Finite Group Databasebeta

← #16817641

Subgroups — #16817641

Order 3712.

112 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 23 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#14271340C211yesmaximal, characteristic
2#14270960C211yesmaximal, characteristic, complemented
3C29×#329C211yesmaximal, characteristic, complemented
4#11745359C411yescharacteristic
5C29×#124C2211yescharacteristic
6#11745304—21no—
7C29×#97—21no—
8#11745184—21no—
9#11745181C411yescharacteristic
10#11745153—21no—
11C2×Q8×C29D411yescharacteristic
12C2×D4×C29C2×C411yescharacteristic
13C2×C22⋊D29—41no—
14#90807—41no—
15D4×D29—41no—
16#90805—21no—
17C2×C8×C29—41no—
18C22⋊C4×C29—41no—
19C42×C29D411yescharacteristic
20#90785—41no—
21#90784—41no—
22#90777—21no—
23#90777—41no—
24C23×C29—21no—
25C22×D29—41no—
26Q8×C29—41no—
27D4×C29—41no—
28C2×C4×C29—21no—
29C2×C4×C29—21no—
30C2×C4×C29C22⋊C411yescharacteristic
31C22⋊D29—42no—
32C22⋊D29—41no—
33C2×Dic29—41no—
34D116—21no—
35C4×D29—41no—
36Dic58—21no—
37C8×C29—42no—
38#6597—41no—
39#6597—81no—
40#1403—291nomaximal, Sylow
41C22×C29—41no—
42C22×C29—81no—
43C22×C29#9911yescharacteristic
44C2×D29—41no—
45C2×D29—161no—
46C4×C29—21no—
47C4×C29—41no—
48C4×C29—41no—
49Dic29—41no—
50#455—291no—
51#355—291no—
52#329D2911yescharacteristic, complemented
53C2×C29—21no—
54C2×C29—81no—
55C2×C29AΣL(1,𝔽16)11yescharacteristic
56D29—81no—
57H(5,𝔽2)—291no—
58#137—581no—
59#124C2×D2911yescharacteristic
60#104—581no—
61#101—581no—
62#100—291no—
63#97—21no—
64C29#140311yescharacteristic, complemented, Sylow
65#41—581no—
66#41—1161no—
67C2×Q8D11611yescharacteristic
68C2×D4—1161no—
69C2×D4—1161no—
70C2×D4C4×D2911yescharacteristic
71Q16—1161no—
72SD16—1161no—
73M16—581no—
74M16—1161no—
75C2×C8—41no—
76C22⋊C4—41no—
77C42C22⋊D2911yescharacteristic
78C23—21no—
79C23—1161no—
80Q8—41no—
81Q8—581no—
82D4—41no—
83D4—581no—
84D4—1162no—
85D4—1161no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—1161no—
89C2×C4—1161no—
90C2×C4#9078111yescharacteristic
91C8—42no—
92C8—1161no—
93C8—2321no—
94C22—41no—
95C22—81no—
96C22—1161no—
97C22—4641no—
98C22#1174515411yescharacteristic
99C4—21no—
100C4—41no—
101C4—41no—
102C4—1161no—
103C2—21no—
104C2—81no—
105C2—2321no—
106C2#1427095111yescharacteristic
subgroupG/H
centerC2#14270951
commutatorC2×D4×C29C2×C4
Frattini#124C2×D29
FittingC29×#329C2
socleC2×C29AΣL(1,𝔽16)
prime radical#11745359C4
cosocleC29×#124C22
hypercenter#329D29
hypocenterC29#1403
LCSG ▷ C2×D4×C29 ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #14270960C2semidirect
3. C29×#329C2semidirect
52. #329D29semidirect
64. C29#1403semidirect

Maximal subgroups

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

subgroupindex
#142713402
#142709602
C29×#3292
#140329