Finite Group Databasebeta

← #20248770

Subgroups — #20248770

Order 6016.

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

normal subgroups only

This group has 468 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×#13094014C211yesmaximal, characteristic
2C2×Q8×Dic47C211yesmaximal, characteristic
3#15689055C211yesmaximal, characteristic
4#15689053C211yesmaximal, characteristic
5#15689042C211yesmaximal, characteristic
6#15689022C212yesmaximal
7#15689020C212yesmaximal
8#15689020C212yesmaximal
9#15689018C212yesmaximal
10#15688974C211yesmaximal, characteristic
11C47×#395C211yesmaximal, characteristic
12#13094014—24no—
13Q8×Dic47—24no—
14C2×C4⋊Dic47C2212yes—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2212yes—
18C2×Dic47⋊C4C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2212yes—
24C2×Dic47⋊C4C2212yes—
25C2×C4×Dic47C2212yes—
26C2×C4×Dic47C2212yes—
27C2×C4×Dic47C2211yescharacteristic
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×Q8×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2212yes—
34C2×C4⋊C4×C47C2211yescharacteristic
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C2×Q8×C47—22no—
38C2×Q8×C47—24no—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2312yes—
43C22×C4×C47C2312yes—
44C22×Dic47C2312yes—
45C22×Dic47C2311yescharacteristic
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C22×Dic47C2312yes—
49C22×Dic47C2311yescharacteristic
50C4⋊C4×C47—22no—
51C4⋊C4×C47—24no—
52C4⋊Dic47—22no—
53C4⋊Dic47—24no—
54C4⋊Dic47—22no—
55C4⋊Dic47—42no—
56Dic47⋊C4—22no—
57Dic47⋊C4—24no—
58Dic47⋊C4—22no—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61Dic47⋊C4—42no—
62Dic47⋊C4Q818yescomplemented
63C4×Dic47—24no—
64C4×Dic47—42no—
65C4×Dic47D414yes—
66C23×C47C2411yescharacteristic
67Q8×C47—28no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—21no—
74C2×C4×C47—21no—
75C2×C4×C47—22no—
76C2×C4×C47—21no—
77C2×C4×C47—21no—
78C2×C4×C47C2×D412yes—
79C2×C4×C47C2×Q814yes—
80C2×C4×C47#4114yes—
81C2×Dic47—22no—
82C2×Dic47—21no—
83C2×Dic47—22no—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—21no—
91C2×Dic47—22no—
92C2×Dic47—21no—
93C2×Dic47C2×D412yes—
94C2×Dic47C2×D412yes—
95C2×Dic47C2×Q814yes—
96C2×Dic47C2×Q814yes—
97C22×C47C22×D411yescharacteristic
98C22×C47C22×Q812yes—
99C22×C47C2×#4112yes—
100C22×C47H(5,𝔽2)11yescharacteristic
101C22×C472−1+411yescharacteristic
102C4×C47—22no—
103C4×C47—24no—
104C4×C47—24no—
105C4×C47—41no—
106C4×C47—41no—
107Dic47—22no—
108Dic47—24no—
109Dic47—41no—
110Dic47—42no—
111Dic47—41no—
112Dic47C4⋊Q814yes—
113#2584—471nomaximal, Sylow
114C2×C47#52511yescharacteristic
115C2×C47C2×C4⋊Q811yescharacteristic
116C2×C47#53711yescharacteristic
117C2×C47#55412yes—
118C2×C47#55712yes—
119C2×#125—471no—
120C2×C4×Q8—471no—
121#398—471no—
122#398—471no—
123#395—471no—
124#395D4711yescharacteristic
125#389—472no—
126#389—472no—
127#389—472no—
128#389—472no—
129C4×C4⋊C4—471no—
130C47#258411yescharacteristic, complemented, Sylow
131C22×Q8C2×D4711yescharacteristic
132#125—944no—
133C4×Q8—944no—
134C2×C4⋊C4—472no—
135C2×C4⋊C4—472no—
136C2×C4⋊C4—471no—
137C2×C4⋊C4—471no—
138C2×C4⋊C4—471no—
139C2×C4⋊C4—471no—
140C2×C4⋊C4—471no—
141C2×C4⋊C4—471no—
142C2×C4⋊C4—472no—
143C2×C4⋊C4—472no—
144C2×C4⋊C4—472no—
145C2×C4⋊C4C2×D4711yescharacteristic
146C2×C4⋊C4C2×D4712yes—
147C2×C42—471no—
148C2×C42—472no—
149C2×C42—472no—
150#95—471no—
151#95—472no—
152#95—472no—
153#95—472no—
154#95C2×D4711yescharacteristic
155#95C2×D4712yes—
156C2×Q8—22no—
157C2×Q8—24no—
158C22×C4—471no—
159C22×C4—472no—
160C22×C4—471no—
161C22×C4—472no—
162C22×C4—471no—
163C22×C4—471no—
164C22×C4C22×D4711yescharacteristic
165C22×C4C22×D4711yescharacteristic
166C22×C4C22×D4711yescharacteristic
167C22×C4C22×D4712yes—
168C22×C4C22×D4712yes—
169C4⋊C4—22no—
170C4⋊C4—24no—
171C4⋊C4—478no—
172C4⋊C4—942no—
173C4⋊C4—942no—
174C4⋊C4—942no—
175C4⋊C4—944no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—944no—
180C4⋊C4—1882no—
181C4⋊C4—1882no—
182C42—474no—
183C42—944no—
184C42—1882no—
185C23C23×D4711yescharacteristic
186Q8—28no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—472no—
198C2×C4—474no—
199C2×C4—472no—
200C2×C4—474no—
201C2×C4—942no—
202C2×C4—941no—
203C2×C4—942no—
204C2×C4—941no—
205C2×C4—942no—
206C2×C4—941no—
207C2×C4—941no—
208C2×C4—942no—
209C2×C4—942no—
210C2×C4—941no—
211C2×C4—942no—
212C2×C4—941no—
213C2×C4D4×D4712yes—
214C2×C4#1062535214yes—
215C2×C4Q8×D4714yes—
216C22C2×D4×D4711yescharacteristic
217C22C2×Q8×D4712yes—
218C22C2×#1062535212yes—
219C22#1309407011yescharacteristic
220C22#1309407211yescharacteristic
221C4—24no—
222C4—22no—
223C4—24no—
224C4—41no—
225C4—41no—
226C4—474no—
227C4—944no—
228C4—942no—
229C4—1881no—
230C4—1882no—
231C4—1881no—
232C2#1568962911yescharacteristic
233C2C4⋊Q8×D4711yescharacteristic
234C2#1568970311yescharacteristic
235C2#1568983112yes—
236C2#1568984812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2584
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
62. Dic47⋊C4Q8semidirect
130. C47#2584semidirect