Finite Group Databasebeta

← #20245453

Subgroups — #20245453

Order 6016.

158 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 47 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
2C2×#13093969C211yesmaximal, characteristic
3#15689508C211yesmaximal, characteristic
4#15689217C211yesmaximal, characteristic, complemented
5Dic47⋊C16C211yesmaximal, characteristic, complemented
6#15688923C211yesmaximal, characteristic
7C47×#358C211yesmaximal, characteristic, complemented
8C2×Dic188C2211yescharacteristic
9C2×#10625336—21no—
10C2×D376C2211yescharacteristic
11#13094013—21no—
12#13093989—21no—
13#13093970—22no—
14#13093969—22no—
15C2×C47⋊C16C2211yescharacteristic
16#13093947—21no—
17C8×Dic47C2211yescharacteristic
18C2×Q16×C47C2211yescharacteristic
19C2×C16×C47C2211yescharacteristic
20#107×C47C2211yescharacteristic
21C2×Q8×C47—21no—
22C2×D188—21no—
23C2×Dic94—21no—
24Q16×C47—21no—
25Q16×C47—21no—
26C2×C8×C47C2311yescharacteristic
27C4⋊C4×C47—21no—
28#10625336—42no—
29(C2×D47)⋊C4—41no—
30(C2×D47)⋊C4—41no—
31Dic47⋊C4—41no—
32C4×Dic47—41no—
33C4×Dic47D411yescharacteristic
34C2×C47⋊C8D411yescharacteristic
35Dic188—21no—
36Dic188D412yes—
37D376—21no—
38D376—21no—
39C16×C47—21no—
40C47⋊C16—21no—
41C22×D47—41no—
42Q8×C47—41no—
43Q8×C47—41no—
44C2×C4×C47—41no—
45C2×C4×C47—41no—
46C2×C4×C47C2×D411yescharacteristic
47C2×Dic47—41no—
48C2×Dic47D811yescharacteristic
49C2×Dic47D811yescharacteristic
50D188—41no—
51D188—41no—
52Dic94—22no—
53Dic94—41no—
54C8×C47C2×D411yescharacteristic
55C8×C47#4111yescharacteristic
56C47⋊C8—21no—
57C22×C47C2×D811yescharacteristic
58C2×D47—81no—
59C2×D47—81no—
60C2×D47—81no—
61C4×C47—81no—
62C4×C47—81no—
63C4×C47#12111yescharacteristic
64C4×C47AGL(1,ℤ/8)11yescharacteristic
65Dic47—21no—
66Dic47—21no—
67Dic47—42no—
68#2211—471nomaximal, Sylow
69C2×C47#45911yescharacteristic
70C2×C47#50811yescharacteristic
71C2×C47#51011yescharacteristic
72D47—161no—
73C2×Q32—471no—
74C2×SD32—471no—
75#495—471no—
76C4×Q16—471no—
77C4⋊C16—471no—
78#358D4711yescharacteristic, complemented
79#357—471no—
80C47#221111yescharacteristic, complemented, Sylow
81C2×Q16—471no—
82C2×Q16C2×D4711yescharacteristic
83C2×SD16—941no—
84C2×D8—471no—
85#124—941no—
86C4×Q8—941no—
87Q32—942no—
88SD32—942no—
89C2×C16—471no—
90C2×C16C2×D4711yescharacteristic
91#107C2×D4711yescharacteristic
92#103—941no—
93C4×C8—471no—
94C2×Q8—21no—
95C2×Q8—941no—
96C2×D4—941no—
97Q16—21no—
98Q16—21no—
99Q16—472no—
100Q16—941no—
101SD16—1882no—
102D8—941no—
103D8—941no—
104C2×C8—471no—
105C2×C8C22×D4711yescharacteristic
106C4⋊C4—21no—
107C4⋊C4—1881no—
108C22⋊C4—1881no—
109C22⋊C4—1881no—
110C42—471no—
111C42—1881no—
112C16—21no—
113C16—941no—
114C23—1881no—
115Q8—41no—
116Q8—41no—
117Q8—942no—
118Q8—1881no—
119D4—1881no—
120D4—1881no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—471no—
124C2×C4—471no—
125C2×C4—1881no—
126C2×C4D4×D4711yescharacteristic
127C8—941no—
128C8#1062535011yescharacteristic
129C8D4×D4711yescharacteristic
130C22—3761no—
131C22—3761no—
132C22—3761no—
133C22D8×D4711yescharacteristic
134C4—81no—
135C4—81no—
136C4—941no—
137C4—941no—
138C4—1882no—
139C4#1309399711yescharacteristic
140C4#1309405111yescharacteristic
141C2—7521no—
142C2#1568931711yescharacteristic
143C2#1568955411yescharacteristic
144C2#1568956511yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#358C2
socleC22×C47C2×D8
hypercenter#358D47
hypocenterC47#2211
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
1. C2×#13093970C2semidirect
4. #15689217C2semidirect
5. Dic47⋊C16C2semidirect
7. C47×#358C2semidirect
78. #358D47semidirect
80. C47#2211semidirect