Finite Group Databasebeta

← C47×#19782 #26059480

Subgroups — C47×#19782 #26059480

Order 12032.

598 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×D8×C47C211yesmaximal, characteristic
2C47×#3360C211yesmaximal, characteristic
3C47×#3328C211yesmaximal, characteristic, complemented
4C47×#3299C211yesmaximal, characteristic, complemented
5C47×#1718C211yesmaximal, characteristic, complemented
6C47×#1703C211yesmaximal, characteristic, complemented
7C47×#1684C211yesmaximal, characteristic, complemented
8C47×#1679C211yesmaximal, characteristic, complemented
9C47×#1674C211yesmaximal, characteristic, complemented
10C47×#1652C211yesmaximal, characteristic, complemented
11C47×#1651C211yesmaximal, characteristic, complemented
12C47×#1644C211yesmaximal, characteristic, complemented
13C47×#1637C211yesmaximal, characteristic, complemented
14C47×#1581C211yesmaximal, characteristic
15C47×#1579C211yesmaximal, characteristic, complemented
16C47×#556C2211yescharacteristic
17C47×#554C2211yescharacteristic
18D4×Q8×C47C2211yescharacteristic
19D4×Q8×C47C2211yescharacteristic
20C47×#500—21no—
21C47×#500C2211yescharacteristic
22C47×#498C2211yescharacteristic
23C47×#488—21no—
24C47×#487C2211yescharacteristic
25C47×#487C2211yescharacteristic
26C47×#487C2211yescharacteristic
27C47×#487C2211yescharacteristic
28C47×#485—21no—
29C47×#484—21no—
30C47×#479—21no—
31C47×#477C2211yescharacteristic
32C47×#476C2211yescharacteristic
33C47×#475C2211yescharacteristic
34C47×#474—21no—
35C47×#474—21no—
36C47×#474C2211yescharacteristic
37C47×#474C2211yescharacteristic
38C47×#470—21no—
39C47×#467—21no—
40C47×#463—21no—
41C47×#462C2211yescharacteristic
42C47×#462C2211yescharacteristic
43C47×#461C2211yescharacteristic
44C47×#451—21no—
45C47×#451—21no—
46C8×Q8×C47C2211yescharacteristic
47C8×Q8×C47C2211yescharacteristic
48C4×Q16×C47C2211yescharacteristic
49C4×SD16×C47—21no—
50C4×D8×C47—21no—
51C4×D8×C47C2211yescharacteristic
52C47×#436C2211yescharacteristic
53C8×D4×C47C2211yescharacteristic
54C47×#419—21no—
55C2×#103×C47—21no—
56C47×#335C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#332C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C22×Q8×C47—21no—
68C22×Q8×C47—21no—
69C2×Q16×C47—21no—
70C2×Q16×C47—21no—
71C2×Q16×C47D411yescharacteristic
72C2×SD16×C47—21no—
73C2×D8×C47D411yescharacteristic
74C2×M16×C47—21no—
75C22×C8×C47—21no—
76C4⋊Q8×C47—21no—
77C4⋊Q8×C47—21no—
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81C4⋊Q8×C47C2311yescharacteristic
82#126×C47—41no—
83#125×C47—21no—
84#124×C47—21no—
85C22⋊Q8×C47—21no—
86C22⋊Q8×C47—21no—
87C22⋊Q8×C47—21no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—41no—
90C22⋊Q8×C47—41no—
91C22⋊Q8×C47—41no—
92C4×Q8×C47—21no—
93C4×Q8×C47C2311yescharacteristic
94C4×Q8×C47C2311yescharacteristic
95C4×D4×C47—21no—
96C4×D4×C47—21no—
97C4×D4×C47—21no—
98C4×D4×C47C2311yescharacteristic
99C4×D4×C47C2311yescharacteristic
100#117×C47—21no—
101C2×C4⋊C4×C47—21no—
102#107×C47—21no—
103#107×C47—21no—
104#107×C47—21no—
105#107×C47—21no—
106#107×C47—21no—
107#107×C47D411yescharacteristic
108#107×C47D411yescharacteristic
109#106×C47—21no—
110#106×C47—21no—
111#106×C47—41no—
112C4⋊C8×C47—21no—
113C4⋊C8×C47—21no—
114C4⋊C8×C47C2311yescharacteristic
115C4⋊C8×C47C2311yescharacteristic
116C4⋊C8×C47C2311yescharacteristic
117C4⋊C8×C47C2311yescharacteristic
118#103×C47—21no—
119#103×C47—21no—
120#103×C47—21no—
121#103×C47—21no—
122#103×C47—21no—
123#103×C47—21no—
124#103×C47—21no—
125#103×C47—21no—
126#103×C47—21no—
127#103×C47—21no—
128#103×C47—21no—
129#103×C47—41no—
130#103×C47D411yescharacteristic
131#103×C47D411yescharacteristic
132#102×C47—21no—
133#102×C47—21no—
134#102×C47—21no—
135#102×C47D411yescharacteristic
136#102×C47D411yescharacteristic
137C22⋊C8×C47—21no—
138C22⋊C8×C47—21no—
139C4×C8×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—41no—
149C2×Q8×C47—41no—
150C2×Q8×C47—42no—
151C2×Q8×C47—42no—
152C2×Q8×C47—81no—
153C2×Q8×C47—81no—
154C2×Q8×C47C2×D411yescharacteristic
155C2×Q8×C47C2×D411yescharacteristic
156C2×D4×C47C2×D411yescharacteristic
157C2×D4×C47C2×D411yescharacteristic
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—41no—
161C22×C4×C47—41no—
162C22×C4×C47—41no—
163Q16×C47—22no—
164Q16×C47—81no—
165Q16×C47—81no—
166SD16×C47—42no—
167D8×C47—22no—
168M16×C47—81no—
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×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×C47—41no—
192C4⋊C4×C47—41no—
193C4⋊C4×C47—41no—
194C4⋊C4×C47C2×D411yescharacteristic
195C4⋊C4×C47C2×D411yescharacteristic
196C4⋊C4×C47C2×D411yescharacteristic
197C4⋊C4×C47C2×D411yescharacteristic
198C22⋊C4×C47—21no—
199C22⋊C4×C47—21no—
200C22⋊C4×C47—41no—
201C22⋊C4×C47—41no—
202C22⋊C4×C47—41no—
203C22⋊C4×C47—41no—
204C22⋊C4×C47—41no—
205C42×C47—21no—
206C42×C47—21no—
207C42×C47—41no—
208C42×C47C2411yescharacteristic
209C23×C47—21no—
210C23×C47—21no—
211Q8×C47—21no—
212Q8×C47—21no—
213Q8×C47—21no—
214Q8×C47—41no—
215Q8×C47—41no—
216Q8×C47—41no—
217Q8×C47—41no—
218Q8×C47—41no—
219Q8×C47—41no—
220Q8×C47—82no—
221Q8×C47—82no—
222Q8×C47—81no—
223Q8×C47#13512yes—
224D4×C47—21no—
225D4×C47—21no—
226D4×C47—21no—
227D4×C47#13712yes—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—82no—
243C2×C4×C47—82no—
244C2×C4×C47—161no—
245C2×C4×C47C22×D411yescharacteristic
246C2×C4×C47C22×D411yescharacteristic
247C2×C4×C47H(5,𝔽2)11yescharacteristic
248C8×C47—21no—
249C8×C47—21no—
250C8×C47—21no—
251C8×C47—21no—
252C8×C47—41no—
253C8×C47—41no—
254C8×C47—41no—
255C8×C47—41no—
256C8×C47—41no—
257#19782C4711yesmaximal, characteristic, direct product factor, Sylow
258C22×C47—22no—
259C22×C47—41no—
260C22×C47—41no—
261C22×C47—41no—
262C22×C47—41no—
263C22×C47—41no—
264C22×C47D4211yescharacteristic
265C4×C47—22no—
266C4×C47—21no—
267C4×C47—41no—
268C4×C47—41no—
269C4×C47—41no—
270C4×C47—41no—
271C4×C47—41no—
272C4×C47—81no—
273C4×C47—81no—
274C4×C47—81no—
275C4×C47—81no—
276C4×C47C2×#13511yescharacteristic
277C4×C47C2×#13711yescharacteristic
278C4×C47#57611yescharacteristic
279C4×C47#57811yescharacteristic
280Q8×D8C2×C4711yescharacteristic
281#3360C2×C4711yescharacteristic
282#3328C2×C4711yescharacteristic, complemented
283#3299C2×C4711yescharacteristic, complemented
284#1718C2×C4711yescharacteristic, complemented
285#1703C2×C4711yescharacteristic, complemented
286#1684C2×C4711yescharacteristic, complemented
287#1679C2×C4711yescharacteristic, complemented
288#1674C2×C4711yescharacteristic, complemented
289#1652C2×C4711yescharacteristic, complemented
290#1651C2×C4711yescharacteristic, complemented
291#1644C2×C4711yescharacteristic, complemented
292#1637C2×C4711yescharacteristic, complemented
293#1581C2×C4711yescharacteristic
294#1579C2×C4711yescharacteristic, complemented
295C2×C47—42no—
296C2×C47—81no—
297C2×C47#327011yescharacteristic
298C2×C47#328011yescharacteristic
299C2×C47#328911yescharacteristic
300#556C22×C4711yescharacteristic
301#554C22×C4711yescharacteristic
302D4×Q8C22×C4711yescharacteristic
303D4×Q8C22×C4711yescharacteristic
304#500—21no—
305#500C22×C4711yescharacteristic
306#498C22×C4711yescharacteristic
307#488—21no—
308#487C22×C4711yescharacteristic
309#487C22×C4711yescharacteristic
310#487C22×C4711yescharacteristic
311#487C22×C4711yescharacteristic
312#485—21no—
313#484—21no—
314#479—21no—
315#477C22×C4711yescharacteristic
316#476C22×C4711yescharacteristic
317#475C22×C4711yescharacteristic
318#474—21no—
319#474—21no—
320#474C22×C4711yescharacteristic
321#474C22×C4711yescharacteristic
322#470—21no—
323#467—21no—
324#463—21no—
325#462C22×C4711yescharacteristic
326#462C22×C4711yescharacteristic
327#461C22×C4711yescharacteristic
328#451—21no—
329#451—21no—
330C8×Q8C22×C4711yescharacteristic
331C8×Q8C22×C4711yescharacteristic
332C4×Q16C22×C4711yescharacteristic
333C4×SD16—21no—
334C4×D8—21no—
335C4×D8C22×C4711yescharacteristic
336#436C22×C4711yescharacteristic
337C8×D4C22×C4711yescharacteristic
338#419—21no—
339C2×#103—21no—
340#335C22×C4711yescharacteristic
341#334C22×C4711yescharacteristic
342#333C22×C4711yescharacteristic
343#332C22×C4711yescharacteristic
344#332C22×C4711yescharacteristic
345#332C22×C4711yescharacteristic
346Q8⋊C8C22×C4711yescharacteristic
347Q8⋊C8C22×C4711yescharacteristic
348D4⋊C8C22×C4711yescharacteristic
349D4⋊C8C22×C4711yescharacteristic
350#322C22×C4711yescharacteristic
351C47#1978211yescharacteristic, direct product factor, Sylow
352C22×Q8—21no—
353C22×Q8—21no—
354C2×Q16—21no—
355C2×Q16—21no—
356C2×Q16D4×C4711yescharacteristic
357C2×SD16—21no—
358C2×D8D4×C4711yescharacteristic
359C2×M16—21no—
360C22×C8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8C23×C4711yescharacteristic
364C4⋊Q8C23×C4711yescharacteristic
365C4⋊Q8C23×C4711yescharacteristic
366C4⋊Q8C23×C4711yescharacteristic
367#126—41no—
368#125—21no—
369#124—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—41no—
375C22⋊Q8—41no—
376C22⋊Q8—41no—
377C4×Q8—21no—
378C4×Q8C23×C4711yescharacteristic
379C4×Q8C23×C4711yescharacteristic
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4C23×C4711yescharacteristic
384C4×D4C23×C4711yescharacteristic
385#117—21no—
386C2×C4⋊C4—21no—
387#107—21no—
388#107—21no—
389#107—21no—
390#107—21no—
391#107—21no—
392#107D4×C4711yescharacteristic
393#107D4×C4711yescharacteristic
394#106—21no—
395#106—21no—
396#106—41no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8C23×C4711yescharacteristic
400C4⋊C8C23×C4711yescharacteristic
401C4⋊C8C23×C4711yescharacteristic
402C4⋊C8C23×C4711yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—41no—
415#103D4×C4711yescharacteristic
416#103D4×C4711yescharacteristic
417#102—21no—
418#102—21no—
419#102—21no—
420#102D4×C4711yescharacteristic
421#102D4×C4711yescharacteristic
422C22⋊C8—21no—
423C22⋊C8—21no—
424C4×C8—21no—
425C4×C8—21no—
426C4×C8C23×C4711yescharacteristic
427C4×C8C23×C4711yescharacteristic
428C4×C8C23×C4711yescharacteristic
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8—42no—
436C2×Q8—42no—
437C2×Q8—81no—
438C2×Q8—81no—
439C2×Q8C2×D4×C4711yescharacteristic
440C2×Q8C2×D4×C4711yescharacteristic
441C2×D4C2×D4×C4711yescharacteristic
442C2×D4C2×D4×C4711yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448Q16—22no—
449Q16—81no—
450Q16—81no—
451SD16—42no—
452D8—22no—
453M16—81no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—81no—
460C2×C8C2×D4×C4711yescharacteristic
461C2×C8C2×D4×C4711yescharacteristic
462C2×C8C2×D4×C4711yescharacteristic
463C2×C8C2×D4×C4711yescharacteristic
464C4⋊C4—21no—
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—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4C2×D4×C4711yescharacteristic
480C4⋊C4C2×D4×C4711yescharacteristic
481C4⋊C4C2×D4×C4711yescharacteristic
482C4⋊C4C2×D4×C4711yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C42—21no—
491C42—21no—
492C42—41no—
493C42C24×C4711yescharacteristic
494C23—21no—
495C23—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—82no—
506Q8—82no—
507Q8—81no—
508Q8#135×C4712yes—
509D4—21no—
510D4—21no—
511D4—21no—
512D4#137×C4712yes—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—161no—
530C2×C4C22×D4×C4711yescharacteristic
531C2×C4C22×D4×C4711yescharacteristic
532C2×C4H(5,𝔽2)×C4711yescharacteristic
533C8—21no—
534C8—21no—
535C8—21no—
536C8—21no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C22—22no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22D42×C4711yescharacteristic
549C4—21no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4C2×#135×C4711yescharacteristic
561C4C2×#137×C4711yescharacteristic
562C4C47×#57611yescharacteristic
563C4C47×#57811yescharacteristic
564C2—42no—
565C2—81no—
566C2C47×#327011yescharacteristic
567C2C47×#328011yescharacteristic
568C2C47×#328911yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC2×D8×C47D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#3328C2semidirect
4. C47×#3299C2semidirect
5. C47×#1718C2semidirect
6. C47×#1703C2semidirect
7. C47×#1684C2semidirect
8. C47×#1679C2semidirect
9. C47×#1674C2semidirect
10. C47×#1652C2semidirect
11. C47×#1651C2semidirect
12. C47×#1644C2semidirect
13. C47×#1637C2semidirect
15. C47×#1579C2semidirect
257. #19782C47direct (N × H)
282. #3328C2×C47semidirect
283. #3299C2×C47semidirect
284. #1718C2×C47semidirect
285. #1703C2×C47semidirect
286. #1684C2×C47semidirect
287. #1679C2×C47semidirect
288. #1674C2×C47semidirect
289. #1652C2×C47semidirect
290. #1651C2×C47semidirect
291. #1644C2×C47semidirect
292. #1637C2×C47semidirect
294. #1579C2×C47semidirect
351. C47#19782direct (N × H)

Maximal subgroups

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

subgroupindex
Q8×D8×C472
C47×#33602
C47×#33282
C47×#32992
C47×#17182
C47×#17032
C47×#16842
C47×#16792
C47×#16742
C47×#16522
C47×#16512
C47×#16442
C47×#16372
C47×#15812
C47×#15792
#1978247