Finite Group Databasebeta

← #20254376

Subgroups — #20254376

Order 6016.

444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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
1#15689674C211yesmaximal, characteristic, complemented
2#124×D47C211yesmaximal, characteristic, complemented
3#15689513C211yesmaximal, characteristic, complemented
4#15689512C211yesmaximal, characteristic, complemented
5#15689485C211yesmaximal, characteristic, complemented
6#15689341C212yesmaximal, complemented
7#15689337C212yesmaximal, complemented
8#15689263C212yesmaximal, complemented
9#15689258C212yesmaximal, complemented
10#15689178C211yesmaximal, characteristic, complemented
11C47×#489C211yesmaximal, characteristic, complemented
12C2×#10625354—21no—
13C2×Q8×D47C2211yescharacteristic
14C2×D4×D47C2211yescharacteristic
15C2×#10625325C2212yescomplemented
16C2×#10625336C2212yescomplemented
17C2×D376C2212yes—
18C2×#10625334C2212yes—
19#13094021C2211yescharacteristic, complemented
20#13094013—21no—
21#13094013C2211yescharacteristic
22#13094012C2211yescharacteristic
23#13094011C2211yescharacteristic
24#13094010—21no—
25#13094010—21no—
26#13093999—21no—
27#13093999C2212yes—
28#13093986—21no—
29#13093986C2212yescomplemented
30C22⋊C4×D47—21no—
31C22⋊C4×D47—21no—
32C42×D47C2211yescharacteristic
33Dic47⋊C8C2212yescomplemented
34#13093947C2212yescomplemented
35#13093944C2212yes—
36(C2×D47)⋊C8C2212yes—
37#13093935C2211yescharacteristic, complemented
38C4⋊Q8×C47C2211yescharacteristic, complemented
39#124×C47C2211yescharacteristic
40#103×C47C2212yescomplemented
41#102×C47C2212yes—
42#97×C47C2211yescharacteristic, complemented
43C23×D47—21no—
44C2×Q8×C47—21no—
45C2×Q8×C47C2311yescharacteristic
46C2×D4×C47C2311yescharacteristic
47C2×C22⋊D47—21no—
48#10625354—44no—
49Q8×D47—42no—
50D4×D47—42no—
51C2×D188—22no—
52C2×D188—21no—
53C2×D188—21no—
54C2×D188C2311yescharacteristic
55C2×D188C2312yes—
56C2×C4×D47—21no—
57C2×C4×D47—22no—
58C2×C4×D47D411yescharacteristic
59C2×C4×D47D411yescharacteristic
60C2×C4×D47C2311yescharacteristic
61C2×Dic94—21no—
62C2×Dic94C2311yescharacteristic
63C2×C8×C47C2312yes—
64C4⋊C4×C47—21no—
65C4⋊C4×C47C2312yes—
66C22⋊C4×C47—21no—
67C22⋊C4×C47—21no—
68C42×C47C2311yescharacteristic
69C22⋊Dic47—21no—
70C22⋊Dic47—21no—
71#10625336—42no—
72#10625334—42no—
73(C2×D47)⋊C4—21no—
74(C2×D47)⋊C4—21no—
75(C2×D47)⋊C4—21no—
76(C2×D47)⋊C4—21no—
77(C2×D47)⋊C4—22no—
78(C2×D47)⋊C4—22no—
79C4×Dic47D411yescharacteristic
80C4×Dic47D411yescharacteristic
81C4×Dic47C2311yescharacteristic
82C2×C47⋊C8C2312yes—
83D376—42no—
84#10625325—42no—
85C23×C47—21no—
86C22×D47—21no—
87C22×D47—22no—
88C22×D47—42no—
89C22×D47—42no—
90C22×D47—42no—
91C22×D47C2×D411yescharacteristic
92Q8×C47—22no—
93Q8×C47—42no—
94D4×C47—22no—
95C2×C4×C47—21no—
96C2×C4×C47—22no—
97C2×C4×C47C2×D411yescharacteristic
98C2×C4×C47C2×D411yescharacteristic
99C2×C4×C47C2411yescharacteristic
100C22⋊D47—42no—
101C2×Dic47—21no—
102C2×Dic47C2×D411yescharacteristic
103C2×Dic47C2×D411yescharacteristic
104C2×Dic47C2×D411yescharacteristic
105D188—22no—
106D188—22no—
107D188—22no—
108D188—42no—
109D188—42no—
110D188—44no—
111C4×D47—22no—
112C4×D47—22no—
113C4×D47—41no—
114C4×D47—44no—
115C4×D47—42no—
116Dic94—22no—
117Dic94—42no—
118C8×C47—22no—
119C47⋊C8—22no—
120C22×C47—41no—
121C22×C47—41no—
122C22×C47—41no—
123C22×C47C22×D411yescharacteristic
124C2×D47—21no—
125C2×D47—21no—
126C2×D47—41no—
127C2×D47—42no—
128C2×D47—42no—
129C2×D47—41no—
130C2×D47—42no—
131C2×D47—41no—
132C2×D47—84no—
133C2×D47AGL(1,ℤ/8)12yes—
134C4×C47—21no—
135C4×C47—21no—
136C4×C47—41no—
137C4×C47—42no—
138C4×C47H(5,𝔽2)12yes—
139Dic47—21no—
140Dic47—21no—
141Dic47—21no—
142Dic47—41no—
143#3213—471nomaximal, Sylow
144C2×C47—81no—
145C2×C47#53511yescharacteristic
146C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
147C2×C47#57511yescharacteristic
148D47—22no—
149D47—82no—
150D47—81no—
151#532—471no—
152C2×#124—471no—
153#496—471no—
154#496—471no—
155#489—471no—
156#489D4711yescharacteristic, complemented
157#463—472no—
158#463—472no—
159#448—472no—
160#447—472no—
161#432—471no—
162C47#321311yescharacteristic, complemented, Sylow
163C2×#41—941no—
164C22×Q8—471no—
165C22×D4—471no—
166C2×SD16—472no—
167C2×SD16—472no—
168C2×D8—472no—
169C2×D8—472no—
170C4⋊Q8C2×D4711yescharacteristic, complemented
171#127—471no—
172#124—471no—
173#124—471no—
174#124—471no—
175#124—941no—
176#124—941no—
177#124—941no—
178#124C2×D4711yescharacteristic
179#121—472no—
180#121—941no—
181C4×D4—472no—
182C4×D4—941no—
183C2×C22⋊C4—941no—
184C2×C22⋊C4—941no—
185C2×C42—471no—
186C4⋊C8—472no—
187#103—472no—
188#103C2×D4712yescomplemented
189#102—472no—
190#102C2×D4712yes—
191C22⋊C8—472no—
192#97—471no—
193#97C2×D4711yescharacteristic, complemented
194C24—941no—
195#41—1884no—
196C2×Q8—21no—
197C2×Q8—471no—
198C2×Q8—941no—
199C2×Q8—1882no—
200C2×Q8C22×D4711yescharacteristic
201C2×D4—471no—
202C2×D4—472no—
203C2×D4—942no—
204C2×D4—941no—
205C2×D4—941no—
206C2×D4—941no—
207C2×D4—1882no—
208C2×D4C22×D4711yescharacteristic
209C22×C4—471no—
210C22×C4—471no—
211C22×C4—471no—
212C22×C4—942no—
213C22×C4—941no—
214SD16—1882no—
215SD16—1882no—
216D8—1882no—
217D8—1882no—
218C2×C8—472no—
219C2×C8C22×D4712yes—
220C4⋊C4—21no—
221C4⋊C4C22×D4712yes—
222C22⋊C4—21no—
223C22⋊C4—21no—
224C22⋊C4—941no—
225C22⋊C4—941no—
226C22⋊C4—942no—
227C22⋊C4—942no—
228C22⋊C4—941no—
229C22⋊C4—941no—
230C22⋊C4—941no—
231C22⋊C4—941no—
232C42—471no—
233C42—471no—
234C42—471no—
235C42C22×D4711yescharacteristic
236C23—21no—
237C23—471no—
238C23—941no—
239C23—942no—
240C23—1882no—
241C23—1882no—
242C23—1882no—
243Q8—22no—
244Q8—42no—
245Q8—942no—
246Q8—1882no—
247D4—22no—
248D4—942no—
249D4—942no—
250D4—942no—
251D4—1882no—
252D4—1882no—
253D4—1884no—
254D4—1882no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—471no—
258C2×C4—471no—
259C2×C4—471no—
260C2×C4—942no—
261C2×C4—942no—
262C2×C4—941no—
263C2×C4—1881no—
264C2×C4—1884no—
265C2×C4—1882no—
266C2×C4D4×D4711yescharacteristic
267C2×C4D4×D4711yescharacteristic
268C2×C4C23×D4711yescharacteristic
269C8—22no—
270C8—942no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—472no—
275C22—941no—
276C22—941no—
277C22—3764no—
278C22—1882no—
279C22—1881no—
280C22—1882no—
281C22—1881no—
282C22—1881no—
283C22—1882no—
284C22C2×D4×D4711yescharacteristic
285C4—21no—
286C4—21no—
287C4—42no—
288C4—41no—
289C4—941no—
290C4—941no—
291C4—941no—
292C4—1881no—
293C4#1309407012yes—
294C2—81no—
295C2—942no—
296C2—3761no—
297C2—3762no—
298C2#1568969111yescharacteristic
299C2AGL(1,ℤ/8)×D4711yescharacteristic
300C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#489C2
socleC22×C47C22×D4
hypercenter#489D47
hypocenterC47#3213
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #15689674C2semidirect
2. #124×D47C2semidirect
3. #15689513C2semidirect
4. #15689512C2semidirect
5. #15689485C2semidirect
6. #15689341C2semidirect
7. #15689337C2semidirect
8. #15689263C2semidirect
9. #15689258C2semidirect
10. #15689178C2semidirect
11. C47×#489C2semidirect
15. C2×#10625325C22semidirect
16. C2×#10625336C22semidirect
19. #13094021C22semidirect
29. #13093986C22semidirect
33. Dic47⋊C8C22semidirect
34. #13093947C22semidirect
37. #13093935C22semidirect
38. C4⋊Q8×C47C22semidirect
40. #103×C47C22semidirect
42. #97×C47C22semidirect
156. #489D47semidirect
162. C47#3213semidirect
170. C4⋊Q8C2×D47semidirect
188. #103C2×D47semidirect
193. #97C2×D47semidirect