Finite Group Databasebeta

← #20252642

Subgroups — #20252642

Order 6016.

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

normal subgroups only

This group has 806 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
1C22×#10625350C211yesmaximal, characteristic, complemented
2C2×#13094052C212yesmaximal, complemented
3C2×#13093998C211yesmaximal, characteristic, complemented
4#15689270C214yesmaximal, complemented
5#15689264C212yesmaximal, complemented
6#15689259C212yesmaximal, complemented
7#15689125C212yesmaximal, complemented
8C47×#407C211yesmaximal, characteristic, complemented
9C2×#10625350—21no—
10C2×#10625350—21no—
11C2×#10625350—28no—
12C2×#10625350C2212yes—
13C2×#10625350C2212yescomplemented
14C22×Dic94C2211yescharacteristic, complemented
15C22×D188C2211yescharacteristic, complemented
16C22×D188C2211yescharacteristic, complemented
17C22×C22⋊D47—21no—
18C22×C22⋊D47—21no—
19C22×C4×D47—21no—
20#13094052—28no—
21C2×#10625325C2214yescomplemented
22C2×D376C2214yescomplemented
23#13093998—21no—
24#13093998—21no—
25#13093998C2212yes—
26#13093998C2212yescomplemented
27C2×C4⋊Dic47C2211yescharacteristic, complemented
28C2×(C2×D47)⋊C4—21no—
29#13093949C2214yescomplemented
30#13093946C2214yescomplemented
31C23×C4×C47C2211yescharacteristic
32C2×M16×C47C2212yescomplemented
33C22⋊C8×C47C2212yescomplemented
34C22⋊C8×C47C2212yescomplemented
35C24×C47D411yescharacteristic
36C23×D47—21no—
37C23×D47—21no—
38C22×C4×C47—24no—
39C22×C4×C47D411yescharacteristic
40C22×C4×C47D411yescharacteristic
41C22×C4×C47D411yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—28no—
46C2×C22⋊D47—22no—
47C2×C22⋊D47—22no—
48C2×C22⋊D47—22no—
49C2×C22⋊D47—22no—
50C2×C22⋊D47—44no—
51C22×Dic47—21no—
52C22×Dic47—21no—
53#10625350—28no—
54#10625350—28no—
55#10625350—24no—
56#10625350—24no—
57#10625350—24no—
58#10625350D418yescomplemented
59C2×D188—21no—
60C2×D188—24no—
61C2×D188—24no—
62C2×D188—21no—
63C2×D188C2312yes—
64C2×D188C2312yes—
65C2×C4×D47—28no—
66C2×C4×D47—22no—
67C2×C4×D47—22no—
68C2×Dic94—21no—
69C2×Dic94—24no—
70C2×Dic94C2312yes—
71M16×C47—24no—
72C2×C8×C47C2314yes—
73(C2×D47)⋊C4—22no—
74(C2×D47)⋊C4—22no—
75C4⋊Dic47—21no—
76C4⋊Dic47C2312yes—
77D376—28no—
78#10625325—28no—
79C23×C47—22no—
80C23×C47—22no—
81C23×C47—41no—
82C23×C47C2×D411yescharacteristic
83C23×C47C2×D411yescharacteristic
84C23×C47C2×D411yescharacteristic
85C22×D47—24no—
86C22×D47—22no—
87C22×D47—22no—
88C22×D47—42no—
89C22×D47—42no—
90C22×D47—42no—
91C22×D47—42no—
92C22×D47—42no—
93C2×C4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47C2×D411yescharacteristic
99C2×C4×C47C2×D411yescharacteristic
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2×D414yes—
102C2×C4×C47C2411yescharacteristic
103C22⋊D47—28no—
104C22⋊D47—28no—
105C22⋊D47—44no—
106C22⋊D47—44no—
107C2×Dic47—24no—
108C2×Dic47—22no—
109C2×Dic47—22no—
110C2×Dic47—42no—
111D188—24no—
112D188—22no—
113D188—24no—
114D188—42no—
115D188C2×D414yescomplemented
116C4×D47—28no—
117C4×D47—28no—
118Dic94—24no—
119Dic94—22no—
120Dic94C2×D414yescomplemented
121C8×C47—24no—
122C22×C47—21no—
123C22×C47—21no—
124C22×C47—21no—
125C22×C47—21no—
126C22×C47—21no—
127C22×C47—21no—
128C22×C47—21no—
129C22×C47—44no—
130C22×C47#12012yes—
131C22×C47AGL(1,ℤ/8)12yescomplemented
132C22×C47C22×D411yescharacteristic
133C2×D47—24no—
134C2×D47—48no—
135C2×D47—42no—
136C2×D47—42no—
137C2×D47—42no—
138C2×D47—42no—
139C2×D47—42no—
140C2×D47—84no—
141C4×C47—21no—
142C4×C47—21no—
143C4×C47#12012yes—
144C4×C47C22×D412yes—
145Dic47—24no—
146Dic47—42no—
147#3006—471nomaximal, Sylow
148C2×C47—22no—
149C2×C47—22no—
150C2×C47—41no—
151C2×C47C2×#12011yescharacteristic
152C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
153C2×C47#57511yescharacteristic
154D47—44no—
155D47—82no—
156C22×#41—471no—
157C2×AGL(1,ℤ/8)—472no—
158C2×#121—471no—
159#449—474no—
160#448—472no—
161#447—472no—
162#417—472no—
163#407D4711yescharacteristic, complemented
164C47#300611yescharacteristic, complemented, Sylow
165C2×#41—472no—
166C2×#41—472no—
167C2×#41—948no—
168C2×#41—941no—
169C2×#41—941no—
170C22×Q8—471no—
171C22×D4—471no—
172C22×D4—471no—
173C22×D4—941no—
174C22×D4—941no—
175C23×C4—941no—
176C23×C4C2×D4711yescharacteristic
177AGL(1,ℤ/8)—948no—
178C2×SD16—474no—
179C2×D8—474no—
180C2×M16C2×D4712yescomplemented
181#121—472no—
182#121—472no—
183#121—941no—
184#121—941no—
185C2×C4⋊C4—471no—
186C2×C22⋊C4—941no—
187#103—474no—
188#102—474no—
189C22⋊C8C2×D4712yescomplemented
190C22⋊C8C2×D4712yescomplemented
191C24—941no—
192C24—941no—
193C24D18811yescharacteristic
194#41—478no—
195#41—944no—
196#41—944no—
197#41—948no—
198#41—948no—
199#41—944no—
200C2×Q8—472no—
201C2×Q8—944no—
202C2×Q8—941no—
203C2×D4—472no—
204C2×D4—472no—
205C2×D4—944no—
206C2×D4—948no—
207C2×D4—942no—
208C2×D4—942no—
209C2×D4—942no—
210C2×D4—942no—
211C2×D4—941no—
212C2×D4—941no—
213C2×D4—944no—
214C2×D4—1884no—
215C22×C4—24no—
216C22×C4—948no—
217C22×C4—941no—
218C22×C4—942no—
219C22×C4—942no—
220C22×C4—941no—
221C22×C4D18811yescharacteristic
222C22×C4D18811yescharacteristic
223C22×C4D18811yescharacteristic
224C22×C4C22×D4711yescharacteristic
225C22×C4C22×D4711yescharacteristic
226C22×C4C22×D4711yescharacteristic
227SD16—948no—
228D8—948no—
229M16—24no—
230C2×C8C22×D4714yes—
231C4⋊C4—472no—
232C4⋊C4—941no—
233C22⋊C4—942no—
234C22⋊C4—942no—
235C23—22no—
236C23—22no—
237C23—41no—
238C23—944no—
239C23—942no—
240C23—942no—
241C23—1882no—
242C23—1882no—
243C23—1882no—
244C23—1882no—
245C23—1882no—
246C23C2×D18811yescharacteristic
247C23C2×D18811yescharacteristic
248C23C2×D18811yescharacteristic
249Q8—474no—
250Q8—944no—
251Q8—942no—
252D4—474no—
253D4—944no—
254D4—948no—
255D4—948no—
256D4—942no—
257D4—944no—
258D4—1884no—
259D4—1884no—
260D4—1882no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—948no—
267C2×C4—944no—
268C2×C4—942no—
269C2×C4—948no—
270C2×C4—942no—
271C2×C4—1882no—
272C2×C4C2×D18811yescharacteristic
273C2×C4C2×D18811yescharacteristic
274C2×C4C2×D18811yescharacteristic
275C2×C4D4×D4714yes—
276C2×C4C23×D4711yescharacteristic
277C8—24no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—44no—
286C22—944no—
287C22—3764no—
288C22—1888no—
289C22—1882no—
290C22—1882no—
291C22—1882no—
292C22—1882no—
293C22—1882no—
294C22#1309399412yes—
295C22#1309405212yescomplemented
296C22C22×D18811yescharacteristic
297C4—21no—
298C4—21no—
299C4—944no—
300C4—1882no—
301C4#1309399412yes—
302C4C2×D4×D4712yes—
303C2—22no—
304C2—22no—
305C2—41no—
306C2—3762no—
307C2—1884no—
308C2C2×#1309399411yescharacteristic
309C2C2×#1309405211yescharacteristic
310C2#1568992311yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#407C2
socleC22×C47C22×D4
hypercenter#407D47
hypocenterC47#3006
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C22×#10625350C2semidirect
2. C2×#13094052C2semidirect
3. C2×#13093998C2semidirect
4. #15689270C2semidirect
5. #15689264C2semidirect
6. #15689259C2semidirect
7. #15689125C2semidirect
8. C47×#407C2semidirect
13. C2×#10625350C22semidirect
14. C22×Dic94C22semidirect
15. C22×D188C22semidirect
16. C22×D188C22semidirect
21. C2×#10625325C22semidirect
22. C2×D376C22semidirect
26. #13093998C22semidirect
27. C2×C4⋊Dic47C22semidirect
29. #13093949C22semidirect
30. #13093946C22semidirect
32. C2×M16×C47C22semidirect
33. C22⋊C8×C47C22semidirect
34. C22⋊C8×C47C22semidirect
58. #10625350D4semidirect
115. D188C2×D4semidirect
120. Dic94C2×D4semidirect
131. C22×C47AGL(1,ℤ/8)semidirect
163. #407D47semidirect
164. C47#3006semidirect
180. C2×M16C2×D47semidirect
189. C22⋊C8C2×D47semidirect
190. C22⋊C8C2×D47semidirect
295. C22#13094052semidirect