Finite Group Databasebeta

← C47×#19168 #26058866

Subgroups — C47×#19168 #26058866

Order 12032.

696 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3141C211yesmaximal, characteristic, complemented
2C47×#3100C211yesmaximal, characteristic
3C2×C47×#476C211yesmaximal, characteristic, complemented
4D4×M16×C47C211yesmaximal, characteristic, complemented
5C47×#1703C212yesmaximal, complemented
6C47×#1697C212yesmaximal, complemented
7C47×#1683C212yesmaximal, complemented
8C47×#1677C212yesmaximal, complemented
9C47×#1565C211yesmaximal, characteristic, complemented
10C47×#1548C211yesmaximal, characteristic, complemented
11C47×#1547C211yesmaximal, characteristic, complemented
12C22×M16×C47—21no—
13C47×#532C2211yescharacteristic
14C2×C4⋊Q8×C47C2211yescharacteristic
15C2×C4×D4×C47C2211yescharacteristic
16C47×#489—22no—
17C47×#487C2212yescomplemented
18C47×#486C2212yescomplemented
19C47×#480—21no—
20C47×#476—21no—
21C47×#476—21no—
22C47×#476C2212yes—
23C47×#476C2212yes—
24C47×#474C2211yescharacteristic
25C47×#474C2211yescharacteristic
26C47×#459C2211yescharacteristic
27C47×#459C2211yescharacteristic
28C47×#447—21no—
29C4×D8×C47—21no—
30C4×D8×C47—21no—
31C47×#436C2212yes—
32C47×#435—22no—
33C8×D4×C47C2212yes—
34C47×#431C2211yescharacteristic
35C2×#106×C47—21no—
36C47×#423C2211yescharacteristic
37C2×C4⋊C8×C47C2211yescharacteristic
38C47×#417—21no—
39C47×#417—21no—
40C2×#102×C47—21no—
41C47×#407—21no—
42C4×M16×C47C2211yescharacteristic
43C47×#335C2212yescomplemented
44C47×#334C2212yescomplemented
45C47×#333C2212yescomplemented
46C47×#333C2212yescomplemented
47C47×#332C2212yescomplemented
48C47×#331C2212yescomplemented
49C2×#41×C47—21no—
50C22×Q8×C47—21no—
51C22×D4×C47D411yescharacteristic
52C23×C4×C47—21no—
53C2×D8×C47—21no—
54C2×D8×C47—21no—
55C2×M16×C47—21no—
56C2×M16×C47—22no—
57C2×M16×C47—44no—
58C2×M16×C47D411yescharacteristic
59C2×M16×C47D411yescharacteristic
60C22×C8×C47—21no—
61C22×C8×C47—22no—
62C4⋊Q8×C47—21no—
63C4⋊Q8×C47—21no—
64C4⋊Q8×C47—21no—
65C4⋊Q8×C47C2311yescharacteristic
66C4⋊Q8×C47C2312yes—
67#127×C47C2311yescharacteristic
68#124×C47—21no—
69#121×C47—21no—
70#121×C47—21no—
71C4×D4×C47—21no—
72C4×D4×C47—21no—
73C4×D4×C47—21no—
74C4×D4×C47—21no—
75C4×D4×C47D411yescharacteristic
76C4×D4×C47D411yescharacteristic
77C4×D4×C47C2311yescharacteristic
78C4×D4×C47C2311yescharacteristic
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47—21no—
81C2×C4⋊C4×C47D411yescharacteristic
82C2×C22⋊C4×C47—21no—
83C2×C42×C47C2311yescharacteristic
84#107×C47—21no—
85#107×C47—21no—
86#106×C47—22no—
87#106×C47—22no—
88C4⋊C8×C47—21no—
89C4⋊C8×C47—21no—
90C4⋊C8×C47C2311yescharacteristic
91C4⋊C8×C47C2311yescharacteristic
92C4⋊C8×C47C2312yes—
93C4⋊C8×C47C2312yes—
94#103×C47—22no—
95#103×C47—22no—
96#102×C47—21no—
97#102×C47—21no—
98#102×C47—22no—
99#102×C47—22no—
100#102×C47—22no—
101#102×C47—22no—
102#102×C47—21no—
103#102×C47—21no—
104C22⋊C8×C47—21no—
105C22⋊C8×C47—22no—
106C22⋊C8×C47—22no—
107#97×C47D412yes—
108C4×C8×C47—21no—
109C4×C8×C47C2312yes—
110C24×C47—21no—
111#41×C47—42no—
112#41×C47—42no—
113C2×Q8×C47—21no—
114C2×Q8×C47—22no—
115C2×Q8×C47—41no—
116C2×Q8×C47—82no—
117C2×D4×C47—22no—
118C2×D4×C47—21no—
119C2×D4×C47—21no—
120C2×D4×C47—21no—
121C2×D4×C47—21no—
122C2×D4×C47—41no—
123C2×D4×C47—41no—
124C2×D4×C47C2×D411yescharacteristic
125C2×D4×C47C2×D411yescharacteristic
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—42no—
132C22×C4×C47—42no—
133C22×C4×C47—41no—
134C22×C4×C47—41no—
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47#4111yescharacteristic
138D8×C47—42no—
139D8×C47—42no—
140M16×C47—22no—
141M16×C47—22no—
142M16×C47—44no—
143M16×C47—42no—
144C2×C8×C47—22no—
145C2×C8×C47—22no—
146C2×C8×C47—21no—
147C2×C8×C47—21no—
148C2×C8×C47—44no—
149C2×C8×C47—42no—
150C2×C8×C47C2×D412yes—
151C2×C8×C47C2×D412yes—
152C4⋊C4×C47—21no—
153C4⋊C4×C47—22no—
154C4⋊C4×C47—22no—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—41no—
158C4⋊C4×C47—41no—
159C4⋊C4×C47C2×D411yescharacteristic
160C4⋊C4×C47C2×D411yescharacteristic
161C22⋊C4×C47—21no—
162C22⋊C4×C47—21no—
163C22⋊C4×C47—21no—
164C22⋊C4×C47—21no—
165C22⋊C4×C47—41no—
166C22⋊C4×C47—41no—
167C42×C47C2×D411yescharacteristic
168C42×C47C2×D411yescharacteristic
169C42×C47#4111yescharacteristic
170C42×C47C2411yescharacteristic
171C23×C47—21no—
172C23×C47—21no—
173C23×C47—42no—
174C23×C47—42no—
175C23×C47—41no—
176C23×C47—81no—
177C23×C47#12111yescharacteristic
178Q8×C47—41no—
179Q8×C47—41no—
180Q8×C47—82no—
181Q8×C47—82no—
182D4×C47—21no—
183D4×C47—21no—
184D4×C47—21no—
185D4×C47—42no—
186D4×C47—41no—
187D4×C47—41no—
188D4×C47—41no—
189D4×C47—41no—
190D4×C47—81no—
191D4×C47—82no—
192D4×C47#13712yes—
193C2×C4×C47—21no—
194C2×C4×C47—21no—
195C2×C4×C47—21no—
196C2×C4×C47—21no—
197C2×C4×C47—41no—
198C2×C4×C47—42no—
199C2×C4×C47—41no—
200C2×C4×C47—41no—
201C2×C4×C47—41no—
202C2×C4×C47—41no—
203C2×C4×C47—42no—
204C2×C4×C47—42no—
205C2×C4×C47—41no—
206C2×C4×C47—42no—
207C2×C4×C47—82no—
208C2×C4×C47—82no—
209C2×C4×C47#12111yescharacteristic
210C2×C4×C47#12111yescharacteristic
211C2×C4×C47#12111yescharacteristic
212C2×C4×C47#13512yes—
213C2×C4×C47AGL(1,ℤ/8)12yes—
214C2×C4×C47C22×D411yescharacteristic
215C2×C4×C47C22×D411yescharacteristic
216C2×C4×C47C2×#4111yescharacteristic
217C8×C47—22no—
218C8×C47—22no—
219C8×C47—42no—
220C8×C47—41no—
221C8×C47—42no—
222C8×C47—41no—
223#19168C4711yesmaximal, characteristic, direct product factor, Sylow
224C22×C47—21no—
225C22×C47—21no—
226C22×C47—22no—
227C22×C47—41no—
228C22×C47—41no—
229C22×C47—41no—
230C22×C47—41no—
231C22×C47—41no—
232C22×C47—84no—
233C22×C47—81no—
234C22×C47—81no—
235C22×C47—81no—
236C22×C47#46312yes—
237C22×C47C2×#12111yescharacteristic
238C4×C47—21no—
239C4×C47—21no—
240C4×C47—21no—
241C4×C47—41no—
242C4×C47—41no—
243C4×C47—81no—
244C4×C47—82no—
245C4×C47#46312yes—
246C4×C47C2×#13511yescharacteristic
247C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
248C4×C47C2×#13711yescharacteristic
249C4×C47#57511yescharacteristic
250#3141C2×C4711yescharacteristic, complemented
251#3100C2×C4711yescharacteristic
252C2×#476C2×C4711yescharacteristic, complemented
253D4×M16C2×C4711yescharacteristic, complemented
254#1703C2×C4712yescomplemented
255#1697C2×C4712yescomplemented
256#1683C2×C4712yescomplemented
257#1677C2×C4712yescomplemented
258#1565C2×C4711yescharacteristic, complemented
259#1548C2×C4711yescharacteristic, complemented
260#1547C2×C4711yescharacteristic, complemented
261C2×C47—22no—
262C2×C47—42no—
263C2×C47—81no—
264C2×C47—161no—
265C2×C47C2×#46311yescharacteristic
266C2×C47#305611yescharacteristic
267C2×C47#306811yescharacteristic
268C22×M16—21no—
269#532C22×C4711yescharacteristic
270C2×C4⋊Q8C22×C4711yescharacteristic
271C2×C4×D4C22×C4711yescharacteristic
272#489—22no—
273#487C22×C4712yescomplemented
274#486C22×C4712yescomplemented
275#480—21no—
276#476—21no—
277#476—21no—
278#476C22×C4712yes—
279#476C22×C4712yes—
280#474C22×C4711yescharacteristic
281#474C22×C4711yescharacteristic
282#459C22×C4711yescharacteristic
283#459C22×C4711yescharacteristic
284#447—21no—
285C4×D8—21no—
286C4×D8—21no—
287#436C22×C4712yes—
288#435—22no—
289C8×D4C22×C4712yes—
290#431C22×C4711yescharacteristic
291C2×#106—21no—
292#423C22×C4711yescharacteristic
293C2×C4⋊C8C22×C4711yescharacteristic
294#417—21no—
295#417—21no—
296C2×#102—21no—
297#407—21no—
298C4×M16C22×C4711yescharacteristic
299#335C22×C4712yescomplemented
300#334C22×C4712yescomplemented
301#333C22×C4712yescomplemented
302#333C22×C4712yescomplemented
303#332C22×C4712yescomplemented
304#331C22×C4712yescomplemented
305C47#1916811yescharacteristic, direct product factor, Sylow
306C2×#41—21no—
307C22×Q8—21no—
308C22×D4D4×C4711yescharacteristic
309C23×C4—21no—
310C2×D8—21no—
311C2×D8—21no—
312C2×M16—21no—
313C2×M16—22no—
314C2×M16—44no—
315C2×M16D4×C4711yescharacteristic
316C2×M16D4×C4711yescharacteristic
317C22×C8—21no—
318C22×C8—22no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8C23×C4712yes—
323C4⋊Q8C23×C4711yescharacteristic
324#127C23×C4711yescharacteristic
325#124—21no—
326#121—21no—
327#121—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4D4×C4711yescharacteristic
333C4×D4D4×C4711yescharacteristic
334C4×D4C23×C4711yescharacteristic
335C4×D4C23×C4711yescharacteristic
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4D4×C4711yescharacteristic
339C2×C22⋊C4—21no—
340C2×C42C23×C4711yescharacteristic
341#107—21no—
342#107—21no—
343#106—22no—
344#106—22no—
345C4⋊C8—21no—
346C4⋊C8—21no—
347C4⋊C8C23×C4712yes—
348C4⋊C8C23×C4712yes—
349C4⋊C8C23×C4711yescharacteristic
350C4⋊C8C23×C4711yescharacteristic
351#103—22no—
352#103—22no—
353#102—22no—
354#102—22no—
355#102—21no—
356#102—21no—
357#102—22no—
358#102—22no—
359#102—21no—
360#102—21no—
361C22⋊C8—21no—
362C22⋊C8—22no—
363C22⋊C8—22no—
364#97D4×C4712yes—
365C4×C8—21no—
366C4×C8C23×C4712yes—
367C24—21no—
368#41—42no—
369#41—42no—
370C2×Q8—21no—
371C2×Q8—22no—
372C2×Q8—41no—
373C2×Q8—82no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4C2×D4×C4711yescharacteristic
382C2×D4C2×D4×C4711yescharacteristic
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4C2×D4×C4711yescharacteristic
393C22×C4C2×D4×C4711yescharacteristic
394C22×C4#41×C4711yescharacteristic
395D8—42no—
396D8—42no—
397M16—22no—
398M16—22no—
399M16—44no—
400M16—42no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—44no—
406C2×C8—42no—
407C2×C8C2×D4×C4712yes—
408C2×C8C2×D4×C4712yes—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4C2×D4×C4711yescharacteristic
417C4⋊C4C2×D4×C4711yescharacteristic
418C22⋊C4—21no—
419C22⋊C4—21no—
420C22⋊C4—21no—
421C22⋊C4—21no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C42C2×D4×C4711yescharacteristic
425C42C2×D4×C4711yescharacteristic
426C42#41×C4711yescharacteristic
427C42C24×C4711yescharacteristic
428C23—21no—
429C23—21no—
430C23—42no—
431C23—42no—
432C23—41no—
433C23—81no—
434C23#121×C4711yescharacteristic
435Q8—41no—
436Q8—41no—
437Q8—82no—
438Q8—82no—
439D4—21no—
440D4—21no—
441D4—21no—
442D4—42no—
443D4—41no—
444D4—41no—
445D4—41no—
446D4—41no—
447D4—81no—
448D4—82no—
449D4#137×C4712yes—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4#121×C4711yescharacteristic
467C2×C4#121×C4711yescharacteristic
468C2×C4#121×C4711yescharacteristic
469C2×C4#135×C4712yes—
470C2×C4AGL(1,ℤ/8)×C4712yes—
471C2×C4C22×D4×C4711yescharacteristic
472C2×C4C22×D4×C4711yescharacteristic
473C2×C4C2×#41×C4711yescharacteristic
474C8—22no—
475C8—22no—
476C8—42no—
477C8—41no—
478C8—42no—
479C8—41no—
480C22—21no—
481C22—21no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—84no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22C47×#46312yes—
493C22C2×#121×C4711yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—41no—
498C4—41no—
499C4—81no—
500C4—82no—
501C4C47×#46312yes—
502C4C2×#135×C4711yescharacteristic
503C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
504C4C2×#137×C4711yescharacteristic
505C4C47×#57511yescharacteristic
506C2—22no—
507C2—42no—
508C2—81no—
509C2—161no—
510C2C2×C47×#46311yescharacteristic
511C2C47×#305611yescharacteristic
512C2C47×#306811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3100C2
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×#3141C2semidirect
3. C2×C47×#476C2semidirect
4. D4×M16×C47C2semidirect
5. C47×#1703C2semidirect
6. C47×#1697C2semidirect
7. C47×#1683C2semidirect
8. C47×#1677C2semidirect
9. C47×#1565C2semidirect
10. C47×#1548C2semidirect
11. C47×#1547C2semidirect
17. C47×#487C22semidirect
18. C47×#486C22semidirect
43. C47×#335C22semidirect
44. C47×#334C22semidirect
45. C47×#333C22semidirect
46. C47×#333C22semidirect
47. C47×#332C22semidirect
48. C47×#331C22semidirect
223. #19168C47direct (N × H)
250. #3141C2×C47semidirect
252. C2×#476C2×C47semidirect
253. D4×M16C2×C47semidirect
254. #1703C2×C47semidirect
255. #1697C2×C47semidirect
256. #1683C2×C47semidirect
257. #1677C2×C47semidirect
258. #1565C2×C47semidirect
259. #1548C2×C47semidirect
260. #1547C2×C47semidirect
273. #487C22×C47semidirect
274. #486C22×C47semidirect
299. #335C22×C47semidirect
300. #334C22×C47semidirect
301. #333C22×C47semidirect
302. #333C22×C47semidirect
303. #332C22×C47semidirect
304. #331C22×C47semidirect
305. C47#19168direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31412
C47×#31002
C2×C47×#4762
D4×M16×C472
C47×#17032
C47×#16972
C47×#16832
C47×#16772
C47×#15652
C47×#15482
C47×#15472
#1916847