Finite Group Databasebeta

← #20253046

Subgroups — #20253046

Order 6016.

484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13094030C211yesmaximal, characteristic, complemented
2#15689701C212yesmaximal, complemented
3#15689378C212yesmaximal, complemented
4#15689373C212yesmaximal, complemented
5#15689349C214yesmaximal, complemented
6C2×#13093956C211yesmaximal, characteristic, complemented
7#15689124C212yesmaximal, complemented
8C2×#135×C47C211yesmaximal, characteristic, complemented
9C2×#10625350C2211yescharacteristic
10#13094030—24no—
11C2×#10625329C2211yescharacteristic
12C2×#10625324C2212yes—
13C2×C8×D47C2212yes—
14#13094003—22no—
15#13094000C2214yes—
16#13093998—22no—
17#13093996—24no—
18#13093995C2214yes—
19C2×C4⋊Dic47C2212yes—
20#13093956C2212yes—
21#13093956C2212yes—
22#13093948C2214yes—
23#13093945C2214yes—
24C2×#41×C47C2212yes—
25#135×C47—24no—
26C2×Q16×C47C2211yescharacteristic
27C2×SD16×C47C2212yes—
28C2×D8×C47C2211yescharacteristic
29C22×C8×C47C2211yescharacteristic
30#41×C47—24no—
31#41×C47—24no—
32C2×Q8×C47C2312yes—
33C2×D4×C47—22no—
34C2×D4×C47C2312yes—
35C22×C4×C47—22no—
36C22×C4×C47C2311yescharacteristic
37C2×C22⋊D47—24no—
38C2×C22⋊D47D412yes—
39C22×Dic47—22no—
40#10625350—22no—
41#10625350—22no—
42C2×D188D411yescharacteristic
43C2×C4×D47C2312yes—
44C2×Dic94D411yescharacteristic
45Q16×C47—22no—
46SD16×C47—24no—
47D8×C47—22no—
48C2×C8×C47D414yescomplemented
49C2×C8×C47C2311yescharacteristic
50C2×C8×C47C2311yescharacteristic
51C22⋊Dic47—24no—
52(C2×D47)⋊C4—24no—
53C4⋊Dic47—22no—
54C4⋊Dic47C2314yes—
55Dic47⋊C4—24no—
56#10625329—22no—
57C2×C47⋊C8C2312yes—
58#10625324—24no—
59C8×D47—24no—
60C23×C47—22no—
61C23×C47C2×D411yescharacteristic
62C22×D47C2×D412yes—
63Q8×C47—22no—
64Q8×C47—22no—
65D4×C47—22no—
66D4×C47—22no—
67D4×C47—44no—
68C2×C4×C47—22no—
69C2×C4×C47—44no—
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D412yes—
72C2×C4×C47#4112yes—
73C2×C4×C47C2411yescharacteristic
74C22⋊D47—24no—
75C22⋊D47—84no—
76C2×Dic47—24no—
77C2×Dic47—82no—
78C2×Dic47C2×D412yes—
79D188—22no—
80C4×D47—22no—
81C4×D47—22no—
82Dic94—22no—
83C8×C47C2×D412yes—
84C8×C47C2×D412yes—
85C47⋊C8—22no—
86C22×C47—22no—
87C22×C47—42no—
88C22×C47—42no—
89C22×C47—42no—
90C22×C47#12112yes—
91C22×C47C22×D411yescharacteristic
92C2×D47—22no—
93C2×D47—24no—
94C4×C47—42no—
95C4×C47#12112yes—
96C4×C47C22×D411yescharacteristic
97C4×C47C2×#4111yescharacteristic
98Dic47—22no—
99Dic47—44no—
100#3060—471nomaximal, Sylow
101C2×C47—22no—
102C2×C47—82no—
103C2×C47C2×#12111yescharacteristic
104C2×C47#57712yes—
105D47—42no—
106C2×#135D4711yescharacteristic, complemented
107C2×#131—471no—
108#537—472no—
109#470—472no—
110#469—472no—
111#465—474no—
112C2×#106—471no—
113#417—472no—
114C47#306011yescharacteristic, complemented, Sylow
115C2×#41—471no—
116C2×#41C2×D4712yes—
117#135—24no—
118C2×Q16C2×D4711yescharacteristic
119C2×SD16C2×D4712yes—
120C2×D8C2×D4711yescharacteristic
121#131—944no—
122C2×M16—471no—
123C2×M16—472no—
124C22×C8—472no—
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—24no—
137#41—24no—
138#41—942no—
139#41—942no—
140C2×Q8—471no—
141C2×Q8C22×D4712yes—
142C2×D4—22no—
143C2×D4—472no—
144C2×D4—471no—
145C2×D4—944no—
146C2×D4C22×D4712yes—
147C22×C4—22no—
148C22×C4—472no—
149C22×C4—942no—
150C22×C4C22×D4711yescharacteristic
151Q16—22no—
152SD16—24no—
153D8—22no—
154M16—942no—
155M16—944no—
156C2×C8—472no—
157C2×C8—944no—
158C2×C8C22⋊D4714yescomplemented
159C2×C8C22×D4711yescharacteristic
160C2×C8C22×D4711yescharacteristic
161C4⋊C4—474no—
162C4⋊C4—944no—
163C4⋊C4—942no—
164C22⋊C4—944no—
165C22⋊C4—944no—
166C23—22no—
167C23—472no—
168C23D4×D4711yescharacteristic
169Q8—22no—
170Q8—22no—
171Q8—942no—
172D4—22no—
173D4—22no—
174D4—44no—
175D4—944no—
176D4—942no—
177D4—3764no—
178C2×C4—22no—
179C2×C4—44no—
180C2×C4—472no—
181C2×C4—942no—
182C2×C4—942no—
183C2×C4—944no—
184C2×C4—3762no—
185C2×C4D4×D4711yescharacteristic
186C2×C4#1062535212yes—
187C2×C4C2×C22⋊D4712yes—
188C2×C4C23×D4711yescharacteristic
189C8—942no—
190C8C2×C22⋊D4712yes—
191C8C2×C22⋊D4712yes—
192C22—22no—
193C22—42no—
194C22—42no—
195C22—42no—
196C22—942no—
197C22—944no—
198C22#1309399512yes—
199C22C2×D4×D4711yescharacteristic
200C4—42no—
201C4—942no—
202C4—1884no—
203C4#1309399512yes—
204C4C22×C22⋊D4711yescharacteristic
205C4C2×#1062535211yescharacteristic
206C2—22no—
207C2—82no—
208C2—1882no—
209C2C2×#1309399511yescharacteristic
210C2#1568993012yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#135×C47C2
socleC22×C47C22×D4
hypercenterC2×#135D47
hypocenterC47#3060
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#13094030C2semidirect
2. #15689701C2semidirect
3. #15689378C2semidirect
4. #15689373C2semidirect
5. #15689349C2semidirect
6. C2×#13093956C2semidirect
7. #15689124C2semidirect
8. C2×#135×C47C2semidirect
48. C2×C8×C47D4semidirect
106. C2×#135D47semidirect
114. C47#3060semidirect
158. C2×C8C22⋊D47semidirect