Finite Group Databasebeta

← #20254147

Subgroups — #20254147

Order 6016.

468 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094004C211yesmaximal, characteristic, complemented
2#121×D47C211yesmaximal, characteristic
3#15689455C212yesmaximal, complemented
4#15689441C211yesmaximal, characteristic, complemented
5#15689353C212yesmaximal, complemented
6#15689351C212yesmaximal, complemented
7#15689275C212yesmaximal, complemented
8#15689264C211yesmaximal, characteristic, complemented
9#15689261C211yesmaximal, characteristic, complemented
10C22⋊C8×D47C211yesmaximal, characteristic, complemented
11C47×#481C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic, complemented
13C2×D4×D47—21no—
14C2×D4×D47C2211yescharacteristic
15C22×C4×D47C2211yescharacteristic
16C2×#10625325C2212yescomplemented
17C2×#10625335C2212yescomplemented
18C2×C8×D47C2212yescomplemented
19#13094004—21no—
20#13094004—21no—
21#13094004C2212yes—
22#13094004C2212yescomplemented
23#13093999C2211yescharacteristic
24#13093998C2211yescharacteristic
25#13093997—21no—
26#13093996—21no—
27#13093995C2211yescharacteristic
28C2×C4⋊Dic47—21no—
29C4⋊C4×D47C2211yescharacteristic
30C2×(C2×D47)⋊C4—21no—
31C22⋊C4×D47—21no—
32#13093955C2212yescomplemented
33#13093949C2212yescomplemented
34#13093947C2212yescomplemented
35#13093944C2212yescomplemented
36C22⋊(C47⋊C8)C2211yescharacteristic, complemented
37(C2×D47)⋊C8C2212yes—
38#121×C47C2211yescharacteristic
39C2×C4⋊C4×C47C2211yescharacteristic, complemented
40#106×C47C2212yescomplemented
41#102×C47C2212yescomplemented
42C22⋊C8×C47C2211yescharacteristic, complemented
43C23×D47—21no—
44C23×D47D411yescharacteristic
45C2×D4×C47—21no—
46C2×D4×C47C2311yescharacteristic
47C22×C4×C47—21no—
48C22×C4×C47C2311yescharacteristic
49C2×C22⋊D47—21no—
50C2×C22⋊D47—21no—
51C2×C22⋊D47—21no—
52C22×Dic47—21no—
53C22×Dic47D411yescharacteristic
54D4×D47—42no—
55D4×D47—44no—
56C2×D188—21no—
57C2×D188C2311yescharacteristic
58C2×C4×D47—21no—
59C2×C4×D47—42no—
60C2×C4×D47D411yescharacteristic
61C2×C4×D47D411yescharacteristic
62C2×C4×D47C2311yescharacteristic
63C2×C4×D47C2311yescharacteristic
64C2×Dic94—21no—
65C2×Dic94—42no—
66C2×Dic94C2312yes—
67C2×C8×C47C2312yes—
68C4⋊C4×C47—21no—
69C4⋊C4×C47C2311yescharacteristic
70C4⋊C4×C47C2312yes—
71C22⋊C4×C47—21no—
72C22⋊Dic47—21no—
73#10625335—42no—
74(C2×D47)⋊C4—22no—
75(C2×D47)⋊C4—22no—
76(C2×D47)⋊C4—21no—
77(C2×D47)⋊C4—21no—
78C4⋊Dic47—22no—
79C4⋊Dic47—22no—
80C4⋊Dic47C2311yescharacteristic
81Dic47⋊C4—21no—
82C2×C47⋊C8C2312yes—
83#10625325—42no—
84C8×D47—42no—
85C23×C47—21no—
86C23×C47C2×D411yescharacteristic
87C22×D47—21no—
88C22×D47—41no—
89C22×D47—41no—
90C22×D47—42no—
91C22×D47—42no—
92C22×D47—42no—
93C22×D47SD1614yescomplemented
94C22×D47C2×D411yescharacteristic
95C22×D47C2×D411yescharacteristic
96D4×C47—22no—
97D4×C47—42no—
98C2×C4×C47—22no—
99C2×C4×C47—21no—
100C2×C4×C47—22no—
101C2×C4×C47—42no—
102C2×C4×C47C2×D411yescharacteristic
103C2×C4×C47C2411yescharacteristic
104C22⋊D47—42no—
105C22⋊D47—42no—
106C22⋊D47—42no—
107C2×Dic47—21no—
108C2×Dic47—22no—
109C2×Dic47—41no—
110C2×Dic47—42no—
111C2×Dic47C2×D411yescharacteristic
112C2×Dic47C2×D411yescharacteristic
113D188—22no—
114D188—42no—
115C4×D47—22no—
116C4×D47—22no—
117C4×D47—41no—
118C4×D47—41no—
119C4×D47—42no—
120Dic94—22no—
121Dic94—22no—
122Dic94—42no—
123C8×C47—22no—
124C47⋊C8—22no—
125C22×C47—21no—
126C22×C47—21no—
127C22×C47—41no—
128C22×C47—41no—
129C22×C47—41no—
130C22×C47C2×SD1612yes—
131C22×C47C22×D411yescharacteristic
132C2×D47—21no—
133C2×D47—21no—
134C2×D47—21no—
135C2×D47—21no—
136C2×D47—44no—
137C2×D47—41no—
138C2×D47—41no—
139C2×D47—41no—
140C2×D47—84no—
141C2×D47C2×SD1612yes—
142C2×D47C2×SD1612yes—
143C4×C47—21no—
144C4×C47—41no—
145C4×C47—42no—
146C4×C47H(5,𝔽2)12yes—
147Dic47—21no—
148Dic47—21no—
149Dic47—42no—
150Dic47—41no—
151#3187—471nomaximal, Sylow
152C2×C47—22no—
153C2×C47—81no—
154C2×C47#53411yescharacteristic
155C2×C47C22×SD1611yescharacteristic
156C2×C47#57511yescharacteristic
157D47—22no—
158D47—22no—
159D47—81no—
160C2×C22⋊Q8—471no—
161C2×#121—471no—
162#483—472no—
163#481—471no—
164#481D4711yescharacteristic, complemented
165#465—472no—
166#465—472no—
167#450—472no—
168#448—471no—
169#448—471no—
170C2×C22⋊C8—471no—
171C47#318711yescharacteristic, complemented, Sylow
172C22×Q8—471no—
173C22×D4—471no—
174C22×D4—941no—
175C23×C4—471no—
176C2×SD16—472no—
177C2×SD16—472no—
178C22×C8—472no—
179C22⋊Q8—472no—
180C22⋊Q8—472no—
181C22⋊Q8—941no—
182C22⋊Q8—941no—
183#121—471no—
184#121—471no—
185#121—471no—
186#121—941no—
187#121—941no—
188#121C2×D4711yescharacteristic
189C2×C4⋊C4—471no—
190C2×C4⋊C4—941no—
191C2×C4⋊C4C2×D4711yescharacteristic, complemented
192C2×C22⋊C4—941no—
193C2×C22⋊C4—941no—
194#106—472no—
195#106C2×D4712yescomplemented
196#103—472no—
197#103—472no—
198#102—472no—
199#102C2×D4712yescomplemented
200C22⋊C8—471no—
201C22⋊C8—472no—
202C22⋊C8C2×D4711yescharacteristic, complemented
203C24—471no—
204C24—941no—
205C2×Q8—472no—
206C2×Q8—941no—
207C2×Q8—1882no—
208C2×D4—21no—
209C2×D4—471no—
210C2×D4—941no—
211C2×D4—941no—
212C2×D4—941no—
213C2×D4—941no—
214C2×D4—1882no—
215C2×D4—1884no—
216C2×D4C22×D4711yescharacteristic
217C22×C4—21no—
218C22×C4—471no—
219C22×C4—471no—
220C22×C4—471no—
221C22×C4—471no—
222C22×C4—471no—
223C22×C4—941no—
224C22×C4—941no—
225C22×C4—1882no—
226C22×C4C22×D4711yescharacteristic
227SD16—1882no—
228SD16—1882no—
229C2×C8—472no—
230C2×C8—1882no—
231C2×C8C22×D4712yes—
232C4⋊C4—21no—
233C4⋊C4—471no—
234C4⋊C4—941no—
235C4⋊C4—942no—
236C4⋊C4—942no—
237C4⋊C4C22×D4712yes—
238C4⋊C4C22×D4711yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—941no—
241C22⋊C4—942no—
242C22⋊C4—942no—
243C22⋊C4—941no—
244C22⋊C4—941no—
245C23—21no—
246C23—471no—
247C23—471no—
248C23—474no—
249C23—941no—
250C23—1881no—
251C23—1881no—
252C23—1882no—
253C23—1882no—
254C23—1882no—
255C23D4×D4711yescharacteristic
256Q8—942no—
257Q8—942no—
258Q8—1882no—
259D4—22no—
260D4—42no—
261D4—942no—
262D4—1882no—
263D4—1882no—
264D4—1882no—
265D4—1882no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—471no—
271C2×C4—471no—
272C2×C4—942no—
273C2×C4—942no—
274C2×C4—941no—
275C2×C4—942no—
276C2×C4—1881no—
277C2×C4—1881no—
278C2×C4—1882no—
279C2×C4—1881no—
280C2×C4—1882no—
281C2×C4D4×D4711yescharacteristic
282C2×C4C23×D4711yescharacteristic
283C8—22no—
284C8—942no—
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—472no—
291C22—472no—
292C22—941no—
293C22—941no—
294C22—941no—
295C22—941no—
296C22—3764no—
297C22—1884no—
298C22—1881no—
299C22—1881no—
300C22—1881no—
301C22SD16×D4712yes—
302C22C2×D4×D4711yescharacteristic
303C4—21no—
304C4—41no—
305C4—42no—
306C4—941no—
307C4—941no—
308C4—1881no—
309C4—1882no—
310C4#1309407012yes—
311C2—22no—
312C2—81no—
313C2—942no—
314C2—942no—
315C2—3761no—
316C2#1568968411yescharacteristic
317C2C2×SD16×D4711yescharacteristic
318C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#481C2
socleC22×C47C22×D4
hypercenter#481D47
hypocenterC47#3187
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. C2×#13094004C2semidirect
3. #15689455C2semidirect
4. #15689441C2semidirect
5. #15689353C2semidirect
6. #15689351C2semidirect
7. #15689275C2semidirect
8. #15689264C2semidirect
9. #15689261C2semidirect
10. C22⋊C8×D47C2semidirect
11. C47×#481C2semidirect
12. C22×Dic94C22semidirect
16. C2×#10625325C22semidirect
17. C2×#10625335C22semidirect
18. C2×C8×D47C22semidirect
22. #13094004C22semidirect
32. #13093955C22semidirect
33. #13093949C22semidirect
34. #13093947C22semidirect
35. #13093944C22semidirect
36. C22⋊(C47⋊C8)C22semidirect
39. C2×C4⋊C4×C47C22semidirect
40. #106×C47C22semidirect
41. #102×C47C22semidirect
42. C22⋊C8×C47C22semidirect
93. C22×D47SD16semidirect
164. #481D47semidirect
171. C47#3187semidirect
191. C2×C4⋊C4C2×D47semidirect
195. #106C2×D47semidirect
199. #102C2×D47semidirect
202. C22⋊C8C2×D47semidirect