Finite Group Databasebeta

← #20243849

Subgroups — #20243849

Order 6016.

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

normal subgroups only

This group has 390 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
1C22×#10625329C211yesmaximal, characteristic, complemented
2C2×#13093998C211yesmaximal, characteristic
3C2×#13093940C212yesmaximal, complemented
4#15688891C212yesmaximal, complemented
5C47×#407C211yesmaximal, characteristic, complemented
6C22×D188C2211yescharacteristic
7C22×C22⋊D47C412yes—
8C2×#10625329—21no—
9C2×#10625329—24no—
10C2×#10625329C2212yes—
11C22×C47⋊C8—21no—
12#13093998—21no—
13#13093998—21no—
14#13093998—21no—
15#13093998—21no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×(C2×D47)⋊C4C412yes—
18#13093940—24no—
19C23×C4×C47C2211yescharacteristic
20C2×M16×C47C2212yes—
21C22⋊C8×C47—21no—
22C22⋊C8×C47—21no—
23C24×C47C2×C411yescharacteristic
24C23×D47C2×C412yes—
25C22×C4×C47—22no—
26C22×C4×C47—22no—
27C22×C4×C47C2×C411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×C4×C47D411yescharacteristic
30C22×C4×C47D411yescharacteristic
31C22×C4×C47D411yescharacteristic
32C22×C4×C47C2311yescharacteristic
33C2×C22⋊D47—22no—
34C2×C22⋊D47—22no—
35C2×C22⋊D47—44no—
36C22×Dic47C2×C412yes—
37C2×D188—22no—
38C2×D188—21no—
39C2×D188—21no—
40C2×D188—22no—
41M16×C47—22no—
42M16×C47—22no—
43C2×C8×C47—22no—
44(C2×D47)⋊C4—22no—
45(C2×D47)⋊C4—22no—
46C4⋊Dic47—21no—
47C4⋊Dic47—21no—
48#10625329—24no—
49#10625329—22no—
50#10625329D414yescomplemented
51C2×C47⋊C8—24no—
52C2×C47⋊C8—22no—
53C23×C47—22no—
54C23×C47—22no—
55C23×C47—41no—
56C23×C47C22⋊C411yescharacteristic
57C23×C47C22⋊C411yescharacteristic
58C23×C47C22×C411yescharacteristic
59C22×D47—22no—
60C22×D47—24no—
61C22×D47—42no—
62C22×D47—42no—
63C2×C4×C47—22no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47C22⋊C411yescharacteristic
71C2×C4×C47C22⋊C411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D412yes—
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47#4112yes—
76C22⋊D47—44no—
77C22⋊D47—44no—
78C2×Dic47—22no—
79C2×Dic47—42no—
80D188—41no—
81D188—42no—
82D188—41no—
83C8×C47—42no—
84C47⋊C8—24no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47—21no—
88C22×C47—21no—
89C22×C47—21no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47—44no—
93C22×C47#10012yescomplemented
94C22×C47C2×C22⋊C411yescharacteristic
95C22×C47C4×D412yes—
96C2×D47—42no—
97C2×D47—42no—
98C2×D47—42no—
99C2×D47—84no—
100C4×C47—21no—
101C4×C47—21no—
102C4×C47#12011yescharacteristic
103C4×C47#12112yes—
104C4×C47#12311yescharacteristic
105Dic47—42no—
106#1900—471nomaximal, Sylow
107C2×C47—22no—
108C2×C47—22no—
109C2×C47—41no—
110C2×C47#38611yescharacteristic
111C2×C47C2×#10011yescharacteristic
112C2×C47#41311yescharacteristic
113D47—82no—
114C22×M16—471no—
115C2×#121—471no—
116C2×#100—472no—
117#407D4711yescharacteristic, complemented
118#343—472no—
119C47#190011yescharacteristic, complemented, Sylow
120C22×D4—472no—
121C22×D4—471no—
122C23×C4C2×D4711yescharacteristic
123C2×M16—472no—
124C2×M16—944no—
125C2×M16—941no—
126C2×M16C2×D4712yes—
127C22×C8—941no—
128#121—941no—
129#121—941no—
130#121—941no—
131#121—941no—
132C2×C4⋊C4—471no—
133C2×C22⋊C4—472no—
134#100—944no—
135C22⋊C8—21no—
136C22⋊C8—21no—
137C24—472no—
138C24C4×D4711yescharacteristic
139C2×D4—942no—
140C2×D4—942no—
141C2×D4—941no—
142C2×D4—942no—
143C2×D4—942no—
144C2×D4—941no—
145C2×D4—1884no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—472no—
149C22×C4C4×D4711yescharacteristic
150C22×C4D18811yescharacteristic
151C22×C4D18811yescharacteristic
152C22×C4C22⋊D4711yescharacteristic
153C22×C4C22⋊D4711yescharacteristic
154C22×C4C22×D4711yescharacteristic
155M16—22no—
156M16—22no—
157M16—474no—
158M16—944no—
159M16—942no—
160C2×C8—22no—
161C2×C8—944no—
162C2×C8—942no—
163C4⋊C4—941no—
164C4⋊C4—941no—
165C22⋊C4—942no—
166C22⋊C4—942no—
167C23—22no—
168C23—22no—
169C23—41no—
170C23—944no—
171C23—942no—
172C23—1882no—
173C23—1882no—
174C23(C2×D47)⋊C411yescharacteristic
175C23(C2×D47)⋊C411yescharacteristic
176C23C2×C4×D4711yescharacteristic
177D4—1884no—
178D4—1884no—
179D4—1881no—
180D4—1882no—
181D4—1881no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—942no—
190C2×C4—1882no—
191C2×C4(C2×D47)⋊C411yescharacteristic
192C2×C4(C2×D47)⋊C411yescharacteristic
193C2×C4C2×D18811yescharacteristic
194C2×C4D4×D4712yes—
195C2×C4#1062535212yes—
196C2×C4C2×C22⋊D4711yescharacteristic
197C8—42no—
198C8—944no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—44no—
207C22—3764no—
208C22—1882no—
209C22—1882no—
210C22—1882no—
211C22#1309394012yescomplemented
212C22C2×(C2×D47)⋊C411yescharacteristic
213C22(C22⋊D47)⋊C412yes—
214C4—21no—
215C4—21no—
216C4—1882no—
217C4#1309399411yescharacteristic
218C4#1309399612yes—
219C4#1309400811yescharacteristic
220C2—22no—
221C2—22no—
222C2—41no—
223C2—3762no—
224C2#1568900011yescharacteristic
225C2C2×#1309394011yescharacteristic
226C2#1568910511yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#407C2
socleC22×C47C2×C22⋊C4
hypercenter#407D47
hypocenterC47#1900
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
1. C22×#10625329C2semidirect
3. C2×#13093940C2semidirect
4. #15688891C2semidirect
5. C47×#407C2semidirect
50. #10625329D4semidirect
93. C22×C47#100semidirect
117. #407D47semidirect
119. C47#1900semidirect
211. C22#13093940semidirect