Finite Group Databasebeta

← #20243218

Subgroups — #20243218

Order 6016.

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

normal subgroups only

This group has 324 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×#13093948C212yesmaximal
2C2×#13093935C211yesmaximal, characteristic
3C4×C4⋊Dic47C211yesmaximal, characteristic
4#15688885C212yesmaximal
5C2×C4×Q8×C47C211yesmaximal, characteristic
6C22×C47⋊C8C2212yes—
7C2×C4⋊Dic47C2212yes—
8C2×C4×Dic47—21no—
9#13093948C418yescomplemented
10#13093935—22no—
11C47⋊#95—21no—
12C22×Q8×C47C2211yescharacteristic
13C4×Q8×C47—22no—
14C4×Q8×C47C414yescomplemented
15C2×C4⋊C4×C47—21no—
16C2×C4⋊C4×C47C2211yescharacteristic
17C2×C42×C47—21no—
18C2×C42×C47C2211yescharacteristic
19C2×Q8×C47—21no—
20C2×Q8×C47—22no—
21C2×Q8×C47C2×C414yes—
22C2×Q8×C47C2×C412yes—
23C22×C4×C47—21no—
24C22×C4×C47—21no—
25C22×C4×C47D411yescharacteristic
26C22×C4×C47D411yescharacteristic
27C22×C4×C47C2311yescharacteristic
28C22×Dic47—22no—
29C4⋊C4×C47—24no—
30C4⋊C4×C47—21no—
31C4⋊C4×C47C2×C412yes—
32C42×C47—24no—
33C42×C47C2×C412yes—
34C42×C47D412yes—
35C4⋊Dic47—22no—
36C4⋊Dic47C2×C414yes—
37C4×Dic47—42no—
38C2×C47⋊C8—22no—
39C2×C47⋊C8—22no—
40C2×C47⋊C8C2×C414yes—
41C23×C47C2×D411yescharacteristic
42Q8×C47—22no—
43Q8×C47—24no—
44Q8×C47C4214yescomplemented
45C2×C4×C47—22no—
46C2×C4×C47—24no—
47C2×C4×C47—21no—
48C2×C4×C47—21no—
49C2×C4×C47—22no—
50C2×C4×C47—22no—
51C2×C4×C47—41no—
52C2×C4×C47—41no—
53C2×C4×C47C22⋊C412yes—
54C2×C4×C47C22⋊C412yes—
55C2×C4×C47C22×C412yes—
56C2×C4×C47C22×C411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47#4112yes—
59C2×Dic47—24no—
60C2×Dic47—42no—
61C2×Dic47—42no—
62C47⋊C8—24no—
63C22×C47C2×C22⋊C411yescharacteristic
64C22×C47C4×D412yes—
65C22×C47AGL(1,ℤ/8)11yescharacteristic
66C22×C47#13711yescharacteristic
67C22×C47#13712yes—
68C4×C47—24no—
69C4×C47—22no—
70C4×C47—22no—
71C4×C47—42no—
72C4×C47C2×C4211yescharacteristic
73C4×C47#11711yescharacteristic
74C4×C47C4×D412yes—
75Dic47—44no—
76#1763—471nomaximal, Sylow
77C2×C47C4×C22⋊C411yescharacteristic
78C2×C47#41711yescharacteristic
79C2×C47#41911yescharacteristic
80C2×C47#44012yes—
81C2×C47#44112yes—
82C2×C4×Q8D4711yescharacteristic
83C2×#103—472no—
84C2×#97—471no—
85C4×C4⋊C4—471no—
86#340—472no—
87C47#176311yescharacteristic, complemented, Sylow
88C22×Q8C2×D4711yescharacteristic
89C22×C8—472no—
90C4×Q8—22no—
91C4×Q8Dic4714yescomplemented
92C2×C4⋊C4—21no—
93C2×C4⋊C4—472no—
94C2×C4⋊C4C2×D4711yescharacteristic
95C2×C42—21no—
96C2×C42—941no—
97C2×C42C2×D4711yescharacteristic
98#103—478no—
99#97—942no—
100#95—941no—
101C2×Q8—22no—
102C2×Q8—21no—
103C2×Q8C4×D4714yes—
104C2×Q8C2×Dic4712yes—
105C22×C4—21no—
106C22×C4—21no—
107C22×C4—942no—
108C22×C4C22⋊D4711yescharacteristic
109C22×C4C22⋊D4711yescharacteristic
110C22×C4C22×D4711yescharacteristic
111C2×C8—474no—
112C2×C8—942no—
113C2×C8—942no—
114C4⋊C4—24no—
115C4⋊C4—21no—
116C4⋊C4—474no—
117C4⋊C4—942no—
118C4⋊C4C2×Dic4712yes—
119C42—24no—
120C42—1882no—
121C42C2×Dic4712yes—
122C42C22⋊D4712yes—
123C23C2×C22⋊D4711yescharacteristic
124Q8—22no—
125Q8—24no—
126Q8C4×Dic4714yescomplemented
127C2×C4—22no—
128C2×C4—24no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—944no—
136C2×C4—1882no—
137C2×C4—1882no—
138C2×C4C22⋊Dic4712yes—
139C2×C4C22⋊Dic4712yes—
140C2×C4C2×C4×D4712yes—
141C2×C4#1062535012yes—
142C2×C4C22×Dic4711yescharacteristic
143C2×C4C2×C22⋊D4711yescharacteristic
144C8—944no—
145C22C2×C22⋊Dic4711yescharacteristic
146C22C4×C22⋊D4712yes—
147C22#1309404911yescharacteristic
148C22#1309405411yescharacteristic
149C22#1309405512yes—
150C4—24no—
151C4—22no—
152C4—22no—
153C4—42no—
154C4—1884no—
155C4C2×C4×Dic4711yescharacteristic
156C4#1309398311yescharacteristic
157C4C4×C22⋊D4712yes—
158C2C4×C22⋊Dic4711yescharacteristic
159C2#1568912411yescharacteristic
160C2#1568913211yescharacteristic
161C2#1568922112yes—
162C2#1568922812yes—
subgroupG/H
centerC23C2×C22⋊D47
commutatorC4×C47C2×C42
FrattiniC22×C4C22×D47
FittingC2×C4×Q8×C47C2
socleC23×C47C2×D4
hypercenterC2×C4×Q8D47
hypocenterC47#1763
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
9. #13093948C4semidirect
14. C4×Q8×C47C4semidirect
44. Q8×C47C42semidirect
87. C47#1763semidirect
91. C4×Q8Dic47semidirect
126. Q8C4×Dic47semidirect