Finite Group Databasebeta

← #20241737

Subgroups — #20241737

Order 6016.

280 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 73 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×#13094007C211yesmaximal, characteristic
2C2×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
3#15688848C212yesmaximal, complemented
4#15688846C212yesmaximal, complemented
5C47×#407C211yesmaximal, characteristic, complemented
6C22×C22⋊D47C411yescharacteristic
7C22×C47⋊C8—21no—
8#13094007—21no—
9#13094007—21no—
10#13094007—21no—
11#13094007—21no—
12C2×Dic47⋊C4C411yescharacteristic
13C2×Dic47⋊C4C2211yescharacteristic
14C2×C22⋊Dic47C411yescharacteristic
15C2×(C2×D47)⋊C4C411yescharacteristic
16C2×(C2×D47)⋊C4C2211yescharacteristic
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—42no—
35C22×Dic47C2×C411yescharacteristic
36C22×Dic47C2×C411yescharacteristic
37C22×Dic47C2×C411yescharacteristic
38M16×C47—42no—
39C2×C8×C47—22no—
40C22⋊Dic47—21no—
41C22⋊Dic47—21no—
42(C2×D47)⋊C4—21no—
43(C2×D47)⋊C4—21no—
44(C2×D47)⋊C4—21no—
45(C2×D47)⋊C4—21no—
46Dic47⋊C4—21no—
47Dic47⋊C4—21no—
48Dic47⋊C4—21no—
49Dic47⋊C4—21no—
50C2×C47⋊C8—22no—
51C2×C47⋊C8—42no—
52C23×C47—22no—
53C23×C47—22no—
54C23×C47—41no—
55C23×C47C22⋊C411yescharacteristic
56C23×C47C22⋊C411yescharacteristic
57C23×C47C22×C411yescharacteristic
58C22×D47—21no—
59C22×D47—22no—
60C22×D47—41no—
61C22×D47—41no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47C22⋊C411yescharacteristic
69C2×C4×C47C22⋊C411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C22⋊D47—42no—
73C22⋊D47—42no—
74C2×Dic47—21no—
75C2×Dic47—21no—
76C2×Dic47—21no—
77C2×Dic47—22no—
78C2×Dic47—41no—
79C2×Dic47—41no—
80C8×C47—42no—
81C47⋊C8—42no—
82C22×C47—21no—
83C22×C47—21no—
84C22×C47—21no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47—21no—
88C22×C47—21no—
89C22×C47—44no—
90C22×C47#9912yes—
91C22×C47C2×C22⋊C411yescharacteristic
92C22×C47#13112yes—
93C2×D47—41no—
94C2×D47—41no—
95C2×D47—41no—
96C2×D47—82no—
97C4×C47—21no—
98C4×C47—21no—
99C4×C47—21no—
100C4×C47—21no—
101Dic47—41no—
102Dic47—41no—
103Dic47—41no—
104#1468—471nomaximal, Sylow
105C2×C47—22no—
106C2×C47—22no—
107C2×C47—41no—
108C2×C47#40811yescharacteristic
109C2×C47C2×#9911yescharacteristic
110C2×C47#41311yescharacteristic
111D47—81no—
112C2×#123—471no—
113#407D4711yescharacteristic, complemented
114C2×C22⋊C8—471no—
115#324—472no—
116#323—472no—
117C47#146811yescharacteristic, complemented, Sylow
118C22×D4—471no—
119C23×C4C2×D4711yescharacteristic
120C2×M16—21no—
121C22×C8—941no—
122#123—941no—
123#123—941no—
124#123—941no—
125#123—941no—
126C2×C4⋊C4—471no—
127C2×C4⋊C4—471no—
128C2×C22⋊C4—471no—
129C2×C22⋊C4—471no—
130C2×C22⋊C4—471no—
131C22⋊C8—21no—
132C22⋊C8—472no—
133C22⋊C8—941no—
134C22⋊C8C2×D4712yes—
135C24—471no—
136C24C4×D4711yescharacteristic
137C2×D4—941no—
138C2×D4—941no—
139C2×D4—1882no—
140C22×C4—42no—
141C22×C4—471no—
142C22×C4—471no—
143C22×C4—471no—
144C22×C4C4×D4711yescharacteristic
145C22×C4D18811yescharacteristic
146C22×C4D18811yescharacteristic
147C22×C4C22⋊D4711yescharacteristic
148C22×C4C22⋊D4711yescharacteristic
149C22×C4C22×D4711yescharacteristic
150M16—42no—
151C2×C8—22no—
152C2×C8—942no—
153C2×C8—1882no—
154C4⋊C4—941no—
155C4⋊C4—941no—
156C4⋊C4—941no—
157C4⋊C4—941no—
158C22⋊C4—941no—
159C22⋊C4—941no—
160C22⋊C4—941no—
161C22⋊C4—941no—
162C22⋊C4—941no—
163C22⋊C4—941no—
164C23—22no—
165C23—22no—
166C23—41no—
167C23—942no—
168C23—941no—
169C23—1881no—
170C23—1881no—
171C23(C2×D47)⋊C411yescharacteristic
172C23(C2×D47)⋊C411yescharacteristic
173C23C2×C4×D4711yescharacteristic
174D4—1882no—
175D4—1882no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—941no—
183C2×C4—941no—
184C2×C4—941no—
185C2×C4—942no—
186C2×C4—1881no—
187C2×C4—1881no—
188C2×C4(C2×D47)⋊C411yescharacteristic
189C2×C4(C2×D47)⋊C411yescharacteristic
190C2×C4C2×D18811yescharacteristic
191C2×C4C2×C22⋊D4711yescharacteristic
192C8—42no—
193C8—1882no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—3762no—
203C22—1881no—
204C22—1881no—
205C22—1881no—
206C22#1309393812yes—
207C22C2×(C2×D47)⋊C411yescharacteristic
208C22#1309403212yes—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—1881no—
214C4—1881no—
215C4—1881no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—3761no—
220C2#1568909111yescharacteristic
221C2C2×#1309393811yescharacteristic
222C2#1568910511yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#407C2
socleC22×C47C2×C22⋊C4
hypercenter#407D47
hypocenterC47#1468
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. C2×C22⋊(C47⋊C8)C2semidirect
3. #15688848C2semidirect
4. #15688846C2semidirect
5. C47×#407C2semidirect
113. #407D47semidirect
117. C47#1468semidirect