Finite Group Databasebeta

← #20254993

Subgroups — #20254993

Order 6016.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094048C211yesmaximal, characteristic, complemented
2#15689767C211yesmaximal, characteristic, complemented
3#15689761C211yesmaximal, characteristic, complemented
4#15689504C211yesmaximal, characteristic, complemented
5#15689369C211yesmaximal, characteristic, complemented
6#15689366C211yesmaximal, characteristic, complemented
7#15689340C211yesmaximal, characteristic, complemented
8#15689336C211yesmaximal, characteristic, complemented
9#15689285C211yesmaximal, characteristic, complemented
10#15689282C211yesmaximal, characteristic, complemented
11#15689257C211yesmaximal, characteristic, complemented
12#15689255C211yesmaximal, characteristic, complemented
13D8×Dic47C211yesmaximal, characteristic, complemented
14#15689199C211yesmaximal, characteristic, complemented
15C2×AGL(1,ℤ/8)×C47C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic, complemented
18#13094048—24no—
19C2×#10625337C2211yescharacteristic, complemented
20C2×#10625325C2211yescharacteristic, complemented
21C2×#10625335C2211yescharacteristic, complemented
22C2×#10625334C2211yescharacteristic
23C2×#10625334C2211yescharacteristic
24C2×#10625324C2211yescharacteristic, complemented
25#13094013C2211yescharacteristic, complemented
26#13094011C2211yescharacteristic, complemented
27#13094007—21no—
28#13094005—21no—
29#13094003C2211yescharacteristic, complemented
30#13094000C2211yescharacteristic, complemented
31#13093998C2211yescharacteristic
32#13093996—21no—
33#13093996—21no—
34#13093995C2211yescharacteristic
35#13093993—21no—
36#13093992—21no—
37D4×Dic47C2211yescharacteristic, complemented
38D4×Dic47C2211yescharacteristic, complemented
39C4×C22⋊D47C2211yescharacteristic
40C2×C22⋊Dic47—21no—
41C2×(C2×D47)⋊C4—21no—
42#13093958C2211yescharacteristic, complemented
43Dic47⋊C8C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093948C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic, complemented
47#13093945C2211yescharacteristic, complemented
48#13093945C2211yescharacteristic, complemented
49#13093945C2211yescharacteristic, complemented
50C22⋊(C47⋊C8)C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52C8×Dic47C2211yescharacteristic, complemented
53C2×#41×C47C2211yescharacteristic
54C22×D4×C47C2211yescharacteristic, complemented
55AGL(1,ℤ/8)×C47—24no—
56C2×SD16×C47C2211yescharacteristic, complemented
57C2×SD16×C47C2211yescharacteristic, complemented
58C2×D8×C47C2211yescharacteristic
59C2×D8×C47C2211yescharacteristic
60C2×M16×C47C2211yescharacteristic, complemented
61C24×C47—21no—
62C23×D47—21no—
63#41×C47—22no—
64#41×C47—41no—
65C2×Q8×C47C2311yescharacteristic
66C2×D4×C47—22no—
67C2×D4×C47—21no—
68C2×D4×C47—21no—
69C2×D4×C47—41no—
70C2×D4×C47C2311yescharacteristic
71C2×D4×C47C2311yescharacteristic
72C2×D4×C47C2311yescharacteristic
73C22×C4×C47—21no—
74C22×C4×C47C2311yescharacteristic
75C2×C22⋊D47—21no—
76C2×C22⋊D47—21no—
77C2×C22⋊D47—21no—
78C2×C22⋊D47—21no—
79C2×C22⋊D47D411yescharacteristic
80C22×Dic47—21no—
81C22×Dic47—21no—
82C22×Dic47—21no—
83#10625352—22no—
84#10625352—41no—
85D4×D47—22no—
86D4×D47—41no—
87C2×D188C2311yescharacteristic
88C2×C4×D47C2311yescharacteristic
89C2×Dic94C2311yescharacteristic
90SD16×C47—22no—
91SD16×C47—22no—
92D8×C47—22no—
93D8×C47D414yescomplemented
94M16×C47—22no—
95C2×C8×C47C2311yescharacteristic
96C2×C8×C47C2311yescharacteristic
97C22⋊Dic47—21no—
98C22⋊Dic47—21no—
99C22⋊Dic47—21no—
100C22⋊Dic47—21no—
101C22⋊Dic47—21no—
102C22⋊Dic47—21no—
103C22⋊Dic47D411yescharacteristic
104#10625337—41no—
105#10625335—22no—
106#10625334—22no—
107#10625334—41no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4—21no—
112(C2×D47)⋊C4D411yescharacteristic
113C4⋊Dic47C2311yescharacteristic
114C4⋊Dic47C2311yescharacteristic
115Dic47⋊C4—21no—
116Dic47⋊C4—21no—
117Dic47⋊C4D411yescharacteristic
118C4×Dic47C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120C2×C47⋊C8C2311yescharacteristic
121#10625325—22no—
122#10625324—22no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—42no—
127C23×C47—42no—
128C23×C47—81no—
129C23×C47C2×D411yescharacteristic
130C22×D47—21no—
131C22×D47—42no—
132C22×D47—42no—
133C22×D47—81no—
134C22×D47C2×D411yescharacteristic
135Q8×C47—21no—
136Q8×C47—21no—
137D4×C47—21no—
138D4×C47—21no—
139D4×C47—21no—
140D4×C47—21no—
141D4×C47—42no—
142D4×C47—42no—
143D4×C47C2×D412yes—
144D4×C47C2×D412yes—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—42no—
149C2×C4×C47C2×D411yescharacteristic
150C2×C4×C47C2411yescharacteristic
151C22⋊D47—41no—
152C22⋊D47—42no—
153C22⋊D47—42no—
154C22⋊D47—81no—
155C22⋊D47—81no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—42no—
160C2×Dic47—81no—
161C2×Dic47—81no—
162C2×Dic47C2×D411yescharacteristic
163C2×Dic47C2×D411yescharacteristic
164C2×Dic47C2×D411yescharacteristic
165D188—21no—
166D188—21no—
167C4×D47—21no—
168C4×D47—21no—
169Dic94—21no—
170Dic94—21no—
171C8×C47—21no—
172C8×C47C2×D412yes—
173C47⋊C8—21no—
174C47⋊C8—21no—
175C22×C47—22no—
176C22×C47—22no—
177C22×C47—21no—
178C22×C47—21no—
179C22×C47—21no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47—41no—
187C22×C47—84no—
188C22×C47C22×D411yescharacteristic
189C2×D47—21no—
190C2×D47—21no—
191C2×D47—21no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—41no—
195C2×D47—84no—
196C4×C47—21no—
197C4×C47—41no—
198C4×C47C22×D411yescharacteristic
199C4×C47H(5,𝔽2)11yescharacteristic
200Dic47—21no—
201Dic47—21no—
202Dic47—21no—
203Dic47—41no—
204Dic47—41no—
205Dic47—41no—
206#3273—471nomaximal, Sylow
207C2×C47—42no—
208C2×C47—41no—
209C2×C47—42no—
210C2×C47—81no—
211C2×C47D4211yescharacteristic
212C2×C47#57511yescharacteristic
213C2×C47#57611yescharacteristic
214D47—41no—
215D47—81no—
216C2×AGL(1,ℤ/8)—471no—
217C2×AGL(1,ℤ/8)D4711yescharacteristic, complemented
218#546—471no—
219#546—471no—
220#495—471no—
221#468—471no—
222#468—471no—
223#463—471no—
224#463—471no—
225#452—471no—
226#452—471no—
227#447—471no—
228#447—471no—
229C4×D8—471no—
230#436—471no—
231C47#327311yescharacteristic, complemented, Sylow
232C2×#41—471no—
233C2×#41C2×D4711yescharacteristic
234C22×D4—471no—
235C22×D4C2×D4711yescharacteristic, complemented
236AGL(1,ℤ/8)—24no—
237AGL(1,ℤ/8)—944no—
238C2×Q16—471no—
239C2×SD16—471no—
240C2×SD16—471no—
241C2×SD16C2×D4711yescharacteristic, complemented
242C2×SD16C2×D4711yescharacteristic, complemented
243C2×D8—471no—
244C2×D8—471no—
245C2×D8C2×D4711yescharacteristic
246C2×D8C2×D4711yescharacteristic
247C2×M16—471no—
248C2×M16C2×D4711yescharacteristic, complemented
249#124—471no—
250#124—471no—
251#123—941no—
252#123—941no—
253C22⋊Q8—471no—
254C22⋊Q8—471no—
255#121—471no—
256#121—471no—
257#121—941no—
258#121—941no—
259#120—941no—
260#120—941no—
261C4×D4—471no—
262C4×D4—471no—
263C4×D4—471no—
264C2×C22⋊C4—941no—
265C2×C22⋊C4—941no—
266#107—471no—
267C4⋊C8—471no—
268#103—471no—
269#103—471no—
270#102—471no—
271#102—471no—
272#102—471no—
273#102—471no—
274C22⋊C8—471no—
275C22⋊C8—471no—
276C4×C8—471no—
277C24—21no—
278C24—941no—
279#41—22no—
280#41—41no—
281#41—942no—
282#41—1881no—
283C2×Q8—471no—
284C2×Q8C22×D4711yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—471no—
290C2×D4—471no—
291C2×D4—941no—
292C2×D4—942no—
293C2×D4—941no—
294C2×D4—941no—
295C2×D4—941no—
296C2×D4—1881no—
297C2×D4C22×D4711yescharacteristic
298C2×D4C22×D4711yescharacteristic
299C2×D4C22×D4711yescharacteristic
300C22×C4—21no—
301C22×C4—471no—
302C22×C4—941no—
303C22×C4—941no—
304C22×C4—941no—
305C22×C4C22×D4711yescharacteristic
306Q16—1881no—
307SD16—22no—
308SD16—22no—
309SD16—942no—
310SD16—942no—
311D8—22no—
312D8—942no—
313D8—1881no—
314D8C22⋊D4714yescomplemented
315M16—22no—
316M16—942no—
317C2×C8—471no—
318C2×C8—471no—
319C2×C8C22×D4711yescharacteristic
320C2×C8C22×D4711yescharacteristic
321C4⋊C4—471no—
322C4⋊C4—471no—
323C4⋊C4—471no—
324C4⋊C4—941no—
325C4⋊C4—941no—
326C22⋊C4—471no—
327C22⋊C4—471no—
328C22⋊C4—941no—
329C22⋊C4—941no—
330C22⋊C4—941no—
331C22⋊C4—941no—
332C22⋊C4—941no—
333C22⋊C4—941no—
334C22⋊C4—941no—
335C22⋊C4—941no—
336C22⋊C4—941no—
337C22⋊C4—941no—
338C42—471no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—42no—
343C23—42no—
344C23—81no—
345C23—471no—
346C23—941no—
347C23—3761no—
348C23—1882no—
349C23—1882no—
350C23D4×D4711yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—941no—
354Q8—941no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—21no—
359D4—42no—
360D4—42no—
361D4—941no—
362D4—941no—
363D4—3761no—
364D4—3761no—
365D4—1881no—
366D4—1882no—
367D4—1882no—
368D4C2×C22⋊D4712yes—
369D4C2×C22⋊D4712yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—42no—
374C2×C4—471no—
375C2×C4—471no—
376C2×C4—471no—
377C2×C4—941no—
378C2×C4—941no—
379C2×C4—941no—
380C2×C4—941no—
381C2×C4—941no—
382C2×C4—3761no—
383C2×C4—3761no—
384C2×C4—1882no—
385C2×C4D4×D4711yescharacteristic
386C2×C4C23×D4711yescharacteristic
387C8—21no—
388C8—941no—
389C8—941no—
390C8C2×C22⋊D4712yes—
391C22—21no—
392C22—22no—
393C22—22no—
394C22—21no—
395C22—21no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—84no—
404C22—941no—
405C22—941no—
406C22—941no—
407C22—3764no—
408C22—1881no—
409C22—1881no—
410C22—1881no—
411C22C2×D4×D4711yescharacteristic
412C4—21no—
413C4—41no—
414C4—941no—
415C4—941no—
416C4—941no—
417C4—1881no—
418C4—1881no—
419C4—1881no—
420C4C22×C22⋊D4711yescharacteristic
421C4#1309406911yescharacteristic
422C2—41no—
423C2—42no—
424C2—42no—
425C2—81no—
426C2—3761no—
427C2—1881no—
428C2D4×C22⋊D4711yescharacteristic
429C2#1568991911yescharacteristic
430C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×AGL(1,ℤ/8)×C47C2
socleC22×C47C22×D4
hypercenterC2×AGL(1,ℤ/8)D47
hypocenterC47#3273
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#13094048C2semidirect
2. #15689767C2semidirect
3. #15689761C2semidirect
4. #15689504C2semidirect
5. #15689369C2semidirect
6. #15689366C2semidirect
7. #15689340C2semidirect
8. #15689336C2semidirect
9. #15689285C2semidirect
10. #15689282C2semidirect
11. #15689257C2semidirect
12. #15689255C2semidirect
13. D8×Dic47C2semidirect
14. #15689199C2semidirect
15. C2×AGL(1,ℤ/8)×C47C2semidirect
17. C2×D4×D47C22semidirect
19. C2×#10625337C22semidirect
20. C2×#10625325C22semidirect
21. C2×#10625335C22semidirect
24. C2×#10625324C22semidirect
25. #13094013C22semidirect
26. #13094011C22semidirect
29. #13094003C22semidirect
30. #13094000C22semidirect
37. D4×Dic47C22semidirect
38. D4×Dic47C22semidirect
42. #13093958C22semidirect
43. Dic47⋊C8C22semidirect
44. #13093949C22semidirect
45. #13093948C22semidirect
46. #13093946C22semidirect
47. #13093945C22semidirect
48. #13093945C22semidirect
49. #13093945C22semidirect
50. C22⋊(C47⋊C8)C22semidirect
51. (C2×D47)⋊C8C22semidirect
52. C8×Dic47C22semidirect
54. C22×D4×C47C22semidirect
56. C2×SD16×C47C22semidirect
57. C2×SD16×C47C22semidirect
60. C2×M16×C47C22semidirect
93. D8×C47D4semidirect
217. C2×AGL(1,ℤ/8)D47semidirect
231. C47#3273semidirect
235. C22×D4C2×D47semidirect
241. C2×SD16C2×D47semidirect
242. C2×SD16C2×D47semidirect
248. C2×M16C2×D47semidirect
314. D8C22⋊D47semidirect