Finite Group Databasebeta

← #20245448

Subgroups — #20245448

Order 6016.

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

normal subgroups only

This group has 158 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
1C2×#13093970C211yesmaximal, characteristic, complemented
2#15689506C211yesmaximal, characteristic
3Q16×Dic47C211yesmaximal, characteristic, complemented
4Dic47⋊C16C211yesmaximal, characteristic, complemented
5#15688928C211yesmaximal, characteristic, complemented
6#15688924C211yesmaximal, characteristic
7C2×SD32×C47C211yesmaximal, characteristic
8C2×Dic188C2211yescharacteristic
9C2×#10625335—21no—
10#13094011—21no—
11Q8×Dic47—21no—
12#13093970—22no—
13C2×C47⋊C16C2211yescharacteristic
14#13093958C2211yescharacteristic
15#13093948—21no—
16C8×Dic47C2211yescharacteristic
17C2×Q16×C47C2211yescharacteristic
18C2×D8×C47C2211yescharacteristic
19SD32×C47—22no—
20C2×C16×C47C2211yescharacteristic
21C2×Q8×C47—21no—
22C2×D4×C47—21no—
23C2×Dic94—21no—
24Q16×C47—21no—
25Q16×C47D412yes—
26D8×C47—21no—
27D8×C47—21no—
28C2×C8×C47C2311yescharacteristic
29C22⋊Dic47—41no—
30C22⋊Dic47—41no—
31#10625335—42no—
32C4⋊Dic47—21no—
33C4⋊Dic47—41no—
34C4×Dic47—41no—
35C4×Dic47D411yescharacteristic
36C2×C47⋊C8D411yescharacteristic
37Dic188—21no—
38Dic188—21no—
39C16×C47—21no—
40C47⋊C16—21no—
41C23×C47—41no—
42Q8×C47—22no—
43Q8×C47—41no—
44D4×C47—41no—
45D4×C47—41no—
46C2×C4×C47—41no—
47C2×C4×C47C2×D411yescharacteristic
48C2×Dic47—41no—
49C2×Dic47—41no—
50C2×Dic47D811yescharacteristic
51C2×Dic47D811yescharacteristic
52Dic94—41no—
53Dic94—41no—
54C8×C47C2×D411yescharacteristic
55C8×C47#4111yescharacteristic
56C47⋊C8—21no—
57C22×C47—81no—
58C22×C47—81no—
59C22×C47—81no—
60C22×C47C2×D811yescharacteristic
61C4×C47—42no—
62C4×C47#12111yescharacteristic
63C4×C47AGL(1,ℤ/8)11yescharacteristic
64Dic47—21no—
65Dic47—21no—
66Dic47—81no—
67Dic47—81no—
68#2211—471nomaximal, Sylow
69C2×C47—161no—
70C2×C47#45911yescharacteristic
71C2×C47#50811yescharacteristic
72C2×C47#51011yescharacteristic
73C2×Q32—471no—
74C2×SD32D4711yescharacteristic
75#495—471no—
76C4×Q16—471no—
77C4⋊C16—471no—
78#358—471no—
79#357—471no—
80C47#221111yescharacteristic, complemented, Sylow
81C2×Q16—471no—
82C2×Q16C2×D4711yescharacteristic
83C2×SD16—941no—
84C2×D8C2×D4711yescharacteristic
85#124—941no—
86C4×Q8—941no—
87Q32—942no—
88SD32—22no—
89C2×C16—471no—
90C2×C16C2×D4711yescharacteristic
91#107—471no—
92#103—941no—
93C4×C8—471no—
94C2×Q8—21no—
95C2×Q8—941no—
96C2×D4—21no—
97Q16—21no—
98Q16—941no—
99Q16—941no—
100Q16C22⋊D4712yes—
101SD16—1882no—
102D8—21no—
103D8—21no—
104C2×C8—471no—
105C2×C8C22×D4711yescharacteristic
106C4⋊C4—941no—
107C4⋊C4—1881no—
108C22⋊C4—1881no—
109C22⋊C4—1881no—
110C42—471no—
111C42—1881no—
112C16—21no—
113C16—941no—
114C23—41no—
115Q8—22no—
116Q8—41no—
117Q8—1881no—
118Q8—1881no—
119D4—41no—
120D4—41no—
121C2×C4—41no—
122C2×C4—471no—
123C2×C4—471no—
124C2×C4—1881no—
125C2×C4—1881no—
126C2×C4D4×D4711yescharacteristic
127C8—941no—
128C8#1062535211yescharacteristic
129C8C2×C22⋊D4711yescharacteristic
130C22—81no—
131C22—81no—
132C22—81no—
133C22D8×D4711yescharacteristic
134C4—42no—
135C4—941no—
136C4—941no—
137C4—3761no—
138C4—3761no—
139C4#1309399611yescharacteristic
140C4#1309404811yescharacteristic
141C2—161no—
142C2#1568931611yescharacteristic
143C2#1568955411yescharacteristic
144C2#1568956211yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC2×SD32×C47C2
socleC22×C47C2×D8
hypercenterC2×SD32D47
hypocenterC47#2211
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#13093970C2semidirect
3. Q16×Dic47C2semidirect
4. Dic47⋊C16C2semidirect
5. #15688928C2semidirect
80. C47#2211semidirect