Finite Group Databasebeta

← #20246645

Subgroups — #20246645

Order 6016.

560 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 157 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
2#15689061C211yesmaximal, characteristic, complemented
3#15689058C211yesmaximal, characteristic, complemented
4#15689054C211yesmaximal, characteristic, complemented
5#15689051C212yesmaximal, complemented
6#15689049C211yesmaximal, characteristic, complemented
7#15689038C212yesmaximal
8C4×Dic47⋊C4C212yesmaximal, complemented
9C4×(C2×D47)⋊C4C212yesmaximal, complemented
10C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
11C2×#117×C47C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2211yescharacteristic
13C22×C4×D47C2211yescharacteristic
14C4×C22⋊D47—24no—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2211yescharacteristic
18C2×C22⋊Dic47C2212yes—
19C2×C22⋊Dic47C2211yescharacteristic
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2211yescharacteristic
23C2×C4×Dic47C2212yes—
24C2×C4×Dic47C2211yescharacteristic
25C47⋊#95C2211yescharacteristic
26C47⋊#95C2211yescharacteristic
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C23×C4×C47C2211yescharacteristic
32#117×C47—24no—
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C4⋊C4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2212yes—
36C2×C42×C47C2212yes—
37C24×C47C2311yescharacteristic
38C23×D47C2311yescharacteristic
39C22×C4×C47—24no—
40C22×C4×C47D414yes—
41C22×C4×C47C2312yes—
42C22×C4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—22no—
46C2×C22⋊D47—22no—
47C2×C22⋊D47—22no—
48C22×Dic47C2312yes—
49C22×Dic47C2311yescharacteristic
50C22×Dic47C2311yescharacteristic
51C22×Dic47C2312yes—
52C22×Dic47C2311yescharacteristic
53C2×C4×D47—22no—
54C2×C4×D47—24no—
55C4⋊C4×C47—22no—
56C4⋊C4×C47—22no—
57C22⋊C4×C47—24no—
58C42×C47—24no—
59C22⋊Dic47—22no—
60C22⋊Dic47—24no—
61(C2×D47)⋊C4—24no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—24no—
64Dic47⋊C4—22no—
65Dic47⋊C4—24no—
66Dic47⋊C4—24no—
67C4×Dic47—22no—
68C4×Dic47—24no—
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—28no—
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×C47C2×D412yes—
89C2×C4×C47C2×D412yes—
90C2×C4×C47#4114yes—
91C22⋊D47—28no—
92C2×Dic47—21no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—21no—
96C2×Dic47—21no—
97C2×Dic47—21no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47#4112yes—
104C2×Dic47#4114yes—
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—42no—
123C4×C47—42no—
124C4×C47#12314yes—
125Dic47—22no—
126Dic47—24no—
127Dic47—41no—
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×#117D4711yescharacteristic, complemented
140#400—471no—
141#399—471no—
142#398—471no—
143#397—471no—
144#397—472no—
145#394—472no—
146C4×C4⋊C4—472no—
147C4×C22⋊C4—471no—
148C4×C22⋊C4—472no—
149C47#239511yescharacteristic, complemented, Sylow
150C22×D4—471no—
151C23×C4—471no—
152C23×C4C2×D4711yescharacteristic
153C4×D4—944no—
154#117—24no—
155C2×C4⋊C4—471no—
156C2×C4⋊C4—472no—
157C2×C4⋊C4—472no—
158C2×C4⋊C4C2×D4711yescharacteristic
159C2×C4⋊C4C2×D4711yescharacteristic
160C2×C22⋊C4—471no—
161C2×C22⋊C4—472no—
162C2×C22⋊C4—471no—
163C2×C22⋊C4—472no—
164C2×C22⋊C4—472no—
165C2×C22⋊C4C2×D4712yes—
166C2×C42—471no—
167C2×C42—472no—
168C2×C42C2×D4712yes—
169#95—472no—
170#95—471no—
171#95—472no—
172#95—471no—
173#95—472no—
174#95—472no—
175C24—471no—
176C24C22×D4711yescharacteristic
177C2×D4—942no—
178C2×D4—942no—
179C2×D4—942no—
180C22×C4—24no—
181C22×C4—472no—
182C22×C4—471no—
183C22×C4—472no—
184C22×C4—471no—
185C22×C4—471no—
186C22×C4—944no—
187C22×C4—942no—
188C22×C4C22⋊D4714yes—
189C22×C4C22×D4712yes—
190C22×C4C22×D4712yes—
191C22×C4C22×D4711yescharacteristic
192C22×C4C22×D4711yescharacteristic
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—944no—
196C4⋊C4—944no—
197C4⋊C4—942no—
198C22⋊C4—24no—
199C22⋊C4—944no—
200C22⋊C4—944no—
201C22⋊C4—944no—
202C22⋊C4—942no—
203C22⋊C4—942no—
204C42—24no—
205C42—944no—
206C42—942no—
207C23—22no—
208C23—21no—
209C23—21no—
210C23—22no—
211C23—472no—
212C23—941no—
213C23—942no—
214C23—941no—
215C23—942no—
216C23C2×C22⋊D4712yes—
217C23C23×D4711yescharacteristic
218D4—948no—
219C2×C4—22no—
220C2×C4—28no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—474no—
228C2×C4—472no—
229C2×C4—941no—
230C2×C4—942no—
231C2×C4—941no—
232C2×C4—942no—
233C2×C4—941no—
234C2×C4—941no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4—942no—
240C2×C4—1884no—
241C2×C4#1062535014yes—
242C2×C4C2×C22⋊D4712yes—
243C2×C4C2×C22⋊D4712yes—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—42no—
248C22—42no—
249C22—942no—
250C22—944no—
251C22—1881no—
252C22—1882no—
253C22—1881no—
254C22C22×C22⋊D4711yescharacteristic
255C22#41×D4711yescharacteristic
256C22#41×D4711yescharacteristic
257C22#41×D4712yes—
258C22C2×#1062535012yes—
259C4—22no—
260C4—42no—
261C4—42no—
262C4—942no—
263C4—944no—
264C4—1881no—
265C4—1882no—
266C4—1881no—
267C4#1309400714yes—
268C2—42no—
269C2—1882no—
270C2C2×#1309400711yescharacteristic
271C2#1568963011yescharacteristic
272C2#1568965112yes—
273C2#1568965112yes—
274C2#1568966911yescharacteristic
subgroupG/H
centerC22×C4C22×D47
commutator, socleC23×C47C24
FrattiniC23C23×D47
FittingC2×#117×C47C2
hypercenterC2×#117D47
hypocenterC47#2395
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #15689061C2semidirect
3. #15689058C2semidirect
4. #15689054C2semidirect
5. #15689051C2semidirect
6. #15689049C2semidirect
8. C4×Dic47⋊C4C2semidirect
9. C4×(C2×D47)⋊C4C2semidirect
10. C4×C22⋊Dic47C2semidirect
11. C2×#117×C47C2semidirect
139. C2×#117D47semidirect
149. C47#2395semidirect