Finite Group Databasebeta

← #20249506

Subgroups — #20249506

Order 6016.

448 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13094022C211yesmaximal, characteristic
2C2×#13094014C211yesmaximal, characteristic
3#15689057C212yesmaximal
4#15689056C212yesmaximal
5#15689044C211yesmaximal, characteristic
6#15689043C211yesmaximal, characteristic
7#15689042C211yesmaximal, characteristic
8#15688992C212yesmaximal
9#15688987C212yesmaximal
10#15688968C211yesmaximal, characteristic
11C47×#395C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13#13094022—24no—
14#13094014—24no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2212yes—
17C2×Dic47⋊C4C2211yescharacteristic
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2212yes—
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2212yes—
24C2×Dic47⋊C4C2212yes—
25C2×C4×Dic47C2211yescharacteristic
26C2×C4×Dic47C2212yes—
27C47⋊#95C2211yescharacteristic
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×Q8×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C4⋊C4×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C2×Q8×C47—22no—
38C2×Q8×C47—42no—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2312yes—
44C22×Dic47C2311yescharacteristic
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C22×Dic47C2312yes—
49C22×Dic47C2311yescharacteristic
50C2×Dic94—22no—
51C2×Dic94—42no—
52C4⋊C4×C47—22no—
53C4⋊C4×C47—42no—
54C4⋊Dic47—22no—
55C4⋊Dic47—42no—
56Dic47⋊C4—22no—
57Dic47⋊C4—22no—
58Dic47⋊C4—22no—
59Dic47⋊C4—22no—
60Dic47⋊C4—24no—
61Dic47⋊C4—24no—
62Dic47⋊C4—42no—
63Dic47⋊C4—42no—
64C4×Dic47D414yes—
65C4×Dic47Q818yescomplemented
66C23×C47C2411yescharacteristic
67Q8×C47—44no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—21no—
72C2×C4×C47—22no—
73C2×C4×C47—21no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—21no—
78C2×C4×C47—21no—
79C2×C4×C47C2×D412yes—
80C2×C4×C47C2×Q814yes—
81C2×Dic47—22no—
82C2×Dic47—21no—
83C2×Dic47—21no—
84C2×Dic47—22no—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—22no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—21no—
92C2×Dic47—21no—
93C2×Dic47C2×D412yes—
94C2×Dic47C2×D412yes—
95C2×Dic47C2×Q814yes—
96C2×Dic47C2×Q814yes—
97Dic94—44no—
98C22×C47C22×D411yescharacteristic
99C22×C47C22×Q812yes—
100C22×C47H(5,𝔽2)12yes—
101C22×C472−1+411yescharacteristic
102C22×C472−1+411yescharacteristic
103C4×C47—22no—
104C4×C47—24no—
105C4×C47—41no—
106C4×C47—42no—
107C4×C47—41no—
108Dic47—22no—
109Dic47—24no—
110Dic47—42no—
111Dic47—41no—
112Dic47—41no—
113Dic47C4⋊Q814yes—
114#2660—471nomaximal, Sylow
115C2×C47C2×C4⋊Q811yescharacteristic
116C2×C47#53511yescharacteristic
117C2×C47#53611yescharacteristic
118C2×C47#54412yes—
119C2×C47#54412yes—
120C2×C4⋊Q8—471no—
121C2×#125—471no—
122#398—472no—
123#398—472no—
124#395—471no—
125#395—471no—
126#395—471no—
127#395D4711yescharacteristic
128#384—472no—
129#382—472no—
130#376—471no—
131C47#266011yescharacteristic, complemented, Sylow
132C22×Q8—471no—
133C22×Q8C2×D4711yescharacteristic
134C4⋊Q8—944no—
135#125—944no—
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⋊C4—472no—
145C2×C4⋊C4—472no—
146C2×C4⋊C4C2×D4711yescharacteristic
147C2×C4⋊C4C2×D4712yes—
148C2×C42—471no—
149C2×C42—472no—
150#95—471no—
151#95—472no—
152#95—472no—
153#95—472no—
154#95—472no—
155#95C2×D4711yescharacteristic
156#95C2×D4712yes—
157C2×Q8—22no—
158C2×Q8—42no—
159C2×Q8—942no—
160C2×Q8—1882no—
161C22×C4—471no—
162C22×C4—472no—
163C22×C4—471no—
164C22×C4—471no—
165C22×C4—472no—
166C22×C4—471no—
167C22×C4C22×D4711yescharacteristic
168C22×C4C22×D4712yes—
169C22×C4C22×D4711yescharacteristic
170C22×C4C22×D4711yescharacteristic
171C22×C4C22×D4712yes—
172C4⋊C4—22no—
173C4⋊C4—42no—
174C4⋊C4—942no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—944no—
178C4⋊C4—944no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4—1882no—
182C4⋊C4—1882no—
183C4⋊C4—1882no—
184C42—474no—
185C42—478no—
186C23C23×D4711yescharacteristic
187Q8—44no—
188Q8—1884no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—472no—
201C2×C4—474no—
202C2×C4—472no—
203C2×C4—474no—
204C2×C4—942no—
205C2×C4—941no—
206C2×C4—942no—
207C2×C4—941no—
208C2×C4—941no—
209C2×C4—941no—
210C2×C4—942no—
211C2×C4—942no—
212C2×C4—942no—
213C2×C4—942no—
214C2×C4—941no—
215C2×C4—941no—
216C2×C4D4×D4712yes—
217C2×C4Q8×D4714yes—
218C22C2×D4×D4711yescharacteristic
219C22C2×Q8×D4712yes—
220C22#1309406912yes—
221C22#1309407111yescharacteristic
222C22#1309407211yescharacteristic
223C4—24no—
224C4—22no—
225C4—42no—
226C4—41no—
227C4—41no—
228C4—474no—
229C4—944no—
230C4—942no—
231C4—1882no—
232C4—1881no—
233C4—1881no—
234C2C4⋊Q8×D4711yescharacteristic
235C2#1568968811yescharacteristic
236C2#1568969611yescharacteristic
237C2#1568975012yes—
238C2#1568975212yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2660
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
65. C4×Dic47Q8semidirect
131. C47#2660semidirect