Finite Group Databasebeta

← #20246652

Subgroups — #20246652

Order 6016.

560 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 147 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×#13093986C211yesmaximal, characteristic
2C2×#13093982C211yesmaximal, characteristic, complemented
3#15689062C211yesmaximal, characteristic, complemented
4#15689060C211yesmaximal, characteristic, complemented
5#15689050C212yesmaximal, complemented
6#15689049C211yesmaximal, characteristic, complemented
7#15689040C212yesmaximal
8C4⋊C4×Dic47C212yesmaximal, complemented
9#15688970C211yesmaximal, characteristic, complemented
10#15688970C212yesmaximal, complemented
11C47×#398C211yesmaximal, characteristic, complemented
12C22×D188C2211yescharacteristic
13C22×C4×D47C2211yescharacteristic
14C22×C4×D47C2211yescharacteristic
15#13093986—24no—
16#13093982—24no—
17C2×C4⋊Dic47C2212yes—
18C2×C4⋊Dic47C2211yescharacteristic
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×C4×Dic47C2212yes—
26C2×C4×Dic47C2212yes—
27C2×C4×Dic47C2211yescharacteristic
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2212yes—
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C4⋊C4×C47C2211yescharacteristic
35#95×C47C2212yes—
36#95×C47C2211yescharacteristic
37C23×D47C2311yescharacteristic
38C23×D47C2311yescharacteristic
39C22×C4×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2312yes—
44C22×Dic47C2312yes—
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C2×D188—22no—
49C2×D188—22no—
50C2×D188—22no—
51C2×C4×D47—24no—
52C2×C4×D47—22no—
53C2×C4×D47—24no—
54C2×C4×D47D414yes—
55C4⋊C4×C47—22no—
56C4⋊C4×C47—22no—
57C4⋊C4×C47—24no—
58(C2×D47)⋊C4—24no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—24no—
61(C2×D47)⋊C4—22no—
62(C2×D47)⋊C4—24no—
63(C2×D47)⋊C4—24no—
64C4⋊Dic47—22no—
65C4⋊Dic47—24no—
66C4×Dic47—24no—
67C4×Dic47—22no—
68C4×Dic47—24no—
69C23×C47C2411yescharacteristic
70C22×D47—21no—
71C22×D47—22no—
72C22×D47—22no—
73C22×D47—22no—
74C22×D47—22no—
75C22×D47—21no—
76C22×D47—21no—
77C22×D47—21no—
78C22×D47C2×D412yes—
79C22×D47#4112yes—
80C2×C4×C47—21no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—21no—
85C2×C4×C47—22no—
86C2×C4×C47—21no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47C2×D412yes—
91C2×C4×C47#4112yes—
92C2×C4×C47#4114yes—
93C2×Dic47—22no—
94C2×Dic47—21no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47C2×D412yes—
102C2×Dic47#4114yes—
103D188—28no—
104C4×D47—28no—
105C4×D47—44no—
106C22×C47C22×D411yescharacteristic
107C22×C47C2×#4112yes—
108C22×C47C2×#4111yescharacteristic
109C22×C47C2×#4111yescharacteristic
110C22×C47C2×#4112yes—
111C2×D47—22no—
112C2×D47—22no—
113C2×D47—22no—
114C2×D47—24no—
115C2×D47—22no—
116C2×D47—41no—
117C2×D47—42no—
118C2×D47—42no—
119C2×D47—42no—
120C2×D47—41no—
121C4×C47—22no—
122C4×C47—22no—
123C4×C47—24no—
124C4×C47—41no—
125C4×C47—42no—
126Dic47—42no—
127Dic47—42no—
128Dic47—41no—
129Dic47#12314yes—
130#2395—471nomaximal, Sylow
131C2×C47C2×#12311yescharacteristic
132C2×C47#52511yescharacteristic
133C2×C47#52912yes—
134C2×C47#52912yes—
135C2×C47#53211yescharacteristic
136D47—42no—
137D47—42no—
138C2×C4×D4—471no—
139C2×#117—471no—
140#400—471no—
141#399—471no—
142#398D4711yescharacteristic, complemented
143#397—471no—
144#397—472no—
145#394—472no—
146C4×C4⋊C4—472no—
147C4×C22⋊C4—472no—
148C4×C22⋊C4—471no—
149C47#239511yescharacteristic, complemented, Sylow
150C22×D4—471no—
151C23×C4—471no—
152C23×C4—471no—
153C4×D4—944no—
154#117—944no—
155C2×C4⋊C4—471no—
156C2×C4⋊C4—472no—
157C2×C4⋊C4C2×D4711yescharacteristic
158C2×C4⋊C4C2×D4711yescharacteristic
159C2×C4⋊C4C2×D4712yes—
160C2×C22⋊C4—472no—
161C2×C22⋊C4—471no—
162C2×C22⋊C4—471no—
163C2×C22⋊C4—472no—
164C2×C22⋊C4—472no—
165C2×C22⋊C4—472no—
166C2×C42—472no—
167C2×C42—471no—
168C2×C42—472no—
169#95—471no—
170#95—472no—
171#95—472no—
172#95—472no—
173#95C2×D4712yes—
174#95C2×D4711yescharacteristic
175C24—471no—
176C24—471no—
177C2×D4—942no—
178C2×D4—942no—
179C2×D4—942no—
180C22×C4—471no—
181C22×C4—474no—
182C22×C4—472no—
183C22×C4—471no—
184C22×C4—472no—
185C22×C4—944no—
186C22×C4—942no—
187C22×C4—944no—
188C22×C4C22×D4711yescharacteristic
189C22×C4C22×D4712yes—
190C22×C4C22×D4711yescharacteristic
191C22×C4C22×D4711yescharacteristic
192C22×C4C22×D4712yes—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—24no—
196C4⋊C4—942no—
197C4⋊C4—944no—
198C22⋊C4—944no—
199C22⋊C4—944no—
200C22⋊C4—942no—
201C22⋊C4—942no—
202C22⋊C4—944no—
203C22⋊C4—944no—
204C42—944no—
205C42—944no—
206C42—942no—
207C23—472no—
208C23—472no—
209C23—941no—
210C23—942no—
211C23—942no—
212C23—941no—
213C23—941no—
214C23—941no—
215C23—942no—
216C23—942no—
217C23C23×D4711yescharacteristic
218D4—948no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—472no—
230C2×C4—474no—
231C2×C4—948no—
232C2×C4—941no—
233C2×C4—942no—
234C2×C4—942no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4—942no—
240C2×C4—1884no—
241C2×C4D4×D4712yes—
242C2×C4#1062535212yes—
243C2×C4#1062535414yes—
244C22—942no—
245C22—942no—
246C22—942no—
247C22—944no—
248C22—942no—
249C22—1881no—
250C22—1882no—
251C22—1882no—
252C22—1882no—
253C22—1881no—
254C22C2×D4×D4711yescharacteristic
255C22#41×D4712yes—
256C22#41×D4711yescharacteristic
257C22C2×#1062535211yescharacteristic
258C22C2×#1062535412yes—
259C4—22no—
260C4—22no—
261C4—24no—
262C4—41no—
263C4—42no—
264C4—474no—
265C4—1882no—
266C4—1881no—
267C4—1882no—
268C2—1882no—
269C2—1882no—
270C2#123×D4711yescharacteristic
271C2#1568963311yescharacteristic
272C2#1568965812yes—
273C2#1568965912yes—
274C2#1568967411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#398C2
hypercenter#398D47
hypocenterC47#2395
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#13093982C2semidirect
3. #15689062C2semidirect
4. #15689060C2semidirect
5. #15689050C2semidirect
6. #15689049C2semidirect
8. C4⋊C4×Dic47C2semidirect
9. #15688970C2semidirect
10. #15688970C2semidirect
11. C47×#398C2semidirect
142. #398D47semidirect
149. C47#2395semidirect