Finite Group Databasebeta

← #20244188

Subgroups — #20244188

Order 6016.

332 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 115 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×#13094022C211yesmaximal, characteristic
2C2×#13093949C211yesmaximal, characteristic
3C2×#13093948C211yesmaximal, characteristic
4C2×#13093947C211yesmaximal, characteristic
5C2×C8×Dic47C211yesmaximal, characteristic
6#15688992C211yesmaximal, characteristic
7C2×#103×C47C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10#13094022—22no—
11#13094022C414yescomplemented
12C2×C4⋊Dic47C2211yescharacteristic
13C2×Dic47⋊C4—22no—
14C2×Dic47⋊C4—22no—
15C2×C4×Dic47C2211yescharacteristic
16#13093949—22no—
17#13093948—22no—
18#13093947—22no—
19C8×Dic47—22no—
20C22×Q8×C47C2211yescharacteristic
21C22×C8×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23#103×C47—22no—
24C2×Q8×C47—21no—
25C2×Q8×C47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47C2×C412yes—
30C22×C4×C47—21no—
31C22×C4×C47—21no—
32C22×C4×C47C2311yescharacteristic
33C22×Dic47—21no—
34C22×Dic47—21no—
35C22×Dic47D412yes—
36C2×Dic94—21no—
37C2×Dic94—21no—
38C2×Dic94—21no—
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94C2×C412yes—
42C2×C8×C47—21no—
43C2×C8×C47—21no—
44C2×C8×C47D412yes—
45C4⋊C4×C47—21no—
46C4⋊C4×C47—21no—
47C4⋊Dic47—21no—
48C4⋊Dic47—21no—
49Dic47⋊C4—28no—
50Dic47⋊C4—44no—
51C4×Dic47C2×C412yes—
52C4×Dic47D412yes—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8D412yes—
56C23×C47C2×D411yescharacteristic
57Q8×C47—22no—
58Q8×C47—22no—
59Q8×C47—41no—
60Q8×C47—41no—
61C2×C4×C47—22no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47—41no—
65C2×C4×C47—42no—
66C2×C4×C47C22×C411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47#4111yescharacteristic
71C2×C4×C47#4111yescharacteristic
72C2×Dic47—22no—
73C2×Dic47—41no—
74C2×Dic47—41no—
75C2×Dic47—41no—
76C2×Dic47—42no—
77C2×Dic47C22⋊C414yes—
78C2×Dic47SD1614yes—
79C2×Dic47Q1614yes—
80Dic94—22no—
81Dic94—22no—
82Dic94—41no—
83Dic94—41no—
84C8×C47—22no—
85C47⋊C8—22no—
86C22×C47C2×C22⋊C411yescharacteristic
87C22×C47#12411yescharacteristic
88C22×C47#12711yescharacteristic
89C22×C47C2×SD1612yes—
90C22×C47C2×Q1612yes—
91C4×C47—42no—
92C4×C47—81no—
93C4×C47C4×D411yescharacteristic
94C4×C47C4×D411yescharacteristic
95C4×C47#12111yescharacteristic
96C4×C47#12111yescharacteristic
97Dic47—42no—
98Dic47—81no—
99Dic47#10318yescomplemented
100#1956—471nomaximal, Sylow
101C2×C47#39011yescharacteristic
102C2×C47C2×#10312yes—
103C2×C47#48712yes—
104C2×C47#49211yescharacteristic
105C2×C47#49411yescharacteristic
106C2×C4⋊Q8—471no—
107C2×#103—471no—
108C2×#103—471no—
109C2×#103—471no—
110C2×#103D4711yescharacteristic
111C2×C4×C8—471no—
112#384—471no—
113C47#195611yescharacteristic, complemented, Sylow
114C22×Q8—471no—
115C22×Q8C2×D4711yescharacteristic
116C22×C8—471no—
117C22×C8C2×D4711yescharacteristic
118C4⋊Q8—474no—
119C4⋊Q8—942no—
120C2×C4⋊C4—471no—
121C2×C4⋊C4—942no—
122C2×C4⋊C4—942no—
123C2×C4⋊C4C2×D4711yescharacteristic
124C2×C42—471no—
125#103—22no—
126#103—942no—
127#103—942no—
128#103—942no—
129C4×C8—942no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—472no—
136C2×Q8—941no—
137C2×Q8—941no—
138C2×Q8—941no—
139C2×Q8—941no—
140C2×Q8—941no—
141C2×Q8C4×D4712yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—472no—
145C22×C4—941no—
146C22×C4—941no—
147C22×C4C22×D4711yescharacteristic
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—472no—
151C2×C8—941no—
152C2×C8—941no—
153C2×C8C22⋊D4712yes—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—948no—
157C4⋊C4—941no—
158C4⋊C4—941no—
159C4⋊C4—1884no—
160C42—472no—
161C42—472no—
162C23D4×D4711yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—942no—
168Q8—942no—
169Q8—1881no—
170Q8—1881no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—42no—
176C2×C4—474no—
177C2×C4—474no—
178C2×C4—474no—
179C2×C4—942no—
180C2×C4—1881no—
181C2×C4—1882no—
182C2×C4—1881no—
183C2×C4—1881no—
184C2×C4C2×C4×D4711yescharacteristic
185C2×C4#1062535011yescharacteristic
186C2×C4D4×D4711yescharacteristic
187C2×C4D4×D4711yescharacteristic
188C2×C4#1062535211yescharacteristic
189C2×C4C2×C22⋊D4711yescharacteristic
190C8—22no—
191C8—942no—
192C22C22⋊C4×D4711yescharacteristic
193C22#1309401011yescharacteristic
194C22#1309402011yescharacteristic
195C22SD16×D4712yes—
196C22Q16×D4712yes—
197C4—42no—
198C4—81no—
199C4—478no—
200C4—3761no—
201C4—1882no—
202C4(C22⋊D47)⋊C411yescharacteristic
203C4C4×C22⋊D4711yescharacteristic
204C4#1309399611yescharacteristic
205C4#1309399711yescharacteristic
206C2#1568902311yescharacteristic
207C2#103×D4712yes—
208C2#1568947212yes—
209C2#1568949411yescharacteristic
210C2#1568950111yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47#1956
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
11. #13094022C4semidirect
99. Dic47#103semidirect
113. C47#1956semidirect