Finite Group Databasebeta

← #20245512

Subgroups — #20245512

Order 6016.

140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 43 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×#13093970C211yesmaximal, characteristic, complemented
2#15689541C211yesmaximal, characteristic
3#15689399C211yesmaximal, characteristic
4#15689395C211yesmaximal, characteristic
5#15688952C211yesmaximal, characteristic, complemented
6#15688940C211yesmaximal, characteristic, complemented
7C47×#362C211yesmaximal, characteristic, complemented
8#13094057—21no—
9#13094055—21no—
10C2×Dic188C2211yescharacteristic
11#13094030C2211yescharacteristic
12#13093970—21no—
13#13093970—21no—
14#13093963—21no—
15C2×C47⋊C16C2211yescharacteristic
16C16×D47—21no—
17#13093960C2211yescharacteristic
18#13093943—21no—
19#13093942—21no—
20C2×Q16×C47C2211yescharacteristic
21M32×C47C2211yescharacteristic
22#108×C47C2211yescharacteristic
23C2×Q8×C47—21no—
24#10625350D411yescharacteristic
25C2×Dic94—21no—
26Q16×C47—21no—
27Q16×C47—21no—
28M16×C47—21no—
29C2×C8×C47C2311yescharacteristic
30#10625337—41no—
31#10625336—41no—
32#10625329—21no—
33#10625329D411yescharacteristic
34Dic188—21no—
35Dic188—21no—
36Dic188—41no—
37#10625325—41no—
38#10625324—21no—
39C8×D47—21no—
40C16×C47—21no—
41C47⋊C16D411yescharacteristic
42C47⋊C16D411yescharacteristic
43Q8×C47—41no—
44Q8×C47—41no—
45C2×C4×C47—41no—
46C2×C4×C47C2×D411yescharacteristic
47C22⋊D47—21no—
48C2×Dic47—41no—
49D188D811yescharacteristic
50C4×D47—21no—
51Dic94—41no—
52Dic94—41no—
53Dic94D811yescharacteristic
54C8×C47—41no—
55C8×C47C2×D411yescharacteristic
56C8×C47#4111yescharacteristic
57C47⋊C8—21no—
58C47⋊C8—41no—
59C22×C47#13511yescharacteristic
60C2×D47—21no—
61C4×C47—81no—
62C4×C47#12111yescharacteristic
63C4×C47C2×D811yescharacteristic
64Dic47—21no—
65Dic47—81no—
66#2222—471nomaximal, Sylow
67C2×C47—21no—
68C2×C47#46611yescharacteristic
69D47—41no—
70C2×Q32—471no—
71#504—471no—
72#473—471no—
73#473—471no—
74#368—471no—
75#362—471no—
76#362D4711yescharacteristic, complemented
77C47#222211yescharacteristic, complemented, Sylow
78#137—941no—
79#137—941no—
80C2×Q16—471no—
81C2×Q16C2×D4711yescharacteristic
82#131—471no—
83Q32—941no—
84Q32—941no—
85M32—941no—
86M32C2×D4711yescharacteristic
87C2×C16—471no—
88C2×C16—941no—
89#108—471no—
90#108C2×D4711yescharacteristic
91#101—941no—
92#101—941no—
93#41—471no—
94C2×Q8—21no—
95C2×Q8—941no—
96Q16—21no—
97Q16—21no—
98Q16—941no—
99Q16—941no—
100Q16—1881no—
101Q16—1881no—
102SD16—1881no—
103SD16—1881no—
104M16—21no—
105M16—471no—
106M16—941no—
107M16—941no—
108C2×C8—941no—
109C2×C8C22×D4711yescharacteristic
110C16—21no—
111C16—471no—
112C16—471no—
113Q8—41no—
114Q8—41no—
115Q8—471no—
116Q8—1881no—
117Q8—1881no—
118D4—471no—
119D4—941no—
120C2×C4—41no—
121C2×C4—941no—
122C2×C4—1881no—
123C2×C4D4×D4711yescharacteristic
124C8—41no—
125C8—941no—
126C8—1881no—
127C8#1062535011yescharacteristic
128C8D4×D4711yescharacteristic
129C22—941no—
130C22#1309404511yescharacteristic
131C4—81no—
132C4—941no—
133C4—3761no—
134C4#1309399711yescharacteristic
135C4D8×D4711yescharacteristic
136C2—21no—
137C2—1881no—
138C2#1568935811yescharacteristic
subgroupG/H
centerC2#15689358
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#362C2
socleC2×C47#466
hypercenter#362D47
hypocenterC47#2222
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
1. C2×#13093970C2semidirect
5. #15688952C2semidirect
6. #15688940C2semidirect
7. C47×#362C2semidirect
76. #362D47semidirect
77. C47#2222semidirect