Finite Group Databasebeta

← #20249294

Subgroups — #20249294

Order 6016.

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

normal subgroups only

This group has 450 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
2#15689056C212yesmaximal, complemented
3#15689054C211yesmaximal, characteristic, complemented
4#15689049C211yesmaximal, characteristic
5#15689045C212yesmaximal
6#15689042C211yesmaximal, characteristic, complemented
7#15689034C211yesmaximal, characteristic
8#15689014C212yesmaximal
9#15689007C212yesmaximal, complemented
10#15688989C211yesmaximal, characteristic, complemented
11C2×C4×Q8×C47C211yesmaximal, characteristic, complemented
12#13094018—24no—
13C2×C4⋊Dic47C2212yes—
14C2×Dic47⋊C4C2211yescharacteristic
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2211yescharacteristic
17C2×Dic47⋊C4C2211yescharacteristic
18C2×Dic47⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2211yescharacteristic
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2211yescharacteristic
22C2×(C2×D47)⋊C4C2211yescharacteristic
23C2×(C2×D47)⋊C4C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2211yescharacteristic
26C47⋊#95C2211yescharacteristic
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C22×Q8×C47C2211yescharacteristic
32C4×Q8×C47—24no—
33C2×C4⋊C4×C47C2212yes—
34C2×C4⋊C4×C47C2211yescharacteristic
35C2×C42×C47C2212yes—
36C2×C42×C47C2211yescharacteristic
37C23×D47C2311yescharacteristic
38C2×Q8×C47—22no—
39C2×Q8×C47—24no—
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2312yes—
45C22×Dic47C2311yescharacteristic
46C22×Dic47C2312yes—
47C22×Dic47C2312yes—
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2311yescharacteristic
50C4⋊C4×C47—24no—
51C4⋊C4×C47—22no—
52C42×C47—24no—
53C42×C47D414yes—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4—22no—
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—24no—
58(C2×D47)⋊C4—42no—
59C4⋊Dic47—42no—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62Dic47⋊C4—22no—
63Dic47⋊C4—24no—
64Dic47⋊C4—42no—
65C23×C47C2411yescharacteristic
66C22×D47—21no—
67C22×D47—22no—
68C22×D47—21no—
69C22×D47—21no—
70C22×D47—22no—
71Q8×C47—28no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47C2×D412yes—
82C2×C4×C47C2×D412yes—
83C2×C4×C47C2×D412yes—
84C2×C4×C47#4114yes—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—21no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—21no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C22×C47C22×D411yescharacteristic
99C22×C47C2×#4112yes—
100C22×C47H(5,𝔽2)11yescharacteristic
101C22×C472−1+411yescharacteristic
102C22×C472−1+412yes—
103C2×D47—41no—
104C2×D47—41no—
105C2×D47—41no—
106C2×D47—42no—
107C2×D47—42no—
108C4×C47—22no—
109C4×C47—24no—
110C4×C47—22no—
111C4×C47—22no—
112C4×C47—42no—
113Dic47—41no—
114Dic47—41no—
115Dic47—41no—
116Dic47—42no—
117Dic47—42no—
118#2637—471nomaximal, Sylow
119C2×C47#52511yescharacteristic
120C2×C47#53611yescharacteristic
121C2×C47#53711yescharacteristic
122C2×C47#54112yes—
123C2×C47#54212yes—
124D47—81no—
125C2×#126—471no—
126C2×C4×Q8D4711yescharacteristic, complemented
127#398—471no—
128#398—472no—
129#397—471no—
130#396—472no—
131#395—471no—
132#393—471no—
133#388—472no—
134#387—472no—
135#382—471no—
136C47#263711yescharacteristic, complemented, Sylow
137C22×Q8C2×D4711yescharacteristic
138#126—944no—
139C4×Q8—24no—
140C2×C4⋊C4—471no—
141C2×C4⋊C4—471no—
142C2×C4⋊C4—471no—
143C2×C4⋊C4—472no—
144C2×C4⋊C4—472no—
145C2×C4⋊C4—472no—
146C2×C4⋊C4C2×D4712yes—
147C2×C4⋊C4C2×D4711yescharacteristic
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—471no—
157#95—471no—
158#95—472no—
159#95—472no—
160#95—472no—
161#95—472no—
162C24—471no—
163C2×Q8—24no—
164C2×Q8—22no—
165C22×C4—471no—
166C22×C4—472no—
167C22×C4—472no—
168C22×C4—471no—
169C22×C4—471no—
170C22×C4C22×D4712yes—
171C22×C4C22×D4712yes—
172C22×C4C22×D4711yescharacteristic
173C22×C4C22×D4711yescharacteristic
174C22×C4C22×D4711yescharacteristic
175C4⋊C4—24no—
176C4⋊C4—22no—
177C4⋊C4—944no—
178C4⋊C4—942no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4—1882no—
182C4⋊C4—1882no—
183C22⋊C4—944no—
184C22⋊C4—942no—
185C22⋊C4—942no—
186C22⋊C4—942no—
187C22⋊C4—1882no—
188C42—24no—
189C42C22⋊D4714yes—
190C23—941no—
191C23—942no—
192C23—941no—
193C23—941no—
194C23—942no—
195C23C23×D4711yescharacteristic
196Q8—28no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—941no—
207C2×C4—941no—
208C2×C4—941no—
209C2×C4—942no—
210C2×C4—942no—
211C2×C4—942no—
212C2×C4—942no—
213C2×C4—942no—
214C2×C4—941no—
215C2×C4—941no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—942no—
219C2×C4#1062535014yes—
220C2×C4C2×C22⋊D4712yes—
221C2×C4C2×C22⋊D4712yes—
222C2×C4C2×C22⋊D4712yes—
223C22—1882no—
224C22—1882no—
225C22—1881no—
226C22—1881no—
227C22—1881no—
228C22C22×C22⋊D4711yescharacteristic
229C22C2×#1062535012yes—
230C22#1309407011yescharacteristic
231C22#1309407111yescharacteristic
232C22#1309407212yes—
233C4—24no—
234C4—22no—
235C4—22no—
236C4—22no—
237C4—42no—
238C4—1882no—
239C4—1882no—
240C4—1881no—
241C4—1881no—
242C4—1881no—
243C2—3761no—
244C2#1568963411yescharacteristic
245C2#1568969711yescharacteristic
246C2#1568970111yescharacteristic
247C2#1568973112yes—
248C2#1568974512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C4×Q8×C47C2
hypercenterC2×C4×Q8D47
hypocenterC47#2637
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #15689056C2semidirect
3. #15689054C2semidirect
6. #15689042C2semidirect
9. #15689007C2semidirect
10. #15688989C2semidirect
11. C2×C4×Q8×C47C2semidirect
126. C2×C4×Q8D47semidirect
136. C47#2637semidirect