Finite Group Databasebeta

← #20241724

Subgroups — #20241724

Order 6016.

316 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 77 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×C4×C22⋊D47C211yesmaximal, characteristic
2#15689087C211yesmaximal, characteristic, complemented
3#15688848C212yesmaximal, complemented
4#15688846C212yesmaximal, complemented
5C47×#407C211yesmaximal, characteristic, complemented
6C22×C22⋊D47C411yescharacteristic
7C22×C4×D47C411yescharacteristic
8C2×#10625329—21no—
9C4×C22⋊D47—21no—
10C4×C22⋊D47—21no—
11C4×C22⋊D47—21no—
12C4×C22⋊D47—21no—
13C2×Dic47⋊C4C2211yescharacteristic
14C2×C22⋊Dic47C411yescharacteristic
15C2×(C2×D47)⋊C4C2211yescharacteristic
16C2×C4×Dic47C411yescharacteristic
17C22⋊(C47⋊C8)—21no—
18C22⋊(C47⋊C8)C2212yes—
19C23×C4×C47C2211yescharacteristic
20C2×M16×C47—21no—
21C22⋊C8×C47—21no—
22C22⋊C8×C47C2212yes—
23C24×C47C2×C411yescharacteristic
24C23×D47C2×C411yescharacteristic
25C22×C4×C47—42no—
26C22×C4×C47C2×C411yescharacteristic
27C22×C4×C47D411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×C4×C47D411yescharacteristic
30C22×C4×C47D411yescharacteristic
31C22×C4×C47C2311yescharacteristic
32C2×C22⋊D47—21no—
33C2×C22⋊D47—21no—
34C2×C22⋊D47—22no—
35C2×C22⋊D47—22no—
36C22×Dic47C2×C411yescharacteristic
37C22×Dic47C2×C411yescharacteristic
38C22×Dic47C2×C411yescharacteristic
39C2×C4×D47—21no—
40C2×C4×D47—21no—
41C2×C4×D47—42no—
42M16×C47—42no—
43C2×C8×C47—22no—
44C22⋊Dic47—21no—
45C22⋊Dic47—21no—
46(C2×D47)⋊C4—21no—
47(C2×D47)⋊C4—21no—
48Dic47⋊C4—21no—
49Dic47⋊C4—21no—
50C4×Dic47—21no—
51C4×Dic47—21no—
52#10625329—42no—
53C2×C47⋊C8—22no—
54C23×C47—21no—
55C23×C47—21no—
56C23×C47—41no—
57C23×C47—41no—
58C23×C47C22⋊C411yescharacteristic
59C23×C47C22⋊C411yescharacteristic
60C23×C47C22×C411yescharacteristic
61C22×D47—21no—
62C22×D47—21no—
63C22×D47—41no—
64C22×D47—41no—
65C22×D47M1612yescomplemented
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—41no—
70C2×C4×C47—41no—
71C2×C4×C47—41no—
72C2×C4×C47C22⋊C411yescharacteristic
73C2×C4×C47C22⋊C411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C22⋊D47—24no—
77C22⋊D47—24no—
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—21no—
81C2×Dic47—21no—
82C2×Dic47—41no—
83C2×Dic47—41no—
84C2×Dic47M1612yescomplemented
85C4×D47—42no—
86C4×D47—42no—
87C8×C47—42no—
88C47⋊C8—42no—
89C22×C47—21no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47—21no—
93C22×C47—21no—
94C22×C47—21no—
95C22×C47—21no—
96C22×C47—21no—
97C22×C47—42no—
98C22×C47—42no—
99C22×C47C2×C22⋊C411yescharacteristic
100C22×C47C2×M1611yescharacteristic
101C22×C47C2×M1611yescharacteristic
102C2×D47—22no—
103C2×D47—42no—
104C2×D47—41no—
105C2×D47—41no—
106C2×D47—42no—
107C4×C47—21no—
108C4×C47—21no—
109C4×C47—21no—
110C4×C47#9912yes—
111Dic47—22no—
112Dic47—41no—
113Dic47—41no—
114#1465—471nomaximal, Sylow
115C2×C47—21no—
116C2×C47—21no—
117C2×C47—41no—
118C2×C47—41no—
119C2×C47#40711yescharacteristic
120C2×C47C2×#9911yescharacteristic
121C2×C47#41311yescharacteristic
122D47—42no—
123C2×C4×D4—471no—
124#407—471no—
125#407D4711yescharacteristic, complemented
126#324—472no—
127#323—472no—
128C47#146511yescharacteristic, complemented, Sylow
129C22×D4—471no—
130C23×C4—471no—
131C23×C4C2×D4711yescharacteristic
132C2×M16—21no—
133C2×M16—941no—
134C4×D4—941no—
135C4×D4—941no—
136C4×D4—941no—
137C4×D4—941no—
138C2×C4⋊C4—471no—
139C2×C22⋊C4—471no—
140C2×C22⋊C4—471no—
141C2×C42—471no—
142C22⋊C8—21no—
143C22⋊C8—472no—
144C22⋊C8—941no—
145C22⋊C8C2×D4712yes—
146C24—471no—
147C24C4×D4711yescharacteristic
148C2×D4—942no—
149C2×D4—942no—
150C2×D4—941no—
151C2×D4—941no—
152C22×C4—42no—
153C22×C4—471no—
154C22×C4—471no—
155C22×C4—471no—
156C22×C4—941no—
157C22×C4—941no—
158C22×C4—1882no—
159C22×C4C4×D4711yescharacteristic
160C22×C4D18811yescharacteristic
161C22×C4D18811yescharacteristic
162C22×C4C22⋊D4711yescharacteristic
163C22×C4C22⋊D4711yescharacteristic
164C22×C4C22×D4711yescharacteristic
165M16—42no—
166M16—1882no—
167C2×C8—22no—
168C2×C8—942no—
169C4⋊C4—941no—
170C4⋊C4—941no—
171C22⋊C4—941no—
172C22⋊C4—941no—
173C22⋊C4—941no—
174C22⋊C4—941no—
175C42—941no—
176C42—941no—
177C23—21no—
178C23—21no—
179C23—41no—
180C23—41no—
181C23—472no—
182C23—941no—
183C23—941no—
184C23—1881no—
185C23—1881no—
186C23(C2×D47)⋊C411yescharacteristic
187C23(C2×D47)⋊C411yescharacteristic
188C23C2×C4×D4711yescharacteristic
189D4—944no—
190D4—944no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—472no—
198C2×C4—941no—
199C2×C4—941no—
200C2×C4—941no—
201C2×C4—941no—
202C2×C4—1882no—
203C2×C4—1882no—
204C2×C4—1881no—
205C2×C4—1881no—
206C2×C4(C2×D47)⋊C411yescharacteristic
207C2×C4(C2×D47)⋊C411yescharacteristic
208C2×C4C2×D18811yescharacteristic
209C2×C4C2×C22⋊D4711yescharacteristic
210C8—42no—
211C8—1882no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22—21no—
220C22—42no—
221C22—42no—
222C22—942no—
223C22—1882no—
224C22—1882no—
225C22—1881no—
226C22—1881no—
227C22C2×(C2×D47)⋊C411yescharacteristic
228C22M16×D4711yescharacteristic
229C22M16×D4711yescharacteristic
230C4—21no—
231C4—21no—
232C4—21no—
233C4—942no—
234C4—1881no—
235C4—1881no—
236C4#1309393812yes—
237C2—21no—
238C2—21no—
239C2—41no—
240C2—41no—
241C2—1882no—
242C2#1568908611yescharacteristic
243C2C2×#1309393811yescharacteristic
244C2#1568910511yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#407C2
socleC22×C47C2×C22⋊C4
hypercenter#407D47
hypocenterC47#1465
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. #15688848C2semidirect
4. #15688846C2semidirect
5. C47×#407C2semidirect
65. C22×D47M16semidirect
84. C2×Dic47M16semidirect
125. #407D47semidirect
128. C47#1465semidirect