Finite Group Databasebeta

← #20247665

Subgroups — #20247665

Order 6016.

700 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 141 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×C22⋊C4×D47C212yesmaximal
2#15689051C212yesmaximal, complemented
3#15689048C211yesmaximal, characteristic, complemented
4#15688997C212yesmaximal, complemented
5#15688994C212yesmaximal, complemented
6#15688985C212yesmaximal, complemented
7#15688985C212yesmaximal, complemented
8#15688978C211yesmaximal, characteristic
9C47×#397C211yesmaximal, characteristic, complemented
10C24×D47C2211yescharacteristic
11C22×C4×D47C2212yes—
12C22×C4×D47C2212yes—
13C2×C4⋊Dic47C2211yescharacteristic, complemented
14C2×Dic47⋊C4C2212yescomplemented
15C2×C22⋊Dic47C2212yes—
16C2×C22⋊Dic47C2211yescharacteristic
17C2×(C2×D47)⋊C4C2212yes—
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C22⋊C4×D47—28no—
22C47⋊#95C2211yescharacteristic, complemented
23C47⋊#95C2212yescomplemented
24C47⋊#95C2212yescomplemented
25C47⋊#95C2212yescomplemented
26C47⋊#95C2212yescomplemented
27C2×C4⋊C4×C47C2211yescharacteristic, complemented
28C2×C22⋊C4×C47C2212yes—
29C2×C22⋊C4×C47C2211yescharacteristic
30#95×C47C2211yescharacteristic, complemented
31#95×C47C2212yescomplemented
32C24×C47C2311yescharacteristic
33C23×D47—24no—
34C23×D47—24no—
35C23×D47—41no—
36C23×D47—41no—
37C23×D47D414yes—
38C23×D47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2312yes—
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C22×Dic47C2312yes—
44C22×Dic47C2312yes—
45C22×Dic47C2312yes—
46C2×C4×D47—24no—
47C2×C4×D47—24no—
48C2×C4×D47—24no—
49C2×C4×D47—24no—
50C2×C4×D47—42no—
51C2×C4×D47—42no—
52C4⋊C4×C47—41no—
53C22⋊C4×C47—24no—
54C22⋊C4×C47—41no—
55C22⋊Dic47—24no—
56C22⋊Dic47—41no—
57(C2×D47)⋊C4—24no—
58(C2×D47)⋊C4—24no—
59(C2×D47)⋊C4—24no—
60(C2×D47)⋊C4—24no—
61C4⋊Dic47—41no—
62Dic47⋊C4—42no—
63C23×C47—22no—
64C23×C47—22no—
65C23×C47—21no—
66C23×C47—21no—
67C23×C47C2×D412yes—
68C23×C47C2411yescharacteristic
69C22×D47—22no—
70C22×D47—22no—
71C22×D47—22no—
72C22×D47—22no—
73C22×D47—216no—
74C22×D47—44no—
75C22×D47—48no—
76C22×D47—44no—
77C22×D47—44no—
78C22×D47C2×D414yes—
79C22×D47#4114yes—
80C22×D47#4114yes—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C4×D47—48no—
101C4×D47—48no—
102C22×C47—24no—
103C22×C47—22no—
104C22×C47—42no—
105C22×C47—41no—
106C22×C47—41no—
107C22×C47C22×D411yescharacteristic
108C22×C47C2×#4112yes—
109C22×C47C2×#4112yes—
110C22×C47H(5,𝔽2)11yescharacteristic
111C22×C47H(5,𝔽2)11yescharacteristic
112C2×D47—24no—
113C2×D47—24no—
114C2×D47—24no—
115C2×D47—24no—
116C2×D47—24no—
117C2×D47—24no—
118C2×D47—416no—
119C2×D47#12318yes—
120C4×C47—42no—
121C4×C47—42no—
122C4×C47—41no—
123C4×C47—41no—
124Dic47—42no—
125Dic47—42no—
126Dic47—42no—
127#2483—471nomaximal, Sylow
128C2×C47—42no—
129C2×C47C2×#12312yes—
130C2×C47#53411yescharacteristic
131C2×C47#55112yes—
132C2×C47#55111yescharacteristic
133C2×C47#55111yescharacteristic
134D47—28no—
135C22×C22⋊C4—472no—
136#397—471no—
137#397—472no—
138#397D4711yescharacteristic, complemented
139#385—472no—
140#385—472no—
141#381—472no—
142#381—472no—
143#379—471no—
144C47#248311yescharacteristic, complemented, Sylow
145C25—471no—
146C23×C4—472no—
147C23×C4—472no—
148C2×C4⋊C4—472no—
149C2×C4⋊C4—471no—
150C2×C4⋊C4C2×D4711yescharacteristic, complemented
151C2×C22⋊C4—472no—
152C2×C22⋊C4—472no—
153C2×C22⋊C4—472no—
154C2×C22⋊C4—472no—
155C2×C22⋊C4—472no—
156C2×C22⋊C4—471no—
157C2×C22⋊C4—948no—
158C2×C22⋊C4C2×D4712yes—
159C2×C22⋊C4C2×D4711yescharacteristic
160#95—471no—
161#95—472no—
162#95—472no—
163#95—472no—
164#95—472no—
165#95C2×D4711yescharacteristic, complemented
166#95C2×D4712yescomplemented
167C24—472no—
168C24—474no—
169C24—944no—
170C24—944no—
171C24—1881no—
172C24—1881no—
173C24C22×D4711yescharacteristic
174C22×C4—472no—
175C22×C4—472no—
176C22×C4—472no—
177C22×C4—944no—
178C22×C4—944no—
179C22×C4—944no—
180C22×C4—944no—
181C22×C4—1882no—
182C22×C4—1882no—
183C22×C4C22×D4712yes—
184C22×C4C22×D4711yescharacteristic
185C22×C4C22×D4711yescharacteristic
186C22×C4C22×D4712yes—
187C4⋊C4—41no—
188C4⋊C4—1882no—
189C4⋊C4—1881no—
190C22⋊C4—24no—
191C22⋊C4—41no—
192C22⋊C4—944no—
193C22⋊C4—944no—
194C22⋊C4—944no—
195C22⋊C4—944no—
196C22⋊C4—944no—
197C22⋊C4—1881no—
198C23—22no—
199C23—22no—
200C23—21no—
201C23—21no—
202C23—474no—
203C23—474no—
204C23—474no—
205C23—9416no—
206C23—942no—
207C23—942no—
208C23—942no—
209C23—942no—
210C23—1884no—
211C23—1888no—
212C23—1884no—
213C23—1884no—
214C23D4×D4712yes—
215C23C23×D4711yescharacteristic
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—942no—
227C2×C4—942no—
228C2×C4—942no—
229C2×C4—942no—
230C2×C4—942no—
231C2×C4—942no—
232C2×C4—942no—
233C2×C4—942no—
234C2×C4—942no—
235C2×C4—1888no—
236C2×C4—1888no—
237C22—24no—
238C22—22no—
239C22—42no—
240C22—41no—
241C22—41no—
242C22—478no—
243C22—944no—
244C22—944no—
245C22—944no—
246C22—944no—
247C22—944no—
248C22—944no—
249C22—18816no—
250C22C2×D4×D4711yescharacteristic
251C22#41×D4712yes—
252C22#41×D4712yes—
253C22#1309406911yescharacteristic
254C22#1309407011yescharacteristic
255C4—41no—
256C4—41no—
257C4—42no—
258C4—42no—
259C4—1882no—
260C4—1882no—
261C4—1882no—
262C2—42no—
263C2—948no—
264C2#123×D4712yes—
265C2#1568968111yescharacteristic
266C2#1568979812yes—
267C2#1568980111yescharacteristic
268C2#1568980311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#397C2
hypercenter#397D47
hypocenterC47#2483
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #15689051C2semidirect
3. #15689048C2semidirect
4. #15688997C2semidirect
5. #15688994C2semidirect
6. #15688985C2semidirect
7. #15688985C2semidirect
9. C47×#397C2semidirect
13. C2×C4⋊Dic47C22semidirect
14. C2×Dic47⋊C4C22semidirect
22. C47⋊#95C22semidirect
23. C47⋊#95C22semidirect
24. C47⋊#95C22semidirect
25. C47⋊#95C22semidirect
26. C47⋊#95C22semidirect
27. C2×C4⋊C4×C47C22semidirect
30. #95×C47C22semidirect
31. #95×C47C22semidirect
138. #397D47semidirect
144. C47#2483semidirect
150. C2×C4⋊C4C2×D47semidirect
165. #95C2×D47semidirect
166. #95C2×D47semidirect