Finite Group Databasebeta

← #20244241

Subgroups — #20244241

Order 6016.

348 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C22×#10625335C211yesmaximal, characteristic
2C2×#13093955C211yesmaximal, characteristic, complemented
3C2×#13093947C211yesmaximal, characteristic, complemented
4C2×#13093945C211yesmaximal, characteristic
5C2×C4×C47⋊C8C211yesmaximal, characteristic, complemented
6#15689029C211yesmaximal, characteristic, complemented
7C47×#390C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C2×#10625335—22no—
10C2×#10625335—22no—
11C2×#10625335C414yescomplemented
12C22×C47⋊C8C2211yescharacteristic
13C22×C47⋊C8C2211yescharacteristic
14C2×C4⋊Dic47C2211yescharacteristic
15#13093955—22no—
16#13093947—22no—
17#13093945—22no—
18C4×C47⋊C8—22no—
19C47⋊#95—22no—
20C22×D4×C47C2211yescharacteristic
21C2×C4⋊C4×C47C2211yescharacteristic
22C2×C22⋊C4×C47—22no—
23C2×C42×C47C2211yescharacteristic
24C24×C47—21no—
25C2×D4×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47—21no—
30C2×D4×C47C2×C412yes—
31C22×C4×C47—21no—
32C22×C4×C47D412yes—
33C22×C4×C47C2311yescharacteristic
34C22×Dic47—21no—
35C22×Dic47—21no—
36C2×Dic94—21no—
37C2×Dic94—21no—
38C2×Dic94—21no—
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94C2×C412yes—
42C4⋊C4×C47—21no—
43C4⋊C4×C47—21no—
44C22⋊C4×C47—44no—
45C42×C47—21no—
46C42×C47—21no—
47#10625335—28no—
48C4⋊Dic47—21no—
49C4⋊Dic47—21no—
50C2×C47⋊C8—21no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8C2×C412yes—
53C2×C47⋊C8D412yes—
54C2×C47⋊C8D412yes—
55C2×C47⋊C8D412yes—
56C23×C47—22no—
57C23×C47—41no—
58C23×C47—41no—
59C23×C47—42no—
60C23×C47—42no—
61C23×C47C2×D411yescharacteristic
62D4×C47—22no—
63D4×C47—22no—
64D4×C47—41no—
65D4×C47—41no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—41no—
69C2×C4×C47—42no—
70C2×C4×C47SD1614yescomplemented
71C2×C4×C47C22×C411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47#4111yescharacteristic
76C2×C4×C47#4111yescharacteristic
77C2×Dic47—22no—
78C2×Dic47—41no—
79C2×Dic47—41no—
80C2×Dic47—41no—
81C2×Dic47—42no—
82Dic94—22no—
83Dic94—22no—
84Dic94—41no—
85Dic94—41no—
86C47⋊C8—22no—
87C47⋊C8C22⋊C414yescomplemented
88C22×C47—42no—
89C22×C47—44no—
90C22×C47—82no—
91C22×C47—81no—
92C22×C47—81no—
93C22×C47C4×D411yescharacteristic
94C22×C47#12111yescharacteristic
95C22×C47#12711yescharacteristic
96C22×C47C2×SD1612yes—
97C22×C47#13512yes—
98C4×C47—24no—
99C4×C47—81no—
100C4×C47C2×C22⋊C411yescharacteristic
101C4×C47C4×D411yescharacteristic
102C4×C47#12111yescharacteristic
103C4×C47#12411yescharacteristic
104Dic47—42no—
105Dic47—81no—
106#1968—471nomaximal, Sylow
107C2×C47—82no—
108C2×C47#39011yescharacteristic
109C2×C47C4×SD1612yes—
110C2×C47#46512yes—
111C2×C47#49211yescharacteristic
112C2×C47#49511yescharacteristic
113C22×SD16—471no—
114C2×#106—471no—
115C2×#103—471no—
116C2×#102—471no—
117C2×C4×C8—471no—
118#391—471no—
119#390D4711yescharacteristic
120C47#196811yescharacteristic, complemented, Sylow
121C22×Q8—471no—
122C22×D4C2×D4711yescharacteristic
123C2×SD16—474no—
124C2×SD16—942no—
125C2×SD16—942no—
126C22×C8—471no—
127C22×C8—471no—
128C2×C4⋊C4—471no—
129C2×C4⋊C4C2×D4711yescharacteristic
130C2×C22⋊C4—22no—
131C2×C42C2×D4711yescharacteristic
132#106—942no—
133#103—942no—
134#102—942no—
135C4×C8—942no—
136#95—942no—
137C24—21no—
138C2×Q8—472no—
139C2×Q8—941no—
140C2×Q8—941no—
141C2×Q8—941no—
142C2×Q8—941no—
143C2×Q8—941no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4C4×D4712yes—
150C22×C4—21no—
151C22×C4—941no—
152C22×C4—941no—
153C22×C4C22⋊D4712yes—
154C22×C4C22×D4711yescharacteristic
155SD16—948no—
156C2×C8—472no—
157C2×C8—472no—
158C2×C8—472no—
159C2×C8—472no—
160C2×C8—941no—
161C2×C8—941no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—941no—
165C4⋊C4—941no—
166C22⋊C4—44no—
167C42—21no—
168C42—21no—
169C23—22no—
170C23—41no—
171C23—41no—
172C23—42no—
173C23—42no—
174C23C2×C22⋊D4711yescharacteristic
175Q8—942no—
176Q8—942no—
177Q8—1881no—
178Q8—1881no—
179D4—22no—
180D4—22no—
181D4—41no—
182D4—41no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—41no—
186C2×C4—42no—
187C2×C4—942no—
188C2×C4—1881no—
189C2×C4—1882no—
190C2×C4—1881no—
191C2×C4—1881no—
192C2×C4#1062533514yescomplemented
193C2×C4C2×C4×D4711yescharacteristic
194C2×C4#1062535011yescharacteristic
195C2×C4D4×D4711yescharacteristic
196C2×C4D4×D4711yescharacteristic
197C2×C4D4×D4711yescharacteristic
198C2×C4#1062535211yescharacteristic
199C8—474no—
200C8—942no—
201C22—42no—
202C22—44no—
203C22—81no—
204C22—81no—
205C22—82no—
206C22C4×C22⋊D4711yescharacteristic
207C22#1309399611yescharacteristic
208C22#1309402011yescharacteristic
209C22C2×#1062533512yes—
210C22#1309404412yes—
211C4—24no—
212C4—81no—
213C4—3761no—
214C4—1882no—
215C4C22⋊C4×D4711yescharacteristic
216C4(C22⋊D47)⋊C411yescharacteristic
217C4#1309399711yescharacteristic
218C4#1309401011yescharacteristic
219C2—82no—
220C2#1568902311yescharacteristic
221C2C4×#1062533512yes—
222C2#1568935012yes—
223C2#1568949511yescharacteristic
224C2#1568950511yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#390C2
socleC23×C47C2×D4
hypercenter#390D47
hypocenterC47#1968
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#13093955C2semidirect
3. C2×#13093947C2semidirect
5. C2×C4×C47⋊C8C2semidirect
6. #15689029C2semidirect
11. C2×#10625335C4semidirect
70. C2×C4×C47SD16semidirect
87. C47⋊C8C22⋊C4semidirect
120. C47#1968semidirect
192. C2×C4#10625335semidirect