Finite Group Databasebeta

← #20253477

Subgroups — #20253477

Order 6016.

488 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689670C211yesmaximal, characteristic, complemented
2C4×D4×D47C211yesmaximal, characteristic, complemented
3#15689443C211yesmaximal, characteristic, complemented
4#15689440C211yesmaximal, characteristic, complemented
5#15689412C211yesmaximal, characteristic, complemented
6#15689411C211yesmaximal, characteristic, complemented
7#15689317C211yesmaximal, characteristic, complemented
8#15689316C211yesmaximal, characteristic, complemented
9#15689258C211yesmaximal, characteristic, complemented
10#15689255C211yesmaximal, characteristic, complemented
11#15689236C211yesmaximal, characteristic, complemented
12#15689233C211yesmaximal, characteristic, complemented
13#15689233C211yesmaximal, characteristic, complemented
14#15689178C211yesmaximal, characteristic, complemented
15C47×#442C211yesmaximal, characteristic, complemented
16C2×#10625350—21no—
17C2×D4×D47C2211yescharacteristic
18C22×C4×D47—21no—
19C2×D376C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
21C2×#10625334C2211yescharacteristic
22#13094023C2211yescharacteristic, complemented
23#13094020C2211yescharacteristic, complemented
24#13094010—21no—
25#13093999C2211yescharacteristic
26#13093997—21no—
27#13093995C2211yescharacteristic
28C4×D188C2211yescharacteristic
29C4×D188C2211yescharacteristic, complemented
30D4×Dic47C2211yescharacteristic
31#13093986C2211yescharacteristic
32C4×C22⋊D47—21no—
33C4×C22⋊D47—21no—
34(C22⋊D47)⋊C4—21no—
35C4⋊C4×D47C2211yescharacteristic
36C22⋊C4×D47—21no—
37C42×D47C2211yescharacteristic
38#13093956C2211yescharacteristic, complemented
39#13093955C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42Dic47⋊C8C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic, complemented
45#13093945C2211yescharacteristic
46#13093945C2211yescharacteristic, complemented
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic, complemented
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51#13093935C2211yescharacteristic, 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—
69D4×D47—22no—
70D4×D47—22no—
71#10625350—44no—
72C2×D188—21no—
73C2×D188C2311yescharacteristic
74C2×D188C2311yescharacteristic
75C2×C4×D47—21no—
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×C4×D47—44no—
80C2×C4×D47D411yescharacteristic
81C2×C4×D47D411yescharacteristic
82C2×C4×D47C2311yescharacteristic
83C2×Dic94—21no—
84D8×C47—22no—
85C2×C8×C47C2311yescharacteristic
86C2×C8×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C22⋊C4×C47—21no—
91C42×C47C2311yescharacteristic
92C22⋊Dic47—21no—
93C22⋊Dic47—21no—
94#10625334—22no—
95#10625334—22no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104C4×Dic47D411yescharacteristic
105C4×Dic47D411yescharacteristic
106C4×Dic47C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109D376—22no—
110C23×C47—21no—
111C23×C47—21no—
112C22×D47—24no—
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—42no—
116C22×D47—42no—
117C22×D47C2×D411yescharacteristic
118D4×C47—21no—
119D4×C47—21no—
120D4×C47—21no—
121D4×C47#4112yescomplemented
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—42no—
125C2×C4×C47—42no—
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C22⋊D47—24no—
130C22⋊D47—42no—
131C22⋊D47—42no—
132C22⋊D47—42no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—42no—
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138C2×Dic47C2×D411yescharacteristic
139D188—21no—
140D188—21no—
141D188—21no—
142D188—42no—
143D188#4112yescomplemented
144C4×D47—22no—
145C4×D47—21no—
146C4×D47—21no—
147C4×D47—22no—
148C4×D47—42no—
149C4×D47—42no—
150C4×D47—42no—
151C4×D47—42no—
152Dic94—42no—
153C8×C47—21no—
154C8×C47—21no—
155C47⋊C8—21no—
156C47⋊C8—21no—
157C22×C47—22no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47C22×D411yescharacteristic
164C2×D47—21no—
165C2×D47—21no—
166C2×D47—22no—
167C2×D47—48no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47AGL(1,ℤ/8)12yes—
174C4×C47—21no—
175C4×C47—21no—
176C4×C47—41no—
177C4×C47—41no—
178C4×C47C2×#4111yescharacteristic
179C4×C47C2×#4111yescharacteristic
180Dic47—21no—
181Dic47—21no—
182Dic47—41no—
183Dic47—41no—
184Dic47AGL(1,ℤ/8)12yes—
185#3109—471nomaximal, Sylow
186C2×C47—42no—
187C2×C47—81no—
188C2×C47#52511yescharacteristic
189C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
191D47—22no—
192D47—42no—
193D47—81no—
194#532—471no—
195C2×C4×D4—471no—
196#481—471no—
197#481—471no—
198#476—471no—
199#476—471no—
200#459—471no—
201#459—471no—
202#447—471no—
203#447—471no—
204#442—471no—
205#442—471no—
206#442—471no—
207#442D4711yescharacteristic, complemented
208#432—471no—
209C47#310911yescharacteristic, complemented, Sylow
210C2×#41—941no—
211C22×D4—471no—
212C23×C4—941no—
213C2×D8—471no—
214C2×D8—471no—
215C2×D8—471no—
216C2×D8C2×D4711yescharacteristic
217C4⋊Q8—471no—
218#127—471no—
219#124—941no—
220#121—471no—
221#121—471no—
222#121—941no—
223C4×D4—471no—
224C4×D4—471no—
225C4×D4—471no—
226C4×D4—471no—
227C4×D4—941no—
228C4×D4—941no—
229C4×D4—941no—
230C4×D4C2×D4711yescharacteristic
231C4×D4C2×D4711yescharacteristic, complemented
232C2×C4⋊C4—471no—
233C2×C22⋊C4—941no—
234C2×C42—471no—
235#106—471no—
236#106—471no—
237#106—471no—
238#106C2×D4711yescharacteristic, complemented
239C4⋊C8—471no—
240C4⋊C8—471no—
241#102—471no—
242#102—471no—
243#102—471no—
244#102—471no—
245#102—471no—
246#102—471no—
247#102C2×D4711yescharacteristic
248#102C2×D4711yescharacteristic, complemented
249C22⋊C8—471no—
250C22⋊C8—471no—
251#97—471no—
252#97C2×D4711yescharacteristic, complemented
253C24—941no—
254#41—1884no—
255C2×Q8—941no—
256C2×D4—471no—
257C2×D4—471no—
258C2×D4—941no—
259C2×D4—941no—
260C2×D4—941no—
261C2×D4—941no—
262C2×D4—942no—
263C2×D4—942no—
264C2×D4—941no—
265C2×D4C22×D4711yescharacteristic
266C2×D4C22×D4711yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—471no—
270C22×C4—471no—
271C22×C4—471no—
272C22×C4—941no—
273C22×C4—941no—
274C22×C4—941no—
275C22×C4—941no—
276C22×C4—941no—
277C22×C4—1884no—
278D8—22no—
279D8—942no—
280D8—942no—
281D8—942no—
282C2×C8—471no—
283C2×C8—471no—
284C2×C8C22×D4711yescharacteristic
285C2×C8C22×D4711yescharacteristic
286C4⋊C4—471no—
287C4⋊C4—471no—
288C4⋊C4—941no—
289C4⋊C4—941no—
290C4⋊C4C22×D4711yescharacteristic
291C4⋊C4C22×D4711yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C22⋊C4—941no—
298C22⋊C4—941no—
299C22⋊C4—941no—
300C42—471no—
301C42—471no—
302C42—471no—
303C42C22×D4711yescharacteristic
304C23—21no—
305C23—21no—
306C23—471no—
307C23—944no—
308C23—941no—
309C23—941no—
310C23—1882no—
311C23—1882no—
312Q8—1882no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—472no—
317D4—944no—
318D4—941no—
319D4—941no—
320D4—941no—
321D4—1882no—
322D4—1882no—
323D4—1882no—
324D4—1882no—
325D4#1062535012yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—471no—
331C2×C4—471no—
332C2×C4—471no—
333C2×C4—942no—
334C2×C4—942no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—1882no—
340C2×C4—1882no—
341C2×C4—1882no—
342C2×C4—1882no—
343C2×C4—1882no—
344C2×C4D4×D4711yescharacteristic
345C2×C4D4×D4711yescharacteristic
346C2×C4C23×D4711yescharacteristic
347C8—21no—
348C8—21no—
349C8—941no—
350C8—941no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—472no—
358C22—941no—
359C22—941no—
360C22—942no—
361C22—1888no—
362C22—1881no—
363C22—1881no—
364C22—1881no—
365C22—1881no—
366C22—1881no—
367C22C2×D4×D4711yescharacteristic
368C4—21no—
369C4—21no—
370C4—41no—
371C4—41no—
372C4—472no—
373C4—941no—
374C4—941no—
375C4—1881no—
376C4—1881no—
377C4#41×D4711yescharacteristic
378C4C2×#1062535011yescharacteristic
379C2—42no—
380C2—81no—
381C2—942no—
382C2—3761no—
383C2—1882no—
384C2#1568963211yescharacteristic
385C2AGL(1,ℤ/8)×D4711yescharacteristic
386C2AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#442C2
socleC22×C47C22×D4
hypercenter#442D47
hypocenterC47#3109
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. #15689670C2semidirect
2. C4×D4×D47C2semidirect
3. #15689443C2semidirect
4. #15689440C2semidirect
5. #15689412C2semidirect
6. #15689411C2semidirect
7. #15689317C2semidirect
8. #15689316C2semidirect
9. #15689258C2semidirect
10. #15689255C2semidirect
11. #15689236C2semidirect
12. #15689233C2semidirect
13. #15689233C2semidirect
14. #15689178C2semidirect
15. C47×#442C2semidirect
22. #13094023C22semidirect
23. #13094020C22semidirect
29. C4×D188C22semidirect
38. #13093956C22semidirect
39. #13093955C22semidirect
40. #13093955C22semidirect
41. Dic47⋊C8C22semidirect
42. Dic47⋊C8C22semidirect
44. #13093946C22semidirect
46. #13093945C22semidirect
48. #13093944C22semidirect
51. #13093935C22semidirect
54. C4×D4×C47C22semidirect
55. #106×C47C22semidirect
57. #102×C47C22semidirect
58. #97×C47C22semidirect
121. D4×C47#41semidirect
143. D188#41semidirect
207. #442D47semidirect
209. C47#3109semidirect
231. C4×D4C2×D47semidirect
238. #106C2×D47semidirect
248. #102C2×D47semidirect
252. #97C2×D47semidirect
325. D4#10625350semidirect