Finite Group Databasebeta

← #20254602

Subgroups — #20254602

Order 6016.

322 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 121 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#15689533C212yesmaximal, complemented
3#15689493C212yesmaximal, complemented
4#15689464C214yesmaximal
5#15689415C212yesmaximal, complemented
6#15689405C212yesmaximal, complemented
7#15689180C211yesmaximal, characteristic
8C47×#533C211yesmaximal, characteristic
9#13094024C2211yescharacteristic
10#13094024C2211yescharacteristic
11#13094016—21no—
12#13094003—21no—
13#13094003C2212yes—
14C4×Dic94—21no—
15C4×Dic94C2212yes—
16#13093983—21no—
17#13093957C2214yes—
18#13093955C2214yes—
19C4⋊(C47⋊C8)C2212yes—
20#13093947C2214yes—
21#13093947C2214yes—
22C22⋊(C47⋊C8)C2212yes—
23#13093935C2212yes—
24C4⋊Q8×C47C2211yescharacteristic
25C4⋊Q8×C47C2211yescharacteristic
26#125×C47C2212yes—
27C22⋊Q8×C47—21no—
28C22⋊Q8×C47—21no—
29C4×Q8×C47—21no—
30C4×Q8×C47—21no—
31#117×C47C2212yes—
32C2×C42×C47C2211yescharacteristic
33C2×Q8×C47—21no—
34C2×Q8×C47—21no—
35C22×C4×C47D411yescharacteristic
36C22×C4×C47D411yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C2×Dic94—21no—
39C2×Dic94C2312yes—
40C4⋊C4×C47—22no—
41C4⋊C4×C47—22no—
42C4⋊C4×C47—21no—
43C4⋊C4×C47—21no—
44C4⋊C4×C47C2312yes—
45C4⋊C4×C47C2312yes—
46C22⋊C4×C47—22no—
47C42×C47—22no—
48C42×C47D411yescharacteristic
49C42×C47D411yescharacteristic
50C42×C47C2311yescharacteristic
51C42×C47C2311yescharacteristic
52C22⋊Dic47—22no—
53C4⋊Dic47—21no—
54C4⋊Dic47—21no—
55C4⋊Dic47—21no—
56C4⋊Dic47C2312yes—
57Dic47⋊C4—22no—
58Dic47⋊C4—22no—
59C4×Dic47—22no—
60C2×C47⋊C8C2314yes—
61C23×C47C2×D411yescharacteristic
62Q8×C47—42no—
63Q8×C47—42no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—41no—
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2411yescharacteristic
75C2×Dic47—22no—
76C2×Dic47—22no—
77Dic94—24no—
78Dic94—42no—
79C47⋊C8—24no—
80C22×C47—21no—
81C22×C47—21no—
82C22×C47—21no—
83C22×C47C22×D411yescharacteristic
84C4×C47—21no—
85C4×C47—21no—
86C4×C47—21no—
87C4×C47—21no—
88C4×C47—42no—
89C4×C47—42no—
90C4×C47#13712yes—
91C4×C472−1+412yes—
92Dic47—42no—
93Dic47—42no—
94#3237—471nomaximal, Sylow
95C2×C47—41no—
96C2×C47#53611yescharacteristic
97C2×C47C2×#13711yescharacteristic
98C2×C47#57511yescharacteristic
99#533—471no—
100#533D4711yescharacteristic
101#501—472no—
102#491—472no—
103#485—474no—
104#477—472no—
105#475—472no—
106#432—471no—
107C47#323711yescharacteristic, complemented, Sylow
108C4⋊Q8—471no—
109C4⋊Q8—471no—
110C4⋊Q8C2×D4711yescharacteristic
111C4⋊Q8C2×D4711yescharacteristic
112#125—941no—
113#125C2×D4712yes—
114C22⋊Q8—21no—
115C22⋊Q8—21no—
116C22⋊Q8—472no—
117C22⋊Q8—941no—
118C4×Q8—21no—
119C4×Q8—21no—
120C4×Q8—472no—
121C4×Q8—941no—
122#117—941no—
123#117C2×D4712yes—
124C2×C42C2×D4711yescharacteristic
125#107—474no—
126#106—474no—
127C4⋊C8—472no—
128#103—474no—
129#103—474no—
130C22⋊C8—472no—
131#97—472no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—472no—
135C2×Q8—941no—
136C22×C4C22⋊D4711yescharacteristic
137C22×C4C22⋊D4711yescharacteristic
138C22×C4C22×D4711yescharacteristic
139C2×C8—474no—
140C4⋊C4—22no—
141C4⋊C4—22no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—472no—
145C4⋊C4—942no—
146C4⋊C4—942no—
147C4⋊C4—941no—
148C4⋊C4—941no—
149C4⋊C4—941no—
150C4⋊C4C22×D4712yes—
151C4⋊C4C22×D4712yes—
152C22⋊C4—22no—
153C22⋊C4—942no—
154C42—22no—
155C42—942no—
156C42C22⋊D4711yescharacteristic
157C42C22⋊D4711yescharacteristic
158C42C22×D4711yescharacteristic
159C42C22×D4711yescharacteristic
160C23C2×C22⋊D4711yescharacteristic
161Q8—42no—
162Q8—42no—
163Q8—944no—
164Q8—1882no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—942no—
171C2×C4—942no—
172C2×C4C2×C22⋊D4711yescharacteristic
173C2×C4C2×C22⋊D4711yescharacteristic
174C2×C4C2×C22⋊D4711yescharacteristic
175C2×C4C2×C22⋊D4711yescharacteristic
176C2×C4C2×C22⋊D4711yescharacteristic
177C2×C4C23×D4711yescharacteristic
178C8—944no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22C22×C22⋊D4711yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—42no—
188C4—42no—
189C4—1882no—
190C4—1882no—
191C4#1309405412yes—
192C4#1309407212yes—
193C2—41no—
194C2#1568969711yescharacteristic
195C2C2×#1309405411yescharacteristic
196C2#1568992111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#533C2
socleC22×C47C22×D4
hypercenter#533D47
hypocenterC47#3237
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #15689533C2semidirect
3. #15689493C2semidirect
5. #15689415C2semidirect
6. #15689405C2semidirect
107. C47#3237semidirect