Finite Group Databasebeta

← #20245451

Subgroups — #20245451

Order 6016.

158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 51 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×Dic376C211yesmaximal, characteristic, complemented
2C2×#13093969C211yesmaximal, characteristic
3#15689507C211yesmaximal, characteristic
4C4×Dic188C211yesmaximal, characteristic, complemented
5#15688928C211yesmaximal, characteristic, complemented
6#15688925C211yesmaximal, characteristic
7C47×C4⋊C16C211yesmaximal, characteristic, complemented
8C2×Dic188C2211yescharacteristic
9C2×Dic188C2211yescharacteristic
10C2×#10625325—21no—
11C2×D376C2211yescharacteristic
12#13094012—21no—
13C4×Dic94—21no—
14Dic376—22no—
15#13093969—22no—
16#13093958C2211yescharacteristic
17#13093949—21no—
18C2×C16×C47C2211yescharacteristic
19C2×C16×C47C2211yescharacteristic
20C4×C8×C47C2211yescharacteristic
21C2×D188—21no—
22C2×Dic94—21no—
23C2×Dic94—21no—
24C2×C8×C47D411yescharacteristic
25C2×C8×C47C2311yescharacteristic
26C42×C47D411yescharacteristic
27(C2×D47)⋊C4—41no—
28(C2×D47)⋊C4—41no—
29C4⋊Dic47—21no—
30Dic47⋊C4—41no—
31C4×Dic47—41no—
32Dic188—21no—
33Dic188—21no—
34Dic188—21no—
35Dic188D412yes—
36D376—21no—
37D376—21no—
38#10625325—42no—
39C16×C47—21no—
40C16×C47—21no—
41C22×D47—41no—
42C2×C4×C47D811yescharacteristic
43C2×C4×C47D811yescharacteristic
44C2×C4×C47C2×D411yescharacteristic
45C2×Dic47—41no—
46C2×Dic47—41no—
47C2×Dic47—41no—
48D188—41no—
49D188—41no—
50Dic94—22no—
51Dic94—41no—
52Dic94—41no—
53Dic94—41no—
54C8×C47—21no—
55C8×C47C2×D411yescharacteristic
56C8×C47#4111yescharacteristic
57C22×C47C2×D811yescharacteristic
58C2×D47—81no—
59C2×D47—81no—
60C2×D47—81no—
61C4×C47—21no—
62C4×C47—21no—
63C4×C47#12111yescharacteristic
64C4×C47AGL(1,ℤ/8)11yescharacteristic
65Dic47—42no—
66Dic47—81no—
67Dic47—81no—
68#2211—471nomaximal, Sylow
69C2×C47#45911yescharacteristic
70C2×C47#50811yescharacteristic
71C2×C47#51011yescharacteristic
72D47—161no—
73C2×Q32—471no—
74C2×SD32—471no—
75#495—471no—
76C4×Q16—471no—
77C4⋊C16D4711yescharacteristic, complemented
78#358—471no—
79#357—471no—
80C47#221111yescharacteristic, complemented, Sylow
81C2×Q16—471no—
82C2×Q16—471no—
83C2×SD16—941no—
84C2×D8—471no—
85#124—941no—
86C4×Q8—941no—
87Q32—942no—
88SD32—942no—
89C2×C16C2×D4711yescharacteristic
90C2×C16C2×D4711yescharacteristic
91#107—471no—
92#103—941no—
93C4×C8C2×D4711yescharacteristic
94C2×Q8—941no—
95C2×Q8—941no—
96C2×D4—941no—
97Q16—472no—
98Q16—941no—
99Q16—941no—
100Q16—941no—
101SD16—1882no—
102D8—941no—
103D8—941no—
104C2×C8D18811yescharacteristic
105C2×C8C22×D4711yescharacteristic
106C4⋊C4—941no—
107C4⋊C4—1881no—
108C22⋊C4—1881no—
109C22⋊C4—1881no—
110C42—1881no—
111C42D18811yescharacteristic
112C16—21no—
113C16—21no—
114C23—1881no—
115Q8—942no—
116Q8—1881no—
117Q8—1881no—
118Q8—1881no—
119D4—1881no—
120D4—1881no—
121C2×C4—1881no—
122C2×C4—1881no—
123C2×C4—1881no—
124C2×C4D37611yescharacteristic
125C2×C4D37611yescharacteristic
126C2×C4C2×D18811yescharacteristic
127C8—21no—
128C8D4×D4711yescharacteristic
129C8#1062535411yescharacteristic
130C22—3761no—
131C22—3761no—
132C22—3761no—
133C22C2×D37611yescharacteristic
134C4—21no—
135C4—21no—
136C4—3761no—
137C4—3761no—
138C4—1882no—
139C4#1309399911yescharacteristic
140C4#1309405211yescharacteristic
141C2—7521no—
142C2#1568931911yescharacteristic
143C2#1568955511yescharacteristic
144C2#1568956611yescharacteristic
subgroupG/H
centerC22C2×D376
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×C4⋊C16C2
socleC22×C47C2×D8
hypercenterC4⋊C16D47
hypocenterC47#2211
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4⋊C16

Complements

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

NH ≅ G/Ntype
1. C2×Dic376C2semidirect
4. C4×Dic188C2semidirect
5. #15688928C2semidirect
7. C47×C4⋊C16C2semidirect
77. C4⋊C16D47semidirect
80. C47#2211semidirect