Finite Group Databasebeta

← #20245593

Subgroups — #20245593

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#15689161C211yesmaximal, characteristic
2#15688950C211yesmaximal, characteristic, complemented
3#15688948C211yesmaximal, characteristic, complemented
4#15688927C211yesmaximal, characteristic, complemented
5#15688927C211yesmaximal, characteristic, complemented
6C22⋊(C47⋊C16)C211yesmaximal, characteristic
7C47×#467C211yesmaximal, characteristic
8#13093983—21no—
9C2×C47⋊C16C2211yescharacteristic
10C2×C47⋊C16C2211yescharacteristic
11#13093958C2211yescharacteristic
12#13093958C2211yescharacteristic
13#13093956—21no—
14C2×Q16×C47C2211yescharacteristic
15C22×C8×C47C2211yescharacteristic
16C22⋊Q8×C47—21no—
17#107×C47C2211yescharacteristic
18#103×C47—21no—
19C2×Q8×C47—21no—
20C22×C4×C47D411yescharacteristic
21Q16×C47—21no—
22Q16×C47—21no—
23C2×C8×C47—21no—
24C2×C8×C47—21no—
25C2×C8×C47D411yescharacteristic
26C2×C8×C47C2311yescharacteristic
27C4⋊C4×C47—21no—
28C4⋊C4×C47—41no—
29C22⋊C4×C47—41no—
30C22⋊Dic47—41no—
31C4⋊Dic47—21no—
32C4⋊Dic47—21no—
33C4×Dic47—41no—
34C47⋊C16—21no—
35C47⋊C16—21no—
36C23×C47D811yescharacteristic
37Q8×C47—41no—
38Q8×C47—41no—
39C2×C4×C47—21no—
40C2×C4×C47—21no—
41C2×C4×C47—41no—
42C2×C4×C47—41no—
43C2×C4×C47D811yescharacteristic
44C2×C4×C47C2×D411yescharacteristic
45C2×Dic47—41no—
46C2×Dic47—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#467D4711yescharacteristic
67#427—471no—
68#367—471no—
69#366—471no—
70#358—471no—
71#358—471no—
72C22⋊C16—471no—
73C47#223711yescharacteristic, complemented, Sylow
74C2×Q16C2×D4711yescharacteristic
75C22×C8C2×D4711yescharacteristic
76C22⋊Q8—21no—
77#117—941no—
78C2×C16—471no—
79C2×C16—471no—
80#107—471no—
81#107—471no—
82#107C2×D4711yescharacteristic
83#106—941no—
84#103—21no—
85C2×Q8—21no—
86C22×C4C22⋊D4711yescharacteristic
87Q16—21no—
88Q16—21no—
89C2×C8—21no—
90C2×C8—21no—
91C2×C8C22⋊D4711yescharacteristic
92C2×C8C22×D4711yescharacteristic
93C4⋊C4—21no—
94C4⋊C4—41no—
95C4⋊C4—941no—
96C4⋊C4—941no—
97C22⋊C4—41no—
98C22⋊C4—1881no—
99C42—1881no—
100C16—941no—
101C16—941no—
102C23#1062533411yescharacteristic
103Q8—41no—
104Q8—41no—
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#1062535211yescharacteristic
115C8#1062535211yescharacteristic
116C22—21no—
117C22—21no—
118C22—21no—
119C22C2×#1062533411yescharacteristic
120C4—21no—
121C4—81no—
122C4—81no—
123C4—3761no—
124C4—3761no—
125C4#1309400511yescharacteristic
126C4#1309405411yescharacteristic
127C2—41no—
128C2#1568943411yescharacteristic
129C2#1568955311yescharacteristic
130C2#1568956411yescharacteristic
subgroupG/H
centerC22C2×#10625334
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#467C2
socleC22×C47C2×D8
hypercenter#467D47
hypocenterC47#2237
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #15688950C2semidirect
3. #15688948C2semidirect
4. #15688927C2semidirect
5. #15688927C2semidirect
73. C47#2237semidirect