Finite Group Databasebeta

← #20243852

Subgroups — #20243852

Order 6016.

390 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 101 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×#13093941C212yesmaximal, complemented
3#15689087C211yesmaximal, characteristic, complemented
4#15688892C212yesmaximal, complemented
5C2×#121×C47C211yesmaximal, characteristic
6C2×#10625329—21no—
7C2×#10625329—24no—
8C2×#10625329C2212yes—
9C2×#10625329C2212yes—
10C22×C47⋊C8—21no—
11#13093941—24no—
12C22⋊(C47⋊C8)—21no—
13C22⋊(C47⋊C8)—21no—
14C22×D4×C47C412yes—
15C22×D4×C47C2211yescharacteristic
16C23×C4×C47C2211yescharacteristic
17#121×C47—21no—
18#121×C47—21no—
19#121×C47—21no—
20#121×C47—21no—
21C2×C4⋊C4×C47C2211yescharacteristic
22C2×C22⋊C4×C47C412yes—
23C24×C47C2×C411yescharacteristic
24C24×C47C2×C412yes—
25C2×D4×C47—22no—
26C2×D4×C47—22no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47—22no—
30C2×D4×C47—22no—
31C2×D4×C47—44no—
32C22×C4×C47—22no—
33C22×C4×C47—22no—
34C22×C4×C47C2×C411yescharacteristic
35C22×C4×C47C2×C412yes—
36C22×C4×C47D411yescharacteristic
37C22×C4×C47D411yescharacteristic
38C22×C4×C47D411yescharacteristic
39C22×C4×C47D411yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C4⋊C4×C47—21no—
42C4⋊C4×C47—21no—
43C22⋊C4×C47—22no—
44C22⋊C4×C47—22no—
45#10625329—24no—
46#10625329—22no—
47#10625329—22no—
48#10625329—22no—
49#10625329D414yescomplemented
50C2×C47⋊C8—24no—
51C2×C47⋊C8—22no—
52C2×C47⋊C8—22no—
53C23×C47—22no—
54C23×C47—22no—
55C23×C47—22no—
56C23×C47—24no—
57C23×C47—41no—
58C23×C47—42no—
59C23×C47—42no—
60C23×C47C22⋊C411yescharacteristic
61C23×C47C22⋊C411yescharacteristic
62C23×C47C22×C411yescharacteristic
63D4×C47—44no—
64D4×C47—44no—
65D4×C47—41no—
66D4×C47—42no—
67D4×C47—41no—
68C2×C4×C47—22no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—21no—
74C2×C4×C47—21no—
75C2×C4×C47—22no—
76C2×C4×C47—42no—
77C2×C4×C47C22⋊C411yescharacteristic
78C2×C4×C47C22⋊C411yescharacteristic
79C2×C4×C47C2×D412yes—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47#4112yes—
83C47⋊C8—24no—
84C47⋊C8—42no—
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—42no—
94C22×C47—42no—
95C22×C47—42no—
96C22×C47—84no—
97C22×C47#10012yescomplemented
98C22×C47C2×C22⋊C411yescharacteristic
99C22×C47C4×D412yes—
100C4×C47—21no—
101C4×C47—21no—
102C4×C47—42no—
103C4×C47#12011yescharacteristic
104C4×C47#12112yes—
105C4×C47#12311yescharacteristic
106#1900—471nomaximal, Sylow
107C2×C47—22no—
108C2×C47—22no—
109C2×C47—41no—
110C2×C47—82no—
111C2×C47#38611yescharacteristic
112C2×C47C2×#10011yescharacteristic
113C2×C47#41311yescharacteristic
114C22×M16—471no—
115C2×#121D4711yescharacteristic
116C2×#100—472no—
117#407—471no—
118#343—472no—
119C47#190011yescharacteristic, complemented, Sylow
120C22×D4Dic4712yes—
121C22×D4C2×D4711yescharacteristic
122C23×C4C2×D4711yescharacteristic
123C2×M16—472no—
124C2×M16—472no—
125C2×M16—944no—
126C2×M16—941no—
127C22×C8—941no—
128#121—21no—
129#121—21no—
130#121—21no—
131#121—21no—
132C2×C4⋊C4C2×D4711yescharacteristic
133C2×C22⋊C4Dic4712yes—
134#100—944no—
135C22⋊C8—941no—
136C22⋊C8—941no—
137C24C2×Dic4711yescharacteristic
138C24C2×Dic4712yes—
139C2×D4—22no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4—22no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—44no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4C2×Dic4711yescharacteristic
149C22×C4C2×Dic4712yes—
150C22×C4C22⋊D4711yescharacteristic
151C22×C4C22⋊D4711yescharacteristic
152C22×C4C22⋊D4711yescharacteristic
153C22×C4C22⋊D4711yescharacteristic
154C22×C4C22×D4711yescharacteristic
155M16—474no—
156M16—944no—
157M16—942no—
158M16—942no—
159M16—942no—
160C2×C8—944no—
161C2×C8—942no—
162C2×C8—942no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C22⋊C4—22no—
166C22⋊C4—22no—
167C23—22no—
168C23—22no—
169C23—22no—
170C23—24no—
171C23—41no—
172C23—42no—
173C23—42no—
174C23C22⋊Dic4711yescharacteristic
175C23C22⋊Dic4711yescharacteristic
176C23C22×Dic4711yescharacteristic
177D4—44no—
178D4—44no—
179D4—41no—
180D4—42no—
181D4—41no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—42no—
191C2×C4C22⋊Dic4711yescharacteristic
192C2×C4C22⋊Dic4711yescharacteristic
193C2×C4D4×D4712yes—
194C2×C4#1062535212yes—
195C2×C4C2×C22⋊D4711yescharacteristic
196C2×C4C2×C22⋊D4711yescharacteristic
197C8—944no—
198C8—1882no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—44no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—84no—
211C22#1309394112yescomplemented
212C22C2×C22⋊Dic4711yescharacteristic
213C22D4×Dic4712yes—
214C4—21no—
215C4—21no—
216C4—42no—
217C4#1309399211yescharacteristic
218C4#1309399612yes—
219C4#1309400511yescharacteristic
220C2—22no—
221C2—22no—
222C2—41no—
223C2—82no—
224C2#1568900311yescharacteristic
225C2C2×#1309394111yescharacteristic
226C2#1568910711yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic47
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#121×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×#121D47
hypocenterC47#1900
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#10625329C2semidirect
2. C2×#13093941C2semidirect
3. #15689087C2semidirect
4. #15688892C2semidirect
49. #10625329D4semidirect
97. C22×C47#100semidirect
119. C47#1900semidirect
211. C22#13093941semidirect