Finite Group Databasebeta

← #20241722

Subgroups — #20241722

Order 6016.

252 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 85 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#15689180C212yesmaximal, complemented
2#15688849C212yesmaximal, complemented
3#15688847C212yesmaximal
4C2×#117×C47C211yesmaximal, characteristic
5C4⋊(C47⋊C8)—22no—
6C22⋊(C47⋊C8)C2214yes—
7#13093935—22no—
8C23×C4×C47C411yescharacteristic
9#117×C47—22no—
10#117×C47—22no—
11C2×C4⋊C4×C47C411yescharacteristic
12C2×C4⋊C4×C47C2211yescharacteristic
13C2×C22⋊C4×C47C411yescharacteristic
14C2×C22⋊C4×C47C2211yescharacteristic
15C2×C42×C47C411yescharacteristic
16C2×C42×C47C2211yescharacteristic
17C24×C47C2×C411yescharacteristic
18C22×C4×C47—22no—
19C22×C4×C47—21no—
20C22×C4×C47—21no—
21C22×C4×C47—22no—
22C22×C4×C47C2×C411yescharacteristic
23C22×C4×C47C2×C411yescharacteristic
24C22×C4×C47C2×C411yescharacteristic
25C22×C4×C47C2×C411yescharacteristic
26C22×C4×C47C2×C411yescharacteristic
27C22×C4×C47C2311yescharacteristic
28C4⋊C4×C47—22no—
29C4⋊C4×C47—22no—
30C22⋊C4×C47—22no—
31C22⋊C4×C47—22no—
32C42×C47—21no—
33C42×C47—21no—
34C42×C47D412yes—
35C42×C47D412yes—
36C2×C47⋊C8—24no—
37C23×C47—21no—
38C23×C47—21no—
39C23×C47—41no—
40C23×C47—41no—
41C23×C47M1612yes—
42C23×C47C22×C411yescharacteristic
43C2×C4×C47—24no—
44C2×C4×C47—24no—
45C2×C4×C47—21no—
46C2×C4×C47—21no—
47C2×C4×C47—21no—
48C2×C4×C47—21no—
49C2×C4×C47—21no—
50C2×C4×C47—21no—
51C2×C4×C47—41no—
52C2×C4×C47—41no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47C22⋊C411yescharacteristic
56C2×C4×C47C22⋊C411yescharacteristic
57C2×C4×C47C22⋊C412yes—
58C2×C4×C47M1612yes—
59C2×C4×C47C2×D412yes—
60C47⋊C8—44no—
61C22×C47—21no—
62C22×C47—21no—
63C22×C47—22no—
64C22×C47—42no—
65C22×C47—42no—
66C22×C47—41no—
67C22×C47—41no—
68C22×C47C2×C22⋊C411yescharacteristic
69C22×C47C2×M1611yescharacteristic
70C22×C47C2×M1611yescharacteristic
71C4×C47—21no—
72C4×C47—21no—
73C4×C47—22no—
74C4×C47—22no—
75C4×C47—22no—
76C4×C47—41no—
77C4×C47—41no—
78#1464—471nomaximal, Sylow
79C2×C47—21no—
80C2×C47—21no—
81C2×C47—42no—
82C2×C47#40711yescharacteristic
83C2×C47#41011yescharacteristic
84C2×C47#41311yescharacteristic
85C2×#117D4711yescharacteristic
86#432—472no—
87#324—472no—
88#323—472no—
89C47#146411yescharacteristic, complemented, Sylow
90C23×C4Dic4711yescharacteristic
91#117—22no—
92#117—22no—
93C2×C4⋊C4Dic4711yescharacteristic
94C2×C4⋊C4C2×D4711yescharacteristic
95C2×C22⋊C4Dic4711yescharacteristic
96C2×C22⋊C4C2×D4711yescharacteristic
97C2×C42Dic4711yescharacteristic
98C2×C42C2×D4711yescharacteristic
99C4⋊C8—942no—
100C22⋊C8—474no—
101#97—942no—
102C24C2×Dic4711yescharacteristic
103C22×C4—22no—
104C22×C4—22no—
105C22×C4—21no—
106C22×C4—21no—
107C22×C4C2×Dic4711yescharacteristic
108C22×C4C2×Dic4711yescharacteristic
109C22×C4C2×Dic4711yescharacteristic
110C22×C4C2×Dic4711yescharacteristic
111C22×C4C2×Dic4711yescharacteristic
112C22×C4C22×D4711yescharacteristic
113C2×C8—944no—
114C4⋊C4—22no—
115C4⋊C4—22no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C42—21no—
119C42—21no—
120C42C22⋊D4712yes—
121C42C22⋊D4712yes—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23#1062532912yes—
127C23C22×Dic4711yescharacteristic
128C2×C4—24no—
129C2×C4—24no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4#1062532912yes—
141C2×C4C22⋊Dic4711yescharacteristic
142C2×C4C22⋊Dic4711yescharacteristic
143C2×C4C22⋊Dic4712yes—
144C2×C4C2×C22⋊D4712yes—
145C8—1884no—
146C22—21no—
147C22—21no—
148C22—22no—
149C22—42no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22C2×C22⋊Dic4711yescharacteristic
154C22C2×#1062532911yescharacteristic
155C22C2×#1062532911yescharacteristic
156C4—22no—
157C4—21no—
158C4—21no—
159C4—22no—
160C4—22no—
161C4—41no—
162C4—41no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#1568908711yescharacteristic
167C2#1568909711yescharacteristic
168C2#1568910711yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic47
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#117×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×#117D47
hypocenterC47#1464
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #15689180C2semidirect
2. #15688849C2semidirect
89. C47#1464semidirect