Finite Group Databasebeta

← #20245562

Subgroups — #20245562

Order 6016.

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

normal subgroups only

This group has 120 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#15689523C211yesmaximal, characteristic, complemented
2#15689240C211yesmaximal, characteristic
3#15688946C211yesmaximal, characteristic, complemented
4#15688945C211yesmaximal, characteristic, complemented
5#15688943C211yesmaximal, characteristic, complemented
6#15688933C211yesmaximal, characteristic
7C47×#360C211yesmaximal, characteristic
8#13094031—21no—
9#13094015—21no—
10#13093964C2211yescharacteristic
11#13093960C2211yescharacteristic
12#13093957—21no—
13#13093956C2211yescharacteristic
14#13093951—21no—
15C8×Dic47C2211yescharacteristic
16#135×C47C2211yescharacteristic
17M32×C47C2211yescharacteristic
18#106×C47C2211yescharacteristic
19#41×C47—21no—
20Q16×C47Q811yescharacteristic
21SD16×C47—21no—
22D8×C47Q811yescharacteristic
23C2×C8×C47C2311yescharacteristic
24C4⋊C4×C47—21no—
25C4⋊Dic47—21no—
26C4⋊Dic47—41no—
27Dic47⋊C4—41no—
28C4×Dic47D411yescharacteristic
29#10625329—21no—
30#10625329—41no—
31C2×C47⋊C8—41no—
32C2×C47⋊C8D411yescharacteristic
33C16×C47—21no—
34C47⋊C16—21no—
35Q8×C47—21no—
36D4×C47—21no—
37D4×C47—41no—
38C2×C4×C47—41no—
39C2×C4×C47—41no—
40C2×C4×C47C2×D411yescharacteristic
41C2×Dic47—21no—
42C2×Dic47—41no—
43C8×C47C2×Q811yescharacteristic
44C8×C47#4111yescharacteristic
45C47⋊C8—41no—
46C47⋊C8SD1611yescharacteristic
47C47⋊C8SD1611yescharacteristic
48C22×C47—41no—
49C22×C47AGL(1,ℤ/8)11yescharacteristic
50C4×C47—41no—
51C4×C47—81no—
52C4×C47C22⋊Q811yescharacteristic
53C4×C47C2×SD1611yescharacteristic
54Dic47—41no—
55Dic47—81no—
56#2231—471nomaximal, Sylow
57C2×C47—21no—
58C2×C47—81no—
59C2×C47#47611yescharacteristic
60#499—471no—
61#443—471no—
62#365—471no—
63#365—471no—
64#364—471no—
65#360—471no—
66#360D4711yescharacteristic
67C47#223111yescharacteristic, complemented, Sylow
68#135C2×D4711yescharacteristic
69#131—941no—
70#125—941no—
71M32—471no—
72M32C2×D4711yescharacteristic
73#108—471no—
74#107—941no—
75#106—471no—
76#106C2×D4711yescharacteristic
77#104—941no—
78C4×C8—471no—
79#41—21no—
80Q16Dic9411yescharacteristic
81SD16—21no—
82D8Dic9411yescharacteristic
83M16—941no—
84M16—1881no—
85C2×C8—471no—
86C2×C8—1881no—
87C2×C8C22×D4711yescharacteristic
88C4⋊C4—21no—
89C4⋊C4—941no—
90C4⋊C4—1881no—
91C4⋊C4—1881no—
92C42—471no—
93C16—21no—
94C16—941no—
95Q8—21no—
96D4—21no—
97D4—41no—
98C2×C4—41no—
99C2×C4—41no—
100C2×C4—941no—
101C2×C4—1881no—
102C2×C4D4×D4711yescharacteristic
103C8—471no—
104C8—471no—
105C8—1881no—
106C8C2×Dic9411yescharacteristic
107C8#1062535211yescharacteristic
108C22—41no—
109C22#1309404811yescharacteristic
110C4—41no—
111C4—81no—
112C4—3761no—
113C4—1881no—
114C4#1309400111yescharacteristic
115C4SD16×D4711yescharacteristic
116C2—21no—
117C2—81no—
118C2#1568941111yescharacteristic
subgroupG/H
centerC2#15689411
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#360C2
socleC2×C47#476
hypercenter#360D47
hypocenterC47#2231
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
1. #15689523C2semidirect
3. #15688946C2semidirect
4. #15688945C2semidirect
5. #15688943C2semidirect
67. C47#2231semidirect