Finite Group Databasebeta

← #20244196

Subgroups — #20244196

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×#13094013C211yesmaximal, characteristic
2C2×#13093948C211yesmaximal, characteristic, complemented
3C2×#13093946C211yesmaximal, characteristic
4C2×#13093944C211yesmaximal, characteristic
5C2×C8×Dic47C211yesmaximal, characteristic, complemented
6#15688988C211yesmaximal, characteristic, complemented
7C2×#103×C47C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10#13094013—22no—
11#13094013C414yescomplemented
12C2×C4⋊Dic47C2211yescharacteristic
13C2×(C2×D47)⋊C4—22no—
14C2×C4×Dic47C2211yescharacteristic
15#13093948—22no—
16#13093946—22no—
17#13093944—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(C2×D47)⋊C4—28no—
48C4⋊Dic47—21no—
49C4⋊Dic47—21no—
50C4×Dic47C2×C412yes—
51C4×Dic47D412yes—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8D412yes—
55C23×C47C2×D411yescharacteristic
56C22×D47—22no—
57C22×D47—41no—
58C22×D47—41no—
59C22×D47—42no—
60C22×D47—42no—
61Q8×C47—22no—
62Q8×C47—22no—
63Q8×C47—41no—
64Q8×C47—41no—
65C2×C4×C47—22no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47—42no—
70C2×C4×C47C22×C411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47#4111yescharacteristic
75C2×C4×C47#4111yescharacteristic
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—41no—
79C2×Dic47—42no—
80C2×Dic47C22⋊C414yes—
81D188—22no—
82D188—22no—
83D188—41no—
84D188—41no—
85C8×C47—22no—
86C47⋊C8—22no—
87C22×C47C2×C22⋊C411yescharacteristic
88C22×C47#12411yescharacteristic
89C22×C47#12711yescharacteristic
90C22×C47#13512yes—
91C22×C47#13512yes—
92C2×D47—42no—
93C2×D47—44no—
94C2×D47—82no—
95C2×D47—81no—
96C2×D47—81no—
97C4×C47—42no—
98C4×C47—81no—
99C4×C47C4×D411yescharacteristic
100C4×C47C4×D411yescharacteristic
101C4×C47#12111yescharacteristic
102C4×C47#12111yescharacteristic
103Dic47—24no—
104Dic47—81no—
105#1958—471nomaximal, Sylow
106C2×C47#39011yescharacteristic
107C2×C47#41612yes—
108C2×C47#48812yes—
109C2×C47#49511yescharacteristic
110C2×C47#49511yescharacteristic
111D47—82no—
112C2×#124—471no—
113C2×#103—471no—
114C2×#103D4711yescharacteristic, complemented
115C2×#102—471no—
116C2×#102—471no—
117C2×C4×C8—471no—
118#382—471no—
119C47#195811yescharacteristic, complemented, Sylow
120C22×Q8C2×D4711yescharacteristic
121C22×D4—471no—
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—22no—
131#103—942no—
132#102—942no—
133#102—942no—
134C4×C8—942no—
135#95—942no—
136C24—941no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8C4×D4712yes—
143C2×D4—472no—
144C2×D4—941no—
145C2×D4—941no—
146C2×D4—941no—
147C2×D4—941no—
148C2×D4—941no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—472no—
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—942no—
168C23—1881no—
169C23—1881no—
170C23—1882no—
171C23—1882no—
172C23D4×D4711yescharacteristic
173Q8—22no—
174Q8—22no—
175Q8—41no—
176Q8—41no—
177D4—942no—
178D4—942no—
179D4—1881no—
180D4—1881no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—474no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4—1881no—
190C2×C4—1882no—
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—3762no—
200C22—3761no—
201C22—3761no—
202C22—1882no—
203C22—1884no—
204C22C22⋊C4×D4711yescharacteristic
205C22#1309401011yescharacteristic
206C22#1309402011yescharacteristic
207C22#1309404512yes—
208C22#1309404712yes—
209C4—42no—
210C4—81no—
211C4—944no—
212C4—3761no—
213C4(C22⋊D47)⋊C411yescharacteristic
214C4C4×C22⋊D4711yescharacteristic
215C4#1309399611yescharacteristic
216C4#1309399711yescharacteristic
217C2—3762no—
218C2#1568902311yescharacteristic
219C2#1568911812yes—
220C2#1568947912yes—
221C2#1568950411yescharacteristic
222C2#1568950811yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47#1958
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×#13093948C2semidirect
5. C2×C8×Dic47C2semidirect
6. #15688988C2semidirect
7. C2×#103×C47C2semidirect
11. #13094013C4semidirect
114. C2×#103D47semidirect
119. C47#1958semidirect