Finite Group Databasebeta

← #20243693

Subgroups — #20243693

Order 6016.

404 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 121 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×#13094003C211yesmaximal, characteristic
2C22×C4⋊Dic47C211yesmaximal, characteristic
3C2×#13093949C212yesmaximal, complemented
4#15688886C212yesmaximal, complemented
5C2×C22⋊C8×C47C211yesmaximal, characteristic
6C22×Dic94C2211yescharacteristic
7C23×Dic47—21no—
8#13094003—22no—
9#13094003C414yescomplemented
10C2×C4⋊Dic47—21no—
11C2×C4⋊Dic47—24no—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2212yes—
14C2×Dic47⋊C4—21no—
15C2×C22⋊Dic47—21no—
16#13093949—24no—
17C23×C4×C47C2211yescharacteristic
18C22×C8×C47C2212yes—
19C22⋊C8×C47—22no—
20C24×C47D411yescharacteristic
21C22×C4×C47—22no—
22C22×C4×C47—22no—
23C22×C4×C47C2×C412yes—
24C22×C4×C47D411yescharacteristic
25C22×C4×C47D412yes—
26C22×C4×C47C2311yescharacteristic
27C22×Dic47—24no—
28C22×Dic47—21no—
29C22×Dic47—21no—
30C22×Dic47—22no—
31C22×Dic47—42no—
32C22×Dic47—42no—
33C2×Dic94—22no—
34C2×Dic94—22no—
35C2×Dic94—21no—
36C2×Dic94C2×C412yescomplemented
37C2×C8×C47—22no—
38C2×C8×C47—22no—
39C2×C8×C47—22no—
40C22⋊Dic47—24no—
41C4⋊Dic47—24no—
42C4⋊Dic47—22no—
43C4⋊Dic47—21no—
44C4⋊Dic47C2×C412yescomplemented
45C4⋊Dic47D414yes—
46Dic47⋊C4—24no—
47C23×C47—21no—
48C23×C47—21no—
49C23×C47—21no—
50C23×C47—21no—
51C23×C47C22⋊C412yes—
52C23×C47SD1612yes—
53C23×C47Q1612yes—
54C23×C47C2×D411yescharacteristic
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—24no—
58C2×C4×C47—24no—
59C2×C4×C47C22⋊C412yes—
60C2×C4×C47C22×C411yescharacteristic
61C2×C4×C47C2×D412yes—
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47#4112yes—
64C2×Dic47—22no—
65C2×Dic47—22no—
66C2×Dic47—24no—
67C2×Dic47—48no—
68C2×Dic47—41no—
69C2×Dic47—41no—
70C2×Dic47—42no—
71C2×Dic47—41no—
72C2×Dic47—42no—
73C2×Dic47—41no—
74Dic94—24no—
75Dic94—42no—
76C8×C47—42no—
77C22×C47—22no—
78C22×C47—22no—
79C22×C47—22no—
80C22×C47—22no—
81C22×C47—22no—
82C22×C47—22no—
83C22×C47#10314yescomplemented
84C22×C47C2×C22⋊C411yescharacteristic
85C22×C47#12011yescharacteristic
86C22×C47#12311yescharacteristic
87C22×C47C2×SD1611yescharacteristic
88C22×C47C2×Q1611yescharacteristic
89C22×C47AGL(1,ℤ/8)11yescharacteristic
90C22×C47#13711yescharacteristic
91C4×C47—22no—
92C4×C47C4×D412yes—
93C4×C47#12112yes—
94Dic47—42no—
95Dic47—42no—
96Dic47—44no—
97#1872—471nomaximal, Sylow
98C2×C47—24no—
99C2×C47#38611yescharacteristic
100C2×C47C2×#10311yescharacteristic
101C2×C47#41711yescharacteristic
102C2×C47#45011yescharacteristic
103C2×C47#45111yescharacteristic
104C2×C47#48311yescharacteristic
105C2×C47#48411yescharacteristic
106C2×C22⋊Q8—471no—
107C22×C4⋊C4—471no—
108C2×#103—472no—
109C2×C22⋊C8D4711yescharacteristic
110#340—472no—
111C47#187211yescharacteristic, complemented, Sylow
112C22×Q8—471no—
113C23×C4—941no—
114C23×C4C2×D4711yescharacteristic
115C22×C8C2×D4712yes—
116C22⋊Q8—474no—
117C22⋊Q8—942no—
118C2×C4⋊C4—472no—
119C2×C4⋊C4—471no—
120C2×C4⋊C4—944no—
121C2×C4⋊C4—941no—
122C2×C4⋊C4—941no—
123C2×C22⋊C4—941no—
124#103—944no—
125C22⋊C8—22no—
126C24D18811yescharacteristic
127C2×Q8—472no—
128C2×Q8—941no—
129C2×Q8—942no—
130C2×Q8—942no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—944no—
134C22×C4—941no—
135C22×C4—941no—
136C22×C4—942no—
137C22×C4—1882no—
138C22×C4—1882no—
139C22×C4C4×D4712yes—
140C22×C4D18811yescharacteristic
141C22×C4C22⋊D4712yes—
142C22×C4C22×D4711yescharacteristic
143C2×C8—22no—
144C2×C8—22no—
145C2×C8—22no—
146C4⋊C4—472no—
147C4⋊C4—474no—
148C4⋊C4—944no—
149C4⋊C4—944no—
150C4⋊C4—942no—
151C4⋊C4—941no—
152C22⋊C4—944no—
153C23—21no—
154C23—21no—
155C23—21no—
156C23—21no—
157C23#1062532512yes—
158C23Dic18812yes—
159C23(C2×D47)⋊C412yes—
160C23C2×D18811yescharacteristic
161Q8—944no—
162Q8—1882no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—942no—
168C2×C4—942no—
169C2×C4—944no—
170C2×C4—1888no—
171C2×C4—1881no—
172C2×C4—1881no—
173C2×C4—1882no—
174C2×C4—1881no—
175C2×C4—1882no—
176C2×C4—1881no—
177C2×C4(C2×D47)⋊C412yes—
178C2×C4C2×C4×D4711yescharacteristic
179C2×C4D4×D4712yes—
180C2×C4#1062535212yes—
181C2×C4C2×C22⋊D4711yescharacteristic
182C8—42no—
183C22—22no—
184C22—22no—
185C22—22no—
186C22—22no—
187C22—22no—
188C22—22no—
189C22#1309394914yescomplemented
190C22C2×(C2×D47)⋊C411yescharacteristic
191C22#1309399411yescharacteristic
192C22#1309400811yescharacteristic
193C22C2×#1062532511yescharacteristic
194C22C2×Dic18811yescharacteristic
195C22#1309405211yescharacteristic
196C22#1309405711yescharacteristic
197C4—22no—
198C4—1882no—
199C4—1884no—
200C4—1882no—
201C4(C22⋊D47)⋊C412yes—
202C4#1309399612yes—
203C2—24no—
204C2#1568900011yescharacteristic
205C2C2×#1309394911yescharacteristic
206C2#1568912511yescharacteristic
207C2#1568927611yescharacteristic
208C2#1568928111yescharacteristic
209C2#1568945411yescharacteristic
210C2#1568945911yescharacteristic
subgroupG/H
centerC23C2×D188
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×C22⋊C8×C47C2
socleC23×C47C2×D4
hypercenterC2×C22⋊C8D47
hypocenterC47#1872
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#13093949C2semidirect
4. #15688886C2semidirect
9. #13094003C4semidirect
36. C2×Dic94C2×C4semidirect
44. C4⋊Dic47C2×C4semidirect
83. C22×C47#103semidirect
111. C47#1872semidirect
189. C22#13093949semidirect