Finite Group Databasebeta

← #20242571

Subgroups — #20242571

Order 6016.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#15689859C211yesmaximal, characteristic
2#15689405C211yesmaximal, characteristic, complemented
3#15689330C211yesmaximal, characteristic, complemented
4#15688867C211yesmaximal, characteristic
5#15688855C211yesmaximal, characteristic, complemented
6#15688855C211yesmaximal, characteristic, complemented
7C47×#486C211yesmaximal, characteristic
8C2×#10625337—21no—
9#13094011—21no—
10#13094011—21no—
11#13094005—22no—
12C4×Dic94C2211yescharacteristic
13C4×Dic94C2211yescharacteristic
14D4×Dic47—21no—
15D4×Dic47—21no—
16#13093955—21no—
17C4⋊(C47⋊C8)C2211yescharacteristic
18C4⋊(C47⋊C8)C2211yescharacteristic
19#13093948—21no—
20#13093947—21no—
21C4⋊Q8×C47C2211yescharacteristic
22#127×C47C2211yescharacteristic
23#102×C47—22no—
24C4×C8×C47C2211yescharacteristic
25C2×Q8×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47D412yes—
29C22×Dic47—22no—
30C2×Dic94D411yescharacteristic
31C2×Dic94D411yescharacteristic
32C2×C8×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C42×C47C2311yescharacteristic
36C22⋊Dic47—22no—
37C22⋊Dic47—22no—
38C22⋊Dic47—22no—
39#10625337—42no—
40C4⋊Dic47D411yescharacteristic
41C4⋊Dic47D411yescharacteristic
42Dic47⋊C4—21no—
43Dic47⋊C4—21no—
44C4×Dic47—21no—
45C4×Dic47—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C23×C47—22no—
49Q8×C47—41no—
50Q8×C47—41no—
51D4×C47—42no—
52D4×C47—41no—
53D4×C47—41no—
54D4×C47—41no—
55D4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×D411yescharacteristic
60C2×Dic47—21no—
61C2×Dic47—21no—
62C2×Dic47—21no—
63C2×Dic47—21no—
64C2×Dic47—82no—
65Dic94—21no—
66Dic94—21no—
67Dic94—21no—
68Dic94—21no—
69C8×C47—41no—
70C47⋊C8—41no—
71C47⋊C8—41no—
72C22×C47—42no—
73C22×C47—42no—
74C22×C47—42no—
75C22×C47#12011yescharacteristic
76C4×C47—21no—
77C4×C47—81no—
78C4×C47#13511yescharacteristic
79C4×C47#13511yescharacteristic
80C4×C47AGL(1,ℤ/8)11yescharacteristic
81C4×C47#13711yescharacteristic
82Dic47—41no—
83Dic47—41no—
84Dic47—41no—
85Dic47—41no—
86#1640—471nomaximal, Sylow
87C2×C47—82no—
88C2×C47#44911yescharacteristic
89C2×C47#45211yescharacteristic
90C2×C47#45511yescharacteristic
91#559—471no—
92#486D4711yescharacteristic
93#475—471no—
94#462—471no—
95#331—471no—
96Q8⋊C8—471no—
97Q8⋊C8—471no—
98C47#164011yescharacteristic, complemented, Sylow
99C2×Q16—941no—
100C4⋊Q8C2×D4711yescharacteristic
101#127C2×D4711yescharacteristic
102#124—941no—
103#124—941no—
104#123—942no—
105C4×Q8—471no—
106C4×Q8—471no—
107C4×D4—941no—
108C4×D4—941no—
109#106—941no—
110C4⋊C8—471no—
111C4⋊C8—471no—
112#103—941no—
113#103—941no—
114#102—22no—
115C4×C8C2×D4711yescharacteristic
116C2×Q8—21no—
117C2×Q8—471no—
118C2×Q8—471no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4C22⋊D4712yes—
122C22×C4—942no—
123Q16—1882no—
124C2×C8—21no—
125C2×C8—941no—
126C2×C8—941no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—471no—
130C4⋊C4—471no—
131C4⋊C4—941no—
132C4⋊C4—941no—
133C22⋊C4—942no—
134C22⋊C4—942no—
135C22⋊C4—942no—
136C42—941no—
137C42—941no—
138C42C22×D4711yescharacteristic
139C23—22no—
140Q8—41no—
141Q8—41no—
142Q8—941no—
143Q8—941no—
144Q8—941no—
145Q8—941no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—41no—
152C2×C4—941no—
153C2×C4—941no—
154C2×C4—941no—
155C2×C4—941no—
156C2×C4—3762no—
157C2×C4D4×D4711yescharacteristic
158C2×C4D4×D4711yescharacteristic
159C2×C4C2×C22⋊D4711yescharacteristic
160C8—41no—
161C8—1881no—
162C8—1881no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#1309399211yescharacteristic
167C4—21no—
168C4—81no—
169C4—1881no—
170C4—1881no—
171C4—1881no—
172C4—1881no—
173C4#1309404311yescharacteristic
174C4#1309404511yescharacteristic
175C4#1309404811yescharacteristic
176C4#1309405311yescharacteristic
177C2—82no—
178C2#1568926511yescharacteristic
179C2#1568928211yescharacteristic
180C2#1568930011yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#486C2
socleC22×C47#120
hypercenter#486D47
hypocenterC47#1640
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #15689405C2semidirect
3. #15689330C2semidirect
5. #15688855C2semidirect
6. #15688855C2semidirect
98. C47#1640semidirect