Finite Group Databasebeta

← C47×#33886 #26073584

Subgroups — C47×#33886 #26073584

Order 12032.

574 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3341C211yesmaximal, characteristic, complemented
2C47×#3280C211yesmaximal, characteristic, complemented
3C47×#2243C211yesmaximal, characteristic, complemented
4C47×#2237C211yesmaximal, characteristic, complemented
5C47×#2234C211yesmaximal, characteristic, complemented
6C47×#2224C211yesmaximal, characteristic, complemented
7C47×#2220C211yesmaximal, characteristic, complemented
8C47×#2215C211yesmaximal, characteristic, complemented
9C47×#2210C211yesmaximal, characteristic, complemented
10C47×#2186C211yesmaximal, characteristic, complemented
11C47×#2184C211yesmaximal, characteristic, complemented
12C47×#2177C211yesmaximal, characteristic, complemented
13C47×#2168C211yesmaximal, characteristic, complemented
14C47×#2140C211yesmaximal, characteristic, complemented
15C47×#2138C211yesmaximal, characteristic, complemented
16C2×#135×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C47×#555—21no—
19C47×#546—21no—
20C2×SD32×C47C2211yescharacteristic, complemented
21C2×D16×C47C2211yescharacteristic
22C2×D16×C47C2211yescharacteristic
23C2×M32×C47C2211yescharacteristic
24C22×C16×C47C2211yescharacteristic, complemented
25C47×#500C2211yescharacteristic, complemented
26C47×#495C2211yescharacteristic
27C47×#482—21no—
28C47×#482—21no—
29C47×#476—21no—
30C47×#467C2211yescharacteristic
31C47×#466C2211yescharacteristic
32C47×#466C2211yescharacteristic
33C47×#466C2211yescharacteristic, complemented
34C47×#463—21no—
35C47×#450—21no—
36C47×#449—21no—
37C4×D8×C47C2211yescharacteristic
38C4×D8×C47C2211yescharacteristic, complemented
39C8×D4×C47C2211yescharacteristic
40C47×#427C2211yescharacteristic
41C47×#427C2211yescharacteristic, complemented
42C47×#367C2211yescharacteristic, complemented
43C47×#366C2211yescharacteristic, complemented
44C47×#366C2211yescharacteristic, complemented
45C47×C4⋊C16C2211yescharacteristic, complemented
46C47×#358C2211yescharacteristic, complemented
47C47×#358C2211yescharacteristic, complemented
48C47×#358C2211yescharacteristic, complemented
49C47×#357C2211yescharacteristic
50C47×#357C2211yescharacteristic
51C47×#357C2211yescharacteristic
52C47×#357C2211yescharacteristic
53C47×#357C2211yescharacteristic
54C47×#357C2211yescharacteristic
55C47×#357C2211yescharacteristic, complemented
56C47×C22⋊C16C2211yescharacteristic
57C47×C22⋊C16C2211yescharacteristic, complemented
58C47×#346C2211yescharacteristic, complemented
59C2×#41×C47—21no—
60C22×D4×C47—21no—
61#135×C47—22no—
62#135×C47—41no—
63C2×Q16×C47C2311yescharacteristic
64C2×SD16×C47—21no—
65C2×SD16×C47—21no—
66C2×D8×C47—22no—
67C2×D8×C47—21no—
68C2×D8×C47—41no—
69C2×D8×C47C2311yescharacteristic
70C2×D8×C47C2311yescharacteristic
71C2×D8×C47C2311yescharacteristic
72C22×C8×C47C2311yescharacteristic
73C22×C8×C47C2311yescharacteristic
74C4⋊Q8×C47—21no—
75#124×C47—21no—
76#124×C47—41no—
77#124×C47—41no—
78#123×C47—41no—
79C22⋊Q8×C47—21no—
80#121×C47—21no—
81#121×C47—21no—
82#121×C47—21no—
83#121×C47—41no—
84#121×C47—41no—
85#120×C47—41no—
86C4×D4×C47—21no—
87C4×D4×C47—21no—
88C4×D4×C47D411yescharacteristic
89#117×C47—21no—
90#117×C47—21no—
91#117×C47—41no—
92C2×C22⋊C4×C47—41no—
93SD32×C47—41no—
94D16×C47—22no—
95D16×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#102×C47—21no—
112#102×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—
120#41×C47—42no—
121#41×C47—81no—
122C2×Q8×C47—21no—
123C2×Q8×C47—41no—
124C2×D4×C47—21no—
125C2×D4×C47—21no—
126C2×D4×C47—21no—
127C2×D4×C47—42no—
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×C47D811yescharacteristic
135C22×C4×C47—41no—
136C22×C4×C47—41no—
137C22×C4×C47—41no—
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×D411yescharacteristic
140Q16×C47—21no—
141Q16×C47—21no—
142SD16×C47—42no—
143SD16×C47—81no—
144D8×C47—21no—
145D8×C47—21no—
146D8×C47—21no—
147D8×C47—21no—
148D8×C47—21no—
149D8×C47—42no—
150D8×C47#4112yes—
151C2×C8×C47—21no—
152C2×C8×C47—21no—
153C2×C8×C47—21no—
154C2×C8×C47—21no—
155C2×C8×C47C2×D411yescharacteristic
156C2×C8×C47C2×D411yescharacteristic
157C2×C8×C47C2×D411yescharacteristic
158C2×C8×C47C2411yescharacteristic
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—41no—
164C4⋊C4×C47—41no—
165C4⋊C4×C47D811yescharacteristic
166C22⋊C4×C47—41no—
167C22⋊C4×C47—41no—
168C22⋊C4×C47—41no—
169C22⋊C4×C47—41no—
170C22⋊C4×C47—41no—
171C22⋊C4×C47—41no—
172C22⋊C4×C47—41no—
173C22⋊C4×C47—41no—
174C22⋊C4×C47—41no—
175C22⋊C4×C47—41no—
176C22⋊C4×C47D811yescharacteristic
177C22⋊C4×C47D811yescharacteristic
178C42×C47—41no—
179C42×C47—41no—
180C42×C47C2×D411yescharacteristic
181C16×C47—21no—
182C16×C47—21no—
183C16×C47—21no—
184C16×C47—21no—
185C23×C47—41no—
186C23×C47—41no—
187C23×C47—41no—
188C23×C47—82no—
189C23×C47—82no—
190C23×C47—161no—
191C23×C47C2×D811yescharacteristic
192C23×C47C2×D811yescharacteristic
193Q8×C47—41no—
194Q8×C47—41no—
195Q8×C47—161no—
196D4×C47—22no—
197D4×C47—41no—
198D4×C47—41no—
199D4×C47—41no—
200D4×C47—41no—
201D4×C47—41no—
202D4×C47—41no—
203D4×C47—82no—
204D4×C47—82no—
205D4×C47—161no—
206D4×C47—161no—
207D4×C47—161no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—41no—
213C2×C4×C47—41no—
214C2×C4×C47—41no—
215C2×C4×C47—41no—
216C2×C4×C47—41no—
217C2×C4×C47—82no—
218C2×C4×C47—82no—
219C2×C4×C47—161no—
220C2×C4×C47C2×D811yescharacteristic
221C2×C4×C47C2×D811yescharacteristic
222C2×C4×C47C2×D811yescharacteristic
223C2×C4×C47C2×D811yescharacteristic
224C2×C4×C47C22×D411yescharacteristic
225C8×C47—21no—
226C8×C47—21no—
227C8×C47—21no—
228C8×C47C2×#4111yescharacteristic
229C8×C47H(5,𝔽2)11yescharacteristic
230#33886C4711yesmaximal, characteristic, direct product factor, Sylow
231C22×C47—21no—
232C22×C47—21no—
233C22×C47—21no—
234C22×C47—21no—
235C22×C47—21no—
236C22×C47—21no—
237C22×C47—42no—
238C22×C47—81no—
239C22×C47—81no—
240C22×C47—81no—
241C22×C47—81no—
242C22×C47—81no—
243C22×C47—81no—
244C22×C47—81no—
245C22×C47—81no—
246C22×C47—164no—
247C22×C47C22×D811yescharacteristic
248C4×C47—21no—
249C4×C47—21no—
250C4×C47—21no—
251C4×C47—21no—
252C4×C47—81no—
253C4×C47—81no—
254C4×C47—81no—
255C4×C47—81no—
256C4×C47—81no—
257C4×C47#54611yescharacteristic
258C4×C47#57711yescharacteristic
259#3341C2×C4711yescharacteristic, complemented
260#3280C2×C4711yescharacteristic, complemented
261#2243C2×C4711yescharacteristic, complemented
262#2237C2×C4711yescharacteristic, complemented
263#2234C2×C4711yescharacteristic, complemented
264#2224C2×C4711yescharacteristic, complemented
265#2220C2×C4711yescharacteristic, complemented
266#2215C2×C4711yescharacteristic, complemented
267#2210C2×C4711yescharacteristic, complemented
268#2186C2×C4711yescharacteristic, complemented
269#2184C2×C4711yescharacteristic, complemented
270#2177C2×C4711yescharacteristic, complemented
271#2168C2×C4711yescharacteristic, complemented
272#2140C2×C4711yescharacteristic, complemented
273#2138C2×C4711yescharacteristic, complemented
274C2×C47—41no—
275C2×C47—41no—
276C2×C47—82no—
277C2×C47—161no—
278C2×C47—161no—
279C2×C47#329411yescharacteristic
280C2×C47#341411yescharacteristic
281C2×C47#341511yescharacteristic
282C2×#135C22×C4711yescharacteristic
283C22×D8C22×C4711yescharacteristic
284#555—21no—
285#546—21no—
286C2×SD32C22×C4711yescharacteristic, complemented
287C2×D16C22×C4711yescharacteristic
288C2×D16C22×C4711yescharacteristic
289C2×M32C22×C4711yescharacteristic
290C22×C16C22×C4711yescharacteristic, complemented
291#500C22×C4711yescharacteristic, complemented
292#495C22×C4711yescharacteristic
293#482—21no—
294#482—21no—
295#476—21no—
296#467C22×C4711yescharacteristic
297#466C22×C4711yescharacteristic
298#466C22×C4711yescharacteristic
299#466C22×C4711yescharacteristic, complemented
300#463—21no—
301#450—21no—
302#449—21no—
303C4×D8C22×C4711yescharacteristic
304C4×D8C22×C4711yescharacteristic, complemented
305C8×D4C22×C4711yescharacteristic
306#427C22×C4711yescharacteristic
307#427C22×C4711yescharacteristic, complemented
308#367C22×C4711yescharacteristic, complemented
309#366C22×C4711yescharacteristic, complemented
310#366C22×C4711yescharacteristic, complemented
311C4⋊C16C22×C4711yescharacteristic, complemented
312#358C22×C4711yescharacteristic, complemented
313#358C22×C4711yescharacteristic, complemented
314#358C22×C4711yescharacteristic, complemented
315#357C22×C4711yescharacteristic
316#357C22×C4711yescharacteristic
317#357C22×C4711yescharacteristic
318#357C22×C4711yescharacteristic
319#357C22×C4711yescharacteristic
320#357C22×C4711yescharacteristic
321#357C22×C4711yescharacteristic, complemented
322C22⋊C16C22×C4711yescharacteristic
323C22⋊C16C22×C4711yescharacteristic, complemented
324#346C22×C4711yescharacteristic, complemented
325C47#3388611yescharacteristic, direct product factor, Sylow
326C2×#41—21no—
327C22×D4—21no—
328#135—22no—
329#135—41no—
330C2×Q16C23×C4711yescharacteristic
331C2×SD16—21no—
332C2×SD16—21no—
333C2×D8—22no—
334C2×D8—21no—
335C2×D8—41no—
336C2×D8C23×C4711yescharacteristic
337C2×D8C23×C4711yescharacteristic
338C2×D8C23×C4711yescharacteristic
339C22×C8C23×C4711yescharacteristic
340C22×C8C23×C4711yescharacteristic
341C4⋊Q8—21no—
342#124—21no—
343#124—41no—
344#124—41no—
345#123—41no—
346C22⋊Q8—21no—
347#121—21no—
348#121—21no—
349#121—21no—
350#121—41no—
351#121—41no—
352#120—41no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4D4×C4711yescharacteristic
356#117—21no—
357#117—21no—
358#117—41no—
359C2×C22⋊C4—41no—
360SD32—41no—
361D16—22no—
362D16—41no—
363M32—41no—
364C2×C16—41no—
365C2×C16C23×C4711yescharacteristic
366C2×C16C23×C4711yescharacteristic
367C2×C16C23×C4711yescharacteristic
368C2×C16C23×C4711yescharacteristic
369#107—21no—
370#107C23×C4711yescharacteristic
371#107C23×C4711yescharacteristic
372#107C23×C4711yescharacteristic
373#107C23×C4711yescharacteristic
374#106—21no—
375#106—21no—
376C4⋊C8D4×C4711yescharacteristic
377#103—21no—
378#102—21no—
379#102—21no—
380#102—21no—
381#102—21no—
382#102—21no—
383C22⋊C8D4×C4711yescharacteristic
384C22⋊C8D4×C4711yescharacteristic
385C4×C8C23×C4711yescharacteristic
386C24—41no—
387#41—42no—
388#41—81no—
389C2×Q8—21no—
390C2×Q8—41no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—42no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—81no—
401C2×D4D8×C4711yescharacteristic
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4C2×D4×C4711yescharacteristic
406C22×C4C2×D4×C4711yescharacteristic
407Q16—21no—
408Q16—21no—
409SD16—42no—
410SD16—81no—
411D8—21no—
412D8—21no—
413D8—21no—
414D8—21no—
415D8—21no—
416D8—42no—
417D8#41×C4712yes—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8C2×D4×C4711yescharacteristic
423C2×C8C2×D4×C4711yescharacteristic
424C2×C8C2×D4×C4711yescharacteristic
425C2×C8C24×C4711yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4D8×C4711yescharacteristic
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4D8×C4711yescharacteristic
444C22⋊C4D8×C4711yescharacteristic
445C42—41no—
446C42—41no—
447C42C2×D4×C4711yescharacteristic
448C16—21no—
449C16—21no—
450C16—21no—
451C16—21no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—82no—
456C23—82no—
457C23—161no—
458C23C2×D8×C4711yescharacteristic
459C23C2×D8×C4711yescharacteristic
460Q8—41no—
461Q8—41no—
462Q8—161no—
463D4—22no—
464D4—41no—
465D4—41no—
466D4—41no—
467D4—41no—
468D4—41no—
469D4—41no—
470D4—82no—
471D4—82no—
472D4—161no—
473D4—161no—
474D4—161no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—82no—
485C2×C4—82no—
486C2×C4—161no—
487C2×C4C2×D8×C4711yescharacteristic
488C2×C4C2×D8×C4711yescharacteristic
489C2×C4C2×D8×C4711yescharacteristic
490C2×C4C2×D8×C4711yescharacteristic
491C2×C4C22×D4×C4711yescharacteristic
492C8—21no—
493C8—21no—
494C8—21no—
495C8C2×#41×C4711yescharacteristic
496C8H(5,𝔽2)×C4711yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—42no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—164no—
513C22C22×D8×C4711yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—81no—
519C4—81no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4C47×#54611yescharacteristic
524C4C47×#57711yescharacteristic
525C2—41no—
526C2—41no—
527C2—82no—
528C2—161no—
529C2—161no—
530C2C47×#329411yescharacteristic
531C2C47×#341411yescharacteristic
532C2C47×#341511yescharacteristic
subgroupG/H
center, socleC22×C47C22×D8
commutator, Frattini, cosocleC2×C8C24×C47
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×#3341C2semidirect
2. C47×#3280C2semidirect
3. C47×#2243C2semidirect
4. C47×#2237C2semidirect
5. C47×#2234C2semidirect
6. C47×#2224C2semidirect
7. C47×#2220C2semidirect
8. C47×#2215C2semidirect
9. C47×#2210C2semidirect
10. C47×#2186C2semidirect
11. C47×#2184C2semidirect
12. C47×#2177C2semidirect
13. C47×#2168C2semidirect
14. C47×#2140C2semidirect
15. C47×#2138C2semidirect
20. C2×SD32×C47C22semidirect
24. C22×C16×C47C22semidirect
25. C47×#500C22semidirect
33. C47×#466C22semidirect
38. C4×D8×C47C22semidirect
41. C47×#427C22semidirect
42. C47×#367C22semidirect
43. C47×#366C22semidirect
44. C47×#366C22semidirect
45. C47×C4⋊C16C22semidirect
46. C47×#358C22semidirect
47. C47×#358C22semidirect
48. C47×#358C22semidirect
55. C47×#357C22semidirect
57. C47×C22⋊C16C22semidirect
58. C47×#346C22semidirect
230. #33886C47direct (N × H)
259. #3341C2×C47semidirect
260. #3280C2×C47semidirect
261. #2243C2×C47semidirect
262. #2237C2×C47semidirect
263. #2234C2×C47semidirect
264. #2224C2×C47semidirect
265. #2220C2×C47semidirect
266. #2215C2×C47semidirect
267. #2210C2×C47semidirect
268. #2186C2×C47semidirect
269. #2184C2×C47semidirect
270. #2177C2×C47semidirect
271. #2168C2×C47semidirect
272. #2140C2×C47semidirect
273. #2138C2×C47semidirect
286. C2×SD32C22×C47semidirect
290. C22×C16C22×C47semidirect
291. #500C22×C47semidirect
299. #466C22×C47semidirect
304. C4×D8C22×C47semidirect
307. #427C22×C47semidirect
308. #367C22×C47semidirect
309. #366C22×C47semidirect
310. #366C22×C47semidirect
311. C4⋊C16C22×C47semidirect
312. #358C22×C47semidirect
313. #358C22×C47semidirect
314. #358C22×C47semidirect
321. #357C22×C47semidirect
323. C22⋊C16C22×C47semidirect
324. #346C22×C47semidirect
325. C47#33886direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33412
C47×#32802
C47×#22432
C47×#22372
C47×#22342
C47×#22242
C47×#22202
C47×#22152
C47×#22102
C47×#21862
C47×#21842
C47×#21772
C47×#21682
C47×#21402
C47×#21382
#3388647