Finite Group Databasebeta

← #20249265

Subgroups — #20249265

Order 6016.

416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×C4×Dic94C211yesmaximal, characteristic
2#15689062C212yesmaximal
3#15689061C212yesmaximal
4#15689054C212yesmaximal
5#15689043C212yesmaximal
6#15689004C214yesmaximal
7#15688991C211yesmaximal, characteristic
8C2×#125×C47C211yesmaximal, characteristic
9C22×Dic94C2211yescharacteristic
10C4×Dic94—24no—
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4C2214yes—
13C2×Dic47⋊C4C2212yes—
14C2×C4×Dic47C2212yes—
15C47⋊#95C2212yes—
16C47⋊#95C2212yes—
17C47⋊#95C2212yes—
18C47⋊#95C2214yes—
19C47⋊#95C2214yes—
20C47⋊#95C2214yes—
21#125×C47—24no—
22C2×C4⋊C4×C47C2212yes—
23C2×C4⋊C4×C47C2212yes—
24C2×C4⋊C4×C47C2211yescharacteristic
25C2×C4⋊C4×C47C2211yescharacteristic
26C2×C42×C47C2211yescharacteristic
27C22×C4×C47C2312yes—
28C22×C4×C47C2312yes—
29C22×C4×C47C2311yescharacteristic
30C22×C4×C47C2311yescharacteristic
31C22×C4×C47C2311yescharacteristic
32C22×Dic47C2314yes—
33C22×Dic47C2312yes—
34C22×Dic47C2312yes—
35C2×Dic94—22no—
36C2×Dic94—24no—
37C4⋊C4×C47—24no—
38C4⋊C4×C47—22no—
39C4⋊C4×C47—22no—
40C4⋊C4×C47—24no—
41C42×C47D414yes—
42C4⋊Dic47—22no—
43Dic47⋊C4—24no—
44Dic47⋊C4—28no—
45C4×Dic47—24no—
46C23×C47C2411yescharacteristic
47C2×C4×C47—22no—
48C2×C4×C47—22no—
49C2×C4×C47—22no—
50C2×C4×C47—22no—
51C2×C4×C47—22no—
52C2×C4×C47—24no—
53C2×C4×C47—24no—
54C2×C4×C47C2×D412yes—
55C2×C4×C47C2×D412yes—
56C2×C4×C47C2×D412yes—
57C2×Dic47—22no—
58C2×Dic47—22no—
59C2×Dic47—22no—
60C2×Dic47—24no—
61C2×Dic47—24no—
62C2×Dic47—24no—
63C2×Dic47—24no—
64C2×Dic47#4114yes—
65Dic94—28no—
66C22×C47C22×D411yescharacteristic
67C22×C47C2×#4112yes—
68C22×C472−1+412yes—
69C22×C472−1+412yes—
70C4×C47—22no—
71C4×C47—22no—
72C4×C47—22no—
73C4×C47—42no—
74C4×C47—42no—
75Dic47—24no—
76Dic47—42no—
77Dic47—44no—
78#2634—471nomaximal, Sylow
79C2×C47#52511yescharacteristic
80C2×C47#53611yescharacteristic
81C2×C47#53611yescharacteristic
82C2×C47#54114yes—
83C2×#125D4711yescharacteristic
84C2×C4×Q8—471no—
85#400—472no—
86#400—472no—
87#398—472no—
88#395—472no—
89#387—474no—
90#383—471no—
91C47#263411yescharacteristic, complemented, Sylow
92C22×Q8—471no—
93#125—24no—
94C4×Q8—944no—
95C2×C4⋊C4—472no—
96C2×C4⋊C4—471no—
97C2×C4⋊C4—474no—
98C2×C4⋊C4C2×D4712yes—
99C2×C4⋊C4C2×D4712yes—
100C2×C4⋊C4C2×D4711yescharacteristic
101C2×C4⋊C4C2×D4711yescharacteristic
102C2×C42—472no—
103C2×C42C2×D4711yescharacteristic
104#95—472no—
105#95—472no—
106#95—472no—
107#95—474no—
108#95—474no—
109#95—474no—
110C2×Q8—944no—
111C2×Q8—942no—
112C22×C4—472no—
113C22×C4—474no—
114C22×C4—472no—
115C22×C4C22×D4712yes—
116C22×C4C22×D4712yes—
117C22×C4C22×D4711yescharacteristic
118C22×C4C22×D4711yescharacteristic
119C22×C4C22×D4711yescharacteristic
120C4⋊C4—24no—
121C4⋊C4—22no—
122C4⋊C4—22no—
123C4⋊C4—24no—
124C4⋊C4—948no—
125C4⋊C4—944no—
126C4⋊C4—942no—
127C42—944no—
128C42C22⋊D4714yes—
129C23C23×D4711yescharacteristic
130Q8—948no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—24no—
137C2×C4—24no—
138C2×C4—474no—
139C2×C4—942no—
140C2×C4—942no—
141C2×C4—942no—
142C2×C4—944no—
143C2×C4—944no—
144C2×C4—944no—
145C2×C4—944no—
146C2×C4C2×C22⋊D4712yes—
147C2×C4C2×C22⋊D4712yes—
148C2×C4C2×C22⋊D4712yes—
149C22C22×C22⋊D4711yescharacteristic
150C22#41×D4712yes—
151C22#1309407112yes—
152C22#1309407212yes—
153C4—22no—
154C4—22no—
155C4—22no—
156C4—42no—
157C4—42no—
158C4—944no—
159C4—1884no—
160C4—1882no—
161C2#1568963011yescharacteristic
162C2#1568969411yescharacteristic
163C2#1568969711yescharacteristic
164C2#1568973214yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#125×C47C2
hypercenterC2×#125D47
hypocenterC47#2634
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
91. C47#2634semidirect