Finite Group Databasebeta

← #20253836

Subgroups — #20253836

Order 6016.

656 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13094052C211yesmaximal, characteristic, complemented
2C2×#13094050C211yesmaximal, characteristic, complemented
3C2×#13094049C211yesmaximal, characteristic, complemented
4#15689669C211yesmaximal, characteristic, complemented
5C2×#13094020C211yesmaximal, characteristic, complemented
6#15689511C212yesmaximal, complemented
7#15689509C212yesmaximal, complemented
8#15689498C212yesmaximal, complemented
9#15689494C212yesmaximal, complemented
10M16×Dic47C211yesmaximal, characteristic, complemented
11C2×AGL(1,ℤ/8)×C47C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C22×D188C2211yescharacteristic
14C22×C22⋊D47—22no—
15#13094052—24no—
16#13094050—24no—
17#13094049—24no—
18C2×#10625325C2212yescomplemented
19C2×#10625335C2212yescomplemented
20C2×#10625336C2212yescomplemented
21C2×D376C2212yescomplemented
22C2×#10625334C2212yescomplemented
23C2×#10625334C2212yescomplemented
24C2×#10625329C2211yescharacteristic
25#13094022C2211yescharacteristic, complemented
26#13094020—22no—
27#13094020C2212yes—
28#13094020C2212yes—
29#13094020C2211yescharacteristic, complemented
30#13094013C2211yescharacteristic, complemented
31#13094011C2211yescharacteristic, complemented
32#13093996—22no—
33C4×C22⋊D47—22no—
34C2×C4×Dic47C2211yescharacteristic
35#13093934C2212yescomplemented
36C8×Dic47C2212yescomplemented
37C2×#41×C47C2211yescharacteristic
38C22×D4×C47C2211yescharacteristic
39AGL(1,ℤ/8)×C47—24no—
40C2×SD16×C47C2212yescomplemented
41C2×D8×C47C2212yescomplemented
42C2×M16×C47C2211yescharacteristic
43C24×C47—21no—
44C23×D47—21no—
45#41×C47—22no—
46#41×C47—22no—
47C2×Q8×C47C2311yescharacteristic
48C2×D4×C47—21no—
49C2×D4×C47—22no—
50C2×D4×C47—22no—
51C2×D4×C47—21no—
52C2×D4×C47C2311yescharacteristic
53C2×D4×C47C2312yes—
54C22×C4×C47—21no—
55C22×C4×C47C2311yescharacteristic
56C2×C22⋊D47—21no—
57C2×C22⋊D47—22no—
58C2×C22⋊D47—24no—
59C2×C22⋊D47—24no—
60C2×C22⋊D47—48no—
61C22×Dic47D412yes—
62#10625350—22no—
63#10625350—22no—
64C2×D188—22no—
65C2×D188—22no—
66C2×D188—21no—
67C2×D188C2311yescharacteristic
68C2×D188C2312yes—
69C2×C4×D47—21no—
70C2×Dic94C2311yescharacteristic
71SD16×C47—24no—
72D8×C47—24no—
73M16×C47D414yescomplemented
74C2×C8×C47C2312yes—
75C22⋊Dic47—22no—
76#10625336—24no—
77#10625335—24no—
78#10625334—24no—
79#10625334—24no—
80(C2×D47)⋊C4—22no—
81Dic47⋊C4—22no—
82C4×Dic47D412yes—
83C4×Dic47C2311yescharacteristic
84C4×Dic47C2311yescharacteristic
85#10625329D414yescomplemented
86C2×C47⋊C8C2312yes—
87D376—24no—
88#10625325—24no—
89C23×C47—21no—
90C23×C47—22no—
91C23×C47—44no—
92C23×C47—42no—
93C23×C47C2×D411yescharacteristic
94C22×D47—21no—
95C22×D47—22no—
96C22×D47—44no—
97C22×D47—42no—
98Q8×C47—21no—
99Q8×C47—21no—
100D4×C47—21no—
101D4×C47—22no—
102D4×C47—21no—
103D4×C47—22no—
104D4×C47—42no—
105D4×C47—42no—
106C2×C4×C47—21no—
107C2×C4×C47—42no—
108C2×C4×C47C2×D411yescharacteristic
109C2×C4×C47C2×D412yes—
110C2×C4×C47C2×D412yes—
111C2×C4×C47C2411yescharacteristic
112C22⋊D47—48no—
113C22⋊D47—42no—
114C22⋊D47—44no—
115C22⋊D47—48no—
116C2×Dic47—24no—
117C2×Dic47—21no—
118C2×Dic47C2×D412yes—
119C2×Dic47C2×D412yes—
120D188—22no—
121D188—21no—
122D188—21no—
123D188—22no—
124D188—42no—
125C4×D47—42no—
126Dic94—21no—
127Dic94—21no—
128C8×C47C2×D414yescomplemented
129C47⋊C8C2×D414yescomplemented
130C22×C47—22no—
131C22×C47—41no—
132C22×C47—42no—
133C22×C47—44no—
134C22×C47—42no—
135C22×C47—84no—
136C22×C47#12712yes—
137C22×C47C22×D411yescharacteristic
138C2×D47—41no—
139C2×D47—42no—
140C2×D47—44no—
141C2×D47—42no—
142C2×D47—84no—
143C4×C47—41no—
144C4×C47#12712yes—
145C4×C47C22×D411yescharacteristic
146C4×C47C22×D411yescharacteristic
147Dic47—22no—
148Dic47—41no—
149Dic47AGL(1,ℤ/8)14yescomplemented
150#3151—471nomaximal, Sylow
151C2×C47—22no—
152C2×C47—81no—
153C2×C47—82no—
154C2×C47C2×#12711yescharacteristic
155C2×C47C2×AGL(1,ℤ/8)12yes—
156D47—81no—
157D47—82no—
158C2×AGL(1,ℤ/8)—471no—
159C2×AGL(1,ℤ/8)—471no—
160C2×AGL(1,ℤ/8)—471no—
161C2×AGL(1,ℤ/8)D4711yescharacteristic, complemented
162#532—471no—
163C2×#127—471no—
164#496—472no—
165#496—472no—
166#493—472no—
167#492—472no—
168C4×M16—471no—
169C47#315111yescharacteristic, complemented, Sylow
170C2×#41—471no—
171C2×#41C2×D4711yescharacteristic
172C22×D4—471no—
173C22×D4—942no—
174C22×D4C2×D4711yescharacteristic
175AGL(1,ℤ/8)—24no—
176AGL(1,ℤ/8)—944no—
177AGL(1,ℤ/8)—944no—
178AGL(1,ℤ/8)—944no—
179C2×SD16—472no—
180C2×SD16—472no—
181C2×SD16—472no—
182C2×SD16C2×D4712yescomplemented
183C2×D8—472no—
184C2×D8—472no—
185C2×D8—472no—
186C2×D8C2×D4712yescomplemented
187C2×M16—471no—
188C2×M16C2×D4711yescharacteristic
189C4⋊Q8—471no—
190#127—472no—
191#127—472no—
192#127—471no—
193#127—942no—
194#124—471no—
195#124—471no—
196#121—942no—
197C4×D4—942no—
198C2×C42—471no—
199#97—472no—
200C4×C8—472no—
201C24—21no—
202C24—941no—
203#41—22no—
204#41—22no—
205#41—942no—
206#41—942no—
207C2×Q8—471no—
208C2×Q8C22×D4711yescharacteristic
209C2×D4—21no—
210C2×D4—22no—
211C2×D4—21no—
212C2×D4—22no—
213C2×D4—471no—
214C2×D4—472no—
215C2×D4—942no—
216C2×D4—944no—
217C2×D4—944no—
218C2×D4—941no—
219C2×D4—942no—
220C2×D4—941no—
221C2×D4—942no—
222C2×D4—1888no—
223C2×D4C22×D4711yescharacteristic
224C2×D4C22×D4712yes—
225C22×C4—21no—
226C22×C4—472no—
227C22×C4—941no—
228C22×C4C22×D4711yescharacteristic
229SD16—24no—
230SD16—944no—
231SD16—944no—
232SD16—944no—
233D8—24no—
234D8—944no—
235D8—944no—
236D8—944no—
237M16—474no—
238M16C22⋊D4714yescomplemented
239C2×C8—472no—
240C2×C8C22×D4712yes—
241C4⋊C4—942no—
242C22⋊C4—942no—
243C22⋊C4—942no—
244C42—472no—
245C42—471no—
246C42—471no—
247C23—21no—
248C23—22no—
249C23—44no—
250C23—42no—
251C23—941no—
252C23—942no—
253C23—1884no—
254C23—1882no—
255C23D4×D4711yescharacteristic
256Q8—21no—
257Q8—21no—
258Q8—941no—
259Q8—941no—
260D4—21no—
261D4—22no—
262D4—21no—
263D4—22no—
264D4—42no—
265D4—42no—
266D4—941no—
267D4—942no—
268D4—941no—
269D4—942no—
270D4—1884no—
271D4—1888no—
272D4—1888no—
273D4—1882no—
274D4—1882no—
275C2×C4—21no—
276C2×C4—42no—
277C2×C4—472no—
278C2×C4—472no—
279C2×C4—944no—
280C2×C4—941no—
281C2×C4—1882no—
282C2×C4D4×D4711yescharacteristic
283C2×C4D4×D4712yes—
284C2×C4C2×C22⋊D4712yes—
285C2×C4C23×D4711yescharacteristic
286C8—474no—
287C8C2×C22⋊D4714yescomplemented
288C22—22no—
289C22—44no—
290C22—42no—
291C22—41no—
292C22—42no—
293C22—84no—
294C22—3764no—
295C22—1884no—
296C22—1882no—
297C22—1881no—
298C22—1882no—
299C22#1309402012yes—
300C22C2×D4×D4711yescharacteristic
301C4—41no—
302C4—474no—
303C4—942no—
304C4—1881no—
305C4#1309402012yes—
306C4C2×D4×D4711yescharacteristic
307C4C22×C22⋊D4711yescharacteristic
308C2—22no—
309C2—82no—
310C2—81no—
311C2—3762no—
312C2—3761no—
313C2C2×#1309402011yescharacteristic
314C2AGL(1,ℤ/8)×D4712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×AGL(1,ℤ/8)×C47C2
socleC22×C47C22×D4
hypercenterC2×AGL(1,ℤ/8)D47
hypocenterC47#3151
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#13094052C2semidirect
2. C2×#13094050C2semidirect
3. C2×#13094049C2semidirect
4. #15689669C2semidirect
5. C2×#13094020C2semidirect
6. #15689511C2semidirect
7. #15689509C2semidirect
8. #15689498C2semidirect
9. #15689494C2semidirect
10. M16×Dic47C2semidirect
11. C2×AGL(1,ℤ/8)×C47C2semidirect
18. C2×#10625325C22semidirect
19. C2×#10625335C22semidirect
20. C2×#10625336C22semidirect
21. C2×D376C22semidirect
22. C2×#10625334C22semidirect
23. C2×#10625334C22semidirect
25. #13094022C22semidirect
29. #13094020C22semidirect
30. #13094013C22semidirect
31. #13094011C22semidirect
35. #13093934C22semidirect
36. C8×Dic47C22semidirect
40. C2×SD16×C47C22semidirect
41. C2×D8×C47C22semidirect
73. M16×C47D4semidirect
85. #10625329D4semidirect
128. C8×C47C2×D4semidirect
129. C47⋊C8C2×D4semidirect
149. Dic47AGL(1,ℤ/8)semidirect
161. C2×AGL(1,ℤ/8)D47semidirect
169. C47#3151semidirect
182. C2×SD16C2×D47semidirect
186. C2×D8C2×D47semidirect
238. M16C22⋊D47semidirect
287. C8C2×C22⋊D47semidirect