Finite Group Databasebeta

← #20254200

Subgroups — #20254200

Order 6016.

466 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689630C211yesmaximal, characteristic, complemented
2#121×D47C211yesmaximal, characteristic, complemented
3#15689452C211yesmaximal, characteristic, complemented
4#15689448C211yesmaximal, characteristic, complemented
5#15689444C211yesmaximal, characteristic, complemented
6#15689435C211yesmaximal, characteristic, complemented
7#15689375C211yesmaximal, characteristic, complemented
8#15689373C211yesmaximal, characteristic, complemented
9#15689372C211yesmaximal, characteristic, complemented
10#15689366C211yesmaximal, characteristic, complemented
11#15689272C211yesmaximal, characteristic, complemented
12#15689268C211yesmaximal, characteristic, complemented
13#15689255C211yesmaximal, characteristic, complemented
14#15689085C211yesmaximal, characteristic, complemented
15C47×#449C211yesmaximal, characteristic, complemented
16C2×D4×D47—21no—
17C2×D4×D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19C2×#10625336C2211yescharacteristic, complemented
20C2×#10625334C2211yescharacteristic, complemented
21C2×#10625324C2211yescharacteristic, complemented
22C2×#10625324C2211yescharacteristic, complemented
23#13094005—21no—
24#13094000C2211yescharacteristic
25#13094000C2211yescharacteristic, complemented
26#13093999C2211yescharacteristic
27#13093998C2211yescharacteristic
28#13093997—21no—
29#13093996—21no—
30#13093995C2211yescharacteristic
31#13093995C2211yescharacteristic
32#13093995C2211yescharacteristic, complemented
33#13093992—21no—
34C4×C22⋊D47—21no—
35C4×C22⋊D47—21no—
36#13093983C2211yescharacteristic, complemented
37C4⋊C4×D47C2211yescharacteristic
38C22⋊C4×D47—21no—
39#13093958C2211yescharacteristic, complemented
40#13093957C2211yescharacteristic, complemented
41#13093956C2211yescharacteristic, complemented
42#13093955C2211yescharacteristic, complemented
43#13093948C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic, complemented
46#13093945C2211yescharacteristic, complemented
47#13093945C2211yescharacteristic, complemented
48#13093945C2211yescharacteristic, complemented
49C22⋊(C47⋊C8)C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic
52C2×#41×C47C2211yescharacteristic, complemented
53C2×SD16×C47C2211yescharacteristic, complemented
54C2×D8×C47C2211yescharacteristic, complemented
55#121×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C23×D47D411yescharacteristic
61#41×C47—41no—
62#41×C47—41no—
63C2×Q8×C47C2311yescharacteristic
64C2×D4×C47—21no—
65C2×D4×C47—21no—
66C2×D4×C47C2311yescharacteristic
67C2×D4×C47C2311yescharacteristic
68C22×C4×C47—21no—
69C22×C4×C47C2311yescharacteristic
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C2×C22⋊D47—21no—
74C2×C22⋊D47—21no—
75C22×Dic47D411yescharacteristic
76D4×D47—41no—
77D4×D47—41no—
78D4×D47—44no—
79C2×D188—21no—
80C2×D188C2311yescharacteristic
81C2×C4×D47—21no—
82C2×C4×D47—41no—
83C2×C4×D47—41no—
84C2×C4×D47D411yescharacteristic
85C2×C4×D47D411yescharacteristic
86C2×C4×D47C2311yescharacteristic
87C2×C4×D47C2311yescharacteristic
88SD16×C47—41no—
89D8×C47—41no—
90C2×C8×C47C2311yescharacteristic
91C2×C8×C47C2311yescharacteristic
92C4⋊C4×C47C2311yescharacteristic
93C22⋊C4×C47—21no—
94C22⋊Dic47—21no—
95C22⋊Dic47—21no—
96C22⋊Dic47—21no—
97C22⋊Dic47—21no—
98#10625336—41no—
99#10625334—41no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104C4⋊Dic47C2311yescharacteristic
105C4⋊Dic47C2311yescharacteristic
106C4⋊Dic47C2311yescharacteristic
107Dic47⋊C4—21no—
108Dic47⋊C4—21no—
109Dic47⋊C4—21no—
110C4×Dic47—21no—
111C2×C47⋊C8C2311yescharacteristic
112C2×C47⋊C8C2311yescharacteristic
113#10625324—41no—
114#10625324—41no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47C2×D411yescharacteristic
118C22×D47—22no—
119C22×D47—21no—
120C22×D47—41no—
121C22×D47—41no—
122C22×D47—42no—
123C22×D47—42no—
124C22×D47—42no—
125C22×D47C2×D411yescharacteristic
126C22×D47C2×D411yescharacteristic
127Q8×C47—21no—
128Q8×C47—21no—
129D4×C47—21no—
130D4×C47—21no—
131D4×C47—21no—
132D4×C47—21no—
133D4×C47—42no—
134D4×C47—42no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—42no—
140C2×C4×C47C2×D411yescharacteristic
141C2×C4×C47C2411yescharacteristic
142C22⋊D47—42no—
143C22⋊D47—42no—
144C22⋊D47—42no—
145C22⋊D47—42no—
146C22⋊D47—42no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—41no—
151C2×Dic47C2×D411yescharacteristic
152C2×Dic47C2×D411yescharacteristic
153D188—21no—
154D188—21no—
155D188—42no—
156C4×D47—21no—
157C4×D47—21no—
158C4×D47—21no—
159C4×D47—21no—
160C4×D47—41no—
161C4×D47—41no—
162C4×D47—42no—
163C8×C47—21no—
164C8×C47—21no—
165C47⋊C8—21no—
166C47⋊C8—21no—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47—21no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47C22×D411yescharacteristic
177C2×D47—21no—
178C2×D47—21no—
179C2×D47—21no—
180C2×D47—21no—
181C2×D47—21no—
182C2×D47—44no—
183C2×D47—41no—
184C2×D47—41no—
185C2×D47—41no—
186C2×D47—84no—
187C2×D47AGL(1,ℤ/8)12yes—
188C4×C47—21no—
189C4×C47—41no—
190C4×C47—41no—
191C4×C47H(5,𝔽2)11yescharacteristic
192C4×C47H(5,𝔽2)11yescharacteristic
193Dic47—21no—
194Dic47—21no—
195Dic47—41no—
196Dic47—41no—
197Dic47—41no—
198#3194—471nomaximal, Sylow
199C2×C47—41no—
200C2×C47—81no—
201C2×C47—81no—
202C2×C47#53411yescharacteristic
203C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
204C2×C47#57511yescharacteristic
205D47—22no—
206D47—41no—
207D47—81no—
208#525—471no—
209C2×#121—471no—
210#483—471no—
211#482—471no—
212#482—471no—
213#480—471no—
214#469—471no—
215#469—471no—
216#468—471no—
217#468—471no—
218#450—471no—
219#449—471no—
220#449D4711yescharacteristic, complemented
221#447—471no—
222#407—471no—
223C47#319411yescharacteristic, complemented, Sylow
224C2×#41C2×D4711yescharacteristic, complemented
225C22×D4—471no—
226C22×D4—941no—
227C23×C4—471no—
228C2×SD16—471no—
229C2×SD16C2×D4711yescharacteristic, complemented
230C2×D8—471no—
231C2×D8C2×D4711yescharacteristic, complemented
232C2×M16—471no—
233C2×M16—471no—
234#123—941no—
235C22⋊Q8—471no—
236C22⋊Q8—471no—
237#121—471no—
238#121—471no—
239#121—471no—
240#121—471no—
241#121—471no—
242#121—941no—
243#121—941no—
244#121C2×D4711yescharacteristic
245#120—941no—
246C4×D4—941no—
247C4×D4—941no—
248#117—471no—
249C2×C4⋊C4—471no—
250C2×C22⋊C4—941no—
251#107—471no—
252#107—471no—
253#106—471no—
254#106—471no—
255#103—471no—
256#103C2×D4711yescharacteristic, complemented
257#102—471no—
258#102—471no—
259#102—471no—
260#102—471no—
261#102—471no—
262#102C2×D4711yescharacteristic, complemented
263C22⋊C8—471no—
264C22⋊C8—471no—
265C22⋊C8—471no—
266C22⋊C8C2×D4711yescharacteristic, complemented
267C24—471no—
268C24—941no—
269#41—41no—
270#41—41no—
271C2×Q8C22×D4711yescharacteristic
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—471no—
275C2×D4—941no—
276C2×D4—941no—
277C2×D4—941no—
278C2×D4—941no—
279C2×D4—941no—
280C2×D4—941no—
281C2×D4—1881no—
282C2×D4—1881no—
283C2×D4—1884no—
284C2×D4C22×D4711yescharacteristic
285C2×D4C22×D4711yescharacteristic
286C22×C4—21no—
287C22×C4—471no—
288C22×C4—471no—
289C22×C4—471no—
290C22×C4—471no—
291C22×C4—471no—
292C22×C4—941no—
293C22×C4—1881no—
294C22×C4—1881no—
295C22×C4C22×D4711yescharacteristic
296SD16—41no—
297SD16—1881no—
298D8—41no—
299D8—1881no—
300M16—1881no—
301M16—1881no—
302C2×C8—471no—
303C2×C8—471no—
304C2×C8C22×D4711yescharacteristic
305C2×C8C22×D4711yescharacteristic
306C4⋊C4—471no—
307C4⋊C4—471no—
308C4⋊C4—471no—
309C4⋊C4—941no—
310C4⋊C4—941no—
311C4⋊C4—941no—
312C4⋊C4C22×D4711yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—941no—
315C22⋊C4—941no—
316C22⋊C4—941no—
317C22⋊C4—941no—
318C22⋊C4—941no—
319C22⋊C4—941no—
320C22⋊C4—941no—
321C22⋊C4—941no—
322C42—941no—
323C23—21no—
324C23—21no—
325C23—471no—
326C23—471no—
327C23—942no—
328C23—941no—
329C23—1881no—
330C23—1881no—
331C23—1882no—
332C23—1882no—
333C23—1882no—
334C23D4×D4711yescharacteristic
335Q8—21no—
336Q8—21no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—941no—
344D4—941no—
345D4—1882no—
346D4—1882no—
347D4—1882no—
348D4—1882no—
349D4—1882no—
350D4—1882no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—471no—
357C2×C4—471no—
358C2×C4—941no—
359C2×C4—941no—
360C2×C4—941no—
361C2×C4—941no—
362C2×C4—941no—
363C2×C4—941no—
364C2×C4—941no—
365C2×C4—1881no—
366C2×C4—1881no—
367C2×C4—1882no—
368C2×C4—1881no—
369C2×C4D4×D4711yescharacteristic
370C2×C4C23×D4711yescharacteristic
371C8—21no—
372C8—21no—
373C8—941no—
374C8—941no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—472no—
385C22—941no—
386C22—941no—
387C22—941no—
388C22—941no—
389C22—941no—
390C22—3764no—
391C22—1884no—
392C22—1881no—
393C22—1881no—
394C22—1881no—
395C22C2×D4×D4711yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—941no—
400C4—941no—
401C4—1881no—
402C4—1881no—
403C4—1881no—
404C4#1309406911yescharacteristic
405C4#1309406911yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—942no—
410C2—3761no—
411C2—1881no—
412C2#1568968311yescharacteristic
413C2AGL(1,ℤ/8)×D4711yescharacteristic
414C2#1568992011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#449C2
socleC22×C47C22×D4
hypercenter#449D47
hypocenterC47#3194
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #15689630C2semidirect
2. #121×D47C2semidirect
3. #15689452C2semidirect
4. #15689448C2semidirect
5. #15689444C2semidirect
6. #15689435C2semidirect
7. #15689375C2semidirect
8. #15689373C2semidirect
9. #15689372C2semidirect
10. #15689366C2semidirect
11. #15689272C2semidirect
12. #15689268C2semidirect
13. #15689255C2semidirect
14. #15689085C2semidirect
15. C47×#449C2semidirect
19. C2×#10625336C22semidirect
20. C2×#10625334C22semidirect
21. C2×#10625324C22semidirect
22. C2×#10625324C22semidirect
25. #13094000C22semidirect
32. #13093995C22semidirect
36. #13093983C22semidirect
39. #13093958C22semidirect
40. #13093957C22semidirect
41. #13093956C22semidirect
42. #13093955C22semidirect
43. #13093948C22semidirect
44. #13093946C22semidirect
45. #13093946C22semidirect
46. #13093945C22semidirect
47. #13093945C22semidirect
48. #13093945C22semidirect
49. C22⋊(C47⋊C8)C22semidirect
52. C2×#41×C47C22semidirect
53. C2×SD16×C47C22semidirect
54. C2×D8×C47C22semidirect
56. #103×C47C22semidirect
57. #102×C47C22semidirect
58. C22⋊C8×C47C22semidirect
220. #449D47semidirect
223. C47#3194semidirect
224. C2×#41C2×D47semidirect
229. C2×SD16C2×D47semidirect
231. C2×D8C2×D47semidirect
256. #103C2×D47semidirect
262. #102C2×D47semidirect
266. C22⋊C8C2×D47semidirect