Finite Group Databasebeta

← #37548840

Subgroups — #37548840

Order 23168.

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#26042183C211yesmaximal, characteristic, complemented
2#26042137C211yesmaximal, characteristic, complemented
3#26041447C211yesmaximal, characteristic
4#19153883—21no—
5#19153875—21no—
6#19153841—21no—
7#19153812C2211yescharacteristic
8#19153743—21no—
9#19153733C411yescharacteristic, complemented
10H(5,𝔽2)×C181C411yescharacteristic, complemented
11C2×#13089685—41no—
12C22⋊#10624382—41no—
13C2×D724D411yescharacteristic
14C2×C22⋊D181—41no—
15#15668436—41no—
16#15668434—41no—
17#15668433—21no—
18C4×Dic181D411yescharacteristic
19#41×C181—21no—
20#41×C181—41no—
21C2×D4×C181—41no—
22C2×D4×C181—41no—
23C2×D4×C181C2×C411yescharacteristic
24C2×#10624382—81no—
25#13089685—81no—
26C22×D181—21no—
27D724—41no—
28C22⋊D181—81no—
29C22⋊D181—81no—
30C2×Dic181—21no—
31#13089678—41no—
32C23×C181—21no—
33C23×C181—41no—
34Q8×C181—21no—
35D4×C181—21no—
36D4×C181—41no—
37D4×C181—42no—
38D4×C181—41no—
39C2×C4×C181—41no—
40C2×C4×C181—41no—
41C2×C4×C181C22⋊C411yescharacteristic
42C22×C181—41no—
43C22×C181—41no—
44C22×C181—81no—
45C22×C181—161no—
46C22×C181#9911yescharacteristic
47C2×D181—41no—
48C2×D181—81no—
49#10624382—161no—
50C4×C181—21no—
51C4×C181—41no—
52Dic181—21no—
53Dic181—21no—
54C2×C181—21no—
55C2×C181—81no—
56C2×C181—81no—
57C2×C181AΣL(1,𝔽16)11yescharacteristic
58D181—81no—
59C181#140211yescharacteristic, complemented, Sylow
60#1402—1811nomaximal, Sylow
61#453—1811no—
62#353—1811no—
63#331—1811no—
64H(5,𝔽2)#1062438211yescharacteristic, complemented
65AGL(1,ℤ/8)—3621no—
66#127—1811no—
67C4⋊C8—3621no—
68#104—3621no—
69#100—1811no—
70#99—3621no—
71#41—21no—
72#41—41no—
73C2×D4—41no—
74C2×D4—41no—
75C2×D4—1811no—
76C2×D4—7241no—
77C2×D4C2×#1062438211yescharacteristic
78SD16—7241no—
79D8—7241no—
80M16—3621no—
81C2×C8—7241no—
82C22⋊C4—7241no—
83C42—1811no—
84C23—21no—
85C23—41no—
86C23—3621no—
87Q8—21no—
88D4—21no—
89D4—41no—
90D4—42no—
91D4—41no—
92D4—14481no—
93D4—14481no—
94D4—7241no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—3621no—
98C2×C4—14481no—
99C2×C4C22⋊#1062438211yescharacteristic
100C8—14481no—
101C8—7241no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—161no—
106C22—14481no—
107C22—7241no—
108C22#1915387411yescharacteristic
109C4—21no—
110C4—41no—
111C4—28961no—
112C4—3621no—
113C4—3621no—
114C2—21no—
115C2—81no—
116C2—81no—
117C2—14481no—
118C2#2604217911yescharacteristic
subgroupG/H
centerC2#26042179
commutatorC2×D4×C181C2×C4
FrattiniC2×D4C2×#10624382
FittingH(5,𝔽2)×C181C4
socleC2×C181AΣL(1,𝔽16)
prime radical#26041447C2
cosocle#19153812C22
hypercenterH(5,𝔽2)#10624382
hypocenterC181#1402
LCSG ▷ C2×D4×C181 ▷ C2×C4×C181 ▷ C22×C181 ▷ C2×C181 ▷ C181
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. #26042183C2semidirect
2. #26042137C2semidirect
9. #19153733C4semidirect
10. H(5,𝔽2)×C181C4semidirect
59. C181#1402semidirect
64. H(5,𝔽2)#10624382semidirect

Maximal subgroups

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

subgroupindex
#260421832
#260421372
#260414472
#1402181