Finite Group Databasebeta

← #20244198

Subgroups — #20244198

Order 6016.

336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 99 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×#13094011C211yesmaximal, characteristic
2C2×#13093949C211yesmaximal, characteristic, complemented
3C2×#13093947C211yesmaximal, characteristic, complemented
4C2×#13093945C211yesmaximal, characteristic
5C2×C8×Dic47C211yesmaximal, characteristic, complemented
6#15688988C211yesmaximal, characteristic, complemented
7C2×#102×C47C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10#13094011—22no—
11#13094011C414yescomplemented
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C22⋊Dic47—22no—
14C2×C4×Dic47C2211yescharacteristic
15#13093949—22no—
16#13093947—22no—
17#13093945—22no—
18C8×Dic47—22no—
19C47⋊#95—22no—
20C22×D4×C47C2211yescharacteristic
21C22×C8×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23#102×C47—22no—
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×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—
47C22⋊Dic47—28no—
48C4⋊Dic47—21no—
49C4⋊Dic47—21no—
50C4×Dic47C2×C412yes—
51C4×Dic47D412yes—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8D412yes—
55C23×C47—22no—
56C23×C47—41no—
57C23×C47—41no—
58C23×C47—42no—
59C23×C47—42no—
60C23×C47C2×D411yescharacteristic
61D4×C47—22no—
62D4×C47—22no—
63D4×C47—41no—
64D4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47—42no—
67C2×C4×C47C22×C411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47#4111yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—41no—
77C2×Dic47—41no—
78C2×Dic47—41no—
79C2×Dic47—42no—
80C2×Dic47C22⋊C414yes—
81Dic94—22no—
82Dic94—22no—
83Dic94—41no—
84Dic94—41no—
85C8×C47—22no—
86C47⋊C8—22no—
87C22×C47—42no—
88C22×C47—44no—
89C22×C47—82no—
90C22×C47—81no—
91C22×C47—81no—
92C22×C47C2×C22⋊C411yescharacteristic
93C22×C47#12411yescharacteristic
94C22×C47#12711yescharacteristic
95C22×C47#13512yes—
96C22×C47#13512yes—
97C4×C47—81no—
98C4×C47C4×D411yescharacteristic
99C4×C47C4×D411yescharacteristic
100C4×C47#12111yescharacteristic
101C4×C47#12111yescharacteristic
102Dic47—24no—
103Dic47—42no—
104Dic47—81no—
105#1958—471nomaximal, Sylow
106C2×C47—82no—
107C2×C47#39011yescharacteristic
108C2×C47#41612yes—
109C2×C47#48812yes—
110C2×C47#49511yescharacteristic
111C2×C47#49511yescharacteristic
112C2×#124—471no—
113C2×#103—471no—
114C2×#103—471no—
115C2×#102—471no—
116C2×#102D4711yescharacteristic
117C2×C4×C8—471no—
118#382—471no—
119C47#195811yescharacteristic, complemented, Sylow
120C22×Q8—471no—
121C22×D4C2×D4711yescharacteristic
122C22×C8—471no—
123C22×C8C2×D4711yescharacteristic
124#124—474no—
125#124—942no—
126C2×C4⋊C4—471no—
127C2×C4⋊C4C2×D4711yescharacteristic
128C2×C22⋊C4—942no—
129C2×C42—471no—
130#103—942no—
131#103—942no—
132#102—22no—
133#102—942no—
134C4×C8—942no—
135#95—942no—
136C24—21no—
137C2×Q8—472no—
138C2×Q8—941no—
139C2×Q8—941no—
140C2×Q8—941no—
141C2×Q8—941no—
142C2×Q8—941no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4C4×D4712yes—
149C22×C4—21no—
150C22×C4—472no—
151C22×C4—941no—
152C22×C4—941no—
153C22×C4C22×D4711yescharacteristic
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—472no—
157C2×C8—941no—
158C2×C8—941no—
159C2×C8C22⋊D4712yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—941no—
163C4⋊C4—941no—
164C22⋊C4—948no—
165C42—472no—
166C42—472no—
167C23—22no—
168C23—41no—
169C23—41no—
170C23—42no—
171C23—42no—
172C23D4×D4711yescharacteristic
173Q8—942no—
174Q8—942no—
175Q8—1881no—
176Q8—1881no—
177D4—22no—
178D4—22no—
179D4—41no—
180D4—41no—
181C2×C4—41no—
182C2×C4—42no—
183C2×C4—474no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4—942no—
187C2×C4—1881no—
188C2×C4—1882no—
189C2×C4—1881no—
190C2×C4—1881no—
191C2×C4C2×C4×D4711yescharacteristic
192C2×C4#1062535011yescharacteristic
193C2×C4D4×D4711yescharacteristic
194C2×C4D4×D4711yescharacteristic
195C2×C4#1062535211yescharacteristic
196C2×C4C2×C22⋊D4711yescharacteristic
197C8—22no—
198C8—942no—
199C22—42no—
200C22—44no—
201C22—82no—
202C22—81no—
203C22—81no—
204C22C22⋊C4×D4711yescharacteristic
205C22#1309401011yescharacteristic
206C22#1309402011yescharacteristic
207C22#1309404312yes—
208C22#1309404512yes—
209C4—81no—
210C4—944no—
211C4—3761no—
212C4—1882no—
213C4(C22⋊D47)⋊C411yescharacteristic
214C4C4×C22⋊D4711yescharacteristic
215C4#1309399611yescharacteristic
216C4#1309399711yescharacteristic
217C2—82no—
218C2#1568902311yescharacteristic
219C2#1568911612yes—
220C2#1568947612yes—
221C2#1568950411yescharacteristic
222C2#1568950611yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#102×C47C2
socleC23×C47C2×D4
hypercenterC2×#102D47
hypocenterC47#1958
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#13093949C2semidirect
3. C2×#13093947C2semidirect
5. C2×C8×Dic47C2semidirect
6. #15688988C2semidirect
11. #13094011C4semidirect
119. C47#1958semidirect