Finite Group Databasebeta

← #20248772

Subgroups — #20248772

Order 6016.

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

normal subgroups only

This group has 468 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×#13094014C211yesmaximal, characteristic
2C2×#13093989C211yesmaximal, characteristic
3#15689054C211yesmaximal, characteristic
4#15689044C211yesmaximal, characteristic
5#15689043C211yesmaximal, characteristic
6#15689020C212yesmaximal
7#15689020C212yesmaximal
8#15689019C212yesmaximal
9#15689018C212yesmaximal
10#15688974C211yesmaximal, characteristic
11C47×#398C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13#13094014—24no—
14#13093989—24no—
15C2×C4⋊Dic47C2212yes—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2211yescharacteristic
18C2×Dic47⋊C4C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2212yes—
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—
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C4⋊C4×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×Dic47C2311yescharacteristic
43C22×Dic47C2311yescharacteristic
44C22×Dic47C2311yescharacteristic
45C22×Dic47C2312yes—
46C22×Dic47C2312yes—
47C22×Dic47C2311yescharacteristic
48C2×Dic94—22no—
49C2×Dic94—24no—
50C4⋊C4×C47—22no—
51C4⋊C4×C47—22no—
52C4⋊C4×C47—42no—
53C4⋊Dic47—22no—
54C4⋊Dic47—24no—
55Dic47⋊C4—22no—
56Dic47⋊C4—24no—
57Dic47⋊C4—22no—
58Dic47⋊C4—22no—
59Dic47⋊C4—22no—
60Dic47⋊C4—24no—
61Dic47⋊C4—42no—
62Dic47⋊C4Q818yescomplemented
63C4×Dic47—24no—
64C4×Dic47—42no—
65C4×Dic47D414yes—
66C23×C47C2411yescharacteristic
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—21no—
72C2×C4×C47—21no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47C2×D412yes—
79C2×C4×C47C2×Q814yes—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—21no—
84C2×Dic47—22no—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—22no—
89C2×Dic47—21no—
90C2×Dic47—21no—
91C2×Dic47C2×D412yes—
92C2×Dic47C2×D412yes—
93C2×Dic47C2×Q814yes—
94C2×Dic47C2×Q814yes—
95C2×Dic47#4114yes—
96Dic94—28no—
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—41no—
105C4×C47—42no—
106C4×C47—41no—
107Dic47—24no—
108Dic47—22no—
109Dic47—24no—
110Dic47—41no—
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#398D4711yescharacteristic
123#395—471no—
124#395—471no—
125#389—472no—
126#389—472no—
127#389—472no—
128#389—472no—
129C4×C4⋊C4—471no—
130C47#258411yescharacteristic, complemented, Sylow
131C22×Q8—471no—
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—472no—
142C2×C4⋊C4—472no—
143C2×C4⋊C4—472no—
144C2×C4⋊C4C2×D4711yescharacteristic
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—944no—
157C2×Q8—942no—
158C22×C4—471no—
159C22×C4—472no—
160C22×C4—472no—
161C22×C4—471no—
162C22×C4—471no—
163C22×C4—471no—
164C22×C4C22×D4711yescharacteristic
165C22×C4C22×D4712yes—
166C22×C4C22×D4711yescharacteristic
167C22×C4C22×D4711yescharacteristic
168C22×C4C22×D4712yes—
169C4⋊C4—22no—
170C4⋊C4—22no—
171C4⋊C4—42no—
172C4⋊C4—478no—
173C4⋊C4—944no—
174C4⋊C4—944no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—944no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4—1882no—
182C42—474no—
183C42—944no—
184C42—1882no—
185C23C23×D4711yescharacteristic
186Q8—948no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—472no—
199C2×C4—474no—
200C2×C4—472no—
201C2×C4—474no—
202C2×C4—474no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—942no—
206C2×C4—941no—
207C2×C4—942no—
208C2×C4—941no—
209C2×C4—941no—
210C2×C4—941no—
211C2×C4—942no—
212C2×C4—941no—
213C2×C4—941no—
214C2×C4D4×D4712yes—
215C2×C4Q8×D4714yes—
216C22C2×D4×D4711yescharacteristic
217C22C2×Q8×D4712yes—
218C22#41×D4712yes—
219C22#1309406911yescharacteristic
220C22#1309407111yescharacteristic
221C4—24no—
222C4—22no—
223C4—41no—
224C4—42no—
225C4—41no—
226C4—474no—
227C4—944no—
228C4—944no—
229C4—942no—
230C4—1881no—
231C4—1881no—
232C2#1568963111yescharacteristic
233C2C4⋊Q8×D4711yescharacteristic
234C2#1568970211yescharacteristic
235C2#1568982712yes—
236C2#1568985012yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#398C2
hypercenter#398D47
hypocenterC47#2584
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #398

Complements

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

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