Finite Group Databasebeta

← #20253012

Subgroups — #20253012

Order 6016.

496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D47C211yesmaximal, characteristic, complemented
2#15689630C211yesmaximal, characteristic
3C2×#13094000C211yesmaximal, characteristic, complemented
4#15689378C212yesmaximal, complemented
5#15689366C212yesmaximal, complemented
6#15689361C212yesmaximal, complemented
7#15689349C212yesmaximal, complemented
8#15689165C211yesmaximal, characteristic, complemented
9#15689132C211yesmaximal, characteristic, complemented
10#15689124C211yesmaximal, characteristic, complemented
11C2×#137×C47C211yesmaximal, characteristic, complemented
12C22×C4×D47C2211yescharacteristic
13C2×#10625329C2211yescharacteristic
14C2×#10625324C2212yes—
15M16×D47—24no—
16C2×C8×D47C2212yes—
17#13094005—21no—
18#13094000—21no—
19#13094000—21no—
20#13094000C2212yes—
21#13094000C2211yescharacteristic
22#13094000C2212yes—
23#13094000C2211yescharacteristic
24#13093995C2211yescharacteristic
25#13093995C2211yescharacteristic
26#13093992—21no—
27C4×C22⋊D47—21no—
28C4×C22⋊D47—21no—
29#13093983C2211yescharacteristic
30C2×C4⋊Dic47C2211yescharacteristic
31C2×Dic47⋊C4—21no—
32C2×(C2×D47)⋊C4—21no—
33#13093958C2212yescomplemented
34#13093956C2212yescomplemented
35#13093948C2212yescomplemented
36#13093948C2212yescomplemented
37#13093948C2212yescomplemented
38#13093945C2212yescomplemented
39C2×#41×C47C2211yescharacteristic
40C22×Q8×C47C2211yescharacteristic
41#137×C47—24no—
42C2×Q16×C47C2212yescomplemented
43C2×SD16×C47C2212yescomplemented
44C2×M16×C47C2211yescharacteristic
45C23×D47D411yescharacteristic
46#41×C47—22no—
47#41×C47—22no—
48C2×Q8×C47—21no—
49C2×Q8×C47—22no—
50C2×Q8×C47—22no—
51C2×Q8×C47C2312yes—
52C2×Q8×C47C2311yescharacteristic
53C2×D4×C47—21no—
54C2×D4×C47C2311yescharacteristic
55C22×C4×C47—21no—
56C22×C4×C47—21no—
57C22×C4×C47C2311yescharacteristic
58C2×C22⋊D47—21no—
59C2×C22⋊D47—21no—
60C22×Dic47—21no—
61C22×Dic47D411yescharacteristic
62C2×C4×D47—22no—
63C2×C4×D47—22no—
64C2×C4×D47D411yescharacteristic
65C2×C4×D47D411yescharacteristic
66C2×C4×D47C2311yescharacteristic
67C2×C4×D47C2311yescharacteristic
68Q16×C47—24no—
69SD16×C47—24no—
70M16×C47D414yescomplemented
71C2×C8×C47C2312yes—
72C22⋊Dic47—21no—
73C22⋊Dic47—21no—
74C22⋊Dic47—21no—
75(C2×D47)⋊C4—22no—
76(C2×D47)⋊C4—22no—
77(C2×D47)⋊C4—21no—
78(C2×D47)⋊C4—21no—
79C4⋊Dic47—21no—
80C4⋊Dic47C2312yes—
81C4⋊Dic47C2311yescharacteristic
82C4⋊Dic47C2311yescharacteristic
83Dic47⋊C4—22no—
84Dic47⋊C4—22no—
85Dic47⋊C4—21no—
86Dic47⋊C4—21no—
87C4×Dic47—21no—
88#10625329—22no—
89C2×C47⋊C8C2312yes—
90#10625324—24no—
91C8×D47—24no—
92C23×C47—21no—
93C23×C47C2×D411yescharacteristic
94C22×D47—22no—
95C22×D47—22no—
96C22×D47—41no—
97C22×D47C2×D411yescharacteristic
98C22×D47C2×D411yescharacteristic
99Q8×C47—22no—
100Q8×C47—21no—
101Q8×C47—22no—
102Q8×C47—21no—
103Q8×C47—42no—
104D4×C47—21no—
105D4×C47—21no—
106D4×C47—42no—
107C2×C4×C47—21no—
108C2×C4×C47—22no—
109C2×C4×C47—42no—
110C2×C4×C47—42no—
111C2×C4×C47C2×D411yescharacteristic
112C2×C4×C47C2×D412yes—
113C2×C4×C47#4112yes—
114C2×C4×C47C2411yescharacteristic
115C22⋊D47—42no—
116C22⋊D47—42no—
117C2×Dic47—22no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—22no—
121C2×Dic47—42no—
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124C4×D47—22no—
125C4×D47—22no—
126C4×D47—21no—
127C4×D47—21no—
128C4×D47—21no—
129C4×D47—21no—
130C8×C47C2×D414yes—
131C47⋊C8—22no—
132C22×C47—21no—
133C22×C47—21no—
134C22×C47—41no—
135C22×C47—41no—
136C22×C47—41no—
137C22×C47#12112yes—
138C22×C47C22×D411yescharacteristic
139C2×D47—21no—
140C2×D47—21no—
141C2×D47—21no—
142C2×D47—21no—
143C2×D47—21no—
144C2×D47—44no—
145C2×D47#13712yescomplemented
146C4×C47—41no—
147C4×C47—42no—
148C4×C47#12112yes—
149C4×C47C22×D411yescharacteristic
150C4×C47C2×#4111yescharacteristic
151Dic47—21no—
152Dic47—21no—
153Dic47—41no—
154Dic47—42no—
155Dic47—41no—
156#3056—471nomaximal, Sylow
157C2×C47—22no—
158C2×C47—81no—
159C2×C47C2×#12111yescharacteristic
160C2×C47C2×#13711yescharacteristic
161C2×C47#57511yescharacteristic
162D47—22no—
163D47—41no—
164C2×#137D4711yescharacteristic, complemented
165C22×M16—471no—
166#525—471no—
167C2×C22⋊Q8—471no—
168#470—472no—
169#468—472no—
170#467—472no—
171#465—472no—
172#428—471no—
173#419—471no—
174#417—471no—
175C47#305611yescharacteristic, complemented, Sylow
176C2×#41C2×D4711yescharacteristic
177C22×Q8C2×D4711yescharacteristic
178C23×C4—471no—
179#137—24no—
180C2×Q16C2×D4712yescomplemented
181C2×SD16C2×D4712yescomplemented
182C2×M16—471no—
183C2×M16—472no—
184C2×M16—944no—
185C2×M16C2×D4711yescharacteristic
186C22×C8—472no—
187#123—941no—
188C22⋊Q8—472no—
189C22⋊Q8—472no—
190C22⋊Q8—471no—
191C22⋊Q8—471no—
192C22⋊Q8—941no—
193C22⋊Q8—941no—
194#121—471no—
195#121—471no—
196#120—941no—
197C4×D4—941no—
198C4×D4—941no—
199#117—471no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4—941no—
202C2×C22⋊C4—941no—
203#107—472no—
204#106—472no—
205#103—472no—
206#103—472no—
207#103—472no—
208#102—472no—
209C24—471no—
210#41—22no—
211#41—22no—
212C2×Q8—21no—
213C2×Q8—22no—
214C2×Q8—22no—
215C2×Q8C22×D4712yes—
216C2×Q8C22×D4711yescharacteristic
217C2×D4—21no—
218C2×D4—941no—
219C2×D4—941no—
220C2×D4C22×D4711yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—471no—
224C22×C4—471no—
225C22×C4—471no—
226C22×C4—471no—
227C22×C4—471no—
228C22×C4—942no—
229C22×C4—942no—
230C22×C4—941no—
231C22×C4C22×D4711yescharacteristic
232Q16—24no—
233SD16—24no—
234M16—942no—
235M16—944no—
236M16C22⋊D4714yescomplemented
237C2×C8—472no—
238C2×C8—944no—
239C2×C8C22×D4712yes—
240C4⋊C4—472no—
241C4⋊C4—471no—
242C4⋊C4—471no—
243C4⋊C4—942no—
244C4⋊C4—942no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C22⋊C4—942no—
249C22⋊C4—942no—
250C22⋊C4—941no—
251C22⋊C4—941no—
252C22⋊C4—941no—
253C22⋊C4—941no—
254C22⋊C4—941no—
255C42—941no—
256C23—21no—
257C23—471no—
258C23—471no—
259C23—942no—
260C23—942no—
261C23—1881no—
262C23D4×D4711yescharacteristic
263Q8—22no—
264Q8—21no—
265Q8—22no—
266Q8—21no—
267Q8—42no—
268D4—21no—
269D4—21no—
270D4—42no—
271D4—1882no—
272D4—1882no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—471no—
278C2×C4—471no—
279C2×C4—942no—
280C2×C4—942no—
281C2×C4—942no—
282C2×C4—941no—
283C2×C4—941no—
284C2×C4—941no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—941no—
288C2×C4—942no—
289C2×C4—1882no—
290C2×C4D4×D4711yescharacteristic
291C2×C4#1062535212yes—
292C2×C4C2×C22⋊D4712yes—
293C2×C4C23×D4711yescharacteristic
294C8—942no—
295C8C2×C22⋊D4714yes—
296C22—21no—
297C22—21no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22—472no—
302C22—941no—
303C22—941no—
304C22—941no—
305C22—941no—
306C22—941no—
307C22—1884no—
308C22#1309399512yes—
309C22C2×D4×D4711yescharacteristic
310C4—41no—
311C4—42no—
312C4—941no—
313C4—941no—
314C4—1881no—
315C4—1882no—
316C4—1881no—
317C4#1309399512yes—
318C4C22×C22⋊D4711yescharacteristic
319C4C2×#1062535211yescharacteristic
320C2—22no—
321C2—81no—
322C2—942no—
323C2—1881no—
324C2C2×#1309399511yescharacteristic
325C2#137×D4711yescharacteristic
326C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#137×C47C2
socleC22×C47C22×D4
hypercenterC2×#137D47
hypocenterC47#3056
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×M16×D47C2semidirect
3. C2×#13094000C2semidirect
4. #15689378C2semidirect
5. #15689366C2semidirect
6. #15689361C2semidirect
7. #15689349C2semidirect
8. #15689165C2semidirect
9. #15689132C2semidirect
10. #15689124C2semidirect
11. C2×#137×C47C2semidirect
33. #13093958C22semidirect
34. #13093956C22semidirect
35. #13093948C22semidirect
36. #13093948C22semidirect
37. #13093948C22semidirect
38. #13093945C22semidirect
42. C2×Q16×C47C22semidirect
43. C2×SD16×C47C22semidirect
70. M16×C47D4semidirect
145. C2×D47#137semidirect
164. C2×#137D47semidirect
175. C47#3056semidirect
180. C2×Q16C2×D47semidirect
181. C2×SD16C2×D47semidirect
236. M16C22⋊D47semidirect