Finite Group Databasebeta

← #20245511

Subgroups — #20245511

Order 6016.

140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 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#15689540C211yesmaximal, characteristic
3#15689398C211yesmaximal, characteristic
4#15688952C211yesmaximal, characteristic, complemented
5#15688939C211yesmaximal, characteristic, complemented
6#15688938C211yesmaximal, characteristic, complemented
7C47×#473C211yesmaximal, characteristic
8#13094054—21no—
9C2×Dic188C2211yescharacteristic
10#13093970—21no—
11#13093970—21no—
12#13093964—21no—
13#13093964C2211yescharacteristic
14C2×C47⋊C16—21no—
15C2×C47⋊C16C2211yescharacteristic
16#13093960C2211yescharacteristic
17#13093942—21no—
18#137×C47—21no—
19C2×Q16×C47C2211yescharacteristic
20#131×C47C2211yescharacteristic
21#108×C47C2211yescharacteristic
22#101×C47—21no—
23#41×C47D411yescharacteristic
24C2×Q8×C47—21no—
25C2×Dic94—21no—
26Q16×C47—21no—
27Q16×C47—21no—
28Q16×C47—41no—
29SD16×C47—41no—
30M16×C47—21no—
31M16×C47—21no—
32M16×C47D411yescharacteristic
33C2×C8×C47—21no—
34C2×C8×C47C2311yescharacteristic
35#10625337—41no—
36#10625335—41no—
37#10625329—21no—
38Dic188—21no—
39Dic188—21no—
40C47⋊C16—21no—
41C47⋊C16D411yescharacteristic
42C47⋊C16D411yescharacteristic
43Q8×C47—41no—
44Q8×C47—41no—
45Q8×C47D811yescharacteristic
46D4×C47—21no—
47D4×C47D811yescharacteristic
48C2×C4×C47—21no—
49C2×C4×C47—41no—
50C2×C4×C47C2×D411yescharacteristic
51C2×Dic47—41no—
52Dic94—41no—
53Dic94—41no—
54C8×C47—21no—
55C8×C47—41no—
56C8×C47C2×D411yescharacteristic
57C8×C47#4111yescharacteristic
58C47⋊C8—41no—
59C22×C47—21no—
60C22×C47#13511yescharacteristic
61C4×C47—21no—
62C4×C47—81no—
63C4×C47#12111yescharacteristic
64C4×C47C2×D811yescharacteristic
65Dic47—81no—
66#2222—471nomaximal, Sylow
67C2×C47—21no—
68C2×C47—41no—
69C2×C47#46611yescharacteristic
70C2×Q32—471no—
71#504—471no—
72#473—471no—
73#473D4711yescharacteristic
74#368—471no—
75#362—471no—
76#362—471no—
77C47#222211yescharacteristic, complemented, Sylow
78#137—21no—
79#137—941no—
80C2×Q16—471no—
81C2×Q16C2×D4711yescharacteristic
82#131C2×D4711yescharacteristic
83Q32—941no—
84Q32—941no—
85M32—471no—
86M32—941no—
87C2×C16—471no—
88C2×C16—941no—
89#108—471no—
90#108C2×D4711yescharacteristic
91#101—21no—
92#101—941no—
93#41C22⋊D4711yescharacteristic
94C2×Q8—21no—
95C2×Q8—941no—
96Q16—21no—
97Q16—21no—
98Q16—41no—
99Q16—941no—
100Q16—941no—
101Q16—1881no—
102SD16—41no—
103SD16—1881no—
104M16—21no—
105M16—21no—
106M16—941no—
107M16C22⋊D4711yescharacteristic
108C2×C8—21no—
109C2×C8C22×D4711yescharacteristic
110C16—471no—
111C16—471no—
112C16—941no—
113Q8—41no—
114Q8—41no—
115Q8—1881no—
116Q8—1881no—
117Q8#1062533411yescharacteristic
118D4—21no—
119D4#1062533411yescharacteristic
120C2×C4—21no—
121C2×C4—41no—
122C2×C4—1881no—
123C2×C4C2×C22⋊D4711yescharacteristic
124C8—21no—
125C8—41no—
126C8—1881no—
127C8D4×D4711yescharacteristic
128C8#1062535211yescharacteristic
129C22—21no—
130C22#1309404411yescharacteristic
131C4—21no—
132C4—81no—
133C4—3761no—
134C4#1309399611yescharacteristic
135C4C2×#1062533411yescharacteristic
136C2—21no—
137C2—41no—
138C2#1568935711yescharacteristic
subgroupG/H
centerC2#15689357
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#473C2
socleC2×C47#466
hypercenter#473D47
hypocenterC47#2222
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #473

Complements

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

NH ≅ G/Ntype
1. C2×#13093970C2semidirect
4. #15688952C2semidirect
5. #15688939C2semidirect
6. #15688938C2semidirect
77. C47#2222semidirect