Finite Group Databasebeta

← #20243857

Subgroups — #20243857

Order 6016.

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

normal subgroups only

This group has 338 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
2C2×#13093943C212yesmaximal, complemented
3#15689087C211yesmaximal, characteristic
4#15688892C212yesmaximal, complemented
5C2×C22⋊Q8×C47C211yesmaximal, characteristic
6C2×#10625329—21no—
7C2×#10625329—24no—
8C2×#10625329C2212yes—
9C2×#10625329C2212yes—
10C22×C47⋊C8—21no—
11#13093943—24no—
12C22⋊(C47⋊C8)—21no—
13C22⋊(C47⋊C8)—21no—
14C22×Q8×C47C2211yescharacteristic
15C23×C4×C47C2211yescharacteristic
16C22⋊Q8×C47—21no—
17C22⋊Q8×C47—21no—
18C22⋊Q8×C47—21no—
19C22⋊Q8×C47—21no—
20C2×C4⋊C4×C47C412yes—
21C2×C4⋊C4×C47C2211yescharacteristic
22C2×C22⋊C4×C47C412yes—
23C24×C47C2×C411yescharacteristic
24C2×Q8×C47—21no—
25C2×Q8×C47—21no—
26C2×Q8×C47—22no—
27C2×Q8×C47—22no—
28C22×C4×C47—22no—
29C22×C4×C47—22no—
30C22×C4×C47C2×C412yes—
31C22×C4×C47C2×C411yescharacteristic
32C22×C4×C47C2×C412yes—
33C22×C4×C47D411yescharacteristic
34C22×C4×C47D411yescharacteristic
35C22×C4×C47D411yescharacteristic
36C22×C4×C47D411yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C4⋊C4×C47—22no—
39C4⋊C4×C47—22no—
40C4⋊C4×C47—21no—
41C4⋊C4×C47—21no—
42C22⋊C4×C47—22no—
43C22⋊C4×C47—22no—
44#10625329—24no—
45#10625329—22no—
46#10625329—22no—
47#10625329—22no—
48#10625329D414yes—
49C2×C47⋊C8—24no—
50C2×C47⋊C8—22no—
51C2×C47⋊C8—22no—
52C23×C47—22no—
53C23×C47—22no—
54C23×C47—41no—
55C23×C47C22⋊C411yescharacteristic
56C23×C47C22⋊C411yescharacteristic
57C23×C47C22×C411yescharacteristic
58Q8×C47—41no—
59Q8×C47—42no—
60Q8×C47—41no—
61C2×C4×C47—22no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—24no—
71C2×C4×C47—42no—
72C2×C4×C47C22⋊C411yescharacteristic
73C2×C4×C47C22⋊C411yescharacteristic
74C2×C4×C47C2×D412yes—
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47#4112yes—
78C47⋊C8—24no—
79C47⋊C8—42no—
80C22×C47—21no—
81C22×C47—21no—
82C22×C47—21no—
83C22×C47—21no—
84C22×C47—21no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47—44no—
88C22×C47#10112yescomplemented
89C22×C47C2×C22⋊C411yescharacteristic
90C22×C47C4×D412yes—
91C4×C47—21no—
92C4×C47—21no—
93C4×C47—42no—
94C4×C47—42no—
95C4×C47#12011yescharacteristic
96C4×C47#12112yes—
97C4×C47#12311yescharacteristic
98#1901—471nomaximal, Sylow
99C2×C47—22no—
100C2×C47—22no—
101C2×C47—41no—
102C2×C47#38611yescharacteristic
103C2×C47C2×#10111yescharacteristic
104C2×C47#41311yescharacteristic
105C22×M16—471no—
106C2×C22⋊Q8D4711yescharacteristic
107C2×#101—472no—
108#407—471no—
109#343—472no—
110C47#190111yescharacteristic, complemented, Sylow
111C22×Q8C2×D4711yescharacteristic
112C23×C4C2×D4711yescharacteristic
113C2×M16—472no—
114C2×M16—472no—
115C2×M16—944no—
116C2×M16—941no—
117C22×C8—941no—
118C22⋊Q8—21no—
119C22⋊Q8—21no—
120C22⋊Q8—21no—
121C22⋊Q8—21no—
122C2×C4⋊C4Dic4712yes—
123C2×C4⋊C4C2×D4711yescharacteristic
124C2×C22⋊C4Dic4712yes—
125#101—944no—
126C22⋊C8—941no—
127C22⋊C8—941no—
128C24C2×Dic4711yescharacteristic
129C2×Q8—22no—
130C2×Q8—22no—
131C2×Q8—21no—
132C2×Q8—21no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4C2×Dic4712yes—
136C22×C4C2×Dic4711yescharacteristic
137C22×C4C2×Dic4712yes—
138C22×C4C22⋊D4711yescharacteristic
139C22×C4C22⋊D4711yescharacteristic
140C22×C4C22⋊D4711yescharacteristic
141C22×C4C22⋊D4711yescharacteristic
142C22×C4C22×D4711yescharacteristic
143M16—474no—
144M16—944no—
145M16—942no—
146M16—942no—
147M16—942no—
148C2×C8—944no—
149C2×C8—942no—
150C2×C8—942no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C22⋊C4—22no—
156C22⋊C4—22no—
157C23—22no—
158C23—22no—
159C23—41no—
160C23C22⋊Dic4711yescharacteristic
161C23C22⋊Dic4711yescharacteristic
162C23C22×Dic4711yescharacteristic
163Q8—41no—
164Q8—42no—
165Q8—41no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—42no—
177C2×C4C22⋊Dic4711yescharacteristic
178C2×C4C22⋊Dic4711yescharacteristic
179C2×C4D4×D4712yes—
180C2×C4#1062535212yes—
181C2×C4C2×C22⋊D4711yescharacteristic
182C2×C4C2×C22⋊D4711yescharacteristic
183C8—944no—
184C8—1882no—
185C22—21no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—44no—
193C22#1309394312yescomplemented
194C22C2×C22⋊Dic4711yescharacteristic
195C22D4×Dic4712yes—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—42no—
200C4#1309399211yescharacteristic
201C4#1309399612yes—
202C4#1309400511yescharacteristic
203C2—22no—
204C2—22no—
205C2—41no—
206C2#1568900311yescharacteristic
207C2C2×#1309394311yescharacteristic
208C2#1568910711yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic47
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×C22⋊Q8×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×C22⋊Q8D47
hypocenterC47#1901
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#13093943C2semidirect
4. #15688892C2semidirect
88. C22×C47#101semidirect
110. C47#1901semidirect
193. C22#13093943semidirect