Finite Group Databasebeta

← #20255549

Subgroups — #20255549

Order 6016.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689838C211yesmaximal, characteristic, complemented
2#15689768C211yesmaximal, characteristic, complemented
3#15689483C211yesmaximal, characteristic, complemented
4#15689467C211yesmaximal, characteristic, complemented
5#15689449C211yesmaximal, characteristic, complemented
6#15689403C211yesmaximal, characteristic, complemented
7#15689368C211yesmaximal, characteristic, complemented
8#15689358C211yesmaximal, characteristic, complemented
9#15689338C211yesmaximal, characteristic, complemented
10#15689265C211yesmaximal, characteristic, complemented
11#15689255C211yesmaximal, characteristic, complemented
12#15689196C211yesmaximal, characteristic, complemented
13#15689126C211yesmaximal, characteristic, complemented
14#15689116C211yesmaximal, characteristic, complemented
15C47×#442C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×#10625335C2211yescharacteristic, complemented
19C2×#10625334C2211yescharacteristic
20C2×#10625324C2211yescharacteristic
21C2×C8×D47C2211yescharacteristic, complemented
22#13094024C2211yescharacteristic, complemented
23#13094012C2211yescharacteristic
24#13094010—21no—
25#13094010—21no—
26#13094008—21no—
27#13094004C2211yescharacteristic
28#13093999C2211yescharacteristic
29#13093998—21no—
30#13093998—21no—
31#13093995C2211yescharacteristic
32#13093995C2211yescharacteristic, complemented
33#13093994—21no—
34C4×D188C2211yescharacteristic
35#13093983—21no—
36#13093982C2211yescharacteristic
37#13093982C2211yescharacteristic, complemented
38C2×(C2×D47)⋊C4—21no—
39#13093957C2211yescharacteristic, complemented
40#13093957C2211yescharacteristic, complemented
41C4⋊(C47⋊C8)C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093947C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093944C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52C2×D8×C47C2211yescharacteristic
53C4×D4×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic, complemented
55#106×C47C2211yescharacteristic, complemented
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic, complemented
58#97×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×D4×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C22×Dic47—21no—
69#10625352—22no—
70#10625352—41no—
71D4×D47—22no—
72D4×D47—41no—
73C2×D188—21no—
74C2×D188D411yescharacteristic
75C2×D188C2311yescharacteristic
76C2×C4×D47C2311yescharacteristic
77C2×C4×D47C2311yescharacteristic
78C2×Dic94—21no—
79C2×Dic94C2311yescharacteristic
80D8×C47—22no—
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C42×C47C2311yescharacteristic
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90#10625335—41no—
91#10625334—41no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4D411yescharacteristic
99(C2×D47)⋊C4D411yescharacteristic
100C4⋊Dic47—21no—
101C4⋊Dic47—21no—
102C4⋊Dic47D411yescharacteristic
103C4⋊Dic47C2311yescharacteristic
104C4⋊Dic47C2311yescharacteristic
105C4×Dic47—21no—
106C4×Dic47—21no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109#10625324—41no—
110C8×D47—41no—
111C23×C47—21no—
112C23×C47—21no—
113C22×D47—21no—
114C22×D47—42no—
115C22×D47—42no—
116C22×D47—81no—
117C22×D47C2×D411yescharacteristic
118C22×D47C2×D411yescharacteristic
119D4×C47—21no—
120D4×C47—21no—
121D4×C47—21no—
122D4×C47#4112yes—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—42no—
126C2×C4×C47—81no—
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—42no—
131C22⋊D47—42no—
132C22⋊D47—81no—
133C22⋊D47—81no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—42no—
138C2×Dic47C2×D411yescharacteristic
139C2×Dic47C2×D411yescharacteristic
140D188—21no—
141D188—21no—
142D188—41no—
143D188—81no—
144C4×D47—21no—
145C4×D47—21no—
146C4×D47—21no—
147C4×D47—21no—
148Dic94—21no—
149Dic94—21no—
150Dic94—81no—
151C8×C47—21no—
152C8×C47—21no—
153C47⋊C8—21no—
154C47⋊C8—21no—
155C22×C47—22no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47C22×D411yescharacteristic
162C2×D47—21no—
163C2×D47—21no—
164C2×D47—21no—
165C2×D47—21no—
166C2×D47—21no—
167C2×D47—21no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—84no—
172C4×C47—21no—
173C4×C47—21no—
174C4×C47—41no—
175C4×C47—41no—
176C4×C47C2×#4111yescharacteristic
177C4×C47H(5,𝔽2)11yescharacteristic
178Dic47—21no—
179Dic47—21no—
180Dic47—41no—
181Dic47—41no—
182Dic47—41no—
183#3319—471nomaximal, Sylow
184C2×C47—42no—
185C2×C47—81no—
186C2×C47#54611yescharacteristic
187C2×C47#57511yescharacteristic
188C2×C47#57611yescharacteristic
189D47—41no—
190D47—41no—
191D47—81no—
192#555—471no—
193#546—471no—
194#489—471no—
195#485—471no—
196#482—471no—
197#474—471no—
198#468—471no—
199#466—471no—
200#463—471no—
201#449—471no—
202#447—471no—
203#442D4711yescharacteristic, complemented
204#435—471no—
205#418—471no—
206#416—471no—
207C47#331911yescharacteristic, complemented, Sylow
208C2×#41—471no—
209C22×D4—471no—
210C2×SD16—471no—
211C2×D8—471no—
212C2×D8C2×D4711yescharacteristic
213C2×M16—471no—
214C22×C8—471no—
215C4⋊Q8—471no—
216#124—471no—
217#124—941no—
218#124—941no—
219#123—941no—
220C22⋊Q8—471no—
221#121—471no—
222#121—471no—
223#121—471no—
224#121—941no—
225#121—941no—
226#120—941no—
227C4×D4—471no—
228C4×D4C2×D4711yescharacteristic
229C4×D4C2×D4711yescharacteristic, complemented
230#117—471no—
231#117—471no—
232#117—941no—
233C2×C22⋊C4—941no—
234#107—471no—
235#107—471no—
236#106C2×D4711yescharacteristic, complemented
237C4⋊C8—471no—
238#103—471no—
239#103—471no—
240#103—471no—
241#102—471no—
242#102—471no—
243#102—471no—
244#102—471no—
245#102—471no—
246#102C2×D4711yescharacteristic
247#102C2×D4711yescharacteristic, complemented
248C22⋊C8—471no—
249C22⋊C8—471no—
250#97C2×D4711yescharacteristic, complemented
251C24—941no—
252#41—942no—
253#41—1881no—
254C2×Q8—471no—
255C2×Q8—941no—
256C2×D4—471no—
257C2×D4—471no—
258C2×D4—941no—
259C2×D4—941no—
260C2×D4—942no—
261C2×D4—941no—
262C2×D4—941no—
263C2×D4—941no—
264C2×D4—1881no—
265C2×D4C22×D4711yescharacteristic
266C2×D4C22×D4711yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—471no—
270C22×C4—471no—
271C22×C4—941no—
272SD16—1881no—
273D8—22no—
274D8—1881no—
275M16—1881no—
276C2×C8—471no—
277C2×C8—471no—
278C2×C8—1881no—
279C2×C8C22×D4711yescharacteristic
280C2×C8C22×D4711yescharacteristic
281C4⋊C4—471no—
282C4⋊C4—471no—
283C4⋊C4—471no—
284C4⋊C4—941no—
285C4⋊C4—941no—
286C4⋊C4C22×D4711yescharacteristic
287C4⋊C4C22×D4711yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—471no—
291C22⋊C4—471no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C22⋊C4—941no—
298C22⋊C4—941no—
299C22⋊C4—941no—
300C42—941no—
301C42—941no—
302C42C22×D4711yescharacteristic
303C23—21no—
304C23—21no—
305C23—471no—
306C23—471no—
307C23—941no—
308C23—3761no—
309C23—1882no—
310C23—1882no—
311Q8—941no—
312Q8—941no—
313Q8—3761no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—941no—
318D4—941no—
319D4—3761no—
320D4—3761no—
321D4—3761no—
322D4—1881no—
323D4—1882no—
324D4—1882no—
325D4#1062535012yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—81no—
330C2×C4—471no—
331C2×C4—471no—
332C2×C4—941no—
333C2×C4—941no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—1882no—
340C2×C4D4×D4711yescharacteristic
341C2×C4D4×D4711yescharacteristic
342C2×C4C23×D4711yescharacteristic
343C8—21no—
344C8—21no—
345C8—941no—
346C8—941no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—941no—
354C22—941no—
355C22—941no—
356C22—941no—
357C22—941no—
358C22—941no—
359C22—3764no—
360C22—1881no—
361C22—1881no—
362C22—1881no—
363C22C2×D4×D4711yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—941no—
369C4—941no—
370C4—1881no—
371C4—1881no—
372C4—1881no—
373C4C2×#1062535011yescharacteristic
374C4#1309407011yescharacteristic
375C2—42no—
376C2—81no—
377C2—3761no—
378C2—1881no—
379C2—1881no—
380C2#1568976911yescharacteristic
381C2#1568991911yescharacteristic
382C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#442C2
socleC22×C47C22×D4
hypercenter#442D47
hypocenterC47#3319
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #15689838C2semidirect
2. #15689768C2semidirect
3. #15689483C2semidirect
4. #15689467C2semidirect
5. #15689449C2semidirect
6. #15689403C2semidirect
7. #15689368C2semidirect
8. #15689358C2semidirect
9. #15689338C2semidirect
10. #15689265C2semidirect
11. #15689255C2semidirect
12. #15689196C2semidirect
13. #15689126C2semidirect
14. #15689116C2semidirect
15. C47×#442C2semidirect
18. C2×#10625335C22semidirect
21. C2×C8×D47C22semidirect
22. #13094024C22semidirect
32. #13093995C22semidirect
37. #13093982C22semidirect
39. #13093957C22semidirect
40. #13093957C22semidirect
41. C4⋊(C47⋊C8)C22semidirect
42. #13093949C22semidirect
43. #13093949C22semidirect
44. #13093947C22semidirect
51. (C2×D47)⋊C8C22semidirect
54. C4×D4×C47C22semidirect
55. #106×C47C22semidirect
57. #102×C47C22semidirect
58. #97×C47C22semidirect
203. #442D47semidirect
207. C47#3319semidirect
229. C4×D4C2×D47semidirect
236. #106C2×D47semidirect
247. #102C2×D47semidirect
250. #97C2×D47semidirect