Finite Group Databasebeta

← #20247690

Subgroups — #20247690

Order 6016.

624 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 173 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×#13094007C212yesmaximal
2C2×C4×C22⋊D47C211yesmaximal, characteristic
3#15689054C212yesmaximal, complemented
4#15689049C212yesmaximal, complemented
5#15689019C212yesmaximal, complemented
6#15688986C212yesmaximal, complemented
7#15688983C211yesmaximal, characteristic, complemented
8#15688980C212yesmaximal, complemented
9C22×C4⋊C4×C47C211yesmaximal, characteristic, complemented
10C22×C22⋊D47C2211yescharacteristic
11C22×C4×D47C2211yescharacteristic
12#13094007—28no—
13C4×C22⋊D47—24no—
14C2×C4⋊Dic47C2212yes—
15C2×Dic47⋊C4C2214yes—
16C2×Dic47⋊C4C2211yescharacteristic
17C2×C22⋊Dic47C2212yes—
18C2×C22⋊Dic47C2211yescharacteristic
19C2×(C2×D47)⋊C4C2214yes—
20C2×(C2×D47)⋊C4C2211yescharacteristic
21C2×C4×Dic47C2211yescharacteristic
22C47⋊#95C2214yes—
23C47⋊#95C2212yes—
24C47⋊#95C2214yes—
25C23×C4×C47C2212yes—
26C23×C4×C47C2211yescharacteristic
27C2×C4⋊C4×C47—24no—
28C2×C4⋊C4×C47C2212yes—
29C2×C4⋊C4×C47C2212yes—
30C24×C47C2311yescharacteristic
31C23×D47C2311yescharacteristic
32C22×C4×C47—24no—
33C22×C4×C47—24no—
34C22×C4×C47—24no—
35C22×C4×C47—24no—
36C22×C4×C47D414yes—
37C22×C4×C47C2314yes—
38C22×C4×C47C2311yescharacteristic
39C22×C4×C47C2311yescharacteristic
40C2×C22⋊D47—22no—
41C2×C22⋊D47—22no—
42C2×C22⋊D47D414yes—
43C22×Dic47C2311yescharacteristic
44C22×Dic47C2311yescharacteristic
45C22×Dic47C2314yes—
46C22×Dic47C2311yescharacteristic
47C2×C4×D47—22no—
48C2×C4×D47—24no—
49C4⋊C4×C47—24no—
50C4⋊C4×C47—24no—
51C22⋊Dic47—22no—
52C22⋊Dic47—24no—
53(C2×D47)⋊C4—28no—
54(C2×D47)⋊C4—22no—
55C4⋊Dic47—24no—
56Dic47⋊C4—22no—
57Dic47⋊C4—28no—
58C4×Dic47—22no—
59C23×C47—22no—
60C23×C47—22no—
61C23×C47C2×D412yes—
62C23×C47C2×D412yes—
63C23×C47#4112yes—
64C23×C47C2411yescharacteristic
65C22×D47—21no—
66C22×D47—22no—
67C22×D47—21no—
68C22×D47—22no—
69C22×D47C2×D412yes—
70C2×C4×C47—22no—
71C2×C4×C47—28no—
72C2×C4×C47—24no—
73C2×C4×C47—24no—
74C2×C4×C47—24no—
75C2×C4×C47—48no—
76C2×C4×C47C2×D412yes—
77C2×C4×C47C2×D412yes—
78C2×C4×C47#4114yes—
79C22⋊D47—28no—
80C2×Dic47—21no—
81C2×Dic47—21no—
82C2×Dic47—21no—
83C2×Dic47—24no—
84C2×Dic47—21no—
85C2×Dic47—24no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—24no—
89C2×Dic47C2×D412yes—
90C4×D47—44no—
91C22×C47—22no—
92C22×C47—22no—
93C22×C47—24no—
94C22×C47—24no—
95C22×C47#12114yes—
96C22×C47C22×D411yescharacteristic
97C22×C47C22×D411yescharacteristic
98C22×C47C2×#4111yescharacteristic
99C22×C47C2×#4112yes—
100C22×C472−1+412yes—
101C2×D47—22no—
102C2×D47—24no—
103C2×D47—41no—
104C2×D47—41no—
105C2×D47—42no—
106C4×C47—22no—
107C4×C47—44no—
108C4×C47#12314yescomplemented
109Dic47—22no—
110Dic47—41no—
111Dic47—41no—
112Dic47—44no—
113#2486—471nomaximal, Sylow
114C2×C47—24no—
115C2×C47C2×#12111yescharacteristic
116C2×C47C2×#12311yescharacteristic
117C2×C47#53611yescharacteristic
118C2×C47#54712yes—
119C2×C47#55212yes—
120D47—42no—
121C2×#123—472no—
122C2×C4×D4—471no—
123C22×C4⋊C4D4711yescharacteristic, complemented
124#398—472no—
125#397—472no—
126#389—472no—
127#381—472no—
128#380—471no—
129#380—472no—
130C47#248611yescharacteristic, complemented, Sylow
131C22×D4—471no—
132C23×C4—471no—
133C23×C4C2×D4712yes—
134C23×C4C2×D4711yescharacteristic
135#123—948no—
136C4×D4—944no—
137C2×C4⋊C4—24no—
138C2×C4⋊C4—471no—
139C2×C4⋊C4—474no—
140C2×C4⋊C4—472no—
141C2×C4⋊C4C2×D4712yes—
142C2×C4⋊C4C2×D4712yes—
143C2×C22⋊C4—471no—
144C2×C22⋊C4—472no—
145C2×C22⋊C4—471no—
146C2×C22⋊C4—474no—
147C2×C42—471no—
148#95—474no—
149#95—472no—
150#95—474no—
151C24—471no—
152C24C22×D4711yescharacteristic
153C2×D4—474no—
154C2×D4—942no—
155C2×D4—942no—
156C22×C4—24no—
157C22×C4—24no—
158C22×C4—24no—
159C22×C4—24no—
160C22×C4—471no—
161C22×C4—471no—
162C22×C4—471no—
163C22×C4—474no—
164C22×C4—944no—
165C22×C4—942no—
166C22×C4C22⋊D4714yes—
167C22×C4C22×D4714yes—
168C22×C4C22×D4711yescharacteristic
169C22×C4C22×D4711yescharacteristic
170C4⋊C4—24no—
171C4⋊C4—24no—
172C4⋊C4—948no—
173C4⋊C4—944no—
174C4⋊C4—942no—
175C22⋊C4—948no—
176C22⋊C4—944no—
177C22⋊C4—942no—
178C22⋊C4—942no—
179C42—942no—
180C23—22no—
181C23—22no—
182C23—472no—
183C23—941no—
184C23—941no—
185C23—942no—
186C23—942no—
187C23D4×D4712yes—
188C23#1062535212yes—
189C23C2×C22⋊D4712yes—
190C23C23×D4711yescharacteristic
191D4—948no—
192C2×C4—22no—
193C2×C4—28no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—48no—
198C2×C4—472no—
199C2×C4—941no—
200C2×C4—941no—
201C2×C4—944no—
202C2×C4—941no—
203C2×C4—941no—
204C2×C4—944no—
205C2×C4—942no—
206C2×C4—944no—
207C2×C4—942no—
208C2×C4—1884no—
209C2×C4#1062535014yes—
210C2×C4C2×C22⋊D4712yes—
211C2×C4C2×C22⋊D4712yes—
212C22—24no—
213C22—24no—
214C22—22no—
215C22—22no—
216C22—944no—
217C22—942no—
218C22—1882no—
219C22—1881no—
220C22—1881no—
221C22#1309399514yes—
222C22C2×D4×D4711yescharacteristic
223C22C22×C22⋊D4711yescharacteristic
224C22C2×#1062535211yescharacteristic
225C22C2×#1062535012yes—
226C22#1309407212yes—
227C4—22no—
228C4—44no—
229C4—942no—
230C4—1884no—
231C4—1881no—
232C4—1881no—
233C4#1309400714yescomplemented
234C2—24no—
235C2—1882no—
236C2C2×#1309399511yescharacteristic
237C2C2×#1309400711yescharacteristic
238C2#1568969711yescharacteristic
239C2#1568977412yes—
240C2#1568980812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC22×C4⋊C4×C47C2
hypercenterC22×C4⋊C4D47
hypocenterC47#2486
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #15689054C2semidirect
4. #15689049C2semidirect
5. #15689019C2semidirect
6. #15688986C2semidirect
7. #15688983C2semidirect
8. #15688980C2semidirect
9. C22×C4⋊C4×C47C2semidirect
108. C4×C47#123semidirect
123. C22×C4⋊C4D47semidirect
130. C47#2486semidirect
233. C4#13094007semidirect