Finite Group Databasebeta

← #20244101

Subgroups — #20244101

Order 6016.

222 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 81 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#15689150C211yesmaximal, characteristic, complemented
2C2×#13093951C211yesmaximal, characteristic
3#15689090C211yesmaximal, characteristic
4C2×#13093934C211yesmaximal, characteristic, complemented
5#15688888C211yesmaximal, characteristic, complemented
6#15688882C211yesmaximal, characteristic, complemented
7C47×#416C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11C2×C4×Dic47C2211yescharacteristic
12C4⋊(C47⋊C8)—22no—
13#13093951—22no—
14C22⋊(C47⋊C8)—22no—
15#13093934—22no—
16C2×#41×C47C2211yescharacteristic
17C22×C8×C47C2211yescharacteristic
18#117×C47C2211yescharacteristic
19#103×C47C412yescomplemented
20#102×C47C412yescomplemented
21#41×C47—21no—
22#41×C47—21no—
23#41×C47—21no—
24#41×C47—21no—
25C2×Q8×C47C2×C411yescharacteristic
26C2×D4×C47—21no—
27C2×D4×C47C2×C411yescharacteristic
28C22×C4×C47—21no—
29C22×C4×C47C2311yescharacteristic
30C22×Dic47—21no—
31C2×C8×C47—21no—
32C2×C8×C47—21no—
33C2×C8×C47C2×C412yes—
34C4⋊C4×C47C2×C412yes—
35C22⋊C4×C47—21no—
36C42×C47—21no—
37C4×Dic47—21no—
38C4×Dic47D412yes—
39#10625329—21no—
40#10625329—21no—
41#10625329—21no—
42#10625329—21no—
43C2×C47⋊C8—21no—
44C2×C47⋊C8—21no—
45C2×C47⋊C8—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8D412yes—
48C23×C47—21no—
49C23×C47#4111yescharacteristic
50Q8×C47—21no—
51Q8×C47—21no—
52D4×C47—21no—
53D4×C47—21no—
54D4×C47—41no—
55D4×C47—41no—
56C2×C4×C47—22no—
57C2×C4×C47—21no—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47C22×C411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47#4111yescharacteristic
64C2×C4×C47#4111yescharacteristic
65C2×C4×C47#4111yescharacteristic
66C2×Dic47—22no—
67C2×Dic47—42no—
68C8×C47—22no—
69C47⋊C8—22no—
70C47⋊C8—41no—
71C47⋊C8—41no—
72C22×C47—22no—
73C22×C47—41no—
74C22×C47—42no—
75C22×C47C4×D411yescharacteristic
76C22×C47#12311yescharacteristic
77C22×C47#12611yescharacteristic
78C4×C47—41no—
79C4×C47—42no—
80C4×C47#11711yescharacteristic
81C4×C47C4×D411yescharacteristic
82C4×C47#12111yescharacteristic
83C4×C47#12411yescharacteristic
84Dic47—42no—
85#1938—471nomaximal, Sylow
86C2×C47—21no—
87C2×C47—21no—
88C2×C47—81no—
89C2×C47#38811yescharacteristic
90C2×C47#44412yes—
91#424—471no—
92C2×#104—471no—
93#416D4711yescharacteristic
94#408—471no—
95C2×#97—471no—
96#341—471no—
97#339—471no—
98C47#193811yescharacteristic, complemented, Sylow
99C2×#41C2×D4711yescharacteristic
100C2×M16—471no—
101C2×M16—471no—
102C22×C8—471no—
103C22×C8C2×D4711yescharacteristic
104#117C2×D4711yescharacteristic
105C2×C42—471no—
106C4⋊C8—942no—
107#104—942no—
108#103Dic4712yescomplemented
109#102Dic4712yescomplemented
110C22⋊C8—942no—
111#97—942no—
112#41—21no—
113#41—21no—
114#41—21no—
115#41—21no—
116C2×Q8C2×Dic4711yescharacteristic
117C2×D4—21no—
118C2×D4C2×Dic4711yescharacteristic
119C22×C4—21no—
120C22×C4—941no—
121C22×C4C22×D4711yescharacteristic
122M16—941no—
123M16—941no—
124M16—941no—
125M16—941no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—472no—
129C2×C8—941no—
130C2×C8—941no—
131C2×C8—941no—
132C2×C8—941no—
133C2×C8C2×Dic4712yes—
134C4⋊C4C2×Dic4712yes—
135C22⋊C4—21no—
136C42—21no—
137C42—472no—
138C42—941no—
139C23—21no—
140C23#1062535211yescharacteristic
141Q8—21no—
142Q8—21no—
143D4—21no—
144D4—21no—
145D4—41no—
146D4—41no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—942no—
152C2×C4—1882no—
153C2×C4#1062535011yescharacteristic
154C2×C4#1062535011yescharacteristic
155C2×C4D4×D4711yescharacteristic
156C2×C4D4×D4711yescharacteristic
157C2×C4#1062535211yescharacteristic
158C2×C4C22×Dic4711yescharacteristic
159C8—22no—
160C8—942no—
161C8—1881no—
162C8—1881no—
163C22—22no—
164C22—42no—
165C22—41no—
166C22D4×Dic4711yescharacteristic
167C22#1309400611yescharacteristic
168C22#1309401711yescharacteristic
169C4—42no—
170C4—41no—
171C4—1882no—
172C4#1309398311yescharacteristic
173C4D4×Dic4711yescharacteristic
174C4#1309399711yescharacteristic
175C4#1309401011yescharacteristic
176C2—21no—
177C2—21no—
178C2—81no—
179C2#1568901611yescharacteristic
180C2#1568924512yes—
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#416C2
socleC22×C47C4×D4
hypercenter#416D47
hypocenterC47#1938
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #15689150C2semidirect
4. C2×#13093934C2semidirect
5. #15688888C2semidirect
6. #15688882C2semidirect
19. #103×C47C4semidirect
20. #102×C47C4semidirect
98. C47#1938semidirect
108. #103Dic47semidirect
109. #102Dic47semidirect