Finite Group Databasebeta

← #20243834

Subgroups — #20243834

Order 6016.

358 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 89 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#15689634C211yesmaximal, characteristic
2C2×#13093983C211yesmaximal, characteristic, complemented
3C2×#13093950C212yesmaximal, complemented
4#15688884C212yesmaximal, complemented
5C47×#407C211yesmaximal, characteristic, complemented
6C2×#10625350C2211yescharacteristic
7#13094007—21no—
8#13094003C412yescomplemented
9#13093998C412yescomplemented
10#13093993—21no—
11C4×C22⋊D47—22no—
12#13093983—24no—
13#13093983C2211yescharacteristic
14C2×C4⋊Dic47—21no—
15C2×C22⋊Dic47—21no—
16C2×C4×Dic47C2212yes—
17#13093950—24no—
18C23×C4×C47C2211yescharacteristic
19C2×M16×C47C2212yes—
20C22⋊C8×C47—22no—
21C24×C47D411yescharacteristic
22C22×C4×C47—22no—
23C22×C4×C47—22no—
24C22×C4×C47C2×C412yes—
25C22×C4×C47D411yescharacteristic
26C22×C4×C47D412yes—
27C22×C4×C47C2311yescharacteristic
28C2×C22⋊D47—22no—
29C2×C22⋊D47—21no—
30C22×Dic47—22no—
31#10625350—22no—
32#10625350—22no—
33C2×D188C2×C411yescharacteristic
34C2×C4×D47—21no—
35C2×Dic94C2×C411yescharacteristic
36M16×C47—22no—
37M16×C47—22no—
38C2×C8×C47—22no—
39C22⋊Dic47—24no—
40C22⋊Dic47—22no—
41C22⋊Dic47—21no—
42(C2×D47)⋊C4—22no—
43C4⋊Dic47—24no—
44C4⋊Dic47C2×C412yes—
45Dic47⋊C4—22no—
46C4×Dic47—22no—
47C4×Dic47—21no—
48C4×Dic47D414yescomplemented
49C23×C47—21no—
50C23×C47—21no—
51C23×C47—42no—
52C23×C47C22⋊C412yes—
53C23×C47C2×D411yescharacteristic
54C22×D47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—24no—
58C2×C4×C47—24no—
59C2×C4×C47C22⋊C412yes—
60C2×C4×C47C22×C411yescharacteristic
61C2×C4×C47C2×D412yes—
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47#4112yes—
64C22⋊D47—44no—
65C22⋊D47—41no—
66C22⋊D47—41no—
67C2×Dic47—22no—
68C2×Dic47—21no—
69C2×Dic47—24no—
70C2×Dic47—44no—
71D188—22no—
72C4×D47—42no—
73Dic94—22no—
74C8×C47—42no—
75C22×C47—22no—
76C22×C47—22no—
77C22×C47—22no—
78C22×C47—22no—
79C22×C47—42no—
80C22×C47—42no—
81C22×C47C2×C22⋊C411yescharacteristic
82C22×C47#12011yescharacteristic
83C22×C47#12311yescharacteristic
84C2×D47—41no—
85C2×D47—42no—
86C4×C47—22no—
87C4×C47C4×D412yes—
88C4×C47#12112yes—
89Dic47—44no—
90Dic47—41no—
91Dic47—42no—
92#1897—471nomaximal, Sylow
93C2×C47—21no—
94C2×C47—21no—
95C2×C47—42no—
96C2×C47#38611yescharacteristic
97C2×C47#42112yes—
98D47—81no—
99#525—471no—
100C2×#117—471no—
101C2×#104—472no—
102#407D4711yescharacteristic, complemented
103#339—472no—
104C47#189711yescharacteristic, complemented, Sylow
105C2×#41—471no—
106C23×C4C2×D4711yescharacteristic
107C2×M16C2×D4712yes—
108#123—941no—
109C22⋊Q8—472no—
110#121—472no—
111#120—941no—
112C4×D4—942no—
113#117—471no—
114#117—944no—
115C2×C4⋊C4—941no—
116C2×C22⋊C4—941no—
117C2×C42—472no—
118#104—944no—
119C22⋊C8—22no—
120C24D18811yescharacteristic
121#41—942no—
122#41—942no—
123C2×Q8—471no—
124C2×D4—471no—
125C2×D4—942no—
126C2×D4—941no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—942no—
130C22×C4—941no—
131C22×C4C4×D4712yes—
132C22×C4D18811yescharacteristic
133C22×C4C22⋊D4712yes—
134C22×C4C22×D4711yescharacteristic
135M16—22no—
136M16—22no—
137C2×C8—22no—
138C4⋊C4—472no—
139C4⋊C4—944no—
140C4⋊C4—942no—
141C22⋊C4—944no—
142C22⋊C4—942no—
143C22⋊C4—941no—
144C22⋊C4—942no—
145C42—474no—
146C42—942no—
147C42—941no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—941no—
152C23(C2×D47)⋊C412yes—
153C23C2×D18811yescharacteristic
154Q8—942no—
155D4—942no—
156D4—1884no—
157D4—1881no—
158D4—1881no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—942no—
164C2×C4—941no—
165C2×C4—944no—
166C2×C4—1884no—
167C2×C4—1882no—
168C2×C4(C2×D47)⋊C412yes—
169C2×C4C2×C4×D4711yescharacteristic
170C2×C4D4×D4712yes—
171C2×C4#1062535212yes—
172C2×C4C2×C22⋊D4711yescharacteristic
173C8—42no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—1881no—
181C22—1882no—
182C22C2×(C2×D47)⋊C411yescharacteristic
183C22#1309399411yescharacteristic
184C22#1309400811yescharacteristic
185C4—22no—
186C4—1884no—
187C4—1881no—
188C4—1882no—
189C4(C22⋊D47)⋊C412yes—
190C4#1309399612yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—3761no—
195C2#1568900011yescharacteristic
196C2#1568913912yes—
subgroupG/H
centerC2×C4C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#407C2
socleC22×C47C2×C22⋊C4
hypercenter#407D47
hypocenterC47#1897
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#13093983C2semidirect
3. C2×#13093950C2semidirect
4. #15688884C2semidirect
5. C47×#407C2semidirect
8. #13094003C4semidirect
9. #13093998C4semidirect
48. C4×Dic47D4semidirect
102. #407D47semidirect
104. C47#1897semidirect