Finite Group Databasebeta

← C47×#33877 #26073575

Subgroups — C47×#33877 #26073575

Order 12032.

610 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3336C211yesmaximal, characteristic, complemented
2D4×D8×C47C211yesmaximal, characteristic
3C47×#2244C211yesmaximal, characteristic, complemented
4C47×#2234C211yesmaximal, characteristic, complemented
5C47×#2232C211yesmaximal, characteristic, complemented
6C47×#2228C211yesmaximal, characteristic, complemented
7C47×#2220C211yesmaximal, characteristic, complemented
8C47×#2217C211yesmaximal, characteristic, complemented
9C47×#2207C211yesmaximal, characteristic, complemented
10C47×#2187C211yesmaximal, characteristic, complemented
11C47×#2187C211yesmaximal, characteristic, complemented
12C47×#2175C211yesmaximal, characteristic, complemented
13C47×#2168C211yesmaximal, characteristic, complemented
14C47×#2140C211yesmaximal, characteristic, complemented
15C2×C47×#357C211yesmaximal, characteristic, complemented
16C22×D8×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C47×#552—21no—
19D42×C47—21no—
20C2×SD32×C47C2211yescharacteristic
21C2×SD32×C47C2211yescharacteristic, complemented
22C2×SD32×C47C2211yescharacteristic, complemented
23C2×M32×C47C2211yescharacteristic, complemented
24C22×C16×C47C2211yescharacteristic, complemented
25C47×#499C2211yescharacteristic, complemented
26C47×#493C2211yescharacteristic
27C47×#485—21no—
28C47×#483—21no—
29C47×#479—21no—
30C47×#467C2211yescharacteristic, complemented
31C47×#467C2211yescharacteristic, complemented
32C47×#466C2211yescharacteristic
33C47×#466C2211yescharacteristic
34C47×#459—21no—
35C47×#447—21no—
36C47×#447—21no—
37C4×Q16×C47C2211yescharacteristic, complemented
38C4×D8×C47C2211yescharacteristic
39C8×D4×C47C2211yescharacteristic
40C47×#427C2211yescharacteristic, complemented
41C2×#107×C47C2211yescharacteristic, complemented
42C47×#367C2211yescharacteristic, complemented
43C47×#366C2211yescharacteristic, complemented
44C47×#366C2211yescharacteristic, complemented
45C47×C4⋊C16C2211yescharacteristic, complemented
46C47×#358C2211yescharacteristic, complemented
47C47×#357C2211yescharacteristic
48C47×#357C2211yescharacteristic
49C47×#357C2211yescharacteristic
50C47×#357C2211yescharacteristic, complemented
51C47×#357C2211yescharacteristic, complemented
52C47×#357C2211yescharacteristic, complemented
53C47×#357C2211yescharacteristic, complemented
54C47×#357C2211yescharacteristic, complemented
55C47×#357C2211yescharacteristic, complemented
56C47×C22⋊C16C2211yescharacteristic, complemented
57C47×C22⋊C16C2211yescharacteristic, complemented
58C47×#346C2211yescharacteristic, complemented
59C22×D4×C47—21no—
60C22×D4×C47—21no—
61C22×D4×C47—41no—
62C2×Q16×C47C2311yescharacteristic
63C2×D8×C47—22no—
64C2×D8×C47—22no—
65C2×D8×C47—21no—
66C2×D8×C47—21no—
67C2×D8×C47—21no—
68C2×D8×C47—41no—
69C2×D8×C47—41no—
70C2×D8×C47C2311yescharacteristic
71C2×D8×C47C2311yescharacteristic
72C2×D8×C47C2311yescharacteristic
73C22×C8×C47C2311yescharacteristic
74C22×C8×C47C2311yescharacteristic
75#127×C47—21no—
76#126×C47—41no—
77#125×C47—21no—
78#125×C47—41no—
79#123×C47—41no—
80C22⋊Q8×C47—21no—
81C22⋊Q8×C47—21no—
82#121×C47—21no—
83#121×C47—21no—
84#121×C47—41no—
85#120×C47—41no—
86#120×C47—41no—
87C4×Q8×C47—21no—
88C4×D4×C47—21no—
89C4×D4×C47D411yescharacteristic
90#117×C47—21no—
91#117×C47—41no—
92C2×C4⋊C4×C47—21no—
93SD32×C47—22no—
94SD32×C47—41no—
95SD32×C47—41no—
96M32×C47—41no—
97C2×C16×C47—41no—
98C2×C16×C47C2311yescharacteristic
99C2×C16×C47C2311yescharacteristic
100C2×C16×C47C2311yescharacteristic
101C2×C16×C47C2311yescharacteristic
102#107×C47—21no—
103#107×C47C2311yescharacteristic
104#107×C47C2311yescharacteristic
105#107×C47C2311yescharacteristic
106#107×C47C2311yescharacteristic
107#106×C47—21no—
108#106×C47—21no—
109C4⋊C8×C47D411yescharacteristic
110#103×C47—21no—
111#103×C47—21no—
112#103×C47—21no—
113#102×C47—21no—
114#102×C47—21no—
115#102×C47—21no—
116C22⋊C8×C47D411yescharacteristic
117C22⋊C8×C47D411yescharacteristic
118C4×C8×C47C2311yescharacteristic
119C24×C47—41no—
120C24×C47—41no—
121C2×Q8×C47—21no—
122C2×D4×C47—21no—
123C2×D4×C47—21no—
124C2×D4×C47—21no—
125C2×D4×C47—42no—
126C2×D4×C47—42no—
127C2×D4×C47—41no—
128C2×D4×C47—41no—
129C2×D4×C47—41no—
130C2×D4×C47—41no—
131C2×D4×C47—41no—
132C2×D4×C47—41no—
133C2×D4×C47—81no—
134C2×D4×C47—81no—
135C2×D4×C47—84no—
136C2×D4×C47D811yescharacteristic
137C22×C4×C47—41no—
138C22×C4×C47—41no—
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D411yescharacteristic
141Q16×C47—21no—
142Q16×C47—21no—
143D8×C47—21no—
144D8×C47—21no—
145D8×C47—21no—
146D8×C47—21no—
147D8×C47—21no—
148D8×C47—42no—
149D8×C47—42no—
150D8×C47—81no—
151D8×C47#4112yes—
152C2×C8×C47—21no—
153C2×C8×C47—21no—
154C2×C8×C47—21no—
155C2×C8×C47—21no—
156C2×C8×C47C2×D411yescharacteristic
157C2×C8×C47C2×D411yescharacteristic
158C2×C8×C47C2×D411yescharacteristic
159C2×C8×C47C2411yescharacteristic
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—41no—
165C4⋊C4×C47—41no—
166C4⋊C4×C47—41no—
167C4⋊C4×C47—41no—
168C4⋊C4×C47—41no—
169C4⋊C4×C47—41no—
170C4⋊C4×C47D811yescharacteristic
171C22⋊C4×C47—41no—
172C22⋊C4×C47—41no—
173C22⋊C4×C47—41no—
174C22⋊C4×C47—41no—
175C22⋊C4×C47—41no—
176C22⋊C4×C47—41no—
177C22⋊C4×C47D811yescharacteristic
178C22⋊C4×C47D811yescharacteristic
179C42×C47—41no—
180C42×C47—41no—
181C42×C47C2×D411yescharacteristic
182C16×C47—21no—
183C16×C47—21no—
184C16×C47—21no—
185C16×C47—21no—
186C23×C47—41no—
187C23×C47—41no—
188C23×C47—41no—
189C23×C47—82no—
190C23×C47—82no—
191C23×C47—82no—
192C23×C47—82no—
193C23×C47—161no—
194C23×C47—161no—
195C23×C47C2×D811yescharacteristic
196C23×C47C2×D811yescharacteristic
197Q8×C47—41no—
198Q8×C47—41no—
199D4×C47—22no—
200D4×C47—22no—
201D4×C47—41no—
202D4×C47—41no—
203D4×C47—41no—
204D4×C47—41no—
205D4×C47—41no—
206D4×C47—82no—
207D4×C47—82no—
208D4×C47—82no—
209D4×C47—82no—
210D4×C47—82no—
211D4×C47—161no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—82no—
222C2×C4×C47—82no—
223C2×C4×C47C2×D811yescharacteristic
224C2×C4×C47C2×D811yescharacteristic
225C2×C4×C47C2×D811yescharacteristic
226C2×C4×C47C2×D811yescharacteristic
227C2×C4×C47C22×D411yescharacteristic
228C8×C47—21no—
229C8×C47—21no—
230C8×C47—21no—
231C8×C47C2×#4111yescharacteristic
232C8×C47H(5,𝔽2)11yescharacteristic
233#33877C4711yesmaximal, characteristic, direct product factor, Sylow
234C22×C47—21no—
235C22×C47—21no—
236C22×C47—21no—
237C22×C47—21no—
238C22×C47—21no—
239C22×C47—42no—
240C22×C47—81no—
241C22×C47—81no—
242C22×C47—81no—
243C22×C47—81no—
244C22×C47—81no—
245C22×C47—81no—
246C22×C47—81no—
247C22×C47—81no—
248C22×C47—164no—
249C22×C47—164no—
250C22×C47#50912yes—
251C22×C47C22×D811yescharacteristic
252C4×C47—21no—
253C4×C47—21no—
254C4×C47—21no—
255C4×C47—21no—
256C4×C47—81no—
257C4×C47—81no—
258C4×C47—81no—
259C4×C47—81no—
260C4×C47—81no—
261C4×C47#54611yescharacteristic
262C4×C47#57711yescharacteristic
263#3336C2×C4711yescharacteristic, complemented
264D4×D8C2×C4711yescharacteristic
265#2244C2×C4711yescharacteristic, complemented
266#2234C2×C4711yescharacteristic, complemented
267#2232C2×C4711yescharacteristic, complemented
268#2228C2×C4711yescharacteristic, complemented
269#2220C2×C4711yescharacteristic, complemented
270#2217C2×C4711yescharacteristic, complemented
271#2207C2×C4711yescharacteristic, complemented
272#2187C2×C4711yescharacteristic, complemented
273#2187C2×C4711yescharacteristic, complemented
274#2175C2×C4711yescharacteristic, complemented
275#2168C2×C4711yescharacteristic, complemented
276#2140C2×C4711yescharacteristic, complemented
277C2×#357C2×C4711yescharacteristic, complemented
278C2×C47—22no—
279C2×C47—41no—
280C2×C47—82no—
281C2×C47—161no—
282C2×C47—161no—
283C2×C47#329411yescharacteristic
284C2×C47C2×#50911yescharacteristic
285C2×C47#341611yescharacteristic
286C22×D8C22×C4711yescharacteristic
287C22×D8C22×C4711yescharacteristic
288#552—21no—
289D42—21no—
290C2×SD32C22×C4711yescharacteristic
291C2×SD32C22×C4711yescharacteristic, complemented
292C2×SD32C22×C4711yescharacteristic, complemented
293C2×M32C22×C4711yescharacteristic, complemented
294C22×C16C22×C4711yescharacteristic, complemented
295#499C22×C4711yescharacteristic, complemented
296#493C22×C4711yescharacteristic
297#485—21no—
298#483—21no—
299#479—21no—
300#467C22×C4711yescharacteristic, complemented
301#467C22×C4711yescharacteristic, complemented
302#466C22×C4711yescharacteristic
303#466C22×C4711yescharacteristic
304#459—21no—
305#447—21no—
306#447—21no—
307C4×Q16C22×C4711yescharacteristic, complemented
308C4×D8C22×C4711yescharacteristic
309C8×D4C22×C4711yescharacteristic
310#427C22×C4711yescharacteristic, complemented
311C2×#107C22×C4711yescharacteristic, complemented
312#367C22×C4711yescharacteristic, complemented
313#366C22×C4711yescharacteristic, complemented
314#366C22×C4711yescharacteristic, complemented
315C4⋊C16C22×C4711yescharacteristic, complemented
316#358C22×C4711yescharacteristic, complemented
317#357C22×C4711yescharacteristic
318#357C22×C4711yescharacteristic
319#357C22×C4711yescharacteristic
320#357C22×C4711yescharacteristic, complemented
321#357C22×C4711yescharacteristic, complemented
322#357C22×C4711yescharacteristic, complemented
323#357C22×C4711yescharacteristic, complemented
324#357C22×C4711yescharacteristic, complemented
325#357C22×C4711yescharacteristic, complemented
326C22⋊C16C22×C4711yescharacteristic, complemented
327C22⋊C16C22×C4711yescharacteristic, complemented
328#346C22×C4711yescharacteristic, complemented
329C47#3387711yescharacteristic, direct product factor, Sylow
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—41no—
333C2×Q16C23×C4711yescharacteristic
334C2×D8—22no—
335C2×D8—22no—
336C2×D8—21no—
337C2×D8—21no—
338C2×D8—21no—
339C2×D8—41no—
340C2×D8—41no—
341C2×D8C23×C4711yescharacteristic
342C2×D8C23×C4711yescharacteristic
343C2×D8C23×C4711yescharacteristic
344C22×C8C23×C4711yescharacteristic
345C22×C8C23×C4711yescharacteristic
346#127—21no—
347#126—41no—
348#125—21no—
349#125—41no—
350#123—41no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353#121—21no—
354#121—21no—
355#121—41no—
356#120—41no—
357#120—41no—
358C4×Q8—21no—
359C4×D4—21no—
360C4×D4D4×C4711yescharacteristic
361#117—21no—
362#117—41no—
363C2×C4⋊C4—21no—
364SD32—22no—
365SD32—41no—
366SD32—41no—
367M32—41no—
368C2×C16—41no—
369C2×C16C23×C4711yescharacteristic
370C2×C16C23×C4711yescharacteristic
371C2×C16C23×C4711yescharacteristic
372C2×C16C23×C4711yescharacteristic
373#107—21no—
374#107C23×C4711yescharacteristic
375#107C23×C4711yescharacteristic
376#107C23×C4711yescharacteristic
377#107C23×C4711yescharacteristic
378#106—21no—
379#106—21no—
380C4⋊C8D4×C4711yescharacteristic
381#103—21no—
382#103—21no—
383#103—21no—
384#102—21no—
385#102—21no—
386#102—21no—
387C22⋊C8D4×C4711yescharacteristic
388C22⋊C8D4×C4711yescharacteristic
389C4×C8C23×C4711yescharacteristic
390C24—41no—
391C24—41no—
392C2×Q8—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—81no—
405C2×D4—81no—
406C2×D4—84no—
407C2×D4D8×C4711yescharacteristic
408C22×C4—41no—
409C22×C4—41no—
410C22×C4C2×D4×C4711yescharacteristic
411C22×C4C2×D4×C4711yescharacteristic
412Q16—21no—
413Q16—21no—
414D8—21no—
415D8—21no—
416D8—21no—
417D8—21no—
418D8—21no—
419D8—42no—
420D8—42no—
421D8—81no—
422D8#41×C4712yes—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8C2×D4×C4711yescharacteristic
428C2×C8C2×D4×C4711yescharacteristic
429C2×C8C2×D4×C4711yescharacteristic
430C2×C8C24×C4711yescharacteristic
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—41no—
439C4⋊C4—41no—
440C4⋊C4—41no—
441C4⋊C4D8×C4711yescharacteristic
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4D8×C4711yescharacteristic
449C22⋊C4D8×C4711yescharacteristic
450C42—41no—
451C42—41no—
452C42C2×D4×C4711yescharacteristic
453C16—21no—
454C16—21no—
455C16—21no—
456C16—21no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—82no—
461C23—82no—
462C23—82no—
463C23—82no—
464C23—161no—
465C23—161no—
466C23C2×D8×C4711yescharacteristic
467C23C2×D8×C4711yescharacteristic
468Q8—41no—
469Q8—41no—
470D4—22no—
471D4—22no—
472D4—41no—
473D4—41no—
474D4—41no—
475D4—41no—
476D4—41no—
477D4—82no—
478D4—82no—
479D4—82no—
480D4—82no—
481D4—82no—
482D4—161no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—82no—
493C2×C4—82no—
494C2×C4C2×D8×C4711yescharacteristic
495C2×C4C2×D8×C4711yescharacteristic
496C2×C4C2×D8×C4711yescharacteristic
497C2×C4C2×D8×C4711yescharacteristic
498C2×C4C22×D4×C4711yescharacteristic
499C8—21no—
500C8—21no—
501C8—21no—
502C8C2×#41×C4711yescharacteristic
503C8H(5,𝔽2)×C4711yescharacteristic
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—42no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—164no—
519C22—164no—
520C22C47×#50912yes—
521C22C22×D8×C4711yescharacteristic
522C4—21no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—81no—
527C4—81no—
528C4—81no—
529C4—81no—
530C4—81no—
531C4C47×#54611yescharacteristic
532C4C47×#57711yescharacteristic
533C2—22no—
534C2—41no—
535C2—82no—
536C2—161no—
537C2—161no—
538C2C47×#329411yescharacteristic
539C2C2×C47×#50911yescharacteristic
540C2C47×#341611yescharacteristic
subgroupG/H
center, socleC22×C47C22×D8
commutator, Frattini, cosocleC2×C8C24×C47
prime radicalD4×D8×C47C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C4×D4×C47 ◁ C8×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3336C2semidirect
3. C47×#2244C2semidirect
4. C47×#2234C2semidirect
5. C47×#2232C2semidirect
6. C47×#2228C2semidirect
7. C47×#2220C2semidirect
8. C47×#2217C2semidirect
9. C47×#2207C2semidirect
10. C47×#2187C2semidirect
11. C47×#2187C2semidirect
12. C47×#2175C2semidirect
13. C47×#2168C2semidirect
14. C47×#2140C2semidirect
15. C2×C47×#357C2semidirect
21. C2×SD32×C47C22semidirect
22. C2×SD32×C47C22semidirect
23. C2×M32×C47C22semidirect
24. C22×C16×C47C22semidirect
25. C47×#499C22semidirect
30. C47×#467C22semidirect
31. C47×#467C22semidirect
37. C4×Q16×C47C22semidirect
40. C47×#427C22semidirect
41. C2×#107×C47C22semidirect
42. C47×#367C22semidirect
43. C47×#366C22semidirect
44. C47×#366C22semidirect
45. C47×C4⋊C16C22semidirect
46. C47×#358C22semidirect
50. C47×#357C22semidirect
51. C47×#357C22semidirect
52. C47×#357C22semidirect
53. C47×#357C22semidirect
54. C47×#357C22semidirect
55. C47×#357C22semidirect
56. C47×C22⋊C16C22semidirect
57. C47×C22⋊C16C22semidirect
58. C47×#346C22semidirect
233. #33877C47direct (N × H)
263. #3336C2×C47semidirect
265. #2244C2×C47semidirect
266. #2234C2×C47semidirect
267. #2232C2×C47semidirect
268. #2228C2×C47semidirect
269. #2220C2×C47semidirect
270. #2217C2×C47semidirect
271. #2207C2×C47semidirect
272. #2187C2×C47semidirect
273. #2187C2×C47semidirect
274. #2175C2×C47semidirect
275. #2168C2×C47semidirect
276. #2140C2×C47semidirect
277. C2×#357C2×C47semidirect
291. C2×SD32C22×C47semidirect
292. C2×SD32C22×C47semidirect
293. C2×M32C22×C47semidirect
294. C22×C16C22×C47semidirect
295. #499C22×C47semidirect
300. #467C22×C47semidirect
301. #467C22×C47semidirect
307. C4×Q16C22×C47semidirect
310. #427C22×C47semidirect
311. C2×#107C22×C47semidirect
312. #367C22×C47semidirect
313. #366C22×C47semidirect
314. #366C22×C47semidirect
315. C4⋊C16C22×C47semidirect
316. #358C22×C47semidirect
320. #357C22×C47semidirect
321. #357C22×C47semidirect
322. #357C22×C47semidirect
323. #357C22×C47semidirect
324. #357C22×C47semidirect
325. #357C22×C47semidirect
326. C22⋊C16C22×C47semidirect
327. C22⋊C16C22×C47semidirect
328. #346C22×C47semidirect
329. C47#33877direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33362
D4×D8×C472
C47×#22442
C47×#22342
C47×#22322
C47×#22282
C47×#22202
C47×#22172
C47×#22072
C47×#21872
C47×#21752
C47×#21682
C47×#21402
C2×C47×#3572
#3387747