Finite Group Databasebeta

← #20244685

Subgroups — #20244685

Order 6016.

262 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 67 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×#13094054C211yesmaximal, characteristic
2C2×#13093959C211yesmaximal, characteristic, complemented
3C2×#13093947C211yesmaximal, characteristic, complemented
4C2×#13093942C211yesmaximal, characteristic, complemented
5#15689090C211yesmaximal, characteristic
6#15688892C211yesmaximal, characteristic, complemented
7C47×#417C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9#13094054—22no—
10#13094054—22no—
11C2×#10625337—21no—
12C2×#10625335—21no—
13C2×#10625329C2211yescharacteristic
14C2×#10625329C2211yescharacteristic
15C22×C47⋊C8C2211yescharacteristic
16#13093959—22no—
17#13093947—22no—
18#13093942—22no—
19C22⋊(C47⋊C8)—22no—
20C2×#41×C47C2211yescharacteristic
21C2×M16×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23#103×C47—21no—
24#102×C47—21no—
25#41×C47—21no—
26#41×C47—21no—
27#41×C47—21no—
28#41×C47—21no—
29C2×Q8×C47D411yescharacteristic
30C2×D4×C47—21no—
31C2×D4×C47D411yescharacteristic
32C22×C4×C47—21no—
33C22×C4×C47—21no—
34C22×C4×C47C2311yescharacteristic
35C22×Dic47—21no—
36C2×Dic94—21no—
37C2×Dic94—21no—
38C2×Dic94—21no—
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94D412yes—
42M16×C47—21no—
43M16×C47—21no—
44C2×C8×C47—21no—
45C4⋊C4×C47—21no—
46C4⋊C4×C47—21no—
47#10625337—24no—
48#10625335—24no—
49#10625329—21no—
50#10625329—21no—
51#10625329—21no—
52#10625329D412yes—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8D412yes—
58C23×C47—21no—
59C23×C47#4111yescharacteristic
60Q8×C47—21no—
61Q8×C47—21no—
62D4×C47—21no—
63D4×C47—21no—
64D4×C47—41no—
65D4×C47—41no—
66C2×C4×C47—21no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47—81no—
71C2×C4×C47C2×D411yescharacteristic
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—41no—
79C2×Dic47—41no—
80Dic94—22no—
81Dic94—22no—
82Dic94—41no—
83Dic94—41no—
84C8×C47—41no—
85C47⋊C8—22no—
86C47⋊C8—22no—
87C47⋊C8—41no—
88C22×C47—21no—
89C22×C47—21no—
90C22×C47—41no—
91C22×C47—41no—
92C22×C47—41no—
93C22×C47#12111yescharacteristic
94C22×C47#12311yescharacteristic
95C22×C47#12411yescharacteristic
96C4×C47—41no—
97C4×C47—81no—
98C4×C47#12011yescharacteristic
99C4×C47#12111yescharacteristic
100C4×C47#12111yescharacteristic
101C4×C47#12311yescharacteristic
102Dic47—42no—
103#2052—471nomaximal, Sylow
104C2×C47—21no—
105C2×C47—21no—
106C2×C47—81no—
107C2×C47#39411yescharacteristic
108C2×C47#47111yescharacteristic
109C2×C47#47311yescharacteristic
110C2×#137—471no—
111C2×#108—471no—
112#417D4711yescharacteristic
113C2×#103—471no—
114C2×#101—471no—
115#408—471no—
116#343—471no—
117C47#205211yescharacteristic, complemented, Sylow
118C2×#41C2×D4711yescharacteristic
119C22×Q8—471no—
120#137—942no—
121#137—942no—
122C2×Q16—941no—
123C2×SD16—941no—
124C2×M16—471no—
125C2×M16—471no—
126C2×M16C2×D4711yescharacteristic
127C22×C8—471no—
128C2×C4⋊C4C2×D4711yescharacteristic
129#108—942no—
130#103—21no—
131#103—942no—
132#102—21no—
133#101—942no—
134C22⋊C8—942no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—472no—
140C2×Q8—941no—
141C2×Q8—941no—
142C2×Q8—941no—
143C2×Q8—941no—
144C2×Q8—941no—
145C2×Q8C22⋊D4711yescharacteristic
146C2×D4—21no—
147C2×D4C22⋊D4711yescharacteristic
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—941no—
151C22×C4C22×D4711yescharacteristic
152Q16—944no—
153SD16—944no—
154M16—21no—
155M16—21no—
156M16—472no—
157M16—941no—
158M16—941no—
159M16—941no—
160C2×C8—21no—
161C2×C8—472no—
162C2×C8—941no—
163C2×C8—941no—
164C2×C8—941no—
165C2×C8—941no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C23—21no—
169C23#1062535211yescharacteristic
170Q8—21no—
171Q8—21no—
172Q8—942no—
173Q8—942no—
174Q8—1881no—
175Q8—1881no—
176D4—21no—
177D4—21no—
178D4—41no—
179D4—41no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—942no—
186C2×C4—1881no—
187C2×C4—1881no—
188C2×C4#1062535011yescharacteristic
189C2×C4#1062535011yescharacteristic
190C2×C4D4×D4711yescharacteristic
191C2×C4D4×D4711yescharacteristic
192C2×C4D4×D4711yescharacteristic
193C2×C4C2×C22⋊D4711yescharacteristic
194C8—41no—
195C8—942no—
196C8—942no—
197C8—1881no—
198C22—21no—
199C22—21no—
200C22—41no—
201C22—41no—
202C22—41no—
203C22#1309399611yescharacteristic
204C22#1309400611yescharacteristic
205C22#1309401011yescharacteristic
206C4—41no—
207C4—81no—
208C4—1882no—
209C4#1309399211yescharacteristic
210C4#1309399711yescharacteristic
211C4#1309399711yescharacteristic
212C4#1309400711yescharacteristic
213C2—21no—
214C2—21no—
215C2—81no—
216C2#1568903811yescharacteristic
217C2#1568938411yescharacteristic
218C2#1568939611yescharacteristic
subgroupG/H
centerC22#13093996
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#417C2
socleC22×C47#121
hypercenter#417D47
hypocenterC47#2052
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#13093959C2semidirect
3. C2×#13093947C2semidirect
4. C2×#13093942C2semidirect
6. #15688892C2semidirect
117. C47#2052semidirect