Finite Group Databasebeta

← #20245457

Subgroups — #20245457

Order 6016.

154 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 49 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
1#15689563C211yesmaximal, characteristic, complemented
2#15689558C211yesmaximal, characteristic
3#15689507C211yesmaximal, characteristic, complemented
4#15688944C211yesmaximal, characteristic, complemented
5#15688938C211yesmaximal, characteristic, complemented
6#15688935C211yesmaximal, characteristic, complemented
7C47×#443C211yesmaximal, characteristic, complemented
8C2×Dic188C2211yescharacteristic
9C2×#10625325—21no—
10C2×D376C2211yescharacteristic
11#13094012—21no—
12#13093970—21no—
13#13093968—21no—
14#13093967—21no—
15#13093965—21no—
16#13093964C2211yescharacteristic
17#13093964C2211yescharacteristic
18#135×C47C2211yescharacteristic
19#131×C47—21no—
20#108×C47C2211yescharacteristic
21#104×C47—21no—
22C4×C8×C47C2211yescharacteristic
23#41×C47—21no—
24C2×D188—21no—
25C2×Dic94—21no—
26Q16×C47D411yescharacteristic
27SD16×C47—21no—
28D8×C47D411yescharacteristic
29M16×C47—21no—
30M16×C47—41no—
31C2×C8×C47—41no—
32C2×C8×C47D411yescharacteristic
33C2×C8×C47C2311yescharacteristic
34C42×C47D411yescharacteristic
35(C2×D47)⋊C4—42no—
36Dic188—21no—
37Dic188—21no—
38D376—21no—
39D376—21no—
40#10625325—41no—
41#10625325—41no—
42C47⋊C16—21no—
43C47⋊C16—21no—
44C22×D47—41no—
45Q8×C47—21no—
46D4×C47—21no—
47D4×C47—41no—
48C2×C4×C47—21no—
49C2×C4×C47—41no—
50C2×C4×C47C2×D411yescharacteristic
51C2×Dic47—41no—
52D188—41no—
53D188—41no—
54Dic94—41no—
55Dic94—41no—
56C8×C47—41no—
57C8×C47D811yescharacteristic
58C8×C47D811yescharacteristic
59C8×C47C2×D411yescharacteristic
60C8×C47#4111yescharacteristic
61C22×C47—41no—
62C22×C47AGL(1,ℤ/8)11yescharacteristic
63C2×D47—82no—
64C2×D47—81no—
65C4×C47—41no—
66C4×C47—41no—
67C4×C47#12111yescharacteristic
68C4×C47C2×D811yescharacteristic
69Dic47—81no—
70#2212—471nomaximal, Sylow
71C2×C47—21no—
72C2×C47—81no—
73C2×C47#45911yescharacteristic
74D47—161no—
75#510—471no—
76#509—471no—
77#495—471no—
78#443D4711yescharacteristic, complemented
79#364—471no—
80#362—471no—
81#361—471no—
82C47#221211yescharacteristic, complemented, Sylow
83#135C2×D4711yescharacteristic
84C2×Q16—471no—
85C2×SD16—941no—
86C2×D8—471no—
87#131—21no—
88#124—941no—
89Q32—941no—
90SD32—941no—
91SD32—941no—
92D16—941no—
93M32—471no—
94M32—471no—
95#108C2×D4711yescharacteristic
96#104—21no—
97C4×C8C2×D4711yescharacteristic
98#41—21no—
99C2×Q8—941no—
100C2×D4—941no—
101Q16—941no—
102Q16—941no—
103Q16D18811yescharacteristic
104SD16—21no—
105SD16—1881no—
106SD16—1881no—
107D8—941no—
108D8—941no—
109D8D18811yescharacteristic
110M16—21no—
111M16—41no—
112C2×C8—41no—
113C2×C8C22⋊D4711yescharacteristic
114C2×C8C22×D4711yescharacteristic
115C22⋊C4—1882no—
116C42C22⋊D4711yescharacteristic
117C16—941no—
118C16—941no—
119C23—1881no—
120Q8—21no—
121Q8—1881no—
122Q8—1881no—
123D4—21no—
124D4—41no—
125D4—1881no—
126D4—1881no—
127C2×C4—21no—
128C2×C4—41no—
129C2×C4—1881no—
130C2×C4C2×C22⋊D4711yescharacteristic
131C8—41no—
132C8#1062533411yescharacteristic
133C8#1062533411yescharacteristic
134C8C2×D18811yescharacteristic
135C8#1062535011yescharacteristic
136C22—41no—
137C22—3762no—
138C22—3761no—
139C22#1309404911yescharacteristic
140C4—41no—
141C4—41no—
142C4—3761no—
143C4#1309399811yescharacteristic
144C4C2×#1062533411yescharacteristic
145C2—21no—
146C2—81no—
147C2—7521no—
148C2#1568931811yescharacteristic
subgroupG/H
centerC2#15689318
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#443C2
socleC2×C47#459
hypercenter#443D47
hypocenterC47#2212
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #15689563C2semidirect
3. #15689507C2semidirect
4. #15688944C2semidirect
5. #15688938C2semidirect
6. #15688935C2semidirect
7. C47×#443C2semidirect
78. #443D47semidirect
82. C47#2212semidirect