Finite Group Databasebeta

← #20243831

Subgroups — #20243831

Order 6016.

442 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 101 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#15689634C211yesmaximal, characteristic
2C2×#13093952C212yesmaximal, complemented
3#15689087C211yesmaximal, characteristic, complemented
4#15688883C212yesmaximal, complemented
5C22×C42×C47C211yesmaximal, characteristic, complemented
6C2×#10625350C2211yescharacteristic
7C2×#10625329C2212yes—
8#13094007—21no—
9#13094003C412yescomplemented
10#13093998C412yescomplemented
11#13093993—21no—
12C4×C22⋊D47—22no—
13#13093983C2211yescharacteristic
14#13093952—24no—
15C22⋊(C47⋊C8)—22no—
16C23×C4×C47—21no—
17C23×C4×C47C2211yescharacteristic
18C2×C42×C47—21no—
19C2×C42×C47—24no—
20C2×C42×C47C2212yes—
21C24×C47D411yescharacteristic
22C22×C4×C47—24no—
23C22×C4×C47—28no—
24C22×C4×C47—22no—
25C22×C4×C47—22no—
26C22×C4×C47—22no—
27C22×C4×C47C2×C412yes—
28C22×C4×C47D411yescharacteristic
29C22×C4×C47D412yes—
30C22×C4×C47C2311yescharacteristic
31C2×C22⋊D47—22no—
32C2×C22⋊D47—21no—
33#10625350—22no—
34#10625350—22no—
35C2×D188C2×C411yescharacteristic, complemented
36C2×C4×D47—21no—
37C2×Dic94C2×C411yescharacteristic, complemented
38C42×C47—24no—
39C42×C47—22no—
40C42×C47D414yescomplemented
41C22⋊Dic47—22no—
42C22⋊Dic47—21no—
43(C2×D47)⋊C4—22no—
44C4⋊Dic47C2×C412yescomplemented
45Dic47⋊C4—22no—
46C4×Dic47—21no—
47#10625329—22no—
48#10625329—22no—
49C2×C47⋊C8—22no—
50C23×C47—24no—
51C23×C47—21no—
52C23×C47—21no—
53C23×C47C22⋊C412yes—
54C23×C47C2×D411yescharacteristic
55C22×D47—21no—
56C2×C4×C47—216no—
57C2×C4×C47—28no—
58C2×C4×C47—21no—
59C2×C4×C47—24no—
60C2×C4×C47—21no—
61C2×C4×C47—24no—
62C2×C4×C47—24no—
63C2×C4×C47C22⋊C412yes—
64C2×C4×C47C22×C411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D412yes—
67C2×C4×C47#4112yes—
68C22⋊D47—44no—
69C22⋊D47—41no—
70C22⋊D47—41no—
71C2×Dic47—22no—
72C2×Dic47—21no—
73D188—22no—
74C4×D47—42no—
75Dic94—22no—
76C47⋊C8—42no—
77C22×C47—24no—
78C22×C47—24no—
79C22×C47—22no—
80C22×C47—22no—
81C22×C47—22no—
82C22×C47#10414yescomplemented
83C22×C47C2×C22⋊C411yescharacteristic
84C22×C47#12011yescharacteristic
85C22×C47#12311yescharacteristic
86C2×D47—41no—
87C2×D47—42no—
88C4×C47—28no—
89C4×C47—22no—
90C4×C47C4×D412yes—
91C4×C47#12112yes—
92Dic47—41no—
93Dic47—42no—
94#1896—471nomaximal, Sylow
95C2×C47—21no—
96C2×C47—24no—
97C2×C47—21no—
98C2×C47#38611yescharacteristic
99C2×C47C2×#10412yes—
100D47—81no—
101#525—471no—
102C22×C42D4711yescharacteristic, complemented
103C2×#104—472no—
104#407—471no—
105#339—472no—
106C47#189611yescharacteristic, complemented, Sylow
107C2×#41—471no—
108C23×C4—21no—
109C23×C4C2×D4711yescharacteristic
110C2×M16—472no—
111#123—941no—
112C22⋊Q8—472no—
113#121—472no—
114#120—941no—
115C4×D4—942no—
116#117—471no—
117C2×C42—21no—
118C2×C42—24no—
119C2×C42C2×D4712yes—
120#104—944no—
121C22⋊C8—942no—
122C24C22⋊D4711yescharacteristic
123#41—942no—
124#41—942no—
125C2×Q8—471no—
126C2×D4—471no—
127C2×D4—942no—
128C2×D4—941no—
129C22×C4—24no—
130C22×C4—28no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—941no—
135C22×C4C4×D4712yes—
136C22×C4D18812yes—
137C22×C4C22⋊D4711yescharacteristic
138C22×C4C22×D4711yescharacteristic
139M16—942no—
140M16—942no—
141C2×C8—942no—
142C4⋊C4—472no—
143C4⋊C4—942no—
144C22⋊C4—942no—
145C22⋊C4—941no—
146C22⋊C4—942no—
147C42—24no—
148C42—22no—
149C42—941no—
150C42C22⋊D4714yescomplemented
151C23—24no—
152C23—21no—
153C23—21no—
154C23—941no—
155C23(C2×D47)⋊C412yes—
156C23C2×C22⋊D4711yescharacteristic
157Q8—942no—
158D4—942no—
159D4—1884no—
160D4—1881no—
161D4—1881no—
162C2×C4—216no—
163C2×C4—28no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—24no—
168C2×C4—24no—
169C2×C4—942no—
170C2×C4—941no—
171C2×C4—1882no—
172C2×C4(C2×D47)⋊C412yes—
173C2×C4C2×C4×D4711yescharacteristic
174C2×C4C2×D18811yescharacteristic
175C2×C4#1062535012yes—
176C2×C4C2×C22⋊D4712yes—
177C8—1882no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—1881no—
184C22—1882no—
185C22#1309395214yescomplemented
186C22C2×(C2×D47)⋊C411yescharacteristic
187C22#1309399311yescharacteristic
188C22#1309400711yescharacteristic
189C4—28no—
190C4—22no—
191C4—1881no—
192C4—1882no—
193C4C4×C22⋊D4712yes—
194C4#1309399812yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—3761no—
199C2#1568900211yescharacteristic
200C2C2×#1309395212yes—
subgroupG/H
centerC2×C4C2×D188
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC22×C42×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC22×C42D47
hypocenterC47#1896
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C2×#13093952C2semidirect
3. #15689087C2semidirect
4. #15688883C2semidirect
5. C22×C42×C47C2semidirect
9. #13094003C4semidirect
10. #13093998C4semidirect
35. C2×D188C2×C4semidirect
37. C2×Dic94C2×C4semidirect
40. C42×C47D4semidirect
44. C4⋊Dic47C2×C4semidirect
82. C22×C47#104semidirect
102. C22×C42D47semidirect
106. C47#1896semidirect
150. C42C22⋊D47semidirect
185. C22#13093952semidirect