Finite Group Databasebeta

← #20254130

Subgroups — #20254130

Order 6016.

358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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
1#15689677C212yesmaximal
2#15689520C211yesmaximal, characteristic, complemented
3#15689501C211yesmaximal, characteristic, complemented
4#15689472C212yesmaximal, complemented
5#15689382C211yesmaximal, characteristic
6#15689380C212yesmaximal
7#15689378C211yesmaximal, characteristic
8#15689231C211yesmaximal, characteristic, complemented
9#15689228C212yesmaximal, complemented
10#15689075C211yesmaximal, characteristic
11C47×#441C211yesmaximal, characteristic, complemented
12C2×Dic188C2211yescharacteristic
13C2×#10625337C2212yes—
14C2×#10625324C2211yescharacteristic
15C2×#10625324C2211yescharacteristic
16#13094023C2212yes—
17#13094022C2212yes—
18#13094014—22no—
19#13094004C2212yes—
20#13094002—22no—
21#13094000C2212yes—
22C4×Dic94—22no—
23C4×Dic94C2212yes—
24#13093981—22no—
25C42×D47C2211yescharacteristic
26#13093956C2211yescharacteristic
27#13093955C2212yes—
28#13093949C2212yes—
29#13093948C2212yes—
30#13093947C2212yes—
31#13093935C2211yescharacteristic
32C8×Dic47C2211yescharacteristic
33C8×Dic47C2211yescharacteristic
34C2×Q16×C47C2211yescharacteristic
35C4×Q8×C47C2212yes—
36#106×C47C2211yescharacteristic
37#103×C47C2212yes—
38#97×C47C2211yescharacteristic
39C2×Q8×C47C2312yes—
40C2×C4×D47D412yes—
41C2×C4×D47C2311yescharacteristic
42C2×Dic94—22no—
43C2×Dic94C2312yes—
44Q16×C47—22no—
45C2×C8×C47C2311yescharacteristic
46C2×C8×C47C2311yescharacteristic
47C4⋊C4×C47—22no—
48C4⋊C4×C47C2312yes—
49C42×C47—22no—
50C42×C47C2311yescharacteristic
51#10625337—24no—
52(C2×D47)⋊C4—22no—
53(C2×D47)⋊C4—22no—
54C4⋊Dic47—22no—
55C4⋊Dic47C2312yes—
56Dic47⋊C4—22no—
57Dic47⋊C4—22no—
58Dic47⋊C4—22no—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61C4×Dic47—22no—
62C4×Dic47D412yes—
63C4×Dic47C2311yescharacteristic
64C2×C47⋊C8C2311yescharacteristic
65C2×C47⋊C8C2311yescharacteristic
66Dic188—22no—
67#10625324—22no—
68#10625324—22no—
69C22×D47C2×D411yescharacteristic
70Q8×C47—22no—
71Q8×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47C2×D412yes—
75C2×C4×C47C2411yescharacteristic
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47C2×D411yescharacteristic
79C2×Dic47C2×D412yes—
80C4×D47—21no—
81C4×D47—21no—
82C4×D47—24no—
83Dic94—22no—
84Dic94—22no—
85Dic94—44no—
86C8×C47—21no—
87C8×C47#4112yes—
88C47⋊C8—21no—
89C47⋊C8#4112yes—
90C22×C47C22×D411yescharacteristic
91C2×D47—21no—
92C2×D47—22no—
93C4×C47—22no—
94C4×C47—42no—
95C4×C47—42no—
96C4×C47C2×#4111yescharacteristic
97C4×C47C2×#4111yescharacteristic
98Dic47—21no—
99Dic47—42no—
100Dic47—42no—
101Dic47#13714yes—
102#3185—471nomaximal, Sylow
103C2×C47#53211yescharacteristic
104C2×C47C2×#13712yes—
105D47—41no—
106#533—472no—
107#498—471no—
108#494—471no—
109#487—472no—
110#470—471no—
111#470—471no—
112#470—472no—
113#441—472no—
114#441—471no—
115#441D4711yescharacteristic, complemented
116C4×M16—471no—
117C47#318511yescharacteristic, complemented, Sylow
118C2×Q16—472no—
119C2×Q16—471no—
120C2×Q16C2×D4711yescharacteristic
121C2×M16—471no—
122C2×M16—471no—
123C4⋊Q8—472no—
124C4⋊Q8—472no—
125#125—942no—
126C22⋊Q8—472no—
127C22⋊Q8—472no—
128C22⋊Q8—942no—
129C4×Q8—472no—
130C4×Q8—942no—
131C4×Q8C2×D4712yes—
132#117—942no—
133C2×C42—471no—
134#106—471no—
135#106—472no—
136#106C2×D4711yescharacteristic
137#103—472no—
138#103—472no—
139#103—472no—
140#103C2×D4712yes—
141#97—471no—
142#97C2×D4711yescharacteristic
143C4×C8—471no—
144C4×C8—471no—
145C2×Q8—472no—
146C2×Q8—942no—
147C2×Q8C22×D4712yes—
148C22×C4—472no—
149C22×C4—471no—
150Q16—22no—
151Q16—944no—
152Q16—942no—
153M16—942no—
154M16—942no—
155C2×C8—471no—
156C2×C8—471no—
157C2×C8C22×D4711yescharacteristic
158C2×C8C22×D4711yescharacteristic
159C4⋊C4—22no—
160C4⋊C4—472no—
161C4⋊C4—942no—
162C4⋊C4—942no—
163C4⋊C4—942no—
164C4⋊C4—942no—
165C4⋊C4—942no—
166C4⋊C4—942no—
167C4⋊C4C22×D4712yes—
168C22⋊C4—942no—
169C22⋊C4—942no—
170C42—22no—
171C42—472no—
172C42—471no—
173C42—942no—
174C42C22×D4711yescharacteristic
175C23—471no—
176Q8—22no—
177Q8—22no—
178Q8—942no—
179Q8—942no—
180Q8—1884no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—472no—
184C2×C4—471no—
185C2×C4—944no—
186C2×C4—941no—
187C2×C4—941no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4D4×D4712yes—
191C2×C4C23×D4711yescharacteristic
192C8—21no—
193C8—472no—
194C8—941no—
195C8#1062535012yes—
196C22—942no—
197C22—941no—
198C22C2×D4×D4711yescharacteristic
199C4—22no—
200C4—42no—
201C4—42no—
202C4—474no—
203C4—941no—
204C4—1882no—
205C4—1882no—
206C4#41×D4711yescharacteristic
207C4C2×#1062535011yescharacteristic
208C2—1881no—
209C2#1568967011yescharacteristic
210C2#137×D4712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#441C2
socleC22×C47C22×D4
hypercenter#441D47
hypocenterC47#3185
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. #15689520C2semidirect
3. #15689501C2semidirect
4. #15689472C2semidirect
8. #15689231C2semidirect
9. #15689228C2semidirect
11. C47×#441C2semidirect
115. #441D47semidirect
117. C47#3185semidirect