Finite Group Databasebeta

← #20245251

Subgroups — #20245251

Order 6016.

160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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×#13093969C211yesmaximal, characteristic
2#15689217C211yesmaximal, characteristic, complemented
3#15689205C211yesmaximal, characteristic
4#15688926C211yesmaximal, characteristic, complemented
5#15688923C211yesmaximal, characteristic
6#15688898C211yesmaximal, characteristic, complemented
7C47×#366C211yesmaximal, characteristic, complemented
8C2×Dic188C2211yescharacteristic
9C2×D376C2211yescharacteristic
10#13093989—21no—
11#13093986—21no—
12#13093969C414yescomplemented
13C2×C47⋊C16C2211yescharacteristic
14#13093947—21no—
15#13093944—21no—
16C8×Dic47C2211yescharacteristic
17C2×C16×C47C2211yescharacteristic
18#107×C47C2211yescharacteristic
19#107×C47C2211yescharacteristic
20C2×D188—21no—
21C2×C4×D47—41no—
22C2×Dic94—21no—
23C2×C8×C47C2311yescharacteristic
24C4⋊C4×C47—21no—
25C4⋊C4×C47—21no—
26(C2×D47)⋊C4—41no—
27Dic47⋊C4—41no—
28C4×Dic47—41no—
29C4×Dic47D411yescharacteristic
30C2×C47⋊C8D411yescharacteristic
31Dic188—21no—
32Dic188C2×C412yescomplemented
33D376—21no—
34D376C2×C412yes—
35C16×C47C2×C412yescomplemented
36C47⋊C16—21no—
37C22×D47—41no—
38C2×C4×C47—41no—
39C2×C4×C47—41no—
40C2×C4×C47C2×D411yescharacteristic
41C2×Dic47—41no—
42C2×Dic47D811yescharacteristic
43C2×Dic47D811yescharacteristic
44D188—22no—
45D188—41no—
46C4×D47—82no—
47Dic94—22no—
48Dic94—41no—
49C8×C47C22×C411yescharacteristic
50C8×C47#4111yescharacteristic
51C47⋊C8—21no—
52C22×C47C2×D811yescharacteristic
53C2×D47—42no—
54C2×D47—81no—
55C2×D47—81no—
56C4×C47—81no—
57C4×C47—81no—
58C4×C47C4×D411yescharacteristic
59C4×C47#13511yescharacteristic
60Dic47—21no—
61Dic47—21no—
62Dic47—42no—
63#2175—471nomaximal, Sylow
64C2×C47C4×D811yescharacteristic
65C2×C47#50911yescharacteristic
66C2×C47#51011yescharacteristic
67D47—82no—
68C2×SD32—471no—
69C4×Q16—471no—
70C4×D8—471no—
71#366D4711yescharacteristic, complemented
72#358—471no—
73#357—471no—
74#346—471no—
75C47#217511yescharacteristic, complemented, Sylow
76C2×Q16—471no—
77C2×D8—471no—
78C4×Q8—941no—
79C4×D4—941no—
80SD32—474no—
81C2×C16—471no—
82C2×C16C2×D4711yescharacteristic
83#107C2×D4711yescharacteristic
84#107C2×D4711yescharacteristic
85#103—941no—
86#102—941no—
87C4×C8—471no—
88C2×Q8—941no—
89C2×D4—941no—
90C22×C4—1881no—
91Q16—472no—
92Q16—941no—
93D8—472no—
94D8—941no—
95C2×C8—471no—
96C2×C8C22×D4711yescharacteristic
97C4⋊C4—21no—
98C4⋊C4—21no—
99C4⋊C4—1881no—
100C22⋊C4—1881no—
101C42—471no—
102C42—1881no—
103C16—941no—
104C16C4×D4712yescomplemented
105C23—1881no—
106Q8—942no—
107Q8—1881no—
108D4—942no—
109D4—1881no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—471no—
113C2×C4—471no—
114C2×C4—3762no—
115C2×C4—1881no—
116C2×C4D4×D4711yescharacteristic
117C8—941no—
118C8C2×C4×D4711yescharacteristic
119C8#1062535411yescharacteristic
120C22—3761no—
121C22—3761no—
122C22—1882no—
123C22D8×D4711yescharacteristic
124C4—81no—
125C4—81no—
126C4—941no—
127C4—941no—
128C4—1882no—
129C4#1309398611yescharacteristic
130C4#1309404711yescharacteristic
131C2—3762no—
132C2#1568920511yescharacteristic
133C2#1568955711yescharacteristic
134C2#1568956511yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC8×C47C22×C4
FrattiniC2×C8C22×D47
FittingC47×#366C2
socleC22×C47C2×D8
hypercenter#366D47
hypocenterC47#2175
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #366

Complements

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

NH ≅ G/Ntype
2. #15689217C2semidirect
4. #15688926C2semidirect
6. #15688898C2semidirect
7. C47×#366C2semidirect
12. #13093969C4semidirect
32. Dic188C2×C4semidirect
35. C16×C47C2×C4semidirect
71. #366D47semidirect
75. C47#2175semidirect
104. C16C4×D47semidirect