Finite Group Databasebeta

← #20249549

Subgroups — #20249549

Order 6016.

434 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 137 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#15689061C211yesmaximal, characteristic, complemented
3#15689058C211yesmaximal, characteristic
4#15689056C212yesmaximal, complemented
5#15689054C211yesmaximal, characteristic, complemented
6#15689049C211yesmaximal, characteristic
7#15689045C212yesmaximal
8#15689018C212yesmaximal, complemented
9#15689013C212yesmaximal
10C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
11C2×#125×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—
24C2×C4×Dic47C2212yes—
25C47⋊#95C2211yescharacteristic
26C47⋊#95C2211yescharacteristic
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31#125×C47—24no—
32C2×C4⋊C4×C47C2212yes—
33C2×C4⋊C4×C47C2212yes—
34C2×C4⋊C4×C47C2211yescharacteristic
35C2×C4⋊C4×C47C2211yescharacteristic
36C2×C42×C47C2211yescharacteristic
37C23×D47C2311yescharacteristic
38C22×C4×C47C2312yes—
39C22×C4×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×Dic47C2312yes—
44C22×Dic47C2311yescharacteristic
45C22×Dic47C2311yescharacteristic
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2312yes—
48C4⋊C4×C47—24no—
49C4⋊C4×C47—24no—
50C4⋊C4×C47—22no—
51C4⋊C4×C47—22no—
52C42×C47D414yes—
53(C2×D47)⋊C4—22no—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4—22no—
56(C2×D47)⋊C4—24no—
57(C2×D47)⋊C4—42no—
58C4⋊Dic47—24no—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62Dic47⋊C4—24no—
63Dic47⋊C4—42no—
64C4×Dic47—42no—
65C23×C47C2411yescharacteristic
66C22×D47—21no—
67C22×D47—22no—
68C22×D47—21no—
69C22×D47—21no—
70C22×D47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
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×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—21no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47#4114yes—
97C22×C47C22×D411yescharacteristic
98C22×C47C2×#4112yes—
99C22×C47H(5,𝔽2)11yescharacteristic
100C22×C472−1+411yescharacteristic
101C22×C472−1+412yes—
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—42no—
111C4×C47—42no—
112Dic47—24no—
113Dic47—41no—
114Dic47—41no—
115Dic47—41no—
116Dic47—42no—
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×#125D4711yescharacteristic, complemented
126#400—471no—
127#399—471no—
128#398—471no—
129#398—472no—
130#397—471no—
131#396—472no—
132#389—472no—
133#388—472no—
134C4×C4⋊C4—471no—
135C47#266411yescharacteristic, complemented, Sylow
136#126—944no—
137#125—24no—
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×D4712yes—
145C2×C4⋊C4C2×D4712yes—
146C2×C4⋊C4C2×D4711yescharacteristic
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×C42—472no—
154C2×C42C2×D4711yescharacteristic
155#95—471no—
156#95—471no—
157#95—472no—
158#95—472no—
159#95—472no—
160#95—472no—
161C24—471no—
162C22×C4—472no—
163C22×C4—472no—
164C22×C4—471no—
165C22×C4—471no—
166C22×C4—471no—
167C22×C4C22×D4712yes—
168C22×C4C22×D4712yes—
169C22×C4C22×D4711yescharacteristic
170C22×C4C22×D4711yescharacteristic
171C22×C4C22×D4711yescharacteristic
172C4⋊C4—24no—
173C4⋊C4—24no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—944no—
177C4⋊C4—944no—
178C4⋊C4—942no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4—1882no—
182C22⋊C4—944no—
183C22⋊C4—942no—
184C22⋊C4—942no—
185C22⋊C4—942no—
186C22⋊C4—1882no—
187C42—1882no—
188C42C22⋊D4714yes—
189C23—941no—
190C23—942no—
191C23—941no—
192C23—941no—
193C23—942no—
194C23C23×D4711yescharacteristic
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—474no—
206C2×C4—942no—
207C2×C4—942no—
208C2×C4—941no—
209C2×C4—941no—
210C2×C4—941no—
211C2×C4—942no—
212C2×C4—942no—
213C2×C4—942no—
214C2×C4—941no—
215C2×C4—941no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4C2×C22⋊D4712yes—
219C2×C4C2×C22⋊D4712yes—
220C2×C4C2×C22⋊D4712yes—
221C22—1882no—
222C22—1881no—
223C22—1881no—
224C22—1881no—
225C22—1882no—
226C22C22×C22⋊D4711yescharacteristic
227C22#41×D4712yes—
228C22#1309407011yescharacteristic
229C22#1309407111yescharacteristic
230C22#1309407212yes—
231C4—22no—
232C4—22no—
233C4—22no—
234C4—42no—
235C4—42no—
236C4—944no—
237C4—1881no—
238C4—1881no—
239C4—1881no—
240C4—1882no—
241C2—3761no—
242C2#1568966911yescharacteristic
243C2#1568969711yescharacteristic
244C2#1568970111yescharacteristic
245C2#1568972112yes—
246C2#1568973212yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#125×C47C2
hypercenterC2×#125D47
hypocenterC47#2664
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #15689061C2semidirect
4. #15689056C2semidirect
5. #15689054C2semidirect
8. #15689018C2semidirect
10. C4×C4⋊Dic47C2semidirect
11. C2×#125×C47C2semidirect
125. C2×#125D47semidirect
135. C47#2664semidirect