Finite Group Databasebeta

← #20253050

Subgroups — #20253050

Order 6016.

484 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13094046C211yesmaximal, characteristic, complemented
2#15689701C212yesmaximal, complemented
3#15689381C212yesmaximal, complemented
4#15689376C212yesmaximal, complemented
5#15689352C214yesmaximal, complemented
6C2×#13093956C211yesmaximal, characteristic, complemented
7#15689125C212yesmaximal, complemented
8C2×#131×C47C211yesmaximal, characteristic, complemented
9C2×#10625350C2212yes—
10#13094046—24no—
11C2×Dic188C2211yescharacteristic
12C2×#10625325C2212yes—
13C2×D376C2211yescharacteristic
14#13094003C2214yes—
15#13094000—22no—
16#13093998C2214yes—
17#13093996—24no—
18#13093995—22no—
19C2×C4⋊Dic47C2212yes—
20#13093956C2212yes—
21#13093956C2212yes—
22#13093949C2214yes—
23#13093946C2214yes—
24C2×#41×C47C2211yescharacteristic
25#131×C47—24no—
26C2×M16×C47C2212yes—
27C2×M16×C47C2211yescharacteristic
28C22×C8×C47C2212yes—
29C22×C8×C47C2211yescharacteristic
30#41×C47—22no—
31#41×C47—22no—
32C2×Q8×C47D411yescharacteristic
33C2×D4×C47D411yescharacteristic
34C2×D4×C47D412yes—
35C22×C4×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C2×C22⋊D47—22no—
38C2×C22⋊D47—24no—
39C22×Dic47—22no—
40#10625350—24no—
41#10625350—24no—
42C2×D188C2312yes—
43C2×C4×D47—22no—
44C2×Dic94C2312yes—
45M16×C47—22no—
46M16×C47—24no—
47C2×C8×C47—24no—
48C2×C8×C47D414yescomplemented
49C2×C8×C47C2312yes—
50C2×C8×C47C2311yescharacteristic
51C2×C8×C47C2311yescharacteristic
52C22⋊Dic47—24no—
53(C2×D47)⋊C4—24no—
54C4⋊Dic47—22no—
55C4⋊Dic47C2314yes—
56Dic47⋊C4—24no—
57Dic188—22no—
58D376—22no—
59#10625325—24no—
60C23×C47C2×D412yes—
61C23×C47C2×D411yescharacteristic
62C22×D47—22no—
63Q8×C47—22no—
64D4×C47—24no—
65D4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47C2×D412yes—
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D412yes—
71C2×C4×C47#4112yes—
72C2×C4×C47C2411yescharacteristic
73C22⋊D47—44no—
74C22⋊D47—84no—
75C2×Dic47—22no—
76C2×Dic47—24no—
77C2×Dic47—82no—
78D188—22no—
79D188—22no—
80C4×D47—44no—
81Dic94—22no—
82Dic94—22no—
83C8×C47—22no—
84C8×C47C2×D412yes—
85C8×C47C2×D412yes—
86C22×C47—22no—
87C22×C47—22no—
88C22×C47—24no—
89C22×C47#12112yes—
90C22×C47C22×D411yescharacteristic
91C2×D47—42no—
92C2×D47—42no—
93C2×D47—42no—
94C4×C47—22no—
95C4×C47#12112yes—
96C4×C47C22×D411yescharacteristic
97C4×C47C2×#4111yescharacteristic
98Dic47—42no—
99Dic47—44no—
100#3060—471nomaximal, Sylow
101C2×C47—22no—
102C2×C47—42no—
103C2×C47C2×#12111yescharacteristic
104C2×C47#57712yes—
105D47—82no—
106C2×#135—471no—
107C2×#131D4711yescharacteristic, complemented
108#537—472no—
109#470—472no—
110#469—472no—
111#465—474no—
112C2×#106—471no—
113#417—472no—
114C47#306011yescharacteristic, complemented, Sylow
115C2×#41—472no—
116C2×#41C2×D4711yescharacteristic
117#135—944no—
118C2×Q16—471no—
119C2×SD16—472no—
120C2×D8—471no—
121#131—24no—
122C2×M16C2×D4711yescharacteristic
123C2×M16C2×D4712yes—
124C22×C8C2×D4712yes—
125C22×C8C2×D4711yescharacteristic
126C22⋊Q8—474no—
127C22⋊Q8—942no—
128#121—474no—
129#121—942no—
130#121—944no—
131C2×C4⋊C4—472no—
132#106—472no—
133#106—472no—
134#103—474no—
135#102—474no—
136#41—22no—
137#41—22no—
138#41—944no—
139#41—944no—
140C2×Q8—472no—
141C2×Q8D18811yescharacteristic
142C2×D4—472no—
143C2×D4—944no—
144C2×D4—942no—
145C2×D4D18812yes—
146C2×D4D18811yescharacteristic
147C22×C4—942no—
148C22×C4—942no—
149C22×C4C22×D4712yes—
150C22×C4C22×D4711yescharacteristic
151Q16—942no—
152SD16—944no—
153D8—942no—
154M16—22no—
155M16—24no—
156C2×C8—24no—
157C2×C8C22⋊D4714yescomplemented
158C2×C8C22×D4712yes—
159C2×C8C22×D4711yescharacteristic
160C2×C8C22×D4711yescharacteristic
161C4⋊C4—474no—
162C4⋊C4—944no—
163C4⋊C4—942no—
164C22⋊C4—944no—
165C22⋊C4—944no—
166C23—942no—
167C23C2×D18812yes—
168C23C2×D18811yescharacteristic
169Q8—22no—
170Q8—942no—
171Q8—942no—
172D4—24no—
173D4—22no—
174D4—942no—
175D4—942no—
176D4—3764no—
177D4—1884no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—944no—
181C2×C4—942no—
182C2×C4—3762no—
183C2×C4—1884no—
184C2×C4C2×D18812yes—
185C2×C4C2×D18811yescharacteristic
186C2×C4#1062535012yes—
187C2×C4C2×C22⋊D4712yes—
188C2×C4C23×D4711yescharacteristic
189C8—22no—
190C8C2×C22⋊D4712yes—
191C8C2×C22⋊D4712yes—
192C22—22no—
193C22—22no—
194C22—24no—
195C22—1882no—
196C22—1882no—
197C22—1882no—
198C22#1309399812yes—
199C22C22×D18811yescharacteristic
200C4—22no—
201C4—1882no—
202C4—1884no—
203C4#1309399812yes—
204C4C22×C22⋊D4711yescharacteristic
205C4C2×#1062535011yescharacteristic
206C2—22no—
207C2—42no—
208C2—3762no—
209C2C2×#1309399811yescharacteristic
210C2#1568993512yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#131×C47C2
socleC22×C47C22×D4
hypercenterC2×#131D47
hypocenterC47#3060
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. C2×#13094046C2semidirect
2. #15689701C2semidirect
3. #15689381C2semidirect
4. #15689376C2semidirect
5. #15689352C2semidirect
6. C2×#13093956C2semidirect
7. #15689125C2semidirect
8. C2×#131×C47C2semidirect
48. C2×C8×C47D4semidirect
107. C2×#131D47semidirect
114. C47#3060semidirect
157. C2×C8C22⋊D47semidirect