Finite Group Databasebeta

← C47×#19455 #26059153

Subgroups — C47×#19455 #26059153

Order 12032.

594 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3228C211yesmaximal, characteristic, complemented
2C47×#3116C211yesmaximal, characteristic, complemented
3C47×#3106C211yesmaximal, characteristic
4C47×#2989C211yesmaximal, characteristic, complemented
5C47×#1702C211yesmaximal, characteristic, complemented
6C47×#1701C211yesmaximal, characteristic, complemented
7C47×#1698C211yesmaximal, characteristic, complemented
8C47×#1697C211yesmaximal, characteristic, complemented
9C47×#1696C211yesmaximal, characteristic, complemented
10C47×#1695C211yesmaximal, characteristic, complemented
11C47×#1692C211yesmaximal, characteristic, complemented
12C47×#1691C211yesmaximal, characteristic, complemented
13C47×#1572C211yesmaximal, characteristic, complemented
14C47×#1551C211yesmaximal, characteristic, complemented
15C47×#1542C211yesmaximal, characteristic, complemented
16C47×#533C2211yescharacteristic
17C47×#532C2211yescharacteristic
18C4×#41×C47C2211yescharacteristic
19C47×#500C2211yescharacteristic
20C47×#498C2211yescharacteristic
21C47×#486C2211yescharacteristic
22C47×#486C2211yescharacteristic
23C47×#485—21no—
24C47×#482—21no—
25C47×#482—21no—
26C47×#482—21no—
27C47×#478—21no—
28C47×#478—21no—
29C47×#477C2211yescharacteristic
30C47×#477C2211yescharacteristic
31C47×#476C2211yescharacteristic
32C47×#476C2211yescharacteristic
33C47×#462C2211yescharacteristic
34C47×#461C2211yescharacteristic
35C47×#460C2211yescharacteristic
36C47×#459C2211yescharacteristic
37C47×#452—21no—
38C47×#449—21no—
39C47×#446C2211yescharacteristic
40C47×#446C2211yescharacteristic
41C47×#441—21no—
42C47×#440—21no—
43C4×SD16×C47—21no—
44C4×D8×C47—21no—
45C47×#436C2211yescharacteristic
46C47×#436C2211yescharacteristic
47C47×#435—21no—
48C47×#435—21no—
49C47×#432—21no—
50C47×#432C2211yescharacteristic
51C47×#431C2211yescharacteristic
52C47×#431C2211yescharacteristic
53C47×#423—21no—
54C2×C4⋊C8×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×#41×C47D411yescharacteristic
69C2×Q16×C47—21no—
70C2×SD16×C47—21no—
71C2×SD16×C47—21no—
72C2×D8×C47—21no—
73C2×M16×C47—21no—
74C2×M16×C47—21no—
75C22×C8×C47—21no—
76C4⋊Q8×C47C2311yescharacteristic
77C4⋊Q8×C47C2311yescharacteristic
78C4⋊Q8×C47C2311yescharacteristic
79#127×C47C2311yescharacteristic
80#125×C47—21no—
81#124×C47—21no—
82C22⋊Q8×C47—21no—
83C22⋊Q8×C47—21no—
84#121×C47—21no—
85#121×C47—21no—
86C4×Q8×C47—21no—
87C4×Q8×C47—21no—
88C4×Q8×C47D411yescharacteristic
89C4×Q8×C47C2311yescharacteristic
90C4×D4×C47—21no—
91C4×D4×C47—21no—
92C4×D4×C47—21no—
93C4×D4×C47—21no—
94C4×D4×C47D411yescharacteristic
95C4×D4×C47C2311yescharacteristic
96#117×C47—21no—
97#117×C47—21no—
98#117×C47D411yescharacteristic
99C2×C42×C47—21no—
100C2×C42×C47C2311yescharacteristic
101#107×C47—21no—
102#107×C47—21no—
103#107×C47—21no—
104#107×C47—21no—
105#106×C47—21no—
106#106×C47—21no—
107#106×C47—21no—
108#106×C47—21no—
109C4⋊C8×C47—21no—
110C4⋊C8×C47—21no—
111C4⋊C8×C47—21no—
112C4⋊C8×C47D411yescharacteristic
113C4⋊C8×C47D411yescharacteristic
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#102×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—
136C22⋊C8×C47D411yescharacteristic
137C22⋊C8×C47D411yescharacteristic
138#97×C47—21no—
139#97×C47—21no—
140#97×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144#41×C47—41no—
145#41×C47—41no—
146#41×C47—82no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47C2×D411yescharacteristic
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—41no—
156C2×D4×C47C2×D411yescharacteristic
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—41no—
161C22×C4×C47C2×D411yescharacteristic
162C22×C4×C47C2×D411yescharacteristic
163C22×C4×C47#4111yescharacteristic
164Q16×C47—42no—
165SD16×C47—42no—
166SD16×C47—42no—
167D8×C47—42no—
168M16×C47—81no—
169M16×C47—81no—
170C2×C8×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—81no—
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—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—41no—
197C22⋊C4×C47—41no—
198C22⋊C4×C47—41no—
199C42×C47—21no—
200C42×C47—21no—
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—42no—
219D4×C47—41no—
220D4×C47—41no—
221D4×C47—41no—
222D4×C47—41no—
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—42no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—81no—
240C2×C4×C47—82no—
241C2×C4×C47#12111yescharacteristic
242C2×C4×C47#12111yescharacteristic
243C2×C4×C47#12111yescharacteristic
244C2×C4×C47C22×D411yescharacteristic
245C2×C4×C47C22×D411yescharacteristic
246C2×C4×C47C2×#4111yescharacteristic
247C8×C47—21no—
248C8×C47—21no—
249C8×C47—21no—
250C8×C47—21no—
251C8×C47—41no—
252C8×C47—41no—
253C8×C47—41no—
254C8×C47—41no—
255C8×C47—41no—
256C8×C47—41no—
257#19455C4711yesmaximal, characteristic, direct product factor, Sylow
258C22×C47—21no—
259C22×C47—21no—
260C22×C47—21no—
261C22×C47—41no—
262C22×C47—41no—
263C22×C47—41no—
264C22×C47—81no—
265C22×C47—81no—
266C22×C47—81no—
267C22×C47C2×#12111yescharacteristic
268C4×C47—21no—
269C4×C47—21no—
270C4×C47—21no—
271C4×C47—21no—
272C4×C47—41no—
273C4×C47—41no—
274C4×C47—41no—
275C4×C47—81no—
276C4×C47—81no—
277C4×C47—81no—
278C4×C47#57511yescharacteristic
279C4×C47#57511yescharacteristic
280C4×C47#57711yescharacteristic
281C4×C47#57811yescharacteristic
282#3228C2×C4711yescharacteristic, complemented
283#3116C2×C4711yescharacteristic, complemented
284#3106C2×C4711yescharacteristic
285#2989C2×C4711yescharacteristic, complemented
286#1702C2×C4711yescharacteristic, complemented
287#1701C2×C4711yescharacteristic, complemented
288#1698C2×C4711yescharacteristic, complemented
289#1697C2×C4711yescharacteristic, complemented
290#1696C2×C4711yescharacteristic, complemented
291#1695C2×C4711yescharacteristic, complemented
292#1692C2×C4711yescharacteristic, complemented
293#1691C2×C4711yescharacteristic, complemented
294#1572C2×C4711yescharacteristic, complemented
295#1551C2×C4711yescharacteristic, complemented
296#1542C2×C4711yescharacteristic, complemented
297C2×C47—41no—
298C2×C47—81no—
299C2×C47—161no—
300C2×C47#304611yescharacteristic
301C2×C47#305411yescharacteristic
302C2×C47#306811yescharacteristic
303#533C22×C4711yescharacteristic
304#532C22×C4711yescharacteristic
305C4×#41C22×C4711yescharacteristic
306#500C22×C4711yescharacteristic
307#498C22×C4711yescharacteristic
308#486C22×C4711yescharacteristic
309#486C22×C4711yescharacteristic
310#485—21no—
311#482—21no—
312#482—21no—
313#482—21no—
314#478—21no—
315#478—21no—
316#477C22×C4711yescharacteristic
317#477C22×C4711yescharacteristic
318#476C22×C4711yescharacteristic
319#476C22×C4711yescharacteristic
320#462C22×C4711yescharacteristic
321#461C22×C4711yescharacteristic
322#460C22×C4711yescharacteristic
323#459C22×C4711yescharacteristic
324#452—21no—
325#449—21no—
326#446C22×C4711yescharacteristic
327#446C22×C4711yescharacteristic
328#441—21no—
329#440—21no—
330C4×SD16—21no—
331C4×D8—21no—
332#436C22×C4711yescharacteristic
333#436C22×C4711yescharacteristic
334#435—21no—
335#435—21no—
336#432—21no—
337#432C22×C4711yescharacteristic
338#431C22×C4711yescharacteristic
339#431C22×C4711yescharacteristic
340#423—21no—
341C2×C4⋊C8C22×C4711yescharacteristic
342#335C22×C4711yescharacteristic
343#335C22×C4711yescharacteristic
344#334C22×C4711yescharacteristic
345#334C22×C4711yescharacteristic
346#333C22×C4711yescharacteristic
347#333C22×C4711yescharacteristic
348#333C22×C4711yescharacteristic
349#333C22×C4711yescharacteristic
350#332C22×C4711yescharacteristic
351#332C22×C4711yescharacteristic
352#331C22×C4711yescharacteristic
353#331C22×C4711yescharacteristic
354C47#1945511yescharacteristic, direct product factor, Sylow
355C2×#41—21no—
356C2×#41D4×C4711yescharacteristic
357C2×Q16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×D8—21no—
361C2×M16—21no—
362C2×M16—21no—
363C22×C8—21no—
364C4⋊Q8C23×C4711yescharacteristic
365C4⋊Q8C23×C4711yescharacteristic
366C4⋊Q8C23×C4711yescharacteristic
367#127C23×C4711yescharacteristic
368#125—21no—
369#124—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372#121—21no—
373#121—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8D4×C4711yescharacteristic
377C4×Q8C23×C4711yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4D4×C4711yescharacteristic
383C4×D4C23×C4711yescharacteristic
384#117—21no—
385#117—21no—
386#117D4×C4711yescharacteristic
387C2×C42—21no—
388C2×C42C23×C4711yescharacteristic
389#107—21no—
390#107—21no—
391#107—21no—
392#107—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396#106—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8D4×C4711yescharacteristic
401C4⋊C8D4×C4711yescharacteristic
402C4⋊C8C23×C4711yescharacteristic
403C4⋊C8C23×C4711yescharacteristic
404C4⋊C8C23×C4711yescharacteristic
405C4⋊C8C23×C4711yescharacteristic
406C4⋊C8C23×C4711yescharacteristic
407C4⋊C8C23×C4711yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8D4×C4711yescharacteristic
425C22⋊C8D4×C4711yescharacteristic
426#97—21no—
427#97—21no—
428#97—21no—
429C4×C8—21no—
430C4×C8C23×C4711yescharacteristic
431C4×C8C23×C4711yescharacteristic
432#41—41no—
433#41—41no—
434#41—82no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C2×D4×C4711yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4C2×D4×C4711yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—41no—
449C22×C4C2×D4×C4711yescharacteristic
450C22×C4C2×D4×C4711yescharacteristic
451C22×C4#41×C4711yescharacteristic
452Q16—42no—
453SD16—42no—
454SD16—42no—
455D8—42no—
456M16—81no—
457M16—81no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—81no—
465C2×C8C2×D4×C4711yescharacteristic
466C2×C8C2×D4×C4711yescharacteristic
467C2×C8C2×D4×C4711yescharacteristic
468C2×C8C2×D4×C4711yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4C2×D4×C4711yescharacteristic
480C4⋊C4C2×D4×C4711yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—41no—
491C42C2×D4×C4711yescharacteristic
492C42C2×D4×C4711yescharacteristic
493C42#41×C4711yescharacteristic
494C42C24×C4711yescharacteristic
495C23—21no—
496C23—41no—
497C23#121×C4711yescharacteristic
498Q8—21no—
499Q8—21no—
500Q8—41no—
501Q8—41no—
502Q8—81no—
503Q8—81no—
504D4—21no—
505D4—21no—
506D4—42no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—81no—
512D4—82no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—81no—
528C2×C4—82no—
529C2×C4#121×C4711yescharacteristic
530C2×C4#121×C4711yescharacteristic
531C2×C4#121×C4711yescharacteristic
532C2×C4C22×D4×C4711yescharacteristic
533C2×C4C22×D4×C4711yescharacteristic
534C2×C4C2×#41×C4711yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22C2×#121×C4711yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4C47×#57511yescharacteristic
566C4C47×#57511yescharacteristic
567C4C47×#57711yescharacteristic
568C4C47×#57811yescharacteristic
569C2—41no—
570C2—81no—
571C2—161no—
572C2C47×#304611yescharacteristic
573C2C47×#305411yescharacteristic
574C2C47×#306811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3106C2
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
1. C47×#3228C2semidirect
2. C47×#3116C2semidirect
4. C47×#2989C2semidirect
5. C47×#1702C2semidirect
6. C47×#1701C2semidirect
7. C47×#1698C2semidirect
8. C47×#1697C2semidirect
9. C47×#1696C2semidirect
10. C47×#1695C2semidirect
11. C47×#1692C2semidirect
12. C47×#1691C2semidirect
13. C47×#1572C2semidirect
14. C47×#1551C2semidirect
15. C47×#1542C2semidirect
257. #19455C47direct (N × H)
282. #3228C2×C47semidirect
283. #3116C2×C47semidirect
285. #2989C2×C47semidirect
286. #1702C2×C47semidirect
287. #1701C2×C47semidirect
288. #1698C2×C47semidirect
289. #1697C2×C47semidirect
290. #1696C2×C47semidirect
291. #1695C2×C47semidirect
292. #1692C2×C47semidirect
293. #1691C2×C47semidirect
294. #1572C2×C47semidirect
295. #1551C2×C47semidirect
296. #1542C2×C47semidirect
354. C47#19455direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32282
C47×#31162
C47×#31062
C47×#29892
C47×#17022
C47×#17012
C47×#16982
C47×#16972
C47×#16962
C47×#16952
C47×#16922
C47×#16912
C47×#15722
C47×#15512
C47×#15422
#1945547