Finite Group Databasebeta

← #20253518

Subgroups — #20253518

Order 6016.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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
1#15689680C211yesmaximal, characteristic
2#15689453C212yesmaximal
3#15689408C212yesmaximal, complemented
4#15689333C212yesmaximal, complemented
5#15689279C212yesmaximal
6#15689228C214yesmaximal, complemented
7#15689180C211yesmaximal, characteristic
8C2×C4×Q8×C47C211yesmaximal, characteristic
9C2×#10625337C2214yes—
10#13094024C2211yescharacteristic
11#13094024C2211yescharacteristic
12#13094016—21no—
13#13094003—21no—
14#13094003C2212yes—
15C4×Dic94—21no—
16C4×Dic94C2212yes—
17#13093983—21no—
18#13093955C2214yes—
19C4⋊(C47⋊C8)C2212yes—
20#13093948C2214yes—
21#13093947C2214yes—
22C22⋊(C47⋊C8)C2212yes—
23#13093935C2212yes—
24C22×Q8×C47C2211yescharacteristic
25C4×Q8×C47—21no—
26C4×Q8×C47—21no—
27C4×Q8×C47C2212yes—
28C4×Q8×C47C2212yes—
29C2×C4⋊C4×C47—21no—
30C2×C4⋊C4×C47C2211yescharacteristic
31C2×C42×C47—21no—
32C2×C42×C47C2211yescharacteristic
33C2×Q8×C47—24no—
34C2×Q8×C47—21no—
35C2×Q8×C47C2312yes—
36C22×C4×C47—21no—
37C22×C4×C47—21no—
38C22×C4×C47D411yescharacteristic
39C22×C4×C47D411yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C2×Dic94—21no—
42C2×Dic94C2312yes—
43C4⋊C4×C47—22no—
44C4⋊C4×C47—22no—
45C4⋊C4×C47—21no—
46C4⋊C4×C47C2312yes—
47C42×C47—22no—
48C42×C47—22no—
49C42×C47D411yescharacteristic
50C42×C47D411yescharacteristic
51C42×C47C2311yescharacteristic
52C42×C47C2311yescharacteristic
53C22⋊Dic47—22no—
54#10625337—28no—
55C4⋊Dic47—21no—
56C4⋊Dic47—21no—
57C4⋊Dic47—21no—
58C4⋊Dic47C2312yes—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61C4×Dic47—22no—
62C2×C47⋊C8C2314yes—
63C23×C47C2×D411yescharacteristic
64Q8×C47—24no—
65Q8×C47—22no—
66Q8×C47#4114yes—
67C2×C4×C47—24no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—42no—
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2411yescharacteristic
80C2×Dic47—22no—
81C2×Dic47—22no—
82Dic94—24no—
83Dic94—42no—
84C47⋊C8—24no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47#13712yes—
88C22×C47C22×D411yescharacteristic
89C4×C47—24no—
90C4×C47—21no—
91C4×C47—21no—
92C4×C47—21no—
93C4×C47—21no—
94C4×C47—42no—
95C4×C47#13712yes—
96C4×C47C2×#4112yes—
97Dic47—42no—
98Dic47—42no—
99#3113—471nomaximal, Sylow
100C2×C47—22no—
101C2×C47#52511yescharacteristic
102C2×C47C2×#13711yescharacteristic
103C2×C47C2×#13711yescharacteristic
104#533—471no—
105C2×C4×Q8D4711yescharacteristic
106#483—472no—
107#475—472no—
108#462—472no—
109#451—472no—
110#441—474no—
111#432—471no—
112C47#311311yescharacteristic, complemented, Sylow
113C22×Q8C2×D4711yescharacteristic
114C2×Q16—474no—
115C4⋊Q8—471no—
116C4⋊Q8—471no—
117#125—941no—
118C22⋊Q8—472no—
119C22⋊Q8—941no—
120C4×Q8—21no—
121C4×Q8—21no—
122C4×Q8—472no—
123C4×Q8—941no—
124C4×Q8C2×D4712yes—
125C4×Q8C2×D4712yes—
126#117—941no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4C2×D4711yescharacteristic
129C2×C42—21no—
130C2×C42C2×D4711yescharacteristic
131#106—474no—
132C4⋊C8—472no—
133#103—474no—
134#103—474no—
135C22⋊C8—472no—
136#97—472no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8—472no—
140C2×Q8—941no—
141C2×Q8C22×D4712yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4C22⋊D4711yescharacteristic
145C22×C4C22⋊D4711yescharacteristic
146C22×C4C22×D4711yescharacteristic
147Q16—948no—
148C2×C8—474no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—21no—
152C4⋊C4—472no—
153C4⋊C4—942no—
154C4⋊C4—942no—
155C4⋊C4—941no—
156C4⋊C4—941no—
157C4⋊C4—941no—
158C4⋊C4C22×D4712yes—
159C22⋊C4—942no—
160C42—22no—
161C42—22no—
162C42—942no—
163C42C22⋊D4711yescharacteristic
164C42C22⋊D4711yescharacteristic
165C42C22×D4711yescharacteristic
166C42C22×D4711yescharacteristic
167C23C2×C22⋊D4711yescharacteristic
168Q8—24no—
169Q8—22no—
170Q8—944no—
171Q8—1882no—
172Q8#1062535014yes—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—942no—
181C2×C4—942no—
182C2×C4C2×C22⋊D4711yescharacteristic
183C2×C4C2×C22⋊D4711yescharacteristic
184C2×C4C2×C22⋊D4711yescharacteristic
185C2×C4C2×C22⋊D4711yescharacteristic
186C2×C4C2×C22⋊D4711yescharacteristic
187C2×C4C23×D4711yescharacteristic
188C8—944no—
189C22—21no—
190C22—21no—
191C22#1309405412yes—
192C22C22×C22⋊D4711yescharacteristic
193C4—24no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—1882no—
200C4—1882no—
201C4#1309405512yes—
202C4C2×#1062535012yes—
203C2—22no—
204C2#1568963411yescharacteristic
205C2C2×#1309405411yescharacteristic
206C2C2×#1309405511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×C4×Q8×C47C2
socleC22×C47C22×D4
hypercenterC2×C4×Q8D47
hypocenterC47#3113
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #15689408C2semidirect
4. #15689333C2semidirect
6. #15689228C2semidirect
112. C47#3113semidirect