Finite Group Databasebeta

← #20246648

Subgroups — #20246648

Order 6016.

560 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 161 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×C4×C22⋊D47C211yesmaximal, characteristic
2C2×#13093983C211yesmaximal, characteristic, complemented
3#15689063C211yesmaximal, characteristic, complemented
4#15689060C211yesmaximal, characteristic, complemented
5#15689055C211yesmaximal, characteristic, complemented
6#15689050C211yesmaximal, characteristic, complemented
7#15689048C212yesmaximal, complemented
8#15689039C212yesmaximal
9C4×C4⋊Dic47C212yesmaximal, complemented
10C4×(C2×D47)⋊C4C212yesmaximal, complemented
11C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2211yescharacteristic
13C22×C4×D47C2211yescharacteristic
14C4×C22⋊D47—24no—
15#13093983—24no—
16C2×C4⋊Dic47C2212yes—
17C2×C4⋊Dic47C2212yes—
18C2×C4⋊Dic47C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×C22⋊Dic47C2212yes—
22C2×C22⋊Dic47C2211yescharacteristic
23C2×(C2×D47)⋊C4C2212yes—
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×C4×Dic47C2212yes—
27C2×C4×Dic47C2211yescharacteristic
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C23×C4×C47C2211yescharacteristic
33C2×C22⋊C4×C47C2212yes—
34C2×C42×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2211yescharacteristic
37C24×C47C2311yescharacteristic
38C23×D47C2311yescharacteristic
39C22×C4×C47—24no—
40C22×C4×C47D414yes—
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2312yes—
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—22no—
46C2×C22⋊D47—22no—
47C2×C22⋊D47—22no—
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2312yes—
50C22×Dic47C2312yes—
51C22×Dic47C2311yescharacteristic
52C22×Dic47C2311yescharacteristic
53C2×C4×D47—22no—
54C2×C4×D47—24no—
55C22⋊C4×C47—24no—
56C42×C47—24no—
57C22⋊Dic47—24no—
58C22⋊Dic47—22no—
59(C2×D47)⋊C4—24no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—24no—
62C4⋊Dic47—22no—
63C4⋊Dic47—22no—
64C4⋊Dic47—24no—
65C4⋊Dic47—24no—
66Dic47⋊C4—22no—
67C4×Dic47—24no—
68C4×Dic47—22no—
69C23×C47—22no—
70C23×C47—21no—
71C23×C47—21no—
72C23×C47—22no—
73C23×C47C2×D412yes—
74C23×C47C2411yescharacteristic
75C22×D47—21no—
76C22×D47—22no—
77C22×D47—22no—
78C22×D47—21no—
79C22×D47#4112yes—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—28no—
84C2×C4×C47—22no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47C2×D412yes—
88C2×C4×C47C2×D412yes—
89C2×C4×C47#4114yes—
90C2×C4×C47#4114yes—
91C22⋊D47—28no—
92C2×Dic47—21no—
93C2×Dic47—21no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—21no—
97C2×Dic47—21no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47#4112yes—
105C4×D47—44no—
106C22×C47—22no—
107C22×C47—22no—
108C22×C47—22no—
109C22×C47—42no—
110C22×C47—42no—
111C22×C47C22×D411yescharacteristic
112C22×C47C2×#4111yescharacteristic
113C22×C47C2×#4111yescharacteristic
114C22×C47C2×#4112yes—
115C22×C47C2×#4112yes—
116C2×D47—22no—
117C2×D47—24no—
118C2×D47—41no—
119C2×D47—42no—
120C2×D47—41no—
121C4×C47—22no—
122C4×C47—24no—
123C4×C47—42no—
124C4×C47#12314yes—
125Dic47—22no—
126Dic47—41no—
127Dic47—42no—
128Dic47—42no—
129Dic47—41no—
130#2395—471nomaximal, Sylow
131C2×C47—42no—
132C2×C47C2×#12311yescharacteristic
133C2×C47#52511yescharacteristic
134C2×C47#52912yes—
135C2×C47#52912yes—
136C2×C47#53211yescharacteristic
137D47—42no—
138C2×C4×D4—471no—
139C2×#117—471no—
140#400—471no—
141#399—471no—
142#398—471no—
143#397—472no—
144#397—471no—
145#394—472no—
146C4×C4⋊C4—472no—
147C4×C22⋊C4—472no—
148C4×C22⋊C4D4711yescharacteristic, complemented
149C47#239511yescharacteristic, complemented, Sylow
150C22×D4—471no—
151C23×C4—471no—
152C23×C4C2×D4711yescharacteristic
153C4×D4—944no—
154#117—944no—
155C2×C4⋊C4—471no—
156C2×C4⋊C4—471no—
157C2×C4⋊C4—471no—
158C2×C4⋊C4—472no—
159C2×C4⋊C4—472no—
160C2×C22⋊C4—472no—
161C2×C22⋊C4—471no—
162C2×C22⋊C4—471no—
163C2×C22⋊C4—472no—
164C2×C22⋊C4—472no—
165C2×C22⋊C4C2×D4712yes—
166C2×C42—472no—
167C2×C42—471no—
168C2×C42C2×D4712yes—
169#95—472no—
170#95—472no—
171#95—472no—
172#95—472no—
173#95C2×D4711yescharacteristic
174#95C2×D4711yescharacteristic
175C24—471no—
176C24C22×D4711yescharacteristic
177C2×D4—942no—
178C2×D4—942no—
179C2×D4—942no—
180C22×C4—24no—
181C22×C4—471no—
182C22×C4—471no—
183C22×C4—471no—
184C22×C4—472no—
185C22×C4—472no—
186C22×C4—942no—
187C22×C4—944no—
188C22×C4D18814yes—
189C22×C4C22×D4712yes—
190C22×C4C22×D4711yescharacteristic
191C22×C4C22×D4712yes—
192C22×C4C22×D4711yescharacteristic
193C4⋊C4—944no—
194C4⋊C4—942no—
195C4⋊C4—942no—
196C4⋊C4—942no—
197C4⋊C4—944no—
198C22⋊C4—24no—
199C22⋊C4—944no—
200C22⋊C4—944no—
201C22⋊C4—942no—
202C22⋊C4—942no—
203C22⋊C4—944no—
204C42—24no—
205C42—944no—
206C42—942no—
207C23—21no—
208C23—21no—
209C23—22no—
210C23—22no—
211C23—472no—
212C23—941no—
213C23—941no—
214C23—942no—
215C23—942no—
216C23C2×D18812yes—
217C23C23×D4711yescharacteristic
218D4—948no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—28no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—472no—
227C2×C4—941no—
228C2×C4—941no—
229C2×C4—941no—
230C2×C4—942no—
231C2×C4—942no—
232C2×C4—941no—
233C2×C4—942no—
234C2×C4—942no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4—1884no—
240C2×C4C2×D18812yes—
241C2×C4C2×D18812yes—
242C2×C4#1062535014yes—
243C2×C4#1062535214yes—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—42no—
248C22—42no—
249C22—942no—
250C22—944no—
251C22—1881no—
252C22—1882no—
253C22—1881no—
254C22C22×D18811yescharacteristic
255C22#41×D4711yescharacteristic
256C22#41×D4711yescharacteristic
257C22C2×#1062535212yes—
258C22C2×#1062535012yes—
259C4—22no—
260C4—24no—
261C4—42no—
262C4—942no—
263C4—1881no—
264C4—1882no—
265C4—1881no—
266C4—1882no—
267C4#1309400814yes—
268C2—42no—
269C2—1882no—
270C2C2×#1309400811yescharacteristic
271C2#1568963511yescharacteristic
272C2#1568965312yes—
273C2#1568965512yes—
274C2#1568967311yescharacteristic
subgroupG/H
centerC22×C4C22×D47
commutator, socleC23×C47C24
FrattiniC23C23×D47
FittingC4×C22⋊C4×C47C2
hypercenterC4×C22⋊C4D47
hypocenterC47#2395
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#13093983C2semidirect
3. #15689063C2semidirect
4. #15689060C2semidirect
5. #15689055C2semidirect
6. #15689050C2semidirect
7. #15689048C2semidirect
9. C4×C4⋊Dic47C2semidirect
10. C4×(C2×D47)⋊C4C2semidirect
11. C4×C22⋊C4×C47C2semidirect
148. C4×C22⋊C4D47semidirect
149. C47#2395semidirect