Finite Group Databasebeta

← C47×#19164 #26058862

Subgroups — C47×#19164 #26058862

Order 12032.

706 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3165C211yesmaximal, characteristic, complemented
2C47×#3101C211yesmaximal, characteristic
3C2×C47×#461C211yesmaximal, characteristic
4D4×M16×C47C211yesmaximal, characteristic
5C47×#1693C212yesmaximal, complemented
6C47×#1691C212yesmaximal, complemented
7C47×#1673C212yesmaximal, complemented
8C47×#1671C212yesmaximal, complemented
9C47×#1565C211yesmaximal, characteristic, complemented
10C47×#1550C211yesmaximal, characteristic, complemented
11C47×#1549C211yesmaximal, characteristic, complemented
12C22×SD16×C47—21no—
13C22×M16×C47—21no—
14C47×#533C2211yescharacteristic
15C2×C4⋊Q8×C47C2211yescharacteristic
16C2×C4×D4×C47C2211yescharacteristic
17C47×#501—22no—
18C47×#500C2212yescomplemented
19C47×#498C2212yescomplemented
20C47×#483—21no—
21C47×#476C2211yescharacteristic
22C47×#476C2211yescharacteristic
23C47×#461—21no—
24C47×#461—21no—
25C47×#461C2212yes—
26C47×#461C2212yes—
27C47×#461C2211yescharacteristic
28C47×#461C2211yescharacteristic
29C47×#450—21no—
30C4×SD16×C47—21no—
31C4×SD16×C47—21no—
32C47×#436C2212yes—
33C47×#435—22no—
34C8×D4×C47C2212yes—
35C47×#431C2211yescharacteristic
36C47×#428—21no—
37C47×#428—21no—
38C47×#423C2211yescharacteristic
39C2×C4⋊C8×C47C2211yescharacteristic
40C2×#103×C47—21no—
41C47×#407—21no—
42C4×M16×C47C2211yescharacteristic
43C47×#335C2212yescomplemented
44C47×#334C2212yescomplemented
45C47×#333C2212yescomplemented
46C47×#332C2212yescomplemented
47C47×#332C2212yescomplemented
48C47×#332C2212yescomplemented
49C22×Q8×C47—21no—
50C22×D4×C47D411yescharacteristic
51C23×C4×C47—21no—
52C2×SD16×C47—21no—
53C2×SD16×C47—21no—
54C2×SD16×C47—22no—
55C2×SD16×C47—22no—
56C2×SD16×C47—44no—
57C2×M16×C47—21no—
58C2×M16×C47—22no—
59C2×M16×C47—44no—
60C2×M16×C47D411yescharacteristic
61C2×M16×C47D411yescharacteristic
62C22×C8×C47—21no—
63C22×C8×C47—22no—
64C4⋊Q8×C47—21no—
65C4⋊Q8×C47—21no—
66C4⋊Q8×C47—21no—
67C4⋊Q8×C47C2312yes—
68C4⋊Q8×C47C2311yescharacteristic
69C4⋊Q8×C47C2311yescharacteristic
70#125×C47—21no—
71C22⋊Q8×C47—21no—
72C22⋊Q8×C47—21no—
73C4×Q8×C47—21no—
74C4×Q8×C47—21no—
75C4×D4×C47—21no—
76C4×D4×C47—21no—
77C4×D4×C47D411yescharacteristic
78C4×D4×C47D411yescharacteristic
79C4×D4×C47C2311yescharacteristic
80C4×D4×C47C2311yescharacteristic
81#117×C47—21no—
82C2×C4⋊C4×C47—21no—
83C2×C4⋊C4×C47—21no—
84C2×C4⋊C4×C47D411yescharacteristic
85C2×C22⋊C4×C47—21no—
86C2×C42×C47C2311yescharacteristic
87#107×C47—22no—
88#107×C47—22no—
89#106×C47—22no—
90#106×C47—22no—
91#106×C47—21no—
92#106×C47—21no—
93C4⋊C8×C47—21no—
94C4⋊C8×C47—21no—
95C4⋊C8×C47C2312yes—
96C4⋊C8×C47C2311yescharacteristic
97C4⋊C8×C47C2311yescharacteristic
98C4⋊C8×C47C2312yes—
99#103×C47—22no—
100#103×C47—22no—
101#103×C47—21no—
102#103×C47—21no—
103#102×C47—21no—
104#102×C47—21no—
105C22⋊C8×C47—21no—
106C22⋊C8×C47—22no—
107C22⋊C8×C47—22no—
108#97×C47D412yes—
109C4×C8×C47—21no—
110C4×C8×C47C2312yes—
111C24×C47—21no—
112C2×Q8×C47—21no—
113C2×Q8×C47—22no—
114C2×Q8×C47—21no—
115C2×Q8×C47—42no—
116C2×Q8×C47—42no—
117C2×Q8×C47—41no—
118C2×D4×C47—22no—
119C2×D4×C47—21no—
120C2×D4×C47—41no—
121C2×D4×C47C2×D411yescharacteristic
122C2×D4×C47C2×D411yescharacteristic
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—42no—
129C22×C4×C47—42no—
130C22×C4×C47—41no—
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47#4111yescharacteristic
134SD16×C47—42no—
135SD16×C47—44no—
136SD16×C47—42no—
137SD16×C47—44no—
138M16×C47—22no—
139M16×C47—42no—
140M16×C47—44no—
141M16×C47SD1614yescomplemented
142C2×C8×C47—22no—
143C2×C8×C47—21no—
144C2×C8×C47—21no—
145C2×C8×C47—22no—
146C2×C8×C47—42no—
147C2×C8×C47—44no—
148C2×C8×C47C2×D412yes—
149C2×C8×C47C2×D412yes—
150C4⋊C4×C47—21no—
151C4⋊C4×C47—21no—
152C4⋊C4×C47—22no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—22no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—41no—
158C4⋊C4×C47—41no—
159C4⋊C4×C47—41no—
160C4⋊C4×C47—41no—
161C4⋊C4×C47C2×D411yescharacteristic
162C4⋊C4×C47C2×D411yescharacteristic
163C22⋊C4×C47—21no—
164C22⋊C4×C47—21no—
165C22⋊C4×C47—21no—
166C22⋊C4×C47—21no—
167C22⋊C4×C47—41no—
168C42×C47—41no—
169C42×C47C2×D411yescharacteristic
170C42×C47C2×D411yescharacteristic
171C42×C47#4111yescharacteristic
172C42×C47C2411yescharacteristic
173C23×C47—21no—
174C23×C47—21no—
175C23×C47—42no—
176C23×C47—42no—
177C23×C47—81no—
178C23×C47#12111yescharacteristic
179Q8×C47—42no—
180Q8×C47—41no—
181Q8×C47—41no—
182Q8×C47—42no—
183Q8×C47—81no—
184Q8×C47—82no—
185D4×C47—21no—
186D4×C47—21no—
187D4×C47—21no—
188D4×C47—42no—
189D4×C47AGL(1,ℤ/8)12yes—
190C2×C4×C47—21no—
191C2×C4×C47—21no—
192C2×C4×C47—21no—
193C2×C4×C47—21no—
194C2×C4×C47—41no—
195C2×C4×C47—42no—
196C2×C4×C47—41no—
197C2×C4×C47—41no—
198C2×C4×C47—41no—
199C2×C4×C47—41no—
200C2×C4×C47—42no—
201C2×C4×C47—42no—
202C2×C4×C47—41no—
203C2×C4×C47—41no—
204C2×C4×C47—42no—
205C2×C4×C47—82no—
206C2×C4×C47#12111yescharacteristic
207C2×C4×C47#12111yescharacteristic
208C2×C4×C47#12111yescharacteristic
209C2×C4×C47C2×SD1612yes—
210C2×C4×C47#13712yes—
211C2×C4×C47C22×D411yescharacteristic
212C2×C4×C47C22×D411yescharacteristic
213C2×C4×C47C2×#4111yescharacteristic
214C8×C47—22no—
215C8×C47—42no—
216C8×C47—42no—
217C8×C47—41no—
218C8×C47—41no—
219C8×C47C2×SD1614yescomplemented
220#19164C4711yesmaximal, characteristic, direct product factor, Sylow
221C22×C47—21no—
222C22×C47—21no—
223C22×C47—22no—
224C22×C47—41no—
225C22×C47—41no—
226C22×C47—41no—
227C22×C47—41no—
228C22×C47—41no—
229C22×C47—84no—
230C22×C47#46112yes—
231C22×C47C2×#12111yescharacteristic
232C4×C47—21no—
233C4×C47—21no—
234C4×C47—21no—
235C4×C47—41no—
236C4×C47—41no—
237C4×C47—82no—
238C4×C47—81no—
239C4×C47—81no—
240C4×C47#46112yes—
241C4×C47C22×SD1611yescharacteristic
242C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
243C4×C47C2×#13711yescharacteristic
244C4×C47#57511yescharacteristic
245#3165C2×C4711yescharacteristic, complemented
246#3101C2×C4711yescharacteristic
247C2×#461C2×C4711yescharacteristic
248D4×M16C2×C4711yescharacteristic
249#1693C2×C4712yescomplemented
250#1691C2×C4712yescomplemented
251#1673C2×C4712yescomplemented
252#1671C2×C4712yescomplemented
253#1565C2×C4711yescharacteristic, complemented
254#1550C2×C4711yescharacteristic, complemented
255#1549C2×C4711yescharacteristic, complemented
256C2×C47—22no—
257C2×C47—42no—
258C2×C47—81no—
259C2×C47C2×#46111yescharacteristic
260C2×C47#305511yescharacteristic
261C2×C47#306911yescharacteristic
262C22×SD16—21no—
263C22×M16—21no—
264#533C22×C4711yescharacteristic
265C2×C4⋊Q8C22×C4711yescharacteristic
266C2×C4×D4C22×C4711yescharacteristic
267#501—22no—
268#500C22×C4712yescomplemented
269#498C22×C4712yescomplemented
270#483—21no—
271#476C22×C4711yescharacteristic
272#476C22×C4711yescharacteristic
273#461—21no—
274#461—21no—
275#461C22×C4711yescharacteristic
276#461C22×C4711yescharacteristic
277#461C22×C4712yes—
278#461C22×C4712yes—
279#450—21no—
280C4×SD16—21no—
281C4×SD16—21no—
282#436C22×C4712yes—
283#435—22no—
284C8×D4C22×C4712yes—
285#431C22×C4711yescharacteristic
286#428—21no—
287#428—21no—
288#423C22×C4711yescharacteristic
289C2×C4⋊C8C22×C4711yescharacteristic
290C2×#103—21no—
291#407—21no—
292C4×M16C22×C4711yescharacteristic
293#335C22×C4712yescomplemented
294#334C22×C4712yescomplemented
295#333C22×C4712yescomplemented
296#332C22×C4712yescomplemented
297#332C22×C4712yescomplemented
298#332C22×C4712yescomplemented
299C47#1916411yescharacteristic, direct product factor, Sylow
300C22×Q8—21no—
301C22×D4D4×C4711yescharacteristic
302C23×C4—21no—
303C2×SD16—22no—
304C2×SD16—22no—
305C2×SD16—21no—
306C2×SD16—21no—
307C2×SD16—44no—
308C2×M16—21no—
309C2×M16—22no—
310C2×M16—44no—
311C2×M16D4×C4711yescharacteristic
312C2×M16D4×C4711yescharacteristic
313C22×C8—21no—
314C22×C8—22no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8C23×C4712yes—
319C4⋊Q8C23×C4711yescharacteristic
320C4⋊Q8C23×C4711yescharacteristic
321#125—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4D4×C4711yescharacteristic
329C4×D4D4×C4711yescharacteristic
330C4×D4C23×C4711yescharacteristic
331C4×D4C23×C4711yescharacteristic
332#117—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4D4×C4711yescharacteristic
336C2×C22⋊C4—21no—
337C2×C42C23×C4711yescharacteristic
338#107—22no—
339#107—22no—
340#106—22no—
341#106—22no—
342#106—21no—
343#106—21no—
344C4⋊C8—21no—
345C4⋊C8—21no—
346C4⋊C8C23×C4712yes—
347C4⋊C8C23×C4711yescharacteristic
348C4⋊C8C23×C4711yescharacteristic
349C4⋊C8C23×C4712yes—
350#103—22no—
351#103—22no—
352#103—21no—
353#103—21no—
354#102—21no—
355#102—21no—
356C22⋊C8—21no—
357C22⋊C8—22no—
358C22⋊C8—22no—
359#97D4×C4712yes—
360C4×C8—21no—
361C4×C8C23×C4712yes—
362C24—21no—
363C2×Q8—21no—
364C2×Q8—22no—
365C2×Q8—21no—
366C2×Q8—42no—
367C2×Q8—42no—
368C2×Q8—41no—
369C2×D4—22no—
370C2×D4—21no—
371C2×D4—41no—
372C2×D4C2×D4×C4711yescharacteristic
373C2×D4C2×D4×C4711yescharacteristic
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—41no—
382C22×C4C2×D4×C4711yescharacteristic
383C22×C4C2×D4×C4711yescharacteristic
384C22×C4#41×C4711yescharacteristic
385SD16—42no—
386SD16—44no—
387SD16—42no—
388SD16—44no—
389M16—22no—
390M16—42no—
391M16—44no—
392M16SD16×C4714yescomplemented
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—42no—
398C2×C8—44no—
399C2×C8C2×D4×C4712yes—
400C2×C8C2×D4×C4712yes—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4C2×D4×C4711yescharacteristic
413C4⋊C4C2×D4×C4711yescharacteristic
414C22⋊C4—21no—
415C22⋊C4—21no—
416C22⋊C4—21no—
417C22⋊C4—21no—
418C22⋊C4—41no—
419C42—41no—
420C42C2×D4×C4711yescharacteristic
421C42C2×D4×C4711yescharacteristic
422C42#41×C4711yescharacteristic
423C42C24×C4711yescharacteristic
424C23—21no—
425C23—21no—
426C23—42no—
427C23—42no—
428C23—81no—
429C23#121×C4711yescharacteristic
430Q8—42no—
431Q8—41no—
432Q8—41no—
433Q8—42no—
434Q8—81no—
435Q8—82no—
436D4—21no—
437D4—21no—
438D4—21no—
439D4—42no—
440D4AGL(1,ℤ/8)×C4712yes—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—82no—
457C2×C4#121×C4711yescharacteristic
458C2×C4#121×C4711yescharacteristic
459C2×C4#121×C4711yescharacteristic
460C2×C4C2×SD16×C4712yes—
461C2×C4#137×C4712yes—
462C2×C4C22×D4×C4711yescharacteristic
463C2×C4C22×D4×C4711yescharacteristic
464C2×C4C2×#41×C4711yescharacteristic
465C8—22no—
466C8—42no—
467C8—42no—
468C8—41no—
469C8—41no—
470C8C2×SD16×C4714yescomplemented
471C22—21no—
472C22—21no—
473C22—22no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—84no—
480C22C47×#46112yes—
481C22C2×#121×C4711yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—41no—
486C4—41no—
487C4—82no—
488C4—81no—
489C4—81no—
490C4C47×#46112yes—
491C4C22×SD16×C4711yescharacteristic
492C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
493C4C2×#137×C4711yescharacteristic
494C4C47×#57511yescharacteristic
495C2—22no—
496C2—42no—
497C2—81no—
498C2C2×C47×#46111yescharacteristic
499C2C47×#305511yescharacteristic
500C2C47×#306911yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC42C24×C47
prime radicalC22×D4×C47D4
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×#3165C2semidirect
5. C47×#1693C2semidirect
6. C47×#1691C2semidirect
7. C47×#1673C2semidirect
8. C47×#1671C2semidirect
9. C47×#1565C2semidirect
10. C47×#1550C2semidirect
11. C47×#1549C2semidirect
18. C47×#500C22semidirect
19. C47×#498C22semidirect
43. C47×#335C22semidirect
44. C47×#334C22semidirect
45. C47×#333C22semidirect
46. C47×#332C22semidirect
47. C47×#332C22semidirect
48. C47×#332C22semidirect
141. M16×C47SD16semidirect
219. C8×C47C2×SD16semidirect
220. #19164C47direct (N × H)
245. #3165C2×C47semidirect
249. #1693C2×C47semidirect
250. #1691C2×C47semidirect
251. #1673C2×C47semidirect
252. #1671C2×C47semidirect
253. #1565C2×C47semidirect
254. #1550C2×C47semidirect
255. #1549C2×C47semidirect
268. #500C22×C47semidirect
269. #498C22×C47semidirect
293. #335C22×C47semidirect
294. #334C22×C47semidirect
295. #333C22×C47semidirect
296. #332C22×C47semidirect
297. #332C22×C47semidirect
298. #332C22×C47semidirect
299. C47#19164direct (N × H)
392. M16SD16×C47semidirect
470. C8C2×SD16×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#31652
C47×#31012
C2×C47×#4612
D4×M16×C472
C47×#16932
C47×#16912
C47×#16732
C47×#16712
C47×#15652
C47×#15502
C47×#15492
#1916447