Finite Group Databasebeta

← #37548841

Subgroups — #37548841

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#26041449C211yesmaximal, characteristic
4#19153883—21no—
5#19153875—21no—
6#19153861C411yescharacteristic, complemented
7#19153844—21no—
8#19153812C2211yescharacteristic
9#19153742—21no—
10#100×C181C411yescharacteristic, complemented
11C2×#13089685—41no—
12C22⋊#10624382—41no—
13#15668449—21no—
14#15668448—41no—
15C2×D724D411yescharacteristic
16C2×C22⋊D181—41no—
17C2×C22⋊D181—41no—
18D4×D181—41no—
19#15668438—41no—
20D1448—41no—
21C4×Dic181D411yescharacteristic
22C2×D4×C181C2×C411yescharacteristic
23M16×C181—21no—
24C2×#10624382—81no—
25#13089685—81no—
26C22×D181—21no—
27C22×D181—41no—
28Dic362—21no—
29D724—21no—
30D724—41no—
31C22⋊D181—42no—
32C22⋊D181—41no—
33C22⋊D181—81no—
34C22⋊D181—81no—
35C2×Dic181—21no—
36C2×Dic181—41no—
37C4×D181—41no—
38C23×C181—21no—
39D4×C181—41no—
40C2×C4×C181C22⋊C411yescharacteristic
41C8×C181—41no—
42C22×C181—41no—
43C22×C181—81no—
44C22×C181#9911yescharacteristic
45C2×D181—41no—
46C2×D181—41no—
47C2×D181—81no—
48C2×D181—161no—
49#10624382—161no—
50C4×C181—21no—
51Dic181—21no—
52Dic181—21no—
53Dic181—41no—
54C2×C181—21no—
55C2×C181—81no—
56C2×C181AΣL(1,𝔽16)11yescharacteristic
57D181—81no—
58D181—81no—
59C181#140211yescharacteristic, complemented, Sylow
60#1402—1811nomaximal, Sylow
61#453—1811no—
62#353—1811no—
63#331—1811no—
64H(5,𝔽2)—1811no—
65AGL(1,ℤ/8)—3621no—
66#127—1811no—
67C4⋊C8—3621no—
68#104—3621no—
69#100#1062438211yescharacteristic, complemented
70#99—3621no—
71#41—3621no—
72#41—7241no—
73C2×D4—1811no—
74C2×D4—7241no—
75C2×D4—7241no—
76C2×D4—7241no—
77C2×D4C2×#1062438211yescharacteristic
78SD16—7241no—
79D8—7241no—
80M16—21no—
81C2×C8—7241no—
82C22⋊C4—7241no—
83C42—1811no—
84C23—21no—
85C23—3621no—
86C23—7241no—
87Q8—3621no—
88D4—41no—
89D4—3621no—
90D4—14481no—
91D4—14481no—
92D4—7241no—
93D4—7242no—
94D4—7241no—
95C2×C4—3621no—
96C2×C4—14481no—
97C2×C4—7241no—
98C2×C4—7241no—
99C2×C4C22⋊#1062438211yescharacteristic
100C8—41no—
101C8—14481no—
102C22—41no—
103C22—81no—
104C22—28961no—
105C22—14481no—
106C22—7241no—
107C22—7241no—
108C22#1915387511yescharacteristic
109C4—21no—
110C4—28961no—
111C4—3621no—
112C4—3621no—
113C4—7241no—
114C2—21no—
115C2—81no—
116C2—14481no—
117C2—14481no—
118C2#2604218011yescharacteristic
subgroupG/H
centerC2#26042180
commutatorC2×D4×C181C2×C4
FrattiniC2×D4C2×#10624382
Fitting#100×C181C4
socleC2×C181AΣL(1,𝔽16)
prime radical#26041449C2
cosocle#19153812C22
hypercenter#100#10624382
hypocenterC181#1402
LCSG ▷ C2×D4×C181 ▷ C2×C4×C181 ▷ C22×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
1. #26042183C2semidirect
2. #26042137C2semidirect
6. #19153861C4semidirect
10. #100×C181C4semidirect
59. C181#1402semidirect
69. #100#10624382semidirect

Maximal subgroups

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

subgroupindex
#260421832
#260421372
#260414492
#1402181