Finite Group Databasebeta

← #20242400

Subgroups — #20242400

Order 6016.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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
1#15689711C211yesmaximal, characteristic
2#15689453C211yesmaximal, characteristic, complemented
3#15689436C211yesmaximal, characteristic, complemented
4#15688859C211yesmaximal, characteristic, complemented
5#15688856C211yesmaximal, characteristic, complemented
6#15688847C211yesmaximal, characteristic, complemented
7C47×#397C211yesmaximal, characteristic, complemented
8#13094017—21no—
9#13094010—21no—
10#13094006—21no—
11#13094003C2211yescharacteristic
12#13093998C2211yescharacteristic
13#13093997—21no—
14#13093993—21no—
15C4×C22⋊D47—21no—
16#13093957—21no—
17#13093955—21no—
18#13093947—21no—
19#13093944—21no—
20C22⋊(C47⋊C8)C2211yescharacteristic
21C22⋊(C47⋊C8)C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23C2×C22⋊C4×C47—21no—
24C2×C22⋊C4×C47C2211yescharacteristic
25#95×C47—21no—
26#95×C47C2211yescharacteristic
27C24×C47D411yescharacteristic
28C22×C4×C47—21no—
29C22×C4×C47—21no—
30C22×C4×C47D411yescharacteristic
31C22×C4×C47C2311yescharacteristic
32C2×C22⋊D47—21no—
33C2×C22⋊D47—21no—
34C2×C22⋊D47—21no—
35C2×D188D411yescharacteristic
36C2×C4×D47—21no—
37C2×Dic94D411yescharacteristic
38C4⋊C4×C47—21no—
39C4⋊C4×C47—21no—
40C22⋊C4×C47—21no—
41C22⋊C4×C47—21no—
42C22⋊C4×C47—42no—
43C22⋊Dic47—21no—
44C22⋊Dic47—21no—
45C22⋊Dic47—21no—
46(C2×D47)⋊C4—21no—
47(C2×D47)⋊C4—21no—
48C4⋊Dic47D411yescharacteristic
49C4⋊Dic47D411yescharacteristic
50Dic47⋊C4—21no—
51Dic47⋊C4—21no—
52C4×Dic47—21no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C23×C47—21no—
56C23×C47—21no—
57C23×C47—21no—
58C23×C47—41no—
59C23×C47—41no—
60C23×C47C2×D411yescharacteristic
61C22×D47—21no—
62C2×C4×C47—21no—
63C2×C4×C47—41no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47—41no—
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C22⋊D47—41no—
74C22⋊D47—41no—
75C22⋊D47—81no—
76C22⋊D47—81no—
77C2×Dic47—21no—
78C2×Dic47—21no—
79C2×Dic47—21no—
80D188—41no—
81C4×D47—81no—
82Dic94—41no—
83C47⋊C8—41no—
84C47⋊C8—41no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47—42no—
88C22×C47—41no—
89C22×C47—41no—
90C22×C47—41no—
91C22×C47—81no—
92C22×C47#12011yescharacteristic
93C22×C47#13511yescharacteristic
94C22×C47AGL(1,ℤ/8)11yescharacteristic
95C2×D47—41no—
96C2×D47—41no—
97C2×D47—41no—
98C4×C47—21no—
99C4×C47—21no—
100C4×C47—41no—
101C4×C47—81no—
102C4×C47—81no—
103Dic47—41no—
104Dic47—41no—
105Dic47—41no—
106#1612—471nomaximal, Sylow
107C2×C47—21no—
108C2×C47—21no—
109C2×C47—81no—
110C2×C47#44911yescharacteristic
111C2×C47#45511yescharacteristic
112C2×C47#45811yescharacteristic
113D47—81no—
114#538—471no—
115#483—471no—
116#480—471no—
117#397D4711yescharacteristic, complemented
118#328—471no—
119#327—471no—
120#323—471no—
121C47#161211yescharacteristic, complemented, Sylow
122#126—941no—
123#124—941no—
124#123—941no—
125C22⋊Q8—471no—
126#121—471no—
127#121—941no—
128#120—941no—
129C4×D4—941no—
130C2×C4⋊C4C2×D4711yescharacteristic
131C2×C22⋊C4—21no—
132C2×C22⋊C4C2×D4711yescharacteristic
133#107—941no—
134#106—941no—
135#103—941no—
136#102—941no—
137C22⋊C8—471no—
138C22⋊C8—471no—
139#95—21no—
140#95C2×D4711yescharacteristic
141C24C22⋊D4711yescharacteristic
142C2×Q8—471no—
143C2×D4—471no—
144C2×D4—941no—
145C2×D4—941no—
146C2×D4—941no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—941no—
150C22×C4C22⋊D4711yescharacteristic
151C22×C4C22×D4711yescharacteristic
152C2×C8—941no—
153C2×C8—941no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—471no—
157C4⋊C4—471no—
158C4⋊C4—941no—
159C4⋊C4—941no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—42no—
163C22⋊C4—941no—
164C22⋊C4—941no—
165C22⋊C4—941no—
166C22⋊C4—941no—
167C22⋊C4—941no—
168C42—941no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—941no—
175C23C2×C22⋊D4711yescharacteristic
176Q8—1881no—
177D4—3761no—
178D4—3761no—
179D4—1881no—
180D4—1881no—
181D4—1881no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—941no—
192C2×C4—941no—
193C2×C4—941no—
194C2×C4—3761no—
195C2×C4D4×D4711yescharacteristic
196C2×C4D4×D4711yescharacteristic
197C8—1881no—
198C8—1881no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—1881no—
207C22—1881no—
208C22—1881no—
209C22#1309399211yescharacteristic
210C22#1309404411yescharacteristic
211C22#1309405011yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—81no—
217C4—1881no—
218C4—1881no—
219C4—1881no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—3761no—
224C2#1568926611yescharacteristic
225C2#1568930011yescharacteristic
226C2#1568931211yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#397C2
socleC22×C47#120
hypercenter#397D47
hypocenterC47#1612
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #15689453C2semidirect
3. #15689436C2semidirect
4. #15688859C2semidirect
5. #15688856C2semidirect
6. #15688847C2semidirect
7. C47×#397C2semidirect
117. #397D47semidirect
121. C47#1612semidirect