Finite Group Databasebeta

← #20244223

Subgroups — #20244223

Order 6016.

408 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 93 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×#13093998C211yesmaximal, characteristic
2C2×#13093938C214yesmaximal, complemented
3C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
4C47×#380C211yesmaximal, characteristic, complemented
5C22×D188C411yescharacteristic, complemented
6C22×C22⋊D47C2212yes—
7#13093998—21no—
8#13093998—21no—
9#13093998—21no—
10#13093998—21no—
11C2×C4⋊Dic47C411yescharacteristic, complemented
12C2×C22⋊Dic47C2212yes—
13C2×(C2×D47)⋊C4C412yescomplemented
14C2×C4×Dic47—21no—
15#13093938—28no—
16C47⋊#95—21no—
17C23×C4×C47C2211yescharacteristic
18C2×C4⋊C4×C47—21no—
19C2×C22⋊C4×C47C2212yes—
20#95×C47—21no—
21C24×C47C2311yescharacteristic
22C23×D47C2×C412yes—
23C22×C4×C47—22no—
24C22×C4×C47—42no—
25C22×C4×C47C2×C411yescharacteristic
26C22×C4×C47C2×C411yescharacteristic
27C22×C4×C47D411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×C4×C47D411yescharacteristic
30C22×C4×C47D411yescharacteristic
31C2×C22⋊D47—24no—
32C2×C22⋊D47—22no—
33C2×C22⋊D47—22no—
34C2×C22⋊D47—24no—
35C22×Dic47—22no—
36C22×Dic47C2×C412yes—
37C2×D188—21no—
38C2×D188—21no—
39C2×D188—42no—
40C4⋊C4×C47—42no—
41C22⋊C4×C47—24no—
42C22⋊Dic47—22no—
43C22⋊Dic47D414yescomplemented
44(C2×D47)⋊C4—22no—
45(C2×D47)⋊C4—22no—
46C4⋊Dic47—21no—
47C4⋊Dic47—21no—
48C4×Dic47—42no—
49C23×C47—41no—
50C23×C47—41no—
51C23×C47C22×C411yescharacteristic
52C23×C47C2×D411yescharacteristic
53C23×C47C2×D412yes—
54C23×C47C2×D411yescharacteristic
55C23×C47#4112yes—
56C22×D47—22no—
57C22×D47—24no—
58C22×D47—42no—
59C22×D47—42no—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—41no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47—42no—
67C2×C4×C47—42no—
68C2×C4×C47—42no—
69C2×C4×C47C22⋊C411yescharacteristic
70C2×C4×C47C22⋊C411yescharacteristic
71C2×C4×C47C22⋊C411yescharacteristic
72C2×C4×C47C22⋊C411yescharacteristic
73C22⋊D47—44no—
74C22⋊D47—42no—
75C22⋊D47—42no—
76C2×Dic47—22no—
77C2×Dic47—24no—
78C2×Dic47—24no—
79C2×Dic47—42no—
80C2×Dic47—42no—
81D188—42no—
82D188—42no—
83C22×C47—21no—
84C22×C47—21no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47—21no—
88C22×C47—21no—
89C22×C47—42no—
90C22×C47—42no—
91C22×C47C2×C22⋊C411yescharacteristic
92C22×C47C4×D412yes—
93C22×C47#12112yes—
94C22×C47#12411yescharacteristic
95C22×C47#12711yescharacteristic
96C2×D47—42no—
97C2×D47—42no—
98C2×D47—42no—
99C2×D47—84no—
100C4×C47—21no—
101C4×C47—21no—
102C4×C47—21no—
103C4×C47—82no—
104C4×C47#9912yescomplemented
105Dic47—44no—
106Dic47—42no—
107#1964—471nomaximal, Sylow
108C2×C47—22no—
109C2×C47—21no—
110C2×C47—22no—
111C2×C47—21no—
112C2×C47#39011yescharacteristic
113C2×C47C2×#9911yescharacteristic
114C2×C47#41011yescharacteristic
115D47—82no—
116C2×#121—471no—
117C2×#99—474no—
118#380D4711yescharacteristic, complemented
119C4×C22⋊C4—471no—
120C47#196411yescharacteristic, complemented, Sylow
121C22×D4—472no—
122C22×D4—471no—
123C23×C4C2×D4711yescharacteristic
124#121—941no—
125#121—941no—
126#121—941no—
127#121—941no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—471no—
130C2×C22⋊C4—472no—
131C2×C22⋊C4—472no—
132C2×C22⋊C4C2×D4712yes—
133C2×C42—941no—
134#99—948no—
135#95—21no—
136#95—941no—
137C24—472no—
138C24C22×D4711yescharacteristic
139C2×D4—942no—
140C2×D4—944no—
141C2×D4—944no—
142C2×D4—942no—
143C2×D4—941no—
144C2×D4—941no—
145C2×D4—1882no—
146C22×C4—22no—
147C22×C4—42no—
148C22×C4—472no—
149C22×C4—942no—
150C22×C4C4×D4711yescharacteristic
151C22×C4C4×D4711yescharacteristic
152C22×C4D18811yescharacteristic
153C22×C4D18811yescharacteristic
154C22×C4C22⋊D4711yescharacteristic
155C22×C4C22⋊D4711yescharacteristic
156C4⋊C4—42no—
157C4⋊C4—941no—
158C4⋊C4—941no—
159C22⋊C4—24no—
160C22⋊C4—474no—
161C22⋊C4—942no—
162C22⋊C4—942no—
163C22⋊C4—942no—
164C42—1882no—
165C23—41no—
166C23—41no—
167C23—944no—
168C23—942no—
169C23—1882no—
170C23—1882no—
171C23C2×C4×D4711yescharacteristic
172C23C2×D18811yescharacteristic
173C23D4×D4712yes—
174C23#1062535412yes—
175C23C2×C22⋊D4711yescharacteristic
176D4—1882no—
177D4—1884no—
178D4—1882no—
179D4—1882no—
180D4—1882no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—942no—
191C2×C4—944no—
192C2×C4—944no—
193C2×C4—1882no—
194C2×C4—1882no—
195C2×C4(C2×D47)⋊C411yescharacteristic
196C2×C4(C2×D47)⋊C411yescharacteristic
197C2×C4(C2×D47)⋊C411yescharacteristic
198C2×C4(C2×D47)⋊C411yescharacteristic
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—42no—
206C22—42no—
207C22—3764no—
208C22—1882no—
209C22—1882no—
210C22—1882no—
211C22C2×(C2×D47)⋊C411yescharacteristic
212C22#1309398612yes—
213C22#1309399912yes—
214C22#1309401311yescharacteristic
215C22#1309402011yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—82no—
220C4—1884no—
221C4—1882no—
222C4#1309393812yescomplemented
223C2—21no—
224C2—22no—
225C2—22no—
226C2—21no—
227C2—3762no—
228C2#1568902411yescharacteristic
229C2C2×#1309393811yescharacteristic
230C2#1568909611yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC23×C47C22×C4
FrattiniC24C22×D47
FittingC47×#380C2
socleC22×C47C2×C22⋊C4
hypercenter#380D47
hypocenterC47#1964
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#13093938C2semidirect
3. C4×C22⋊Dic47C2semidirect
4. C47×#380C2semidirect
5. C22×D188C4semidirect
11. C2×C4⋊Dic47C4semidirect
13. C2×(C2×D47)⋊C4C4semidirect
43. C22⋊Dic47D4semidirect
104. C4×C47#99semidirect
118. #380D47semidirect
120. C47#1964semidirect
222. C4#13093938semidirect