Finite Group Databasebeta

← #20245596

Subgroups — #20245596

Order 6016.

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

normal subgroups only

This group has 132 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#15689364C211yesmaximal, characteristic
2#15688950C211yesmaximal, characteristic, complemented
3#15688948C211yesmaximal, characteristic, complemented
4#15688926C211yesmaximal, characteristic, complemented
5#15688926C211yesmaximal, characteristic, complemented
6C22⋊(C47⋊C16)C211yesmaximal, characteristic
7C47×#427C211yesmaximal, characteristic
8C2×Dic188C2211yescharacteristic
9#13094003—21no—
10C2×C47⋊C16C2211yescharacteristic
11C2×C47⋊C16C2211yescharacteristic
12#13093958C2211yescharacteristic
13#13093949—21no—
14C22×C8×C47C2211yescharacteristic
15#117×C47—21no—
16#107×C47C2211yescharacteristic
17#107×C47C2211yescharacteristic
18#106×C47—21no—
19C22×C4×C47D411yescharacteristic
20C2×Dic94—21no—
21C2×C8×C47—21no—
22C2×C8×C47—21no—
23C2×C8×C47D411yescharacteristic
24C2×C8×C47C2311yescharacteristic
25C4⋊C4×C47—21no—
26C4⋊C4×C47—21no—
27C22⋊C4×C47—41no—
28C42×C47—41no—
29C22⋊Dic47—41no—
30C4⋊Dic47—21no—
31Dic47⋊C4—41no—
32Dic188—21no—
33Dic188—21no—
34C47⋊C16—21no—
35C47⋊C16—21no—
36C23×C47D811yescharacteristic
37C2×C4×C47—21no—
38C2×C4×C47—21no—
39C2×C4×C47—41no—
40C2×C4×C47—41no—
41C2×C4×C47D811yescharacteristic
42C2×C4×C47C2×D411yescharacteristic
43C2×Dic47—41no—
44C2×Dic47—41no—
45Dic94—41no—
46Dic94—41no—
47C8×C47—21no—
48C8×C47#4111yescharacteristic
49C8×C47#4111yescharacteristic
50C22×C47—21no—
51C22×C47—21no—
52C22×C47—21no—
53C22×C47C2×D811yescharacteristic
54C4×C47—21no—
55C4×C47—81no—
56C4×C47—81no—
57C4×C47#12311yescharacteristic
58C4×C47#13711yescharacteristic
59Dic47—81no—
60Dic47—81no—
61#2237—471nomaximal, Sylow
62C2×C47—41no—
63C2×C47#48011yescharacteristic
64C2×C47#50811yescharacteristic
65C2×C47#51011yescharacteristic
66#467—471no—
67#427D4711yescharacteristic
68#367—471no—
69#366—471no—
70#358—471no—
71#358—471no—
72C22⋊C16—471no—
73C47#223711yescharacteristic, complemented, Sylow
74C2×Q16—471no—
75C22×C8C2×D4711yescharacteristic
76C22⋊Q8—941no—
77#117—21no—
78C2×C16—471no—
79C2×C16—471no—
80#107—471no—
81#107C2×D4711yescharacteristic
82#107C2×D4711yescharacteristic
83#106—21no—
84#103—941no—
85C2×Q8—941no—
86C22×C4C22⋊D4711yescharacteristic
87Q16—941no—
88Q16—941no—
89C2×C8—21no—
90C2×C8—21no—
91C2×C8C22⋊D4711yescharacteristic
92C2×C8C22×D4711yescharacteristic
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—941no—
96C4⋊C4—1881no—
97C22⋊C4—41no—
98C22⋊C4—1881no—
99C42—41no—
100C16—941no—
101C16—941no—
102C23#1062533411yescharacteristic
103Q8—1881no—
104Q8—1881no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—1881no—
110C2×C4—1881no—
111C2×C4#1062533411yescharacteristic
112C2×C4C2×C22⋊D4711yescharacteristic
113C8—21no—
114C8#1062535011yescharacteristic
115C8#1062535011yescharacteristic
116C22—21no—
117C22—21no—
118C22—21no—
119C22C2×#1062533411yescharacteristic
120C4—21no—
121C4—81no—
122C4—81no—
123C4—3761no—
124C4—3761no—
125C4#1309400711yescharacteristic
126C4#1309405511yescharacteristic
127C2—41no—
128C2#1568943611yescharacteristic
129C2#1568955311yescharacteristic
130C2#1568956311yescharacteristic
subgroupG/H
centerC22C2×#10625334
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#427C2
socleC22×C47C2×D8
hypercenter#427D47
hypocenterC47#2237
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #427

Complements

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

NH ≅ G/Ntype
2. #15688950C2semidirect
3. #15688948C2semidirect
4. #15688926C2semidirect
5. #15688926C2semidirect
73. C47#2237semidirect