Finite Group Databasebeta

← #20253339

Subgroups — #20253339

Order 6016.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689689C211yesmaximal, characteristic
2#15689604C211yesmaximal, characteristic, complemented
3#15689450C211yesmaximal, characteristic, complemented
4#15689448C211yesmaximal, characteristic, complemented
5#15689445C211yesmaximal, characteristic, complemented
6#15689444C211yesmaximal, characteristic, complemented
7#15689441C211yesmaximal, characteristic, complemented
8#15689440C211yesmaximal, characteristic, complemented
9#15689438C211yesmaximal, characteristic, complemented
10#15689164C211yesmaximal, characteristic, complemented
11#15689160C211yesmaximal, characteristic, complemented
12#15689126C211yesmaximal, characteristic, complemented
13#102×D47C211yesmaximal, characteristic, complemented
14#15689088C211yesmaximal, characteristic, complemented
15C47×#480C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×#10625324C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20#13094020—21no—
21#13094010—21no—
22#13093999C2211yescharacteristic
23#13093998C2211yescharacteristic
24#13093995C2211yescharacteristic
25#13093994—21no—
26#13093992—21no—
27#13093989—21no—
28#13093986—21no—
29C4×C22⋊D47—21no—
30C4×C22⋊D47—21no—
31#13093983C2211yescharacteristic, complemented
32#13093982C2211yescharacteristic
33#13093982C2211yescharacteristic
34#13093982C2211yescharacteristic, complemented
35C4⋊C4×D47C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic, complemented
37#13093958C2211yescharacteristic, complemented
38#13093957C2211yescharacteristic, complemented
39#13093956C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41#13093955C2211yescharacteristic, complemented
42#13093955C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52#121×C47C2211yescharacteristic
53C2×C4⋊C4×C47C2211yescharacteristic, complemented
54#107×C47C2211yescharacteristic, complemented
55#107×C47C2211yescharacteristic, complemented
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47D411yescharacteristic
68C2×C22⋊D47D411yescharacteristic
69D4×D47—22no—
70D4×D47—22no—
71#10625350—22no—
72#10625350—22no—
73C2×D188—21no—
74C2×D188D411yescharacteristic
75C2×D188C2311yescharacteristic
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47C2311yescharacteristic
79C2×C4×D47C2311yescharacteristic
80C2×Dic94D411yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C4⋊C4×C47—21no—
84C4⋊C4×C47C2311yescharacteristic
85C4⋊C4×C47C2311yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C22⋊C4×C47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106#10625324—22no—
107C8×D47—22no—
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110C22×D47—21no—
111C22×D47—42no—
112C22×D47—81no—
113C22×D47—81no—
114C22×D47C2×D411yescharacteristic
115C22×D47C2×D411yescharacteristic
116D4×C47—21no—
117D4×C47—21no—
118D4×C47—81no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—81no—
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2411yescharacteristic
127C22⋊D47—22no—
128C22⋊D47—22no—
129C22⋊D47—42no—
130C22⋊D47—81no—
131C22⋊D47—81no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137D188—22no—
138D188—21no—
139D188—21no—
140D188—81no—
141C4×D47—21no—
142C4×D47—21no—
143C4×D47—81no—
144C4×D47—81no—
145C4×D47#4112yes—
146C4×D47#4112yes—
147Dic94—22no—
148C8×C47—21no—
149C8×C47—21no—
150C47⋊C8—21no—
151C47⋊C8—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47C22×D411yescharacteristic
159C2×D47—21no—
160C2×D47—21no—
161C2×D47—21no—
162C2×D47—21no—
163C2×D47—21no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—84no—
168C2×D47#12312yes—
169C4×C47—21no—
170C4×C47—41no—
171C4×C47—41no—
172C4×C47—41no—
173C4×C47C2×#4111yescharacteristic
174C4×C47C2×#4111yescharacteristic
175Dic47—21no—
176Dic47—41no—
177Dic47—41no—
178Dic47—41no—
179Dic47#12312yes—
180#3096—471nomaximal, Sylow
181C2×C47—41no—
182C2×C47—81no—
183C2×C47C2×#12311yescharacteristic
184C2×C47#57611yescharacteristic
185C2×C47#57711yescharacteristic
186D47—22no—
187D47—41no—
188D47—81no—
189#535—471no—
190#520—471no—
191#482—471no—
192#482—471no—
193#482—471no—
194#482—471no—
195#481—471no—
196#481—471no—
197#480—471no—
198#480D4711yescharacteristic, complemented
199#428—471no—
200#427—471no—
201#418—471no—
202C2×#102—471no—
203#408—471no—
204C47#309611yescharacteristic, complemented, Sylow
205C2×#41—471no—
206C22×D4—471no—
207C2×M16—471no—
208C22×C8—471no—
209#127—941no—
210#124—941no—
211#121—471no—
212#121—471no—
213#121—471no—
214#121C2×D4711yescharacteristic
215#120—941no—
216#120—941no—
217C4×Q8—941no—
218C4×D4—941no—
219C4×D4—941no—
220C4×D4—941no—
221#117—471no—
222#117—471no—
223#117—471no—
224#117—471no—
225C2×C4⋊C4—471no—
226C2×C4⋊C4—471no—
227C2×C4⋊C4C2×D4711yescharacteristic, complemented
228#107—471no—
229#107—471no—
230#107C2×D4711yescharacteristic, complemented
231#107C2×D4711yescharacteristic, complemented
232#106—471no—
233#106—471no—
234#106—471no—
235#106—471no—
236#102—471no—
237#102—471no—
238#102—471no—
239#102—471no—
240#102—471no—
241#102—471no—
242#102C2×D4711yescharacteristic
243#102C2×D4711yescharacteristic
244C22⋊C8—471no—
245C22⋊C8—471no—
246C22⋊C8—471no—
247C22⋊C8C2×D4711yescharacteristic, complemented
248C24—941no—
249#41—942no—
250#41—942no—
251C2×Q8—471no—
252C2×D4—21no—
253C2×D4—471no—
254C2×D4—471no—
255C2×D4—471no—
256C2×D4—471no—
257C2×D4—941no—
258C2×D4—942no—
259C2×D4—942no—
260C2×D4—941no—
261C2×D4—941no—
262C2×D4—941no—
263C2×D4C22×D4711yescharacteristic
264C22×C4—21no—
265C22×C4—471no—
266C22×C4—471no—
267C22×C4—941no—
268C22×C4—941no—
269C22×C4C22×D4711yescharacteristic
270M16—942no—
271C2×C8—471no—
272C2×C8—471no—
273C2×C8—942no—
274C2×C8C22×D4711yescharacteristic
275C2×C8C22×D4711yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—471no—
278C4⋊C4—471no—
279C4⋊C4—471no—
280C4⋊C4—941no—
281C4⋊C4—941no—
282C4⋊C4C22×D4711yescharacteristic
283C4⋊C4C22×D4711yescharacteristic
284C4⋊C4C22×D4711yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C42—941no—
294C42—941no—
295C42—941no—
296C42—941no—
297C23—21no—
298C23—471no—
299C23—471no—
300C23—941no—
301C23—3761no—
302C23—3761no—
303C23—1882no—
304C23D4×D4711yescharacteristic
305Q8—942no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—942no—
310D4—942no—
311D4—942no—
312D4—941no—
313D4—941no—
314D4—3761no—
315D4—3761no—
316D4—3761no—
317D4—1882no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—81no—
324C2×C4—471no—
325C2×C4—472no—
326C2×C4—472no—
327C2×C4—471no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4—941no—
333C2×C4—3761no—
334C2×C4—3761no—
335C2×C4D4×D4711yescharacteristic
336C2×C4C23×D4711yescharacteristic
337C8—21no—
338C8—21no—
339C8—941no—
340C8—941no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—472no—
348C22—941no—
349C22—941no—
350C22—941no—
351C22—941no—
352C22—941no—
353C22—3764no—
354C22—1881no—
355C22—1881no—
356C22—1881no—
357C22C2×D4×D4711yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—472no—
363C4—941no—
364C4—1881no—
365C4—1881no—
366C4—1881no—
367C4#41×D4711yescharacteristic
368C4#41×D4711yescharacteristic
369C2—41no—
370C2—81no—
371C2—942no—
372C2—3761no—
373C2—1881no—
374C2#123×D4711yescharacteristic
375C2#1568992411yescharacteristic
376C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#480C2
socleC22×C47C22×D4
hypercenter#480D47
hypocenterC47#3096
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #15689604C2semidirect
3. #15689450C2semidirect
4. #15689448C2semidirect
5. #15689445C2semidirect
6. #15689444C2semidirect
7. #15689441C2semidirect
8. #15689440C2semidirect
9. #15689438C2semidirect
10. #15689164C2semidirect
11. #15689160C2semidirect
12. #15689126C2semidirect
13. #102×D47C2semidirect
14. #15689088C2semidirect
15. C47×#480C2semidirect
31. #13093983C22semidirect
34. #13093982C22semidirect
36. C4⋊C4×D47C22semidirect
37. #13093958C22semidirect
38. #13093957C22semidirect
39. #13093956C22semidirect
40. #13093955C22semidirect
41. #13093955C22semidirect
42. #13093955C22semidirect
49. C22⋊(C47⋊C8)C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. (C2×D47)⋊C8C22semidirect
53. C2×C4⋊C4×C47C22semidirect
54. #107×C47C22semidirect
55. #107×C47C22semidirect
58. C22⋊C8×C47C22semidirect
198. #480D47semidirect
204. C47#3096semidirect
227. C2×C4⋊C4C2×D47semidirect
230. #107C2×D47semidirect
231. #107C2×D47semidirect
247. C22⋊C8C2×D47semidirect