Finite Group Databasebeta

← #20253183

Subgroups — #20253183

Order 6016.

440 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689679C211yesmaximal, characteristic, complemented
2C4×D4×D47C211yesmaximal, characteristic
3#15689424C211yesmaximal, characteristic, complemented
4#15689423C211yesmaximal, characteristic, complemented
5#15689420C211yesmaximal, characteristic, complemented
6#15689412C211yesmaximal, characteristic, complemented
7#15689411C211yesmaximal, characteristic, complemented
8#15689402C211yesmaximal, characteristic, complemented
9#15689401C211yesmaximal, characteristic, complemented
10#15689164C211yesmaximal, characteristic, complemented
11#15689162C211yesmaximal, characteristic, complemented
12#15689145C211yesmaximal, characteristic, complemented
13#15689126C211yesmaximal, characteristic
14#15689126C211yesmaximal, characteristic
15C47×#478C211yesmaximal, characteristic, complemented
16C2×D4×D47C2211yescharacteristic
17C22×C4×D47—21no—
18C2×#10625324C2211yescharacteristic
19C2×#10625324C2211yescharacteristic
20#13094023C2211yescharacteristic, complemented
21#13094023C2211yescharacteristic, complemented
22#13094016C2211yescharacteristic, complemented
23#13094002—21no—
24#13094002—21no—
25#13093989—21no—
26#13093989—21no—
27C4×D188C2211yescharacteristic
28D4×Dic47C2211yescharacteristic
29#13093986C2211yescharacteristic
30C4×C22⋊D47—21no—
31(C22⋊D47)⋊C4—21no—
32#13093982C2211yescharacteristic
33#13093982C2211yescharacteristic
34C4⋊C4×D47C2211yescharacteristic
35C22⋊C4×D47—21no—
36C42×D47C2211yescharacteristic
37#13093958C2211yescharacteristic, complemented
38#13093957C2211yescharacteristic, complemented
39#13093957C2211yescharacteristic, complemented
40#13093956C2211yescharacteristic, complemented
41#13093955C2211yescharacteristic, complemented
42#13093955C2211yescharacteristic, complemented
43C4⋊(C47⋊C8)C2211yescharacteristic, complemented
44Dic47⋊C8C2211yescharacteristic, complemented
45Dic47⋊C8C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093945C2211yescharacteristic
50#13093944C2211yescharacteristic
51#13093944C2211yescharacteristic
52#125×C47C2211yescharacteristic, complemented
53C4×D4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic, complemented
55#106×C47C2211yescharacteristic, complemented
56C4⋊C8×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C2×C22⋊D47—21no—
63C22×Dic47—21no—
64D4×D47—22no—
65D4×D47Q814yescomplemented
66C2×D188C2311yescharacteristic
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47—44no—
71C2×C4×D47D411yescharacteristic
72C2×C4×D47D411yescharacteristic
73C2×C4×D47C2311yescharacteristic
74C2×Dic94—21no—
75C2×Dic94—21no—
76C2×C8×C47C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C42×C47C2311yescharacteristic
85C22⋊Dic47—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47D411yescharacteristic
101C4×Dic47D411yescharacteristic
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105#10625324—22no—
106#10625324—22no—
107C23×C47—21no—
108C22×D47—21no—
109C22×D47—24no—
110C22×D47—42no—
111C22×D47—42no—
112C22×D47C2×D411yescharacteristic
113D4×C47—21no—
114D4×C47C2×Q812yes—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—42no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C22⋊D47—24no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—42no—
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130D188—21no—
131D188C2×Q812yes—
132C4×D47—22no—
133C4×D47—41no—
134C4×D47—42no—
135C4×D47—42no—
136C4×D47—42no—
137C4×D47C2×Q812yes—
138C4×D47#4112yes—
139Dic94—42no—
140Dic94—42no—
141C8×C47—21no—
142C8×C47—21no—
143C47⋊C8—21no—
144C47⋊C8—21no—
145C22×C47—22no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47C22×D411yescharacteristic
149C2×D47—21no—
150C2×D47—21no—
151C2×D47—22no—
152C2×D47—48no—
153C2×D47—41no—
154C2×D47—41no—
155C2×D47C22⋊Q812yes—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47C22×Q811yescharacteristic
162C4×C47C2×#4111yescharacteristic
163Dic47—21no—
164Dic47—41no—
165Dic47—41no—
166Dic47—41no—
167Dic47C22⋊Q812yes—
168Dic47AGL(1,ℤ/8)12yes—
169#3077—471nomaximal, Sylow
170C2×C47—42no—
171C2×C47C2×C22⋊Q811yescharacteristic
172C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C47#57511yescharacteristic
174D47—22no—
175D47—42no—
176#533—471no—
177C2×C4×D4—471no—
178#478—471no—
179#478—471no—
180#478—471no—
181#478D4711yescharacteristic, complemented
182#476—471no—
183#476—471no—
184#474—471no—
185#474—471no—
186#428—471no—
187#428—471no—
188#423—471no—
189#418—471no—
190#418—471no—
191C47#307711yescharacteristic, complemented, Sylow
192C22×D4—471no—
193C23×C4—941no—
194C2×M16—471no—
195C2×M16—471no—
196C4⋊Q8—471no—
197C4⋊Q8—471no—
198#125—471no—
199#125C2×D4711yescharacteristic, complemented
200C22⋊Q8—941no—
201C22⋊Q8—941no—
202C4×Q8—941no—
203C4×Q8—941no—
204C4×D4—471no—
205C4×D4—471no—
206C4×D4—471no—
207C4×D4—941no—
208C4×D4—941no—
209C4×D4C2×D4711yescharacteristic
210#117—471no—
211#117—471no—
212C2×C4⋊C4—471no—
213C2×C22⋊C4—941no—
214C2×C42—471no—
215#107—471no—
216#107—471no—
217#107—471no—
218#107C2×D4711yescharacteristic, complemented
219#106—471no—
220#106—471no—
221#106—471no—
222#106C2×D4711yescharacteristic, complemented
223C4⋊C8—471no—
224C4⋊C8—471no—
225C4⋊C8—471no—
226C4⋊C8C2×D4711yescharacteristic, complemented
227#102—471no—
228#102—471no—
229#102—471no—
230#102—471no—
231#102—471no—
232#102—471no—
233#102C2×D4711yescharacteristic
234#102C2×D4711yescharacteristic
235C24—941no—
236C2×Q8—941no—
237C2×Q8—941no—
238C2×D4—474no—
239C2×D4—471no—
240C2×D4—942no—
241C2×D4—941no—
242C2×D4C22×D4711yescharacteristic
243C22×C4—21no—
244C22×C4—471no—
245C22×C4—471no—
246C22×C4—471no—
247C22×C4—941no—
248C22×C4—941no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4—1884no—
252M16—942no—
253M16—942no—
254C2×C8—471no—
255C2×C8—471no—
256C2×C8C22×D4711yescharacteristic
257C2×C8C22×D4711yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—471no—
261C4⋊C4—471no—
262C4⋊C4—471no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4C22×D4711yescharacteristic
269C4⋊C4C22×D4711yescharacteristic
270C4⋊C4C22×D4711yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C42—471no—
278C42—471no—
279C42—471no—
280C42—941no—
281C42—941no—
282C42C22×D4711yescharacteristic
283C23—21no—
284C23—471no—
285C23—944no—
286C23—941no—
287C23—1882no—
288C23—1882no—
289Q8—1882no—
290Q8—1882no—
291D4—21no—
292D4—472no—
293D4—944no—
294D4—941no—
295D4Q8×D4712yes—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—471no—
301C2×C4—471no—
302C2×C4—472no—
303C2×C4—472no—
304C2×C4—471no—
305C2×C4—942no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—1881no—
310C2×C4—1882no—
311C2×C4—1882no—
312C2×C4—1882no—
313C2×C4—1882no—
314C2×C4D4×D4711yescharacteristic
315C2×C4D4×D4711yescharacteristic
316C2×C4C23×D4711yescharacteristic
317C8—21no—
318C8—21no—
319C8—941no—
320C8—941no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—472no—
325C22—941no—
326C22—941no—
327C22—942no—
328C22—1888no—
329C22—1881no—
330C22—1881no—
331C22C2×D4×D4711yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—472no—
338C4—472no—
339C4—941no—
340C4—1881no—
341C4—1881no—
342C4—1881no—
343C4C2×Q8×D4711yescharacteristic
344C4#41×D4711yescharacteristic
345C2—42no—
346C2—942no—
347C2—1882no—
348C2C22⋊Q8×D4711yescharacteristic
349C2AGL(1,ℤ/8)×D4711yescharacteristic
350C2#1568992011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#478C2
socleC22×C47C22×D4
hypercenter#478D47
hypocenterC47#3077
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #15689679C2semidirect
3. #15689424C2semidirect
4. #15689423C2semidirect
5. #15689420C2semidirect
6. #15689412C2semidirect
7. #15689411C2semidirect
8. #15689402C2semidirect
9. #15689401C2semidirect
10. #15689164C2semidirect
11. #15689162C2semidirect
12. #15689145C2semidirect
15. C47×#478C2semidirect
20. #13094023C22semidirect
21. #13094023C22semidirect
22. #13094016C22semidirect
37. #13093958C22semidirect
38. #13093957C22semidirect
39. #13093957C22semidirect
40. #13093956C22semidirect
41. #13093955C22semidirect
42. #13093955C22semidirect
43. C4⋊(C47⋊C8)C22semidirect
44. Dic47⋊C8C22semidirect
45. Dic47⋊C8C22semidirect
52. #125×C47C22semidirect
54. #107×C47C22semidirect
55. #106×C47C22semidirect
56. C4⋊C8×C47C22semidirect
65. D4×D47Q8semidirect
181. #478D47semidirect
191. C47#3077semidirect
199. #125C2×D47semidirect
218. #107C2×D47semidirect
222. #106C2×D47semidirect
226. C4⋊C8C2×D47semidirect