Finite Group Databasebeta

← #20244239

Subgroups — #20244239

Order 6016.

348 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 103 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×#10625336C211yesmaximal, characteristic
2C2×#13093955C211yesmaximal, characteristic, complemented
3C2×#13093946C211yesmaximal, characteristic
4C2×C8×Dic47C211yesmaximal, characteristic, complemented
5#15689030C211yesmaximal, characteristic, complemented
6#15689024C211yesmaximal, characteristic
7C2×#103×C47C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C2×#10625336—22no—
10C2×#10625336—22no—
11C2×#10625336C414yescomplemented
12C22×C47⋊C8C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×(C2×D47)⋊C4—22no—
15C2×C4×Dic47C2211yescharacteristic
16#13093955—22no—
17#13093946—22no—
18C8×Dic47—22no—
19C47⋊#95—22no—
20C22×Q8×C47C2211yescharacteristic
21C22×C8×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23#103×C47—22no—
24C23×D47—21no—
25C2×Q8×C47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47C2×C412yes—
31C22×C4×C47—21no—
32C22×C4×C47—21no—
33C22×C4×C47C2311yescharacteristic
34C22×Dic47—21no—
35C22×Dic47D412yes—
36C2×D188—21no—
37C2×D188—21no—
38C2×D188—21no—
39C2×D188—21no—
40C2×D188—21no—
41C2×D188C2×C412yes—
42C2×C8×C47—21no—
43C2×C8×C47—21no—
44C2×C8×C47D412yes—
45C4⋊C4×C47—21no—
46C4⋊C4×C47—21no—
47#10625336—28no—
48(C2×D47)⋊C4—44no—
49C4⋊Dic47—21no—
50C4⋊Dic47—21no—
51C4×Dic47—21no—
52C4×Dic47—21no—
53C2×C47⋊C8C2×C412yes—
54C2×C47⋊C8D412yes—
55C2×C47⋊C8D412yes—
56C23×C47C2×D411yescharacteristic
57C22×D47—22no—
58C22×D47—41no—
59C22×D47—41no—
60C22×D47—42no—
61C22×D47—42no—
62Q8×C47—22no—
63Q8×C47—22no—
64Q8×C47—41no—
65Q8×C47—41no—
66C2×C4×C47—22no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47—42no—
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—22no—
79C2×Dic47—41no—
80C2×Dic47—42no—
81C2×Dic47SD1614yescomplemented
82D188—22no—
83D188—22no—
84D188—41no—
85D188—41no—
86C8×C47—22no—
87C47⋊C8C22⋊C414yescomplemented
88C22×C47C4×D411yescharacteristic
89C22×C47#12111yescharacteristic
90C22×C47#12711yescharacteristic
91C22×C47C2×SD1612yes—
92C22×C47#13512yes—
93C2×D47—42no—
94C2×D47—44no—
95C2×D47—82no—
96C2×D47—81no—
97C2×D47—81no—
98C4×C47—42no—
99C4×C47—81no—
100C4×C47C2×C22⋊C411yescharacteristic
101C4×C47C4×D411yescharacteristic
102C4×C47#12111yescharacteristic
103C4×C47#12411yescharacteristic
104Dic47—24no—
105Dic47—81no—
106#1968—471nomaximal, Sylow
107C2×C47#39011yescharacteristic
108C2×C47C4×SD1612yes—
109C2×C47#46512yes—
110C2×C47#49211yescharacteristic
111C2×C47#49511yescharacteristic
112D47—82no—
113C22×SD16—471no—
114C2×#106—471no—
115C2×#103D4711yescharacteristic, complemented
116C2×#102—471no—
117C2×C4×C8—471no—
118#391—471no—
119#390—471no—
120C47#196811yescharacteristic, complemented, Sylow
121C22×Q8C2×D4711yescharacteristic
122C22×D4—471no—
123C2×SD16—474no—
124C2×SD16—942no—
125C2×SD16—942no—
126C22×C8—471no—
127C22×C8C2×D4711yescharacteristic
128C2×C4⋊C4—471no—
129C2×C4⋊C4C2×D4711yescharacteristic
130C2×C22⋊C4—942no—
131C2×C42—471no—
132#106—942no—
133#103—22no—
134#102—942no—
135C4×C8—942no—
136#95—942no—
137C24—941no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8C4×D4712yes—
144C2×D4—472no—
145C2×D4—941no—
146C2×D4—941no—
147C2×D4—941no—
148C2×D4—941no—
149C2×D4—941no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—472no—
153C22×C4—941no—
154C22×C4C22×D4711yescharacteristic
155SD16—948no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—472no—
159C2×C8—472no—
160C2×C8—472no—
161C2×C8C22⋊D4712yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—941no—
165C4⋊C4—941no—
166C22⋊C4—1884no—
167C42—941no—
168C42—941no—
169C23—942no—
170C23—1881no—
171C23—1881no—
172C23—1882no—
173C23—1882no—
174C23D4×D4711yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—41no—
178Q8—41no—
179D4—942no—
180D4—942no—
181D4—1881no—
182D4—1881no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—42no—
188C2×C4—474no—
189C2×C4—942no—
190C2×C4—942no—
191C2×C4—1881no—
192C2×C4—1882no—
193C2×C4C2×C4×D4711yescharacteristic
194C2×C4#1062535011yescharacteristic
195C2×C4D4×D4711yescharacteristic
196C2×C4D4×D4711yescharacteristic
197C2×C4#1062535211yescharacteristic
198C2×C4C2×C22⋊D4711yescharacteristic
199C8—22no—
200C8—474no—
201C22—3761no—
202C22—3761no—
203C22—3762no—
204C22—1882no—
205C22—1884no—
206C22(C22⋊D47)⋊C411yescharacteristic
207C22#1309399711yescharacteristic
208C22#1309402011yescharacteristic
209C22SD16×D4712yes—
210C22#1309404712yes—
211C4—42no—
212C4—81no—
213C4—944no—
214C4—3761no—
215C4C22⋊C4×D4711yescharacteristic
216C4C4×C22⋊D4711yescharacteristic
217C4#1309399611yescharacteristic
218C4#1309401011yescharacteristic
219C2—3762no—
220C2#1568902311yescharacteristic
221C2#1568920812yes—
222C2#1568935512yes—
223C2#1568949411yescharacteristic
224C2#1568950811yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47#1968
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×#13093955C2semidirect
4. C2×C8×Dic47C2semidirect
5. #15689030C2semidirect
7. C2×#103×C47C2semidirect
11. C2×#10625336C4semidirect
81. C2×Dic47SD16semidirect
87. C47⋊C8C22⋊C4semidirect
115. C2×#103D47semidirect
120. C47#1968semidirect