Finite Group Databasebeta

← #20241714

Subgroups — #20241714

Order 6016.

440 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C22×(C2×D47)⋊C4C211yesmaximal, characteristic
2#15689087C211yesmaximal, characteristic, complemented
3#15688846C214yesmaximal, complemented
4C47×#407C211yesmaximal, characteristic, complemented
5C24×D47C411yescharacteristic
6C23×Dic47C411yescharacteristic
7C2×#10625329—21no—
8C2×(C2×D47)⋊C4—21no—
9C2×(C2×D47)⋊C4—21no—
10C2×(C2×D47)⋊C4—21no—
11C2×(C2×D47)⋊C4—21no—
12C2×(C2×D47)⋊C4C412yes—
13C2×(C2×D47)⋊C4C2212yes—
14C22⋊(C47⋊C8)—21no—
15C22⋊(C47⋊C8)C2212yescomplemented
16C23×C4×C47C2211yescharacteristic
17C2×M16×C47—21no—
18C22⋊C8×C47—21no—
19C22⋊C8×C47C2212yescomplemented
20C24×C47C2×C411yescharacteristic
21C23×D47—21no—
22C23×D47—21no—
23C23×D47—24no—
24C23×D47—42no—
25C23×D47—42no—
26C23×D47C2×C412yes—
27C22×C4×C47—42no—
28C22×C4×C47C2×C411yescharacteristic
29C22×C4×C47D411yescharacteristic
30C22×C4×C47D411yescharacteristic
31C22×C4×C47D411yescharacteristic
32C22×C4×C47D411yescharacteristic
33C22×C4×C47C2311yescharacteristic
34C22×Dic47—21no—
35C22×Dic47—21no—
36C22×Dic47—42no—
37C22×Dic47C2×C412yes—
38M16×C47—42no—
39C2×C8×C47—22no—
40(C2×D47)⋊C4—22no—
41(C2×D47)⋊C4—22no—
42(C2×D47)⋊C4—22no—
43(C2×D47)⋊C4—22no—
44#10625329—42no—
45C2×C47⋊C8—22no—
46C23×C47—22no—
47C23×C47—22no—
48C23×C47—22no—
49C23×C47C22⋊C411yescharacteristic
50C23×C47C22⋊C411yescharacteristic
51C23×C47C22×C411yescharacteristic
52C22×D47—24no—
53C22×D47—24no—
54C22×D47—22no—
55C22×D47—22no—
56C22×D47—416no—
57C22×D47—42no—
58C22×D47—42no—
59C22×D47—42no—
60C22×D47—42no—
61C22×D47—42no—
62C22×D47—42no—
63C22×D47M1614yescomplemented
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47C22⋊C411yescharacteristic
71C2×C4×C47C22⋊C411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×Dic47—22no—
75C2×Dic47—42no—
76C2×Dic47—42no—
77C2×Dic47—42no—
78C8×C47—42no—
79C47⋊C8—42no—
80C22×C47—28no—
81C22×C47—21no—
82C22×C47—21no—
83C22×C47—21no—
84C22×C47—21no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47#9912yes—
88C22×C47#10012yes—
89C22×C47C2×C22⋊C411yescharacteristic
90C22×C47C2×M1612yes—
91C2×D47—24no—
92C2×D47—48no—
93C2×D47—48no—
94C2×D47—44no—
95C2×D47—42no—
96C2×D47—42no—
97C2×D47—44no—
98C4×C47—21no—
99C4×C47—21no—
100C4×C47—21no—
101C4×C47—21no—
102Dic47—42no—
103#1462—471nomaximal, Sylow
104C2×C47—22no—
105C2×C47—22no—
106C2×C47—22no—
107C2×C47#40711yescharacteristic
108C2×C47C2×#9911yescharacteristic
109C2×C47C2×#10011yescharacteristic
110D47—44no—
111C22×C22⋊C4—471no—
112#407—471no—
113#407D4711yescharacteristic, complemented
114#323—474no—
115C47#146211yescharacteristic, complemented, Sylow
116C25—471no—
117C23×C4—471no—
118C23×C4C2×D4711yescharacteristic
119C2×M16—21no—
120C2×M16—941no—
121C2×C22⋊C4—472no—
122C2×C22⋊C4—472no—
123C2×C22⋊C4—941no—
124C2×C22⋊C4—941no—
125C2×C22⋊C4—941no—
126C2×C22⋊C4—941no—
127C22⋊C8—21no—
128C22⋊C8—472no—
129C22⋊C8—941no—
130C22⋊C8C2×D4712yescomplemented
131C24—472no—
132C24—944no—
133C24—941no—
134C24—941no—
135C24—1882no—
136C24—1882no—
137C24C4×D4711yescharacteristic
138C22×C4—42no—
139C22×C4—472no—
140C22×C4—941no—
141C22×C4—941no—
142C22×C4—1882no—
143C22×C4C4×D4711yescharacteristic
144C22×C4D18811yescharacteristic
145C22×C4D18811yescharacteristic
146C22×C4C22⋊D4711yescharacteristic
147C22×C4C22⋊D4711yescharacteristic
148C22×C4C22×D4711yescharacteristic
149M16—42no—
150M16—1882no—
151C2×C8—22no—
152C2×C8—942no—
153C22⋊C4—942no—
154C22⋊C4—942no—
155C22⋊C4—942no—
156C22⋊C4—942no—
157C23—22no—
158C23—22no—
159C23—22no—
160C23—474no—
161C23—944no—
162C23—944no—
163C23—942no—
164C23—942no—
165C23—1882no—
166C23—1882no—
167C23—18816no—
168C23—1882no—
169C23—1882no—
170C23—1882no—
171C23—1882no—
172C23(C2×D47)⋊C411yescharacteristic
173C23(C2×D47)⋊C411yescharacteristic
174C23C2×C4×D4711yescharacteristic
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—942no—
182C2×C4—1882no—
183C2×C4—1882no—
184C2×C4—1882no—
185C2×C4(C2×D47)⋊C411yescharacteristic
186C2×C4(C2×D47)⋊C411yescharacteristic
187C2×C4C2×D18811yescharacteristic
188C2×C4C2×C22⋊D4711yescharacteristic
189C8—42no—
190C8—1882no—
191C22—28no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—944no—
199C22—1884no—
200C22—1888no—
201C22—1888no—
202C22—1884no—
203C22—1882no—
204C22—1882no—
205C22#1309393812yes—
206C22#1309394012yes—
207C22C2×(C2×D47)⋊C411yescharacteristic
208C22M16×D4712yes—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—1882no—
214C2—22no—
215C2—22no—
216C2—22no—
217C2—1884no—
218C2#1568908611yescharacteristic
219C2C2×#1309393811yescharacteristic
220C2C2×#1309394011yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#407C2
socleC22×C47C2×C22⋊C4
hypercenter#407D47
hypocenterC47#1462
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. #15689087C2semidirect
3. #15688846C2semidirect
4. C47×#407C2semidirect
15. C22⋊(C47⋊C8)C22semidirect
19. C22⋊C8×C47C22semidirect
63. C22×D47M16semidirect
113. #407D47semidirect
115. C47#1462semidirect
130. C22⋊C8C2×D47semidirect