Finite Group Databasebeta

← #20241721

Subgroups — #20241721

Order 6016.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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×#13093982C211yesmaximal, characteristic
2#15689177C212yesmaximal, complemented
3#15688849C211yesmaximal, characteristic, complemented
4#15688846C212yesmaximal
5C47×#324C211yesmaximal, characteristic, complemented
6C22×C4×D47C411yescharacteristic
7#13093982—22no—
8#13093982—22no—
9C2×C4⋊Dic47C411yescharacteristic
10C2×(C2×D47)⋊C4C411yescharacteristic
11C2×(C2×D47)⋊C4C2211yescharacteristic
12C2×C4×Dic47C411yescharacteristic
13C2×C4×Dic47C2211yescharacteristic
14Dic47⋊C8—22no—
15C22⋊(C47⋊C8)C2212yes—
16#13093934—22no—
17C2×C4⋊C4×C47C2211yescharacteristic
18C22⋊C8×C47C2212yes—
19C23×D47C2×C411yescharacteristic
20C22×C4×C47C2×C411yescharacteristic
21C22×C4×C47C2×C411yescharacteristic
22C22×C4×C47C2311yescharacteristic
23C22×Dic47C2×C411yescharacteristic
24C22×Dic47C2×C411yescharacteristic
25C22×Dic47C2×C411yescharacteristic
26C2×C4×D47—22no—
27C2×C4×D47—22no—
28C2×C4×D47—21no—
29C2×C4×D47—21no—
30C2×C8×C47—22no—
31C4⋊C4×C47—22no—
32(C2×D47)⋊C4—22no—
33(C2×D47)⋊C4—22no—
34C4⋊Dic47—22no—
35C4×Dic47—21no—
36C4×Dic47—21no—
37C4×Dic47D412yes—
38C4×Dic47D412yes—
39C2×C47⋊C8—22no—
40C23×C47C22×C411yescharacteristic
41C22×D47—21no—
42C22×D47—21no—
43C22×D47—41no—
44C22×D47—41no—
45C22×D47M1612yes—
46C2×C4×C47—21no—
47C2×C4×C47—21no—
48C2×C4×C47—21no—
49C2×C4×C47—41no—
50C2×C4×C47—41no—
51C2×C4×C47M1612yes—
52C2×C4×C47C2×D412yes—
53C2×Dic47—21no—
54C2×Dic47—21no—
55C2×Dic47—21no—
56C2×Dic47—41no—
57C2×Dic47—41no—
58C2×Dic47C22⋊C411yescharacteristic
59C2×Dic47C22⋊C411yescharacteristic
60C2×Dic47C22⋊C412yes—
61C4×D47—24no—
62C4×D47—24no—
63C8×C47—42no—
64C47⋊C8—42no—
65C22×C47—21no—
66C22×C47—21no—
67C22×C47C2×C22⋊C411yescharacteristic
68C22×C47C2×M1611yescharacteristic
69C22×C47C2×M1611yescharacteristic
70C2×D47—22no—
71C2×D47—42no—
72C2×D47—41no—
73C2×D47—41no—
74C2×D47—42no—
75C4×C47—22no—
76C4×C47—22no—
77C4×C47—41no—
78Dic47—21no—
79Dic47—21no—
80Dic47—22no—
81Dic47—41no—
82#1464—471nomaximal, Sylow
83C2×C47—21no—
84C2×C47—21no—
85C2×C47#40711yescharacteristic
86C2×C47#41011yescharacteristic
87C2×C47#41311yescharacteristic
88D47—42no—
89C2×#117—471no—
90#432—472no—
91#324—471no—
92#324D4711yescharacteristic, complemented
93#323—472no—
94C47#146411yescharacteristic, complemented, Sylow
95C23×C4—471no—
96#117—942no—
97#117—942no—
98C2×C4⋊C4—471no—
99C2×C4⋊C4C2×D4711yescharacteristic
100C2×C22⋊C4—471no—
101C2×C22⋊C4—471no—
102C2×C42—471no—
103C2×C42—471no—
104C4⋊C8—942no—
105C22⋊C8—472no—
106C22⋊C8C2×D4712yes—
107#97—942no—
108C24—471no—
109C22×C4—471no—
110C22×C4—471no—
111C22×C4—471no—
112C22×C4—941no—
113C22×C4—941no—
114C22×C4—942no—
115C22×C4—942no—
116C22×C4C4×D4711yescharacteristic
117C22×C4C4×D4711yescharacteristic
118C22×C4C22×D4711yescharacteristic
119C2×C8—22no—
120C2×C8—942no—
121C4⋊C4—22no—
122C4⋊C4—942no—
123C22⋊C4—942no—
124C22⋊C4—942no—
125C42—472no—
126C42—472no—
127C42—941no—
128C42—941no—
129C23—472no—
130C23—941no—
131C23—941no—
132C23—1881no—
133C23—1881no—
134C23C2×C4×D4711yescharacteristic
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—471no—
141C2×C4—471no—
142C2×C4—472no—
143C2×C4—944no—
144C2×C4—944no—
145C2×C4—941no—
146C2×C4—941no—
147C2×C4—941no—
148C2×C4—1881no—
149C2×C4—1881no—
150C2×C4#1062532412yes—
151C2×C4D4×D4712yes—
152C8—42no—
153C8—1882no—
154C22—21no—
155C22—21no—
156C22—942no—
157C22—1882no—
158C22—1882no—
159C22—1881no—
160C22—1881no—
161C22C22⋊C4×D4711yescharacteristic
162C22M16×D4711yescharacteristic
163C22C2×#1062532411yescharacteristic
164C4—22no—
165C4—22no—
166C4—41no—
167C4—941no—
168C4—941no—
169C4—942no—
170C4—1881no—
171C2—21no—
172C2—21no—
173C2—1882no—
174C2#1568908511yescharacteristic
175C2#1568909511yescharacteristic
176C2#1568910611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#324C2
socleC22×C47C2×C22⋊C4
hypercenter#324D47
hypocenterC47#1464
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #15689177C2semidirect
3. #15688849C2semidirect
5. C47×#324C2semidirect
92. #324D47semidirect
94. C47#1464semidirect