Finite Group Databasebeta

← #20254197

Subgroups — #20254197

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#15689633C211yesmaximal, characteristic, complemented
2#121×D47C211yesmaximal, characteristic, complemented
3#15689455C211yesmaximal, characteristic, complemented
4#15689449C211yesmaximal, characteristic, complemented
5#15689445C211yesmaximal, characteristic, complemented
6#15689435C211yesmaximal, characteristic, complemented
7#15689374C211yesmaximal, characteristic, complemented
8#15689369C211yesmaximal, characteristic, complemented
9#15689367C211yesmaximal, characteristic, complemented
10#15689275C211yesmaximal, characteristic, complemented
11#15689269C211yesmaximal, characteristic, complemented
12#15689265C211yesmaximal, characteristic, complemented
13#15689255C211yesmaximal, characteristic, complemented
14#15689086C211yesmaximal, characteristic, complemented
15C47×#469C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic, complemented
17C2×D4×D47—21no—
18C2×D4×D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20C2×#10625325C2211yescharacteristic, complemented
21C2×#10625335C2211yescharacteristic, complemented
22C2×#10625334C2211yescharacteristic, complemented
23C2×#10625329C2211yescharacteristic, complemented
24#13094006—21no—
25#13094004C2211yescharacteristic
26#13094003C2211yescharacteristic, complemented
27#13093999C2211yescharacteristic
28#13093998C2211yescharacteristic
29#13093997—21no—
30#13093996—21no—
31#13093995C2211yescharacteristic
32#13093995C2211yescharacteristic
33#13093992—21no—
34D4×Dic47—21no—
35(C22⋊D47)⋊C4—21no—
36#13093982C2211yescharacteristic, complemented
37C4⋊C4×D47C2211yescharacteristic
38C22⋊C4×D47—21no—
39#13093958C2211yescharacteristic, complemented
40#13093957C2211yescharacteristic, complemented
41#13093955C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093947C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic, complemented
45#13093945C2211yescharacteristic, complemented
46#13093945C2211yescharacteristic, complemented
47#13093944C2211yescharacteristic, complemented
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52C2×D8×C47C2211yescharacteristic, complemented
53C2×M16×C47C2211yescharacteristic, complemented
54#121×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic, complemented
56#106×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C23×D47D411yescharacteristic
61C2×D4×C47—21no—
62C2×D4×C47—21no—
63C2×D4×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C22×Dic47—21no—
72C22×Dic47D411yescharacteristic
73#10625352—41no—
74#10625352—41no—
75D4×D47—41no—
76D4×D47—41no—
77D4×D47—44no—
78C2×D188—21no—
79C2×D188C2311yescharacteristic
80C2×C4×D47—21no—
81C2×C4×D47—41no—
82C2×C4×D47—41no—
83C2×C4×D47D411yescharacteristic
84C2×C4×D47D411yescharacteristic
85C2×C4×D47C2311yescharacteristic
86C2×C4×D47C2311yescharacteristic
87C2×Dic94C2311yescharacteristic
88D8×C47—41no—
89M16×C47—41no—
90C2×C8×C47C2311yescharacteristic
91C2×C8×C47C2311yescharacteristic
92C4⋊C4×C47C2311yescharacteristic
93C4⋊C4×C47C2311yescharacteristic
94C22⋊C4×C47—21no—
95C22⋊C4×C47—21no—
96C22⋊Dic47—21no—
97C22⋊Dic47—21no—
98C22⋊Dic47—21no—
99#10625335—41no—
100#10625334—41no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4—21no—
105C4⋊Dic47—21no—
106C4⋊Dic47C2311yescharacteristic
107C4⋊Dic47C2311yescharacteristic
108Dic47⋊C4—21no—
109Dic47⋊C4—21no—
110C4×Dic47—21no—
111#10625329—41no—
112C2×C47⋊C8C2311yescharacteristic
113C2×C47⋊C8C2311yescharacteristic
114#10625325—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
127D4×C47—21no—
128D4×C47—21no—
129D4×C47—21no—
130D4×C47—21no—
131D4×C47—42no—
132D4×C47—42no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47C2×D411yescharacteristic
138C2×C4×C47C2411yescharacteristic
139C22⋊D47—42no—
140C22⋊D47—42no—
141C22⋊D47—42no—
142C22⋊D47—42no—
143C22⋊D47—42no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—41no—
148C2×Dic47—42no—
149C2×Dic47C2×D411yescharacteristic
150C2×Dic47C2×D411yescharacteristic
151D188—21no—
152D188—21no—
153D188—42no—
154C4×D47—21no—
155C4×D47—21no—
156C4×D47—21no—
157C4×D47—21no—
158C4×D47—41no—
159C4×D47—41no—
160C4×D47—42no—
161Dic94—21no—
162Dic94—21no—
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#469D4711yescharacteristic, complemented
216#468—471no—
217#468—471no—
218#450—471no—
219#449—471no—
220#449—471no—
221#447—471no—
222#407—471no—
223C47#319411yescharacteristic, complemented, Sylow
224C2×#41—471no—
225C22×D4—471no—
226C22×D4—941no—
227C23×C4—471no—
228C2×SD16—471no—
229C2×SD16—471no—
230C2×D8—471no—
231C2×D8C2×D4711yescharacteristic, complemented
232C2×M16—471no—
233C2×M16C2×D4711yescharacteristic, complemented
234#123—941no—
235C22⋊Q8—471no—
236C22⋊Q8—471no—
237#121—471no—
238#121—471no—
239#121—471no—
240#121—471no—
241#121—941no—
242#121—941no—
243#121C2×D4711yescharacteristic
244#121C2×D4711yescharacteristic, complemented
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#106C2×D4711yescharacteristic, complemented
255#103—471no—
256#103—471no—
257#102—471no—
258#102—471no—
259#102—471no—
260#102—471no—
261#102C2×D4711yescharacteristic, complemented
262#102C2×D4711yescharacteristic, complemented
263C22⋊C8—471no—
264C22⋊C8—471no—
265C22⋊C8—471no—
266C22⋊C8—471no—
267C24—471no—
268C24—941no—
269#41—1881no—
270#41—1881no—
271C2×Q8—471no—
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—471no—
287C22×C4—471no—
288C22×C4—471no—
289C22×C4—471no—
290C22×C4—471no—
291C22×C4—941no—
292C22×C4—941no—
293C22×C4—1881no—
294C22×C4—1881no—
295C22×C4C22×D4711yescharacteristic
296SD16—1881no—
297SD16—1881no—
298D8—41no—
299D8—1881no—
300M16—41no—
301M16—1881no—
302C2×C8—471no—
303C2×C8—471no—
304C2×C8C22×D4711yescharacteristic
305C2×C8C22×D4711yescharacteristic
306C4⋊C4—471no—
307C4⋊C4—471no—
308C4⋊C4—941no—
309C4⋊C4—941no—
310C4⋊C4—941no—
311C4⋊C4C22×D4711yescharacteristic
312C4⋊C4C22×D4711yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
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—941no—
336Q8—941no—
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—471no—
356C2×C4—471no—
357C2×C4—941no—
358C2×C4—941no—
359C2×C4—941no—
360C2×C4—941no—
361C2×C4—941no—
362C2×C4—941no—
363C2×C4—941no—
364C2×C4—1881no—
365C2×C4—1881no—
366C2×C4—1882no—
367C2×C4—1881no—
368C2×C4—1882no—
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#1309407011yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—942no—
410C2—3761no—
411C2—1881no—
412C2#1568968111yescharacteristic
413C2AGL(1,ℤ/8)×D4711yescharacteristic
414C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#469C2
socleC22×C47C22×D4
hypercenter#469D47
hypocenterC47#3194
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #15689633C2semidirect
2. #121×D47C2semidirect
3. #15689455C2semidirect
4. #15689449C2semidirect
5. #15689445C2semidirect
6. #15689435C2semidirect
7. #15689374C2semidirect
8. #15689369C2semidirect
9. #15689367C2semidirect
10. #15689275C2semidirect
11. #15689269C2semidirect
12. #15689265C2semidirect
13. #15689255C2semidirect
14. #15689086C2semidirect
15. C47×#469C2semidirect
16. C2×#10625352C22semidirect
20. C2×#10625325C22semidirect
21. C2×#10625335C22semidirect
22. C2×#10625334C22semidirect
23. C2×#10625329C22semidirect
26. #13094003C22semidirect
36. #13093982C22semidirect
39. #13093958C22semidirect
40. #13093957C22semidirect
41. #13093955C22semidirect
42. #13093949C22semidirect
43. #13093947C22semidirect
44. #13093946C22semidirect
45. #13093945C22semidirect
46. #13093945C22semidirect
47. #13093944C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. (C2×D47)⋊C8C22semidirect
52. C2×D8×C47C22semidirect
53. C2×M16×C47C22semidirect
55. #121×C47C22semidirect
56. #106×C47C22semidirect
57. #102×C47C22semidirect
58. #102×C47C22semidirect
215. #469D47semidirect
223. C47#3194semidirect
231. C2×D8C2×D47semidirect
233. C2×M16C2×D47semidirect
244. #121C2×D47semidirect
254. #106C2×D47semidirect
261. #102C2×D47semidirect
262. #102C2×D47semidirect