Finite Group Databasebeta

← #20245252

Subgroups — #20245252

Order 6016.

160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×#13093968C211yesmaximal, characteristic
2C4×Dic188C211yesmaximal, characteristic, complemented
3#15688948C211yesmaximal, characteristic, complemented
4#15688926C211yesmaximal, characteristic, complemented
5#15688924C211yesmaximal, characteristic
6#15688899C211yesmaximal, characteristic, complemented
7C4×D8×C47C211yesmaximal, characteristic
8C2×Dic188C2211yescharacteristic
9C4×Dic94—21no—
10#13093968C414yescomplemented
11C2×C47⋊C16C2211yescharacteristic
12C2×C47⋊C16C2211yescharacteristic
13#13093958C2211yescharacteristic
14#13093949—21no—
15C2×D8×C47C2211yescharacteristic
16C4×D4×C47—21no—
17#107×C47C2211yescharacteristic
18#102×C47—21no—
19C4×C8×C47C2211yescharacteristic
20C2×D4×C47—21no—
21C22×C4×C47—41no—
22C2×Dic94—21no—
23D8×C47—21no—
24D8×C47C2×C412yes—
25C2×C8×C47D411yescharacteristic
26C2×C8×C47C2311yescharacteristic
27C4⋊C4×C47—21no—
28C22⋊C4×C47—41no—
29C42×C47D411yescharacteristic
30C4⋊Dic47—21no—
31Dic47⋊C4—41no—
32C4×Dic47—41no—
33Dic188—21no—
34Dic188C2×C412yescomplemented
35C47⋊C16—21no—
36C47⋊C16C2×C412yescomplemented
37C23×C47—41no—
38D4×C47—22no—
39D4×C47—41no—
40C2×C4×C47—41no—
41C2×C4×C47—82no—
42C2×C4×C47D811yescharacteristic
43C2×C4×C47D811yescharacteristic
44C2×C4×C47C2×D411yescharacteristic
45C2×Dic47—41no—
46C2×Dic47—41no—
47Dic94—22no—
48Dic94—41no—
49C8×C47—21no—
50C8×C47C22×C411yescharacteristic
51C8×C47#4111yescharacteristic
52C22×C47—42no—
53C22×C47—81no—
54C22×C47—81no—
55C22×C47C2×D811yescharacteristic
56C4×C47—21no—
57C4×C47—21no—
58C4×C47—81no—
59C4×C47C4×D411yescharacteristic
60C4×C47#13511yescharacteristic
61Dic47—42no—
62Dic47—81no—
63#2175—471nomaximal, Sylow
64C2×C47—82no—
65C2×C47C4×D811yescharacteristic
66C2×C47#50911yescharacteristic
67C2×C47#51011yescharacteristic
68C2×SD32—471no—
69C4×Q16—471no—
70C4×D8D4711yescharacteristic
71#366—471no—
72#358—471no—
73#357—471no—
74#346—471no—
75C47#217511yescharacteristic, complemented, Sylow
76C2×Q16—471no—
77C2×D8C2×D4711yescharacteristic
78C4×Q8—941no—
79C4×D4—21no—
80SD32—474no—
81C2×C16—471no—
82C2×C16—471no—
83#107—471no—
84#107C2×D4711yescharacteristic
85#103—941no—
86#102—21no—
87C4×C8C2×D4711yescharacteristic
88C2×Q8—941no—
89C2×D4—21no—
90C22×C4—41no—
91Q16—472no—
92Q16—941no—
93D8—21no—
94D8C4×D4712yes—
95C2×C8C22⋊D4711yescharacteristic
96C2×C8C22×D4711yescharacteristic
97C4⋊C4—21no—
98C4⋊C4—941no—
99C4⋊C4—1881no—
100C22⋊C4—41no—
101C42—1881no—
102C42C22⋊D4711yescharacteristic
103C16—472no—
104C16—941no—
105C23—41no—
106Q8—942no—
107Q8—1881no—
108D4—22no—
109D4—41no—
110C2×C4—41no—
111C2×C4—82no—
112C2×C4—1881no—
113C2×C4—1881no—
114C2×C4#1062533411yescharacteristic
115C2×C4#1062533411yescharacteristic
116C2×C4C2×C22⋊D4711yescharacteristic
117C8—21no—
118C8C2×C4×D4711yescharacteristic
119C8#1062535011yescharacteristic
120C22—42no—
121C22—81no—
122C22—81no—
123C22C2×#1062533411yescharacteristic
124C4—21no—
125C4—21no—
126C4—81no—
127C4—3761no—
128C4—1882no—
129C4C4×C22⋊D4711yescharacteristic
130C4#1309404411yescharacteristic
131C2—82no—
132C2C4×#1062533411yescharacteristic
133C2#1568955911yescharacteristic
134C2#1568956311yescharacteristic
subgroupG/H
centerC22C2×#10625334
commutatorC8×C47C22×C4
FrattiniC2×C8C22×D47
FittingC4×D8×C47C2
socleC22×C47C2×D8
hypercenterC4×D8D47
hypocenterC47#2175
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
2. C4×Dic188C2semidirect
3. #15688948C2semidirect
4. #15688926C2semidirect
6. #15688899C2semidirect
10. #13093968C4semidirect
34. Dic188C2×C4semidirect
36. C47⋊C16C2×C4semidirect
75. C47#2175semidirect