Finite Group Databasebeta

← #20241723

Subgroups — #20241723

Order 6016.

316 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 69 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×(C22⋊D47)⋊C4C211yesmaximal, characteristic
2#15689085C212yesmaximal, complemented
3#15688848C212yesmaximal, complemented
4#15688847C211yesmaximal, characteristic, complemented
5C47×#323C211yesmaximal, characteristic, complemented
6C22×C22⋊D47C411yescharacteristic
7C23×Dic47C411yescharacteristic
8C22×C4×D47C2211yescharacteristic
9C2×#10625324—22no—
10(C22⋊D47)⋊C4—22no—
11(C22⋊D47)⋊C4—22no—
12C2×Dic47⋊C4C2211yescharacteristic
13C2×(C2×D47)⋊C4C411yescharacteristic
14C2×C4×Dic47C411yescharacteristic
15C22⋊(C47⋊C8)C2212yes—
16(C2×D47)⋊C8—22no—
17C2×C22⋊C4×C47C2211yescharacteristic
18C22⋊C8×C47C2212yes—
19C24×C47C2×C411yescharacteristic
20C23×D47C2×C411yescharacteristic
21C22×C4×C47C2×C411yescharacteristic
22C22×C4×C47C2311yescharacteristic
23C2×C22⋊D47—22no—
24C2×C22⋊D47—22no—
25C2×C22⋊D47—22no—
26C22×Dic47—21no—
27C22×Dic47—21no—
28C22×Dic47—42no—
29C22×Dic47C2×C411yescharacteristic
30C22×Dic47C2×C411yescharacteristic
31C22×Dic47C2×C411yescharacteristic
32C2×C4×D47—42no—
33C2×C4×D47D412yes—
34C2×C4×D47D412yes—
35C2×C8×C47—22no—
36C22⋊C4×C47—22no—
37(C2×D47)⋊C4—22no—
38Dic47⋊C4—22no—
39C4×Dic47—21no—
40C4×Dic47—21no—
41C2×C47⋊C8—22no—
42#10625324—44no—
43C23×C47—21no—
44C23×C47—21no—
45C23×C47—41no—
46C23×C47—41no—
47C23×C47M1612yescomplemented
48C23×C47C22×C411yescharacteristic
49C22×D47—21no—
50C22×D47—21no—
51C22×D47—41no—
52C22×D47—41no—
53C22×D47C22⋊C412yes—
54C2×C4×C47—21no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47C2×D412yes—
58C22⋊D47—28no—
59C2×Dic47—21no—
60C2×Dic47—21no—
61C2×Dic47—22no—
62C2×Dic47—21no—
63C2×Dic47—42no—
64C2×Dic47—42no—
65C2×Dic47—41no—
66C2×Dic47C22⋊C411yescharacteristic
67C2×Dic47C22⋊C411yescharacteristic
68C2×Dic47M1612yescomplemented
69C4×D47—24no—
70C4×D47—42no—
71C8×C47—42no—
72C47⋊C8—42no—
73C22×C47—21no—
74C22×C47—21no—
75C22×C47—22no—
76C22×C47—42no—
77C22×C47—42no—
78C22×C47—41no—
79C22×C47—41no—
80C22×C47C2×C22⋊C411yescharacteristic
81C22×C47C2×M1611yescharacteristic
82C22×C47C2×M1611yescharacteristic
83C2×D47—22no—
84C2×D47—22no—
85C2×D47—22no—
86C2×D47—42no—
87C2×D47—42no—
88C4×C47—22no—
89C4×C47—41no—
90Dic47—22no—
91Dic47—21no—
92Dic47—41no—
93Dic47#9912yes—
94#1465—471nomaximal, Sylow
95C2×C47—21no—
96C2×C47—21no—
97C2×C47—42no—
98C2×C47#40711yescharacteristic
99C2×C47C2×#9911yescharacteristic
100C2×C47#41311yescharacteristic
101D47—42no—
102C2×C4×D4—471no—
103#407—472no—
104#324—472no—
105#323—471no—
106#323D4711yescharacteristic, complemented
107C47#146511yescharacteristic, complemented, Sylow
108C22×D4—471no—
109C23×C4—471no—
110C23×C4—471no—
111C2×M16—942no—
112C4×D4—942no—
113C4×D4—942no—
114C2×C4⋊C4—471no—
115C2×C22⋊C4—471no—
116C2×C22⋊C4C2×D4711yescharacteristic
117C2×C42—471no—
118C22⋊C8—472no—
119C22⋊C8—942no—
120C22⋊C8C2×D4712yes—
121C24—471no—
122C24C4×D4711yescharacteristic
123C2×D4—942no—
124C2×D4—942no—
125C2×D4—942no—
126C22×C4—471no—
127C22×C4—471no—
128C22×C4—472no—
129C22×C4—472no—
130C22×C4—471no—
131C22×C4—941no—
132C22×C4—941no—
133C22×C4—1882no—
134C22×C4—1882no—
135C22×C4C4×D4711yescharacteristic
136C22×C4C22×D4711yescharacteristic
137M16—1884no—
138C2×C8—22no—
139C2×C8—942no—
140C4⋊C4—942no—
141C22⋊C4—22no—
142C22⋊C4—942no—
143C42—941no—
144C42—941no—
145C23—21no—
146C23—21no—
147C23—41no—
148C23—41no—
149C23—472no—
150C23—941no—
151C23—941no—
152C23—1881no—
153C23—1881no—
154C23#1062532412yescomplemented
155C23C2×C4×D4711yescharacteristic
156D4—948no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—471no—
161C2×C4—471no—
162C2×C4—472no—
163C2×C4—944no—
164C2×C4—942no—
165C2×C4—941no—
166C2×C4—941no—
167C2×C4—941no—
168C2×C4—1882no—
169C2×C4—1882no—
170C2×C4—1882no—
171C2×C4—1881no—
172C2×C4D4×D4712yes—
173C8—42no—
174C8—1882no—
175C22—21no—
176C22—21no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—942no—
183C22—942no—
184C22—942no—
185C22—1882no—
186C22—1882no—
187C22C22⋊C4×D4711yescharacteristic
188C22M16×D4711yescharacteristic
189C22C2×#1062532411yescharacteristic
190C4—22no—
191C4—41no—
192C4—472no—
193C4—942no—
194C4—941no—
195C4—1881no—
196C2—21no—
197C2—21no—
198C2—42no—
199C2—1882no—
200C2#1568908511yescharacteristic
201C2#99×D4711yescharacteristic
202C2#1568910411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#323C2
socleC22×C47C2×C22⋊C4
hypercenter#323D47
hypocenterC47#1465
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #15689085C2semidirect
3. #15688848C2semidirect
4. #15688847C2semidirect
5. C47×#323C2semidirect
47. C23×C47M16semidirect
68. C2×Dic47M16semidirect
106. #323D47semidirect
107. C47#1465semidirect
154. C23#10625324semidirect