Finite Group Databasebeta

← #20244709

Subgroups — #20244709

Order 6016.

288 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 85 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×#10625337C211yesmaximal, characteristic
2C2×Dic47⋊C8C211yesmaximal, characteristic
3C2×#13093949C211yesmaximal, characteristic
4#15689030C211yesmaximal, characteristic
5#15689028C211yesmaximal, characteristic
6#15688885C211yesmaximal, characteristic
7C2×#103×C47C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C2×#10625337—22no—
10C2×#10625337—22no—
11C2×#10625337—22no—
12C22×C47⋊C8C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C4×Dic47C2211yescharacteristic
15Dic47⋊C8—22no—
16#13093949—22no—
17C47⋊#95—21no—
18C47⋊#95—21no—
19C47⋊#95—21no—
20C47⋊#95—21no—
21C22×Q8×C47C2211yescharacteristic
22C22×C8×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24#103×C47—22no—
25C2×Q8×C47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47D412yes—
31C22×C4×C47—21no—
32C22×C4×C47—21no—
33C22×C4×C47C2311yescharacteristic
34C22×Dic47—21no—
35C22×Dic47—21no—
36C22×Dic47D411yescharacteristic
37C22×Dic47D411yescharacteristic
38C2×Dic94—21no—
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94—21no—
42C2×Dic94—21no—
43C2×Dic94D412yes—
44C2×C8×C47—21no—
45C2×C8×C47—21no—
46C2×C8×C47—21no—
47C4⋊C4×C47—21no—
48C4⋊C4×C47—21no—
49#10625337—28no—
50C4⋊Dic47—21no—
51C4⋊Dic47—21no—
52C4×Dic47—21no—
53C4×Dic47—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C2×C47⋊C8D412yes—
57C23×C47C2×D411yescharacteristic
58Q8×C47—22no—
59Q8×C47—22no—
60Q8×C47—41no—
61Q8×C47—41no—
62C2×C4×C47—22no—
63C2×C4×C47—41no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47#4111yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C2×Dic47—21no—
75C2×Dic47—21no—
76C2×Dic47—21no—
77C2×Dic47—22no—
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—41no—
81C2×Dic47—41no—
82C2×Dic47—41no—
83C2×Dic47—41no—
84C2×Dic47—41no—
85C2×Dic47Q1612yescomplemented
86Dic94—22no—
87Dic94—22no—
88Dic94—41no—
89Dic94—41no—
90C8×C47—41no—
91C47⋊C8—22no—
92C22×C47#12111yescharacteristic
93C22×C47#12111yescharacteristic
94C22×C47#12111yescharacteristic
95C22×C47C2×Q1611yescharacteristic
96C22×C47#13511yescharacteristic
97C22×C47#13711yescharacteristic
98C22×C47#13711yescharacteristic
99C4×C47—42no—
100C4×C47—81no—
101C4×C47#12011yescharacteristic
102C4×C47#12311yescharacteristic
103C4×C47#12311yescharacteristic
104C4×C47#12411yescharacteristic
105Dic47—22no—
106Dic47—42no—
107Dic47—41no—
108Dic47—81no—
109#2056—471nomaximal, Sylow
110C2×C47#39411yescharacteristic
111C2×C47#46211yescharacteristic
112C2×C47#46211yescharacteristic
113C2×C47#46411yescharacteristic
114C2×C47#46411yescharacteristic
115C2×C47#46711yescharacteristic
116C2×C47#47011yescharacteristic
117C22×Q16—471no—
118C2×C4⋊C8—471no—
119C2×#103—471no—
120C2×#103D4711yescharacteristic
121#391—471no—
122#391—471no—
123#340—471no—
124C47#205611yescharacteristic, complemented, Sylow
125C22×Q8—471no—
126C22×Q8C2×D4711yescharacteristic
127C2×Q16—942no—
128C2×Q16—942no—
129C2×Q16—942no—
130C22×C8—471no—
131C22×C8C2×D4711yescharacteristic
132C2×C4⋊C4—471no—
133C2×C4⋊C4C2×D4711yescharacteristic
134C2×C42—471no—
135C4⋊C8—942no—
136#103—22no—
137#103—942no—
138#95—941no—
139#95—941no—
140#95—941no—
141#95—941no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—21no—
145C2×Q8—21no—
146C2×Q8—21no—
147C2×Q8—472no—
148C2×Q8—941no—
149C2×Q8—941no—
150C2×Q8—941no—
151C2×Q8—941no—
152C2×Q8—941no—
153C2×Q8C22⋊D4712yes—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—471no—
157C22×C4—471no—
158C22×C4—941no—
159C22×C4—941no—
160C22×C4C22×D4711yescharacteristic
161Q16—948no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—472no—
166C2×C8—941no—
167C2×C8—941no—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—941no—
171C4⋊C4—941no—
172C42—941no—
173C42—941no—
174C23D4×D4711yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—41no—
178Q8—41no—
179Q8—942no—
180Q8—942no—
181Q8—1881no—
182Q8—1881no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—472no—
190C2×C4—941no—
191C2×C4—941no—
192C2×C4—941no—
193C2×C4—942no—
194C2×C4—941no—
195C2×C4—941no—
196C2×C4—1881no—
197C2×C4—1881no—
198C2×C4—1881no—
199C2×C4—1881no—
200C2×C4—1881no—
201C2×C4#1062535011yescharacteristic
202C2×C4#1062535011yescharacteristic
203C2×C4D4×D4711yescharacteristic
204C2×C4D4×D4711yescharacteristic
205C2×C4#1062535211yescharacteristic
206C2×C4C2×C22⋊D4711yescharacteristic
207C8—41no—
208C8—942no—
209C22#1309399611yescharacteristic
210C22#1309399711yescharacteristic
211C22#1309399711yescharacteristic
212C22Q16×D4711yescharacteristic
213C22#1309404511yescharacteristic
214C22#1309405311yescharacteristic
215C22#1309405611yescharacteristic
216C4—42no—
217C4—81no—
218C4—942no—
219C4—3761no—
220C4—1882no—
221C4—1881no—
222C4#1309399211yescharacteristic
223C4#1309400611yescharacteristic
224C4#1309400711yescharacteristic
225C4#1309401011yescharacteristic
226C2#1568903811yescharacteristic
227C2#1568933111yescharacteristic
228C2#1568933211yescharacteristic
229C2#1568934311yescharacteristic
230C2#1568934811yescharacteristic
231C2#1568936311yescharacteristic
232C2#1568938011yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47#2056
LCSG ▷ C22×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
85. C2×Dic47Q16semidirect
124. C47#2056semidirect