect
287. #1685C2×C47semidirect
288. #1683C2×C47semidirect
289. #1677C2×C47semidirect
290. #1676C2×C47semidirect
291. #1666C2×C47semidirect
292. #1565C2×C47semidirect
293. #1543C2×C47semidirect
294. #1542C2×C47semidirect
352. C47#19253direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32472
C47×#32332
C47×#31822
C47×#29692
C47×#17042
C47×#16982
C47×#16952
C47×#16852
C47×#16832
C47×#16772
C47×#16762
C47×#16662
C47×#15652
C47×#15432
C47×#15422
#1925347