Finite Group Databasebeta

← #16834615

Subgroups — #16834615

Order 3712.

112 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 20 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#14272069C211yesmaximal, characteristic, complemented
2#14272019C211yesmaximal, characteristic, complemented
3#14271336C211yesmaximal, characteristic
4C29×2−1+4C411yescharacteristic, complemented
5#11745311—21no—
6#11745309C2211yescharacteristic
7#11745218—21no—
8#11745215—21no—
9#11745185—21no—
10#11745184C411yescharacteristic, complemented
11#41×C29—21no—
12#41×C29—41no—
13#41×C29—41no—
14C2×Q8×C29—41no—
15C2×Q8×C29C2×C411yescharacteristic
16C2×D116D411yescharacteristic
17C22⋊#1181—41no—
18C2×#6599—41no—
19#90784—41no—
20#90782—41no—
21#90781—41no—
22C4×Dic29D411yescharacteristic
23#90777—21no—
24C22×D29—21no—
25C2×#1181—81no—
26Q8×C29—21no—
27Q8×C29—41no—
28Q8×C29—41no—
29D4×C29—21no—
30D4×C29—41no—
31D4×C29—41no—
32C2×C4×C29—21no—
33C2×C4×C29—41no—
34C2×C4×C29—42no—
35C2×C4×C29C22⋊C411yescharacteristic
36C2×Dic29—21no—
37D116—41no—
38#6599—42no—
39#6597—41no—
40#1404—291nomaximal, Sylow
41C22×C29—41no—
42C22×C29#9911yescharacteristic
43C2×D29—41no—
44C2×D29—81no—
45#1181—161no—
46C4×C29—21no—
47C4×C29—41no—
48C4×C29—41no—
49Dic29—41no—
50#454—291no—
51#354—291no—
52#329—291no—
53C2×C29—21no—
54C2×C29—81no—
55C2×C29AΣL(1,𝔽16)11yescharacteristic
56D29—81no—
572−1+4#118111yescharacteristic, complemented
58AGL(1,ℤ/8)—581no—
59#124—291no—
60#104—581no—
61#101—291no—
62#99—581no—
63#97—581no—
64C29#140411yescharacteristic, complemented, Sylow
65#41—21no—
66#41—41no—
67#41—41no—
68C2×Q8—41no—
69C2×Q8C2×#118111yescharacteristic
70C2×D4—291no—
71SD16—1161no—
72D8—1161no—
73M16—581no—
74C2×C8—1161no—
75C22⋊C4—1161no—
76C22⋊C4—1161no—
77C42—291no—
78C23—581no—
79Q8—21no—
80Q8—41no—
81Q8—41no—
82D4—21no—
83D4—41no—
84D4—41no—
85D4—1161no—
86C2×C4—21no—
87C2×C4—41no—
88C2×C4—42no—
89C2×C4—581no—
90C2×C4—2321no—
91C2×C4C22⋊#118111yescharacteristic
92C8—1161no—
93C8—1162no—
94C22—41no—
95C22—1161no—
96C22—2321no—
97C22#1174522711yescharacteristic
98C4—21no—
99C4—41no—
100C4—41no—
101C4—1161no—
102C4—4641no—
103C2—21no—
104C2—81no—
105C2—2321no—
106C2#1427206311yescharacteristic
subgroupG/H
centerC2#14272063
commutatorC2×Q8×C29C2×C4
FrattiniC2×Q8C2×#1181
FittingC29×2−1+4C4
socleC2×C29AΣL(1,𝔽16)
prime radical#14271336C2
cosocle#11745309C22
hypercenter2−1+4#1181
hypocenterC29#1404
LCSG ▷ C2×Q8×C29 ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #14272069C2semidirect
2. #14272019C2semidirect
4. C29×2−1+4C4semidirect
10. #11745184C4semidirect
57. 2−1+4#1181semidirect
64. C29#1404semidirect

Maximal subgroups

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

subgroupindex
#142720692
#142720192
#142713362
#140429