Finite Group Databasebeta

← #15689299

Subgroups — #15689299

Order 3008.

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

normal subgroups only

This group has 152 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#13094070C211yesmaximal, characteristic
2#13094055C211yesmaximal, characteristic, complemented
3#13094013C211yesmaximal, characteristic, complemented
4#13093951C211yesmaximal, characteristic, complemented
5#13093950C211yesmaximal, characteristic, complemented
6#13093940C211yesmaximal, characteristic, complemented
7#137×C47C211yesmaximal, characteristic, complemented
8#41×C47C2211yescharacteristic
9C2×Q8×C47C2211yescharacteristic, complemented
10#10625354—21no—
11D4×D47—22no—
12D4×D47—21no—
13#10625350—21no—
14#10625350C2211yescharacteristic
15C2×D188—21no—
16C2×D188C2211yescharacteristic
17Q16×C47—21no—
18SD16×C47—21no—
19M16×C47C2211yescharacteristic, complemented
20#10625337—21no—
21#10625336—21no—
22(C2×D47)⋊C4—22no—
23C4×Dic47C2211yescharacteristic, complemented
24#10625329C2211yescharacteristic, complemented
25C22×D47—22no—
26C22×D47D412yes—
27Q8×C47—21no—
28Q8×C47—21no—
29Q8×C47D411yescharacteristic
30D4×C47—21no—
31D4×C47D411yescharacteristic
32C2×C4×C47—21no—
33C2×C4×C47—21no—
34C2×C4×C47C2311yescharacteristic
35C22⋊D47—22no—
36C22⋊D47—21no—
37C2×Dic47—21no—
38D188—22no—
39D188—21no—
40D188—21no—
41D188D411yescharacteristic
42C4×D47—22no—
43C4×D47—21no—
44Dic94D411yescharacteristic
45C8×C47—21no—
46C47⋊C8—21no—
47C22×C47—21no—
48C22×C47C2×D411yescharacteristic
49C2×D47—22no—
50C2×D47—21no—
51C2×D47—42no—
52C2×D47—82no—
53C4×C47—21no—
54C4×C47—41no—
55C4×C47C2×D411yescharacteristic
56C4×C47C2×D411yescharacteristic
57Dic47—21no—
58Dic47—41no—
59C2×C47—21no—
60C2×C47—41no—
61C2×C47#12011yescharacteristic
62D47—42no—
63D47—41no—
64#455—471nomaximal, Sylow
65C47#45511yescharacteristic, complemented, Sylow
66H(5,𝔽2)—471no—
67#137—471no—
68#137D4711yescharacteristic, complemented
69#124—471no—
70#104—471no—
71#104—471no—
72#100—471no—
73#41—471no—
74#41—941no—
75#41—941no—
76#41C2×D4711yescharacteristic
77C2×Q8C2×D4711yescharacteristic, complemented
78C2×D4—471no—
79C2×D4—941no—
80C2×D4—942no—
81C2×D4—941no—
82Q16—21no—
83Q16—941no—
84SD16—21no—
85SD16—941no—
86M16—471no—
87M16C2×D4711yescharacteristic, complemented
88C22⋊C4—942no—
89C42—471no—
90C23—472no—
91C23—942no—
92Q8—21no—
93Q8—21no—
94Q8—471no—
95Q8C22⋊D4711yescharacteristic
96D4—21no—
97D4—471no—
98D4—942no—
99D4—942no—
100D4—941no—
101D4—941no—
102D4—941no—
103D4C22⋊D4711yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—942no—
107C2×C4—941no—
108C2×C4—941no—
109C2×C4C22×D4711yescharacteristic
110C8—21no—
111C8—941no—
112C22—21no—
113C22—941no—
114C22—942no—
115C22—3762no—
116C22—1882no—
117C22D4×D4711yescharacteristic
118C4—21no—
119C4—41no—
120C4—941no—
121C4—1881no—
122C4D4×D4711yescharacteristic
123C4C2×C22⋊D4711yescharacteristic
124C2—21no—
125C2—41no—
126C2—1881no—
127C2—1882no—
128C2#1309399211yescharacteristic
subgroupG/H
centerC2#13093992
commutator, cosocleC2×C4×C47C23
FrattiniC2×C4C22×D47
Fitting#137×C47C2
socleC2×C47#120
prime radical#13094070C2
hypercenter#137D47
hypocenterC47#455
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #13094055C2semidirect
3. #13094013C2semidirect
4. #13093951C2semidirect
5. #13093950C2semidirect
6. #13093940C2semidirect
7. #137×C47C2semidirect
9. C2×Q8×C47C22semidirect
19. M16×C47C22semidirect
23. C4×Dic47C22semidirect
24. #10625329C22semidirect
65. C47#455semidirect
68. #137D47semidirect
77. C2×Q8C2×D47semidirect
87. M16C2×D47semidirect

Maximal subgroups

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

subgroupindex
#130940702
#130940552
#130940132
#130939512
#130939502
#130939402
#137×C472
#45547