Finite Group Databasebeta

← #20245599

Subgroups — #20245599

Order 6016.

132 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 45 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#15689365C211yesmaximal, characteristic
2#15689160C211yesmaximal, characteristic
3#15688948C211yesmaximal, characteristic, complemented
4#15688928C211yesmaximal, characteristic, complemented
5#15688926C211yesmaximal, characteristic, complemented
6(C2×D47)⋊C16C211yesmaximal, characteristic
7C47×#367C211yesmaximal, characteristic, complemented
8C2×Dic188C2211yescharacteristic
9C2×C8×D47C2211yescharacteristic
10#13094004—21no—
11#13093982—21no—
12C2×C47⋊C16C2211yescharacteristic
13#13093958C2211yescharacteristic
14#13093955—21no—
15#13093947—21no—
16C2×C16×C47C2211yescharacteristic
17#107×C47C2211yescharacteristic
18#107×C47C2211yescharacteristic
19C2×C4×D47D411yescharacteristic
20C2×Dic94—21no—
21C2×C8×C47C2311yescharacteristic
22C4⋊C4×C47—21no—
23C4⋊C4×C47—21no—
24(C2×D47)⋊C4—41no—
25(C2×D47)⋊C4—41no—
26C4⋊Dic47—21no—
27C4⋊Dic47—41no—
28C4×Dic47—41no—
29C2×C47⋊C8D411yescharacteristic
30Dic188—21no—
31Dic188—21no—
32C8×D47—21no—
33C8×D47—21no—
34C16×C47—21no—
35C47⋊C16—21no—
36C22×D47D811yescharacteristic
37C2×C4×C47—41no—
38C2×C4×C47—41no—
39C2×C4×C47C2×D411yescharacteristic
40C2×Dic47—41no—
41C2×Dic47—41no—
42C2×Dic47D811yescharacteristic
43C4×D47—21no—
44C4×D47—21no—
45Dic94—41no—
46Dic94—41no—
47C8×C47#4111yescharacteristic
48C8×C47#4111yescharacteristic
49C47⋊C8—21no—
50C22×C47C2×D811yescharacteristic
51C2×D47—21no—
52C2×D47—21no—
53C2×D47—21no—
54C4×C47—81no—
55C4×C47—81no—
56C4×C47#12311yescharacteristic
57C4×C47#13711yescharacteristic
58Dic47—21no—
59Dic47—81no—
60Dic47—81no—
61#2237—471nomaximal, Sylow
62C2×C47#48011yescharacteristic
63C2×C47#50811yescharacteristic
64C2×C47#51011yescharacteristic
65D47—41no—
66#467—471no—
67#427—471no—
68#367D4711yescharacteristic, complemented
69#366—471no—
70#358—471no—
71#358—471no—
72C22⋊C16—471no—
73C47#223711yescharacteristic, complemented, Sylow
74C2×Q16—471no—
75C22×C8—471no—
76C22⋊Q8—941no—
77#117—941no—
78C2×C16—471no—
79C2×C16C2×D4711yescharacteristic
80#107—471no—
81#107C2×D4711yescharacteristic
82#107C2×D4711yescharacteristic
83#106—941no—
84#103—941no—
85C2×Q8—941no—
86C22×C4—471no—
87Q16—941no—
88Q16—941no—
89C2×C8—471no—
90C2×C8—941no—
91C2×C8—941no—
92C2×C8C22×D4711yescharacteristic
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—941no—
96C4⋊C4—1881no—
97C22⋊C4—1881no—
98C22⋊C4—1881no—
99C42—1881no—
100C16—21no—
101C16—941no—
102C23—471no—
103Q8—1881no—
104Q8—1881no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—471no—
108C2×C4—941no—
109C2×C4—941no—
110C2×C4—1881no—
111C2×C4—1881no—
112C2×C4D4×D4711yescharacteristic
113C8—941no—
114C8#1062535011yescharacteristic
115C8#1062535411yescharacteristic
116C22—941no—
117C22—941no—
118C22—941no—
119C22D8×D4711yescharacteristic
120C4—81no—
121C4—81no—
122C4—941no—
123C4—3761no—
124C4—3761no—
125C4#1309400911yescharacteristic
126C4#1309405611yescharacteristic
127C2—1881no—
128C2#1568943811yescharacteristic
129C2#1568955411yescharacteristic
130C2#1568956211yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#367C2
socleC22×C47C2×D8
hypercenter#367D47
hypocenterC47#2237
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

Complements

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

NH ≅ G/Ntype
3. #15688948C2semidirect
4. #15688928C2semidirect
5. #15688926C2semidirect
7. C47×#367C2semidirect
68. #367D47semidirect
73. C47#2237semidirect