Finite Group Databasebeta

← #20245447

Subgroups — #20245447

Order 6016.

158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 51 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×#13093968C211yesmaximal, characteristic
3C4×Dic188C211yesmaximal, characteristic, complemented
4C4⋊(C47⋊C16)C211yesmaximal, characteristic, complemented
5#15688927C211yesmaximal, characteristic, complemented
6#15688924C211yesmaximal, characteristic
7C47×#495C211yesmaximal, characteristic
8C2×Dic188C2211yescharacteristic
9C4×Dic94—21no—
10#13093970—22no—
11#13093968—22no—
12C2×C47⋊C16C2211yescharacteristic
13C2×C47⋊C16C2211yescharacteristic
14#13093958C2211yescharacteristic
15#13093949—21no—
16C2×Q16×C47C2211yescharacteristic
17C2×SD16×C47—21no—
18C2×D8×C47C2211yescharacteristic
19#124×C47—21no—
20C4×C8×C47C2211yescharacteristic
21C2×Q8×C47—21no—
22C2×D4×C47—21no—
23C2×Dic94—21no—
24Q16×C47—21no—
25Q16×C47—21no—
26SD16×C47—42no—
27D8×C47—21no—
28D8×C47—21no—
29C2×C8×C47D411yescharacteristic
30C2×C8×C47C2311yescharacteristic
31C22⋊C4×C47—41no—
32C22⋊C4×C47—41no—
33C42×C47D411yescharacteristic
34C4⋊Dic47—21no—
35Dic47⋊C4—41no—
36C4×Dic47—41no—
37Dic188—21no—
38Dic188D412yes—
39C47⋊C16—21no—
40C47⋊C16—21no—
41C23×C47—41no—
42Q8×C47—41no—
43Q8×C47—41no—
44D4×C47—41no—
45D4×C47—41no—
46C2×C4×C47—41no—
47C2×C4×C47D811yescharacteristic
48C2×C4×C47D811yescharacteristic
49C2×C4×C47C2×D411yescharacteristic
50C2×Dic47—41no—
51C2×Dic47—41no—
52Dic94—22no—
53Dic94—41no—
54C8×C47—21no—
55C8×C47C2×D411yescharacteristic
56C8×C47#4111yescharacteristic
57C22×C47—81no—
58C22×C47—81no—
59C22×C47—81no—
60C22×C47C2×D811yescharacteristic
61C4×C47—21no—
62C4×C47—21no—
63C4×C47—81no—
64C4×C47#12111yescharacteristic
65C4×C47AGL(1,ℤ/8)11yescharacteristic
66Dic47—42no—
67Dic47—81no—
68#2211—471nomaximal, Sylow
69C2×C47—161no—
70C2×C47#45911yescharacteristic
71C2×C47#50811yescharacteristic
72C2×C47#51011yescharacteristic
73C2×Q32—471no—
74C2×SD32—471no—
75#495D4711yescharacteristic
76C4×Q16—471no—
77C4⋊C16—471no—
78#358—471no—
79#357—471no—
80C47#221111yescharacteristic, complemented, Sylow
81C2×Q16—471no—
82C2×Q16C2×D4711yescharacteristic
83C2×SD16—21no—
84C2×D8C2×D4711yescharacteristic
85#124—21no—
86C4×Q8—941no—
87Q32—942no—
88SD32—942no—
89C2×C16—471no—
90C2×C16—471no—
91#107—471no—
92#103—941no—
93C4×C8C2×D4711yescharacteristic
94C2×Q8—21no—
95C2×Q8—941no—
96C2×D4—21no—
97Q16—21no—
98Q16—21no—
99Q16—472no—
100Q16—941no—
101SD16—42no—
102D8—21no—
103D8—21no—
104C2×C8C22⋊D4711yescharacteristic
105C2×C8C22×D4711yescharacteristic
106C4⋊C4—941no—
107C4⋊C4—1881no—
108C22⋊C4—41no—
109C22⋊C4—41no—
110C42—1881no—
111C42C22⋊D4711yescharacteristic
112C16—941no—
113C16—941no—
114C23—41no—
115Q8—41no—
116Q8—41no—
117Q8—942no—
118Q8—1881no—
119D4—41no—
120D4—41no—
121C2×C4—41no—
122C2×C4—1881no—
123C2×C4—1881no—
124C2×C4#1062533411yescharacteristic
125C2×C4#1062533411yescharacteristic
126C2×C4C2×C22⋊D4711yescharacteristic
127C8—21no—
128C8D4×D4711yescharacteristic
129C8#1062535211yescharacteristic
130C22—81no—
131C22—81no—
132C22—81no—
133C22C2×#1062533411yescharacteristic
134C4—21no—
135C4—21no—
136C4—81no—
137C4—3761no—
138C4—1882no—
139C4#1309399511yescharacteristic
140C4#1309405011yescharacteristic
141C2—161no—
142C2#1568931511yescharacteristic
143C2#1568955311yescharacteristic
144C2#1568956311yescharacteristic
subgroupG/H
centerC22C2×#10625334
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#495C2
socleC22×C47C2×D8
hypercenter#495D47
hypocenterC47#2211
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#13093970C2semidirect
3. C4×Dic188C2semidirect
4. C4⋊(C47⋊C16)C2semidirect
5. #15688927C2semidirect
80. C47#2211semidirect