Finite Group Databasebeta

← #20241725

Subgroups — #20241725

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×#13093986C211yesmaximal, characteristic
2#15689085C212yesmaximal, complemented
3#15688849C211yesmaximal, characteristic, complemented
4#15688846C212yesmaximal, complemented
5C47×#324C211yesmaximal, characteristic, complemented
6C22×D188C411yescharacteristic
7C22×C4×D47C411yescharacteristic
8C22×C4×D47C2211yescharacteristic
9C2×#10625324—22no—
10#13093986—22no—
11#13093986—22no—
12C2×(C2×D47)⋊C4C411yescharacteristic
13C2×(C2×D47)⋊C4C2211yescharacteristic
14C2×C4×Dic47C411yescharacteristic
15C22⋊(C47⋊C8)C2212yes—
16(C2×D47)⋊C8—22no—
17C2×C4⋊C4×C47C2211yescharacteristic
18C22⋊C8×C47C2212yes—
19C23×D47C2×C411yescharacteristic
20C23×D47C2×C411yescharacteristic
21C22×C4×C47C2×C411yescharacteristic
22C22×C4×C47C2×C411yescharacteristic
23C22×C4×C47C2311yescharacteristic
24C22×Dic47C2×C411yescharacteristic
25C22×Dic47C2×C411yescharacteristic
26C2×D188—22no—
27C2×D188—22no—
28C2×D188—22no—
29C2×C4×D47—21no—
30C2×C4×D47—21no—
31C2×C4×D47—42no—
32C2×C4×D47—42no—
33C2×C4×D47D412yes—
34C2×C4×D47D412yes—
35C2×C8×C47—22no—
36C4⋊C4×C47—22no—
37(C2×D47)⋊C4—22no—
38(C2×D47)⋊C4—22no—
39C4×Dic47—21no—
40C4×Dic47—21no—
41C2×C47⋊C8—22no—
42#10625324—44no—
43C23×C47C22×C411yescharacteristic
44C22×D47—21no—
45C22×D47—21no—
46C22×D47—21no—
47C22×D47—21no—
48C22×D47—41no—
49C22×D47—41no—
50C22×D47—41no—
51C22×D47—41no—
52C22×D47C22⋊C412yes—
53C22×D47M1612yescomplemented
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47M1612yescomplemented
60C2×C4×C47C2×D412yes—
61C2×Dic47—22no—
62C2×Dic47—21no—
63C2×Dic47—41no—
64C2×Dic47C22⋊C411yescharacteristic
65C2×Dic47C22⋊C411yescharacteristic
66D188—28no—
67C4×D47—24no—
68C4×D47—42no—
69C4×D47—42no—
70C4×D47—42no—
71C8×C47—42no—
72C47⋊C8—42no—
73C22×C47—21no—
74C22×C47—21no—
75C22×C47C2×C22⋊C411yescharacteristic
76C22×C47C2×M1611yescharacteristic
77C22×C47C2×M1611yescharacteristic
78C2×D47—22no—
79C2×D47—22no—
80C2×D47—22no—
81C2×D47—22no—
82C2×D47—42no—
83C2×D47—42no—
84C2×D47—42no—
85C2×D47—41no—
86C2×D47—41no—
87C2×D47—42no—
88C4×C47—22no—
89C4×C47—22no—
90C4×C47—41no—
91Dic47—21no—
92Dic47—41no—
93Dic47#9912yes—
94#1465—471nomaximal, Sylow
95C2×C47—21no—
96C2×C47—21no—
97C2×C47#40711yescharacteristic
98C2×C47C2×#9911yescharacteristic
99C2×C47#41311yescharacteristic
100D47—42no—
101D47—42no—
102C2×C4×D4—471no—
103#407—472no—
104#324—471no—
105#324D4711yescharacteristic, complemented
106#323—472no—
107C47#146511yescharacteristic, complemented, Sylow
108C22×D4—471no—
109C23×C4—471no—
110C23×C4—471no—
111C2×M16—942no—
112C4×D4—942no—
113C4×D4—942no—
114C2×C4⋊C4C2×D4711yescharacteristic
115C2×C22⋊C4—471no—
116C2×C22⋊C4—471no—
117C2×C42—471no—
118C22⋊C8—472no—
119C22⋊C8—942no—
120C22⋊C8C2×D4712yes—
121C24—471no—
122C24—471no—
123C2×D4—942no—
124C2×D4—942no—
125C2×D4—942no—
126C22×C4—471no—
127C22×C4—472no—
128C22×C4—472no—
129C22×C4—471no—
130C22×C4—941no—
131C22×C4—941no—
132C22×C4—1882no—
133C22×C4—1882no—
134C22×C4C4×D4711yescharacteristic
135C22×C4C4×D4711yescharacteristic
136C22×C4C22×D4711yescharacteristic
137M16—1884no—
138C2×C8—22no—
139C2×C8—942no—
140C4⋊C4—22no—
141C22⋊C4—942no—
142C22⋊C4—942no—
143C42—941no—
144C42—941no—
145C23—472no—
146C23—472no—
147C23—941no—
148C23—941no—
149C23—941no—
150C23—941no—
151C23—1881no—
152C23—1881no—
153C23—1881no—
154C23—1881no—
155C23C2×C4×D4711yescharacteristic
156D4—948no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—471no—
163C2×C4—471no—
164C2×C4—944no—
165C2×C4—942no—
166C2×C4—941no—
167C2×C4—1882no—
168C2×C4—1882no—
169C2×C4—1882no—
170C2×C4—1881no—
171C2×C4#1062532412yescomplemented
172C2×C4D4×D4712yes—
173C8—42no—
174C8—1882no—
175C22—21no—
176C22—21no—
177C22—942no—
178C22—942no—
179C22—942no—
180C22—942no—
181C22—1882no—
182C22—1882no—
183C22—1882no—
184C22—1882no—
185C22—1881no—
186C22—1881no—
187C22C22⋊C4×D4711yescharacteristic
188C22M16×D4711yescharacteristic
189C22C2×#1062532411yescharacteristic
190C4—22no—
191C4—22no—
192C4—41no—
193C4—472no—
194C4—941no—
195C4—1881no—
196C2—21no—
197C2—21no—
198C2—1882no—
199C2—1882no—
200C2#1568908511yescharacteristic
201C2#99×D4711yescharacteristic
202C2#1568910611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#324C2
socleC22×C47C2×C22⋊C4
hypercenter#324D47
hypocenterC47#1465
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. #15689085C2semidirect
3. #15688849C2semidirect
4. #15688846C2semidirect
5. C47×#324C2semidirect
53. C22×D47M16semidirect
59. C2×C4×C47M16semidirect
105. #324D47semidirect
107. C47#1465semidirect
171. C2×C4#10625324semidirect