Finite Group Databasebeta

← #20248540

Subgroups — #20248540

Order 6016.

672 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 139 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
2C2×C22⋊C4×D47C211yesmaximal, characteristic
3#15689049C211yesmaximal, characteristic, complemented
4#15689036C211yesmaximal, characteristic, complemented
5#15689035C211yesmaximal, characteristic, complemented
6#15689016C212yesmaximal, complemented
7#15689015C212yesmaximal, complemented
8#15688985C212yesmaximal, complemented
9#15688978C212yesmaximal
10#15688970C211yesmaximal, characteristic, complemented
11C47×#397C211yesmaximal, characteristic, complemented
12C24×D47C2211yescharacteristic
13C22×Dic94C2211yescharacteristic, complemented
14C22×C4×D47C2211yescharacteristic
15C22×C4×D47C2211yescharacteristic
16#13094004—24no—
17C2×C4⋊Dic47C2212yescomplemented
18C2×C22⋊Dic47C2211yescharacteristic
19C2×C22⋊Dic47C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2212yes—
26C22⋊C4×D47—24no—
27C2×C4×Dic47C2212yescomplemented
28C47⋊#95C2211yescharacteristic, complemented
29C47⋊#95C2212yescomplemented
30C47⋊#95C2212yescomplemented
31C47⋊#95C2212yescomplemented
32C2×C4⋊C4×C47C2211yescharacteristic, complemented
33C2×C22⋊C4×C47C2212yes—
34C2×C22⋊C4×C47C2211yescharacteristic
35#95×C47C2211yescharacteristic, complemented
36#95×C47C2212yescomplemented
37C24×C47C2311yescharacteristic
38C23×D47—22no—
39C23×D47—22no—
40C23×D47—22no—
41C23×D47—24no—
42C23×D47—42no—
43C23×D47C2311yescharacteristic
44C23×D47C2311yescharacteristic
45C22×C4×C47C2312yes—
46C22×C4×C47C2311yescharacteristic
47C22×C4×C47C2312yes—
48C22×C4×C47C2311yescharacteristic
49C22×Dic47C2311yescharacteristic
50C22×Dic47C2312yes—
51C22×Dic47C2312yes—
52C22×Dic47C2311yescharacteristic
53C2×C4×D47—22no—
54C2×C4×D47—24no—
55C2×C4×D47—42no—
56C2×C4×D47D414yes—
57C2×Dic94—22no—
58C2×Dic94—42no—
59C4⋊C4×C47—22no—
60C22⋊C4×C47—24no—
61C22⋊C4×C47—22no—
62C22⋊Dic47—22no—
63C22⋊Dic47—42no—
64(C2×D47)⋊C4—24no—
65(C2×D47)⋊C4—24no—
66(C2×D47)⋊C4—24no—
67(C2×D47)⋊C4—22no—
68(C2×D47)⋊C4—22no—
69(C2×D47)⋊C4—42no—
70C4⋊Dic47—24no—
71C4×Dic47—42no—
72C23×C47—21no—
73C23×C47—21no—
74C23×C47—22no—
75C23×C47—22no—
76C23×C47#4112yes—
77C23×C47C2411yescharacteristic
78C22×D47—21no—
79C22×D47—21no—
80C22×D47—22no—
81C22×D47—28no—
82C22×D47—21no—
83C22×D47—22no—
84C22×D47—21no—
85C22×D47—22no—
86C22×D47—48no—
87C22×D47—48no—
88C22×D47—44no—
89C22×D47—44no—
90C22×D47C2×D412yes—
91C22×D47#4112yes—
92C22×D47#4114yes—
93C2×C4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—21no—
96C2×C4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47—22no—
100C2×C4×C47—22no—
101C2×C4×C47—22no—
102C2×C4×C47C2×D412yes—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—21no—
106C2×Dic47—22no—
107C2×Dic47—22no—
108C2×Dic47—22no—
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—22no—
112C2×Dic47C2×D412yes—
113C4×D47—44no—
114C4×D47—44no—
115Dic94—44no—
116C22×C47—22no—
117C22×C47—24no—
118C22×C47—41no—
119C22×C47—41no—
120C22×C47—42no—
121C22×C47C22×D411yescharacteristic
122C22×C47C2×#4111yescharacteristic
123C22×C47C2×#4112yes—
124C22×C47C2×#4111yescharacteristic
125C22×C47H(5,𝔽2)12yes—
126C2×D47—22no—
127C2×D47—22no—
128C2×D47—24no—
129C2×D47—24no—
130C2×D47—22no—
131C2×D47—24no—
132C2×D47—416no—
133C2×D47—41no—
134C2×D47—41no—
135C2×D47—42no—
136C2×D47#12414yes—
137C4×C47—22no—
138C4×C47—42no—
139C4×C47—41no—
140C4×C47—42no—
141Dic47—22no—
142Dic47—41no—
143Dic47—42no—
144Dic47—42no—
145#2561—471nomaximal, Sylow
146C2×C47—42no—
147C2×C47#52511yescharacteristic
148C2×C47C2×#12411yescharacteristic
149C2×C47#53411yescharacteristic
150C2×C47#55112yes—
151C2×C47#55112yes—
152D47—24no—
153D47—42no—
154C2×C22⋊Q8—471no—
155C22×C22⋊C4—471no—
156#397—471no—
157#397D4711yescharacteristic, complemented
158#393—471no—
159#393—471no—
160#388—472no—
161#388—472no—
162#381—472no—
163#379—472no—
164C4×C22⋊C4—471no—
165C47#256111yescharacteristic, complemented, Sylow
166C25—471no—
167C22×Q8—471no—
168C23×C4—471no—
169C23×C4—471no—
170C22⋊Q8—944no—
171C2×C4⋊C4—472no—
172C2×C4⋊C4C2×D4711yescharacteristic, complemented
173C2×C22⋊C4—471no—
174C2×C22⋊C4—471no—
175C2×C22⋊C4—471no—
176C2×C22⋊C4—472no—
177C2×C22⋊C4—472no—
178C2×C22⋊C4—472no—
179C2×C22⋊C4—472no—
180C2×C22⋊C4—472no—
181C2×C22⋊C4—944no—
182C2×C22⋊C4C2×D4711yescharacteristic
183C2×C22⋊C4C2×D4712yes—
184C2×C42—472no—
185#95—471no—
186#95—472no—
187#95—472no—
188#95—472no—
189#95C2×D4711yescharacteristic, complemented
190#95C2×D4712yescomplemented
191C24—471no—
192C24—471no—
193C24—942no—
194C24—942no—
195C24—944no—
196C24—942no—
197C24—1882no—
198C24C22×D4711yescharacteristic
199C2×Q8—942no—
200C2×Q8—1882no—
201C22×C4—471no—
202C22×C4—474no—
203C22×C4—471no—
204C22×C4—472no—
205C22×C4—472no—
206C22×C4—942no—
207C22×C4—944no—
208C22×C4—1882no—
209C22×C4C22×D4711yescharacteristic
210C22×C4C22×D4712yes—
211C22×C4C22×D4712yes—
212C22×C4C22×D4711yescharacteristic
213C4⋊C4—22no—
214C4⋊C4—944no—
215C22⋊C4—24no—
216C22⋊C4—22no—
217C22⋊C4—942no—
218C22⋊C4—944no—
219C22⋊C4—944no—
220C22⋊C4—944no—
221C22⋊C4—942no—
222C22⋊C4—942no—
223C22⋊C4—1882no—
224C22⋊C4—1882no—
225C42—1882no—
226C23—21no—
227C23—22no—
228C23—21no—
229C23—22no—
230C23—472no—
231C23—474no—
232C23—472no—
233C23—948no—
234C23—941no—
235C23—941no—
236C23—942no—
237C23—941no—
238C23—942no—
239C23—941no—
240C23—942no—
241C23—1888no—
242C23—1884no—
243C23—1888no—
244C23—1884no—
245C23#1062535212yes—
246C23C23×D4711yescharacteristic
247Q8—1884no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—472no—
258C2×C4—942no—
259C2×C4—941no—
260C2×C4—942no—
261C2×C4—942no—
262C2×C4—942no—
263C2×C4—942no—
264C2×C4—942no—
265C2×C4—942no—
266C2×C4—942no—
267C2×C4—1884no—
268C2×C4—1884no—
269C2×C4D4×D4712yes—
270C22—24no—
271C22—22no—
272C22—42no—
273C22—41no—
274C22—41no—
275C22—474no—
276C22—944no—
277C22—944no—
278C22—942no—
279C22—942no—
280C22—944no—
281C22—942no—
282C22—18816no—
283C22—1882no—
284C22—1881no—
285C22—1881no—
286C22C2×D4×D4711yescharacteristic
287C22#41×D4712yes—
288C22#41×D4711yescharacteristic
289C22C2×#1062535211yescharacteristic
290C22#1309407012yes—
291C4—22no—
292C4—42no—
293C4—42no—
294C4—41no—
295C4—942no—
296C4—1882no—
297C4—1881no—
298C4—1882no—
299C2—42no—
300C2—944no—
301C2—1882no—
302C2#1568963311yescharacteristic
303C2#124×D4711yescharacteristic
304C2#1568968411yescharacteristic
305C2#1568979612yes—
306C2#1568979812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#397C2
hypercenter#397D47
hypocenterC47#2561
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#13094004C2semidirect
3. #15689049C2semidirect
4. #15689036C2semidirect
5. #15689035C2semidirect
6. #15689016C2semidirect
7. #15689015C2semidirect
8. #15688985C2semidirect
10. #15688970C2semidirect
11. C47×#397C2semidirect
13. C22×Dic94C22semidirect
17. C2×C4⋊Dic47C22semidirect
27. C2×C4×Dic47C22semidirect
28. C47⋊#95C22semidirect
29. C47⋊#95C22semidirect
30. C47⋊#95C22semidirect
31. C47⋊#95C22semidirect
32. C2×C4⋊C4×C47C22semidirect
35. #95×C47C22semidirect
36. #95×C47C22semidirect
157. #397D47semidirect
165. C47#2561semidirect
172. C2×C4⋊C4C2×D47semidirect
189. #95C2×D47semidirect
190. #95C2×D47semidirect