Finite Group Databasebeta

← #15689307

Subgroups — #15689307

Order 3008.

142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 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#13094071C211yesmaximal, characteristic
2#13094057C211yesmaximal, characteristic, complemented
3#13094054C211yesmaximal, characteristic, complemented
4#13094024C211yesmaximal, characteristic, complemented
5#13093952C211yesmaximal, characteristic, complemented
6#13093942C211yesmaximal, characteristic, complemented
7#104×C47C211yesmaximal, characteristic, complemented
8#41×C47C2211yescharacteristic
9Q8×D47—21no—
10#10625352—21no—
11#10625352—22no—
12#10625350—21no—
13#10625350C2211yescharacteristic
14C2×Dic94—21no—
15C2×Dic94C2211yescharacteristic
16C2×Dic94C2211yescharacteristic
17M16×C47C2211yescharacteristic
18C42×C47C2211yescharacteristic
19#10625337—21no—
20#10625335—21no—
21C4⋊Dic47—22no—
22#10625329C2211yescharacteristic
23Dic188—21no—
24#10625325—21no—
25Q8×C47D411yescharacteristic
26D4×C47—21no—
27D4×C47D411yescharacteristic
28C2×C4×C47—21no—
29C2×C4×C47—21no—
30C2×C4×C47C2311yescharacteristic
31C22⋊D47—22no—
32C22⋊D47—21no—
33C2×Dic47—22no—
34C2×Dic47—21no—
35C2×Dic47D412yes—
36D188D411yescharacteristic
37C4×D47—22no—
38C4×D47—21no—
39Dic94—22no—
40Dic94—21no—
41Dic94—21no—
42Dic94—21no—
43Dic94—21no—
44Dic94D411yescharacteristic
45C8×C47—21no—
46C47⋊C8—21no—
47C22×C47—21no—
48C22×C47C2×D411yescharacteristic
49C2×D47—21no—
50C4×C47—22no—
51C4×C47—21no—
52C4×C47C2×D411yescharacteristic
53C4×C47C2×D411yescharacteristic
54Dic47—22no—
55Dic47—21no—
56Dic47—41no—
57C2×C47—21no—
58C2×C47—41no—
59C2×C47#12011yescharacteristic
60D47—41no—
61#456—471nomaximal, Sylow
62C47#45611yescharacteristic, complemented, Sylow
632−1+4—471no—
64#137—471no—
65#137—471no—
66C4⋊Q8—471no—
67#104—471no—
68#104D4711yescharacteristic, complemented
69#101—471no—
70#41—471no—
71#41—941no—
72#41—942no—
73#41—941no—
74#41C2×D4711yescharacteristic
75C2×Q8—471no—
76C2×Q8—471no—
77C2×Q8—941no—
78C2×Q8—941no—
79Q16—941no—
80Q16—941no—
81SD16—941no—
82SD16—941no—
83M16—471no—
84M16C2×D4711yescharacteristic
85C4⋊C4—942no—
86C42C2×D4711yescharacteristic
87Q8—471no—
88Q8—942no—
89Q8—941no—
90Q8—941no—
91Q8—941no—
92Q8—941no—
93Q8D18811yescharacteristic
94D4—21no—
95D4—471no—
96D4—942no—
97D4—941no—
98D4D18811yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—472no—
102C2×C4—942no—
103C2×C4—942no—
104C2×C4—941no—
105C2×C4—941no—
106C2×C4C22×D4711yescharacteristic
107C8—21no—
108C8—941no—
109C22—21no—
110C22—941no—
111C22D4×D4711yescharacteristic
112C4—22no—
113C4—21no—
114C4—942no—
115C4—941no—
116C4—1881no—
117C4C2×D18811yescharacteristic
118C4D4×D4711yescharacteristic
119C2—21no—
120C2—41no—
121C2—1881no—
122C2#1309399411yescharacteristic
subgroupG/H
centerC2#13093994
commutator, cosocleC2×C4×C47C23
FrattiniC2×C4C22×D47
Fitting#104×C47C2
socleC2×C47#120
prime radical#13094071C2
hypercenter#104D47
hypocenterC47#456
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #13094057C2semidirect
3. #13094054C2semidirect
4. #13094024C2semidirect
5. #13093952C2semidirect
6. #13093942C2semidirect
7. #104×C47C2semidirect
62. C47#456semidirect
68. #104D47semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130940712
#130940572
#130940542
#130940242
#130939522
#130939422
#104×C472
#45647