Finite Group Databasebeta

← #20253394

Subgroups — #20253394

Order 6016.

448 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689677C211yesmaximal, characteristic, complemented
2C4×D4×D47C211yesmaximal, characteristic
3#15689455C211yesmaximal, characteristic, complemented
4#15689452C211yesmaximal, characteristic, complemented
5#15689412C211yesmaximal, characteristic, complemented
6#15689411C211yesmaximal, characteristic, complemented
7#15689327C211yesmaximal, characteristic, complemented
8#15689326C211yesmaximal, characteristic, complemented
9#15689275C211yesmaximal, characteristic
10#15689272C211yesmaximal, characteristic
11C4×#10625325C211yesmaximal, characteristic, complemented
12C4×#10625336C211yesmaximal, characteristic, complemented
13C4×#10625335C211yesmaximal, characteristic, complemented
14#15689174C211yesmaximal, characteristic, complemented
15C4×SD16×C47C211yesmaximal, characteristic, complemented
16C2×D4×D47C2211yescharacteristic
17C22×C4×D47—21no—
18C2×#10625325C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×#10625336C2211yescharacteristic
21#13094023C2211yescharacteristic, complemented
22#13094022C2211yescharacteristic, complemented
23#13094014—21no—
24#13094004C2211yescharacteristic
25#13094002—21no—
26#13094000C2211yescharacteristic
27C4×Dic94—21no—
28C4×Dic94C2211yescharacteristic, complemented
29C4×D188C2211yescharacteristic
30D4×Dic47C2211yescharacteristic
31#13093986C2211yescharacteristic
32C4×C22⋊D47—21no—
33(C22⋊D47)⋊C4—21no—
34#13093981—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#13093949C2211yescharacteristic, complemented
44#13093948C2211yescharacteristic, complemented
45#13093947C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C4×C47⋊C8C2211yescharacteristic, complemented
52C2×SD16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic, complemented
54C4×D4×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic, complemented
56#103×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C2×C22⋊D47—21no—
64C22×Dic47—21no—
65D4×D47—22no—
66D4×D47—22no—
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47—44no—
72C2×C4×D47D411yescharacteristic
73C2×C4×D47D411yescharacteristic
74C2×C4×D47C2311yescharacteristic
75C2×Dic94—21no—
76C2×Dic94C2311yescharacteristic
77SD16×C47—22no—
78C2×C8×C47C2311yescharacteristic
79C2×C8×C47C2311yescharacteristic
80C4⋊C4×C47—21no—
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C42×C47—21no—
85C42×C47C2311yescharacteristic
86C22⋊Dic47—21no—
87#10625336—22no—
88#10625335—22no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93C4⋊Dic47—21no—
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102C4×Dic47—21no—
103C4×Dic47D411yescharacteristic
104C4×Dic47D411yescharacteristic
105C4×Dic47C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108#10625325—22no—
109C23×C47—21no—
110C22×D47—24no—
111C22×D47—21no—
112C22×D47—42no—
113C22×D47—42no—
114C22×D47C2×D411yescharacteristic
115Q8×C47—21no—
116Q8×C47—21no—
117D4×C47—21no—
118D4×C47#4112yes—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—42no—
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2411yescharacteristic
126C22⋊D47—24no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—42no—
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133C2×Dic47C2×D411yescharacteristic
134D188—21no—
135D188#4112yes—
136C4×D47—21no—
137C4×D47—21no—
138C4×D47—41no—
139C4×D47—42no—
140C4×D47—42no—
141C4×D47—42no—
142C4×D47SD1614yescomplemented
143Dic94—21no—
144Dic94—21no—
145Dic94—42no—
146C8×C47—21no—
147C8×C47—21no—
148C47⋊C8—21no—
149C47⋊C8—21no—
150C22×C47—22no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47C22×D411yescharacteristic
154C2×D47—21no—
155C2×D47—21no—
156C2×D47—22no—
157C2×D47—48no—
158C2×D47—41no—
159C2×D47—41no—
160C2×D47C2×SD1612yes—
161C4×C47—21no—
162C4×C47—41no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47C2×SD1612yes—
166C4×C47C2×#4111yescharacteristic
167C4×C47C2×#4111yescharacteristic
168Dic47—21no—
169Dic47—21no—
170Dic47—41no—
171Dic47—41no—
172Dic47—41no—
173Dic47C2×SD1612yes—
174#3101—471nomaximal, Sylow
175C2×C47—42no—
176C2×C47#52511yescharacteristic
177C2×C47C22×SD1611yescharacteristic
178C2×C47#57511yescharacteristic
179D47—22no—
180D47—42no—
181#533—471no—
182C2×C4×D4—471no—
183#483—471no—
184#483—471no—
185#476—471no—
186#476—471no—
187#461—471no—
188#461—471no—
189#450—471no—
190#450—471no—
191C4×SD16—471no—
192C4×SD16—471no—
193C4×SD16—471no—
194C4×SD16D4711yescharacteristic, complemented
195#431—471no—
196C47#310111yescharacteristic, complemented, Sylow
197C22×D4—471no—
198C23×C4—941no—
199C2×SD16—471no—
200C2×SD16—471no—
201C2×SD16—471no—
202C2×SD16C2×D4711yescharacteristic
203C4⋊Q8—471no—
204C4⋊Q8—471no—
205#125—941no—
206C22⋊Q8—471no—
207C22⋊Q8—471no—
208C22⋊Q8—941no—
209C4×Q8—471no—
210C4×Q8—941no—
211C4×Q8C2×D4711yescharacteristic, complemented
212C4×D4—471no—
213C4×D4—471no—
214C4×D4—471no—
215C4×D4—941no—
216C4×D4—941no—
217C4×D4C2×D4711yescharacteristic
218#117—941no—
219C2×C4⋊C4—471no—
220C2×C22⋊C4—941no—
221C2×C42—471no—
222#106—471no—
223#106—471no—
224#106—471no—
225#106C2×D4711yescharacteristic, complemented
226C4⋊C8—471no—
227C4⋊C8—471no—
228#103—471no—
229#103—471no—
230#103—471no—
231#103C2×D4711yescharacteristic, complemented
232#102—471no—
233#102—471no—
234#102—471no—
235#102C2×D4711yescharacteristic
236C22⋊C8—471no—
237C22⋊C8—471no—
238C4×C8—471no—
239C4×C8C2×D4711yescharacteristic, complemented
240C24—941no—
241C2×Q8—471no—
242C2×Q8—941no—
243C2×Q8C22×D4711yescharacteristic
244C2×D4—471no—
245C2×D4—941no—
246C2×D4—942no—
247C2×D4—942no—
248C2×D4C22×D4711yescharacteristic
249C22×C4—21no—
250C22×C4—471no—
251C22×C4—471no—
252C22×C4—471no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4—1884no—
258SD16—22no—
259SD16—942no—
260SD16—942no—
261SD16—942no—
262C2×C8—471no—
263C2×C8—471no—
264C2×C8C22×D4711yescharacteristic
265C2×C8C22×D4711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—471no—
268C4⋊C4—471no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4—941no—
276C4⋊C4C22×D4711yescharacteristic
277C4⋊C4C22×D4711yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C42—21no—
285C42—471no—
286C42—471no—
287C42—471no—
288C42—941no—
289C42C22×D4711yescharacteristic
290C23—21no—
291C23—471no—
292C23—944no—
293C23—941no—
294C23—1882no—
295C23—1882no—
296Q8—21no—
297Q8—21no—
298Q8—941no—
299Q8—941no—
300Q8—1882no—
301D4—21no—
302D4—472no—
303D4—944no—
304D4—941no—
305D4#1062535012yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—471no—
311C2×C4—474no—
312C2×C4—471no—
313C2×C4—471no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—1881no—
320C2×C4—1882no—
321C2×C4—1882no—
322C2×C4—1882no—
323C2×C4—1882no—
324C2×C4D4×D4711yescharacteristic
325C2×C4D4×D4711yescharacteristic
326C2×C4C23×D4711yescharacteristic
327C8—21no—
328C8—21no—
329C8—941no—
330C8—941no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—472no—
335C22—941no—
336C22—941no—
337C22—942no—
338C22—1888no—
339C22—1881no—
340C22—1881no—
341C22C2×D4×D4711yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—472no—
347C4—941no—
348C4—941no—
349C4—1881no—
350C4—1881no—
351C4—1881no—
352C4SD16×D4712yes—
353C4#41×D4711yescharacteristic
354C4C2×#1062535011yescharacteristic
355C2—42no—
356C2—942no—
357C2—1882no—
358C2#1568963211yescharacteristic
359C2C2×SD16×D4711yescharacteristic
360C2#1568992011yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×SD16×C47C2
socleC22×C47C22×D4
hypercenterC4×SD16D47
hypocenterC47#3101
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #15689677C2semidirect
3. #15689455C2semidirect
4. #15689452C2semidirect
5. #15689412C2semidirect
6. #15689411C2semidirect
7. #15689327C2semidirect
8. #15689326C2semidirect
11. C4×#10625325C2semidirect
12. C4×#10625336C2semidirect
13. C4×#10625335C2semidirect
14. #15689174C2semidirect
15. C4×SD16×C47C2semidirect
21. #13094023C22semidirect
22. #13094022C22semidirect
28. C4×Dic94C22semidirect
38. #13093956C22semidirect
39. #13093955C22semidirect
40. #13093955C22semidirect
41. Dic47⋊C8C22semidirect
42. Dic47⋊C8C22semidirect
43. #13093949C22semidirect
44. #13093948C22semidirect
45. #13093947C22semidirect
51. C4×C47⋊C8C22semidirect
53. C4×Q8×C47C22semidirect
55. #106×C47C22semidirect
56. #103×C47C22semidirect
58. C4×C8×C47C22semidirect
142. C4×D47SD16semidirect
194. C4×SD16D47semidirect
196. C47#3101semidirect
211. C4×Q8C2×D47semidirect
225. #106C2×D47semidirect
231. #103C2×D47semidirect
239. C4×C8C2×D47semidirect