Finite Group Databasebeta

← #20249547

Subgroups — #20249547

Order 6016.

434 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13094018C211yesmaximal, characteristic
2C2×#13094016C211yesmaximal, characteristic, complemented
3#15689063C211yesmaximal, characteristic, complemented
4#15689060C211yesmaximal, characteristic
5#15689055C211yesmaximal, characteristic, complemented
6#15689053C212yesmaximal, complemented
7#15689050C211yesmaximal, characteristic
8#15689045C212yesmaximal
9#15689021C212yesmaximal, complemented
10#15689014C212yesmaximal
11C4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
12#13094018—24no—
13#13094016—24no—
14C2×C4⋊Dic47C2212yes—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2212yes—
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2211yescharacteristic
27C2×(C2×D47)⋊C4C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2212yes—
33C2×C42×C47C2212yes—
34C2×C42×C47C2211yescharacteristic
35#95×C47C2211yescharacteristic
36#95×C47C2211yescharacteristic
37C23×D47C2311yescharacteristic
38C22×C4×C47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2312yes—
43C22×Dic47C2311yescharacteristic
44C22×Dic47C2312yes—
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C4⋊C4×C47—24no—
49C42×C47—42no—
50C42×C47D414yes—
51(C2×D47)⋊C4—22no—
52(C2×D47)⋊C4—22no—
53(C2×D47)⋊C4—22no—
54(C2×D47)⋊C4—24no—
55(C2×D47)⋊C4—42no—
56C4⋊Dic47—22no—
57C4⋊Dic47—22no—
58C4⋊Dic47—24no—
59C4⋊Dic47—42no—
60Dic47⋊C4—24no—
61Dic47⋊C4—24no—
62Dic47⋊C4—22no—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65C23×C47C2411yescharacteristic
66C22×D47—21no—
67C22×D47—22no—
68C22×D47—21no—
69C22×D47—22no—
70C22×D47—21no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—21no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47C2×D412yes—
81C2×C4×C47C2×D412yes—
82C2×C4×C47C2×D412yes—
83C2×C4×C47#4114yes—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—21no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—21no—
97C22×C47C22×D411yescharacteristic
98C22×C47C2×#4112yes—
99C22×C47H(5,𝔽2)11yescharacteristic
100C22×C472−1+412yes—
101C22×C472−1+411yescharacteristic
102C2×D47—41no—
103C2×D47—41no—
104C2×D47—41no—
105C2×D47—42no—
106C2×D47—42no—
107C4×C47—22no—
108C4×C47—22no—
109C4×C47—22no—
110C4×C47—24no—
111C4×C47—42no—
112Dic47—42no—
113Dic47—41no—
114Dic47—41no—
115Dic47—42no—
116Dic47—41no—
117#2664—471nomaximal, Sylow
118C2×C47#53211yescharacteristic
119C2×C47#53611yescharacteristic
120C2×C47#53711yescharacteristic
121C2×C47#53912yes—
122C2×C47#54112yes—
123D47—81no—
124C2×#126—471no—
125C2×#125—471no—
126#400—471no—
127#399—471no—
128#398—472no—
129#398—471no—
130#397—471no—
131#396—472no—
132#389—472no—
133#388—472no—
134C4×C4⋊C4D4711yescharacteristic, complemented
135C47#266411yescharacteristic, complemented, Sylow
136#126—944no—
137#125—944no—
138C2×C4⋊C4—472no—
139C2×C4⋊C4—472no—
140C2×C4⋊C4—471no—
141C2×C4⋊C4—471no—
142C2×C4⋊C4—471no—
143C2×C4⋊C4—471no—
144C2×C4⋊C4—471no—
145C2×C4⋊C4—472no—
146C2×C4⋊C4—472no—
147C2×C4⋊C4C2×D4712yes—
148C2×C22⋊C4—471no—
149C2×C22⋊C4—471no—
150C2×C22⋊C4—471no—
151C2×C22⋊C4—472no—
152C2×C22⋊C4—472no—
153C2×C42C2×D4712yes—
154C2×C42C2×D4711yescharacteristic
155#95—472no—
156#95—472no—
157#95—472no—
158#95—472no—
159#95C2×D4711yescharacteristic
160#95C2×D4711yescharacteristic
161C24—471no—
162C22×C4—471no—
163C22×C4—471no—
164C22×C4—471no—
165C22×C4—472no—
166C22×C4—472no—
167C22×C4C22×D4712yes—
168C22×C4C22×D4711yescharacteristic
169C22×C4C22×D4711yescharacteristic
170C22×C4C22×D4711yescharacteristic
171C22×C4C22×D4712yes—
172C4⋊C4—24no—
173C4⋊C4—944no—
174C4⋊C4—944no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—942no—
180C4⋊C4—944no—
181C4⋊C4—1882no—
182C22⋊C4—942no—
183C22⋊C4—942no—
184C22⋊C4—942no—
185C22⋊C4—944no—
186C22⋊C4—1882no—
187C42—42no—
188C42D18814yes—
189C23—941no—
190C23—942no—
191C23—941no—
192C23—942no—
193C23—941no—
194C23C23×D4711yescharacteristic
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—941no—
205C2×C4—941no—
206C2×C4—941no—
207C2×C4—942no—
208C2×C4—942no—
209C2×C4—942no—
210C2×C4—942no—
211C2×C4—942no—
212C2×C4—942no—
213C2×C4—941no—
214C2×C4—942no—
215C2×C4—941no—
216C2×C4—942no—
217C2×C4C2×D18812yes—
218C2×C4C2×D18812yes—
219C2×C4C2×D18812yes—
220C2×C4#1062535014yes—
221C22—1882no—
222C22—1881no—
223C22—1881no—
224C22—1881no—
225C22—1882no—
226C22C22×D18811yescharacteristic
227C22C2×#1062535012yes—
228C22#1309406911yescharacteristic
229C22#1309407112yes—
230C22#1309407211yescharacteristic
231C4—22no—
232C4—22no—
233C4—22no—
234C4—24no—
235C4—42no—
236C4—1881no—
237C4—1882no—
238C4—1881no—
239C4—1881no—
240C4—1882no—
241C2—3761no—
242C2#1568967311yescharacteristic
243C2#1568969911yescharacteristic
244C2#1568970411yescharacteristic
245C2#1568971512yes—
246C2#1568973112yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC4×C4⋊C4×C47C2
hypercenterC4×C4⋊C4D47
hypocenterC47#2664
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#13094016C2semidirect
3. #15689063C2semidirect
5. #15689055C2semidirect
6. #15689053C2semidirect
9. #15689021C2semidirect
11. C4×C4⋊C4×C47C2semidirect
134. C4×C4⋊C4D47semidirect
135. C47#2664semidirect