Finite Group Databasebeta

← #16834611

Subgroups — #16834611

Order 3712.

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

normal subgroups only

This group has 122 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#14272067C211yesmaximal, characteristic, complemented
2#14272021C211yesmaximal, characteristic, complemented
3#14271331C211yesmaximal, characteristic
4C29×H(5,𝔽2)C411yescharacteristic, complemented
5#11745311—21no—
6#11745302C2211yescharacteristic
7#11745220—21no—
8#11745215—21no—
9#11745185—21no—
10#11745181C411yescharacteristic, complemented
11#41×C29—21no—
12#41×C29—41no—
13C2×D4×C29—41no—
14C2×D4×C29—41no—
15C2×D4×C29C2×C411yescharacteristic
16C2×C22⋊D29—41no—
17C2×D116D411yescharacteristic
18C22⋊#1181—41no—
19C2×#6599—41no—
20#90784—41no—
21#90782—41no—
22C4×Dic29D411yescharacteristic
23#90777—21no—
24C23×C29—21no—
25C23×C29—41no—
26C22×D29—21no—
27C2×#1181—81no—
28Q8×C29—21no—
29D4×C29—21no—
30D4×C29—41no—
31D4×C29—42no—
32D4×C29—41no—
33C2×C4×C29—41no—
34C2×C4×C29—41no—
35C2×C4×C29C22⋊C411yescharacteristic
36C22⋊D29—81no—
37C22⋊D29—81no—
38C2×Dic29—21no—
39D116—41no—
40#6599—81no—
41#6597—41no—
42#1402—291nomaximal, Sylow
43C22×C29—41no—
44C22×C29—41no—
45C22×C29—81no—
46C22×C29—161no—
47C22×C29#9911yescharacteristic
48C2×D29—41no—
49C2×D29—81no—
50#1181—161no—
51C4×C29—21no—
52C4×C29—41no—
53Dic29—21no—
54Dic29—21no—
55#453—291no—
56#353—291no—
57#331—291no—
58C2×C29—21no—
59C2×C29—81no—
60C2×C29—81no—
61C2×C29AΣL(1,𝔽16)11yescharacteristic
62D29—81no—
63H(5,𝔽2)#118111yescharacteristic, complemented
64AGL(1,ℤ/8)—581no—
65#127—291no—
66C4⋊C8—581no—
67#104—581no—
68#100—291no—
69#99—581no—
70C29#140211yescharacteristic, complemented, Sylow
71#41—21no—
72#41—41no—
73C2×D4—41no—
74C2×D4—41no—
75C2×D4—291no—
76C2×D4—1161no—
77C2×D4C2×#118111yescharacteristic
78SD16—1161no—
79D8—1161no—
80M16—581no—
81C2×C8—1161no—
82C22⋊C4—1161no—
83C42—291no—
84C23—21no—
85C23—41no—
86C23—581no—
87Q8—21no—
88D4—21no—
89D4—41no—
90D4—42no—
91D4—41no—
92D4—1161no—
93D4—2321no—
94D4—2321no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—581no—
98C2×C4—2321no—
99C2×C4C22⋊#118111yescharacteristic
100C8—1161no—
101C8—2321no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—161no—
106C22—1161no—
107C22—2321no—
108C22#1174522711yescharacteristic
109C4—21no—
110C4—41no—
111C4—581no—
112C4—581no—
113C4—4641no—
114C2—21no—
115C2—81no—
116C2—81no—
117C2—2321no—
118C2#1427206311yescharacteristic
subgroupG/H
centerC2#14272063
commutatorC2×D4×C29C2×C4
FrattiniC2×D4C2×#1181
FittingC29×H(5,𝔽2)C4
socleC2×C29AΣL(1,𝔽16)
prime radical#14271331C2
cosocle#11745302C22
hypercenterH(5,𝔽2)#1181
hypocenterC29#1402
LCSG ▷ C2×D4×C29 ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #14272067C2semidirect
2. #14272021C2semidirect
4. C29×H(5,𝔽2)C4semidirect
10. #11745181C4semidirect
63. H(5,𝔽2)#1181semidirect
70. C29#1402semidirect

Maximal subgroups

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

subgroupindex
#142720672
#142720212
#142713312
#140229